Nitride Semiconductors: Handbook on Materials and Devices

Pierre Ruterana, Martin Albrecht, Jörg Neugebauer

Nitride Semiconductors Handbook on Materials and Devices

Pierre Ruterana, Martin Albrecht, Jörg Neugebauer Nitride Semiconductors Handbook on Materials and Devices

Pierre Ruterana, Martin Albrecht, Jörg Neugebauer

Nitride Semiconductors Handbook on Materials and Devices

Editors Pierre Ruterana Laboratoire d’Etude et de Recherches sur les Matériaux France e-mail: [email protected] Martin Albrecht University of Erlangen Germany e-mail: [email protected] Jörg Neugebauer Fritz-Haber-Institute of Max-Planck-Society Germany e-mail: [email protected]

1st edition

n This book was carefully produced. Nevertheless, authors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at © 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim All rights reserved (including those of translation in other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Printed in the Federal Republic of Germany Printed on acid-free paper

Cover Picture P. Gibart et al: Scanning electron microscope image showing the epitaxial lateral overgrowth of GaN from hexagonal openings

Composition K+V Fotosatz GmbH, Beerfelden Printing betz-druck gmbh, Darmstadt Bookbinding Litges & Dopf Buchbinderei GmbH, Heppenheim ISBN

3-527-40387-6

V

Contents Preface

XVII

List of Contributors Part 1 1

1.1 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.5.1 1.2.5.2 1.2.6 1.2.6.1 1.2.6.2 1.3 1.3.1 1.3.2 1.3.3 1.4 1.4.1 1.4.2 1.4.3

Material

XIX 1

High-Pressure Crystallization of GaN

3

Izabella Grzegory, Stanisław Krukowski, Michaeł Leszczyn´ski, Piotr Perlin, Tadeusz Suski, and Sylwester Porowski Introduction 4 High-Pressure Crystallization of GaN 5 Thermodynamics – Properties of GaN-Ga-N2 System 5 Dissolution Kinetics of N2 and Crystal Growth Mechanism 8 What Happens with GaN at High Temperature when the N2 Pressure is too Low? 12 Crystallization of GaN Using High Nitrogen Pressure Solution Growth (HNPSG) Method – Experimental 13 Properties of GaN Single Crystals Obtained by HNPSG Method 14 Crystals Grown without Intentional Seeding 14 Seeded Growth of GaN by HNPS Method 18 Physical Properties of GaN Crystals, Grown by HNPS Method 21 Point Defects 21 Extended Defects 24 Epitaxy on Bulk GaN 26 Introduction 26 Metalorganic Chemical Vapor Epitaxy on GaN Substrates in HPRC Unipress 26 Molecular Beam Epitaxy 32 Optoelectronic Devices 35 Introduction 35 Light Emitting Diodes Fabricated on Bulk GaN in HPRC 35 Laser Diode Structures 36

VI

Contents

1.5 1.6 1.7

Conclusions 40 Acknowledgment References 41

41

2

Epitaxial Lateral Overgrowth of GaN

2.1 2.1.1 2.1.2 2.1.2.1 2.1.2.2 2.1.3 2.1.3.1 2.1.3.2 2.1.3.3 2.1.3.4 2.1.3.5 2.2 2.2.1 2.2.2 2.2.3 2.3 2.3.1 2.3.1.1 2.3.1.2 2.3.1.3 2.3.1.4 2.3.2 2.3.2.1 2.3.2.2 2.3.2.3 2.3.2.4 2.3.2.5 2.3.3 2.3.4 2.3.4.1 2.3.4.2 2.3.4.3 2.3.5 2.3.6 2.3.7 2.4 2.4.1 2.4.2 2.4.2.1

Pierre Gibart, Bernard Beaumont, and Philippe Vennéguès Heteroepitaxial GaN 46 Introduction 46 Growth of GaN/Sapphire and 6H-SiC Templates 48 2D Growth Mode (GaN/Sapphire) 48 3D Growth Mode (GaN/Sapphire) 49 Defects in GaN/Sapphire and GaN/6H-SiC 51 Extended Defects 51 Native Defects 52 Defect-Related Optical Properties 52 Device Performance Limitations 54 Electronic Properties of Defects 54 Epitaxial Lateral Overgrowth (ELO) 56 Standard ELO 56 Rationale 56 Experimental 58 One-Step Lateral Overgrowth (1S-ELO) 59 ELO in MOVPE 59 Morphology and Defects 59 Structural Assessment 63 Kinetics 64 In-Depth Optical Assessment of MOVPE ELO GaN 65 HVPE 66 In-Depth Assessment of HVPE ELO GaN 67 Stripe Openings along h1120i 68 Selective Area Epitaxy (SAE) 72 (C2H5)2GaCl as Ga Source 72 Stress Generation 73 Sublimation 74 New Developments 75 ELO on Si 75 Using W as Mask 75 Maskless ELO 75 Improvements of the Standard ELO Method 76 Pendeo-Epitaxy 77 ELO of Cubic GaN 80 Two-Step ELO (2S-ELO) 80 Experimental (MOVPE) 80 In-Depth Assessment of 2S-ELO 84 Cathodoluminescence 84

45

Contents

2.4.2.2 2.4.2.3 2.4.2.4 2.4.2.5 2.4.3 2.4.4 2.4.5 2.5 2.5.1 2.5.2 2.6 2.7 2.8 3

3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.3 3.3.1 3.3.2 3.3.3 3.3.3.1 3.3.3.2 3.3.3.3 3.3.3.4 3.3.3.5 3.3.4 3.3.4.1 3.3.4.2 3.3.4.3 3.3.4.4 3.3.5 3.4 3.4.1 3.4.2 3.4.3 3.4.3.1 3.4.3.2

Luminescence of GaN by Epitaxial Lateral Overgrowth 88 Time-resolved Photoluminescence 89 Deep Level Transient Spectroscopy (DLTS) 89 Strain Distribution 90 Assessment of HVPE 91 ELO and Yellow Luminescence 93 Conclusion 95 New Trends 95 3S-ELO 95 Further Improvements 96 Theoretical Analysis of ELO 97 Acknowledgments 98 References 99 Plasma-Assisted Molecular Beam Epitaxy of III–V Nitrides

107

Alexandros Georgakilas, Hock Min NG, and Philomela Komninou Introduction 108 The Nitrogen Plasma Source 109 The Different Sources 109 The Nitrogen Plasma 111 Characterization of the HD25 RF Source by Optical Emission Spectroscopy 115 Which is the Best Source? 118 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE 120 Structure of the GaN {0001} Surfaces 120 GaN Substrate Preparation 127 Physical Understanding of the Growth on GaN (0001) Surfaces 131 Growth Chemistry 131 GaN Evaporation 132 Ga Adsorption and Desorption 132 Growth Rates as a Function of III and V Fluxes 134 The GaN Growth Regimen – a Phase Diagram 135 Characteristics and Optimization of the (0001) GaN Growth 140 Description of RFMBE Experiments 141 Characterization of Materials Properties 142 Optimized Growth with Interruptions 145 Conclusions 145 Doping of GaN 145 Heteroepitaxial Growth 148 Substrates for PAMBE GaN Heteroepitaxy 148 Important Issues in the Heteroepitaxy of GaN-on-Al2O3 (0001) 149 Electron Microscopy Investigation of Nitridated Al2O3 Interfaces 150 Experimental 150 Observation and Analysis of Interfacial Defect Content 151

VII

VIII

Contents

3.4.4 3.4.5 3.5 3.5.1 3.5.2 3.5.2.1 3.5.2.2 3.5.2.3 3.5.3 3.5.3.1 3.5.3.2 3.5.4 3.5.4.1 3.5.5 3.5.5.1 3.5.5.2 3.5.5.3 3.6 3.7 3.8 4

4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.3 4.3.1 4.3.2 4.3.3 4.3.4 4.3.5 4.3.5.1 4.3.5.2 4.3.5.3

Effect of Al2O3 Nitridation on the Polarity and Microstructure of GaN Epilayers 156 Conclusions 161 III-Nitride Alloys and Device Heterostructures 163 Growth Model for Ternary III-Nitrides 163 InGaN 165 Phase Separation and Ordering of InGaN 166 Effect of Atomic Hydrogen on the Incorporation of In 167 InGaN LEDs 169 AlGaN 169 UV LEDs 171 UV Detectors 171 GaN/AlGaN MQWs for Intersubband Transitions 173 Electron Scattering Time between Subbands 178 AlGaN/GaN Heterostructures for Electronic Devices 179 AlGaN/GaN HFETs 180 AlGaN/GaN HBTs 181 AlGaN/GaN RTDs 181 Conclusions and Perspectives 181 Acknowledgments 182 References 182 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

193

Agnès Trassoudaine, Robert Cadoret, and Eric Aujol General Points on HVPE 194 Introduction 194 Principle of HVPE 195 Use of HVPE 196 Problems Associated with GaN Growth 197 Thermodynamical Study 198 Thermodynamical Characteristics 199 Partition Functions of the Molecules 202 Calculation of the Partial Pressures 205 Thermodynamical Study of the GaN Deposit 206 Kinetic Study 207 Introduction 207 Relations Between the {001} GaAs and (00.1) GaN Epitaxy Statistical Treatment of the Dynamic Equilibrium Surface-Vapor Phase 209 Mass-Transfer Phase 215 Crystal Growth Phase 216 H2 Growth Mechanism 217 GaCl3 Growth Mechanism 219 Spiral Growth of an Exact (00.1) Face, Burton-Cabrera-Frank Mechanism 220

208

Contents

4.3.6 4.3.7 4.3.8 4.3.8.1 4.3.8.2 4.3.9 4.4 4.5 4.6 5

5.1 5.2 5.2.1 5.2.2 5.2.2.1 5.2.2.2 5.2.3 5.2.3.1 5.2.3.2 5.2.4 5.3 5.3.1 5.3.2 5.3.3 5.3.3.1 5.3.3.2 5.3.3.3 5.3.3.4 5.3.4 5.3.4.1 5.3.4.2 5.3.5 5.3.5.1 5.3.5.2 5.3.5.3 5.3.6 5.4 5.4.1 5.4.2

Search for the Model Parameters 220 Search for the Mass Transfer and Parasitic Nucleation Effects 224 New Mechanism of Growth at Negative Values of c 227 Experimental Results 227 Third Growth Mechanism 230 Discussion 231 Results 233 Conclusions 236 References 236 Growth and Properties of InN 241

Valery Davydov, Albert Klochikhin, Sergey Ivanov, Jochen Aderhold, and Akio Yamamoto Introduction 242 Growth of InN by Plasma-Assisted Molecular Beam Epitaxy 244 Introduction 244 InN PAMBE Growth Peculiarities 245 Role of Different Nitrogen Species in PAMBE 245 Maintenance of Stoichiometric Conditions During InN Growth by PAMBE 246 Undoped InN Growth by PAMBE with Different Initial Stages 248 Growth and Epilayer Morphology 248 Interface with Sapphire, XRD Characterization and Hall Measurements 251 Summary 256 Growth of InN by Metalorganic Molecular Beam Epitaxy 257 Introduction 257 MOMBE as a Growth Technique for InN 257 Growth Process 258 Growth System 258 Substrate Preparation 258 Nitridation 258 Nucleation Layer Growth 259 Influence of Growth Parameters on Surface Morphology 259 Influence of Growth Temperature 259 Influence of V/III Ratio 260 Dependence of Structural and Electrical Properties of InN Grown by MOMBE on V/III Ratio 263 Raman Measurements 263 XRD Measurements 264 Hall Measurements 264 Summary 265 Metalorganic Vapor Phase Epitaxy of InN 265 Introduction 265 Experimental 266

IX

X

Contents

5.4.3 5.4.4 5.4.5 5.5 5.5.1 5.5.2 5.5.2.1 5.5.2.2 5.5.3 5.5.3.1 5.5.3.2 5.5.3.3 5.5.3.4 5.5.3.5 5.5.3.6 5.5.3.7 5.5.3.8 5.5.3.9 5.5.3.10 5.5.4 5.6 5.7 5.8

Surface Morphology and Growth Rate of MOVPE InN 267 Electrical Properties of MOVPE InN 270 Summary 274 Physical Properties of Hexagonal InN 274 Introduction 274 Lattice Dynamics of Single-Crystalline InN Layers 275 First-Order Raman Scattering 275 Phonon Dispersion in InN 278 Electronic Structure of Single-Crystalline InN Layers 280 Characterization of Samples 280 Absorption and Luminescence in InN 281 Luminescence and Absorption of Crystals with High Electron Concentrations 282 Temperature Dependence of the Luminescence Band Shape Concentration Dependence of PL Band and Absorption Coefficient 284 Photoluminescence Excitation and Photomodulated Reflectance Spectra 285 Optical Spectra of InxGa1–xN Layers 286 Wide-Gap InN-based Samples 287 Postgrowth Treatment of InN Samples 288 Proton Irradiation 289 Summary 289 Conclusions 290 Acknowledgments 290 References 291

6

Surface Structure and Adatom Kinetics of Group-III Nitrides

6.1 6.2 6.2.1 6.2.2 6.3 6.3.1 6.3.1.1 6.3.1.2 6.3.1.3 6.3.1.4 6.3.2 6.3.2.1 6.3.3 6.3.3.1 6.3.3.2 6.3.3.3

Jörg Neugebauer Introduction 295 Method 296 Thermodynamic Equilibrium 296 Kinetics 299 Bare GaN Surfaces 299 Nonpolar Surfaces 299 Wurtzite GaN (1100) 300 Wurtzite GaN (1200) 301 Cubic GaN (110) 301 General Trends 302 Polar Cubic GaN Surfaces 303 GaN (001) Surface 303 Polar Wurtzite Surfaces 306 GaN (0001) Surface 307 GaN (0001) Surface 308 GaN (1101) Surface 310

295

284

Contents

6.3.4.1 6.3.4.2 6.3.4.3 6.4 6.4.1 6.4.2 6.5 6.6 6.7

General Trends and Comparison with Traditional Semiconductors 311 General Trends 311 Comparison with Traditional Semiconductors 312 Conclusions 313 Adatom Kinetics 313 Diffusion of Adatoms on Equilibrium GaN Surfaces 314 Diffusion on Nonequilibrium Surfaces 315 Consequences for Growth 315 Acknowledgments 316 References 317

Part 2

Defects and Interfaces

6.3.4

7

7.1 7.2 7.2.1 7.2.2 7.2.2.1 7.2.2.2 7.2.2.3 7.3 7.4 7.4.1 7.4.2 7.4.3 7.5 7.6 7.6.1 7.6.2 7.6.3 7.7 7.8 7.9 A.1 A.2 A.3 A.4 7.10

319

Topological Analysis of Defects in Nitride Semiconductors

321

Georgios P. Dimitrakopulos, Philomela Komninou, Theodoros Karakostas, and Robert C. Pond Introduction 321 Defect Characterization 324 Defect Characterization by a Volterra-like Approach 324 Defect Characterization by Circuit Mapping 326 Circuits in Perfect Crystals 328 Circuits in Imperfect Crystals and Circuit Mapping 331 Circuit Mapping of Interfacial Defects 331 Crystalline Structures and Experimental Details 333 Dislocations in GaN Epilayers 337 Threading Dislocations 337 Stacking-fault Dislocations 341 Interfacial Dislocations and Dislocation Models of Interfacial Structure 345 Inversion and Stacking Disorder in Relation to Epitaxial Structure 349 Interface and Fault Junction Lines 356 Interactions of Inversion Domain Boundaries with Stacking Faults 356 Double-positioning Twinning 361 Junction Lines between Hexagonal and Cubic Nitride Phases 367 Conclusions 369 Acknowledgments 370 Appendix: The Frank Coordinate System for Hexagonal and Trigonal Crystallography 370 Projection from a Higher Dimension 371 Crystallographic Calculations 372 Reciprocal Space 373 Matrix Algebra 374 References 375

XI

XII

Contents

8

8.1 8.2 8.2.1 8.2.1.1 8.2.1.2 8.2.2 8.2.3 8.2.4 8.2.5 8.2.5.1 8.2.5.2 8.2.6 8.2.6.1 8.2.6.2 8.2.6.3 8.2.6.4 8.3 8.3.1 8.3.2 8.3.3 8.3.4 8.3.4.1 8.3.4.2 A. B. 8.3.4.3 8.3.5 8.4 8.4.1 8.4.2 8.4.2.1 8.4.2.2 8.4.2.3 A. B. 8.4.2.4 8.5 8.5.1 8.5.2 8.5.3

Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

379

Pierre Ruterana, Ana M. Sánchez, and Gérard Nouet Introduction 380 Crystallographic Considerations 382 Substrates 382 Sapphire 382 Silicon Carbide 383 Epitaxial Layers 385 Epitaxial Relationships 385 Bicrystallographic Analysis of Interfacial Defects 386 Growth on SiC 389 Stacking Faults in 2H Polytype 390 Defects at Interface Steps 390 Growth on Sapphire 393 Geometrical Modeling of the First Monolayers Growth 393 Planar Defects 398 Stepless Surface 399 Steps 399 Dislocations 401 Misfit Dislocations 401 Threading Dislocations 401 Nanopipes 403 Grain Boundaries 403 The R = 19 Boundary 404 The R = 7 Boundary 406 The R = 7 Symmetric Boundary 406 The R = 7 Asymmetric Boundary 409 The R = 31 Symmetric Boundary 409 Formation 411 Stacking Faults 412 Basal Stacking Faults 412 Prismatic Stacking Faults 415 Morphology of the {1120} Stacking Faults Inside the Epitaxial Layers 415 Identification of the Stacking Fault Atomic Structure 416 Formation Mechanisms 419 On (0001) 6H-SiC Surface 419 On (0001) Sapphire 420 Relative Stability of the Atomic Configurations 421 Inversion Domain Boundaries 422 Identification of the Inversion Domains 423 Atomic Models of the Boundary 425 Atomic Structures of the Boundary 426

Contents

8.5.4 8.5.5 8.5.6 8.6 8.7 8.8 9

9.1 9.2 9.3 9.4 9.5 9.5.1 9.5.2 9.5.3 9.5.3.1 9.5.3.2 A. B. C. D. E. 9.5.4 9.5.5 9.6 9.7 9.8 9.9 9.9.1 9.9.2 9.9.3 9.9.4 9.9.5 9.9.6 9.9.7 9.10 9.11 9.12

Atomic Structure of Boundary Plane and Epitaxial Layer Morphology 429 Interaction with Basal Stacking Faults Formation 432 Discussion and Conclusions 433 Acknowledgments 436 References 436

430

Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-based Epitaxial Layers 439

Slawomir Kret, Pierre Ruterana, Claude Delamarre, Tarek Benabbas, and Pawel Dluzewski Introduction 439 Suitable Images for Quantitative Analysis 442 Digitization 444 Noise 446 Strain Measurement 451 Domain of Application 451 Assumptions 451 Peak-finding Procedure 452 Overview 452 Procedure 453 Selection of Area of Interest 453 Noise Reduction 453 Detection of the Lattice Sites 455 Reference Area and Calculation of the Base Vectors 456 Lattice Distortion in Discrete and Quasicontinuum Form 456 The Geometric-Phase Method 460 Peak Finding Versus Geometric Phase 466 Foil-Thickness Effect 467 From Strain to Stress 472 Local Chemical Composition 475 Atomic-Structure Retrieval 478 Artefact-free Sample and Signal-to-Noise Ratio 479 Defect-Structure Determination Strategies 480 Preprocessing of Image Data and Image Simulations 480 Quality Functions (Goodness-of-Fit Criteria) 481 Determination of the Imaging Parameters 481 Optimization Strategies 482 Precision of the Structure Retrieval 482 Discussion and Conclusions 483 Acknowledgments 484 References 485

XIII

XIV

Contents

Part 3

Processing and Devices

489

10

Ohmic Contacts to GaN

491

10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9

Philip J. Hartlieb, Robert F. Davis, and Robert J. Nemanich Introduction 492 Principles of Metal-Semiconductor Contacts 493 Measurement Techniques 496 Experimental Studies of Ohmic Contacts to n-Type GaN 497 Experimental Studies of Ohmic Contacts to p-Type GaN 507 Conclusions 522 Directions for Future Research 522 Acknowledgments 523 References 524

11

Electroluminescent Diodes and Laser Diodes

11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8

Hiroshi Amano Introduction 529 Historical Overview 530 White LEDs 534 UV LEDs 536 Violet LDs 541 Summary 542 Acknowledgments 544 References 544

12

12.1 12.2 12.2.1 12.2.2 12.2.3 12.2.4 12.2.5 12.3 12.3.1 12.3.1.1 12.3.1.2 12.3.2 12.3.3 12.3.4 12.3.5

529

GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors 547

Hadis Morkoç and Lianghong Liu Introduction 548 Electron Transport Properties in GaN and GaN/AIGaN Heterostructures 550 Bulk Mobility in GaN 552 Polarization Effects, Mobility and Electron Concentration in 2 DEG Systems 556 Partial Strain Relaxation 567 Low-field Transport in 2 DEG Systems 570 High-Field Transport 574 Modulation-Doped Field Effect Transistors (MODFETs) 576 MODFET Model 577 Drain Current Model in MODFETs 583 I–V Characteristics 585 Experimental Considerations 586 Schottky Barriers for Gates 589 Contacts to GaN 592 Experimental Performance of GaN MODFETs 594

Contents

12.3.6 12.3.7 12.3.8 12.3.8.1 12.3.8.2 12.4 12.5 12.6 12.7 13

13.1 13.2 13.3 13.3.1 13.3.2 13.4 13.4.1 13.4.1.1 13.4.1.2 13.4.1.3 13.4.2 13.4.2.1 13.4.2.2 13.4.2.3 13.4.2.4 13.4.2.5 13.4.2.6 13.4.3 13.4.3.1 13.4.3.2 13.4.3.3 13.4.3.4 13.4.4 13.4.4.1 13.4.4.2 13.4.4.3 13.4.4.4 13.4.4.5 13.4.5 13.4.5.1 13.4.5.2

Power Amplifiers 601 Anomalies in GaN/AlGaN MODFETs 603 Low-Frequency and High-Frequency Noise Performance 608 Low-Frequency Noise 608 High-Frequency Noise 611 Heterojunction Bipolar Transistors 614 Conclusions 617 Acknowledgments 618 References 619 GaN-Based UV Photodetectors

627

Franck Omnes and Eva Monroy Introduction 627 UV to Visible Contrast 631 Si and SiC UV Photodetectors 632 Silicon-Based UV Photodiodes 632 SiC-Based UV Photodetectors 634 III-Nitride-Based UV Photodetectors 635 Photoconductors 635 Spectral Response 635 Time Response 639 Effect of a Frequency Modulation of the Incident Optical Signal AlGaN-Based Schottky Barrier Photodiodes 641 Electrical Properties 641 Responsivity 642 Time Response 643 Noise and Detectivity 644 Epitaxial Lateral Overgrown (ELOG) GaN-Based Schottky Barrier Photodiodes 645 Application of AlGaN Photodetectors to the Simulation of the Biological Effects of UV Light 645 Metal-Semiconductor-Metal (MSM) Photodiodes 646 Electrical Properties 647 Spectral Response 648 Time Response 649 Noise 650 p-n and p-i-n Photodiodes 650 Spectral Response 651 Time Response 652 Noise 653 p-i-n Photodiodes on ELOG GaN 653 GaN-Based Avalanche Photodiodes 654 Phototransistors 655 Bipolar Phototransitors 655 Field Effect Phototransistors 656

640

XV

XVI

Contents

13.5 13.6 13.7

Conclusions 656 Acknowledgments 657 References 657

Subject Index

661

XVII

Preface Semiconductor-based devices have been successfully used in a wide range of applications ranging from microelectronics to optoelectronic devices and chemical sensors. While the main interest has been on elemental semiconductors (Si, Ge) and “traditional” III–V semiconductors (GaAs, GaP, InP, etc. . . .), recently the nitride semiconductors have become a subject of intense research. The unique features of these materials (InN, GaN, AlN and their alloys) i.e., a wide direct bandgap, strong chemical bonds, and a high melting temperature make them well suite for designing and fabricating optoelectronic and high temperature/high power devices. Soon, it has been realized that these materials have also unique characteristics which had not been encountered in traditional semiconductors and which often require fundamentally different approaches and techniques. This handbook brings about the latest insight into these issues with specific emphasis on growth, defects structure, and industrial applications in a compact yet comprehensive manner. It consists of three sections (Growth, Defects and Interfaces, Processes and Devices) with a total of thirteen chapters written by different authors. The first section covers the fundamentals of the technologically relevant growth techniques (bulk crystal growth from the liquid phase, metal-organic chemical vapor deposition, molecular beam epitaxy, and hydride vapor phase epitaxy) in a concise overview of their advantages and limitations. It further encompasses the specific techniques used in the various methods to overcome group-III nitride-related problems such as the low sublimation temperature or high dislocation densities. Finally, based on first principles calculations, the thermodynamic stability and the kinetic processes on surfaces are identified, giving direct insight in experimentally observed growth phenomena and mechanisms. The second section is devoted to the characterization of structure and properties of nitride interfaces and defects. Based on a combination of topological theory, atomistic modeling, and high resolution transmission electron microscopy, the influence of defects on properties are discussed. Specific focus is given on defect structures commonly found in nitrides such as threading dislocations, or inversion domain boundaries. The section also includes a detailed discussion of phase distribution in InGaN alloys at nanometer scale and their relation to localization and quantum confinement effects.

XVIII

Preface

The third section gives a comprehensive overview on processing and device-related issues. It starts with the fundamental and applied aspects of n- and p-type ohmic contacts, it next addresses history, state of the art, and future challenges of modern nitride-based devices. The section covers both optoelectronic active (light emitting diodes and lasers) and passive devices (UV photodetectors), as well as electronic devices (FETs). The editors P. Ruterana, J. Neugebauer, M. Albrecht

XIX

List of Contributors Jochen Aderhold Laboratorium für Informationstechnologie Universität Hannover Schneiderberg 32 30167 Hannover Germany Hiroshi Amano Department of Materials Science and Engineering Meijo University 1-501 Shiogamaguchi, Tempaku-ku Nagoya 467-8502 Japan [email protected] Eric Aujol LASMEA, UMR-CNRS 6602 Université Blaise Pascal Les Cézeaux 63177 Aubière Cedex France Bernard Beaumont Lumilog S.A. 2720, Chemin Saint Bernard Les Moulins I 06220 Vallauris France

Tarek Benabbas Laboratoire de Structure et Propriétés de l’Etat Solide (UPRESA 8008) USTL, Bâtiment C6 59655 Villeneuve d’Ascq cedex France Robert Cadoret LASMEA, UMR-CNRS 6602 Université Blaise Pascal Les Cézeaux 63177 Aubière Cedex France Robert F. Davis Department of Materials Science and Engineering North Carolina State University Raleigh North Carolina 27695-7907 Valery Davydov Ioffe Physico-Technical Institute of RAS Politekhnicheskaya 26 St. Petersburg 194021 Russia [email protected]

XX

List of Contributors

Claude Delamarre Laboratoire de Physique du Solide E.S.P.C.I., CNRS UPR 05 10 rue Vauquelin 75231 Paris cedex 05 France

Philip J. Hartlieb Clemson University Dept. of Chemistry H.L. Hunter Laboratories Rm. 414 Clemson, SC 29634 [email protected]

P. Dluzewski Institute of Fundamental Technological Research, PAS ul. Swietokrzyska 21 02-049 Warszawa Poland

Sergey Ivanov Ioffe Physico-Technical Institute of RAS Politekhnicheskaya 26 St. Petersburg 194021 Russia

Georgios P. Dimitrakopulos Aristotle University of Thessaloniki Department of Physics Solid State Section 54124 Thessaloniki Greece Pierre Gibart Lumilog S.A. 2720, Chemin Saint Bernard Les Moulins I 06220 Vallauris France [email protected] Alexandros Georgakilas Institute of Electronic Structure and Laser FORTH and Department of Physics University of Crete 71110 Heraklion Greece [email protected] Izabella Grzegory High Pressure Research Center Polish Academy of Sciences Unipress Sokołowska 29/37 01-142 Warsaw Poland [email protected]

Theodoros Karakostas Aristotle University of Thessaloniki Department of Physics Solid State Section 54124 Thessaloniki Greece Albert Klochikhin Ioffe Physico-Technical Institute of RAS Politekhnicheskaya 26 St. Petersburg 194021 Russia Philomela Komninou Department of Physics Aristotle University of Thessaloniki 54124 Thessaloniki Greece [email protected] Slawomir Kret Institute of Physics, PAS Al. Lotników 32/46 02-668 Warszawa Poland Stanisław Krukowski High Pressure Research Center Polish Academy of Sciences Unipress Sokołowska 29/37 01-142 Warsaw Poland

XXI

´ ski Michał Leszczyn High Pressure Research Center Polish Academy of Sciences Unipress Sokołowska 29/37 01-142 Warsaw Poland Lianghong Liu Virginia Commonwealth University Department of Electrical Engineering and Physics Department 601 W. Main Street P.O. Box 843072 Richmond, VA 23284-3072 Eva Monroy Dept. de Recherche Fondamentale sur la Matière Condensée, SP2M CEA-Grenoble 17, rue des Martyrs 38054 Grenoble Cedex 9 France Hadis Morkoç Virginia Commonwealth University Department of Electrical Engineering and Physics Department 601 W. Main Street P.O. Box 843072 Richmond, VA 23284-3072 [email protected] Robert J. Nemanich Department of Physics North Carolina State University Raleigh North Carolina 27695-7902 Jörg Neugebauer Fritz-Haber-Institut der MPG Faradayweg 4–6 14195 Berlin Germany [email protected]

Franck Omnes CRHEA-CNRS 1, rue Bernard Grégory Sophia Antipolis 06560 Valbonne France [email protected] Hock Min Ng Bell Laboratories, Lucent Technologies 600 Mountain Avenue Murray Hill New Jersey USA Gérard Nouet LERMAT, FRE 2149 CNRS, ISMRA 6 Bd du Maréchal Juin 14050 Caen Cedex France Piotr Perlin High Pressure Research Center Polish Academy of Sciences Unipress Sokołowska 29/37 01-142 Warsaw Poland Robert C. Pond University of Liverpool Department of Engineering Materials Science & Engineering Liverpool, L69 3GH UK Sylwester Porowski High Pressure Research Center Polish Academy of Sciences Unipress Sokołowska 29/37 01-142 Warsaw Poland

XXII

List of Contributors

Pierre Ruterana LERMAT, FRE 2149 CNRS, ISMRA 6 Bd du Maréchal Juin 14050 Caen Cedex France [email protected] Ana Mª Sánchez LERMAT, FRE 2149 CNRS, ISMRA 6 Bd du Maréchal Juin 14050 Caen Cedex France Tadeusz Suski High Pressure Research Center Polish Academy of Sciences Unipress Sokołowska 29/37 01-142 Warsaw Poland

Agnès Trassoudaine LASMEA, UMR-CNRS 6602 Université Blaise Pascal Les Cézeaux 63177 Aubière Cedex France [email protected] Philippe Vennéguès CRHEA-CNRS 1, rue Bernard Grégory Sophia Antipolis 06560 Valbonne France Akio Yamamoto Department of Electrical and Electronics Engineering Fukui University 3-9-1 Bunkyo Fukui 910-8507 Japan

Part 1

Material

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1

High-Pressure Crystallization of GaN Izabella Grzegory, Stanisław Krukowski, Michaeł Leszczyn´ski, Piotr Perlin, Tadeusz Suski, and Sylwester Porowski

Abstract

Because of the high bonding energy of the N2 molecule, the III–V semiconducting nitrides, especially GaN and InN, require high N2 pressure to be stable at the high temperatures necessary for the growth of high-quality single crystals. The properties of the GaN-Ga(l)-N2 system are reviewed in this chapter. Based on the experimental equilibrium p-T-x data and quantum-mechanical modeling of the interaction of the N2 molecule with liquid Ga surface, the conditions for crystallization of GaN have been established. The crystals obtained under high pressure are of the best structural quality, with dislocation densities as low as 10–100 cm–2, which is several orders of magnitude better than crystals grown by other techniques. The high nitrogen pressure solution growth (HNPSG) method allows us to obtain both n-type substratequality crystals, for optoelectronics, and highly resistive crystals for electronic applications. Due to their very high structural quality, the HNPSG grown crystals are excellent substrates for epitaxial growth of quantum-confined structures. This opens up new possibilities for optoelectronic devices, especially short-wavelength highpower laser diodes (LDs) and efficient UV light emitting diodes (LEDs). The epitaxial growth and physical properties of GaN-based device structures, supporting the

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1 High-Pressure Crystallization of GaN

above conclusions, are discussed in this chapter. In the last section, the progress of blue laser technology in HPRC is briefly reviewed.

1.1

Introduction

GaN and its alloys with AlN and InN recently became the basic materials for short-wavelength optoelectronics. This was mainly due to their direct energy gaps covering the whole visible spectrum and a large part of the UV range (6.2, 3.4, and 1.9 eV for AlN, GaN, and InN, respectively). These materials, besides being a prime object of interest of device engineers, are also an exciting subject of research for a physicist. This is because of their outstanding position in the III–V family of semiconductors. GaN, InN, and AlN, unlike other III–V materials are hard, partially ionic semiconductor compounds of high chemical and thermal stability. From the point of view of ionicity they rather resemble II–VI compounds such as ZnS, from the point of view of their hardness and chemical inertness they are similar to diamond or BN. Although GaN was first synthesized a long time ago (in the early 1930s), the interest in this group of semiconductors was limited due to the extreme difficulties of growing them in single-crystalline form. This latter fact arose from their thermodynamic properties: such as in the case of GaN the melting temperature is very high – 2500 8C – and is accompanied by a high equilibrium nitrogen pressure of *45,000 bar. In the period 1965–1975, Jacques Pankove and his students did pioneering work in growing and characterizing gallium nitride. Pankove himself was, even at this time, aware of the importance of this material in yet to exist new branches of electronics and optoelectronics. In the middle of the 1970s Pankove gave up nitride research, owing to technical difficulties at that time. The return of nitrides occurred in 1989 thanks to the Japanese scientists Amano, Akasaki, and Nakamura, who overcame the problems of growth and p-type doping. They used modern metalorganic chemical vapor deposition (MOCVD) techniques to grow nitride (GaN, InGaN) layers on sapphire substrates. They also used a post-growth activation process to get p-type material. From this time onwards, the development of this material was strongly influenced by the industrial demand for short-wave light emitting diodes (LEDs) and lasers. At present, high brightness blue and green LEDs and low-power blue laser diodes (LDs) are commercially available [1]. On the other hand, however, the development of GaN-based technology was, and still is, strongly limited by difficulties in obtaining large, high-quality GaN crystals that could be used as substrates for epitaxial deposition of multilayer quantum-confined structures necessary for devices. This is a direct consequence of thermodynamic properties of GaN [2] (and also AlN [3]). In particular, it is the melting conditions which are so extreme, that the application of the common growth methods from stoichiometric liquids is technically impossible. The High Pressure Research Center, UNIPRESS, has been involved in the research related to bulk gallium nitride growth and physical

1.2 High-Pressure Crystallization of GaN

properties for almost twenty years. In this chapter we would like to give a summary of the activity of High Pressure Research Center in the field of nitride crystal growth. In particular, we will address the problem of bulk GaN crystal growth and its use as substrates for MOCVD epitaxial deposition.

1.2

High-Pressure Crystallization of GaN 1.2.1

Thermodynamics – Properties of GaN-Ga-N2 System

In Table 1.1 melting temperatures and pressures of most typical semiconductor materials are compared. The melting temperature T M, and the corresponding equilibrium pressure at melting of GaN, AlN, and InN has not been measured. The quoted melting temperatures have been calculated by the use of Van Vechten’s quantum dielectric theory of chemical bonding [4]. The corresponding pressure follows from the extrapolation of the experimental equilibrium data [5, 6]. The table shows that both temperature and pressure at melting of GaN are much higher than that for typical semiconductors. They seem to be rather similar to the conditions used for high-pressure synthesis of diamond. Due to these extreme melting conditions, GaN (like AlN [3] and InN [7]) cannot be grown from its stoichiometric melt by the Czochralski or Bridgman methods commonly used for typical semiconductors. It has to be crystallized by methods that allow bulk growth at lower temperatures and pressures. Gallium nitride is a strongly bonded compound (with bonding energy of 9.12 eV atom–1 pair [8]) in comparison with typical III–V semiconductors like GaAs (bonding energy of 6.5 eV atom–1 pair). Consequently, the free energy of the crystal is very low in relation to the reference state of free N and Ga atoms. On the other hand, the N2 molecule is also strongly bonded (4.9 eV atom–1). Therefore, the free energy of GaN constituents at their normal states, Ga and N2, is close to that of the crystal. This is illustrated in Fig. 1.1 where the free energy of

Tab. 1.1 Melting conditions of semiconductors

Crystal

TM (8C)

pM (atm)

Si GaAs GaP AlN GaN InN

1400 1250 1465 3200 2500 1900

<1 15 30 200 45,000 > 60,000

Diamond (synthesis)

1600

60,000

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1 High-Pressure Crystallization of GaN

GaN (1 mole) and the free energy of the system of its constituents (Ga + ½ N2) are shown as a function of temperature and N2 pressure. With increasing temperature, the Gibbs composite free energy of the constituents, G(T), decreases faster than G(T) of the crystal and, at higher temperatures, GaN becomes thermodynamically unstable. The crossing of G(T) curves determines the equilibrium temperature where GaN coexists with its constituents at a given N2 pressure. The application of pressure increases the free energy of the constituents to a higher degree than G(T) of the crystal. As a consequence, the equilibrium point shifts to higher temperatures and the GaN stability range extends. The equilibrium pN2–T conditions for GaN have been studied by several groups [7, 9, 10]. The most complete and consistent results have been obtained by Karpinski et al. [5, 6] by direct synthesis and decomposition experiments, using both a gas-pressure technique (for pressures up to 20 kbar) and a high-pressure anvil technique (up to 70 kbar). A curve following from these data is shown in Fig. 1.2. Crystallization processes dis-

Gibbs free energy of GaN and its constituents.

Fig. 1.1

Fig. 1.2

[11, 12].

Equilibrium curve for GaN

1.2 High-Pressure Crystallization of GaN

cussed in this chapter have been carried out at N2 pressure up to 20 kbar, which corresponds to the GaN stability limit of 1960 K. These conditions are marked in Fig. 1.2. As was shown in [6] for pressures up to 20 kbar, the equilibrium curve can be described by the Van’t Hoff equation: 1 d ln aN2 DHF ˆ R 2 d…1=T†

…1†

where DHF is the formation enthalpy of GaN, aN2 is the equilibrium activity of N2 gas, with DHF constant and equal to –37.7 kcal mole–1. The extension of the GaN stability range by the application of pressure allows the growth of GaN crystals from the solution in liquid Ga. In Fig. 1.3 we show the experimental N solubility data [8] resulting from the annealing of Ga in N2 atmosphere at the three-phase equilibrium conditions. Even the highest temperature, experimentally accessible, at 1960 K, is quite far from the melting temperature of GaN (Table 1.1). Therefore the N concentrations are not high (below 1 at%) and the growth times have to be long to get high-quality crystals with dimensions appropriate for research and applications. Therefore, times of more than one hundred hours are required to obtain reasonable crystal yields. The solid line in Fig. 1.3 is the liquidus line for the Ga–GaN system calculated for an ideal solution approximation using the estimated Van Vechten GaN melting temperature of 2790 K [4]. For this approximation the solubility can be expressed as follows: n ˆ n0 exp

DHsol kT

…2†

where DHsol is the heat of dissolution. For GaN, DHsol = 44.7 kcal mole–1 (0.49 eV/bond) and expresses the bonding energy in the crystal in relation to its mother phase – the solution [8].

Liquidus line for Ga– GaN system: the solid line was calculated in the ideal solution approximation.

Fig. 1.3

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1 High-Pressure Crystallization of GaN

Our analysis of the thermodynamic properties of GaN-Ga(l)-N2 system explains the high pressures required to extend the GaN stability condition up to those temperatures needed for crystallization. The pressure, however, is also important for the kinetics of GaN synthesis. This is analyzed in the next section. 1.2.2

Dissolution Kinetics of N2 and Crystal Growth Mechanism

The nature of the GaN-Ga(l)-N2 system plays an important role not only in the thermodynamics of this system. Moreover, the kinetic properties are very different from those of other III–V systems, which entails the use of nonconventional crystal growth techniques. This also affects the models used in the description of the microscopic properties of the system and simulation procedures. Although the physical properties of these three phases are completely different, ranging from the gas (N2) to metallic liquid (Ga) and semiconductor solid (GaN), they have some common features. The most important is the fact that the atoms in all three phases are very strongly bound. Molecular nitrogen is the strongest bonded diatomic molecule in nature with a dissociation energy of 9.76 eV [8]. Liquid gallium is characterized by a high enthalpy of evaporation, equal to 2.81 eV atom–1 (271 kJ mole–1), which is reflected in the high boiling point of 4000 K [11, 12]. Similarly, solid GaN is strongly bonded, with the energy 9.12 eV/atom pair, which leads to a high melting temperature of, according to a Van Vechten estimate, 2790 K [4]. GaN synthesis from its constituents proceeds via dissolution of nitrogen in liquid gallium, transport of nitrogen to the cooler regions of the liquid and the growth from the solution. These stages include dissociation of N2 molecules, which is an energetically costly process. It is therefore expected that the dissociation process involves significant changes of binding energy of the molecule, greatly exceeding the typical thermal motion energies, of 0.15 eV. It is likely that the dissociation occurs during the adsorption of N2 molecules on the liquid Ga surface. The feasibility of this mechanism was explored using the density functional theory (DFT), which models many-body effects quantum mechanically [13]. Since thermal motion of the Ga atoms plays a minor role, the Born-Oppenheimer approximation can be used. An infinite Ga surface can be simulated by finite clusters of Ga atoms [14, 15]. The two different orientations of the N2 molecule – parallel and perpendicular to the surface – were used in the QM calculations [14]. The results include the electron charge distribution, the position of the atoms, and the total energies of the system. In Fig. 1.4 b we present the change of the total energy of the system in function of the distance between Ga surface and N2 molecule. The results obtained for the parallel configuration are presented. As shown in these diagrams, the nitrogen-gallium interaction is negligible for distances greater than 4 Å for which the energy zero level is adopted. At closer distances the energy increases sharply to reach 4.8 eV for d = 1.6 Å and then sharply decreases. As shown in Fig. 1.4 b, the excess energy increase occurs when the N-N distance is only slightly increased whereas the decrease occurs after the

1.2 High-Pressure Crystallization of GaN

(a)

(b)

a Geometry of the model used for DFT calculations: h – the distance between the molecule and the interface, d – N–N interatomic distance in N2 molecule. Open circles – N atoms, full – Ga atoms; b excess Fig. 1.4

(c) energy of the system as a function of the distance between the N2 molecule and metal cluster: squares – Al, triangles – Ga, circles – In; c N-N distance versus the distance between the N2 molecule and Ga cluster.

N-N distance increased suddenly to more than 3.2 Å. This dramatic change indicates that N2 dissociation takes place about 1.6 Å above the Ga surface. The dissociation of N2 molecules is confirmed by the plot of the electronic charge distribution in Fig. 1.5. The constant charge surface was plotted for the three selected Ga-N2 distances: 4.0 Å, 1.6 Å, and 1.0 Å. For the first two cases the electronic charge is concentrated in the region between N atoms, for the last case the charge is shifted to the region between Ga and N atoms, confirming the disso-

Fig. 1.5 Electron constant density surface for N2, parallel to 19 atoms Ga cluster for three selected NGa distances: h = 2.6 Å, h = 1.6 Å, and h = 1.0 Å [14, 15].

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1 High-Pressure Crystallization of GaN

ciation of the N2 molecule and the creation of a chemical bond between two N atoms and Ga surface atoms. The same behavior is observed for other group III metals: Al and In. The energy barriers are: 3.2 eV for Al and 5.8 eV for In, again much lower than the N2 dissociation energy (9.76 eV/molecule), indicating a strong catalytic influence of the group III metal surface. The calculation of the interaction of N2 molecule, oriented perpendicular to the Ga surface also confirmed the feasibility of this molecular dissociation mechanism at the surface. Generally, the energy barriers are much lower for this orientation: 3.0 eV for Al, 3.4 eV for Ga, and 3.6 eV for In. Since the interatomic distances are much larger for the In cluster, one can expect that the energy barriers for Al and Ga are relatively overestimated due to the higher stiffness of these two clusters. Using these energy barriers, the N2 dissociation rate on the metal surfaces was calculated. In these calculations the vibrational energy was accounted for. Since the energy barrier is much higher for the parallel than for the perpendicular N2 orientation, the rotational energy was neglected. The impingement rate was obtained from the ideal gas approximation using Maxwell–Boltzmann distribution. The reaction rate was determined as the fraction of the molecules that can pass over the energy barrier determined from the QM calculations. The temperature dependence of the nitrogen dissociation reaction rate for Ga, Al, and In surfaces, at a gas pressure of 20 kbar, is presented in Fig. 1.6. Nitrogen dissolved into liquid Ga, at the surface of the hotter region, is transported into the cooler regions of the liquid by convection and diffusion. There, the GaN growth proceeds via three main stages. The initial stage is heterogeneous nucleation of GaN on Ga surface. During the second stage from numerous GaN growing crystals, the most favorably located grow much faster and dominate the less-favored ones. The final stage is the growth of small number of single crystals

Average dissociation rate of N2 on a liquid group III metal surface calculated using the ideal gas approximation; Al – dashed line; Ga – dotted line; In – solid line (p = 20 kbar).

Fig. 1.6

1.2 High-Pressure Crystallization of GaN

in the supersaturated solution of nitrogen in liquid Ga. The last stage is crucial for the results of the crystallization process. Due to the high bonding energy and crystallographic structure of the main surfaces, growth of GaN crystals is strongly anisotropic. This is reflected in the shape of the GaN crystals, which are hexagonal platelets. From this observation it follows that the growth rates are the fastest for {1011} and {1011}, slower for {1010} and the slowest for (0001) and (0001) surfaces. The flat faces of GaN crystals indicate that they grow in a layer-by-layer manner. Depending on the structure of the crystals and thermodynamic conditions at the interface, several growth regimes can be distinguished. One of the most efficient growth centers is screw dislocations [24, 25]. Since in the wurtzite GaN structure the screw dislocations have much higher energy than edge dislocations, their fraction in total dislocation density is small. In the case of the growth of good-quality GaN crystals, the role of screw dislocation is negligible. In the absence of the screw dislocation the morphological properties of GaN growth mode results from the competition between new nucleation sites and growing step fronts. These two processes have different size dependences on their relative rates and subsequent importance for the growth mode. At stable thermodynamic conditions, the 2D-nucleation rate is proportional to the surface area, whereas the completion rate is inversely proportional to the dominant linear size of the surface. In most cases it is proportional to the inverse of the square root of the surface area. Hence, one can expect that for some cases the transition from nucleation to step-completion controlled growth occurs. Growth controlled by 2D nucleation is morphologically stable, i.e., it preserves the flat faces of growing crystals. In most cases, the surfaces (1010) and (0001) are atomically flat with several steps. The growth rate can be assessed using the Becker-Doring nucleation law. The rate is strongly dependent on supersaturation at the surface. Assuming that the edge energy is due to two broken bonds per atom site and using dissolution energy as the broken bond energy difference, the rate can be expressed as a function of the supersaturation [8]. For experimental growth rates, these calculations give 48% supersaturation at the growth zone, which is in good agreement with the estimation obtained from the temperature difference in the crucible and the composition-temperature (x-T) phase diagram [8]. For other GaN faces the surfaces are not so flat. Three-dimensional growth occurs when the surface nucleation rate is higher than the step-layer completion rate. This can be caused either by extremely fast nucleation resulting from relatively high supersaturation or by step pinning due to kink poisoning by the impurities. Also, the presence of screw dislocation growth centers can cause a similar effect. If growth is much faster in some local region of the surface, then hills and valleys are likely to result. A transition to morphological unstable forms occurs if such a feature leads to run-away growth in that vicinity, i.e., positive feedback. This type of growth is sometimes observed in the growth of (0001) surfaces, i.e., Ga-terminated.

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1.2.3

What Happens with GaN at High Temperature when the N2 Pressure is too Low?

Both the increase of the thermodynamic potential of gaseous nitrogen and the enhancement of the creation of the atomic nitrogen at the Ga surface can be achieved by other (not compression) methods, like the excitement of N2 plasma or the use of species containing nitrogen bonds that are weaker than the N2 molecule. It was demonstrated [8] that in a microwave nitrogen plasma of 60 Torr and a temperature as low as 1100 8C, a very efficient GaN (and even InN!) synthesis is possible. The excited N2 gas was a very efficient source to saturate Ga droplets with atomic nitrogen, forming a GaN crust on the droplet surface. However, since the pressure in the system was much lower than the equilibrium one (about 100 bar for 1100 8C), the N2 gas phase started to nucleate and grow in the liquid. This results in the formation of the structure shown in Fig. 1.7, which is an empty “Ga droplet” covered with an irregular polycrystalline GaN crust. The formation of the N2 bubbles in the supersaturated Ga : N liquid was also observed if the pressure in the system containing GaN crystals (dipped in the Ga : N solution) was intentionally dropped below the equilibrium value. At this point, N2 bubbles nucleated on the surface of the crystals, and then with crystals being locally in contact with the gas start to decompose as it tries to restore the equilibrium condition. However, when the system was cooled, the liquid at the interface becomes supersaturated with nitrogen leading to GaN crystallization at the outer surface. Two examples of GaN crystals with local decomposition features on their surfaces are shown in Fig. 1.8 together with the schematic illustration of the described process.

The result of GaN synthesis from the liquid Ga and N2 plasma. The liquid has been pushed out from the initial droplet covered by the GaN crust, by the growing N2 bubbles. Fig. 1.7

1.2 High-Pressure Crystallization of GaN

Decomposition of GaN in the supersaturated Ga : N solution if the pressure in the system drops below the equilibrium value. Local decomposition features supporting the proposed mechanism are visible on the crys-

Fig. 1.8

tal surfaces: a N2 bubbles start to nucleate in the liquid, some of them nucleate on the GaN crystal surfaces; b during cooling the interfaces cover with GaN since the solution is supersaturated.

1.2.4

Crystallization of GaN Using High Nitrogen Pressure Solution Growth (HNPSG) Method – Experimental

At present, GaN is crystallized in gas pressure vessels with volumes up to 1500 cm3 allowing crucibles with a working volume of 50–100 cm3. The high-pressure-high-temperature reactor consists of a pressure chamber and a multizone furnace. It is also equipped with additional systems necessary for in situ annealing in vacuum, electronic stabilization and programmability of pressure and temperature. At the periphery, the water cools the pressure chamber. Pressure in the chamber is stabilized with a precision better than 10 bar. The temperature is measured by an array of thermocouples in the furnace and coupled with the standard input power control electronic systems based on Eurotherm units. This allows a stabilization of temperature to ± 0.2 8C and programmable changes of temperature distribution in the crucible. An example of a high-pressure apparatus, constructed in HPRC, is presented in Fig. 1.9. GaN crystals presented in this chapter were grown from nitrogen solutions in pure liquid gallium or in Ga alloyed with 0.2–0.5 at% of Mg or Be at pressures in the range of 10–20 kbar and temperatures of 1400–1600 8C. Magnesium and beryllium, as the most efficient acceptors in GaN, were added to the growth solutions in order to dope the crystal p-type.

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Fig. 1.9

High-pressure apparatus, constructed in HPRC for crystallization of GaN.

Supersaturation in the growth solution has been attained by the deliberate application of a temperature gradient of 2–20 8C cm–1 along the axis of the crucible. This method was chosen since the axial temperature gradients in multizone furnaces, working at high gas pressure, can be controlled with high precision and the method assures a continuous flow of nitrogen from the hotter part of the solution to the cooler one. Crystallization experiments performed without intentional seeding resulted in crystals nucleating spontaneously on the internal surface of polycrystalline GaN crusts (covering liquid Ga) in the cooler zone of the solution. A typical duration of the growth process was 120–150 h. The slow cooling down, while keeping uniform temperature inside the crucible, was not applied due to small concentrations of nitrogen in the liquid gallium (Fig. 1.3). The crystallization at constant temperature, under a N2 overpressure was also not applied since then the crystallization can occur only on the Ga surface and stops if the whole surface is covered with GaN. 1.2.5

Properties of GaN Single Crystals Obtained by HNPSG Method 1.2.5.1 Crystals Grown without Intentional Seeding

The GaN crystals grown by the high nitrogen pressure solution method are of wurtzite structure, mainly in the form of hexagonal platelets. The wurtzite structure of GaN crystal is presented in Fig. 1.10. As shown in the figure, the subse-

1.2 High-Pressure Crystallization of GaN

quent planes consist of the atoms of the same kind. In one of these two planes, the atoms are bonded to three atoms. From the upper side, Ga atoms are denoted as black and N atoms denoted by yellow. These planes are energetically stable, therefore the sides are denoted as the N-side and the Ga-side. The large hexagonal surfaces of bulk GaN crystals correspond to (0001) polar crystallographic planes. Conventionally the N-side is denoted as (0001) and the Ga-side as the (0001) surface. The side faces of the crystals are mainly the polar {1011} and also non-polar {1010} planes. Crystals in the form of hexagonal platelets grow with a rate, along h1010i directions (perpendicular to the c-axis), below 0.1 mm h–1, and have perfect morphology indicating a stable layer-by-layer growth mode. They are transparent, with flat mirror-like faces. The habit of the crystals does not change for solutions contain-

Fig. 1.10 The crystallographic structure of GaN crystals. Ga and N atoms are denoted by black and yellow, respectively.

Fig. 1.11 GaN crystals grown in high-pressure chambers of different size. The numbers are proportional to the diameters of the

chambers. The distances between grid lines correspond to 1 mm. The schematic cross section of the hexagonal platelet is shown.

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1 High-Pressure Crystallization of GaN

ing Mg or Be. The average size of crystals, grown without any intentional seeding, scales with the diameter of the high-pressure reactor as is shown in Fig. 1.11. As one can deduce from the form of the crystals, the growth is strongly anisotropic being much faster (about 100 times) in directions perpendicular to the caxis. This relation is valid at supersaturations corresponding to an average growth rate in h1010i directions, of 0.05–0.1 mm h–1. An increase of the supersaturation enhances the growth along the c-direction, which leads to the unstable needle-like forms. The supersaturation in the growth solution is determined mainly by the growth temperature, temperature gradients, mass transport mechanisms in gallium, and also by the local surroundings for a particular crystal (i.e., the presence of neighboring crystals). For crystallization of large GaN crystals, it is crucial to control the supersaturation in order to avoid acceleration of the growth near edges and corners of the growing crystal. For excessively high supersaturation, the edge nucleation on the hexagonal faces of GaN platelets is often observed, which is the first step to the unstable growth on that particular face. The result of such a growth is shown in Fig. 1.12 a. In the extreme cases of very high supersaturations, the growth along the c-direction proceeds by edge nucleation. The growth becomes very fast and leads to the formation of well-developed {1010} faces. Since the lateral growth on the c-face is still slow, the resulting crystals are hollow needles elongated in the c-directions (Fig. 1.12 b). The tendency to unstable growth is stronger for one of the polar {0001} faces of the platelets. On this side, morphological features like macrosteps, periodic inclusions of solvent or cellular growth structures are routinely observed. The opposite surface is always mirror-like and often atomically flat. For crystals grown without an intentional doping (strongly n-type – see next section) the unstable surface always corresponds to the Ga-polar (0001) face of GaN, whereas for crystals doped with Mg (semi-insulating – see next section) it is always the opposite N-polar (0001) face. Therefore, the presence of Mg (if sufficient to compensate free electrons) changes microscopic growth mechanisms on the {0001} polar surfaces of

(a)

Fig. 1.12 a Edge nucleation on (0001) face of pressure-grown GaN crystal. c-axis is perpendicular to the figure plane; b hollow

(b)

GaN crystal with (1010) face formed at increased supersaturation.

1.2 High-Pressure Crystallization of GaN

GaN [18]. If the doping level is too low and the resulting crystals are still n-type, the morphology is similar to crystallization without doping. This suggests that the position of the Fermi level in the crystal influences the microscopic processes occurring on the growing surfaces. Such a suggestion is consistent with the results of ab initio calculations [19, 20] showing that the formation energies of both native and impurity-related point defects in GaN are very sensitive to the position of the Fermi level in the crystal. Figure 1.13 shows the cross-sectional SEM scan of the n-type GaN platelet. Periodic structure is visible on the Ga-polar (0001) surface of the crystal. Such features are often observed in many of the solution-grown crystals as a result of constitutional supercooling of the growth solution at the crystallization front. This phenomenon will be explained in the next section and a method to suppress such an instability will be discussed. The polarity of the crystal surfaces was identified by etching in hot alkali water solutions since the Ga-polar surface is inert to etching, whereas the N-polar one etches well for both types of crystals. The method was calibrated using convergent beam electron diffraction (CBED) [21, 22] and X-ray photoelectron spectroscopy (XPS) [23] data. From the analysis of the growth of GaN crystals without an intentional seeding, it follows that in the case of the growth along h1010i directions, at a growth rate of 0.05–0.1 mm h–1, the crystal is morphologically stable. In the case of the growth along the h1120i directions, the crystal is morphologically stable for even higher rates. Therefore the size of the stable platelets should depend on the growth time (and volume of the solution) and further scaling of the crystal size with time and the volume of the crucible should be possible. It is also clear that the seeded growth into directions perpendicular to the c-axis should occur rapidly, in a stable way, especially along the h1120i directions. Seeded growth along the directions parallel to the c-axis seems to be much more challenging since the observed growth rates are small and the growth shows

Fig. 1.13 Cellular growth on the Gapolar (0001) surface of GaN crystal. c-axis is perpendicular to the figure plane.

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1 High-Pressure Crystallization of GaN

susceptibility to instability. In the next section, the results of growth using GaN seeds are presented.

1.2.5.2 Seeded Growth of GaN by HNPS Method

The thin GaN platelets, described in the previous section, can be used for further crystallization as seed crystals. Depending on seed preparation and the configuration of the experiment, it is possible to enforce the growth in directions perpendicular or parallel to the c-axis. As was already mentioned, the growth on the GaN {0001} polar surfaces is very slow and often unstable. Features like macrosteps at the edges and the periodic cellular structures suggest possible instability mechanisms. For macrosteps at the edges the quite obvious reason is the accelerated growth at the edges exposed to the nitrogen flux (coming from the hotter part of the solution). This can be avoided by the elimination of the edges by configuring the intentional seeding experiment shown in Fig. 1.14 c. Such a configuration also achieves much more uniform supersaturation across the growing surface, which is a very important condition for stable solution growth, especially if the growing surfaces are relatively large. Cellular growth is often a result of constitutional supercooling (Tiller et al. [24]) of the solution, which is graphically explained in Fig. 1.10 a and b. The principal cause is a very low temperature gradient and high thermal and low solute diffusivity. Assuming that the crystallization from the solution of the concentration CN is rapid, leads to the creation of a depleted zone at the crystallization front (Fig. 1.13 a). Due to low solute diffusivity the concentration cannot be recovered by the diffusional flux of new species. The concentration profile in front of the growing crystal can be transformed into an effective temperature profile (TL on the Fig. 1.13 b) via liquidus relation. This effective temperature profile can be compared to a real temperature gradient at the crystallization front. If the gradient is relatively small – like the one labeled GNS, the effective temperature in front of the growing surface can be lower than the real temperature. If each advancement in growth leads to further enhancement and the local depletion at the sides of the growing cell then this front becomes inherently unstable, across the growth front and thus a cellular structure evolves like the one shown in Fig. 1.12. The condition for stable growth can be expressed by the relation [25]: GL > V

C…1

k†… m† kD

…3†

where GL is the temperature gradient at the crystallization front, V – growth rate, k – distribution coefficient, equal to the solid and liquid equilibrium concentration ratio, D – diffusion coefficient of the solute in the growth solution and m – the liquidus slope of the temperature-concentration (T-x) phase diagram. The parameters at the left-hand side of relation (3) can be controlled experimentally using the growth configuration of Fig. 1.14.

1.2 High-Pressure Crystallization of GaN

(a)

(b)

Fig. 1.14 Schematic illustration of creation of constitutional supercooling in front of growing crystal: a creation of the depleted zone at the crystallization front due to incorporation of the solute into the growing crystal; b different temperature gradients applied at the crys-

(c) tallization front related to the equilibrium liquidus temperature profile corresponding to the concentration profile of Fig. 1.10 a; c configuration used for seeded growth of GaN on {0001} polar surfaces of GaN substrates.

N-type GaN platelets have been used for seeded crystallization in order to suppress the cellular growth on the Ga-polar (0001) surface. The N-polar (0001) surfaces have also been used for comparison. The surfaces were prepared as for epitaxy: they were polished mechanically and then the surface damage removed by mechanochemical polishing for the N-polar surface [26] and by reactive ion etching (RIE) for the Ga-polar surface. The experiments were performed in the vertical configuration, similar to that from Fig. 1.14 c. Large positive temperature gradients of the order of 100 8C cm–1 have been applied at the average crystallization temperature of about 1500 8C. After 20–50 h process times the substrates with the new crystals were removed from the solution and investigated. The result of a 50-h growth time on the Gapolar surface is shown in Fig. 1.15 where both the optical and SEM images of the substrate with the new grown crystal are presented. The new material was transparent, colorless and grown as a single hillock 6 mm in diameter. The periodic, cellular structures were no longer present. The dominant growth mechanism was the propagation of the macrosteps from the hil-

(a)

(b)

GaN substrate with the new grown material on the Ga-polar surface: a optical image (distance between the grid lines – 1 mm); b SEM image.

Fig. 1.15

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1 High-Pressure Crystallization of GaN

(a)

Fig. 1.16 Morphology of GaN crystal grown on Ga-polar surface of GaN substrate in a 50h process. SEM images of the growth hillock surface at different magnifications: a large-

(b)

scale view of the surface morphology; b surface-fine structure associated with the growth process .

lock center. The position of the hillock center most likely corresponds to the minimum of the supersaturation resulting from the radial temperature gradients in the growth solution. Macrosteps are shown clearly in Fig. 1.16 a and b. Such growth features are frequently observed for crystallization from solution, since the surface diffusion is relatively slow in comparison to the growth from the vapor phase, where the growth proceeds by the propagation of monoatomic steps. In contrast, growth on the N-polar surface was mainly by the propagation of the macrosteps. Several growth centers have also been observed for similar experiment conditions. It is still not clear if this is related to differences in surface nucleation mechanisms for the different polarities or due to the imperfect preparation of the surface. The average growth rates observed in these experiments were between 4 and 8 lm h–1 for both polarities, depending on supersaturation at the growth front, which is a function of temperature gradient and the width of liquid Ga layer over the substrate. Microscopic observation of cross sections of the samples (Fig. 1.17) showed that the growth was stable in terms of continuity of the new-grown material, i.e., inclusions of the solvent and/or voids were not observed. The interfaces between substrates (80–100 lm thick) and the new-grown crystals were not visible, indicating that the surface preparation and the wetting procedures before seeding were performed correctly. XRD analysis shows that the material grown by the method just described has a similar structural quality to that of the substrate used. These directional crystallization experiments are being continued to find the optimum configuration for stable growth of bulk GaN along the h0001i directions. In particular, in order to limit the step bunching, the supersaturation across the growing surface should be more uniform. This can be achieved by the reduction of radial temperature gradients and/or by decreasing the width of Ga layer over the substrate. This method allows the possibility of growing thick crystals, which can be sliced into platelets of standardized shape as shown in Fig. 1.18.

1.2 High-Pressure Crystallization of GaN Fig. 1.17 SEM scan of the cross section of GaN crystal grown on Ga surface of GaN substrate for 40 h.

(a)

(b)

Fig. 1.18 GaN substrate crystal, obtained by slicing of the new material, grown by directional crystallization along c-axis.

1.2.6

Physical Properties of GaN Crystals, Grown by HNPS Method 1.2.6.1 Point Defects

As was already mentioned, N2 molecules dissociate on contact with the Ga surface. However, to approach the surface they have to overcome a large (about 3.5 eV) potential barrier, which substantially lowers the rate of nitrogen dissociation and its further dissolution in the metal. For oxygen interacting with Ga, there is no potential barrier for dissociation [27] and therefore traces of this impurity in the growth system are a source of the unintentional oxygen doping of GaN. Consequently, the crystals are strongly n-type with a free electron concentration of about 5 ´ 1019 cm–3 (metallic conductivity) and a mobility of about 60 cm2 V–1s–1 [28]. These free carriers can be fully eliminated by adding Mg acceptors to the liquid gallium solution. Then the resistivity of the crystals increases to 104–106 X cm at 300 K.

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1 High-Pressure Crystallization of GaN

Usually the GaN : Mg crystals become p-type with an activation energy of 150 meV, at temperatures slightly exceeding 300 K. More detailed analysis of the electrical properties of pressure-grown Mg-doped GaN crystals can be found in Ref. [29]. The presence of the native point defects in the crystals has been checked by positron annihilation measurements [30]. High concentrations of gallium vacancies, VGa, have been found in the conductive crystals, in contrast to the Mg-doped samples where no Ga-vacancies were observed. This agreed with theoretical predictions that the formation energy of VGa decreases with an increase of the Fermi level energy [19, 20] suggesting that thermodynamics plays a central role in the creation of these defects. The difference in the PL spectra [31] of the conductive (strong yellow emission) and Mg-doped crystals (no yellow emission, blue Mg-related signal) supported the inference that VGa is involved in yellow luminescence in GaN. Quite a different picture is observed for doping with beryllium [18]. The GaN : Be crystals are also highly resistive with a temperature-independent activation energy of 1.46 eV for temperatures up to at least 1000 K. But their PL spectra are dominated by a very strong yellow luminescence, and thus the crystals contain lots of gallium vacancies [18] similar to highly conductive crystals grown without intentional doping. So it is very probable that these crystals were n-type during high-temperature growth and became semi-insulating during the cooling-down period. Such behavior can be related to two possible configurations of Be atoms in the GaN lattice (BeGa – acceptor and Bei – donor) and their redistribution as a function of temperature. The two opposite GaN faces, corresponding of low polar indices {0001} and {1011} crystallographic planes in wurtzite structure, which appear in the pressuregrown GaN crystals, are nonequivalent regarding their atomic structure. This is reflected by the asymmetry of the physical properties of the plate-like crystals

Fig. 1.19 Photoluminescence of GaN layer, grown on the different sides of polished plate

let grown using intentional seeding (substrate) and the platelet (substrate) itself.

1.2 High-Pressure Crystallization of GaN

grown without intentional seeding. In Fig. 1.19, an example of such an asymmetry is presented. The material grown with N-polarity differs in its PL properties to the material grown with the Ga-polarity, which indicates that the point defects are incorporated into the crystal in different ways. Additionally, the spectra from the material grown on the {0001} N- or Ga-polar surfaces (seeded growth) are similar in character to the spectra from corresponding substrate surfaces. Since the platelets were polished before being used as seeds, the suggestion arises that the platelets themselves also demonstrate a polar character despite being grown mainly along the fastest growth h1010i directions, which follows from their morphology. The strong support for this inference is the micro-Raman scattering measurements of the free electron concentration [32] distribution across the cleaved, as grown GaN platelet [33]. Figure 1.20 shows that the borderline be-

Fig. 1.20 Distribution of free electron concentration across the GaN platelet measured by micro-Raman scattering technique [33].

Fig. 1.21 The arrangement of atoms on the polar surfaces of GaN.

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1 High-Pressure Crystallization of GaN

tween materials of higher (N-side) and lower (Ga-side) electron concentration is situated inside the crystal effectively dividing it into two parts. This suggests that the microscopic (atomic scale) processes responsible for the formation of both native and impurity-related point defects, occur mainly on the {1011} polar faces of the growing GaN crystals independent of whether the growth is perpendicular or parallel to the c-axis. This explains another result of the positron annihilation measurements [34], showing that the concentration of Ga vacancies is much higher at the Ga-side than at the N-side of the n-type GaN platelets. It seems surprising at first sight since, on the Ga-polar (0001) surface, the surface Ga atoms are bonded to the surface by three bonds, whereas to the opposite one it is bonded to one bond only. We assume that the incorporation of the Ga atoms occurs on the {1011} polar surfaces. On the (1011) face adjacent to the (0001) one, Ga atoms can be bonded by one or two bonds whereas on the opposite (1011) polar surface adjacent to the (0001) one, the Ga surface atoms are bonded by two or three bonds. The arrangement of the atoms on the relevant polar surfaces of GaN is shown in Fig. 1.21. It follows from the above that the lateral (perpendicular to the c-axis) growth of the platelet does not occur on the nonpolar {1010} surfaces (at least it is not predominant) since then a plateau in the diagram of Fig. 1.20 should be observed.

1.2.6.2 Extended Defects

The structure of the HNPSG-grown GaN crystals has been studied by X-ray diffraction (XRD) [35], transmission electron microscopy (TEM) [21, 36, 37], defect selective etching (DSE) [38], and atomic force microscopy (AFM) on the homoepitaxial layers [39, 40]. In the case of the conductive crystals, the shape of the (0002) X-ray rocking curves (CuK radiation) depends on the size of the crystal. The full widths at half maximum (FWHM) are 20–30 arcsec for 1-mm crystals and 30–40 arcsec for 1–3mm ones. For larger platelets the rocking curves are often split into a few ~30– 40 arcsec peaks showing the presence of low-angle (1–3 arcmin) boundaries separating grains a few millimeters in size. Misorientation between grains increases monotonically from end to end of the crystal [32]. It has been suggested that this can be related to the polar character of the platelet growth, leading to some stress and its subsequent relaxation through the formation of the low-angle boundaries. As shown by Liliental-Weber [21], using TEM examination, the N-polar (0001) surface of the n-type pressure-grown GaN crystals (especially for the smaller ones) is often atomically flat (2–3 monolayer steps present) and the crystals under this surface are practically free of extended defects. On the opposite Ga-terminated face, the surface is rough and the platelet contains a number of extended defects like stacking faults, dislocation loops, and Ga microprecipitates in the layer extending to 10% of its entire thickness. It seems that the presence of these defects is related to the growth instabilities often observed on the Ga-polar surface of crystals grown without intentional doping.

1.2 High-Pressure Crystallization of GaN

Detailed TEM studies of Mg-doped crystals are reported in [37]. In particular, it is shown that the introduction of Mg induces the formation of a set of specific extended defects, mainly the stacking faults situated at the {0001} polar surfaces. Using crystals as substrates for epitaxy, the near surface material, often the result of the unstable growth, has to be removed by polishing and subsequent reactive ion etching (Ga-side) or mechanochemical polishing (N-side). Generally, extended defects are not observed by TEM in crystals used as substrates for both N and Ga polarity epitaxial growth. Therefore, if the epitaxy is properly optimized both the substrate and quantum well structures do not contain dislocations. Unfortunately, TEM allows us to analyze only a very small area of the samples. Therefore, in order to assess the dislocation densities in GaN, the defect-selective etching methods have been developed [38]. It was shown that etching in molten KOH-NaOH eutectics reveals dislocations in both GaN heteroepitaxial layers and GaN pressure-grown single crystals. Examples are presented in Fig. 1.22. Figure 1.22 a shows the result of defect-selective etching of typical GaN heteroepitaxial layer grown by MOCVD on sapphire substrate. A high density of the etch pits is evident. The same method applied for bulk crystals reveals a very small etch pits density (10–100 cm–2). A typical pit observed on both heteroepitaxial layers and crystals is shown in Fig. 1.22 c. The pattern in Fig. 1.22 b is the result of DSE of GaN single crystal with dislocations generated intentionally by indentation with a diamond. Etch pits surround the imprint of the diamond showing the area over which dislocations have relieved stress and that the remaining material is dislocation-free.

(a)

(b)

Defect selective etching of GaN: a GaN/sapphire heteroepitaxial layer after etching in molten KOH–NaOH eutectics [38]; b GaN pressure-grown single crystal after indentation with diamond and etching in molten

Fig. 1.22

(c) KOH-NaOH eutectics [38], the average size of the star-like pattern is 100 lm; c etch pit (EP) on the GaN crystal surface after etching in molten KOH-NaOH eutectics [38], observed density of EP – 10–102 cm2.

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1 High-Pressure Crystallization of GaN

1.3

Epitaxy on Bulk GaN 1.3.1

Introduction

The spectacular development of GaN-based optoelectronic devices was possible due to elaboration of the two-step metal organic chemical vapor deposition (MOCVD) process for the growth of (GaAlIn)N epitaxial structures on highly mismatched sapphire substrates. In these structures dislocation densities are as high as 108–1010 cm–2, but, nevertheless, very efficient luminescence is possible from the structures containing InGaN [41]. It has been suggested by Deguchi et al. [41] that such a high conversion efficiency occurs due to strong localization of carriers in potential wells caused by compositional fluctuations in InGaN alloys, which prevents diffusion of carriers to dislocations. In this model, the influence of dislocations on the optical efficiency of InGaN can be eliminated if the distance between dislocations exceeds the size of the potential fluctuations. However, for high injection currents (i.e., in LDs), the potential minima are too shallow to contain all the injected carriers and therefore for lasers, the reduction of dislocation density in the material is much more important than for LEDs. The above model explains in a consistent way the following characteristics of the optoelectronic devices developed by Nakamura (the unquestionable leader in the field of GaN-based technology and optoelectronics): – The nitride LEDs containing In in their active structures are much more efficient than LEDs with pure GaN-active layers (not alloyed with In) [42]. – InGaN LEDs efficiency does not depend on dislocation density (if Al2O3 or ELOG are used) in contrast to the efficiency of In-free UV diodes. – At high injection currents, the high dislocation density decreases the efficiency, even for InGaN LEDs. Therefore, one can expect that the elimination of dislocations from the structures should lead to: – High-efficiency In-free UV LEDs. – Higher efficiency and higher power of both UV and visible laser diodes than is possible with dislocated structures. – Longer lifetimes. In the following, both In-free and In-containing structures are considered and the results supporting the above expectations are presented. 1.3.2

Metalorganic Chemical Vapor Epitaxy on GaN Substrates in HPRC Unipress

Metalorganic vapor phase epitaxy (MOVPE) is the most commonly used technique for growing III-N layers. The initial experience in MOVPE homoepitaxial growth on Unipress GaN substrates was gained at Warsaw University by Pakula et al.

1.3 Epitaxy on Bulk GaN Fig. 1.23

MOVPE nitride apparatus in HPRC.

[43], at the Wroclaw Technical University by Leszczynski et al. [44], at Ulm University by Kamp et al. [45], and at CRHEA-CNRS-France by Leszczynski et al. [46]. Since 1999, when the Unipress MOVPE system was completed, almost all research on MOVPE growth on bulk GaN substrates has been done with this equipment. The MOVPE system was designed by M. Panek (Wroclaw TU) and P. Prystawko (Unipress). It can employ either vertical or T-shape reactors. The gases (N2, H2, and NH3) are purified to ppb level by getter purifiers. The following metalorganic compounds are used: trimethylgallium (TMG – (CH3)3Ga), trimethylaluminum (TMA – (CH3)3Al), trimethylindium (TMI – (CH3)3In) for growing (Al,Ga,In)N layers, bis(cyclopentadienyl)magnesium (Cp2Mg) for Mg-doping, SiH4 for Si-doping. The substrate is heated by an inductive coil that induces current in a graphite (SiC-coated) susceptor. The MOVPE apparatus constructed at HPRC is presented in Fig. 1.23. The growth is monitored by laser reflectometry. A typical scan obtained during the InGaN-based laser-structure growth is shown in Fig. 1.24. Each oscillation corre-

Fig. 1.24 Optical reflectance measured during growth of quantum structure by MOVPE.

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1 High-Pressure Crystallization of GaN

sponds to an increase of about 1300 Å of the growing layer. The figure shows that during such a complicated growth (more than 100 different layers) the amplitude of oscillation remains almost constant for the same chemical composition, which means that the surface does not roughen. Using laser reflectometry, it is possible to control the growth so that one can determine the deposited layer width with 2– 3 Å accuracy, which is necessary for the multiple quantum wells (MQW). The first important finding was that a Ga-terminated (0001) face (see Fig. 1.10) incorporates acceptors much easier than N-terminated (0001) face. Likewise, the N-terminated face incorporates donors, also impurities, like oxygen, more easily [47]. As p-doping is a crucial point for constructing optoelectronic nitride devices, the Ga-face was chosen for further research. This choice created the problem of surface preparation: the N-face can be easily mechanochemically polished, but the Ga-face is chemically inert. Therefore, we had to develop the procedure of chemical cleaning and reactive ion etching (RIE) [46]. If the surface preparation and the conditions of the epitaxial growth are optimized, the structural quality of GaN homoepitaxial layers, in terms of dislocation density, follows the structure of the GaN substrates. Figure 1.25 compares the surface morphology of GaN epitaxial layers deposited by MOVPE on GaN substrate and on sapphire substrate in the same run. The atomic step flow for homoepitaxial GaN is not perturbed by dislocations, to the extent seen for heteroepitaxy on sapphire substrates. Hence, the homoepitaxial GaN layers seem to reproduce the crystallographic quality of the substrates. Figure 1.26 shows the X-ray diffraction rocking curve consisting of two peaks: one for the GaN substrate grown at high pressure, one for the homoepitaxial layer. Both peaks have FWHM (full widths at half maxima) of 20 arcsec, similar to the calculations made for perfect GaN analyzed on this particular XRD system. The peaks are separated because lattice of the GaN bulk crystal is slightly expanded by free electrons and point defects [48].

(a)

(b)

Fig. 1.25 Surface morphology of GaN epitaxial layers deposited by MOVPE on different substrates: a GaN pressure-grown crystal; b sapphire (AFM – courtesy of G. Nowak).

1.3 Epitaxy on Bulk GaN Fig. 1.26 X-ray diffraction rocking curve of MOVPEgrown GaN homoepitaxial undoped layer.

If a GaN homoepitaxial layer is nearly dislocation-free, its optical properties depend mostly on the concentration and distribution of point defects incorporated during the epitaxial growth. It is therefore a function of the purity of the growth system, the growth conditions and the substrate orientation. Due to the lack of strain and the high degree of homogeneity of the homoepitaxial GaN, the exciton-related peaks in low-temperature PL spectra are usually very narrow. The FWHM of the bound exciton lines of the layers grown by MOCVD (i.e., [49, 50]) on the Ga-polar surfaces of the GaN substrates are less than 0.5 meV (Fig. 1.27).

(a) Fig. 1.27 Low-temperature PL spectra of GaN homoepitaxial layers: a grown by MOVPE on the Ga-polar surface of GaN substrate;

(b) b grown on N-polar surfaces (exactly oriented and vicinal) of GaN substrates.

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1 High-Pressure Crystallization of GaN

For layers deposited on the N-polar surfaces the spectra are usually much wider due to the enhanced and nonuniform incorporation of unintentional impurities on this chemically active side of the crystal. This can be suppressed by the use of surfaces vicinal to the (0001) as was shown by Zauner et al. [51] who obtained narrow excitonic spectra for GaN layers grown on misoriented N-polar surface wafers (Fig. 1.27 b). Time-resolved PL has been also studied at high excitations [52] for GaN layers grown by MOCVD on sapphire and pressure-grown GaN substrates. A decay time (at RT) of 450 ps was measured for homoepitaxial material, which was five times longer than for corresponding heteroepitaxial layer grown under the same conditions. Figure 1.28 shows the decay of spontaneous luminescence measured at high excitation, close to the stimulated emission threshold for homo- and heteroepitaxial GaN. Optically pumped low-temperature (LT) stimulated emission [53] experiments confirmed that the nearly dislocation-free GaN is a much more efficient source of light than GaN-containing dislocations. The stimulated emission of a GaN homoepitaxial layer grown by MOCVD started at the excitation power density lower than 1 MW cm–2, whereas for GaN grown on SiC it was at 10 MW cm–2. The homoepitaxial layer stimulated emission peak was narrow, about 5 meV compared to about 40 meV for GaN grown on SiC. The nearly dislocation-free InGaN epitaxial layers and quantum wells were grown on pressure-grown GaN substrates, using MOVPE by Leszczynski et al. [54], at the High Pressure Research Center. In Fig. 1.29 a TEM image of one of the InGaN MQWs grown in Warsaw, demonstrates that the structure is dislocation-free. Dislocations in the structures grown on almost dislocation-free substrates can appear as a result of the lattice mismatch between GaN and its ternaries InGaN and AlGaN. This was analyzed by Leszczynski et al. [54] by X-ray measurements of the lattice parameters of various GaN-based epitaxial layers deposited on GaN

Fig. 1.28 Spontaneous luminescence transients for GaN films grown on sapphire (solid squares) and on GaN substrates (open circles) [52].

1.3 Epitaxy on Bulk GaN Fig. 1.29 InGaN MQW grown on the Ga-polar (0001) surface of GaN substrate by MOCVD [39], TEM – courtesy of M. Albrecht [36].

(a)

(b)

Fig. 1.30 Critical conditions for III-N ternaries: a X-ray data: open circles – AlGaN relaxed, open squares – AlGaN strained, filled squares – InGaN strained, open squares – InGaN relaxed; b TEM image of the multilayerstructure deposited on GaN substrate by

MOCVD, the sequence of layers from the lower left corner: n-GaN, n-Al0.11Ga0.89N/n-GaN superlattice, n-GaN, In0.09Ga0.91N, p-GaN, p-Al0.14Ga0.86N/p-GaN superlattice, p-GaN – courtesy of M. Albrecht and J. Borysiuk.

substrates as a function of InGaN (AlGaN) composition and thickness. It was shown that the range of quantum-well thickness and composition required for laser diodes is well within the limit-line imposed by the (Blakeslee) critical thickness for dislocation formation. These results are collected on the diagram in Fig. 1.30 a. Figure 1.30 b shows an example of the multilayer structure similar to the full structure of a blue laser diode. This example confirms that no mismatch dislocations are generated if the structure is grown on dislocation-free GaN substrate. TEM and AFM techniques can probe only an area of a few square micrometers. Using XRD we examined an area of a few square millimeters. Figure 1.31 presents an experimental scan for a laser structure compared to a theoretical simulation using a dynamical X-ray diffraction theory. For GaN and AlGaN layers (on the right-hand side of the scan) the peaks are very narrow, not broadened by com-

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32

1 High-Pressure Crystallization of GaN Fig. 1.31 X-ray scan of laser structure. For comparison, the Xray intensity of a simulated perfect structure is presented.

positional fluctuations. For InGaN, as is observed by all growers, the peaks are slightly broader than for a perfect structure due to fluctuation in the composition. 1.3.3

Molecular Beam Epitaxy

Nitride research by MBE started development substantially later than MOVPE, but, due to higher purity, better interface quality, and easier p-doping MBE it has become a widely used tool in research on nitrides. As with epitaxy on bulk GaN we do not need LT (low-temperature) buffer layers and the MBE method seems to be especially suited for deposition of nitrides on dislocation-free substrates. The MBE experiments were conducted in collaboration with Ulm University (M. Kamp), CRHEA (J. Massies and N. Grandjean), Minnesota University (R. Helm) and Nottingham University (T. Foxon) and gave many results that confirmed that a combination of the dislocation-free GaN substrates and MBE can give high-performance device structures. The MBE technique has been used mainly for the growth of GaN/AlGaN structures [36, 55–57]. Nearly dislocation-free GaN/AlGaN multiquantum wells and structures have been grown on the N-polar surfaces of GaN crystals by RF plasma-assisted MBE (PAMBE) [36, 55] and on the Ga-polar surfaces by MBE with a NH3 nitrogen source (RMBE) [36, 55]. As a rule, the optical properties of the structures without dislocations were much better than for similar structures grown, under the same conditions, on sapphire. The example shown in Fig. 1.32, presents the integrated PL intensities from the same QW structures (8 ML GaN SQW with the Al0.1Ga0.9N 50-nm barriers) grown by RMBE [58] on sapphire and bulk pressure-grown GaN substrates. It is shown that for the structure deposited on GaN, the PL is much stronger, especially at RT. For the structure grown on GaN substrate, the PL intensity starts to decrease with temperature only at about 100 K mainly due to the thermal escape of carriers from the quantum well towards the AlGaN barriers, as was observed for classical III–V QW heterostructures with dislocation densities lower than 103 cm–2 [57]. For the heteroepitaxial structure, the presence of dislocations strongly influences the non-radia-

1.3 Epitaxy on Bulk GaN

tive recombination processes. The PL intensity starts to decrease at much lower temperatures due to nonradiative recombination of excitons at dislocations. For devices on dislocation-free substrates, it is especially important that further increases of emission efficiency are achieved by increasing of the Al content in the barriers. This opens up the possibility for construction of highly efficient UV LEDs and lasers. The semi-insulating GaN : Mg substrates have been used for growth of GaN/ AlGaN heterostructures with a two-dimensional electron gas (2DEG) by RFMBE [56]. The Hall mobility for this 2DEG is as high as 60–100 ·103 cm2 V–1 s–1 at

Fig. 1.32 Temperature dependence of the integrated PL intensity of homoepitaxial (squares) and heteroepitaxial (circles) GaN/Al0.1Ga0.9N QWs [58].

Fig. 1.33 Longitudinal (Rxx) and transverse (Rxy) magnetoresistance versus magnetic field at 1.5 K and 50 mK. Shubnikov de Haas oscillations begin at 1.8 T. The insert shows the low-field part of the SdHO after the normalization by the low-field resistance value, R0.

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1 High-Pressure Crystallization of GaN

1.5 K, one of the highest reported for GaN. The Shubnikov-de-Haas oscillations starting at 1.8 T with well-defined QHE indicates the high quality of the MBEgrown heterostructure (Fig. 1.33). From the analysis of the scattering processes it was suggested that in a nearly dislocation-free structure ionized-impurity scattering was the dominant low-temperature mobility-limiting mechanism. If the substrate is dislocation-free, strain relaxation processes in low-misfit heteroepitaxy is unaffected by the presence of threading dislocations. Both elastic and plastic relaxation have been studied [36] for GaN/AlGaN multilayer structures grown by plasma-assisted MBE on GaN pressure-grown substrates. It was shown that the crystal growth and relaxation in III-nitrides is not that different from conventional III–V systems. Elastic strain relaxation by sinusoidal undulation of the AlGaN layers has been observed, above a critical thickness. This critical thickness depends on the Al content. An example of the AlGaN surface morphology with the sinusoidal undulation is shown in Fig. 1.34. Results obtained in [55] indicate new possibilities for obtaining low misfit heteroepitaxial growth that include selforganized formation of quantum-confinement structures.

Fig. 1.34 Surface morphology (AFM – courtesy of R. Campion) of 40-nm Al0.1Ga0.9N layer grown by plasma-assisted MBE on N-polar surface of GaN substrate.

Fig. 1.35 New nitride-dedicated MBE machine, in HPRC.

1.4 Optoelectronic Devices

The results of the MBE deposition of nitride structures on dislocation-free substrates have been an excellent stimulation to continue the research. Figure 1.35 shows the MBE V-100 machine installed recently in HPRC, intended to develop the optimum methods of growing dislocation-free nitrides, especially those based on In-free GaN/AlGaN quantum well structures. This machine is expected to allow a greater degree of control in optimizing the structural and electrical properties of p-type layers on quantum-well structures.

1.4

Optoelectronic Devices 1.4.1

Introduction

HNPSG GaN crystals have been used by Nakamura [59] as substrates for the InGaN MQW-based 405-nm laser. Continuous wave (CW) 30-mW devices with lifetime exceeding 3000 h have been constructed. The 30 mW power has been achieved at a current of 62 mA. For typical InGaN MQW LDs on sapphire [1], at a current of 62 mA, the output power was then (end of 1999) about 15 mW and their lifetime did not exceed 300 h. This increase in efficiency and lifetime confirmed that dislocations are the main limiting factors for high-power GaN-based lasers. This result may have finally proved that the use of our substrates provides a chance to increase the power of GaN-based laser diodes (LDs). 1.4.2

Light Emitting Diodes Fabricated on Bulk GaN in HPRC

Based on the MOVPE growth technique described in Sect. 1.3.2, we have fabricated a number of light emitting diodes (LEDs). An example of such a diode, obtained in HPRC, is presented in Fig. 1.36.

Fig. 1.36 Unipress blue LED grown on GaN substrate by MOVPE technique.

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1 High-Pressure Crystallization of GaN

a I-V dependence of our “blue” LED in comparison with a commercial Nichia device; b electroluminescence spectrum of homoepitaxial LED.

Fig. 1.37

The typical structure of these devices was the following: first a 2 lm GaN : Si (n = 5 ´ 1018 cm–3) buffer was deposited on the Ga-face of a GaN crystal, followed by 10 ´ multiquantum well (MQW) In0.11Ga0.89N/GaN (35 Å/80 Å). The structure was completed by growing 0.2-lm thick GaN : Mg (hole concentration p = 3 ´ 1017 cm–3). A semitransparent (100 Å/50 Å) Ni/Au contact was deposited on the top of the structure using an e-gun evaporator and annealed in oxygen at 450 8C. Tested devices have dimensions of 300 ´ 300 lm. Figure 1.37 a and b show electrical and optical properties of these diodes. It is clearly seen in Fig. 1.37 a that the I–V characteristics of our homoepitaxial diode are quite similar to commercially available LEDS produced by Nichia Chemicals. The diodes have a series resistance of about 7–15 X, very similar to those above-mentioned Nichia devices. However, one should remember that in the case of thin semitransparent contacts the device series resistance may be seriously influenced by in-plane current spreading. Our metal contacts are characterized by a contact resistance of 2– 5 ´ 10–3 X cm2. 1.4.3

Laser Diode Structures

The HPRC “blue” laser diode design follows that of the classical separate-confinement heterostructure (SCH) laser. Figure 1.38 shows the details of the structure. The active layer is formed by In0.1Ga0.9N/GaN (30 Å/80 Å) 5–10 ´ multiquantum well. It is worth noting here that the laser structure is fully strained with no additional dislocations generated. For optical pumping tests, the structures were cleaved to form 500-lm long cavities (Fig. 1.39 a). For electrical testing, Ni/Au metal contacts were deposited in the form of stripes having a width of 10 lm. In GaN lasers the most severe problem is the low coefficient of optical reflection. The coefficient can be increased by deposition of a dielectric layer such as SiO2/ ZrO2, on the facets (Fig. 1.39 b). As a result, the coefficient has been increased to 50%. This allowed a decrease in the optical injection threshold by a factor of two. In the last two years, we have successfully demonstrated that homoepitaxially

1.4 Optoelectronic Devices Fig. 1.38 Design of our “blue” light emitting laser diode structure.

(a)

(b)

Fig. 1.39 a laser resonators obtained by cleaving of GaN substrates with the depos-

ited MQW structures; b influence of SiO2/ZrO2 mirror coatings on the laser performance.

grown GaN epilayers show narrow stimulated emission lines (under optical pumping conditions) at relatively low threshold power densities [60]. The optical pumping of the laser structures described above demonstrated that they are characterized by a low optical excitation threshold of about 200 kW cm–2. The optical emission spectra of HPRC laser are shown in Fig. 1.40. Recently, a current-injection laser diode, which utilizes a bulk GaN substrate, has been constructed at HPRC. The GaN substrate crystal was grown by the

37

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1 High-Pressure Crystallization of GaN

Fig. 1.40 Emission spectra below and above laser threshold. Spectra measured at room

temperature under optical excitation from the third harmonic of a YAG laser.

Fig. 1.41 The emission spectra below lasing threshold, measured at T = –40 8C. Operating currents are indicated in the legend. Biasing parameters are as specified in the text.

HNPSG method, described in Sect. 1.2. The laser structure was deposited on the conducting substrate by MOCVD techniques, presented in Sect. 1.3.2. The laser diode is a separate-confinement heterostructure device. The active layer of the laser is In0.09Ga0.91N/In0.01Ga0.99N 5 repetition multiquantum well. The active layer is stacked between two 0.1-lm GaN : Si and GaN : Mg waveguiding layers. The n-type cladding is 120 repetition 25 Å/25 Å GaN/Al0.15Ga0.85N silicon-doped superlattice. P-type cladding is formed by a Mg-doped 0.36-lm thick Al0.08Ga0.92N layer. The structure was capped by a 0.1-lm highly Mg-doped GaN contact layer. The device was processed as a narrow stripe, oxide isolated laser. The stripe width is 10 lm. The laser diode was operated under pulsed current conditions with a pulse width of 200 ns at a frequency of 1 kHz. The diode was tested at temperatures between –40 8C and –10 8C. Figure 1.41 shows the emission spectra below the threshold current while Fig. 1.42 demonstrates the lasing spectrum just above the threshold. The dominant emission wavelength is 425 nm. Typically, two to four distinctive modes were observed. Figure 1.43 shows the optical emission for an increasing current. Output power in a pulse reached almost 8 mW at 2 A. The measurement

1.4 Optoelectronic Devices Fig. 1.42 The emission spectrum of the laser diode above threshold, measured at T = –40 8C. The diode is run at a current of 1.5 A. Biasing parameters are as specified in the text.

Fig. 1.43

Output power (in pulse) as a function of the device current (at T = –40 8C).

was made at a nominal temperature T = –40 8C. The sharp decrease of efficiency in the high current region can be associated with device heating and the higher temperature of the device. The increase of the optical output of the device as a function of the current is presented in more detail in Fig. 1.44. In the upper part the camera presents an eye-view perspective of the device both below and above the threshold. In the bottom row the optical power measured in the pulse is shown. The laser diode is the first laser diode realized on a true bulk GaN substrate in HPRC and we are the 8th institution worldwide to demonstrate the current-injection laser based on GaN [2]. We believe that this achievement opens a path to fast development of dislocation-free, high-power laser diodes operating in the blue and UV spectral ranges.

39

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1 High-Pressure Crystallization of GaN

Fig. 1.44 Optical emission of the laser diode for increasing electric current: top – camera-

view; bottom – output power (in pulse). The measurement was made at –40 8C.

1.5

Conclusions

The results presented in this review summarize the long-term research program based on application of various physical methods in the physics and technology of group III metal nitride semiconductors. The most essential results, obtained at the High Pressure Research Center, can be divided into the following points: – the thermodynamic properties of group III metal systems in pressures up to 20 kbar and temperatures up to 2000 K have been determined; – the kinetic properties of the adsorption and dissolution reaction of molecular nitrogen in liquid group III metals have been modeled satisfactorily; – crystal growth of substrate-quality GaN crystals has been investigated. The research led to the development of the technology for the growth of substratequality n-type GaN crystals for optoelectronics; – the two basic epitaxy methods MOVPE and MBE were developed and applied for the deposition of high-quality homoepitaxial layers and quantum-well structures; – the application of homoepitaxy allowed us to obtain high-quality layers as a result of atomic step-flow growth. The electric and optical properties of the layer are far superior to those obtained on sapphire and silicon carbide substrates; – the development of the QW structures and processing technology allowed us to obtain blue LEDs of an efficiency comparable with the best heteroepitaxial devices. Recently, LDs have also been grown successfully; – the development of dislocation-free nitride layers and structures allows the limitations arising from indium-related carrier localization, used in standard LED and low-power blue LD devices to be avoided. This opens up the possibility of the construction of high-power LDs and UV LEDs.

1.7 References

1.6

Acknowledgment

All research that led to the development of this device has been performed within Poland’s Governmental Strategic Program: “Development of Blue Optoelectronics” (established by KBN and the Ministry of Economics) project no. 8 T11 G 001 2000 C/5013 and supported by EU Project “Center of Excellence” no. ICA1-CT2000-70005. We would like to gratefully acknowledge the collaborating institutions in Poland: Institute of Electronic Materials Technology, Electrical Measuring Instrument Works – LUMEL S.A., Institute of Electron Technology, Institute of Physics of Polish Academy of Sciences; Institute of Optoelectronics of Military Academy of Technology; Institute of Experimental Physics of Warsaw University, Institute of Vacuum Technology; Institute of Microsystems Technology of Wroclaw University of Technology and many foreign laboratories who helped us in both scientific and technological aspects of this project. The calculations were made using the computing facilities of the Interdisciplinary Center for Mathematical and Computational Modeling (ICM) of Warsaw University.

1.7

References 1 2 3 4 5 6 7

8 9 10

11

S. Nakamura and G. Fasol, The Blue Laser Diode (Springer-Verlag Berlin, 1997). S. Porowski and I. Grzegory, J. Cryst. Growth 178, 174 (1997). G. A. Slack and T. F. McNelly, J. Cryst. Growth 34, 263 (1976). J. A. Van Vechten, Phys. Rev. B 7, 1479 (1973). J. Karpinski, J. Jun, and S. Porowski, J. Cryst. Growth 66, 1 (1984). J. Karpinski and S. Porowski, J. Cryst. Growth 66, 11 (1984). J. B. MacChesney, P. M. Bridenbaugh, and P. B. O’Connor, Mater. Res. Bull. 5, 783 (1970). I. Grzegory, PhD Thesis, Inst. Physics PAS Warsaw, 1995 (in Polish). C. D. Thurmond and R. A. Logan, J. Electrochem. Soc. 119, 622 (1972). R. Madar, G. Jacob, J. Hallais, and R. Fruchard, J. Cryst. Growth 31, 197 (1975). W. P. Glushko (ed.) Termodinamiczeskije swojstwa indiwidualnych weszczestw, (Nauka, Moscow, 1979) (in Russian).

12

13 14

15

16

17 18

19 20

W. E. Zinowiev, Teplofiziczeskije swojstwa metallow pri wysokich temperaturach (Metallurgia Moscow 1989) (in Russian). B. Delley, J. Chem. Phys. 92, 508 (1990). Z. Romanowski, S. Krukowski, I. Grzegory, and S. Porowski, J. Chem. Phys. 114, 6353 (1990). Z. Romanowski, S. Krukowski, I. Grzegory, and S. Porowski, J. Cryst. Growth 189/190, 159 (1998). W. K. Burton, N. Cabrera, and F. C. Frank, Phil. Trans. Roy. Soc. London A 243, 299 (1951). J. D. Weeks and G. H. Gilmer, Adv. Chem. Phys. 40, 157 (1979). T. Suski, E. Litwin-Staszewska, P. Perlin, P. Winiewski, H. Teisseyre, I. Grzegory, M. Bockowski, S. Porowski, K. Saarinen, and J. Nissila, J. Cryst. Growth 230, 368 (2001). J. Neugebauer and C. G. Van de Walle, Phys. Rev. B 50, 8067 (1994). P. Boguslawski, E. L. Briggs, and J. Bernholc, Phys. Rev. B 51, 17255 (1995).

41

42

1 High-Pressure Crystallization of GaN 21

22

23

24

25 26

27

28

29

30

31

32

33

Z. Liliental-Weber, EMIS Datareview Series No. 23 (INSPEC, The Institution of Electrical Engineers, London, 1999) p. 230. J. L. Rouviere, J. L. Weyher, M. Seelmann-Eggebert, and S. Porowski, Appl. Phys. Lett. 73, 668 (1998). M. Seelmann-Eggebert, J. L. Weyher, H. Obloh, H. Zimmermann, A. Rar, and S. Porowski, J. Cryst. Growth 210, 151 (2000). W. A. Tiller, K. A. Jackson, J. W. Rutter, and B. Chalmers, Acta Met. 1, 428 (1953). W. A. Tiller, J. Cryst. Growth 2, 345 (1968). J. L. Weyher, S. Müller, I. Grzegory, and S. Porowski, J. Cryst. Growth 182, 17 (1997) S. Krukowski, M. Bockowski, B. Lucznik, I. Grzegory, S. Porowski, T. Suski, and Z. Romanowski, J. Phys. Condens. Matter 13, 8881 (2001). P. Perlin, J. Camassel, W. Knap, T. Talercio, J. C. Chervin, T. Suski, I. Grzegory, and S. Porowski, Appl. Phys. Lett. 67, 2524 (1995). E. Litwin-Staszewska, T. Suski, R. Piotrzkowski, I. Grzegory, M. Bockowski, J. L. Robert, L. Konczewicz, D. Wasik, E. Kaminska, D. Cote, and B. Clerjaud, J. Appl. Phys. 89, 7960 (2001). K. Saarinen, T. Laine, S. Kuisma, P. ´ ski, J. M. BaraHautojarvi, L. Dobrzyn nowski, K. Pakuła, R. Ste˛pniewski, M. Wojdak, A. Wysmołek, T. Suski, M. ´ ski, I. Grzegory, and S. PoLeszczyn rowski, Phys. Rev. Lett. 79, 3030 (1997). S. Porowski, M. Bockowski, B. Lucznik, I. Grzegory, M. Wroblewski, H. Teisseyre, M. Leszczynski, E. LitwinStaszewska, T. Suski, P. Trautman, K. Pakula, and J. M. Baranowski, Acta Phys. Pol. A 92, 958 (1997). P. Perlin, J. Camassel, W. Knap, T. Taliercio, J. C. Chervin, T. Suski, I. Grzegory, and S. Porowski, Appl. Phys. Lett. 67, 2524 (1995). E. Frayssinet, W. Knap, S. Krukowski, P. Perlin, P. Wisniewski, T. Suski, I. Grzegory, and S. Porowski, J. Cryst. Growth 230, 442 (2001).

34

35

36

37

38

39 40 41

42 43

44

45

46

T. Suski, J. Jun, M. Leszczynski, H. Teisseyre, I. Grzegory, S. Porowski, G. Dollinger, K. Saarinen, T. Laine, J. Nissila, W. Burkhard, W. Kriegseis, and B. K. Meyer, Mater. Sci. Eng. B 59, 1 (1998). M. Leszczynski, I. Grzegory, H. Teisseyre, T. Suski, M. Bockowski, J. Jun, J. M. Baranowski, S. Porowski, and J. Domagala, J. Cryst. Growth 169, 235 (1996). S. H. Christiansen, M. Albrecht, H. P. Strunk, C. T. Foxon, D. Korakakis, I. Grzegory, and S. Porowski, Phys. Stat. Sol. (a) 176, 285 (1999). Z. Liliental-Weber, M. Benamara, W. Swider, J. Washburn, I. Grzegory, S. Porowski, R. D. Dupuis, and C. J. Eiting, Physica B 273/274, 124 (1999). J. L. Weyher, P. D. Brown, J. L. Rouviere, T. Wosinski, A. R. A. Zauner, and I. Grzegory, J. Cryst. Growth 210, 151 (2000). M. Leszczynski, P. Prystawko, and G. Nowak, private communication. M. Leszczynski and P. Prystawko, private communication. T. Deguchi, T. Azuhata, T. Sota, S. Chichibu, and S. Nakamura, Mater. Sci. Eng. B 50 251 (1997). S. Nakamura, IEICE Trans. Electron. E83-C, 529 (2000). K. Pakula, A. Wysmolek, K. P. Korona, J. M. Baranowski, R. Stepniewski, I. Grzegory, M. Bockowski, J. Jun, S. Krukowski, M. Wroblewski, and S. Porowski, Solid State Commun. 97, 919 (1996). M. Leszczynski, P. Prystawko, A. Sliwinski, T. Suski, E. Litwin-Staszewska, S. Porowski, R. Paszkiewicz, M. Tlaczala, B. Beaumont, P. Gibart, A. Barski, R. Langer, W. Knap, E. Frayssinet, and P. Wisniewski, Acta Phys. Pol. 94, 437 (1998). M. Kamp, C. Kirchner, V. Schwegler, A. Pelzmann, K. J. Ebeling, M. Leszczynski, I. Grzegory, T. Suski, and S. Porowski, MRS Internet J. Nitride Semicon. Res. 4S1, G10, 2 (1999). M. Leszczynski, B. Beaumont, E. Frayssinet, W. Knap, P. Prystawko, T. Suski,

1.7 References

47

48

49

50

51

52

53

I. Grzegory, and S. Porowski, Appl. Phys. Lett. 75, 222 (1999). P. Prystawko, M. Leszczynski, B. Beaumont, P. Gibart, E. Frayssinet, W. Knap, P. Wisniewski, M. Bockowski, T. Suski, and S. Porowski, Phys. Stat. Sol. (b) 210, 437 (1998). M. Leszczynski, H. Teisseyre, T. Suski, I. Grzegory, M. Bockowski, J. Jun, S. Porowski, K. Pakula, J. M. Baranowski, C. T. Foxon, and T. S. Cheng, Appl. Phys. Lett. 69, 73 (1996). A. Wysmolek, M. Potemski, R. Stepniewski, J. Lusakowski, K. Pakula, J. M. Baranowski, G. Martinez, P. Wyder, I. Grzegory, and S. Porowski, Phys. Stat. Sol. (b) 216, 11 (1999). C. Kirchner, V. Schwegler, F. Eberhard, M. Kamp, K. J. Ebeling, K. Kornitzer, T. Ebner, K. Thonke, R. Sauer, P. Prystawko, M. Leszczynski, I. Grzegory, and S. Porowski, Appl. Phys. Lett. 75, 1098 (1999). A. R. A. Zauner, J. L. Weyher, M. Plomb, V. Kirilyuk, I. Grzegory, W. J. P. van Enckevort, J. J. Schermer, P. R. Hageman, and P. K. Larsen, J. Cryst. Growth 210, 435 (2000). S. Jursenas, N. Kurilcik, G. Kurilcik, A. Zukauskas, P. Prystawko, M. Leszczynski, T. Suski, P. Perlin, I. Grzegory, and S. Porowski, Appl. Phys. Lett. 78, 3776 (2001). J. Chr. Holst, A. Hoffman, M. Leszczynski, and S. Porowski, private communication.

54

55

56

57

58

59 60

M. Leszczynski, P. Prystawko, R. Czernecki, J. Lehnert, T. Suski, P. Perlin, P. Wisniewski, I. Grzegory, G. Nowak, S. Porowski, and M. Albrecht, J. Cryst. Growth 231, 352 (2001). C. T. Foxon, C. S. Davis, S. V. Novikov, O. H. Hughes, T. S. Cheng, D. Korakakis, N. F. Jeffs, I. Grzegory, and S. Porowski, Phys. Stat. Sol. (a) 176, 723 (1999). E. Frayssinet, W. Knap, P. Lorenzini, N. Grandjean, J. Massies, C. Skierbiszewski, T. Suski, I. Grzegory, S. Porowski, G. Simin, X. Hu, M. A. Khan, M. S. Shur, R. Gaska, and D. Maude, Appl. Phys. Lett. 77, 2551 (2000). J. D. Lambkin, D. J. Dunstan, K. P. Homewood, L. K. Howard, and M. T. Emeny, Appl. Phys. Lett. 57, 1986 (1990). N. Grandjean, B. Damilano, J. Massies, G. Neu, H. Teisseyre, I. Grzegory, S. Porowski, M. Gallart, P. Lefebvre, B. Gil, and M. Albrecht, J. Appl. Phys. 88, 183 (2000). S. Nakamura, private communication. I. Grzegory, M. Bockowski, S. Krukowski, B. Lucznik, M. Wroblewski, J. L. Weyher, M. Leszczynski, P. Prystawko, R. Czernecki, J. Lehnert, G. Nowak, P. Perlin, H. Teisseyre, W. Purgal, W. Krupczynski, T. Suski, L. Dmowski, E. Litwin-Staszewska, C. Skierbiszewski, S. Lepkowski, and S. Porowski, Acta Phys. Pol. A Suppl. 100, 229 (2001).

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2

Epitaxial Lateral Overgrowth of GaN Pierre Gibart, Bernard Beaumont, and Philippe Vennéguès

Abstract

Since there is no GaN bulk single crystal commercially available, the whole technological development of GaN-based devices relies on heteroepitaxy. Most of the current device structures are grown on sapphire or 6H-SiC. However, since their lattice parameters and thermal expansion coefficients are not well matched to GaN, the epitaxial growth generates huge densities of dislocations (109 to 1011 cm–2). Using appropriate nucleation layers allows a reducing of the dislocation density into the low 108 cm–2 ranges. Laser diodes have been demonstrated in the late 1990s with such defective layers. The real breakthrough in the laser technology has been the dramatic improvement of the laser diode lifetime at the end of 1997, with the lifetime reaching 10,000 h. This has been made possible with the implementation of the epitaxial lateral overgrowth technology (ELO), which significantly reduces the dislocations density. Numerous defects are generated in the heteroepitaxy of GaN, with threading dislocations (TDs) being the most prevalent. A novel method of reducing the defect density has been the epitaxial lateral overgrowth (ELO) technology, where parts of the highly dislocated starting GaN are masked with a dielectric mask, after which growth is restarted. At the beginning of the second step, deposition only occurs within the openings while no deposition is observed on the mask. This is referred to as selective area epitaxy (SAE). The TDs are prevented from propagating into the overlayer by the dielectric mask, whereas GaN grown above the opening (coherent growth) keeps the same TDs density as the template, at least during the early stages of the

46

2 Epitaxial Lateral Overgrowth of GaN

growth. The ELO technique is achievable in metal organic vapor phase epitaxy (MOVPE), halide vapor phase epitaxy (HVPE) and even in sublimation growth. Currently, two main ELO technologies exist: the simpler one involves a single growth step on the striped opening. In this one-step-ELO (1S-ELO), growth in the opening remains in registry with the GaN template underneath (coherent part), whereas GaN over the mask extends laterally (wings). This leads to two grades, namely highly dislocated GaN above the openings, and low dislocation density GaN above the masks. With this technique, devices have to be fabricated on the wings. Therefore, conversely, in the two-step-ELO (2S-ELO) process, the growth conditions of the first step are monitored to obtain triangular stripes. Inside these stripes, the threading dislocations arising from the templates are bent by 908 when they encounter the inclined lateral facet. In the second step, the growth conditions are modified to achieve full coalescence. In this two-step ELO, only the coalescence boundaries are defective. In-depth characterization of these ELO GaN layers reveals that the intermediate stages of the process induce inhomogeneous impurity incorporation and stress distribution. However, the ELO technology produces high-quality GaN, with TDs densities in the mid 106 cm–2, linewidths of the low-temperature photoluminescence (PL) near band gap recombination peaks below 1 meV, and deep electron traps concentration below 1014 cm–3 (compared to mid 1015 cm–3 in standard GaN). Numerous modifications of the ELO process have been proposed in order either to avoid technological steps (mask less ELO) or to improve it (pendeo-epitaxy). Basically developed on either sapphire or 6HSiC, the ELO technology is also achievable on (111)Si or (111)3C-SiC/Si provided that an appropriate buffer layer is grown to avoid cracks. To further reduce the TDs density, multiple steps of ELO have also been implemented. Self-supported GaN with at least ELO quality at an affordable cost is believed to be the next breakthrough in the GaN technology. Unfortunately, an in-depth understanding of the basic ELO process is still missing, i.e., the growth anisotropy and the bending of dislocations. First-principle calculations on the ELO process are also urgently needed.

2.1

Heteroepitaxial GaN 2.1.1

Introduction

The III–V compound semiconductor family have proven high performance in high-speed electronics, optical emitters, i.e., laser diodes, (LDs), light emitting diodes, (LEDs) and detectors. However, for efficient operation, high crystalline quality is required. Growth technologies for large-scale substrates are currently greatly advanced for Si and to a lesser extent for GaAs, even less so for InP and other III–V substrates. For GaN, bulk crystals are not readily available. Bulk GaN is intrinsically very difficult to grow because of the high vapor pressure of nitro-

2.1 Heteroepitaxial GaN

gen at the melting point of GaN. GaN single crystals (about 1 cm2) are, however, produced by high-temperature-high-pressure growth, mainly at UNIPRESS (Poland). Even though these crystals are very valuable for basic physics and demonstration of ultimate performance of devices, their size and potential production volume do not by far meet the industrial needs. Other methods such as growth in molten metals are currently under development and have thus far produced small high-quality crystals. Gallium nitride is a very interesting III–V semiconductor, having a band gap ideal for blue LDs and LEDs. The binary and ternary alloys in the systems (Al,Ga,In)N allow band-gap engineering over the entire visible spectrum. In addition, GaN and other III–V nitride semiconductor alloys are most promising for high-power, high-temperature electronic devices. Major developments in wide-gap III–V nitride semiconductors have recently led to the commercial production of high-brightness LEDs and to the demonstration of room-temperature violet laser light emission in InGaN-MQWs-based heterostructures under continuous-wave (cw) operation. Violet laser diodes (LDs) with an output power of 5 mW have already been commercialized. GaN is currently grown in the form of epitaxial layers mainly by MOVPE, HVPE, and MBE. In most cases, single-crystal sapphire (Al2O3) wafers are used as substrates. Although 6H-SiC is a promising substrate material with its 3.5% misfit, these wafers are still too expensive. Potentially more appropriate substrates like LiAlO2, MgAl2O4, ScMgAlO4, ZnO, and Hf have been tested in several laboratories. Even though good-quality GaN epilayers were obtained (although not significantly better than GaN/sapphire), the use of such materials does not solve the problem of the lack of GaN substrates. Therefore, for the time being, GaN layers have to be grown by heteroepitaxy. This usually requires several steps including the nitridation of the sapphire substrate, the deposition of a low-temperature buffer layer and the heat treatment of this nucleation layer. These processes are widely documented and seem to vary greatly between laboratories. The lattice parameters and the thermal expansion coefficients of sapphire and SiC are not well matched to GaN. The epitaxial growth therefore generates huge densities of dislocations (109 to 1011 cm–2). These dislocations propagate up to the surface, degrading the performance of optical and electronic devices. Using appropriate nucleation layers reduces the dislocations density into the mid-108 cm–2 range. Increasing the thickness of GaN epilayers does not result in a significant decrease of the dislocation density. LDs were demonstrated in the late 1990s with such defective layers. The real breakthrough in the laser technology has been, however, the dramatic improvement of the laser diode lifetime at the end of 1997 [1] with lifetimes reached up to 10,000 h. This has been made possible with the implementation of the epitaxial lateral overgrowth (ELO) technology, which significantly reduces the dislocations density. Consequently, laser diodes structures are currently grown on this new generation of substrates. Improved device performances were also obtained with the ELO technology in other devices, like LEDs and UV photodetectors. However, this technique is not new. Growth anisotropies in HVPE were already reported in the mid-1960s [2]. Lateral overgrowth has been implemented to reduce

47

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2 Epitaxial Lateral Overgrowth of GaN

defects in several epitaxial systems, mainly GaAs/Si. The enhanced lateral growth rate in the HVPE of GaAs has been used to produce reusable substrates [3]. The ELO process was also used in Si technology [4]. 2.1.2

Growth of GaN/Sapphire and 6H-SiC Templates

Since no GaN substrate is currently available, GaN layers will for the time being have to be grown by heteroepitaxy [5]. Using sapphire as a substrate requires several processing steps including the nitridation of the sapphire (0001), the deposition of a low-temperature buffer layer (AlN or GaN), followed by heat treatment of the nucleation layer and growth at a high temperature (1000–1100 8C) [6–9]. In highly mismatched systems, like GaN/sapphire, the heteroepitaxial growth requires the deposition of a low-temperature nucleation layer (NL). Indeed, there are several approaches to obtain this NL, with the techniques basically employing either a 2D or 3D growth. When using 6H-SiC as a substrate, a low-temperature NL is not required, however, GaN cannot be directly grown on 6H-SiC. Therefore, a AlN or AlGaN buffer layer must be epitaxially grown on SiC prior to the deposition of GaN. For the ELO technologies, it is important to get templates with the lowest achievable densities of TDs.

2.1.2.1 2D Growth Mode (GaN/Sapphire)

Several authors have described the formation of the microstructure of GaN films directly grown on sapphire [10, 11]. The AlN or GaN buffer layer provides a high density of nuclei, completely covering the substrate for low growth temperatures due to the low surface diffusivity. Afterwards, this NL is heated to the growth temperature. These processes are widely documented and seem to vary significantly between laboratories. The electrical and optical properties of the subsequent layers depend strongly on the conditions under which the nucleation layer was achieved. In the case of the GaN buffer layer, the layer deposited at 500–600 8C is composed of highly c-oriented grains where the metastable cubic GaN and the stable hexagonal GaN coexist. The growth mode is basically 2D in nature. Cross-sectional high-resolution transmission electron microscopy (HRTEM) investigations [12] have shown that the microstructure of the NL is composed of grains having a columnar shape with a width of about 20 nm. Cubic grains dominate and contain less basal stacking faults than hexagonal ones. This indicates that, at this temperature, the cubic structure is the most stable one. The epitaxial relationships are: ‰0001ŠSapphire ==‰111ŠGaN cubic

and

‰0001ŠSapphire ==‰0001ŠGaN hexagonal

‰1010ŠSapphire ==‰110ŠGaN cubic and

or

‰1010ŠSapphire ==‰1120ŠGaN hexagonal

2.1 Heteroepitaxial GaN

Finally, the NL is heated rapidly to the growth temperature. During this stage, the microstructure of the buffer layer changes drastically. It now consists of a film of constant thickness (about 30 nm) with islands on its top surface. A phase transformation from cubic to hexagonal was recently reported [13], but it is also worth mentioning that, even after annealing, the NL entirely covers the sapphire surface. The final growth occurs between 1050 and 1080 8C. In the GaN/sapphire obtained following this process, the misorientation of grains from the epitaxial relationships can reach 0.2–0.58. Room-temperature Hall measurements show that the lowest electron concentration in undoped GaN layers is 5 ´ 1016 cm–3, but the corresponding electron mobility does not exceed 300 cm2 V–1 s–1. From TEM plan-view observations, a dislocation density in the GaN epilayers within the 1010 cm–2 range was measured. The symmetric (0002) diffraction peak deduced from X-ray rocking curves (x-scan) presents a full width at half-maximum (FWHM) typically in the 350–550 arcsec range. The low-temperature photoluminescence (PL) spectrum is dominated by band-edge excitonic transitions: neutral donor bound excitons (I2) and free excitons A. The linewidth of the bound exciton line is about 4 meV. At lower energy, two longitudinal optical (LO) phonon replica of the free A exciton appear at 3.386 and 3.295 eV. At low energies (*3.27 eV), the band related to donor-acceptor recombination is nearly absent due to the low concentration of residual acceptors. Finally, at 2.2 eV, a wide band, which is usually called the “yellow band”, the origin of which is still controversial, appears.

2.1.2.2 3D Growth Mode (GaN/Sapphire)

By using essentially the epitaxial overgrowth principle (see Sect. 2.2), i.e., involving localized but maskless growth, a new growth process, referred to as the “3D growth process”, has been implemented to obtain better quality GaN materials. Silicon has been reported to act as a “surfactant”, i.e., it plays an important role in changing the growth mode from 2D to 3D [14–16]. Using this surfactant effect of silicon, GaN quantum dots on AlxGa1–xN surfaces have been realized by MBE and MOVPE. The exposure of the sapphire substrate prior to the deposition of a GaN NL under simultaneous silane and ammonia flows fundamentally influences the quality of GaN epilayers grown by MOVPE. This step of the growth process will be referred to as “Si/N treatment” [17]. During the annealing up to 1080 8C, this process induces a dramatic morphological change of the GaN NL from a flat layer fully capping the substrate; to a high density of 3D GaN islands (200–400 nm large and 100–200 nm high) surrounded by the bare sapphire substrate (see Fig. 2.1). It has been observed that two parameters are of critical importance to induce the 3D growth process: (1) the composition of the carrier gas (N2 or N2+H2) and (2) the duration of the Si/N treatment [16]. The GaN island formation is achievable only when H2 is present in the carrier gas. H2 seems to act as a “morphactant” as Eagleasham et al. [18] called impurities, which favored particular equilibrium shapes of islands. Recent studies [19] have also reported that the appearance of islands is strongly related to the H2 concentration in the reactor chamber.

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2 Epitaxial Lateral Overgrowth of GaN SEM micrograph of an as-grown GaN nucleation layer at 600 8C, and after subsequently annealing at 1080 8C.

Fig. 2.1

The heat treatment and the high-temperature growth are carried out as for the 2D NL. This Si/N treatment at the early stage of the growth has been implemented by other groups and lead to TDs in the low 108 cm–2 [20, 21]. The densities of defects of material grown with a 3D mode were recently reduced to the mid-107 cm–2 range, as measured by atomic force microscopy [22]. The FWHM of X-ray rocking curves lies in the 180–360 arcsec range. Hall electron mobility in the range 500–700 cm2 V–1s–1 (300 K), with background carrier concentration in the low 1016 cm–3, was obtained for GaN films grown with an adequate Si/N treatment time. When measuring the PL intensity of 3D GaN layers, an increase in the intensity by a factor of about 20 is observed as compared to the 2D-growth mode. This gain in radiative efficiency is well correlated to the decrease by a factor of about 50 of the dislocation density, thus confirming the nonradiative recombination nature of some of the dislocations in GaN [23, 24]. However, high-temperature island coalescence results in a tensile stress at the growth temperature. When cooling, the thermal lattice mismatch between GaN and sapphire overcompensates the intrinsic stress thus producing a residual compressive stress, which is greater than from GaN grown from a 2D NL [25]. Obviously, other approaches have also proven to be efficient in the growth of high-quality templates producing TDs densities in the low 108 cm–2 range. Most of these methods promote a lateral growth mode similar the Si/N treatment. Details can be found in the original papers. In short, these technologies may be summarized as follows: – Low-temperature interlayers. The insertion of a low-temperature GaN or AlN interlayer between high-temperature-grown GaN reduces the TDs densities down to the low 108 cm–2 range [26–28]. TEM observations showed a significant reduction of dislocations with a screw component [29] and were found to terminate at the interlayer [25, 27]. Similar features were observed in GaN growth using dimethylhydrazine as nitrogen precursor [30, 31]. According to the authors, the mechanisms of reduction of dislocations would be similar to those in the ELO technology:

2.1 Heteroepitaxial GaN

– Optimization of the growth rate of the nucleation layer [32–34]. – Thermal annealing of the GaN buffer layer of appropriate thickness [35–38]. – Slight misorientation of the sapphire substrate. It was found that a slight misorientation of the sapphire by about 0.178 significantly improves the surface morphology [39]. – Composition of the carrier gas. Optimizing the V/III ratio during the nucleation phase was found to be relevant for the achievement of mid-108 cm–2 dislocation density [40]. An appropriate combination of H2 and N2 carrier gases was found to reduce the residual strain and to improve the quality of GaN [41]. – Indium doping. Indium is known to act as a surfactant in the growth of GaN. Even though In is not incorporated into the GaN lattice at the typical growth temperatures of GaN, In in the vapor phase decreases the TDs density, narrows the PL linewidth, and increases the free exciton recombination lifetime and strain relief [42–44]. In addition, the electron trap concentration was reported to be reduced [45]. In situ annealing at the early stage of growth also improves the crystalline quality [46]. – High-pressure growth. The crystal quality of GaN has been significantly improved, as evidenced by etch pitch density (EPD) evaluation, when growing GaN at high pressures (up to 1.6 atm) [47]. – Three steps. A three-step approach involving an AlN layer grown by atomic layer epitaxy (ALE) and the standard two-step growth leads to high-quality templates with TDs in the low 108 cm–2 range [48]. Whatever the growth technology though, the TD density of GaN template is never better than in the mid107 cm–2 range. In MBE, the insertion of multistacked AlN/GaN quantum dots decreases the TDs density by several orders of magnitude. The basic mechanism involved is believed to be the termination of TDs in the quantum dots [49]. 2.1.3

Defects in GaN/Sapphire and GaN/6H-SiC 2.1.3.1 Extended Defects

The microstructure of these layers consists of slightly misoriented (tilted and twisted) columns [50]. The size of GaN columns varies from 1 lm to 5 lm depending on growth conditions, the larger the grains the lower the TDs density. These misoriented layers indeed retain the coarse morphology of the nuclei deposited on the sapphire. The dislocations in the boundaries compensate both tilt (by screw TDs) and twist (by edge TDs) misorientations [51]. Numerous defects are generated in the heteroepitaxy of GaN on sapphire, such as threading dislocations (TDs), nanopipes, inversions domains and prismatic planar defects. Atomic structures of extended defects are reviewed in Ref. [52]. Three types of TDs are currently observed: a type, edge (with Burger vector 13 h1120i); c, screw h0001i and mixed a+c (13 h1123i). In heteroepitaxial GaN, whatever the growth method, the typical TDs density ranges between 109 to 1010 cm–2, with roughly an equivalent partition between pure edge and mixed dislocations. Screw dislocations represent

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a very small fraction, 0.1 to 1%. In high-quality GaN, stacking disorder and partial dislocations are located at the interface and originate from the low-temperature nucleation layer. The different types of dislocations are unambiguously characterized using (0002) and {1120} TEM dark field images: a-type dislocations are in contrast in {1120} dark fields and extinguished in (0002) dark field, c-type dislocations are in contrast in (0002) dark field and extinguished in {1120} dark fields whereas a+c-type dislocations are in contrast in both dark fields. With such a high density of threading edge dislocations, it was difficult to believe that high-performance optoelectronic devices could be realized from this type of material. In the early days of GaN device fabrication, researchers even believed that the dislocations were simply electrically inert during a light-emitting process.

2.1.3.2 Native Defects

In addition to these extended defects, epitaxial GaN contains native defects, the nature of which has been widely discussed. Numerous papers and theoretical calculations on the electronic properties of such defects have been published and their review goes beyond the scope of the present report. In short, nonintentionally doped GaN is n-type, several residual donors have been identified: oxygen, silicon, H+, nitrogen vacancy, VN, and interstitial Ga, Gai. Gallium vacancies VGa have been recognized as the main residual acceptor. This VGa was theoretically found to also form complexes with H and O impurities. Deep states have been identified by DLTS. In the early report on HVPE GaN [53], DLTS showed three electron traps, E1, E2, and E3 with activation energies 0.264, 0.580, and 0.665 eV. Later, Hacke [54] found that the same two levels, E1 and E2 appear in concentrations of about 2 ´ 1013 cm–3 in MOVPE samples. Recently, Auret [55] has also reported the presence of two electron traps in nonintentionally doped (NID) GaN with activation energies of 0.27 and 0.61 eV. Other minor traps were also found. A hole trap at 0.81 eV, with a concentration insensitive to the extended defect density and doping level was found in GaN, and possibly ascribed to an isolated Ga vacancy [56]. Unfortunately, the deep states related to extended defects have not yet been identified.

2.1.3.3 Defect-Related Optical Properties

Whatever their nature, extended or point defects may introduce states in the gap. Low-temperature photoluminescence (PL) spectra of standard GaN exhibit several peaks that have been assigned to well-recognized recombinations, free excitons XA, XB, and XC, donor bound excitons, D8X (also labelled I2), acceptor bound excitons, A8X (also labelled I1), and donor-acceptor bands, D8A8 and their LO phonon replica. An additional peak is occasionally observed at 3.41 eV, which is believed to be linked to stacking faults or inversion domains. A broad band centered around 2.2 eV, the so-called yellow luminescence (YL), is also often observed. This YL is currently understood as resulting from a transition between shallow donors and a deep acceptor, the nature of which remains under discussion.

2.1 Heteroepitaxial GaN

Depression at the surface of GaN at the emergence of a TD (from Heying [50]); AFM picture of the surface of a GaN epitaxial

Fig. 2.2

layer. Dark spots correspond to emerging dislocations. The scan length is 5 lm.

When merging at the free surface, the TDs give rise to surface depressions [57]. These depressions are easily identified by atomic force microscopy (AFM), and even assigned to either an edge, mixed or screw TD (Fig. 2.2). Recently, more direct evidence indicates that threading dislocations can be optically and electrically active. In particular, atomic force microscopy (AFM) combined with cathodoluminescence (CL) [58] as well as plan-view transmission electron microscopy (TEM) combined with CL [22] clearly show threading dislocations to be precisely related to dark spots in band-edge emission CL images. This effect could be explained as resulting from the deficiency of minority carriers at threading dislocations. TDs also reduce the photoluminescence intensity. Figure 2.3

Relationship between the PL intensity and EPD, which corresponds to the number of screw and mixed dislocations (from Tojyo et al. [59]).

Fig. 2.3

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from Tojyo et al. [59] displays the PL intensity as a function of the TDs densities with a screw component. Dislocations are negatively charged; this is supported by the effects seen in low transverse mobility measurements [60, 61] near surface electrical properties observed by AFM, scanning capacitance microscopy [62], and selective photoelectrochemical etching [63]. Cathodoluminescence (CL) mapping of the surface of GaN epilayers and ELO GaN will give pertinent details about the TDs distribution (see for instance Fig. 2.28 and Marchand [64]). Scanning reflection electron microscopy (SREM) as demonstrated by Watanabe [65] can also reveal TDs at the GaN surface as well as tilts in the overgrown areas. It would, however, be of great interest to directly link given TDs (edge, mixed or screw) to a given nonradiative center. Using HCl vapor-phase etching, Hino [66] was able to identify three kinds of distinctive etch pits corresponding to the three types of TDs. Comparing the PL intensity to the etch pit density, Hino concluded that TD with a screw component should behave as the dominant nonradiative centers in GaN. Time-resolved PL (TRPL) also provides useful information about the quality of the material. The TRPL lifetime at low temperatures (<10 K for I2) reaches 650 ps for GaN homoepitaxial layers grown on GaN bulk single crystals, whereas it is only 35 to 100 ps in heteroepitaxial layers and 200–300 ps for ELO GaN (limited by deep traps). In the latest very best ELO GaN, a lifetime of 1.3 ns has been reported [67].

2.1.3.4 Device Performance Limitations

The limited effect on GaN high-efficiency light emitting diodes of a surprisingly high density of threading dislocations has led to considerable interest in determining their fundamental properties [68]. Although early work [52, 69, 70] suggested that threading dislocations are radiative combination centers, the improvement in optical properties that has been achieved [71] by reducing the threading dislocation density in the ELO method, provides circumstantial evidence that dislocations do have a deleterious effect. Indeed, the extended defects deteriorate the optical and transport properties of epitaxial GaN [61, 72]. Threading dislocations act as Coulomb scattering centers [61, 73] and their density in standard heteroepitaxy is still too high to obtain GaN-based devices such as laser diodes with commercially compatible lifetimes. It is therefore of critical interest to get a full picture of the electronic properties of these extended defects, to correlate defects (point or extended) to given states in the gap, to establish to what extent they limit device performances, and to implement new approaches in heteroepitaxy in order to decrease their density.

2.1.3.5 Electronic Properties of Defects

Since extended defects have, to some extent, a deleterious effect on the optoelectronic properties of GaN, it is of great interest to theoretically predict their electronic state. Several calculations have been published and sometimes do not lead

2.1 Heteroepitaxial GaN

to converging conclusions. For screw dislocations with full core structure, deep states with energies at 0.9 and 1.6 eV above the valence band have been predicted, and also shallow states around EC–0.2 eV [77]. A recent first-principle total energy calculation showed that a screw dislocation having a Ga-filled core is energetically more favorable than the hollow core structure [74]. This screw dislocation also generates states within the band gap. It has been previously shown that pure edge and mixed dislocations have the same projected core image, which consists of an 8-fold ring [75] (Fig. 2.4). Calculations of the electronic states of pure edge TDs show that they do not introduce deep states in the gap, but possibly shallow levels [76], with the energetically favored structure having a closed core. The formation energies of full core, and different open core TDs were also evaluated for Fermi levels ranging from Ev to Ec [77]. Indeed, the electronic structure of edge dislocations depends upon the structure of the core [78, 79]. The electronic structure of pure edge threading dislocations was studied by atomic resolution Z-contrast imaging and electron energy loss spectroscopy (EELS). EELS showed a significant increase of the first peak of the nitrogen K-edge at the dislocation core compared to the dislocation-free regions, reflecting the reduced C6v symmetry. However, no absorption was seen within the gap [80].

View of the relaxed core of an edge TD as deduced from the Zcontrast imaging technique in transmission electron microscopy (from Xin [76]).

Fig. 2.4

View along [0001] of a domain boundary on {1120} planes.

Fig. 2.5

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In addition to TDs, several kinds of domain boundaries have been observed. As an example, the configuration of a prismatic stacking fault composed of 4- and 8fold rings is displayed (Fig. 2.5). Total-energy calculations for domain boundaries in {1120} planes show that these defects do not introduce deep states in the gap [81, 82]. Conversely, another theoretical evaluation [83] predicts that stacking faults create an electronic level 0.13 eV above the valence band. Yellow luminescence originates from a deep state, 0.8 to 1 eV above the valence band [84]. Several theoretical evaluations have postulated that the deep state responsible for the YL could be a complex, gallium vacancy-oxygen, VGa-O, [85], or nitrogen antisite, NGa [86–88]. As suggested by Elsner [77] the stress field in the core of dislocations could act as a trap for impurities like oxygen or intrinsic defects like VGa and thereby could trap VGa-O complexes. Such a complex gives a deep acceptor state, which may be responsible for the YL.

2.2

Epitaxial Lateral Overgrowth (ELO) 2.2.1

Standard ELO

The most promising way to still further reduce the density of dislocations in GaN layers is the epitaxial lateral overgrowth (ELO) process that has been implemented in both metalorganic vapor phase epitaxy (MOVPE) [89–92] and hydride vapor phase epitaxy (HVPE) [93, 94]. In practice, low reverse-bias leakage current light emitting diodes, long-lifetime bluefish violet LDs, and low dark current AlGaN photodetectors were achieved on ELO GaN substrates. The ELO technique has lately attracted considerable attention, since a blue laser diode grown on an ELO GaN substrate resulted in the achievement of a projected lifetime longer than 10,000 h [1]. The ELO technology relies on specific properties of MOVPE, HVPE, and sublimation growth, i.e., selective epitaxy and growth anisotropy. Review papers on MOVPE-ELO [95, 96] and ELO on (111)Si have been published [97]. 2.2.2

Rationale

Selective epitaxy corresponds to spatially controlled growth of an epitaxial layer through openings in a masking material, which is typically a dielectric such as silicon dioxide or Si nitride. A major problem in selective area epitaxy is the ability to provide real selectivity, with growth only in the openings and no deposition formed on the mask. This can be achieved when the supersaturation of the growth nutrients on the dielectric mask is sufficiently low to prevent any deposition whilst the nucleation barrier on the exposed substrate in the openings is low in comparison. In VPE (MOVPE or HVPE), the suppression of growth on the mask depends on the growth parameters, temperature, pressure, and mole fraction of active species.

2.2 Epitaxial Lateral Overgrowth (ELO) Selective epitaxy of GaN. After the epitaxial growth of GaN and the deposition of a silicon nitride dielectric mask, pinpoint openings are made. Subsequent growth then occurs only within the openings. After filling these openings, lateral growth starts and produces pyramids with {1101} facets [99]. In many papers, this is often referred to selective area epitaxy (SAE). Fig. 2.6

Kato et al. [98] first reported selective epitaxy of GaN/sapphire by MOVPE. Figure 2.6 illustrates the selective epitaxy of GaN. Growth anisotropy corresponds to the occurrence of different growth rates on different crystallographic planes. This has been observed in HVPE for at least two decades. For instance, there are two orders of magnitude difference between the growth rates of the {111}Ga and {111}As surfaces in GaAs. These features are strongly supported by the analysis of the orientational dependence of the growth rate associated with surface kinetics. Growth anisotropy in MOVPE also occurs, but to a limited extent. This was evidenced on growth on preferentially etched or masked GaAs substrates or on GaAs spheres [100]. In MOVPE, growth anisotropy occurs because the diffusing molecular species are preferentially incorporated into different crystallographic sites. This means that although molecules are brought in a MOVPE system to the growing interface with uniform flows, incorporation occurs after kinetically controlled diffusion of adsorbed species on the surface. MOVPE is a process occurring at very high supersaturation and the growth rate is controlled by the diffusion of active species through a boundary layer. The growth rate on substrates with different orientations therefore does not show any significant differences. Consequently, growth anisotropy in MOVPE occurs only when diffusing molecules experience different surface structures within their mean free path ks. The combined effect of selective epitaxy and growth anisotropy is actually used to fabricate quantum structures. After the opening in the dielectric is filled, lateral overgrowth occurs due to growth anisotropy. This lateral overgrowth reflects the growth anisotropy and can produce very unusual features, for instance an AlGaAs/GaAs laser emitting on the six facets of an hexagonal lateral overgrowth layer. Such features are not observed in molecular beam epitaxy (MBE); therefore the ELO technology is not achievable in MBE [101].

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2.2.3

Experimental

The ELO technology can be described as follows: first, a few lm thick GaN layer is grown on sapphire or 6H-SiC. Next, a dielectric (SiO2 or SiN) mask is deposited using well-established technologies like CVD or PECVD. Using standard photolithographic techniques, a set of parallel stripes, separated by window areas, is opened in the mask. During the initial regrowth, either in MOVPE [102] or HVPE [94] or even sublimation growth [103, 104], selective area epitaxy is achieved, which means that the subsequent growth is initiated in the windows without any nucleation on the dielectric mask. Under proper conditions and once the GaN growing film reaches the top of the stripes, epitaxial lateral growth over the mask starts and finally leads to a full coalescence and to a smooth surface suitable for device fabrication. The basic idea (Fig. 2.7) is that this technique may lead to a filtering of the defects: above the windows, the microstructure of the underlying GaN template is reproduced, whereas the laterally grown material (over the mask) is defect-free. The masked areas stop the propagation of threading dislocations that arise from the template, since lateral growth proceeds from TD-free vertical facets.

Schematic representation of ELO; black lines represent dislocations.

Fig. 2.7

SEM image showing the ELO from the hexagonal openings.

Fig. 2.8

2.3 One-Step Lateral Overgrowth (1S-ELO)

2.3

One-Step Lateral Overgrowth (1S-ELO)

In principle, it would be possible to achieve full coalescence of the pyramids shown in Fig. 2.6 after a long growth run. Actually, after 7 h of growth, coalescence was obtained for some part (Fig. 2.8), however, the surface was not smooth enough for any device fabrication [105]. Tiny fluctuations in the gaseous flows enhance the growth of the larger pyramids (Ostwald ripening). Currently, all the ELO technology relies on stripes opening along well-defined crystallographic directions. In the 1S-ELO, a single growth step is achieved on a pattern-masked GaN template. During this growth stage, lateral overgrowth occurs under constant growth conditions. Although the basic mechanisms of ELO in MOVPE, HVPE or sublimation growth involve the same processes, each growth method will be discussed separately. 2.3.1

ELO in MOVPE 2.3.1.1 Morphology and Defects

The lateral overgrowth rates and the equilibrium facets developed in the process depend on both the crystallographic orientation of the stripes openings and the growth parameters, i.e., temperature, V/III ratio in the vapor phase, reactor pressure, composition of the carrier gas (H2, N2), and the fill factor (ratio of the stripe opening to the pattern period) [106–110]. It has been demonstrated that the lateral expansion is easier when the stripes are aligned along a h1100iGaN direction [89]. With this alignment, the morphology gradually changes from triangular stripes to rectangular cross section with a (0001) top facet and {1120} sidewalls as the growth temperature increases [107]. Conversely, for stripes along the h1120i direction, the lateral overgrowth is limited by a slow growth rate along the {1101} facets, which are the most stable facets in GaN. The lateral growth rate along the h1100i stripe is much faster than that along h1120i [90, 101, 106]. In a systematic study, Hiramatsu [110] investigated the morphology of ELO GaN starting from either h1120i or h1100i stripes as a function of the growth pressure (p) and temperature (T) used. For h1120i openings, triangular stripes with {1101} facets are formed independent of the temperature and the pressure. Conversely, for h1100i stripes, the final shape depends significantly on the growth conditions. This is illustrated (Fig. 2.9 a), which displays the morphologies of ELO structures as a function of temperature and pressure. Actually, the diagram can be divided in four regions: – in I, for T < 925 8C, the morphology is poor, – in II, the sidewalls of the triangular stripes are {1122} facets, as in I, but with a smooth surface, – in III, when increasing T or decreasing p, compared to region II, the sidewalls evolve from {1122} to vertical {1120} facets (such an evolution as a function of T was previously reported by Nam [90, 91],

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a)

a SEM photographs of lateral overgrowth of GaN from h1100i stripes at different temperatures or pressures; b schematic evolution of the morphology of ELO GaN from h1120i and h1100i stripes as a function of temperature and pressure (from Hiramatsu [110]). Fig. 2.9

b)

– finally, in region IV at even lower p or higher T, the (0001) surface becomes rough. These general trends are schematically given in Fig. 2.9 b. Starting from GaN stripes selectively nucleated in a window, a flat surface is obtained provided that the ratio of the lateral to vertical growth rates is high enough. The final goal is to get full coalescence from {1120} sidewalls. For MOVPE, this anisotropy of the growth rates can be enhanced by either increasing the growth temperature (>1100 8C) [111] or by introducing (MeCp)2Mg in the vapor phase but keeping the

2.3 One-Step Lateral Overgrowth (1S-ELO) Fig. 2.10 SEM photograph of GaN localized islands grown on a patterned silicon nitride mask with [Mg]/[Ga] = 0.14 in the vapor phase.

growth temperature in the standard range of GaN MOVPE growth (1000–1100 8C) [112, 113]. It has been shown that the addition of Mg in the vapor phase enhances the VR/VC, ratio of the growth rate along the Rh1101i and Ch0001i directions, respectively. Figure 2.10 illustrates this effect. The islands were grown in conditions identical to those corresponding to Fig. 2.6, but Mg in the form of (MeCp)2Mg was added in the vapor phase ([Mg]/ [Ga]*0.14), with VR/VC reaching 4 [90, 91, 114]. A surfactant effect of the isoelectronic impurity, antimony, has been recently evidenced; the presence of Sb in the gas phase has a significant effect on the facet formation. The addition of Sb favors the appearance of {1120} facets similar to an increase of the temperature in Fig. 2.9, or to the addition of Mg (see Sect. 2.4) [115]. The composition of the carrier gas (H2 versus N2) is also a key parameter, controlling the lateral overgrowth, as well as the growth selectivity. In short, from experiments carried out on h1100i stripes on MOVPE GaN, Tadatomo [108] and Kawaguchi [116–118] concluded that H2 as a carrier gas produces smooth surfaces, but a low lateral growth rate. Conversely, N2 enhances the lateral growth rate, but the surface quality is poor. As a conclusion, it appears that a mixture H2 +N2, 1 : 1, gives the best compromise between fast lateral overgrowth and smooth surfaces. Another way to control the morphology of overgrown stripes is to modulate the V/III ratio. This was done by Zhang [119] using NH3 flow modulation. Experimentally, this is achieved by controlled interruptions of the NH3 flow in the ELOMOVPE process. The lateral growth increases with the duration of the flow interruption. It is possible to tune the growth conditions to enhance the lateral growth and to get full coalescence. Fareed [120] also proposed this flow-modulation approach of ELO for the ELO on 6H-SiC with stripes on a SiO2 mask patterned along h1120i direction. Using different NH3 flow-off times, a controlled evolution of the morphology from triangular stripes with {1101} facets to rectangular {1100} facets was observed. The rectangular shape is obtained for a 5-s NH3 flow interruption in an 8-s cycle, and corresponds to a lateral to vertical growth rate ratio of 4 : 1. It should be noted that this evolution is very similar to the one displayed in region II of Fig. 2.9 b. In the first achievements of ELO GaN, the lateral growth was induced from the beginning of the regrowth in order to rapidly obtain both coalescence and flat sur-

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face. With this process, the defect-free (or low defect density) GaN was limited to the region of lateral expansion above the mask, excluding the coalescence boundaries [72], whereas the GaN above the window stripes replicates the defect density of the GaN template. Indeed, as discussed later, the situation is more complicated, with dislocation half-loops possibly created in the 1S-ELO technology. As an illustration, Fig. 2.11 displays a cross-sectional TEM image along the [1010] zone axis (images projected along the direction of the stripes) of an ELO GaN substrate. The lateral expansion has been induced, in this case, by a growth temperature of 1120 8C. Full coalescence is achieved and the film is smooth for a thickness of 1.75 lm. The behavior of the dislocations is as expected for a standard ELO process: the dislocations under the mask terminate when they encounter the amorphous mask whereas the dislocations thread through the windows in the upper material up to the surface. Actually, in one-step ELO, two regions can be identified: above the openings (coherent growth) and above the mask (lateral

Fig. 2.11 Cross-sectional image along the [1010] zone axis of a standard ELO film; black arrows show the limits of the mask.

Fig. 2.12 AFM scan of a 1S-ELO on (111)Si showing the wing and coherent regions together with coalescence boundaries.

2.3 One-Step Lateral Overgrowth (1S-ELO)

overgrowth regions also called wings). However, at the interface between two laterally growing GaN layers, extended defects (TDs and dislocation half loops) are generated. In the central region over the mask, the overgrown GaN does not adhere to the amorphous mask and a void can be observed between the mask and the overgrown GaN (Fig. 2.11). The presence of these voids does not degrade the upper material quality and the flatness of the resulting film. An AFM scan of a 1S-ELO GaN on (111)Si reveals these different regions: coherent with high TDs densities, wings with almost no observable TDs, and coalescence boundaries (Fig. 2.12). The decrease of the mean density of defects counted over the entire surface only depends on the ratio between the width of the mask and the width of the window. The almost defect-free regions are well adapted to the fabrication of devices. Nevertheless, with this 1S-ELO method, device size is limited to the width of the mask stripes (Nichia has produced their first laser diodes with lifetime of 10,000 h on these low dislocation density stripes). For ELO using h1100i openings, TDs originating from the starting layer propagate to the top surface of the regrown GaN. As expected, there is a much lower density of observable dislocations in the overgrown GaN above the mask. When using h1120i openings, ELO stripes exhibit a triangular cross section. In this case, dislocations originating from the template bend at 908 when they encounter the {1101} growing facet. This bending of TDs is also observed in triangular stripes with {1122} lateral facets obtained from h1100i stripes when growth conditions correspond to region II of Fig. 2.9. This is illustrated in Sect. 2.4, Fig. 2.26. This mechanism of TDs bending leading to a drastic reduction of TDs was also observed in the pyramids obtained in selective area epitaxy [102]. The same behavior of TDs has also been observed during mass transport in GaN [121]. In order to demonstrate the effect of transport on the bending of TDs, trench stripes were patterned on the surface of a MOVPE GaN along the h1120i direction. Then, these structures were then annealed at 1100 8C under N2 + NH3. It was assumed that during this process, Ga atoms diffuse on the convex part of the surface and are incorporated at the concave part. Once {1101} facets are formed, higher index facets appear and the trench is gradually buried. Interestingly, dislocation-free regions were obtained after this mass-transport process. As in the ELO process, TDs bend at 908 when they reach the {1101} facets. It is assumed that these dislocations bend towards the free surface to minimize the free energy of the system.

2.3.1.2 Structural Assessment

TEM and AFM microstructural studies on ELO GaN obtained from bonding of {1120} sidewalls, initiated from h1100i stripes, indicate that the ELO GaN is free of mixed-character TDs [65, 92, 109]. The upper limit is estimated to be 5 ´ 106 cm–2. The coherently grown GaN has the same mixed and pure edge TD density as the substrate. A small number of pure edge dislocations with line direction in the basal plane along the h1100i direction appear above the edges of the

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mask. Indeed, in the overgrown region, the nature of defects and their density depend on the shape (width, periodicity, and crystallographic orientation) of the stripes. Because of the complex structure of ELO GaN with three materials, i.e., substrate, mask and GaN with different thermal expansion coefficients, additional mechanisms may take place. Dislocation generation or propagation can accommodate the stress induced in this structure. TEM planar views on the topmost part of an ELO structure reveals, in addition to well-known features, arrays of dislocations between the coherent and wing regions that run roughly along the stripe direction [122, 123]. At the coalescence region above the middle of the mask, similar inplane dislocations are evidenced (see also Sect. 2.4). These dislocations have segments close to the boundary, which bend, in the form of half-loops, into the wings [122]. It is believed that these dislocations originate from the shear stress developed during and after growth due to thermal coefficient mismatches between the three materials forming the ELO structure. Hacke et al. [124] observed by cathodoluminescence nonradiative lines in ELO GaN/SiC at 308 from the h1100i stripes. These are screw dislocations forming loops. Once again, it is assumed that these extended defects are generated as a result of a shear stress. At the meeting front, a void, like a pinhole with {1101} facets is often observed. Misorientation between the two meeting fronts results also in grain boundaries with much larger tilt and twist components than those observed in GaN/sapphire. This tilt is, to some extent, detrimental for the fabrication of high-performance optical devices and therefore must be reduced or eliminated. These tilts have been observed for both MOVPE and HVPE ELO GaN from either h1100i or h1120i-oriented stripes [92, 125]. These tilts, of the order of 18 can be evidenced by X-ray diffraction. Indeed, the tilt can be directly correlated with the stripe geometry and growth conditions. Low tilt (*0.18) can be achieved by either increasing the thickness [125] or tailoring growth conditions of uncoalesced stripes to get a low wing tilt and then quickly achieve coalescence in a second step by changing the growth conditions [126].

2.3.1.3 Kinetics

In ELO, growth does not occur on the dielectric mask. As a result, the gallium molecular species brought to the growth interface are not depleted over the mask, thus creating an additional supply of active species that can be transported via diffusion to the open areas. This leads to a growth-rate enhancement on the open regions, especially those adjacent to the mask, relative to the rate of the unpatterned growth. A model based on steady-state gas-phase diffusive transport was formulated and Coltrin [127] has proposed growth-rate enhancement. Indeed, the mechanism of growth enhancement has been subject of controversies over the years. Two alternative explanations were addressed: transport of molecular species by gas-phase diffusion or by surface diffusion on the mask. It is currently assumed that short-range diffusion < 10 lm occurs during III–V growth, but for longer dis-

2.3 One-Step Lateral Overgrowth (1S-ELO)

tances gas-phase diffusion is the dominant mass-transport mechanism. To prove this, Mitchell et al. [127] carried out SAE experiments and ELO on Si(111). For SAE, deep trenches were etched into the surface of the mask as barriers to lateral transport by surface diffusion, if any, and the SAE thickness profile exhibited the same profile whether or not trenches were present. This, therefore, demonstrates that the growth enhancement in ELO results from gas-phase diffusion.

2.3.1.4 In-Depth Optical Assessment of MOVPE ELO GaN

In order to properly study ELO GaN at different stages of the overgrowth, local characterization tools such as microphotoluminescence (l-PL), micro-Raman, cathodoluminescence and time-resolved PL (TRPL) should be implemented. This reveals local strain and nonuniform free carrier concentrations. It is expected that the reduction of TDs density of the ELO technology also leads to a decrease of the tilt of the c-axis and the twist of the c-plane. Actually, Kobayashi [128] showed using X-ray rocking curve measurements that in ELO GaN (MOVPE and HVPE), the “tilt and twist” angles are significantly reduced (and the improvement is more significant for the twist angle). However, in MOVPE the tilting and twisting strongly depends on the stripe orientation of the pattern h1120i or h1100i, which is closely related to the difference in the growth process. Using l-Raman spectroscopy, Pophristic et al. [129] showed from the position of the A1 (LO) phonon that ELO GaN is doped up to 1 ´ 1017 cm–3, and this residual doping is assumed to come from the SiN mask. CL is a useful tool for the mapping of emerging TDs as will be illustrated in Sect. 2.4. A 365-nm monochromatic CL image reveals that in the coherent region, above the opening, the CL shows mottled luminescence contrast as usually observed in MOVPE GaN. Conversely, the ELO material extending on both sides of the seed region exhibits very low optically active defects. These ELO regions are terminated by the coalescence boundaries characterized by dark CL lines [130]. To further analyze the vertical and horizontal propagation of TDs, Rosner [131] intercalated a GaInN SQW in the ELO structure and used the 421-nm CL mapping to determine the defect arrangement as a function of the depth in the film. The images he obtained showed that the lateral defects do not propagate into the upper part of the film. For ELO GaN on AlN/6H-SiC with h1100i stripes, CL imaging of uncoalesced stripes reveal details about TDs propagation and impurities incorporation [132]. When the shape of the overgrown GaN corresponds to trapezoidal cross-sectional stripes (like in Fig. 2.9, region II), the fast vertical growth rate results in the incorporation of a high density of defects and produces a strong yellow emission in the coherent region, whereas on the triangular part, a blue emission is clearly visible. On a rectangular cross-sectional GaN (like in Fig. 2.9, region III), most of the YL originates from the region between the stripes. PL measurements show an additional band at 3.4643 eV (most likely linked to a donor incorporated in the ELO process) and a blue-shifted emission compared to the underlying GaN. This

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shows that the ELO GaN exhibits improved material quality and reduced biaxial strain. In addition, these results are consistent with Raman scattering data where a reduced linewidth and a slight shift of the E2 phonon in the ELO region are observed [132]. ELO GaN results from a growth process involving different materials (dielectric mask, substrate) with different lattice parameters and thermal coefficients, and involves several thermal cycles. Therefore such a system generates stresses. Their magnitude and spatial distribution have been modeled (for the system GaN/AlN6H-SiC with SiO2 mask) using finite element analysis [133]. It was shown that localized compressive stress fields up to *3 GPa occur at the edge of the ELO GaN in the vicinity of the GaN/dielectric interface. Other calculations were published (see Sect. 2.4, 2S-ELO). Internal stress fields are also believed to assist the generation of horizontal dislocations [134]. SEA: On GaN pyramidal structures partially coalesced along the [1100] direction, spatially resolved CL demonstrates that the coalescence region exhibits stronger and more uniform luminescence than the pyramidal sidewalls [135]. Stress analysis on SAE pyramids gives compressive stress in the buffer layer, tensile on facets, and full relaxation in the mid to upper part of the pyramid [136]. Interestingly, the thermal conductivity measured using high spatial resolution conductivity of ELO GaN was found to be 1.7–1.8 W cm–1 K–1, values significantly higher than in bulk material (1.3 W cm–1 K–1 [137, 138]). A similar observation was reported by Luo [139] who measured 1.55 W cm–1 K–1 on ELO GaN. 2.3.2

HVPE

Among several advantages, HVPE presents high growth rates (30–100 lm h–1) suitable for producing bulk GaN crystals, thus paving the way toward free-standing GaN. In most cases, the starting substrate was a GaN/sapphire template grown by MOVPE. However, for thick layers ³ 20 lm on sapphire, cracks occur. Kato [98] first demonstrated selective epitaxy and lateral overgrowth, he showed that {1101} facets appear in GaN from openings in the h1120i direction. Fully coalesced HVPE GaN layers were eventually obtained from openings in the h1120i direction with widths ranging from 1 to 4 lm, with a period of 7 lm [93] after several tens of lm in thickness. The dislocation density was reduced from 109– 1010 cm–2 to 5 ´ 107 cm–2, and further reduced for large thicknesses. The best value obtained was 8 ´ 106 cm–2 for a 560-lm thick layer [140]. The starting MOVPE layer was observed to contain 109 dislocations cm–2, consisting mainly of pure edge, some mixed and very few screw dislocations. As expected, almost all these dislocations propagated into the HVPE layer and no new ones appeared at the interface in a standard regrowth process. However, in the ELO, dislocations from the openings are bent at 908 and afterwards propagate laterally, thus never reaching the surface [94]. Besides, dislocations originating from the MOVPE template are piled up on the mask. This method was named FIELO for facet-initiated ELO,

2.3 One-Step Lateral Overgrowth (1S-ELO)

by the authors. Free-standing GaN was obtained from thermal-induced strain during the cooling of the HVPE wafer after growth. In a more detailed study [125] two types of defects, called D1 and D2, were identified in ELO HVPE GaN, with stripes along h1120i. D1 originated from the center of the mask, whereas D2 came from the two edges. Indeed, D1 originates from the coalescence of two lateral overgrowing GaN. D1 consisted of two groups of dislocations, an array of dislocation segments along the h0001i direction, the other group of dislocations running vertically along the h0001i direction. The D2 defects consisted of arrays of dislocations parallel to the h1120i direction that form a tilt boundary. The tilt angle between two neighboring GaN was estimated to be 18. Defect generation in regions close to the mask (similar to D2) were assumed to originate from the shear stress occurring in these regions [141]. It has been experimentally demonstrated that in MOVPE at 1300 K, GaN grows under a constant tensile stress on sapphire [142]. As the stripes extend vertically and laterally, the expanding material boundaries may require the generation of dislocations and the onset of c-axis tilting. Finite element simulation of the stress distribution shows that at high temperatures, the tensile stress in the GaN seed layer and the thermal stress from the mask result in a high shear stress at the growth facets. The relaxation of this shear stress is assumed to be the driving force resulting in the generation of dislocations and on the c-axis tilting during lateral growth [141]. It should be stressed that the higher growth rate in HVPE ELO compared to MOVPE should be responsible for D2 dislocations and more pronounced c-axis tilting.

2.3.2.1 In-Depth Assessment of HVPE ELO GaN

In HVPE, as in MOVPE-ELO, coalescence does not occur in the same way for stripes oriented along the h1100i or h1120i directions [93, 143–145]. The stripes during the ELO process developed into different shapes. Triangular stripes with {1101} side facets are obtained from openings along h1120i directions, and rectangular stripes with {1120} facets from openings along the h1100i direction. ELO growth with openings along the h 1120i direction does not result in a flat surface unless a very thick layer is grown, whereas along h1100i it does [146]. For stripes along h1100i, the facet structure not only depends on the temperature but also on the composition of the carrier gas H2 + N2. For pure N2, the TDs do not experience 908 bending, whereas in a mixture N2 + H2 1 : 1 a more efficient reduction of TDs occurs via 908 bending [147]. In standard ELO, two regions are clearly identified: the overgrown region over the mask and the coherent growth. In the analysis reported by Holst [146] l-PL and TRPL have been carried out at different areas of the cross section of an ELO GaN with opening along both the h1100i and h1120i directions. Confocal l-Raman spectroscopy allows the mapping of the free carrier concentration. On a thick ELO sample grown by HVPE (similar to the one presented in Fig. 2.18), an optical micrograph on a cross section reveals triangular stripes

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above the openings, which extend laterally until coalescence. Mapping of the free carrier concentration n was obtained from the scan of the LO phonon-plasma (LPP) couple mode. In the triangular stripes, n was found to reach 1020 cm–3 whereas n*1019 cm–3 in the coalescence region where the two laterally growing GaN meet, located above the triangular stripes. The authors explain these features by enhanced incorporation of O and Si (most likely coming from the SiO2 mask) in the coherent part [148]. Additional Kelvin microscopy reveals that compensating acceptors, which could be VGa, are also incorporated in the triangular stripes [149].

2.3.2.2 Stripe Openings along h1120i

Cross-sectional CL mapping, together with SEM image of ELO along h1120i, is shown in Fig. 2.13 (Bertram [150]). In the coherent growth, a triangle exhibits a homogeneous emission at 3.463 eV. The ELO region is dominated by an inhomogeneous blue-shifted emission around 3.483 eV. Conversely, a red-shifted (3.425 eV) CL peak dominates in the coalescence boundaries. Figure 2.14 displays several CL (5 K) spectra taken at different spots of both zones. Spectra in the coherent growth region (spectra h on Fig. 2.14) show sharp excitonic lines with the free exciton X, D8X (two donors) and A8X. With increasing distance from the substrate, an 8-meV blue-shift is observed for all lines. In the ELO region, broad and blue-shifted CL emission is observed (Fig. 2.14, spectra d and f). Additional l-Raman scattering experiments were carried out on the same spots. The E2 mode is directly related to the local strain whereas the free carrier concentration is deduced from the LO-phonon-plasmon-coupled modes (LPP). Results are displayed on Fig. 2.15. A red and blue line for the coherent and the overgrown regions indicates line scans over the cross section, respectively. The free carrier density in the overgrown region jumps to about 1019 cm–3 above the buffer and

(a)

(b)

SEM (a) and CL (b) images of two different regions: coherently grown above the

Fig. 2.13

openings and overgrown above the SiO2 stripes (from Bertram [150]).

2.3 One-Step Lateral Overgrowth (1S-ELO)

Fig. 2.14 CL wavelength image and local CL spectra from the ELO region and the coherently grown GaN (from Bertram [150]).

afterwards remains constant. In the coherent region it starts at a low level (<1018 cm–3) above the apex and a jump up to 1.3 ´ 1019 cm–3 is observed. It is worth noticing that this data is in full agreement with CL mapping. These results show that the distribution of residual donors is inhomogeneous and that strong impurity incorporation occurs in the ELO region. The local distribution of biaxial stress is deduced from the E2 Raman mode as shown in Fig. 2.15 b. Without getting into deeper details about the distribution of stresses, once again l-Raman re-

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veals inhomogeneities. Local probe analysis in ELO GaN oriented in the h1120i direction led to the following conclusions: – In the coherent-grown region, when the (0001) facet disappears, most of the TDs have undergone a 908 bending and the top part of the coherent triangle is virtually dislocation-free. The CL spectra become extremely narrow as shown by the evolution from k to n.

(a)

(b)

Fig. 2.15 l-Raman scan along the c-axis of overgrowth GaN (in blue) and coherently grown GaN (in red), a free carrier density; b biaxial compressive stress (from Bertram [150]).

2.3 One-Step Lateral Overgrowth (1S-ELO)

– In the ELO regions lower qualities are evidenced, most likely because of enhanced impurity incorporation (spectrum d and Fig. 2.15 a). – In the coalescence region, the CL spectra are wide as well as red-shifted due to the generation of defects at the coalescence boundary (spectrum c). Stripe Openings along h1100i Cross-sectional CL mapping and SEM images are shown on Fig. 2.16 together with CL spectra taken at different spots of the coherent and ELO regions [151]. The coherent growth part gives a uniform monochromatic rectangle dominated by CL emission at 3.467 eV. The CL spectra of this coherent part exhibits sharp D8X recombination at 3.467 eV (Fig. 2.17 c and e).

Fig. 2.16 SEM and CL image of a cross section of HVPE ELO sample (from Kaschner [151]).

Fig. 2.17 CL wavelength image and local CL spectra of different region of the sample shown in Fig. 2.16 (from Kaschner [151]).

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As observed for stripes along h1120i, the overgrown region is red-shifted. This red-shift results from incorporation of impurities in the coalescence region. TRPL measurements strengthen the basic conclusions deduced from CL and l-Raman. Decay time constants in the coherent grown region of samples with h1100i stripes reach about 220 ps, indicating high-quality material. l-PL provides similar information, with the spectra being dominated by two peaks D8X and XA, both peaks showing a weak intensity on the coherent region and a high intense in the wings. From the analysis of the cross-sectional l-PL it is deduced that the incorporation of donors is enhanced within the wing regions, but once GaN coalesces on the mask, the incorporation of donors is suppressed [152]. As experimentally shown in Sect. 2.3.2.1, HVPE ELO layers present a stress distribution. This was analyzed using simulations based on continuum elastic theory. In the calculations, the lattice mismatch a is adjusted to reproduce the biaxial stress in the GaN buffer layer and was taken to be zero for the amorphous SiO2 mask. As a result, the calculated biaxial stress rxx distribution fits rather well with the experimental values deduced from l-Raman data. The ELO GaN is under biaxially compressing stress; rxx relaxes rapidly through the window to –0.32 GPa and to –0.45 GPa for h1120i and h1100i stripes, respectively. Along the mask, the ELO GaN is also under biaxial stress [153].

2.3.2.3 Selective Area Epitaxy (SAE)

l-Raman imaging was also achieved on hexagonal islands grown by selective epitaxy HVPE on sapphire without a GaN seed. Stress mapping was obtained from the E2 phonon mode. The GaN above the openings exhibited a biaxial compressive stress of *0.19 GPa. In the ELO region, the stress is reduced to 0.15 GPa. Also, in this part the absence of the A1 (LO) band reveals that the free carrier density is high. Above the openings, the A1 band appears, indicating a low carrier concentration [154]. This stress distribution on SAE GaN was also evidenced by lCL. More precisely, it was observed that at the base of the pyramids, a strongly red-shifted luminescence, D8X appeared at 3.433 eV. Within 3 lm from the base, the emission, however, occurred at the relaxed value of 3.471 eV. l-Raman analysis provided consistent results with the CL data. From the E2 phonon mode, it can be deduced that the upper part of the pyramid is fully relaxed whereas the E2 mode is shifted by 4 cm–1 in the buffer layer. This corresponds to a stress tensor element rxx = ryy = –0.95 GPa [155].

2.3.2.4 (C2H5)2GaCl as Ga Source

When using diethylchlorine gallium (C2H5)2GaCl as Ga source in a MOVPE reactor, GaCl is produced at the growth interface and indeed occurs by a HVPE chemistry. The basic features described in Sect. 2.3.2 are therefore observed [156, 157]. This alternative method might be interesting for achieving high growth rates. Actually, the growth rate was found to increase with the growth temperature, with the vertical rate also increasing with decreasing V/III ratio. The commonly ob-

2.3 One-Step Lateral Overgrowth (1S-ELO)

Fig. 2.18 Composite TEM image showing 4 periods of ELO GaN. Four families of disloca-

tions labelled (I) to (IV) can be identified (from Dunn [157]).

served tilt decreases with decreasing lateral-to-vertical growth rate ratio [158]. An in-depth investigation of a 16-lm thick ELO material obtained from this method led to the discovery of four sets of dislocations. Fig. 2.18 shows a construction of TEM images corresponding to 4 periods of the ELO structure. In (I), TDs coherent with the substrate above the openings (as usual), in (II) TDs in the coalescence region, in (III) a V-shaped complex of dislocation loops and finally in (IV) longitudinal dislocations that run over the windows after experiencing a 908 bending. TDs in (I) in the ELO process bend away from the c-axis (most of them at 908). As they reach the coalescence plane, most of them bend again to thread to the surface. In the coalescence plane, in addition to TDs, a wall of parallel dislocations appears (parallel to the substrate) and has Burgers vectors in the basal plane. Rectangular loops in the (1100) plane produce a V-shaped arrangement of edge dislocations (Fig. 2.18 (III)), which are centered on each coalescence plane. These loops are formed at the coalescence boundaries and propagate into the ELO GaN.

2.3.2.5 Stress Generation

As in MOVPE, high stresses are generated by thermal and lattice mismatch. Since, in HVPE, the thickness is much higher than in MOVPE, the high stresses generated by the mismatch when GaN is cooled to 20 8C lead to high dislocation fields. When the shear stress reaches a critical value, slip and plastic deformations occur that produce a large density of defects. Indeed, high densities of dislocations start at the tip of the cracks, then propagate and form a V-shaped network [159].

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2.3.3

Sublimation

The starting template is MOVPE-grown GaN. Sublimation is achieved from a Ga source (at about 1000–1100 8C) under a NH3 flow. Figure 2.19 is a SEM top-view image of a selectively regrown GaN layer using 10-lm wide stripe opening. The starting mask pattern was a star with 12 consecutive openings. It is established that the lateral growth is the highest when the stripes are along the 1100i direction (as in MOVPE and HVPE). However, with stripes along the h1120i direction, the lateral overgrowth is lower than for the h1100i direction and coalescence is difficult to achieve. As in MOVPE and HVPE, in the region of regrowth, TDs from the underlying GaN bent at 908 when they intersect the {1101} side facet. The parallel propagation of TDs extends over the mask until they reach the middle of the mask where they again intersect a {1101} side facet formed in the middle of the mask. Finally, they propagate to the surface. Above the SiO2 mask,

Fig. 2.19 a SEM image of GaN with star-like mask, after growth of 1 h; b SEM image of ELO GaN with stripe opening along h1100i (from Wang [161]).

2.3 One-Step Lateral Overgrowth (1S-ELO)

the dislocation density is reduced to 106 cm–2, whereas above the openings it reaches 109 cm–2 [104, 160–162].

2.3.4

New Developments 2.3.4.1 ELO on Si

The ELO technology was developed using either sapphire or 6H-SiC as substrate and either silicon dioxide or silicon nitride as dielectric mask. This somehow limits the quality of the ELO GaN (stress distribution, diffusion and incorporation of O) and makes the removal of the primary substrate difficult. The use of Si as a substrate is very attractive for the epitaxial growth of GaN despite intrinsic difficulties (cracks). Si is a cheap, high-quality substrate, which can be chemically removed. ELO technology is currently implemented using (111)Si as a substrate [106, 117, 163, 164] as well as SAE [165–168]. However, GaN cannot be directly grown on Si, and an intermediate AlN or AlGaN layer should be grown first [168]. If not, the thermal mismatch between Si and GaN produces cracks when the GaN thickness exceeds 2 lm. Therefore AlGaN/GaN multilayers release most of the strain and allows subsequent ELO technology [169]. Actually, the quality of ELO GaN on Si(111) in terms of TDs densities does reach either ELO/sapphire or ELO/SiC [170]. Kobayashi [171] proposed an original approach of ELO/Si. In a first step, AlAs and then GaAs are grown on Si(111) using well-established technologies of growth of AlAs and GaAs on Si. Stripes are then formed on GaAs as usual by photolithography, and then an oxidation step selectively converts AlAs to AlOx and produces a Ga2O3 template on top of AlOx. The remaining GaAs is then removed. GaN growth is subsequently initiated only on the Ga2O3 template and results in a lateral growth over the AlOx stripe.

2.3.4.2 Using W as Mask

Tungsten was used instead of SiO2 or silicon nitride as a mask and, at first sight, led to similar results, although W reacted somehow with ammonia at the growth temperature [172, 173]. However, the tilting of the c-axis direction is smaller when using a W mask instead of SiO2 [126, 173]. In order to avoid decomposition at the high temperature of GaN by W, a buried W mask could be implemented in an underlying AlGaN/GaN layer, thereby leading to ELO free from damage [174, 175].

2.3.4.3 Maskless ELO

1S-ELO requires two epitaxial growth steps, one masking and one photolithography step. A simpler ELO process without significantly degrading the final quality of the ELO-GaN would be of great interest. Smart et al. [176] presented a new approach in which the regrowth step is avoided by initiating the ELO process di-

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rectly on the masked-patterned substrates (SiC or sapphire). To initiate growth, an AlGaN nucleation layer is deposited (which wets the exposed substrate but not the silicon nitride mask). GaN is then deposited and proceeds both vertically and laterally. AFM studies show TDs densities in the mid-108 cm–2 in the coherent region and *106 cm–2 in the ELO region. A further step towards simplification of the ELO technology was reached by the growth of textured sapphire substrates [177]. In this simplified process a substrate is etched to form mesas prior to a single growth sequence. Growth takes place laterally to produce GaN cantilevers that finally coalesce laterally. Cantilever epitaxy (CE) results in a significant reduction of TDs density (<107 cm–2) above the support mesa. TDs in the edge region turn and further extend laterally into the cantilever. Compared to standard ELO, the dislocation density at the coalescence front and at the mesa is assumed to be lower. To date, this method presents the limitation of the 1S-ELO. Provided further improvements are brought to the process, this method may produce low dislocation densities GaN at lower cost than standard ELO. However, even though a significant decrease of dislocations is reached by CE, a wing tilt of roughly 0.88 was observed for CE of GaN on SiC and (111) Si [178]. Another alternative was proposed by Sano et al. [179–181] in which the starting substrate (sapphire, SiC or (111) Si) is periodically grooved with stripes parallel to the h1100i GaN direction. On such grooved substrates, a fast vertical growth rate produces triangular stripes with {1122} facets like in the ELO process that finally coalesce (except for (111) Si substrates). Low dislocation density GaN was produced with this method, with nearly similar crystallographic quality to ELO. The coalescence boundaries, however, also produce high densities of TDs. In a slightly different modification, Strittmatter [182] used structured (111) Si substrates with grooves parallel to Si h110i, GaN grows on the bottom of the grooves and then the V/III ratio is increased to enhance the lateral growth rate and obtain full coalescence. As is usually observed, the wing areas exhibit improved optical and crystallographic quality. In the search for simpler technologies, an ELO process in which nucleation is performed on a sapphire substrate patterned with a SiO2 mask was proposed, thereby restricting nucleation and further lateral growth within the openings. Direct lateral overgrowth occurs on these SiO2-patterned sapphire substrates. Although ELO quality was achieved, the random nucleation does not allow smooth coalesced films [183]. 2.3.5

Improvements of the Standard ELO Method

It is desirable to have a continuous GaN layer of low defect density over the entire substrate so that devices can be fabricated anywhere, instead of being confined to small areas. A method first proposed by Nam et al. [184] involving repeating the second step by placing the mask stripes directly over the opening of the first ELO mask. This double ELO, however, requires two photolithography steps and three growth steps.

2.3 One-Step Lateral Overgrowth (1S-ELO)

In multiple-step ELO processes, growth conditions are usually changed to induce rapid full coalescence (i.e., increasing the temperature, the V/III ratio or decreasing the pressure). 2.3.6

Pendeo-Epitaxy

Another technology was recently reported, the so-called pendeo-epitaxy (PE), which yields a continuous low-density layer [133, 185–189]. Review papers on PE have been recently published and only the main features will be summarized [190, 191]. Basically, in the PE, etched columnar GaN posts are capped with a mask layer. Afterwards, GaN growth proceeds laterally and vertically until it coalesces between and over the mask located on top of the columns, thereby creating a continuous layer. The process is schematically displayed in Fig. 2.20. Compared to ELO, PE presents two advantages: (i) initiation of growth from a GaN facet different from (0001), and (ii) in the case of 6H-SiC substrate, the use of the substrate as mask. This process has been extended to Si(111) as a substrate with the insertion of a 3C-SiC layer between AlN and the (111) Si substrate. The seed microstructures are rectangular stripes oriented along the h1100i direction and exhibit {1120} facets. This therefore implies initiation of the growth from a GaN plane other than (0001).

Fig. 2.20 Schematic representation of different steps for growth in the technique of pendeo-epitaxy (PE): a GaN template; b etched GaN columns prior to growth; c partial

growth of PE GaN showing growth only from the sidewalls; d fully coalesced growth of GaN (from Thomson [185]).

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Fig. 2.21 a GaN grown over masked GaN posts; b GaN grown on unmasked submic-

rometer post; c TEM photograph of b (from Gehrke [194]).

This new technology has recently been widely developed and significantly improved (see for instance Ref. [192]). Among the drawbacks common to ELO, in the standard process, voids are formed above the mask. In addition, coalescence boundaries due to misregistry between two laterally growing fronts are formed. As a consequence, a wavy surface morphology is formed (Fig. 2.21 a). Tilting by 0.28 is also present in GaN grown over the mask. Even though the mask on top of the GaN seed posts stops the TDs, it is also responsible for coalescence boundaries and tilt in the GaN growing over the mask. In an investigation of pendeo-epitaxy of GaN on sapphire, Kim et al. [192] identify two types of coalescence boundaries at the mask and window regions. In addition to this, thin voids are observed on the SiO2 mask, whereas triangular voids are formed in the coalescence region on sapphire. Actually, dislocations are generated at the two types of coalescence regions as well as at both sides of the mask edges, as observed by Sakai [125]. In order to avoid these deleterious effects, sub-micrometer seed post have been made by electron beam lithography and the mask has been suppressed. As a result, voids above the seed are not formed (Fig. 2.21 b). TEM revealed a strong reduction of the TDs density, with no dislocations generated in the coalescence region, with some TDs propagate vertically from the GaN seed post (Fig. 2.21 c). In addition, in these films, no tilt was observed. Indeed, this represents a significant improvement of the standard pendeo-epitaxy method [193, 194]. Unmasked PE has also been implemented on (111)Si. Reacting Si with propane produced a thin intermediate 3C-SiC layer. Compared to ELO, the ratio between the lateral and vertical growth rate is four times larger for PE [195]. At least for the system GaN/AlN/6H-SiC, the curvatures observed in ELO resulting from residual stress, are significantly reduced in PE. Using the same basic assumptions as in ELO, Zheleva et al. [196] calculated the stress distribution in PE and found that it ranges from compressive (3.8 GPa) to tensile (0.6 GPa) stress that is localized within the GaN/column window. In maskless pendeo-epitaxy, the crystallographic tilt of the wing was found to result from the strain relaxation of the starting stripe along the c-axis. Finite elements simulation indicated that c-plane stress is partially relieved within the wing regions [197, 198]. In a rather similar method, the lateral overgrowth is initiated from trenches (LOFT, lateral overgrowth from trenches) [199]. Trenches are etched into the GaN

2.3 One-Step Lateral Overgrowth (1S-ELO)

thin films, after which the bottom of the trenches and the top surfaces of the mesas are masked with SiO2. Afterwards, GaN is regrown. As in the case of pendeoepitaxy, GaN regrown from the sidewalls has a much lower dislocation density, since the threading dislocation propagate in the direction perpendicular to the surface. Compared to standard ELO, this LOFT method allows a significant reduction of the TDs density over the entire wafer using only one step. The TDs density in the top part of the regrown GaN was reduced to 6 ´ 107 cm–2 from the original density of 8 ´ 109 cm–2. The residual TDs either leaked from the sidewalls of the trenches or were generated in the regions where two growth fronts pinched off. A new modification of both of the ELO and PE concepts was demonstrated and called “air-bridged ELO” [200–202]. In this method, which relies on the basic principles of both methods, the GaN starting epilayer is grooved along the h1100i directions using standard photolithography and etching. Afterwards, silicon nitride is deposited on the etched bottom of the trenches and on the sidewalls of the trapezoid ridge stripes (Fig. 2.22). Regrowth starts from the stripes and extends laterally forming ELO GaN with {1120} facets, which finally coalesce. A gap is formed above the mask, thereby giving almost free-standing GaN. In this method, the tilt angle of the c-axis relative to the seed GaN is only 0.088. Most likely, the empty gap between the dielectric silicon nitride and ELO GaN prevents stress develop-

Fig. 2.22 a Schematic of the “air-bridged ELO”, see text (from Kidoguchi [201]); b SEM cross-sectional image of the beginning of the

regrowth, markers are AlGaN; c after full coalescence.

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ment as theoretically predicted by Zheleva et al. [196] however, a high density of TDs still remains above the seed regions. 2.3.7

ELO of Cubic GaN

Cubic GaN is first deposited on (001) GaAs. Then stripe openings are made on a SiO2 mask as usual along the h110i and h110i directions. Growth occurs only within the window (SAE). Trapezoidal stripes are obtained with a (001) top surface and {111}B lateral facets, but full coalescence is not reached. In the PL spectra, a 13-meV red-shift was observed as a result of stress release of the SAE cubic GaN [203].

2.4

Two-Step ELO (2S-ELO) 2.4.1

Experimental (MOVPE)

Since the lateral overgrowth depends on parameters, like temperature, carrier gas, V/III ratio, etc., several two-step schemes are conceivable. Two-step ELO initiated at a low V/III ratio (to produce smooth vertical {1120} sidewalls) and continued with an increased V/III ratio (to increase the lateral growth) has been reported [109]. However, even though such a process produces a smooth morphology, TDs are still present in the coherent growth region. To avoid this drawback, other technologies like double-layer ELO have been proposed [101, 204]. In this alternative ELO, the mask is rotated by 608(or 908) after the first ELO layer, therefore allowing the growth of stripes along another equivalent h1100i direction. This results in the reduction of dislocations over the windows as shown in Fig. 2.23.

Fig. 2.23

Monochromatic CL (excitation 364 nm) for double-layer ELO (from Yu [101]).

2.4 Two-Step ELO (2S-ELO)

Using basically the same concept to eliminate the remaining TDs in the coherent region, Davis [205] proposed a technology in which the second mask has a lateral offset from the first array of openings. More precisely, the first ELO GaN is made with stripe openings along the h1100i direction, after which the second mask covers all the coherent GaN from the first step (where the TDs density remains high), thus preventing the TDs from propagating into the second ELO layer. Consequently, the entire final layer exhibits a low dislocation density. A similar two-step ELO was proposed by Ikeda [205] and Sugiura [206]. Another original two-step ELO process was recently developed [105], which allows a larger defect reduction, especially above the window stripes [105, 112, 207– 209]. This process takes advantage of the phenomena of dislocation bending, which has been observed by several authors [93, 122] and already discussed. In the first step of this process, a vertical expansion is favored, whereas a lateral expansion is promoted in the second step. Indeed, the first step is the growth of GaN at 1040 8C as in the standard ELO process. The growth rate GC of the top (0001) facet is higher than the growth rate GS of the inclined {1122} lateral facets. The growth rate of the (0001) plane, GC/ GS = 3. This first step is pursued until the top facet completely vanishes. The formation of the apex is critical. At this stage, the cross-sectional shape of the ELO GaN is triangular with {1212} facets (Fig. 2.24 a). Then, in a second step, the lateral growth is favored (the growth rate of the lateral facets is higher than the growth rate of the top one) by either introducing (MeCp)2Mg in the vapor phase

(a) Fig. 2.24 Schematic representation of the two stages of the 2S-ELO process a at the end of the first step (vertical growth rate higher than lateral growth rate). The shape is a triangular with {1212} facet. H is the angle between [0001] and [1122], GC the growth rate of the (0001) plane, GS the growth rate of (1122), GC/GS = 3, depends on the anisotropy of the

(b) growth. Red lines represent the behavior of TDs inside the triangular stripes; b during the second step, i.e., growth at high temperature or introduction of Mg, GS > GC: flattening occurs, GS/GC*2, coalescence boundaries are formed together with voids. The red lines represent the behavior of TDs up to the coalescence boundaries.

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at the same temperature or by increasing the temperature up to 1120 8C until complete coalescence and smoothing of the surface is achieved. Figure 2.24 b schematically represents the second step of the process leading to full coalescence. Figure 2.25 A is a typical image of a two-step (2S)-ELO sample at the end of the second step, viewed in cross section along the [1010] zone axis. The second step (lateral growth) is, in the present case, induced by the introduction of (MeCp)2Mg in the vapor phase. The resulting microstructure is similar to when the lateral growth is induced by an 1120 8C growth temperature. It takes 1.5 h to achieve full coalescence and smoothing of the surface, resulting in a thickness of 12 lm. Henceforth, the behavior of the dislocations is different from that in standard ELO. Indeed, the dislocations under the masks are also blocked when they encountered the mask. The dislocations above the window first propagate vertically (as in the standard ELO), but afterwards bend by 908 to adopt a direction along the (0001) basal plane. It should be mentioned that this behavior is observed whatever the nature of the dislocations (a, c or a + c). Some of the dislocations adopt an intermediate inclined direction before bending in the basal plane. Dashed lines in Fig. 2.25 a indicate the bending points. It should be noted that dislocations close to the edge of the mask experience bending first. A vertical growth rate higher than the lateral growth rate leads to intermediate overgrown material shapes as represented by dotted lines in Fig. 2.25 b. As soon as a vertical dislocation line gets sufficiently close to the edge between the top and inclined facets, it bends to adopt a new direction in the basal plane. This general picture can be understood in the framework of image dislocation and image forces, as already proposed [122, 210]. A dislocation generates a stress field, which should be compensated when the dislocation line gets close enough

A Cross section along the [1010] zone axis of a 2S-ELO film at the end of the first step. Dashed white lines join the dislocation bending points; B schematic representation of 2S-ELO. Dotted lines represent the

Fig. 2.25

shape of the ELO material at different stages of the first part of the 2S-ELO process. Dashed black lines join the successive edges of the top C facet. Continuous black lines represent dislocations.

2.4 Two-Step ELO (2S-ELO)

to surfaces to leave the free surfaces stress-free. An image dislocation is a virtual dislocation located outside the material, which generates a stress field compensating at the free surface the stress field of the actual inner dislocation. Such image dislocations induce attractive forces acting on inner dislocations. In the present case, the image force has no effect (for symmetry reasons) on the dislocations when they are perpendicular to a (0001) surface without lateral facets within the interaction range. On the other hand, it moves their lines in the basal plane when the TDs become close enough to an inclined facet. In fact, during the first step of 2S-ELO, the lateral inclined facet moves progressively toward the dislocation lines. The lateral facets first reach the dislocation lines that are closest to the edge of the mask and reach the dislocations located just in the center of the window afterwards. These may not bend and still propagate vertically to the surface, since in this case, interactions with both the left and right free surfaces ((1212) and (1212)) may compensate each other. A straightforward explanation of the 908 bending could be the following: bending results from the general principle of minimization of the free enthalpy of the system. During growth, dislocations follow a direction leading to minimum enthalpy. As the line energy of a dislocation depends also on its character, the energy of a screw being the lowest, bending at 908 of an edge eventually produces a screw dislocation, or introduces a screw component thus lowering the enthalpy of the system. Figure 2.26 is a cross-sectional image of a 2S-ELO GaN at the end of the second step, i.e., after coalescence and smoothing. Figure 2.27 is an AFM picture of the top surface of a 2S-ELO. Only mixed dislocations emerge at the top surface. The total density of dislocations measured on the whole surface is 4.7 ´ 107 cm–2, with the coalescence boundaries clearly visible. The bending of most of the dislocations results in a drastic reduction of their density in the upper part of the film, i.e., for a thickness greater than the height of the pyramids obtained at the end of the first growth step. After bending, most of the dislocations have a line parallel to [1210], which extends to the coalescence

Fig. 2.26 Cross section along the [1010] zone axis of a 2SELO at the end of the second step.

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2 Epitaxial Lateral Overgrowth of GaN Fig. 2.27 AFM scan of the top surface of 2S-ELO GaN, only mixed dislocations are merging. The total TDs density measured on the whole surface is 4.7 ´ 107 cm–2. TDs concentrate in the coalescence boundaries.

boundary with the overgrown GaN coming from the adjacent stripe. The boundary is therefore an area of defect accumulation. Several types of behaviors of the dislocations in the boundary have been observed and were reviewed by Vennéguès [208]. Voids are clearly visible over the mask. These voids have a basal triangular shape with an extension over their top apex. Most of the lateral dislocations are blocked when they encounter such a void and therefore do not extend further. Other possible behaviors of these lateral dislocations when they reach the coalescence boundary were identified: – bending down to the void resulting in their termination therein, – bending up in the boundary and threading up to the surface. Hiramatsu et al. [211] used the same basic principle in a 2S-ELO called FACELO for facet-controlled epitaxial lateral overgrowth. Hiramatsu established a p-T, V–III diagram (Fig. 2.9) to tune the shape of the lateral overgrown GaN. In this technology, no tilt of the c-axis or the ELO layer is observed. Actually, the mechanism of propagation of TDs after bending may depend on their nature. According to Honda et al. [212, 213] mixed dislocations bend towards the voids as already discussed, whereas edge dislocations are bent in the direction of the mask stripe. 2.4.2

In-Depth Assessment of 2S-ELO 2.4.2.1 Cathodoluminescence

CL images have been realized in order to investigate surfaces larger in area than in TEM. As previously discussed, dislocations with a screw component are predicted to introduce deep states in the gap and to act as nonradiative recombination centers in GaN, and are therefore in contrast in CL images. It has been verified that there is a one-to-one correspondence between the CL dark spots and the emerging dislocations.

2.4 Two-Step ELO (2S-ELO)

Fig. 2.28 a CL map of a GaN layer grown with the two-step process; b CL map of a GaN layer grown with the regular ELO pro-

cess. Mark: 20 lm. Yu [101] reported a picture similar to b.

CL at 90 K was therefore performed to assess the density of emerging dislocations. At 90 K, the CL collected from the undoped upper layer of the ELO GaN is dominated by the decay of the free exciton A. Figure 2.28 shows for comparison the top-view monochromatic CL mapping (k = 358 nm corresponding to the free exciton A) of a 2S-ELO GaN sample (Fig. 2.28 a) and of a 1S-ELO GaN sample (Fig. 2.28 b) grown in a single step i.e., using planarizing anisotropy from the very beginning. These two samples are overgrown on similar GaN templates i.e., same reactor and same mask patterns. For both samples, full coalescence was achieved and no topography contrast was observed in secondary electron images. Dislocations pointing up appear as black points. Dislocations are organized along lines parallel to the stripe direction as expected. Lines with a high density of dislocations (white arrows) alternate with lines with a lower density of dislocations (black arrows). The distance between these lines is 5 lm. The highly defective lines correspond to the coalescence boundaries whereas the other lines correspond to the center of the windows. The filtering of the defects through the dislocation bending phenomena is therefore not fully efficient and dislocations located just in the center of the window, i.e., dislocation that meet the apex of the pyramid at the end of the first stage of the 2S-ELO processes, may not bend and may extend up to the surface. A few dislocations are present in the material between the lines. The density of defects over the entire surface is 1.7 ´ 107 cm–2. When considering the areas between the coalescence boundaries (10 lm wide), the density is 107 cm–2. This density decreases to 5 ´ 106 cm–2 in the regions between the coalescence boundaries (10 lm wide). Subsequently, the TD density is reduced by at least one order of magnitude compared to the GaN layers grown with the 3D GaN buffer layer process. In Fig. 2.28 b, the distribution of the emerging dislocations observed at the surface of the regular ELO sample is quite different. The four horizontal arrows still indicate the coalescence boundaries, where the dark spots arrangement is similar to that seen in the 2S-ELO GaN. Above the seed regions (indicated by *), however, the defect density remains high enough so that the mean distance between spot centers is lower than the penetration depth of electrons and individual spots can

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hardly be distinguished. As a result, the CL intensity collected from the seed region is very low compared to the adjacent laterally overgrown GaN. The comparison of Fig. 2.28 a and b clearly demonstrates that the 2S-ELO processes allow a drastic decrease of the density of the dislocations emerging from the seed regions, whereas the standard ELO process does not. A further evidence of the bending of TDs during the first step is provided by CL imaging of a sample etched at a depth of 2 and 4 lm (Fig. 2.29) [214]. After bending, TDs propagate along the h1120i direction until they meet the coalescence boundary. This is also evidenced on a bevel edge of a 2S-ELO GaN (Fig. 2.30) recorded with the A exciton transition. The horizontal dark line located in the lower part of the image is a dislocation parallel to the top surface (TDs after 908 bending), which runs from the seed to the coalescence boundary. The

Fig. 2.29 CL imaging of 2S-ELO GaN etched at different thickness, 2 lm, upper images, 4 lm, lower ones. The cut triangular stripes appear in dark in the integrated intensity CL

and in yellow in the CL wavelength image (L). Note that, after bending, TDs propagate in the [1120] directions and appear as dark lines in CL (from Riemann [215]).

Fig. 2.30 UV CL monochromatic image recorded at 90 K on a bevel edge of a 2S-ELO GaN. The luminescent triangles correspond to laterally overgrown material whereas the dark triangle corresponds to the coherent part. Coalescence boundaries and TDs are running parallel to the c-plane after bending. In the top surface, the dark spot corresponds to merging dislocations.

2.4 Two-Step ELO (2S-ELO)

dark spots located on the top surface can be either individual dislocations or tangles of dislocations that quench the UV luminescence [215, 216]. Cross-sectional CL mapping has been achieved on 2S-ELO. Data are displayed in Fig. 2.31 for coalescence using Mg. (Similar features were obtained when coalescence results from an increase of the growth temperature.) The different steps of the process can be identified in the near band gap CL spectra (Fig. 2.31) [217]. Basically, the CL spectra reveal: – The buffer layer (with a D8X emission at 3.477 eV). – The coherent growth above the openings where the TDs bend at 908 inside a triangular stripe with {1122} facets. This region is highly defective; the near band gap emission almost disappeared whereas a strong YL is observed. On the lateral edges of these stripes, a broad near band gap emission results from the incorporation of impurities. This high defect density region is restricted to the initial coherent growth.

A: low quantum efficiency B, C: broad NBG emission Fig. 2.31 Local spectra from the overgrown region (e) and (f) broadened near band gap emission; c narrowing of the CL linewidth with advancing lateral growth; d dominance

D: sharp excitonic lines ) perfect crystal quality

of DAP remission due to Mg incorporation; a, b sharp excitonic peaks of the NID upper GaN layer after the 2S-ELO process.

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– When, alternatively, Mg is added in the vapor phase at the second stage of the process, the CL spectra are dominated by donor-acceptor pairs (DAP) recombination. – Finally, a nonintentionally doped GaN is grown on top of the structure. The CL spectra exhibit extremely sharp excitonic lines. The surface emission shows well-resolved X and D8X recombination lines with lateral homogeneity less than 0.7 meV for both alternative methods compared to 3 to 4 meV for GaN/sapphire. – When, in the second step, the growth temperature is monitored to get full coalescence, CL linewidths get narrower with advancing growth, accompanied with a decrease of impurity incorporation (not shown).

2.4.2.2 Luminescence of GaN by Epitaxial Lateral Overgrowth

Figure 2.32 shows the luminescence spectrum of undoped GaN grown on top of a pseudosubstrate obtained by the two-step process described above after reactor cleaning to minimize Mg contamination. This kind of spectrum is representative and has been observed with small variations for different samples grown following the same process. The main feature is the sharpness of the peaks. GaN layers grown directly on sapphire in the same reactor have FWHM of about 3 meV in the best cases. FWHMs below 1 meV are achieved for bound excitons for 2S-ELO samples. This is comparable to results reported for HVPE GaN [218]. The free excitons A and B as well as the three emission lines labelled A* attributed to excited states of A following Hoffmann are well resolved [219].

Fig. 2.32 Low-temperature luminescence spectrum measured on undoped GaN grown on top of a pseudo-GaN substrate obtained by the two-step overgrowth process. Bound excitons give very sharp (FWHM < 1 meV) and intense peaks. Free exciton A, B, and A* lines attributed to excited states of A are resolved.

2.4 Two-Step ELO (2S-ELO)

2.4.2.3 Time-resolved Photoluminescence

Low-temperature-photoinduced changes of the reflectivity of resonantly excited exciton dynamics yield free exciton lifetimes of 375 ps at 60 K [219]. In 1S-ELO a value of 720 ps was measured at room temperature [220].

2.4.2.4 Deep Level Transient Spectroscopy (DLTS)

Defect concentration (cm–3)

As recalled in the introduction, three main traps were evidenced in GaN, EO2, EO5, and EO6. Although the chemical nature of these traps is still unknown, the evolution of their respective densities for different growth technologies brings useful information about their influence on the optoelectronic properties. Figure 2.33, from Auret [221], displays the free carrier density and the densities of the three main electron traps for standard MOVPE-grown GaN (519 and 521), for MOVPE GaN grown by 3D nucleation (590), ELOG-GaN (ELOG), and HVPE samples from MIT. It should be stressed that the EO6 trap does not appear in MOVPE samples. In standard heteroepitaxial GaN/sapphire, with ND–NA*1017 cm–3, the density of EO2 and EO5 reaches about 1015 cm–3. In 3D nucleation GaN, EO2 drops below 1013 cm–3 for a room temperature mobility of *900 cm2 V–1 s–1. Conversely, although EO2 remains in the mid-1013 cm–3 in ELOG GaN (thus higher than in 3D-nucleation GaN), EO5 is significantly reduced. At this stage, although it has been proven that the 3D-nucleation and the ELOG technologies reduce the densities of electron traps by several orders of magnitude, it is to date not possible to link a given trap to a given extended defect.

Fig. 2.33 Deep state together with residual donor concentrations in GaN grown following different VPE technologies: G519-521, MOVPE/sapphire, G590, 3D-nucleation, ELOG, MIT-HVPE (from Auret [222]).

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2.4.2.5 Strain Distribution

In ELO material, stresses are generated as a result of the mismatch in thermal expansion coefficients between the substrate, GaN, and the SiN mask. The stress distribution in ELO GaN (or pendeo) is usually deduced from l-Raman mapping and analyzed in terms of finite elements (FE). In 2S-ELO, the magnitude of the stress distribution was deduced from the scan of the changes of the E2 phonon frequency using a confocal Renishaw l-Raman system [222]. A highly localized stress of –1 GPa is located at the coalescence boundaries, whereas in the ELO part the measured stress was –0.5 GPa. Besides, a difference in compressive biaxial stress of 0.07 GPa was determined between the ELO window and the overgrown region. It is also shown from FE analysis that the stress distribution depends on the shape of the voids [223]. Stress at the coalescence boundaries in the vicinity of the tip of a triangular void is –0.6 GPa and decreases to –0.25 GPa towards the top surface (Fig. 2.34 b). A compressive stress *0.32 GPa near the SiN mask in the overgrown region (Fig. 2.34 c) was determined. It was also deduced from photoluminescence excitation spectroscopy that the strain in ELO material is stronger than in GaN/sapphire. However, the strain re-

Fig. 2.34 a Mesh of FE model of 2S-ELO on sapphire; b–d distributions of stress fields in

Pa along the x(S11), y(S22), and z(S33) direction respectively. Size 0.5 ´ 0.5 lm2.

2.4 Two-Step ELO (2S-ELO)

mains constant when the temperatures vary, thereby making device fabrication more convenient [224]. 2.4.3

Assessment of HVPE

Even though the research effort on 2S-ELO in HVPE was much less intense than in MOVPE, the 2S-ELO technology is achievable in HVPE. The basic mechanisms are, however, not identical and the experimental conditions to change the growth anisotropy are significantly different. Indeed, the morphology is controlled by the composition of the carrier gas. When starting from h1100i mask openings, under N2 at 1050 8C, the equilibrium shape of the overgrowth leads to trapezoidal stripes with (0001) top facets and {1122} lateral facets, whereas under H2, the lateral growth rate is significantly reduced and triangular stripes with {1122} lateral facets are obtained. So, in the first step, stripes with triangular cross section are grown under a N2 : H2 mixture. In a second step, using pure N2 enhances lateral growth. Figure 2.35 shows the cross-sectional SEM image of a 60-lm 2S-ELO HVPE layer obtained as follows: in the first step with H2 +N2 as carrier gas (using 5 lm window/10 lm mask stripe openings), growth proceeds until the growth fronts from two adjacent {1122} facets meet. In the second step, pure nitrogen is used as carrier gas to achieve full coalescence and a flat surface (Fig. 2.35) [225]. The behavior of TDs is relatively similar to what was observed in 2S-ELO in MOVPE, they first propagate coherently with the TDs from the substrate, then most of them bend at 908 and propagate horizontally to terminate in the coalescence boundaries. Some bend at 908 in two steps (Fig. 2.36). Once again cross-sectional wavelength-resolved CL allows an in-depth evaluation of the evolution of the crystallographic quality and the density of incorporated impurities to be obtained. This is displayed in Fig. 2.37. The region A is the seed re-

Fig. 2.35 Cross-sectional SEM images of a 60-lm HVPE thick GaN layer showing the initial coalescence followed by a planar growth (openings 5 lm, period 15 lm) (from Wagner [226]).

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Fig. 2.36 TEM photograph of the dislocations in 2S-HVPE, marked region corresponds to those in Fig. 2.37 (from Wagner [226]).

(a)

(c)

(b)

12 lm

12 lm

Fig. 2.37 a SEM image; b CL wavelength cross-sectional mapping; c CL intensity images of a 2SHVPE ELO (thickness 15 lm) (from Wagner [226]).

gion, region B is grown in registry with the template presents about the same optical and crystallographic qualities: relatively narrow near band gap emission. Region C is laterally overgrown. The CL exhibits a broad blue-shifted emission with a high integrated intensity (most likely originating from defects or donor impurity concentration).

2.4 Two-Step ELO (2S-ELO)

2.4.4

ELO and Yellow Luminescence

Since in the ELO technology, whatever the process, TDs are not propagating uniformly through the layer, it would be possible to correlate the local occurrence of YL (evidenced from either l-PL or CL mapping) to the distribution of TDs or impurities or both. We have investigated, by spatially resolved photoluminescence, the GaN overgrown from hexagonal openings and partially coalesced pyramids obtained by MOVPE [105, 226]. Different positions of the overgrowth were analyzed, i.e., the edge of the coalesced pyramids, the center, the starting pyramids and the GaN underneath the dielectric. Whereas the photoluminescence (PL) spectra of starting pyramids and GaN underneath the dielectric are nearly the same, a drastic difference between the edge and the center of coalesced pyramids is observed. Two PL bands are observed at 300 K, namely the band-edge transition, at 3.41 eV and the yellow luminescence (YL) around 2.2 eV. The highest intensity of the 3.41 eV peak comes from the edge of the overgrowth and the lowest from the center. Conversely, the YL intensity is the strongest by one order of magnitude at the center of the overgrowth region. CL spectra, taken from an array of GaN islands obtained by SAE, show that the yellow emission comes from the pyramid apex. From the dislocations distribution in the pyramid, Li et al. [227] conclude that the YL emission does not come from TDs (which are almost eliminated within the penetration depth of 20-keV electrons), but from Si and O impurities incorporated as complexes with Ga vacancies and trapped in the stress field of dislocations [77]. From top-view and cross-sectional wavelength-resolved CL of SAE GaN on (111)Si, Cho et al. [228] point out similar features. Band-edge emission is nonuniform and is the highest at the top of the apex and over the lateral area, whereas YL originates from the part of the pyramid coherently grown from the openings. In 2S-ELO, we have investigated the wavelength distribution of a cross section of an ELO/sapphire by l-PL (Fig. 2.38). The YL appears only inside the triangular stripes and the coalescence boundaries. Conversely, it does not appear in any other part of the structure. Actually, TDs from the template continue to propagate

Fig. 2.38 CL wavelength image of a 2S-ELO, the YL appears only in the triangular stripes growth during the first step of the process (from Riemann [222]).

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2 Epitaxial Lateral Overgrowth of GaN Fig. 2.39 l-SIMS analysis of O concentration in a 2S-ELO sample on an 8 ´ 8 lm2 spot. The schematic of the ELO triangular stripe is plotted on the appropriate scale.

in registry inside the triangular stripe. However, the template does not show YL and is therefore a further proof that TDs are not responsible for YL. In order to better understand the YL that only occurs inside the triangular stripes above the openings of 2S-ELO (Fig. 2.38), l-SIMS analysis was carried out at the openings and at the coalescence boundaries (Fig. 2.39). The size of the etched spot was 8 lm. Two main features should be highlighted, (i) even though the mask is silicon nitride the incorporation of O during the first step is high, being several 1018 cm–3 (the incorporation of O in the template GaN is also significant, what means that O from the sapphire substrate diffuses), (ii) during the second step, the O concentration decreases significantly below 1018 cm–3. A test SIMS analysis on the non-ELO part of the sample shows that O incorporation on (0001) facets decreases with increasing temperature ([O] !(–E/kT) with E*2.3 eV). Inside the triangular stripes, the incorporation of O is slightly less than on the laterally overgrown part. Figure 2.39 can be understood as follows: after the growth of triangular stripes, the growth temperature is increased up to 1150 8C to enhance the lateral growth. The significantly high incorporation of O*2 ´ 1018 cm–3 results from growth on {1122} facets. It is well known that the incorporation of O in GaN is facet and polarity dependent. Above the apex, (0001) facets reappear, and [O] is decreased due to both temperatureand facet-dependent incorporation. A straightforward conclusion is that the strong YL, and consequently the low UV luminescence in the coalescence region of ELOG GaN, is linked to the occurrence of specific defects that act as nonradiative recombination centers. As suggested by Elsner et al. [77] the stress field in the core of dislocations could act as a trap for impurities like oxygen or intrinsic defects like VGa, and thereby enhance VGa-O complexes formation. This is also supported by the l-SIMS data.

2.5 New Trends

2.4.5

Conclusion

Improvements of the filtering of defects in ELO technology are achievable. More precisely, new modifications of the process, in which dislocations in the coalescence boundaries will be reduced, are in progress.

2.5

New Trends

The basic question put forward is the following: by how much should we reduce the dislocation density in GaN, and should we further improve the ELO technology? Nowadays, efforts to get better materials are taking place worldwide. 2.5.1

3S-ELO

It has been demonstrated that several steps led to ELO GaN with wider usable surfaces, free of emerging TDs. Even better quality can be foreseen with more than 2 steps at the expense of higher complexity. At Nichia [229], a three-step process has been implemented that reduces the TDs density in the mid-105 cm–2, and thereby allows the fabrication of LDs lasting 15,000 h with an output power of 30 mW. In this 3S-ELO, a standard MOVPE ELO GaN is first grown as discussed in Sect. 2.3.1. Then, on top of this ELO GaN, a 200-lm thick HVPE layer is grown. The sapphire substrate is then removed by polishing to get a 150-lm

Fig. 2.40 AFM scan of the top surface of 3S-ELO GaN, only mixed dislocations are merging. The total TDs density measured on the whole surface is 1 ´ 107 cm–2; between coalescence boundaries the TDs density is < 1 ´ 106 cm–2. TDs concentrate in the coalescence boundaries.

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free-standing GaN layer. Finally in the last step another ELO GaN is grown on top of this self-supported GaN. The final density of TDs decreases down to 7 ´ 105 cm–2. 1S-ELO on 2S-ELO with the mask in the second step located exactly above the first mask (to eliminate coalescence boundaries) further reduces the TDS density [230]. 2S-ELO on 1S-ELO produces similar results [231]. Figure 2.40 shows the AFM picture of the top surface of 3S-ELO, the TDs density over the entire surface is 1 ´ 107 cm–2, with very few TDs appearing between the coalescence boundaries (100-lm2 surfaces with only 1 dislocation gives a TDs density of 106 cm–2). In a recent new approach, starting from grooved stripe substrate as in [179–181], Ishida et al. [232] showed that when employing two regrowths on periodically grooved structure, the density of TDs went down to 6.3 ´ 106 cm–2. Once again, the bending of dislocations has proven to be efficient in reducing the TDs density. However, such achievements are obtained at the expense of an additional technological step. High-quality GaN substrates must remain at an affordable cost. 2.5.2

Further Improvements

Despite the incredibly high densities of dislocations in heteroepitaxial GaN, highly efficient optoelectronic devices have been fabricated and are currently entering our lives. However, it has been shown that long-lifetime laser diodes as demonstrated by Nichia required better quality GaN. ELO GaN brought material with dislocations density in the 106 cm–2 ranges, and made possible the fabrication of laser diodes. As discussed in the present chapter, ELO samples do not yet offer a full surface suitable for laser technology. Even the best-achieved material using 2S-ELO provides only 10 lm defect-free stripes that are usable. Besides, GaN ELO on sapphire does not provide an easily cleavable substrate for the laser diode technology. Although removing the substrate has been achieved, this remains a delicate task. It would be much more convenient to get self-supported GaN with ELO quality. This is already achieved by removing the sapphire substrate of the ELO GaN (or pendeo) GaN. A simpler route would be growing high-quality heteroepitaxial GaN on a chemically removable substrate (or sacrificial layer like Si, ZnO, LiAlO2, NdGaO3, and GaAs). Sumitomo [233] claimed that such self-supported GaN substrates will be on the market by 2002. These layers will be obtained from thick HVPE GaN on NdGaO3 and more recently on GaAs. Other techniques are also foreseen like the so-called smart-cut process (after hydrogen implantation and lift-off), very thin *100-nm GaN layers can be obtained and then thickened by HVPE. Figure 2.41 displays, on the same scale, the near band gap PL spectra of three “good-quality GaN layers”: a) GaN/sapphire using 3D nucleation, TDs density 5 ´ 108 cm–2, with a low-temperature PL linewidth of 3–4 meV. b) 2S-ELO GaN/sapphire, TDs density 5 ´ 106 cm–2, LT PL linewidth, < 1 meV. c) Homoepitaxial GaN grown on single crystal from UNIPRESS (Poland), TDs < 105 cm–2, LT PL linewidth < 0.1 meV.

2.6 Theoretical Analysis of ELO Fig. 2.41 Low-temperature PL spectra of 3D-nucleation GaN, ELO GaN and homoepitaxial GaN. Note the huge difference in bound exciton (I2) PL linewidth, 3–4 meV for 3D-nucleation GaN, < 1 meV for ELO and 0.1 meV for homoepitaxial GaN. Note also the different positions of the I2 peak, which corresponds to different degrees of biaxial compressive stress.

It should also be stressed that both ELO and heteroepitaxial GaN/sapphire are blue-shifted with respect of homoepitaxial GaN. This is due to biaxial compressive strain. Unquestionably, the best quality is achieved on homoepitaxial layers and the very few devices made on such substrates exhibit outstanding properties (l > 60,000 cm2 V–1s–1 in 2DEG [234], high-power LDs (UNIPRESS)). So far, the present technologies (high-temperature-high-pressure solution growth) do not produce the number of substrates matching the production needs. New projects are emerging; General Electric reported that a high-pressure-high-temperature growth facility is underway. New approaches are under development, e.g., solution growth in molten Na, sublimation growth. Indeed, the quality of GaN substrates is linked to the application that needs it, 3D-nucleation GaN/sapphire is good enough for LEDs, however, long-lifetime LDs requires at least ELO/GaN, and self-supported GaN of ELO quality would be more efficient.

2.6

Theoretical Analysis of ELO

From the above experimental background it appears that the lateral-to-vertical growth rate ratio depends on various parameters: temperature, pressure, composition of the gaseous phase, V/III ratio in the vapor phase, even NH3 flow interruptions. This means that any theoretical analysis should explain these features. Besides this, growth anisotropy, other features related to the facet-dependent incorporation of impurities or the role of impurities like Mg or Si in the growth morphology.

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Currently, MOVPE is understood as a mass-transfer-limited process: molecular species are brought to the growing interface where they are incorporated after surface diffusion. Quantifying the growth rates for different crystallographic facets requires an in-depth analysis of mass transfer and, more precisely, the accurate determination of surface kinetics constants for each facet. However, a correct analysis first requires the knowledge of surface reconstruction for different facets in the growth conditions. Incorporation of impurities strongly depends on the nature of the surface (and of the polarity) and as experimentally proven in ELOG GaN or homoepitaxial GaN growth on N or Ga faces. To date, modeling of the growth rate in MOVPE was analyzed on the basis of gas-phase kinetics coupled by a transport model describing flow, heat, and mass transfer. Several pertinent papers have been published that analyze the flow dynamics and the gas-phase chemistry [235–237]. However, gas–surface reactions were oversimplified. An appropriate model to fully describe the anisotropic growth rate must include the surface kinetics of incorporation of Ga and N molecular species for (0001), {1101} or {1120} facets. In the absence of such data from experiments, quantum chemistry should be developed to calculate the surface kinetics constants. Henceforth, this theoretical approach remains to be made!

2.7

Acknowledgments

This work is supported by the EU under contract TMR-EU 1999-00040 “IPAM”. At CHREA, the implementation of the 2S-ELO was initiated in the frame of LTREU contract “LAQUANI” 20968, continued with the support of EU (contracts BE “RAINBOW” BRPR-CT96-0340, INTAS 96-1031, EURONIM G5RD-CT-200100470), of ESA (contract ESTEC/13522/99) then developed with the support of the “Région Provence Côte d‘Azur”, the ANVAR (French Agency for Valorization of Research), the Ministry of Research and Technology and CNRS. The authors would like to acknowledge collaborating efforts and stimulating discussions with their colleagues at CRHEA, at ENS (Drs. E. Deleporte and M. Voos), at LSPES (Drs. B. Sieber and Dassonville), their partners in European Contracts, the Universities of Pretoria (SA) (Profs. D. Auret and S. Goodman), Magdeburg (Germany) (Prof. J. Christen and Dr. T. Riemann), and E. Feltin and E. Frayssinet, who provided unpublished results. Critical reading of the chapter by Drs. M. Leroux, G. Nataf, M.C. Wagener, and Prof. J.-P. Faurie is gratefully acknowledged.

2.8 References

2.8

References 1

2 3 4 5 6 7 8

9 10

11

12

13

14 15 16

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, Y. Sugimoto, T. Kozaki, H. Umemoto, M. Sano, and K. Chocho, Proceedings of ICNS’97, Tokushima, Japan, K. Hiramatsu (ed.) (1997), p. 444; J. Cryst. Growth 189/190, 820 (1998). D. W. Shaw, J. Electrochem. Soc. 113, 904(1966). R. W. McClelland, C. O. Bolzer, and J. C. C. Fan, Appl. Phys. Lett. 37, 560 (1980). L. Jastrzebski, J. Cryst. Growth 63, 493– 526 (1983). L. Liu and J.H. Edgar, Mater. Sci. Eng. 274, 1–67 (2002). O. Ambacher, J. Phys. D: Appl. Phys. 31, 2653–2710 (1998). H. Morkoç, Mater. Sci. Eng. R 33, 135– 207 (2001). B. Beaumont, P. Vennéguès, and P. Gibart, Optoelectronic Properties of Semiconductors and Superlattices, Gordon & Breach, O. Manasreh (ed.) to be published, 2002. P. Gibart and B. Beaumont, Proc. SPIE, to be published (2002). K. Hiramatsu, S. Itoh, H. Amano, I. Akasaki, N. Kuwano, T. Shiraishi, and K. Oki, J. Cryst. Growth 115, 628 (1991). I. Akasaki, H. Amano, Y. Koide, K. Hiramatsu, and N. Sawaki, J. Cryst. Growth 98, 98 (1989). P. Vennéguès, B. Beaumont, M. Vaille, and P. Gibart, J. Cryst. Growth 173, 249 (1997). X. H. Wu, P. Fini, S. Keller, E. J. Tarsa, B. Heying, U. K. Mishra, S. P. DenBaars, and J. S. Speck, Jpn. J. Appl. Phys. 35, 1648 (1996); X.H. Wu, D. Kapolnek, E.J. Tarsa, B. Heying, S. Keller, B. P. Keller, U. K. Mishra, S.P. DenBaars, and J.S. Speck, Appl. Phys. Lett. 68, 1371 (1996). S. Tanaka, S. Iwai, and Y. Aoyagi, Appl. Phys. Lett. 69, 4096 (1996). X.-Q. Shen, S. Tanaka, S. Iwai, and Y. Aoyagi, Appl. Phys. Lett. 72, 344 (1998). S. Haffouz, H. Lahrèche, P. Vennéguès, B. Beaumont, F. Omnès, and P. Gibart, Appl. Phys. Lett. 73, 1278 (1998).

17

18

19

20

21 22

23

24

25

26

27

28

29

30

S. Haffouz, B. Beaumont, P. Vénnègues, and P. Gibart, Phys. Stat. Sol. (a) 176, 677 (1999). D. J. Eagleasham, F. C. Unterwald, and D. C. Jacobson, Phys. Rev. Lett. 70, 966 (1993). J. Han, T.-B. Ng, R. M. Biefeld, M. H. Crawford, and D. M. Follstaedt, Appl. Phys. Lett. 71, 3114 (1997). S. Haffouz, V. Kirilyuk, P. R. Hageman, L. Macht, J. L. Weyher, and P. K. Larsen, Appl. Phys. Lett. 79, 2390–2392 (2001). S. Sakai, T. Wang, Y. Morishima, and Y. Naoi, J. Cryst. Growth 221, 334 (2000). E. Frayssinet, B. Beaumont, J. P. Faurie, P. Gibart, Zs. Makkai, B. Pécz, P. Lefebvre, P. Valvin, MRS Internet J. Nitride Semicond. Res. 7, 8 (2002). S. J. Rosner, E. C. Car, M. J. Ludowise, G. Girolami, and H. I. Erikson, Appl. Phys. Lett. 70, 420 (1997). T. Sugahara, H. Sato, M. Hao, Y. Naoi, S. Kurai, S. Tottori, K. Yamashita, K. Nishino, L. T. Romano, and S. Sakai, Jpn. J. Appl. Phys. 37, 398 (1998). T. Böttcher, S. Einfeldt, S. Figge, R. Chierchia, H. Heinke, D. Hommel, and J. S. Speck, Appl. Phys. Lett. 78, 1976 (2001). M. Iwaya, T. Takeuchi, S. Yamaguchi, C. Wetzel, H. Amano, and I. Akasaki, Jpn. J. Appl. Phys. 37, L316 (1998). H. Amano, M. Iwaya, T. Kashima, M. Katsuragawa, I. Akasaki, J. Han, S. Hearne, J. A. Floro, E. Chason, and J. Figiel, Jpn. J. Appl. Phys. 37, L1540 (1998). Chien-Cheng Yang, Meng-Chyi Wu, Chin-An Chang, and Gou-Chung Chi, J. Appl. Phys. 85, 8427–8431 (1999); Chien-Cheng Yang, Meng-Chyi Wu, Gou-Chung Chi, J. Appl. Phys. 86, 6120–6123 (1999). D. D. Koleske, M. E. Twigg, A. E. Wickenden, R. L. Henry, R. J. Gorman, and J. A. Freitas, Appl. Phys. Lett. 75, 3141 (1999). E. D. Bourret-Courchesne, S. Kellermann, K. M. Yu, M. Benamara, Z. Liliental-Weber, J. Washburn, S. J. C. Ir-

99

100

2 Epitaxial Lateral Overgrowth of GaN

31

32

33

34

35

36

37

38

39

40

41

42

43

vine, and A. Stafford, Appl. Phys. Lett. 77, 3562–3564 (2000). M. Benamara, Z. Liliental-Weber, S. Kellermann, W. Swider, J. Washburn, J. Mazur, and E. D. Bourret-Courchesne, J. Cryst. Growth 218, 447 (2000). Hyung Koun Cho, Jeong Yong Lee, Ki Soo Kim, Gye Mo Yang, Jae Ho Song, and Phil Won Yu, J. Appl. Phys. 89, 2617 (2000). Ki Soo Kim, Chang Seok Oh, Kang Jea Lee, Gye Mo Yang, Chang-Hee Hong, Kee Young Lim, Hyung Jae Lee, and Akihiko Yoshikawa, J. Appl. Phys. 85, 8441 (1999). Hyung Koun Cho, Jeong Yong Lee, Ki Soo Kim, Gye Mo Yang, Jae Ho Song, and Phil Won Yu, J. Appl. Phys. 89, 2671 (2001). Takahiro Ito, Masatomo Sumiya, Yasushi Takano, Kohji Ohtsuka, and Shunro Fuke, Jpn. J. Appl. Phys. 38, 649 (1999). T. Wang, T. Shirahama, H. B. Sun, H. X. Wang, J. Bai, S. Sakai, H. Misawa, Appl. Phys. Lett. 76, 2220 (2000). Tadao Hashimoto, Masaaki Yuri, Masahiro Ishida, Yoshitami Terakoshi, Osamu Imafuji, Takashi Sugino, and Kunio Itoh, Jpn. J. Appl. Phys. 38, 6605 (1999). H. Z. Xu, K. Takahashi, C. X. Wang, Z. G. Wang, Y. Okada, M. Kawabe, I. Harrison, and C. T. Foxon, J. Cryst. Growth 222, 110 (2001). Takayuki Yuasa, Yoshihiro Ueta, Yuhzoh Tsuda, Atushi Ogawa, Mototaka Taneya, and Katsutoshi Takao, Jpn. J. Appl. Phys. 38, L703–L705 (1999). S. Figge, T. Böttcher, S. Einfeldt, and D. Hommel, J. Cryst. Growth 221, 262 (2000). Shigeo Yamaguchi, Michihiko Kariya, Masayoshi Kosaki, Yohei Yukawa, Shugo Nitta, Hiroshi Amano, and Isamu Akasaki, J. Appl. Phys. 89, 7820 (2001). G. Pozina, J. P. Bergman, B. Monemar, S. Yamaguchi, H. Amano, and I. Akasaki, Appl. Phys. Lett. 76, 3388 (2000). Shigeo Yamaguchi, Michihiko Kariya, Shugo Nitta, Hiroshi Amano, and Isamu Akasaki, Appl. Phys. Lett. 75, 4106 (1999).

44

45

46

47

48

49

50 51

52 53

54

55

56

57

58

59

60

S. Yamaguchi, M. Kariya, S. Nitta, T. Kashima, M. Kosaki, Y. Yukawa, H. Amano, and I. Akasaki, J. Cryst. Growth 221, 327 (2000). H. M. Chung, W. C. Chuang, Y. C. Pan, C. C. Tsai, M. C. Lee, W. H. Chen, W. K. Chen, C. I. Chiang, C. H. Lin, and H. Chang, Appl. Phys. Lett. 76, 897 (2000). Da-Cheng Lu, Chengxin Wang, Hairong Yuan, Xianglin Liu, and Xiaohui Wang, J. Cryst. Growth 221, 356 (2000). T. Asano, K. Yanashima, T. Asatsuma, T. Hino, T. Yamaguchi, S. Tomiya, K. Funato, T. Kobayashi, and M. Ikeda, Phys. Stat. Sol. (a) 176, 23 (1999). B. L. Liu, M. Lachab, A. Jia, A. Yoshikawaa, and K. Takahashi, J. Cryst. Growth, 234, 637 (2002). D. Huang, M. A. Reshchikov, F. Yun, T. King, A. A. Baski, and H. Morkoç, Appl. Phys. Lett. 80, 216 (2002). F. A. Ponce, MRS Bull. 22, 51 (1997). W. Quian, G. S. Rohrer, M. Skowronski, K. Doverspike, L. B. Rowland, and D. K. Gaskill, Appl. Phys. Lett. 67, 2284 (1995). P. Ruterana and G. Nouet, Phys. Stat. Sol. (b) 227, 177–228 (2001). P. Hacke, T. Detchprohm, K. Hiramatsu, N. Sawaki, K. Tadatomo, and K. Miyake, J. Appl. Phys. 76, 304 (1994). P. Hacke, H. Nakayama, T. Detchprohm, K. Hiramatsu, and N. Sawaki, Appl. Phys. Lett. 68, 1362 (1996). F. D. Auret, S. A. Goodman, F. K. Koschnick, J.-M. Spaeth, B. Beaumont, and P. Gibart, Appl. Phys. Lett. 74, 407 (1999). P. Muret, A. Philippe, E. Monroy, E. Muñoz, B. Beaumont, F. Omnès, and P. Gibart, J. Appl. Phys. 91, 2998 (2002). B. Heying, E. J. Tarsa, C. R. Elsass, P. Fini, S. P. DenBaars, and J. S. Speck, J. Appl. Phys. 85, 6470 (1999). X. H. Wu, C. R. Elsass, A. Abare, M. Mack, S. Keller, P. M. Petroff, S. P. DenBaars, J. S. Speck, and S. J. Rosner, Jpn. J. Appl. Phys. Part 2 37, L398 (1998). T. Tojyo, T. Asano, M. Takeya, T. Hino, S. Kijima, S. Goto, S. Uchida, and M. Ikeda, Jpn. J. Appl. Phys. 40, 3206 (2001). N. G. Weimann, L. F. Eastman, D. Dharanipal, H. M. Ng, and T. D. Moustakas, J. Appl. Phys. 83, 3656 (1998).

2.8 References 61

62

63 64

65 66

67

68

69

70 71

72

73

74 75

J. L. Farvaque, Phys. Rev. B 62, 2536, (2000); J.-L. Farvacque, Z. Bougrioua, and I. Moerman, Phys. Rev. B 63, 115202 (2001). P. J. Hansen, Y. E. Strausser, A. N. Erickson, E. J. Tarsa, P. Kozodoy, E. G. Brazel, J. P. Ibbetson, U. Mishra, V. Narayanamurti, S. P. DenBaars, and J. S. Speck, Appl. Phys. Lett. 72, 2247 (1998). C. Youtsey, L. T. Romano, and I. Adesida, Appl. Phys. Lett. 73, 797 (1998). H. Marchand, J. P. Ibbetson, P. T. Fini, P. Kozodoy, S. Keller, S. DenBaars, J. S. Speck, and U. K. Mishra. MRS Internet J. Nitride Semicond. Res. 3, 3 (1998). H. Watanabe, Appl. Phys. Lett. 77, 1786 (2000). T. Hino, S. Tomiya, T. Miyajima, K. Yanashima, S. Hashimoto, and M. Ikeda, Appl. Phys. Lett. 76, 3421 (2000). S. F. Chichibu, K. Torii, T. Deguchi, T. Sato, A. Setoguchi, H. Nakanishi, T. Azuhata, and S. Nakamura, Appl. Phys. Lett. 76, 1576 (2000). S. D. Lester, F. A. Ponce, M. G. Craford, and D. A. Steigerwald, Appl. Phys. Lett. 66, 1249 (1995). J. Elsner, R. Jones, P. K. Sitch, V. D. Porezag, M. Elstner, T. Frauenheim, M. I. Heggie, S. Oberg, and P. R. Briddon, Phys. Rev. Lett. 79, 3672 (1997). J. S. Speck and S. J. Rosner, Physica B 273/274, 24 (1999). S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, Y. Sugimoto, T. Kozaki, H. Umemoto, M. Sano, and K. Chocho, Appl. Phys. Lett. 72, 211 (1998). S. Keller, B. P. Keller, Y. F. Wu, B. Heying, D. Kapolnek, J. S. Speck, U. K. Mishra, and S. P. DenBaars, Appl. Phys. Lett. 68, 1525 (1996). T.-B. Ng, J. Han, R. M. Biefeld, and M. V. Weckwerth, J. Electron. Mater. 27, 190 (1998). J. E. Northrup, Appl. Phys. Lett. 78, 2288 (2001). Y. Xin, S. J. Pennycook, N. D. Browning, P. D. Nellist, S. Sivananthan, J.-P. Faurie, and P. Gibart, Appl. Phys. Lett. 72, 2680 (1998).

76

77 78 79

80

81 82 83 84

85 86

87 88 89

90

91

92

93

J. Elsner, M. Kaukonen, M. I. Heggie, M. Haugk, Th. Frauenheim, and R. Jones, Phys. Rev. 58, 15357 (1998). F. Wright and J. Furthmuller, Appl. Phys. Lett. 72, 3467 (1998). Seung Mi Lee et al. Phys. Rev. B 61, 16033 (2000). T. Temmemle, M. Albrecht, H. P. Strunk, A. T. Blumenau, M. I. Heggie, J. Elsner, T. Frauenheim, H. P. D. Schenk, and P. Gibart, Inst. Phys. Conf. Ser. 169, 323 (2001). Y. Xin, E. M. James, I. Arslan, S. Sivananthan, N. D. Browning, S. J. Pennycook, F. Omnès, B. Beaumont, J.-P. Faurie, and P. Gibart, Appl. Phys. Lett. 76, 466 (2000). C. Stampfl and C. G. Van de Walle, Phys. Rev. B 57, R15052 (1998). J. E. Northrup, Appl. Phys. Lett. 72, 2316 (1998). Z. Z. Bandic, T. C. McGill, and Z. Ikonic, Phys. Rev. B 56, 35664 (1997). E. Calleja, F. J. Sanchez, F. Calle, J. M. G. Tijero, J. L. Sanchez-Rojas, B. Beaumont, P. Lorenzini, and P. Gibart, Phys. Rev. B 55, 4689 (1997). J. Neugebauer and C. Van de Walle, Appl. Phys. Lett. 69, 503 (1995). T. Mattila, A. P. Seitsonen, and R. M. Nieminen, Phys. Rev. B 54(3),1474 (1996). T. Mattila and R. M. Nieminen, Phys. Rev. B 55, 9571 (1997). H. M. Chen, Y. F. Chen, M. C. Lee, and M. S. Feng, Phys. Rev. B 56, 6942 (1997). D. Kapolnek, S. Keller, R. Vetury, R. D. Underwood, P. Kozodoy, S. P. Denbaars, and U. K. Mishra, Appl. Phys. Lett. 71, 1204 (1997). O.-H. Nam, M. D. Bremser, B. L. Ward, R. J. Nemanich, and R. F. Davis, Jpn. J. Appl. Phys. 36(5A), L532 (1997). O.-H. Nam, M. D. Bremser, T. S. Zheleva, and R. F. Davis, Appl. Phys. Lett. 71, 2638 (1997). H. Marchand, X. H. Wu, J. P. Ibbetson, P. T. Fini, P. Kozodoy, S. Keller, J. S. Speck, S. P. DenBaars, and U. K. Mishra, Appl. Phys. Lett. 73, 747 (1998). A. Usui, H. Sunakawa, A. Sakai, and A. A. Yamaguchi, Jpn. J. Appl. Phys. 36, L899 (1997).

101

102

2 Epitaxial Lateral Overgrowth of GaN 94 A. Sakai, H. Sunakawa, and A. Usui, 95

96

97

98

99

100

101

102

103 104

105

106

107

108

109

Appl. Phys. Lett. 71, 2259 (1997). T. S. Zheleva, Ok-Hyun Nam, W. M. Ashmawi, J. D. Griffin, and R. F. Davis, J. Cryst. Growth 222, 706 (2001). T. S. Zheleva, F. Karoui, K. Kirchner, M. Derenge, K. A. Jones, R. D. Vispute, and T. Venkatesan, Mater. Res. Soc. Symp. Proc. 636, G5.1.1. (2001). R. F. Davis, T. Gehrke, K. J. Linthicum, E. Preble, Pradeep Rajagopal, C. Ronning, C. Zorman, and Mehran Mehregany, J. Cryst. Growth 231, 335 (2001). Y. Kato, S. Kitamura, K. Hiramatsu, and N. Sawaki, J. Cryst. Growth 144, 133 (1994). T. Akasaka, Y. Kobayashi, S. Ando, and N. Kobayashi, Appl. Phys. Lett. 71, 2196 (1997). P. Gibart, A. Tromson-Carli, Y. Monteil, and A. Rudra, J. Phys. 50, C5–529 (1989). Zhonghai Yu, M. A. L. Johnson, J. D. Brown, N. A. El-Masry, J. F. Muth, J. W. Cook Jr, J. F. Schetzina, K. W. Haberern, H. S. Kong, and J. A. Edmond, MRS Internet J. Nitride Semicond. Res. 4S1, G4.3 (1999). T. S. Zheleva, O.-H. Nam, M. D. Bremser, and R. F. Davis, Appl. Phys. 71, 2472 (1997). S. Kurai, K. Nishino, and S. Sakai, Jpn. J. Appl. Phys. 36, L184 (1997). J. Wang, S. Tottori, H. Sato, M.-S. Hao, Y. Ishikawa, T. Sugahara, K. Yamashita, and S. Sakai, Jpn. J. Appl. Phys. 37, 4475 (1998). B. Beaumont, P. Gibart, M. Vaille, S. Haffouz, G. Nataf, and A. Bouillé, J. Cryst. Growth 189/190, 97 (1998). J. Park, P. A. Grudowski, C. J. Eiting, and R. D. Dupuis, Appl. Phys. Lett. 73, 333 (1998). O.-H. Nam, T. S. Zheleva, M. D. Bremser, and R. F. Davis, J. Electron. Mater. 27, 233 (1998). Kazuyuki Tadatomo, Yoichiro Ohuchi, Hiroaki Okagawa, Hirotaka Itoh, Hideto Miyake, and Kazumasa Hiramatsu, MRS Internet J. Nitride Semicond. Res. 4S1, G3.1 (1999). H. Marchand, J. P. Ibbetson, P. T. Fini, X. H. Wu, S. Keller, S. P. DenBaars,

110

111

112

113 114

115 116

117

118

119 120

121

122

J. S. Speck, and U. K. Mishra, MRS Internet J. Nitride Semicond. Res. 4S1, G4.5 (1999). K. Hiramatsu, K. Nishiyama, A. Motogaito, H. Miyake, Y. Iyechika, and T. Maeda, Phys. Stat. Sol. (a) 176, 535 (1999). H. Marchand, J. P. Ibbetson, P. T. Fini, S. P. DenBaars, J. S. Speck, and U. K. Mishra, J. Cryst. Growth 195, 328 (1998). B. Beaumont, M. Vaille, G. Nataf, A. Bouillé, J.-C. Guillaume, P. Vennéguès, S. Haffouz, and P. Gibart, MRS Internet J. Nitride Semicond. Res. 3, 20 (1998); B. Beaumont, P. Gibart, J.C. Guillaume, G. Nataf, M. Vaille, and S. Haffouz, WO98 02212. B. Beaumont, S. Haffouz, and P. Gibart, Appl. Phys. Lett. 72(8), 921 (1998). S. Haffouz, B. Beaumont, and P. Gibart, MRS Internet J. Nitride Semicond. Res. 3, 8 (1998). L. Zhang, H. F. Tang, and T. F. Kuech, Appl. Phys. Lett. 79, 3059 (2001). Yasutoshi Kawaguchi, Shingo Nambu, Hiroki Sone, Masahito Yamaguchi, Hideto Miyake, Kazumasa Hiramatsu, Nobuhiko Sawaki, Yasushi Iyechika, and Res Takayoshi Maeda, MRS Internet J. Nitride Semicond. Res. 4S1, G4.1 (1999). Y. Kawaguchi, S. Nambu, M. Yamaguchi, N. Sawaki, H. Miyake, K. Hiramatsu, K. Tsukamoto, N. Kuwano, and K. Oki, Phys. Stat. Sol. (a) 176, 561 (1999). Y. Kawaguchi, Y. Honda, M. Yamaguchi, N. Sawaki, and K. Hiramatsu, Phys. Stat. Sol. (a) 176, 553 (1999). X. Zhang, P. D. Dapkus, and D. H. Rich, Appl. Phys. Lett. 77, 1496 (2000). R. S. Qhalid Fareed, J. W. Yang, Jianping Zhang, Vinod Adivarahan, Vinamra Chaturvedi, and M. Asif Khan, Appl. Phys. Lett. 77, 2343 (2000). Shugo Nitta, Takayuki Kashima, Michihiko Kariya, Yohei Yukawa, Shigeo Yamaguchi, Hiroshi Amano, and Isamu Akasaki, MRS Internet J. Nitride Semicond. Res. 5S1, W2.8 (2000). Z. Lilienthal-Weber, M. Benamara, W. Swider, J. Washburn, J. Park, P. A. Grudowski, C. J. Eiting, and R. D. Du-

2.8 References

123 124

125

126

127

128

129

130 131

132

133

134

135

136

puis, MRS Internet J. Nitride Semicond. Res. 4S1, G4.6 (1999). Z. Liliental-Weber, and D. Cherns, J. Appl. Phys. 89, 7833 (2001). P. Hacke, K. Domen, A. Kuramata, T. Tanahashi, and O. Ueda, Appl. Phys. Lett. 76, 2547 (2001). A. Sakai, H. Sunakawa, and A. Usui, Appl. Phys. Lett. 73, 481 (1998); A. Sakai, H. Sunakawa, A. Kimura, and A. Usui, Appl. Phys. Lett. 76, 442 (2000). P. Fini, L. Zhao, B. Moran, M. Hansen, H. Marchand, J. P. Ibbetson, S. P. DenBaars, U. K. Mishra, and J. S. Speck, Appl. Phys. Lett. 75, 1706 (1999). C. C. Mitchell, M. E. Coltrin, and Jung Han, J. Cryst. Growth 222, 144 (2001); M. E. Coltrin, C. C. Willan, M. E. Bartram, Jung Han, N. Missert, M. H. Crawford, and A. G. Baca, MRS Internet J. Nitride Semicond. Res. 4S1, G6.9 (1999). K. Kobayashi, A. Atsushi Yamaguchi, S. Kimura, H. Sunakawa, A. Kimura, and A. Usui, Jpn. J. Appl. Phys. 38, L611 (1999). M. Pophristic, F. H. Long, M. Schurman, J. Ramer, and I. T. Ferguson, Appl. Phys. Lett. 74, 3519 (1999). X. Li, S. G. Bishop, and J. J. Coleman, Appl. Phys. Lett. 73, 1179 (1998). S. J. Rosner, G. Girolami, H. Marchand, P. T. Fini, J. P. Ibbetson, L. Zhao, S. Keller, U. K. Mishra, S. P. DenBaars, and J. S. Speck, Appl. Phys. Lett. 74, 2035 (1999). J. A. Freitas Jr, Ok-Hyun Nam, R. F. Davis, G. V. Saparin, and S. K. Obyden, Appl. Phys. Lett. 72, 2990 (1998). T. S. Zheleva, W. M. Ashmawi, Ok-Hyun Nam, and R. F. Davis, Appl. Phys. Lett. 74, 2492 (1999). Noriyuki Kuwano, Kayo Horichi, Koji Kagawa, Shigefumi Nishimoto, and Manabu Sueyoshi, J. Cryst. Growth 237–239, 1047 (2002). X. Li, P. W. Bohn, Jeongyong Kim, J. O. White, and J. J. Coleman, Appl. Phys. Lett. 76, 3031 (2000). Q. K. K. Liu, A. Hoffman, H. Siegle, A. Kaschner, C. Thomsen, J. Christen, and F. Bertram, Appl. Phys. Lett. 74, 3122 (1999).

137 V. M. Asnin, F. H. Pollak, J. Ramer, M.

138

139

140

141

142

143

144

145

146

147

148

149

150

Schurman, and I. Ferguson, J. Appl. Phys. 75, 1240 (1999). D. I. Florescu, V. M. Asnin, F. H. Pollak, A. M. Jones, J. C. Ramer, M. J. Schurman, and I. Ferguson, Appl. Phys. Lett. 77, 1464 (2000). C.-Y. Luo, H. Marchand, D. R. Clarke, and S. P. DenBaars, Appl. Phys. Lett. 75, 4151 (1999). A. Usui, H. Sunakawa, K. Kobayashi, H. Watanabe, and M. Mizuta, Mater. Res. Soc. Symp. Proc. 639, G5.6.1 (2001). T. S. Kuan, C. K. Inoki, Y. Hsu, D. L. Harris, R. Zhang, S. Gu, and T. F. Kuech, MRS Internet J. Nitride Semicond. Res. 5S1, W2.6 (2000). S. Hearne, E. Chason, J. Han, J. A. Floro, J. Figiel, J. Hunter, H. Amano, and I. S. T. Tsong, Appl. Phys. Lett. 74, 356 (1999). K. Hiramatsu, H. Matsushima, T. Shibata, N. Sawaki, K. Tadatomo, H. Okagawa, Y. Ohuchi, Y. Honda, and T. Matsue, Mater. Res. Soc. Symp. Proc. 482, 257 (1998). G. Nataf, B. Beaumont, A. Bouillé, S. Haffouz, M. Vaille, and P. Gibart, J. Cryst. Growth 192, 73 (1998). O. Parillaud, V. Wagner, H. J. Buehlmann, and M. Ilegems, MRS Internet J. Nitride Semicond. Res. 3, 40 (1998). J. Holst, A. Kaschner, A. Hoffmann, P. Fischer, F. Bertram, T. Riemann, J. Christen, K. Hiramatsu, T. Shibata, and N. Sawaki, Appl. Phys. Lett. 75, 3647 (1999). Shinya Bohyama, Kenji Yoshikawa, Hiroyuki Naoi, Hideto Miyake, Kazumasa Hiramatsu, Yasushi Iyechika, and Takayosi Maeda, Jpn. J. Appl. Phys. 41, 75 (2002). M. J. Matthews, J. W. P. Hsu, Shulin Gu, and T. F. Kuech, Appl. Phys. Lett. 79, 3086 (2001). J. W. P. Hsu, M. J. Matthews, D. Abusch-Magder, R. N. Kleiman, D. V. Lang, S. Richter, S. L. Gu, and T. F. Kuech, Appl. Phys. Lett. 79, 761 (2001). F. Bertram, T. Riemann, J. Christen, A. Kaschner, A. Hoffmann, C. Thomsen, K. Hiramatsu, T. Shibata, and N. Sawaki, Appl. Phys. Lett. 74, 359 (1999).

103

104

2 Epitaxial Lateral Overgrowth of GaN 151 A. Kaschner, A. Hoffmann, C. Thom-

152

153

154

155

156

157

158

159

160

161

162

163

164

165

sen, F. Bertram, T. Riemann, J. Christen, K. Hiramatsu, T. Shibata, and N. Sawaki, Appl. Phys. Lett. 74, 3320 (1999). Masahiro Yoshimoto, Junji Saraie, and Shuji Nakamura, Jpn. J. Appl. Phys. 40, L386 (2001). Q. Liu, A. Hoffmann, A. Kaschner, C. Thomsen, J. Christen, P. Veit, and R. Clos, Jpn. J. Appl. Phys. 39, L958 (2000). M. Holtz, M. Seon, T. Prokofyeva, H. Temkin, R. Singh, F. P. Dabkowski, and T. D. Moustakas, Appl. Phys. Lett. 75, 1757 (1999). Q. K. K. Liu, A. Hoffmann, H. Siegle, A. Kaschner, C. Thomsen, J. Christen, and F. Bertram, Appl. Phys. Lett. 75, 3122 (1999). R. Zhang, L. Zhang, D. M. Hansen, M. P. Boleslawski, K. L. Chen, D. Q. Lu, B. Shen, Y. D. Zheng, and T. F. Kuech, MRS Internet J. Nitride Semicond. Res. 4S1, G4.7 (1999). K. A. Dunn, S. Babcock, D. S. Stone, R. J. Matyi, Ling Zhang, and T. F. Kuech, MRS Internet J. Nitride Semicond. Res. 5S1, W2.11 (2000). L. Zhang, S. L. Gu, R. Zhang, D. M. Hansen, M. P. Boleslawski, and T. F. Kuech, J. Cryst. Growth 235, 115 (2002). Z. Feng, E. Lovell, R. Engelstad, T. Kuech, and S. Babcock, Appl. Phys. Lett. 80, 1547 (2002). M. Hao, S. Mahanty, T. Sugahara, Y. Morishima, H. Takenaka, J. Wang, S. Tottori, K. Nishino, Y. Naoi, and S. Sakai, J. Appl. Phys. 85, 6497 (1999). Jie Wang, R. S. Qhalid Fareed, M. Hao, S. Mahanty, S. Tottori, Y. Ishikawa, T. Sugahara, Y. Morishima, K. Nishino, M. Osinski, and S. Sakai, J. Appl. Phys. 85, 1895 (1999). R. S. Qhalid Fareed, S. Tottori, T. Inaoka, K. Nishino, and S. Sakai, J. Cryst. Growth 207, 174 (1999). Y. Kawaguchi, Y. Honda, H. Matsushima, M. Yamaguchi, K. Hiramatsu, and N. Sawaki, Jpn. J. Appl. Phys. 37, L966 (1998). P. Kung, D. Walker, M. Hamilton, J. Diaz, and M. Razeghi, Appl. Phys. Lett. 74, 570 (1999). Zhigang Mao, S. McKernan, C. B. Carter, Wei Yang, and S. A. McPherson,

166

167

168

169 170

171

172 173

174

175

176

177

178

179

MRS Internet J. Nitride Semicond. Res. 4S1, G3.13 (1999). Wei Yang, S. A. McPherson, Zhigang Mao, S. McKerman, and C. B. Carter, J. Cryst. Growth 204, 273 (1999). Shigeyasu Tanaka, Yasutoshi Kawaguchi, Nobuhiko Sawaki, Michio Hibino, and Kazumasa Hiramatsu, Appl. Phys. Lett. 76, 2701 (2000). Y. Honda, Y. Kawaguchi, Y. Ohtake, S. Tanaka, M. Yamaguchi, and N. Sawaki, J. Cryst. Growth 230, 346 (2001). E. Feltin et al., Appl. Phys. Lett. to be published. Shigeyasu Tanaka, Yoshio Honda, Nobuhiko Sawaki, and Michio Hibino, Appl. Phys. Lett. 79, 955 (2001). N. P. Kobayashi, J. T. Kobayashi, X. Zhang, P. D. Dapkus, and D. H. Rich, Appl. Phys. Lett. 74, 2836 (1999). Y. Kawaguchi et al., Jpn. J. Appl. Phys. 37, L845 (1998). H. Sone, S. Nambu, Y. Kawaguchi, M. Yamaguchi, H. Miyake, K. Hiramatsu, Y. Iyechika, T. Maeda, and N. Sawaki, Jpn. J. Appl. Phys. 38, L356 (1999). Hideto Miyake, Motoo Yamaguchi, Masahiro Haino, Atsushi Motogaito, Kazumasa Hiramatsu, Shingo Nambu, Yasutoshi Kawaguchi, Nobuhiko Sawaki, Yasushi Iyechika, Takayoshi Maeda, and Isamu Akasaki, MRS Internet J. Nitride Semicond. Res. 5S1, W2.3 (2000). Masahiro Haino, Motoo Yamaguchi, Hideto Miyake, Atsushi Motogaito, Kazumasa Hiramatsu, Yasutoshi Kawaguchi, Nobuhiko Sawaki, Yasushi Iyechika, Takayoshi Maeda, Ying-Jay Yang, Jia-Liang Yen, Fuh-Shyang Yang, and Ching-Yen Lin, Jpn. J. Appl. Phys. 39, L390 (2000). J. A. Smart, E. M. Chumbes, A. T. Schremer, and J. R. Shealy, Appl. Phys. Lett. 75, 3820 (1999). C. I. H. Ashby, C. C. Mitchell, Jung Han, N. A. Missert, P. P. Provencio, D. M. Follstaedt, G. M. Peake, and L. Griego, Appl. Phys. Lett. 77, 3233 (2000). T. M. Katona, M. D. Craven, P. T. Fini, J. S. Speck, and S. P. DenBaars, Appl. Phys. Lett. 79, 2907 (2001). Shigekazu Sano, Theeradetch Detchprohm, Shingo Mochizuki, Satoshi

2.8 References

180

181

182

183 184

185

186

187

188

189

190

191

Kamiyama, Hiroshi Amano, and Isamu Akasaki, J. Cryst. Growth 235, 129 (2002). Theeradetch Detchprohm, Masahiro Yano, Shigekazu Sano, Ryo Nakamura, Shingo Mochiduki, Tetsuya Nakamura, Hiroshi Amano, and Isamu Akasaki, Jpn. J. Appl. Phys. 40, L16 (2001). T. Detchprohm, M. Yano, R. Nakamura, S. Sano, S. Mochiduki, T. Nakamura, H. Amano, and I. Akasaki, Mater. Res. Soc. Symp. Proc. 639, G5.7.1 (2001). A. Strittmatter, S. Rodt, L. Reißmann, D. Bimberg, H. Schröder, E. Obermeier, T. Riemann, J. Christen, and A. Krost, Appl. Phys. Lett. 78, 727 (2001). X. Zhang, R. R. Li, P. D. Dapkus, and D. H. Rich, Appl. Phys. Lett. 77, 2213 (2000). O.-H. Nam, T. S. Zheleva, M. D. Bremser, D. B. Thomson, and R. F. Davis, Mater. Res. Soc. Symp. Proc. 482, 301 (1998). D. B. Thomson, T. Gehrke, K. J. Linthicum, P. Rapagopal, and R. F. Davis, MRS Internet J. Nitride Semicond. Res. 4S1, G3.37 (1999). K. Linthicum, T. Gehrke, D. Thomson, E. Carlson, P. Rajagopal, T. Smith, D. Batchelor, and R. Davis, Appl. Phys. Lett. 75, 196 (1999). K. J. Linthicum, T. Gehrke, D. B. Thomson, K. M. Tracy, E. P. Carlson, T. P. Smith, T. S. Zheleva, C. A. Zorman, M. Mehregany, and R. F. Davis, MRS Internet J. Nitride Semicond. Res. 4S1, G4.9 (1999). T. Gehrke, K. J. Linthicum, D. B. Thomson, P. Rajagopal, A. D. Batchelor, and R. F. Davis, MRS Internet J. Nitride Semicond. Res. 4S1, G3.2 (1999). T. S. Zheleva, S. A. Smith, D. B. Thomson, T. Gehrke, K. J. Linthicum, Pradeep Rajagopal, E. Carlson, W. M. Ashmawi, and R. F. Davis, MRS Internet J. Nitride Semicond. Res. 4S1, G3.38 (1999). R. F. Davis, T. Gehrke, K. J. Linthicum, T. S. Zheleva, E. A. Preble, P. Rajagopal, C. A. Zorman, and M. Mehregany, J. Cryst. Growth 225, 134–140 (2001). R. F. Davis, T. Gehrke, K. J. Linthicum, P. Rajagopal, A. M. Roskowski, T. Zheleva, E. A. Preble, C. A. Zorman, M. Mehregany, U. Schwarz, J. Schuck, and R. Grober, MRS Internet J. Nitride Semicond. Res. 6, 14 (2001).

192 Ig-Hyeon Kim, C. Sone, Ok-Hyun Nam,

193

194

195 196

197

198

199

200

201

202

203

204 205 206

207

208

Yong-Jo Park, and Taeil Kim, Appl. Phys. Lett. 75, 4109 (1999). T. Gehrke, K. J. Linthicum, Pradeep Rajagopal, E. A. Preble, and R. F. Davis, MRS Internet J. Nitride Semicond. Res. 5S1, W2.4 (2000). T. Gehrke, K. J. Linthicum, E. Preble, P. Rajagopal, C. Ronning, C. Zorman, M. Mehregany, and R. F. Davis, J. Electron. Mater. 29, 306 (2000). T. S. Zheleva, W. M. Ashmawi, and K. A. Jones, Phys. Stat. Sol. (a) 176, 545 (1999). T. S. Zheleva, S. A. Smith, D. B. Thomson, K. J. Linthicum, P. Rajagopal, and R. F. Davis, J. Electron. Mater. 28, L5 (1999). S. Einfeldt, A. M. Roskowski, E. A. Preble, and R. F. Davis, Appl. Phys. Lett. 80, 953 (2002). A. M. Roskowski, P. Q. Miraglia, E. A. Preble, S. Einfeldt, T. Stiles, R. F. Davis, J. Schuck, R. Grober, and U. Schwarz, Phys. Stat. Sol. (a) 188, 729– 732 (2001). Y. Chen, R. Schneider, S. Y. Wang, R. S. Kern, C. H. Chen, and C. P. Kuo, Appl. Phys. Lett. 75, 2062 (1999). Isao Kidoguchi, Akihiko Ishibashi, Gaku Sugahara, and Yuzaburoh Ban, Appl. Phys. Lett. 76, 3768 (2000). Isao Kidoguchi, Akihiko Ishibashi, Gaku Sugahara, Ayumu Tsujimura, and Yuzaburoh Ban, Jpn. J. Appl. Phys. 39, L453 (2000). Akihiko Ishibashi, Isao Kidoguchi, Gaku Sugahara, and Yuzaburoh Ban, J. Cryst. Growth 221, 338 (2001). Yi Fu, Hui Yang, D. G. Zhao, X. H. Zheng, S. F. Li, Y. P. Sun, Z. H. Feng, Y. T. Wang, and L. H. Duan, J. Cryst. Growth 225, 45 (2001). R. F. Davis, O.-H. Nam, T. Zheleva, and M. Bremser, WO99/44224. M. Ikeda, US 6111277 (2000). L. Sugiura, M. Ishikawa, S. Nunoue, M. Onomura, and M. Yamamoto, US 6015979 (2000). P. Vennéguès, B. Beaumont, V. Bousquet, M. Vaille, and P. Gibart, J. Appl. Phys. 87, 4175 (2000). B. Beaumont, V. Bousquet, P. Vennéguès, M. Vaille, A. Bouillé, P. Gibart, S.

105

106

2 Epitaxial Lateral Overgrowth of GaN

209

210 211

212

213

214 215

216

217

218 219

220

221 222

223

224

Dassonneville, A. Amokrane, and B. Sieber, Phys. Stat. Sol. (a) 176, 567 (1999). V. Bousquet, P. Vennéguès, B. Beaumont, M. Vaille, and P. Gibart, Phys. Stat. Sol. (b) 216, 691 (1999). J. Hirth and J Lothe, in Theory of Dislocations (Wiley, New York, 1982). K. Hiramatsu, K. Nishiyama, M. Onishi, H. Mizutani, M. Narukawa, A. Motogaito, H. Miyake, Y. Iyechika, and T. Maeda, J. Cryst. Growth 221, 316 (2000). Yoshiaki Honda, Yasushi Iyechika, Takayoshi Maeda, Hideto Miyake, and Kazumasa Hiramatsu, Jpn. J. Appl. Phys. 40, L309 (2001). H. Miyake, M. Narukawa, K. Hiramatsu, H. Naoi, Y. Iyechika, and T. Maeda, Phys. Stat. Sol. (a) 188, 725 (2001). T. Riemann and J. Christen, private communication (2000). S. Dassonneville, A. Amokrane, B. Sieber, J.-L. Farvacque, B. Beaumont, P. Gibart, J.-D. Ganiere, and K. Leifer, J. Appl. Phys. 89, 7966 (2001). S. Dassonneville, A. Amokrane, B. Sieber, J.-L. Farvacque, B. Beaumont, and P. Gibart, J. Appl. Phys. 89, 3736 (2001). J. Christen, T. Riemann, B. Beaumont, and P. Gibart, MRS 2000, Fall meeting (2000). A. Hoffmann and L. Eckey, Mater. Sci. Forum 264/268, 1259 (1998). S. Hess, F. Walraet, R.A. Taylor, J. F. Ryan, B. Beaumont, and P. Gibart, Phys. Rev. B 58, R15973 (1998). M. Wraback, H. Shen, C. J. Eiting, J. C. Carrano, and R. D. Dupuis, MRS Internet J. Nitride Semicond. Res. 5S1, W11.55 (2000). F. D. Auret, private communication (2000). M. Kuball, M. Benyoucef, B. Beaumont, and P. Gibart, J. Appl. Phys. 90, 3956 (2001). M. Benyoucef, M. Kuball, G. Hill, M. Wisnom, B. Beaumont, and P. Gibart, Appl. Phys. Lett. 79, 4127 (2001). D. E. Deleporte, C. Guénaud, M. Voos, B. Beaumont, and P. Gibart, J. Appl. Phys. 89, 1116 (2001).

225 V. Wagner, Thesis, EPFL, Lausanne,

226

227 228

229

230

231 232

233 234

235

236

237

(2001); S. Gradecˇak, V. Wagner, M. Ilegems, T. Riemann, J. Christen, and P. Stadelmann, Appl. Phys. Lett. 80, 2866 (2002); V. Wagner, O. Parillaud, H. J. Bühlmann, M. Ilegems, S. Gradecˇak, P. Stadelmann, T. Riemann, and J. Christen, J. Appl. Phys. to be published (2002). P. Gibart, B. Beaumont, and Chua Soo-Jin, J. Cryst. Growth 201/202, 365 (1999). X. Li, P. W. Bohn, and J. J. Coleman, Appl. Phys. Lett. 75, 4049 (1999). Yong-Hoon Cho, H. M. Kim, T. W. Kang, J. J. Song, and W. Yang, Appl. Phys. Lett. 80, 1141 (2002). Shin-ichi Nagahama, Naruhito Iwasa, Masayuki Senoh, Toshio Matsushita, Yasunobu Sugimoto, Hiroyuki Kiyoku, Tokuya Kozaki, Masahiko Sano, Hiroaki Matsumura, Hitoshi Umemoto, Kazuyuki Chocho, and Takashi Mukai, Jpn. J. Appl. Phys. 39, L647 (2000). H. Miyake, H. Mizutani, K. Hiramatsu, Y. Iyechika, Y. Honda, and T. Maeda, Mater. Res. Symp. Proc. 639, G5.3.1 (2001). B. Beaumont, and E. Frayssinet, to be published (2002). M. Ishida, M. Ogawa, K. Orita, O. Imafuji, M. Yuri, T. Sugino, and K. Itoh, J. Cryst. Growth 221, 345 (2000). http://www.sei.co.jp/top_e/f_products.html. E. Frayssinet, W. Knap, P. Lorenzini, N. Grandjean, J. Massies, C. Skierbiszewski, T. Suski, I. Grzegory, S. Porowski, G. Simin, X. Hu, M. Asif Khan, M.S. Shur, R. Gaska, and D. Maude, Appl. Phys. Lett. 77, 2551 (2000). R. P. Pawlowski, C. Theodoropoulos, A. G. Salinger, T. J. Mountziaris, H. K. Moffat, J. N. Shadid, and E. J. Thrush, J. Cryst. Growth 221, 622 (2000). C. Theodoropoulos, T. J. Mountziaris, H. K. Moffat, and J. Han, J. Cryst. Growth 217, 65 (2000). K. Harafuji, Y. Hasegawa, A. Ishibashi, A. Tsujimura, I. Kidoguchi, Y. Ban, and K. Ohnaka, Jpn. J. Appl. Phys. 39, 6180 (2000).

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Plasma-Assisted Molecular Beam Epitaxy of III–V Nitrides Alexandros Georgakilas, Hock Min Ng, and Philomela Komninou

Abstract

The application of the nitrogen plasma source-assisted molecular beam epitaxy method (PAMBE) for the growth of GaN and related compounds is reviewed, with emphasis on the growth-dependent material properties. Results comparing the two major types of plasma sources are reviewed and a thorough analysis of a typical RF plasma source is presented. Theoretical and experimental results representing the current understanding of the growth of hexagonal (0001) GaN are reviewed; a growth phase diagram is presented and experimental results are given. The area of GaN doping is reviewed. The issues of substrate nitridation, buffer/ nucleation layer and GaN polarity selection in the heteroepitaxy of GaN on Al2O3 (0001) substrates are addressed in relation to their structural characteristics at the atomic scale. The growth of ternary nitride alloys and heterostructures and the utilization of the material in the fabrication of electronic and optoelectronic devices are reviewed. The main conclusions on the achievements and perspectives of the PAMBE growth method are given.

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3 Plasma-Assisted Molecular Beam Epitaxy of III–V Nitrides

3.1

Introduction

Molecular beam epitaxy (MBE) [1] is an epitaxial growth method that has enabled the realization of the most advanced semiconductor heterostructure materials in the last two decades. In the case of III-arsenide semiconductors, the enormous progress in the control of the MBE growth and the development of MBE equipment has transformed MBE from a sophisticated research tool into a method of commercial production of advanced semiconductor materials [1–6], which are directed to the production of high-frequency electronic components (MESFETs, HEMTs, MMICs) as well as optoelectronic devices such as laser diodes. Efficient solutions have been also found to overcome the initially very discouraging difficulties in the MBE growth of III-phosphides and MBE has well established its capability to be a production tool of advanced III-phosphide heterostructure materials [6–8]. For a more detailed review of the technology and development of MBE for various material systems, readers are referred to Refs. [9–17]. III-Nitrides (GaN, AlN, InN, BN, and their alloys) are the representative family of III–V semiconductors in the class of wide band gap semiconductors, where they coexist and compete mainly with SiC, ZnO, diamond (C), and ZnSe. The rapid progress in the development of III-nitride materials and devices and the fast commercialization of products have attracted the attention of the majority of the compound (III–V or II–VI) semiconductor research community in the recent years. Correspondingly, the MBE growth of III-nitrides has risen to a high priority research objective, with efforts appearing initially in the first half of the last decade and increasing to enormous levels in the recent years. MBE growth of III-nitrides is, however, an activity still limited to the research arena, contrary to the metalorganic vapor phase epitaxy (MOVPE or MOCVD) which is used to grow the material of the main commercialized III-nitride components, i.e., InGaN light emitting diodes (LEDs) and laser diodes (LDs). This chapter intends to give an overview of the current capabilities and physical understanding of a major division of the III-nitride MBE growth method; the plasma-assisted MBE of III-nitrides. This refers basically to an MBE approach employing a remote compact plasma source to produce a beam of reactive nitrogen species from a source of inert N2 gas. The second major III-nitride MBE division being the reactive MBE, where a reactive NH3 gas source is used to supply N atoms to the growing crystal, is not covered at all within the extent of this chapter. The application of the nitrogen plasma source assisted molecular beam epitaxy method (PAMBE) for the growth of GaN and related compounds is reviewed, with emphasis on the growth-dependent material properties. Results comparing the two major types of plasma sources are first reviewed and a thorough analysis of a typical RF plasma source is presented. Theoretical and experimental results representing the current understanding of homoepitaxial-like PAMBE growth of hexagonal (0001) GaN are reviewed; the dependence of the surface structure and growth mechanisms on the III/V adatom concentration and correlation with the GaN surface morphology. A growth phase diagram is presented. The GaN sub-

3.2 The Nitrogen Plasma Source

strate preparation is reviewed and experimental results for the PAMBE GaN growth on MOVPE-grown GaN/Al2O3 (0001) templates are given. The GaN doping is reviewed. The heteroepitaxial GaN growth on different substrate types and/ or orientations is then discussed. Systematic results contributing towards a comprehensive understanding of the PAMBE growth of hexagonal GaN on Al2O3 (0001) substrates are presented; the issues of substrate nitridation treatment, buffer/nucleation layer and GaN polarity selection are addressed in relation to their structural characteristics at the atomic scale. The PAMBE growth of ternary nitride alloys and heterostructures is then reviewed and the utilization of PAMBEgrown material in the fabrication of electronic and optoelectronic devices is discussed. The chapter ends with conclusions on the achievements and perspectives of the PAMBE growth of III-nitride semiconductors.

3.2

The Nitrogen Plasma Source 3.2.1

The Different Sources

Due to the inert nature of nitrogen, the MBE growth of III-nitrides requires the use of energetic nitrogen species that may be produced by compact remote plasma sources such as the electron cyclotron resonance (ECR) microwave source [18– 27] and the radio frequency (RF) source [28–32]. Various types of ion [33–36] and supersonic jet [37–39] sources have also been investigated but they have not been used extensively in the growth of III-nitrides. An MBE process that uses a nitrogen plasma source, is commonly referred to as plasma-assisted MBE (PAMBE) and a typical growth chamber is given in Fig. 3.1. Most of the initial work in the PAMBE of III-nitrides was based on ECR sources, while the RF source dominates the recent PAMBE work, since it provides higher growth rate, operates at higher vacuum, and includes lower molecular ion content. Schematics and descriptions of typical conflat flange ECR and RF plasma sources have been published in [25–27] and [28], respectively. The ECR sources operate at 2.45 GHz, which enables the plasma to be confined to a small volume [40]. Nitrogen is introduced and plasma is created in the ECR tube, where a pyrolytic boron nitride (PBN) liner and aperture are commonly used to minimize contamination from sputtering of the source walls. An axial magnetic field is produced in the ECR tube by an electromagnetic solenoid, designed to match the ECR frequency to the 2.45-GHz microwave radiation, which is coupled to the ECR tube through an alumina dielectric waveguide. The strength of the field can be tuned by varying the coil current. The 2.45-GHz microwave radiation is generated by a magnetron and supplied to the ECR tube through a coaxial cable, mode converter, and the dielectric waveguide. The coupling of the microwave power to the plasma is dominated by an ECR absorption mechanism under low-pressure conditions. By adjusting the slug tuner, the reflected microwave power can be con-

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Schematic drawing of a typical plasma-assisted MBE system that is used for the growth of III-nitride semiconductors. It is equipped with a nitrogen RF plasma source

Fig. 3.1

and a 1600 l s–1 turbomolecular pump. The N2 gas is introduced through a 0–2 sccm mass flow controller and a purifier.

sistently maintained below 20 W during the ECR condition. Commercial ECR sources have been available from several companies, such as ASTeX [20–22, 24– 26, 43–45], Wavemat [23] and Irie [42]. The RF sources operate at 13.56 MHz with a typical maximum power of 600 W. To minimize contamination, the discharge is electrodeless and the plasma is contained in a small cylindrical PBN discharge tube capped with a PBN aperture (exit plate). Nitrogen is introduced into the PBN tube and RF energy at 13.56 MHz is inductively coupled through a water-cooled copper coil to create the plasma. It is considered [40, 41] that the formed plasma sheath confines ions and electrons within the plasma discharge zone, allowing primarily the low-energy (<10 eV) neutral species to escape. Commercial RF sources for generation of reactive nitrogen species in MBE machines have been available from many companies, such as: Oxford Applied Research models MPD21 [28, 29, 44, 46], CARS-25 [31, 47–50] and HD25 [32, 47, 51], SVTA [30, 46], EPI Vacuum Products model Unibulb [46, 48–50], Addon [52], Eiko Co. [42] and Taisei Industry [53]. The currently available RF sources have been well tested and can provide growth rates in the order of 1.0 l m h–1. For example, at FORTH we have grown GaN layers at 0.6 lm h–1 using the HD25 source with an RF power of 400 W and 1.5 ´ 10–5 Torr nitrogen pressure [51]. On the contrary, the ECR sources have been limited to low growth rates, typically 0.05–0.15 lm h–1 [44], because of the pres-

3.2 The Nitrogen Plasma Source

ence of a trade-off between growth rate and ion damage [22, 29]. Improved growth results with an ECR source could be obtained by applying various strategies for charged species reduction [22, 25, 27]. 3.2.2

The Nitrogen Plasma

Nitrogen plasmas have been shown to include a variety of excited species: excited neutral molecules (N*2), ionized molecules (N+2), atoms (N) and ionized atoms (N+) [22, 29, 30, 32, 40–44, 46–50, 54]. A complete description of the states and transitions of N*2 and N+2 and the energy levels resulting from recombination of various (ground state or excited) nitrogen atoms has been given in [54]. The energy of the activated species N*2 (A3å+u, B3Pg, a1Pg, C3Pu), N+2 (2å+g) and N (4S, 2P, 2D) was compared [55] to the difference in the Gibbs free energy of the reaction 2Ga(l) + N2(g) ? 2GaN(s) at typical growth conditions (temperature of 800 8C and nitrogen pressure of 10–6 Torr) and it was found that all species provide sufficient energy to form GaN. The following possible GaN synthesis reactions were proposed [55]: Ga…1† ‡ 1=2 N2 …g† ! GaN…s†

…1†

where N*2 = A3å+u, B3Pg, a1Pg, C3Pu Ga…1† ‡ 1=2 N‡ 2 …g† ‡ e ! GaN…s†

…2†

where N+2 = 2å+g Ga…1† ‡ N…g† ! GaN…s†

…3†

where N = 4S Ga…1† ‡ N …g† ! GaN…s†

…4†

where N = 2P, 2D. The exact composition of the nitrogen beam exiting from a plasma source can be very important for the PAMBE growth, since the different nitrogen species might have a different influence on the growth process. Adjusting the input power and gas flow may control the composition of the nitrogen plasma beam [41, 43]. However, the producers of the commercially available sources do not characterize them in terms of nitrogen species in the plasma. This is why it is important to develop methods for monitoring with good accuracy the composition of the nitrogen plasma on-line during growth. Different means have been used for analyzing the composition of the nitrogen plasma beams. Optical emission spectroscopy methods [22, 29, 30, 32, 41, 43, 44, 46, 47] show the species that are present in the plasma and can provide information about the dependence of the line or band emission intensity (related to the

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relative density) of various species on the RF power and nitrogen gas flow. Optical detectors are used to monitor the total emitted light [28, 31], sometimes in combination with filters [28], as a measure of the density of active nitrogen species. The type and flux of nitrogen species have also been studied by using a quadrupole mass spectrometer in direct line of sight to the plasma source [42, 48–50], in some cases with a combined capability of electrostatic deflection of incoming ions [48–50]. Faraday cup [26–28, 47] and Langmuir probes [22, 25] have been used to examine the presence of ions in the nitrogen radical beam out of the beam exit plate. Among these methods, optical emission spectra (Figs. 3.2 to 3.6) can provide accurate real-time monitoring of the plasma composition inside the source. In general, three spectral ranges of optical emission from nitrogen plasmas are distinguished: (a) 300–500 nm, (b) 500–700 nm, and (c) 700–900 nm. The 300– 500 nm wavelength range includes emissions of the second positive system of N2(C3Pu? B3Pg transitions), with the largest peaks at 316, 337, 357, 380 and 400 nm and emissions of the first negative system of N+2(B2å+u ? X2å+g transitions), with sharp peaks at 391 and 428 nm [43, 44]. In the 500–700 nm range, emissions of the first positive system of N2(B3Pg ? A3å+u transitions) are observed [22, 29, 40, 41, 46], as three bands of regularly spaced emission peaks with strongest peaks [43, 44] within each band at 540, 590, and 660 nm, respectively. They are believed to occur as a result of recombination of ground state (4S) nitrogen atoms [22, 28, 29, 41]. In the 700–900 nm range, emission bands with band heads at 760, 820 [22, 29, 44], 870 [29] and 890 nm [43] have been recognized and attrib-

Optical emission spectra for an HD25 RF plasma source operating with 0.56sccm gas flow. The upper trace corresponds to an injected RF power of 500 W and the lower trace to 78 W.

Fig. 3.2

3.2 The Nitrogen Plasma Source

Optical emission spectrum for an HD25 RF plasma source operating at the high brightness mode with 78 W injected power and 0.56-sccm gas flow. The molecular bands are clearly observed. Small atomic lines appear superimposed at 745, 821, and 869 nm.

Fig. 3.3

Optical emission of the triplet of lines at 742.4, 744.2, and 746.8 nm in an HD25 source operated at 500 W power and 0.56 sccm gas flow.

Fig. 3.4

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A weak N II line of ionized nitrogen atom is observed in the emission spectrum of an HD25 source operating at 500 W power

Fig. 3.5

(upper trace) but not for operation at 78 W power (lower trace). The gas flow is 0.56 sccm.

uted, by different teams, to the 1st positive system of N2 [43, 44] or to the socalled Y bands of N2(B3åu ? B3Pg transitions) [22, 29], a system that is also associated with recombination of ground-state nitrogen atoms. The fine structure of these bands was attributed to changes in the rotational energy of the nitrogen molecule [43]. However, high-resolution spectroscopy analysis revealed that atomic nitrogen lines were also superimposed on the molecular bands in this near-IR spectral region at 745, 821, and 869 nm [43, 44]. The triplet of lines at 742.3, 744.2, and 746.8 nm was attributed to 3s4P–3p4S0 transitions, the seven-line multiplet of peaks between 818.5 and 824.2 was connected to 3s4P–3p4P0 transitions and the four-line multiplet of peaks at 856.8, 859.4, 862.9, and 865.5 nm was attributed to 3s2P–3p2P0 transitions of atomic nitrogen. Seven peaks between 868.0 and 872.8 nm were also observed and explained as part of an eight-line multiplet of lines associated with 3s4P–3p4D0 transitions in atomic nitrogen [43]. Following the work of Vaudo et al. [43], it has become common practice to attribute the emissions in the 740–900 nm wavelength range to atomic nitrogen transitions [22, 29, 40, 46, 47].

3.2 The Nitrogen Plasma Source

Optical emission spectra of an HD25 RF plasma source for (a) different powers for 0.56 sccm gas flow; (b) different gas flows for 400 W RF power.

Fig. 3.6

3.2.3

Characterization of the HD25 RF Source by Optical Emission Spectroscopy

At FORTH, a nitrogen RF plasma source is used for PAMBE (RFMBE) growth of III-nitrides, which is a model HD25 of Oxford with basic characteristics similar to those reported elsewhere [28]. The source has a PBN discharge tube capped with a PBN exit plate. The RF energy from an Advanced Energy RFX 600 two-stage power generator is fed inductively to the discharge that develops in the PBN tube through a water-cooled coil, which ensures that the surrounding components would not degrade due to overheating during operation. The generator has a power output maximum of 600 W into a 50-X load. The nitrogen is introduced via an MKS mass flow controller with a maximum nitrogen gas flow rate of

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2.0 sccm. The source may be operated continuously at a maximum RF power of 600 W. Under certain power levels and flow rates, plasma is created within the discharge tube. Then the flow rate can be reduced while maintaining the discharge. There are two stable modes in which the HD25 source can operate: low brightness (LB) and high brightness (HB). The HB is the mode in which the source runs most efficiently and is characterized by the emission of a far more intense light than the LB mode. Often, the LB mode is the first to strike, and the source switches to the HB mode as the RF power is increased and the gas flow is reduced. The emission from the plasma may be observed through a Kodial window, which is on the axis of the gas feed tube and allows a direct view to the central region of the discharge. The Kodial window allows more than 90% of the emitted radiation with wavelengths between 400 and 2000 nm to be transmitted through it. Since it is well established [30, 44, 46, 48] that the plasma from a nitrogen RF source has a very small content of ionized molecules of nitrogen (that have intense emission between 316 and 400 nm), we analyzed [56] the optical emission of the source in the wavelength region between 500 and 900 nm, where both excited molecular nitrogen and atomic nitrogen have an intense emission. The emission spectra from the nitrogen plasma were obtained using a spectrometer model SM240 of CVI Spectral Products equipped with 830 grooves/mm grating, the maximum response being at 800 nm. The wavelength domain is 500– 1000 nm, the entrance slit is 25 lm, the resolution is 0.6 nm and the wavelength sampling step is 0.27 nm. The analyzed light is introduced into the spectrometer with the use of an optical fiber. The measurements are recorded by means of a computer interconnected with a PCI-1200 12-bit 100-kHz interface board. All of the spectra intensities were normalized, so that the plots have on the vertical scale of intensity the same units (considered as arbitrary units). Two characteristic emission spectra for a high (500 W) and a low (78 W) input RF power have been plotted together in Fig. 3.2. The 1st positive system molecular bands [43] at 540, 590, 660, 760, 870, and 890 nm exist in both spectra and they can be clearly seen for the lower power of 78 W in the magnified vertical scale plot of Fig. 3.3. Transitions between vibrational levels are responsible for the fine structure of these bands. Very intense emission lines of neutral nitrogen atom (N) were observed in the near-IR spectral region at 745, 821, and 869 nm for high RF power (Fig. 3.2) while the N emission was extremely weak at low power (Figs. 3.2 and 3.3). The high intensity triplet of lines at 742.4, 744.2, and 746.8 nm that corresponds to 3s4P– 3p4S0 transitions of N is resolved in Fig. 3.4. The N emission also included the multiplet between 818.5 and 824.2 nm due to 3s4P–3p4P0 transitions, the multiplet of peaks at 856.8, 859.4, 862.9, and 865.5 nm related to 3s2P–3p2P0 transitions and several peaks between 868.0 and 872.8 nm, being part of the eight-line multiplet of lines associated with 3s4P–3p4D0 transitions. A weak emission line was also observed at 648.2 nm. It was identified as the N II line of ionized nitrogen atom (N+) [57, 58] and is considered to correspond to the 2s1P0–3p1P transition of the nitrogen ion. This line can be easily observed

3.2 The Nitrogen Plasma Source

superimposed on the molecular band in the magnified vertical scale plot of Fig. 3.5. It could be observed over the molecular band only at injected powers higher than 100 W for a gas flow of 0.56 sccm. The onset of this line might be due to the increase of the electron density in the plasma [59]. Its intensity increased with power faster than the molecular band intensity, but much slower than the intensity of the neutral atom lines (Fig. 3.6 a). This N+ line has not been observed previously in the analysis of other RF plasma sources but this might be related to the use of much lower resolution spectrometer gratings for the analysis of the entire 500–900 nm spectral range. The intensity of all the components of the spectrum (both atomic lines and molecular bands) increased monotonically with power, as can be seen in Fig. 3.6 a. However, the dependence on the nitrogen gas flow was more complex (Fig. 3.6 b). The behavior of the amplitude of the lines was different in different gas flow regimes at the same RF power, behavior reflecting the modification in the density of the upper level of the transition. The intensity of the lines in the triplet at 742.3, 744.1, and 746.8 was increasing until about 0.8 sccm for 500 W injected power or until 1 sccm for 400 W injected power and then decreased slowly. The intensity of the lines from the multiplet at 820 nm increased until 1.5 sccm and then decreased for 500 W injected power, while for 400 W injected power the intensity was increasing within the examined flow rates. These results suggest an enhanced recombina-

Dependence of the intensity of the neutral nitrogen atom lines at 742.4, 744.2, 746.8, 818.5, 821.6, and 824.2 nm, the ionized nitrogen atom N II line at 648.2 nm and a

Fig. 3.7

point in the molecular band at 720 nm, on the gas flow in an HD25 RF source operating at 400 W power.

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tion of nitrogen atoms after their concentration has reached a critical value. The N II line at 648.2 and the amplitude of the molecular bands was increasing with nitrogen flow both for 400 W and 500 W injected power. The dependence of the intensity of various atomic lines on the gas flow for 400 W power is shown in Fig. 3.7. It is worth noticing that there are no dramatic intensity changes with increasing flow, except the fast increase of the neutral atom lines for flow up to 0.5 sccm. If we assume a local thermodynamic equilibrium for the plasma, the line intensity integrated over the line profile, I, and expressed in terms of statistic weights for the upper gm and the lower gn levels, the absorption oscillator strength fmn and the population density of the upper level Nm, is: Iˆ

gre 3 gn x fmn Nm : 2pc gm

…5†

This means that an increase in the line intensity, with the variation of power or gas flow, reflects an increase of the population of the upper level of the transition that generates the emission line. However, a proportional increase should also be expected for the concentration of excited species at the lower energy levels, as well as for the overall concentration of the corresponding kind (atom or excited molecule) of species in the plasma. This quantitative interpretation of the optical emission intensities can be justified by considering the good agreement of optical emission spectroscopy with mass spectrometry analysis of the exact species contained in a RF plasma nitrogen beam [42]. In conclusion, it has been found that the HD25 source is a very efficient RF source for the production of atomic nitrogen. Significant N concentrations can be achieved at low gas flow, thus allowing to preserve a better vacuum environment in the MBE growth chamber. Operating this source at 400 W and 0.56 sccm we could grow cubic and hexagonal GaN with a growth rate of over 0.6 lm h–1. However, a low concentration of nitrogen ions also exists and their effects on the GaN growth should be taken into account. 3.2.4

Which is the Best Source?

There have been several studies comparing the performance characteristics of ECR and RF sources [42, 44, 45, 60], as well as the characteristics of different products of RF sources [46, 47–50]. Taking into account these results, together with those of studies concerning various individual sources, we may proceed to draw some general conclusions, although it should be noticed that contradictory results might also exist. The ECR sources produce mainly excited molecular species, consisting of 2nd positive series excited N2 and N+2 and little or no atomic nitrogen. On the contrary, the RF sources typically produce high densities of atomic nitrogen and excited molecular nitrogen of the 1st positive system [44]. The much higher content of atomic nitrogen in the RF plasma than that of the ECR plasma has been directly confirmed by mass

3.2 The Nitrogen Plasma Source

spectroscopy analysis of the corresponding beams [42]. Optical emission transitions related to molecular ions have not been found in the RF sources, except for one observation of a N+2 transition at 391 nm for low-pressure discharge [41]. Ionized atom lines at approximately 776 and 854 nm were observed in a SVTA RF source [30], while at FORTH we observed a N+ line at 648.2 nm in a HD25 RF source. In any case, the fact that ionic species indeed exist also in nitrogen beams created from RF sources has been well proved by techniques detecting directly the presence of ions in the beam [47–50]. Moreover, according to mass spectroscopy experiments [48, 49], the atomic ion flux was typically two to three times larger than that of the molecular ions for an Oxford CARS-25 source. The detrimental effects of the higher ion content of the ECR source on the GaN material properties have been shown by comparing the material properties of layers grown by RF and ECR sources [44, 45, 60]. Higher-quality GaN layers were consistently grown with an Oxford MPD21 RF source at higher growth rates than those grown with an ASTeX ECR source [44]. The crystal damage in layers grown with the ECR source and highly negative substrate bias was comparable to that observed for ion-implantation processes [45]. Optical admittance spectroscopy revealed distinct transitions between the bands and electronic states in n-type GaN grown with an RF source, while broad bands occurred in the ECR grown samples, attributed to potential fluctuations due to structural inhomogeneities induced by the ECR source [60]. Finally, a deep level emission about 2.2 eV appeared in the photoluminescence spectra of layers grown with an Irie ECR source, while it could be suppressed in layers grown with an Eiko RF source [42]. All these ECR results are typical of the introduction of point defects by plasma-induced damage in the GaN layers [60]. While the elimination of ions using an RF source is an obvious choice, an issue has been raised about the preferred kind of reactive nitrogen species [39, 42, 46, 48–50, 55]: nitrogen atoms or A3å+u metastable nitrogen molecules. Considering the lifetimes of the excited nitrogen molecular states it has been concluded that only the N2(A3å+u) metastable species can reach the substrate in PAMBE growth [41]. Both N and N2(A3å+u) have potential energies considerably higher than the required Gibbs free energy to drive the GaN synthesis reaction [55]. The nitrogen atoms, once formed, are known to live for very long times, having lifetimes on the order of seconds, due to the fact that the formation of a nitrogen molecule by collision of two atoms requires an additional interaction with a third body, such as the source walls [40]. This would lead to an enrichment of the plasma with nitrogen atoms until a steady state is reached involving wall collisions. Indeed, large amounts of atomic nitrogen have been realized in modern RF sources and very high GaN growth rates have been achieved [46, 47, 51]. Comparing different models of RF sources, it was shown that the growth rates increased proportionally to the available amount of atomic nitrogen [46, 47]. These results suggest that nitrogen atoms are important reactive species for GaN growth [47] as well as the (A3å+u) metastable molecules [46]. A GaN (0001) growth rate of 0.6 lm h–1 was achieved at 900 8C for an EPI Unibulb source producing a flux particularly rich in atomic nitrogen [46].

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However, there have been experimental results [39, 48–50] suggesting that higher growth rates may be achieved at high substrate temperatures when GaN is grown with a beam dominated by N2(A3å+u) species. In one case, a corona discharge supersonic free jet was employed and GaN was grown on various cubic or hexagonal substrates with nitrogen incorporation efficiency independent of the substrate temperature in the range of 600–900 8C [39]. In another case, the decrease of the GaN (0001) growth rate with increasing substrate temperature was correlated to the dominating reactive species in different RF sources. The decrease of the growth rate was consistent with the GaN decomposition rate, when an EPI Unibulb RF source was used that was estimated to produce a beam rich in N2(A3å+u), while a premature decrease in the growth rate was observed with an Oxford CARS-25 source producing a beam rich in atomic nitrogen [48–50]. It was suggested that ionic and neutral atomic nitrogen might increase the GaN (0001) surface decomposition. The overall study on the characterization of RF plasma sources has already established some important rules for the source design. The temperature of the walls of the RF discharge zone has been found to dramatically affect the ion content of the plasma, which decreases to a very low level at temperatures above room temperature [47]. A reduction of the ion content also occurs by reducing the size of the holes in the PBN aperture [28, 47–50] while their number can be increased to achieve a sufficient flux of reactive nitrogen species. Finally, the experimental results suggest that the input power and gas flow may be used to control the composition of the nitrogen plasma beam. The levels of atomic nitrogen increase by increasing the input power and decreasing the N2 gas flow [30, 43]. However, a similar trend has also been reported for the ionic species [41]. This behavior is explained by enhanced recombination at high nitrogen pressures in the plasma, due to an increased probability of collisions. 3.3

Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE 3.3.1

Structure of the GaN {0001} Surfaces

The wurtzite crystal structure is not centrosymmetric and so the (0001) and (0001† surfaces of a GaN crystal are not equivalent [62]. To distinguish between them, we have to consider what kind of atoms (Ga or N) would exist on the final {0001} atomic plane of each surface, if it is required that each of these atoms has three bonds to atoms of the atomic plane directly underneath and one remaining dangling bond for bonding to the next atomic plane. Under this understanding, we can refer to the two different surfaces as the Ga-face or N-face and it is common to associate the (0001) orientation with the Ga-face and the (0001† orientation with the N-face [63–73]. Alternatively, the (0001) and (0001† GaN surfaces are also identified as (0001)A and (0001)B, respectively [74]. The (0001) or (0001† orientation of a GaN surface is an important property of the surface that determines its physical and chemical properties. It is common to

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

distinguish the exact orientation of a {0001} surface by referring to the polarity of the surface. Furthermore, when a GaN thin film is grown on different substrates, the polarity of its surface coincides with the so-called polarity of the film (Ga-face or Ga-polar and N-face or N-polar). The atomic structure of the surface is very important for the epitaxial growth. It is well known that the surface reconstructions during GaAs MBE growth are characteristic of the surface stoichiometry and growth temperature. They can be used to control the growth kinetics and optimize the quality of the grown epilayers. In the case of III-nitrides, the surface reconstructions carry additional very important information concerning the polarity of the films. A series of systematic investigations [63–73] has well established the range of reconstructions that may appear on each GaN {0001} surface. The reconstructions were determined using reflected high-energy electron diffraction (RHEED), low energy electron diffraction (LEED) and scanning tunneling microscopy (STM). The 1 ´ 1, 3 ´ 3, 6 ´ 6, and c (6 ´ 12) reconstructions were identified for the N-face while the 2 ´ 2, 5 ´ 5, 6 ´ 4, and “1 ´ 1” were the main reconstructions for the Gaface [64]. A 1 ´ 2 reconstruction and, on occasions, 3 ´ 2 and 2 ´ 3 RHEED patterns were also observed for the Ga-face [65]. The chemical composition of the surfaces was estimated by Auger electron spectroscopy (AES) and first-principles total-energy calculations were used to identify possible atomic structures. Smith et al. [64] have constructed schematic phase diagrams for the four main surface reconstructions observed for the N and Ga faces, which are shown in Fig. 3.8 a and b, respectively. The corresponding RHEED patterns, as viewed along the [1120] azimuth are also shown in Fig. 3.8. The different reconstructions correspond to different surface stoichiometry and specifically, the Ga coverage increases from left to right in both diagrams of Fig. 3.8. An important difference in the PAMBE growth of GaN, in comparison to the MBE growth of GaAs and other conventional III–V semiconductors, is that only a 1 ´ 1 surface structure is observed during GaN growth. The higher-order reconstructions are observed after the end of growth, in general at lower temperatures and are induced by depositing different amounts of Ga or N atoms on the surface, in combination with annealing treatments for excess material removal or surface ordering (depending on the polarity of the surface). The N face (Fig. 3.8 a) [64] was prepared by nucleating and growing GaN directly on sapphire using RFMBE. The RHEED pattern was a streaky 1 ´ 1 during growth. The 1 ´ 1 surface of Fig. 3.8 a has the lowest Ga concentration and was produced by heating the as-grown film surface to high temperature (*800 8C) in order to remove excess Ga adatoms. The 3 ´ 3, 6 ´ 6, and c (6 ´ 12) reconstructions were produced by depositing submonolayer quantities of Ga onto this 1 ´ 1. These reconstructions, however, existed only below *300 8C (Fig. 3.8 a). By increasing the temperature, the structures underwent reversible order-disorder phase transitions and the non-integral RHEED features disappeared. The Ga face (Fig. 3.8 b) [64] was prepared by homoepitaxial growth of GaN by RFMBE on a MOVPE-grown GaN-on-sapphire template. A streaky 1 ´ 1 RHEED pattern was observed during growth under Ga-rich conditions. Upon cooling, the

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Schematic phase diagrams illustrating the coverage and temperature dependence of the reconstructions existing on the: a N-face; b Ga-face. Ga coverage increases from left to right in both diagrams. Temperatures given correspond to either order-disorder transitions or annealing transitions. Fig. 3.8

Cross-hatched regions indicate either mixed or intermediate phases. RHEED patterns for both the Ga and N face, as viewed along the [112¯0] azimuth, are also shown (Fig. 1 from [64], reprinted with permission from Smith et al., Appl. Phys. Lett. 72, 2114 (1998). Copyright 1998, American Institute of Physics).

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

1 ´ 1 converted to a structure referred to as “1 ´ 1” (with quotation marks) or pseudo-1 ´ 1 at *350 8C. This unusual “1 ´ 1” structure was characterized by the appearance of satellite lines just outside the integral order lines when viewed along the [1120] azimuth. Additional RHEED patterns from this structure have been presented in Ref. [69]. The “1 ´ 1” was annealed at 750 8C to remove excess Ga atoms and then the RHEED pattern changed to a 1 ´ 2 (not shown in Fig. 3.8), with a weak 1/2-order streak. Deposition of Ga onto the 1 ´ 2 surface at room temperature removed the 1/2-order streak and no fractional order streaks appeared. However, by depositing 1/2 monolayer (ML) of Ga, annealing the surface to 700 8C and cooling, the 5 ´ 5 reconstruction was formed. Further deposition of an additional 1/2 ML Ga, annealing to 700 8C and cooling, resulted in the formation of the 6 ´ 4 reconstruction. The 6 ´ 4 reconstruction underwent a reversible phase transition at *250 8C, while the 5 ´ 5 structure was observed up to 700 8C. Deposition of about 1 ML Ga onto the 6 ´ 4, followed by a rapid anneal to 700 8C, resulted also to the “1 ´ 1” structure [68]. Finally, a 2 ´ 2 RHEED pattern was obtained by annealing the 5 ´ 5 at *600 8C or nitriding the surface at *600 8C. The systematic experimental and theoretical work of Refs. [63–73] has concluded on possible models of the various surface structures, which have been outlined in Ref. [66]. First, it has been pointed out [66] that reconstructions on both types of {0001} GaN surfaces are unusual in that they consist of metallic layers of Ga, bonded onto the GaN. On the contrary, most semiconductor surfaces prefer to be nonmetallic, since the opening of a surface gap provides a mechanism for lowering the energy of the system. The fact that the separation of Ga atoms in bulk Ga is typically 2.7–2.8 Å, considerably smaller than the lattice constant of GaN, 3.19 Å, would also be expected not to favor the surface metallic Ga layers. Nevertheless, the 1 ´ 1 structure of the (0001† surface was found to consist of 1 ML of Ga atoms (adlayer), located in sites above the N atoms of a N-terminated GaN bilayer [63]. Charge transfer from Ga to N atoms is considered to stabilize this structure (the Ga atoms in the adlayer are slightly positively charged so that there is a coulombic repulsion between them) [66]. The stability of a gallided (0001† surface was also confirmed in Ref. [74], by studying RHEED intensity variations in combination with desorption mass spectroscopy (DMS). The 3 ´ 3, 6 ´ 6, and c (6 ´ 12) reconstructions are formed by additional Ga adatoms weakly bound on top of the 1 ´ 1 Ga adlayer. In particular, the 3 ´ 3 structure contains one additional atom per 3 ´ 3 cell compared with the 1 ´ 1 [63]. A lateral relaxation of the nearestneighbor Ga adlayer atoms allows the adatom to move much closer to the adlayer plane, thereby stabilizing the structure [63]. The 3 ´ 3, 6 ´ 6, and c (6 ´ 12) reconstructions are characterized by reversible order-disorder phase transitions at *300 8C, due to the weak bonding of the Ga adatoms. The (0001) surface, in N-rich conditions, is terminated with an arrangement of adatoms with each adatom forming three bonds to underlying Ga atoms [66]. Probably, both N and Ga atoms are involved as adatoms, as can be concluded by considering the relative surface energies that have been calculated by Northrup et al. [73] and are shown in Fig. 3.9. The stability of the 2 ´ 2 N and 2 ´ 2 Ga adatom structures is also suggested by theoretical results in Refs. [75–78]. STM observa-

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Relative energies of the surfaces are plotted as a function of the Ga chemical potential. For Ga-rich conditions the most stable structure is the laterally contracted Ga bilayer (Fig. 4 from [73], reprinted with permission

Fig. 3.9

from J. E. Northrup, J. Neugebauer, R. M. Feenstra and A. R. Smith, Physical Review B61, 9932 (2000). Copyright 2000 by the American Physical Society).

tions showed that the 2 ´ 2 surface is well ordered only in small domains and this is consistent with the fact that the 1/2-order diffraction lines in RHEED are not very sharp [65]. Given that the 2 ´ 2 structure is formed by nitridation, it seems most likely that it corresponds to N adatoms at the H3 hollow site, as suggested by theory [68, 75]. However, the nitridation could be converting the surface from a Ga-rich structure to a less Ga-rich structure, with the 2 ´ 2 being the Ga adatom. In that case, the calculations indicate that the Ga adatom prefers the T4 site, right above the second layer N atoms [68, 75]. For the 5 ´ 5 reconstruction, the experimental results suggest a structure consisting of adatoms in H3 and T4 sites with three adatoms and a dangling bond site (located at a Ga rest atom) per 5 ´ 5 unit cell [68]. The 6 ´ 4 structure is quite complicated, probably involving more than simply adatoms and/or vacancies on the surface [68]. In the Ga-rich limit, the pseudo-1 ´ 1 structure of the (0001) surface consists of a fluid-like overlayer of Ga [68, 69, 73, 77]. On the basis of RHEED and LEED diffraction observations and modeling of AES Ga/N peak intensities, it was proposed [68] that there are two monolayers of Ga on top of the Ga-terminated GaN bilayer, with these Ga layers assuming something close to their bulk spacing so that they form an incommensurate structure on the surface. Furthermore, Northrup et al. [73] using first-principles total-energy calculations provided theoretical evidence (Fig. 3.9) in favor of a mobile laterally contracted bilayer structure containing p *2.3 ML of Ga, as shown in Fig. 3.10. The structure was modeled using a 3  3 cell, which allowed p modeling of hexagonal Ga adlayers with a reduced Ga–Ga spacing of ac = ( 3/2)a1 ´ 1 = 2.75 Å, since a1 ´ 1 = 3.17 Å is the inplane spacing of

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

Ga atoms on the 1 ´ 1 ideal surface. The lattice vectors of the overlayer were rotated by 30 degrees with respect to those of the substrate. In thispstructure  (Fig. 3.10), layer 1 contains 3 atoms and layer 0 contains 4 atoms, in each 3  3 cell. In the Ga-rich limit the energy of this laterally contracted Ga bilayer structure was the lowest of any structure examined, as shown in Fig. 3.9. In particular, it was lower than the Ga adatom structure by 0.25 eV/1 ´ 1. Several inequivalent registries of layer 0 relative to layerp1 were considered but within a tolerance of about 0.02 eV/1 ´ 1 the energy of the 3  3 laterally contracted bilayer structure was independent of the registry with the substrate. This is consistent with sufficient mobility of the Ga atoms that explains the observation of a 1 ´ 1 corrugation pattern in STM [68], as a result of the time averaging inherent in the STM measurements. The stability of the laterally contracted bilayer structure is understood by considering the energy benefit of a reduced Ga–Ga spacing in the surface adlayers. The Ga bilayer model for the stable structure of the (0001) surface under Garich conditions is also supported by recent experimental results of another research group [79, 80], who studied the amount of excess Ga on the surface by measuring the transient in the specularly reflected RHEED intensity. An issue that has been discussed concerns the incommensurate structure of the bilayer [66] since STM imaging of the (0001) surface did not yield the expected incommensurate pattern (i.e., series of fringes) and the observed atomic spacing

Fig. 3.10 A schematic representation of a laterally contracted Ga bilayer above a Ga-terminated (0001) substrate. The average separations between layers are z12 = 2.54 Å and z01 = 2.37 Å. The filled and open circles in layer 0 represent a time-averaged image of the Ga atoms. The filled circles in layer 0 correspond to the positions at a particular time. The time-averaged vertical corrugation of layer 0 is approximately 0.16 Å. Note: In this projection the laterally contracted monolayer (layer 0) has been rotated by 30 degrees for ease of viewing (Fig. 3 a from [73], reprinted with permission from J. E. Northrup, J. Neugebauer, R. M. Feenstra and A. R. Smith, Physical Review B61, 9932 (2000). Copyright 2000 by the American Physical Society).

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corresponded to the 1 ´ 1 spacing (19 Å) as opposed to a value 1/6 or 1/12 smaller than this (as implied by the diffraction results [69]). However, 3-fold symmetry and nearly 12 ´ spacing and with substructure within each unit cell of nearly 1 ´ spacing have been observed by STM on a small region of a (0001† surface, which was adjacent to an open-core screw dislocation. It was thought that this observation could probably correspond to the “1 ´ 1” reconstruction on a small (0001) inversion domain [66]. In this case, it was considered likely that the details of the “1 ´ 1” reconstruction were frozen in place due to the small size of the (0001) region. There have also been several other investigations of the structure of the two GaN {0001} surfaces [81–89]. In particular, an analytic discussion of theoretical calculations is given in Ref. [81]. surface reconstructions have been p p Additional observed, such as the 10 ´ 10, 5 3 ´ 2 13 and 4 ´ 4 for the (0001) face and 6 ´ 8, p 7  7, and 2 ´ 3 for the N-face [75, 77]. A 2 ´ 2 reconstruction has been also rep ported for a (0001† surface [82] and a ( 3  3) R308 for a (0001) surface [83]. The observation of a 2 ´ 1 RHEED pattern on a (0001† surface has been understood as indicating a poorly ordered 2 ´ 2 reconstructed surface, in which the 2-fold periodicity is more easily seen with the electron beam oriented along the [1120] azimuth [82]. Several reports have indicated the sensitivity of the surface reconstruction on the presence of contaminants [67, 72, 83, 84]. A 4 ´ 4 reconstruction on the N-polar surface has been connected to oxygen or arsenic p contamination [83, 84]. We have seen [85] that In atoms induce a stable ( 3  3) R308 reconstruction (1 ´ 3 RHEED pattern) on the GaN (0001) surface after sufficient nitridation and the same reconstruction has been observed in InGaN growth under N-rich conditions [71]. Systematic experimental work [67, 70, 72] has suggested that the 2 ´ 2 reconstruction of GaN (0001) when it is observed during growth by PAMBE [27, 44, 83, 86, 87] should be induced by impurities such as As or Mg. It should be noticed that since many GaN MBE growth chambers had been used previously for III-arsenides, it is considered very likely that unintentional arsenic atoms may be involved in some of the observed reconstructions. It was shown that a partial pressure of 10–9 Torr of arsenic significantly modified the growth kinetics (As behaved as surfactant) and induced a 2 ´ 2 surface reconstruction during growth of GaN (0001) [67]. The proposed model of this 2 ´ 2 structure consists of one As-adatom per 2 ´ 2 unit cell [67, 88]. Furthermore, adding small amounts of Ga to the arsenic-induced 2 ´ 2 surface resulted to the formation of 4 ´ 4 and 5 ´ 5 reconstructions [72], in agreement to that reported in Ref. [76]. A 4 ´ 4 reconstruction was also observed at low temperature in Ref. [27]. A 2 ´ 2 reconstruction is also observed on the (0001) surface during MBE growth with NH3 gas source [74] and could be related to the adsorption of H atoms [78]. Finally, LEED patterns of clean GaN {0001} 1 ´ 1 surfaces, prepared in ultrahigh vacuum (UHV) by various treatments including heating at temperatures above 830 8C, have also exhibited splitting of the normal order spots into circular sextets (multiplets of six spots) as a function of the primary electron energy [89]. Such

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

LEED observations have been attributed to faceting of the surface [90]. However, another explanation [89] attributes the splitting to oppositely oriented, regular step arrays in the [21 10], [1120] and [1210] directions on the GaN {0001} surfaces. The multiplets of sharp spots were evolving from weak diffused rings when the annealing temperature was increased above 830 8C and this was explained by the formation of straight step edges oriented perpendicular to the [21 10], [1120] and [1210] directions, i.e., rotated by 608 each. Quantitative analysis of the data gave terrace widths of 11.0 ± 1.0 Å and step heights of 5.25 ± 0.2 Å. This surface structure may be the result of the development of “growth” spirals around the screw dislocations by thermal etching of the surface, similarly to growth spirals observed for Ga-rich growth [63, 69]. 3.3.2

GaN Substrate Preparation

An important issue in the homoepitaxial growth of semiconductors is the preparation of an atomically clean and smooth substrate surface. Ex situ substrate cleaning methods aim to remove any metallic and organic contamination from the substrate surface and usually end with the formation of a thin passivating oxide on it (of thickness similar to the native oxide). Substrate preparation within the MBE UHV system (in situ) usually includes a preliminary heating for outgassing of adsorbed gases in a preparation chamber and a final heating for oxide removal and preparation of an atomically clean surface within the growth chamber. The amount of oxide depends on the semiconductor material (e.g., it is less in InP compared to GaAs) but its complete removal is an absolute requirement for good epitaxial growth [91]. The oxide desorption temperature is usually similar to the temperature used for epitaxial growth (e.g., it is 580–600 8C for GaAs and 500– 530 8C for InP). The ex situ and in situ preparation of a GaN surface has been the subject of a large number of investigations, but for practical reasons the present discussion will be limited to a sample of representative and very relevant to GaN MBE reports [90, 92–97]. Rather extensive overviews of the studies in this area are given in Refs. [90] and [94]. A common finding of all the investigations is that a GaN surface that has been exposed to the air is contaminated with oxygen and carbon [90, 92–95]. A common characteristic of all the X-ray photoelectron spectroscopy (XPS) studies of the GaN surface oxide is the observation, in general, of two components of the O 1 s peak centered at 531.3–531.6 eV and 532.4–532.7 eV, respectively [93–95]. It is commonly accepted that the low-energy O 1 s component corresponds to stoichiometric Ga2O3. This assignment has been justified by observing that the corresponding oxide could be removed with NH4OH [93] and HCl [95] etches. Another support comes from the fact that UV/O3 oxidation results in an oxide dominated by the low-energy O 1 s XPS peak and solutions of HCl, NH4OH, and HF were very effective for oxide removal [94]. Prabhakaran et al. [93] have concluded that the native GaN oxides appear to be predominantly in the Ga2O3 form. They also

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suggested that the oxide may contain some component of mixed oxynitride of Ga, which is also soluble in alkali. Contrary to the low-energy O 1 s XPS peak, a general consensus is missing for the high-energy O 1 s peak at *532.7 eV. Prabhakaran et al. [93] reported only that it could be removed by argon ion sputtering while the *531.3 eV O 1 s peak remained. A similar result was reported by Shalish et al. [95], but they also noticed that sputtering on oxidized gallium removed the 532.7 eV O 1 s peak concurrently with a removal of the C 1 s peak. On the basis of this observation, they suggested that the high-energy O 1 s peak corresponds to C–O bonding. A different explanation was, however, given by King et al. [94], who attributed this peak to OH– species (hydroxides). This oxide component was dominant on GaN surfaces after solvent cleaning and prior to UV/O3 exposure. All the reports [90, 92–95] indicate the presence of carbon contamination on the GaN surface with a main C 1 s XPS peak at *285.7 eV. This is considered [94] typical of adventitious carbon and is indicative of a mixture of C–O and C–H bonding [94]. Prabhakaran et al. [93] have also reported the shifting of the C 1 s peak to the lower binding energy of 283.7 eV after sputter cleaning, and suggested that this is an atomic-type of carbon that gets incorporated into the crystal on exposure of the sample to air or during growth. Shalish et al. [95] have observed a C 1 s component at 289.9 eV, which was attributed to the carboxylic group (COOH) and, after etching in HCl, a peak at 287.7 eV assigned to C–Cl bonds. Concerning the ex situ GaN preparation, the reported work [93–95] definitely suggests using an HCl or HF, or perhaps NH4OH etch for oxide removal prior to the introduction of the GaN substrates in the MBE system. The various etchants, however, do not substantially affect the C contamination, while the UV/O3 oxidation treatment was found to be most useful for the removal of gross carbon contamination [94]. Experiments for the in situ preparation of the GaN surface have revealed an unusual difficulty to combine the chemical purity of the surface with its structural integrity, stoichiometry, and atomic level flatness. The C and O contamination cannot be removed by heating in UHV up to temperatures of 900–1000 8C [90, 94], while GaN decomposition occurs above *800 8C [94]. The difficulty to desorb oxides from GaN is attributed to the strength of the Ga–N bonds [94]. The oxides probably desorb as either Ga–O or N–O species instead of O2 and this requires breaking the strong Ga–N bonds. Annealing of GaN in fluxes of N and Ga are then considered necessary to maintain the stoichiometry of the surface [94]. Concerning carbon, it was concluded that most of the C–O bonded carbon desorbs at temperatures £ 500–600 8C leaving on the surface only C–H bonded carbon, which apparently desorbs at much higher temperatures [94]. Cleaning methods that use ion bombardment of the surface are certainly able to remove the impurities. However, they also produce crystal damage that can be annealed only at very high temperatures, which also yield a defective surface [90]. The reported experimental studies [90, 92, 94] suggest that efficient cleaning of GaN may be realized under NH3 and Ga fluxes. Heating the GaN surface under NH3 at 800–900 8C is certainly effective to remove C but contradictory results have

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

been reported for oxygen [90, 94]. King et al. [94] concluded that atomically clean surfaces were obtained by annealing in NH3 at 800 8C and the surface exhibited 2 ´ 2 reconstruction in LEED. However, Bermudez et al. [90] found only partial removal of oxygen after annealing in NH3 up to 900 8C. They attributed this to the fact that the reaction Ga2O3 + 2 NH3 ? 2 GaN + 3 H2O is endothermic by *0.79 eV/O atom; hence, reduction of Ga2O3 by NH3 may require temperatures above 900 8C, while the reaction 3 C + 4 NH3 ? 3 CH4 + 2 N2 is exothermic by about 6.7 eV/C atom [90]. The surface was undamaged, as suggested by LEED. Khan et al. [92] obtained atomically clean GaN surfaces by deposition of *2 ML Ga at 620 8C and annealing at 670 8C or exposure of the surface to a Ga flux of *5 ML min–1 at 900 8C. The finally observed O contamination was close to the AES sensitivity limit and the CKLL peak intensity was below 2% that of NKLL. Very strong 1 ´ 1 patterns were observed in RHEED and LEED. The efficiency of the Ga cleaning method was also confirmed by Bermudez et al. [90], who also pointed out that a Ga metal overlayer impedes loss of N. In situ RHEED observations of GaN surfaces that have been exposed to air show the absence of any amorphous native oxide layer on the surface, in contrast to what happens for the arsenide semiconductors [96]. The GaN surface is active towards the adsorption of oxygen and other impurities, due to the large number of unsaturated dangling bonds [97]. However, the oxidation process does not proceed to form a thick oxide layer due to the GaN chemical inertness. Thus, it is possible to grow GaN overlayers by RFMBE after whatever desorption occurs by heating the GaN substrate up to the growth temperature of *700 8C. At FORTH, we constantly use the following steps for ex situ preparation of *2lm GaN/Al2O3 (0001) MOVPE-grown templates 1. Degrease in hot acetone, propan-2-ol 2. Rinse in deionized water (DI) 3. Etch in 1 : 10 HF : H2O 4. Rinse in DI and N2 blow drying The templates are loaded on holders with indium bonding and are introduced in the multichamber MBE system where they are subject to 1. Outgassing up to 600 8C in the load chamber 2. Outgassing up to 700 8C in the growth chamber, while the N plasma has been ignited but it is not incident on the surface (this is not critical for the very low substrate temperatures, i.e., < 300 8C) The growth starts after annealing for *5 min at 700 8C.

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3 Plasma-Assisted Molecular Beam Epitaxy of III–V Nitrides Fig. 3.11 XTEM micrograph showing the homoepitaxial growth of a *0.4 lm GaN layer by RFMBE on a *2 lm GaN/Al2O3 (0001) MOVPE template. A structurally perfect epilayer/substrate interface is observed (indicated by the arrow).

HRTEM image, viewed along the [1120] axis of GaN, showing a region of the GaN MBE/GaN MOCVD interface. A perfect epitaxial growth has occurred.

Fig. 3.12

This process might not exclude that some O and C impurities are buried at the epilayer/substrate interface. However, even if they are present they do not have any effect on the structural quality of the overlayer, as shown in Figs. 3.11 and 3.12 [98]. Figure 3.11 shows a cross-sectional transmission electron microscopy (XTEM) image, taken along the [1120] axis of GaN, of a sample consisting of *0.4 lm GaN grown by RFMBE on a *2 lm GaN/Al2O3 (0001) MOVPE template. The epilayer/template interface is indicated by the arrow and it is hardly visible, suggesting a very low degree of disorder on the interface plane. The perfect epitaxial growth was confirmed by high-resolution TEM (HRTEM) observations, as is visible in the HRTEM image of Fig. 3.12. We have not observed the formation of any kind of extended crystal defects at the epilayer/template interface except threading dislocations from the substrate that propagate into the GaN epilayer crossing the interface, as shown in Fig. 3.11. We would like to point out here that heating of the GaN template above 700 8C resulted in surface roughening. The roughening was also favored, in general, by the incidence of the N beam during the heating of the GaN substrate. The surface

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

roughening at high temperature may indicate the efficient activation of the oxide thermal desorption process and thus the 700 8C should not be considered as a strict limit for the GaN heating. The roughened surface could be smoothed again by GaN overgrowth under optimized conditions. An in-depth investigation of the electronic properties of the epilayer/template interface should be undertaken in the future for the concrete definition of the optimum treatment for in situ preparation of the GaN surface. However, the described process is convenient and fast and allows to easily preserve the flatness of the MOVPE GaN wafers, something sufficient for most of the current applications of the RFMBE grown material. 3.3.3

Physical Understanding of the Growth on GaN (0001) Surfaces 3.3.3.1 Growth Chemistry

Newman [55] has discussed the important issues involved in the MBE synthesis of GaN. The conventional III–V semiconductors are grown with high quality under conditions (temperature, pressure) where the III–V compound and a vapor are thermodynamically stable. To overcome kinetic barriers of epitaxy, it has been empirically found that the optimum substrate temperature for the growth of highquality single-crystal thin films is *1/2 to 2/3 of the melt temperature. In the case of III-nitrides, however, synthesis occurs under conditions in which GaN is not the thermodynamically stable phase. In addition, the temperature of MBE growth (typically < 1123 K) is significantly below *1/2 of the theoretically predicted melt temperature (Tm = *2793 K) [55]. Typical MBE growth conditions for GaN fall within an area of the phase diagram in which Ga liquid and molecular nitrogen gas have the lowest free energy [55]. More reactive nitrogen species, such as those produced by a plasma source, provide sufficient energy to form GaN (see Eqs. (1–4) in Sect. 3.2.2). The synthesis of GaN involves a metastable growth process that is controlled by a competition between the forward reaction (GaN formation), which depends on the arrival of activated nitrogen species on the surface and the reverse reaction (GaN decomposition) [55]. The rate of GaN decomposition is very slow because of an unusually large kinetic barrier of decomposition, due to the strong metal-N bonds at the surface and so synthesis becomes possible under the used growth conditions. Driving the forward reaction at a sufficient rate facilitates growth at a higher temperature and at a lower pressure than is thermodynamically stable for GaN(s). However, practical limitations on the maximum flux of activated nitrogen limit the temperature of GaN MBE growth to *35% (900 8C) of the melt temperature (Tm = *2793 K) [55]. This relatively low growth temperature creates concerns for the material quality that can be achieved in PAMBE [99]. Newman [55] also pointed out that high kinetic energy species from the plasma (> 40 eV) on the film surface will cause an enhancement in the decomposition rate. Ideally, the impingement of a neutral or ion beam would be tuned to satisfy the resonant energy (and momentum) condition that enhances the surface diffusion rate, without significantly enhancing desorption or decomposition.

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3.3.3.2 GaN Evaporation

The evaporation of GaN from the surface of thin films has been studied by heating in vacuum [100, 101]. Guha et al. [100] reported a decomposition rate of 3– 4 ML min–1 at 830 8C, and Grandjean et al. [101] found that the decomposition rate is nearly zero below 750 8C, increases rapidly above 800 8C and reaches 1 lm h–1 at 850 8C. This means that it may be impossible to grow GaN at high temperatures that approach those used in MOVPE. The GaN decomposition is not important for the usual PAMBE growth process that is made at temperatures below 750 8C. 3.3.3.3 Ga Adsorption and Desorption

Several studies [86, 100, 102, 103] have revealed that the incident Ga atoms are not fully incorporated in the growing GaN film at the usual growth temperatures in PAMBE (700–750 8C) even when an excess of N-flux is present (III/V flux ratio < 1). The Ga incorporation ratio depends sensitively on the growth temperature, as shown in Fig. 3.13 [100]. Guha et al. [100] studied the surface lifetime of Ga adatoms on the GaN (0001) surface in the absence of an active nitrogen flux. They used a mass spectrometer mounted in direct line of sight to the wafer and monitored the desorbed Ga signal (mass 69) after pulses of Ga that did not exceed 1 ML deposition of Ga. The determined Ga lifetimes were from approximately 0.6–5 ns in the 685–750 8C range and the activation energy for Ga desorption was E % 2.2 ´ 0.2 eV, which is similar to the value of 2.5 eV for Ga desorption from a GaAs (111) surface [104].

Fig. 3.13 Measured incorporation ratio behavior for Ga during GaN growth as a function of reciprocal growth temperature. The Ga arrival rate was *0.6 ML s–1 and the active nitrogen flux was 0.8 ML s–1 (Fig. 2 from [100], reprinted with permission from Guha et al., Appl. Phys. Lett. 69, 2879 (1996). Copyright 1996, American Institute of Physics).

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

It should be mentioned here that according to the recent work of Mula et al. [80] the accumulation of Ga on a (0001) GaN surface may not be a linear function of time for deposition of more than 2 ML of Ga. Under appropriate Ga flux and substrate temperature conditions a dynamically stable Ga bilayer is formed on the GaN surface and no further Ga accumulation occurs. It has also been reported [79] that a dynamically stable Ga bilayer exists also on the surface during GaN growth within a range of Ga flux and substrate temperature (see below). Guha et al. [100] also studied the incorporation ratio of Ga during GaN growth by monitoring the reflected Ga signal detected by the mass spectrometer and the results are shown in Fig. 3.13. The incorporation ratio was defined as I = {R'– R(T)}/R', where R(T) was the reflected Ga signal at temperature T and R' was the reflected signal at a high enough temperature where all of the incident Ga was desorbed. Figure 3.13 suggests that when there is an active nitrogen flux present, a Ga adatom has a finite lifetime on a GaN surface during which it will diffuse on the surface and then either incorporate into the growing crystal, or desorb [100]. It is assumed that the activation energy for desorption is greater than the activation energy for surface diffusion. As the growth temperature increases, the residence time of a Ga adatom on the surface decreases: thus, the probability for encountering nitrogen adatoms for successful incorporation into the crystal decreases and the incorporation ratio drops. At lower temperatures, on the other hand, the residence times of Ga adatoms are long enough that almost all of them can encounter nitrogen adatoms and are incorporated into the crystal, resulting in a near unity incorporation ratio. The authors [100] pointed out that the absolute position of the curve of Fig. 3.13 is not of significance, since it is a consequence only of the specific growth conditions used during measurements. Similar results for Ga desorption during growth have been reported by other groups [86, 102, 103]. In particular, Hacke et al. [86] have studied the appearance of the 2 ´ 2 reconstruction on a GaN (0001) surface as a function of the Ga flux and substrate temperature. The transition from 2 ´ 2 to 1 ´ 1 surface reconstruction occurred by increasing the amount of Ga adatoms on the surface. When the substrate temperature was increased, an exponentially increasing amount of Ga flux was required to maintain the surface at the transition. This indicates the reduction of the residence time of Ga adatoms on the surface, with increased substrate temperature, in agreement with the plot of Fig. 3.13. The determined activation energies for Ga desorption were between 2.22 and 3.25 eV; the weighted mean was 2.76 eV. This activation energy is similar to that of evaporation of metallic Ga. Partial incorporation of the incident Ga flux was also observed by Iliopoulos and Moustakas [103], who determined a Ga incorporation probability equal to 0.75 for the growth of AlGaN films at 750 8C under N-rich conditions (III/V flux ratio < 1).

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3.3.3.4 Growth Rates as a Function of III and V Fluxes

We can distinguish two growth regimes as far as it concerns the dependence of the GaN growth rate on the III and V element fluxes (JGa and JN, respectively): the Ga-stable growth regime and the N-stable growth regime [105, 106]. In the Ga-stable regime, the GaN growth rate is limited by the amount of available reactive nitrogen and excess Ga is present on the surface. The growth rate increases monotonically with increasing flux of reactive nitrogen species (JN). This growth regime corresponds to the so-called Ga-rich growth conditions, which for sufficiently low substrate temperatures (where Ga and N desorption is negligible) is equivalent to the requirement that JGa/JN>1. The excess Ga can be thermally desorbed from the surface (GaN does not decompose) by employing a proper growth temperature; otherwise some Ga droplets are formed, as shown in Fig. 3.14. In the N-stable regime, the GaN growth rate is limited by the amount of available Ga atoms, i.e., the growth rate increases monotonically with the flux of Ga atoms (JGa). This regime corresponds to the so-called N-rich growth conditions and occurs for any substrate temperature when JGa/JN < 1. In this case, an increase of the substrate temperature contributes to the N-stabilization of the surface since it increases the Ga desorption rate. Myoung et al. [102] have applied a precursor-mediated model to investigate the GaN growth kinetics. The physical processes are essentially the same with those discussed by Guha et al. [100] for the interpretation of the results of Fig. 3.13. The Ga atoms arriving at the surface are adsorbed into a mobile, weakly bound precursor state. The Ga adatoms migrate on the surface and some of them move to a chemisorbed state, while others thermally desorb from the surface. When the Ga atoms encounter atomic nitrogen in a chemisorbed state, the forward reaction to form GaN occurs. Desorption from the chemisorbed state and decomposition of the bulk were ignored since the plasma sources do not produce high kinetic energy species and so the growth kinetics were determined by the JGa/JN ratio. The model gave growth rates that fitted well with the experimental results.

Fig. 3.14 SEM micrograph showing the formation of Ga droplets with a density of 5 ´ 104 cm–2 on the surface of a GaN film that was grown under Ga-rich growth conditions.

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

3.3.3.5 The GaN Growth Regimen – a Phase Diagram

Several studies have revealed the decisive role of the III/V ratio on the GaN (0001) surface for the growth mode and the structural, electrical and optical properties of the GaN films that are grown by PAMBE [51, 67, 70, 79, 80, 86, 102, 105–116]. Moustakas [110] pointed out that layer-by-layer growth of GaN occurs in the Garich regime. Subsequent work of many groups [51, 70, 102, 108, 111, 112] has fully justified that high-quality GaN films can be grown by PAMBE under Ga-stabilized surface conditions. Tarsa et al. [111] showed the significant effects of the III/V flux ratio (JGa/JN) on the surface morphology, structure and optical properties of GaN layers grown by RFMBE on MOVPE-grown GaN “templates”. GaN layers grown with low JGa/JN (N-stable growth) displayed a granular surface morphology and a tilted columnar structure with a high density of stacking faults. In contrast, films grown with high JGa/JN (Ga-stable growth) exhibited a smooth surface morphology with characteristic spiral growth hillocks and some Ga droplets. The spiral growth hillocks [115–117] are composed of monolayer height steps and terraces and result from step-flow growth around mixed edge/screw dislocations. Since each mixed dislocation pins two steps, the spiral hillocks consist of two interlocking spiral ramps [115]. Typical spiral hillocks on GaN surfaces are shown in Fig. 3.15. Smith et al. [70] used RHEED to study the transition between smooth and rough surface morphology in the homoepitaxial growth of GaN by RFMBE on MOVPE-grown GaN templates. For constant JN, they determined the critical JGa that corresponded to the transition between streaky and spotty RHEED patterns (smooth and rough surface, respectively) as a function of the growth temperature. The critical JGa was independent of substrate temperature below 700 8C, while it

Fig. 3.15 AFM micrograph showing the characteristic spiral hillocks with monolayer height steps on a *0.8 lm GaN film grown on (0001) Al2O3 under Ga-rich conditions. The rms roughness of the surface is 0.37 nm.

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Fig. 3.16 Phase diagram for PAMBE GaN homoepitaxy, for an active N flux of about 0.3 ML s–1. a–d refer to the four regimes corresponding to different Gaadlayer coverage: a almost no Ga accumulation (“N-rich” regime); b less than a Ga bilayer (“slightly Ga-rich” regime); c a Ga bilayer (“Ga-rich” regime); d Ga-droplets on top of a Ga bilayer (“very Ga-rich” regime) (Fig. 2 from Adelman et al. [79], reprinted courtesy of the authors and Wiley-VCH). Note that regimes b and c together correspond to the “intermediate” regime in the phase diagram of Heying et al. [107, 108].

increased above 700 8C. This was similar to the behavior of the Ga desorption from a GaN (0001) surface (Fig. 3.13). Heying et al. [107, 108] investigated the characteristic surface morphologies of GaN grown by PAMBE under various JGa/JN and substrate temperature conditions and identified three growth regimes on a surface structure diagram (JGa/JN versus substrate temperature). These were termed “Ga-droplet”, “intermediate”, and “N-stable” regimes; the first two being Ga stable and the last one being Nstable. A slightly modified growth diagram [79] from that of Heying et al. [107, 108] is shown in Fig. 3.16. The “Ga-droplet” regime corresponds to high Ga fluxes and low substrate temperatures. In this regime, the GaN films are grown with streaky RHEED patterns and exhibit Ga droplets on their surface. The “intermediate regime” corresponds to intermediate Ga fluxes and high substrate temperatures. It is characterized by the growth of films with streaky RHEED patterns but without Ga droplets on the surface. The boundary between the two Ga-stable regimes has an Arrhenius dependence on the substrate temperature and an activation energy of 2.8 eV. Finally, the N-stable regime appears with low Ga fluxes for all substrate temperatures and it is characterized by films with spotty RHEED patterns and rough surfaces. A film grown within the N-stable regime exhibited a very rough, cratered [107] or a heavily pitted morphology [108]. A film grown in the intermediate regime consisted

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

Fig. 3.17 AFM micrographs showing the surface morphology of different regions of an RFMBE-grown GaN/Al2O3 2-inch wafer: a near the edge of the wafer; b an intermediate zone; c center of the wafer. The III/V flux ratio was increasing monotonically from the center

to the edge of the wafer, so that only the region near the wafer’s edge corresponded to the “Ga-droplet” regime. The scan size is 2 ´ 2 lm and the z-axis full scale is 5 nm in all AFM micrographs.

of large, flat, smooth mesas separated by facetted trench features [107, 108]. A film grown in the Ga-droplet regime showed no pit features but a uniform, atomically flat surface [107, 108] and the characteristic spiral growth hillocks [107]. We observed a qualitatively similar behavior for the surface morphology of *0.8-lm thick GaN/AlGaN epilayers grown by RFMBE on (0001) Al2O3 substrates (Fig. 3.17) [118]. The III/V flux ratio varied across the 2-inch Al2O3 wafer due to different radial nonuniformity of the III and V fluxes, so that the III/V flux ratio was maximum at the edge and minimum at the center of the wafer. The GaN surface morphology for the highest, intermediate, and lowest III/V ratio on the wafer is given in Fig. 3.17 a–c, respectively. Figure 3.17 a corresponds to GaN grown within the “Ga-droplet” regime. The step-flow growth mode is evident and the surface is characterized by spiral hillocks with monolayer height steps. Surface pits appear as we move out of the area with Ga droplets, although the stepflow growth mode is still evident (Fig. 3.17 b). Finally, the density and apparent size of the surface pits are maximum at the lowest III/V flux ratio on the center of the wafer (Fig. 3.17 c). The presence of surface pits (depressions) was correlated to the defect structure of the films [107]. It was found that the pits in the N-stable regime corresponded to the termination of mixed and pure edge threading dislocations (TDs). The larger, deeper pits were correlated to mixed dislocations and the shallower pits to edge dislocations. Both dislocation types were also involved at the large pits (trenches) observed in the films grown within the intermediate regime. These large pits appeared to be associated with groupings of TDs that were predominantly edge TDs forming low-angle grain boundaries. The correlation between surface pits and threading dislocations is also confirmed by our results [51, 98], as shown in Fig. 3.11. A theoretical analysis of the dislocation-mediated surface morphology (pinned steps, surface depressions, spiral hillocks) of GaN layers, grown by MBE or

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MOVPE, has been made by Heying et al. [115], using the theories of Burton, Cabrera and Frank. The electron mobility in thin GaN films (doped with Si at *5 ´ 1016 cm–3) [108] or two-dimensional electron gas (2DEG) GaN/AlGaN structures [109] was also investigated as a function of JGa/JN, for constant growth temperature. Within the intermediate regime, the mobility increased with JGa and peaked at the highest JGa just below that necessary to form Ga droplets (at the boundary between “intermediate” and “Ga droplet” regimes). A thin film grown under such conditions exhibited the highest 300 K mobility of 1191 cm2 V–1 s–1, which is probably the highest value ever measured for GaN material. The mobilities dropped for structures grown within the “Ga-droplet” regime. The thin film grown within the N-stable regime was insulating [108]. A physical understanding of the overall experimental findings that highlight the critical role of the III/V flux ratio in PAMBE GaN growth may be built on the outcomes of the theoretical work of Zywietz et al. [114], who studied the diffusion of Ga and N atoms on (0001) and (0001† GaN surfaces using total-energy densityfunctional theory. It was determined that Ga adatoms have a diffusion barrier approximately four times lower than that of N adatoms on Ga-terminated (0001) and (0001† surfaces. This is due to the fact that the adsorbed Ga atoms interact with the substrate by delocalized metallic Ga–Ga bonds, which are weak (Ga melts at 30 8C) and the adatoms behave almost like a liquid film on the surface. N adatoms are unstable on the surface against evaporation as N2 molecules, but they can be kinetically stabilized at the surface due to their low surface mobility (migration is required for N2 formation). Thus, extended regions of the surface may be covered by (excess) N adatoms under N-rich growth conditions. In this case, the mobility of Ga atoms is significantly reduced since strong Ga–N bonds would have to be broken during Ga migration. Finally, the authors of Ref. [114] suggested that the determined diffusion barriers should be considered as lower limits of the effective diffusion barriers on a real surface (with defects, impurities, steps, etc.). The III/V flux ratio and substrate temperature, during PAMBE growth of GaN, determine the surface adlayer, hence, the adatom mobility on the growth surface [114]. Ga-rich growth conditions result in a small amount of excess N on the surface and the Ga adatoms are highly mobile. This results in 2D growth by a stepflow mode and leads to planarization of the surface and a reduction of the formation of stacking faults [114] and point defects [108]. The N adatoms are also efficiently incorporated if excess Ga adatoms are present on the surface, since the probability that fast-moving Ga atoms capture N atoms is much higher than the process where N atoms form molecules and desorb from the surface [114]. On the other hand, N-rich growth conditions result in N-terminated surfaces and a significantly shorter Ga diffusion length [114]. Reduction of the diffusion length to less than the mean distance between the binding sites should lead to statistical roughening of the surface. In addition, adatoms may be “trapped” at wrong sites and this favors the nucleation of stacking faults. Thus, slightly Garich conditions are expected to be optimal for the growth of GaN.

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

The qualitative conclusions of the above discussion should not be altered by considering the formation of the contracted Ga bilayer on the (0001) GaN surface under Ga-rich conditions (see below), since the lateral mobility of atoms in this adlayer is also expected to be high [73]. To interpret their experimental results, Heying et al. [107, 108] anticipated a continuous increase of the Ga-adlayer coverage with increasing Ga flux (JGa). An increase of the Ga-adlayer coverage should increase the adatom surface diffusion and reduce the surface pit density, which is completely eliminated in the “Ga droplet” regime. The semi-insulating properties of a film grown in the N-stable regime were attributed to the formation of some compensating center (point defect or point defect complex) that traps free carriers. Increase of the Ga-adlayer coverage within the intermediate regime is expected to suppress the formation of this compensating center, so that the mobility and electron concentration increase with JGa, with the optimum properties achieved at the highest Ga flux within the intermediate regime (at the boundary between “intermediate” and “Ga-droplet” regimes). The degradation of the electrical properties within the “Ga-droplet” regime is attributed [108] to the inferior quality of the material that is grown under the Ga droplets [116]. The issue of the Ga-adlayer coverage has been elaborated by recent experimental work [79, 80]. Mula et al. [80] investigated the adsorption and desorption of Ga on the (0001) GaN surface by analyzing the transients of the RHEED specular spot during Ga deposition, Ga vacuum desorption and Ga consumption by exposure to N. A pseudo-oscillatory transient with duration that depended on the Ga cell temperature (TGa) was observed after opening the Ga cell shutter. After closing the Ga shutter and opening the N shutter, a RHEED transient roughly symmetric to the adsorption transient but with a shorter duration was observed. The duration of the desorption transient (tdes) initially increased with the Ga deposition time (tads) but it remained constant (saturated) above a certain value of tads (7 s in the experiment), even when tads = 1 h was used. This was attributed to the formation of a dynamically stable Ga-adlayer on the (0001) GaN surface. The thickness (d) of the Ga-adlayer was determined by the formula dˆ

UGaN ; …1=tN 1=tdes †

…6†

where UGaN was the GaN growth rate under N-limited conditions and tN was the duration of the transient for Ga-adlayer consumption under N. The measurements were made for several substrate temperatures (TS) in the 700–740 8C range and in all cases a Ga film thickness of d = 2.7 ± 0.3 ML was determined. This was practically considered to coincide with the predicted [73] Ga bilayer that contains 2.3 ML of Ga, in terms of GaN atomic surface density. The Ga-adlayer coverage during GaN growth was investigated by Adelman et al. [79] by measuring the tdes of the excess Ga after interrupting the GaN growth by shuttering of both the Ga and N fluxes. From the shape and duration of the RHEED transients the authors discriminated four growth regimes, as shown in

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Fig. 3.16. RHEED transients exhibiting a full oscillation were observed only in regime C, for 1045 8C £ TGa £ 1075 8C with TS = 740 8C and were considered to correspond to the desorption of a Ga bilayer. Then the four regimes were associated to different Ga-adlayer coverages on the GaN surface: (a) “N-rich” regime: almost no Ga accumulates on the surface; (b) “slightly Ga-rich” regime with Ga coverage less than a bilayer; (c) “Ga-rich” regime with a Ga bilayer present on the surface; (d) “very Ga-rich” regime: accumulation of Ga droplets on top of the Ga bilayer. Based on these results, the authors constructed a phase diagram of the Ga-adlayer coverage during GaN growth as a function of impinging Ga flux and substrate temperature (TS) for a fixed active N flux, which is shown in Fig. 3.16. Within regime (c), GaN films were grown in step-flow mode as was indicated by the observation of smooth surfaces with about 40-nm terraces, the observation of spirals induced by screw dislocations and the absence of RHEED oscillations. The authors of Ref. [79] pointed out that there is evidence for a growth window leading to smooth GaN surface without Ga accumulation. Finally, before closing this section, it should be mentioned that some other studies contributing towards a better physical insight into the GaN growth mechanisms are given in Refs. [119–124].

3.3.4

Characteristics and Optimization of the (0001) GaN Growth

The ultimate objective in the development of a new growth technique is to achieve the capability for controlled and reproducible growth of high-quality material for device applications. In the case of PAMBE of III-nitrides, the control and optimization of the growth process appears particularly complex and difficult. As described in Sect. 3.3.3, the growth parameters (substrate temperature, Ga and reactive nitrogen fluxes) must be tuned within a rather short range of values (that depend on each other) for successful GaN growth. An obvious first limitation arises from the inability to determine and control with absolute accuracy the values of the growth parameters in an MBE system. The situation is even more complicated in PAMBE from the fact that there is no direct way for measuring the exact flux of the active nitrogen atoms that is available for growth on the substrate surface. Furthermore, GaN PAMBE is normally carried out at substrate temperatures where it is known that partial incorporation of Ga atoms occurs. Another problem comes from the fact that the optimum growth window is practically defined by reference to its results, i.e., the material characteristics, and these can be assessed only by evaluating already-grown structures. RHEED is a useful growth-monitoring tool but conventional observations of RHEED patterns do not allow the degree of judgment required for fine tuning of the PAMBE GaN growth conditions. A growth-tuning methodology based on the observation of RHEED transients [79, 80] appears possible. However, it will always be necessary to correlate any in situ observations to the properties of material grown under the corresponding growth conditions.

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

In the process of optimizing the multiparameter-dependent PAMBE GaN growth, we need to understand the sensitivity of the material characteristics on the values of various growth parameters. It has been common practice [79, 107– 109, 112] to keep the flux of reactive nitrogen species (JN) and the substrate temperature (TS) constant and to modify the flux of Ga atoms (JGa), hence the III/V flux ratio (JGa/JN). We have also followed a different approach, where we studied the sensitivity of the growth on TS [125]. A PAMBE GaN growth optimization should ideally address simultaneously the surface, microstructure, and electrical and optical properties of the epitaxial layers. Any intrinsic difficulties for simultaneously optimizing all the aspects of material quality should be identified. An atomically smooth GaN surface should not co-exist with Ga droplets, since they correspond to local regions of degraded material quality. However, device-quality heterostructure materials require abrupt interfaces and this raises the achievement of atomically smooth and defect-free surfaces as the first priority. In the following, we report on experiments [125] aimed at highlighting the role of TS in the growth of GaN and AlGaN layers and to identify growth conditions resulting to AlGaN/GaN quantum well (QW) heterostructure material appropriate for device applications (no Ga droplets, high optoelectronic quality).

3.3.4.1 Description of RFMBE Experiments

Seven samples with epitaxial structure (from top to bottom) of 30 nm Al0.23Ga0.77N/*3.5 nm GaN/30 nm Al0.23Ga0.77N/60 nm GaN were grown by RFMBE (Fig. 3.1) on MOVPE-GaN templates consisting of *2 lm thick GaN buffer layers on Al2O3 (0001) substrates. The III/V flux ratio was kept constant at approximately 1.8 while the substrate temperature was varied in the range of 680– 800 8C. Our growth experiments corresponded to moving horizontally, parallel to the temperature axis, from 680 8C to 800 8C in the RFMBE growth phase diagram (Fig. 3.16), as shown in Fig. 3.18. The growth was interrupted between the different layers, typically for 3 min, in order to stabilize the set Ga, Al and N fluxes before the growth of each layer. A

Fig. 3.18 Qualitative phase diagram for PAMBE, on which the investigated range of substrate temperature is shown. The fluxes were kept constant and the III/V flux ratio was approximately 1.8.

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main shutter was used to block all the beams to the substrate surface. An additional sample was grown at 680 8C with periodic growth interruptions under exposure of the surface to the N-beam (nitridation). Each interruption and nitridation step lasted 20 s and was repeated every 2 min for the GaN and every 2.5 min for the AlGaN layers, respectively. For all the samples, the growth was terminated by closing the main shutter and stopping the substrate heating power. The latter resulted to a reduction of the substrate temperature with an initial rate of *100 8C min–1.

3.3.4.2 Characterization of Materials Properties

The growth temperature of 680 8C was within the “Ga-droplet” regime, as concluded by the presence of Ga-droplets on the surface of the corresponding sample at a density of *5 ´ 104 cm–2, with average diameter and height of 6 lm and 1.4 lm, respectively (Fig. 3.14). The amount of Ga atoms within the droplets was calculated to be *12% of the total amount of Ga atoms incorporated in the GaN/ AlGaN crystal. No Ga droplets appeared for TS equal to 700 8C, 725 8C, 750 8C, 775 8C, and 800 8C, indicating that these temperatures corresponded to the “intermediate” growth regime [107]. The RHEED patterns during growth of the GaN layers were typically streaky for all the investigated growth temperatures, suggesting a smooth surface morphology. Spotty RHEED patterns were observed only for the initial *5 nm of GaN growth at 775 8C and 800 8C but they became streaky with the continuation of GaN growth. A significant difference, however, was observed for the brightness of the 1 ´ 1 GaN RHEED patterns; they were characteristically dark with almost invisible 01 and 01 diffraction streaks for TS up to 725 8C while the brightness significantly increased for TS = 750 8C and above. A notable surface roughening was suggested by the RHEED observations to be built continuously during the growth of AlGaN layers for TS between 750 8C and 800 8C. The surface morphology of the samples was examined by contact mode AFM using a Digital Nanoscope IIIa microscope. No surface pretreatment was used except for an HCl bath to remove Ga droplets from the sample grown at 680 8C. AFM produced results in agreement with the RHEED observations but also allowed the microscopic details of the surfaces to be distinguished. AFM micrographs of a MOVPE-GaN template and three MBE samples grown at 680 8C, 700 8C, and 720–750 8C are shown in Fig. 3.19. The MOVPE-GaN templates exhibited atomically smooth surfaces consisting of terraces separated by monolayer height steps, as shown in Fig. 3.19 a. Pits were also present on the surface and corresponded to sites of step pinning, which indicates that the observed surface pits were related to the surface termination of threading dislocations with a screw component [111, 115]. The sample grown at 680 8C (Fig. 3.19 b), within the Ga-droplet regime, was characterized by a smooth surface with the spiral hillocks that form around threading dislocations with a screw component [115] and consisted of terraces separated by monolayer height steps. A step-flow growth mechanism was followed in this case. Similar hillocks

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

also dominated the surface morphology of the sample grown at 700 8C (Fig. 3.19 c), within the intermediate regime, but the atomic steps were weakly resolved as a result of increased nucleation on the terraces. Small nuclei were indeed observable in the AFM micrograph of Fig. 3.19 c. Surface hillocks associated with threading dislocations were also observed for higher TS, such as TS = 725 8C. However, these hillocks did not exhibit steps; pinholes appeared at their centers instead. The occurrence of such hillocks on samples grown at similar temperatures was variable, indicating a significant role of the substrate structure and preparation. However, a generic characteristic of the surface of samples grown at temperatures higher than *720 8C was the presence of surface pits (depressions) correlated to the mixed character of threading dislocations, as shown in Fig. 3.19 d. The sample shown in Fig. 3.19 d was grown with TS = 720 8C for the GaN layers and TS = 750 8C for the AlGaN layers. Some wavi-

Fig. 3.19 AFM micrographs for the surface of a a MOVPE-grown GaN template; b–d AlGaN/GaN QW heterostructures (see text) grown at different substrate temperatures: b TS = 680 8C, c TS = 700 8C; d TS = 720 8C for

GaN and TS = 750 8C for AlGaN layers. The rms roughness is 0.2 nm (a); 0.4 nm (b); 0.5 nm (c); 0.6 nm (d). The scan size is 4 ´ 4 lm and the z-axis full scale is 5 nm in all micrographs.

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ness of the surface that corresponds to the spiral hillock-related morphologies of Fig. 3.19 b and c is obvious. Surface pits have been reported for the “N-stable” regime by Heying et al. [107, 108] but our experiments (Figs. 3.17 and 3.19) suggest that they also form in the “intermediate” regime, in conditions that probably correspond to the “Ga-rich” regime as defined by Adelmann et al. [79]. Surface depressions existed also on all samples grown at temperatures higher than 725 8C but the important characteristic for TS between 750 8C and 800 8C was the appearance of surface “grains” attributed to three-dimensional islands of AlGaN that became more evident with increasing growth temperature. The trend for three-dimensional growth of AlGaN at high TS is obviously related to a strain-relaxation mechanism. It seems that the increased Ga coverage on the AlGaN surface at low TS stabilizes the two-dimensional growth of strained AlGaN, so that the Ga has a surfactant effect for the growth of AlGaN on GaN (0001) similar to that found for the growth of GaN on AlN (0001) [80]. Photoluminescence (PL) measurements at 20 K revealed a trend for degradation of the AlGaN/GaN QW emission characteristics (peak intensity and linewidth) with increasing TS and this is attributed to the increasing roughness at the AlGaN/GaN QW interfaces. The best AlGaN/GaN QW was apparently grown at 680 8C, within the “Ga-droplets” regime, in these experiments. Figure 3.20 gives two characteristic 20 K PL spectra for TS = 680 8C and TS = 800 8C. The QW emission dominates the PL spectrum for TS = 680 8C, while emissions from the AlGaN barriers and GaN buffer layer dominate the PL spectrum for TS = 800 8C. In the latter case, a QW emission could not been distinguished from emissions below the GaN band gap that were related to impurities and deep levels of the GaN buffer layer and the n+GaN template. The gradual variation of material properties with TS in the range of 680–800 8C suggests that the substrate temperature may be a proper tool for adjusting the RFMBE growth conditions to the desired growth regime. Layers with a sufficiently smooth surface and without Ga droplets can be grown very close to the “Ga-droplet” regime (TS = 700 8C in these experiments).

Fig. 3.20 20 K PL spectra of two AlGaN/ GaN QW heterostructures grown at the extreme substrate temperatures (TS) of 680 8C (dashed line) and 800 8C (continuous line) of the investigated temperature range. Intense QW emission for TS = 680 8C suggests well-defined QW interfaces.

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE Fig. 3.21 20 K PL spectrum of a structure with four *1.3 nm GaN QWs that were formed between 10 nm AlGaN barriers grown under Ga-rich conditions by AlGaN growth interruption and surface nitridation. The intense QW emission is indicative of the high quality of thin AlGaN/GaN QW interfaces that can be achieved with this method.

3.3.4.3 Optimized Growth with Interruptions

Device-quality layers should be free of Ga-droplets but all the results suggest that the optimum AlGaN/GaN heterojunction can be grown within the “Ga-droplet” regime. For this reason, we developed a growth process that used TS = 680 8C (“Gadroplet” regime) but the growth was interrupted periodically (every 2–2.5 min) by closing the III-element shutter(s) and the surface was nitridated for 20 s. This process indeed solved the problem of Ga-droplets and preserved the step-flow growth mechanism. Furthermore, the exposure of the Ga-rich AlGaN surface to the N-beam (nitridation) resulted in the growth of thin GaN layers by consumption of Ga accumulated on the AlGaN surface, and thus to the formation of thin AlGaN/GaN QWs with high-quality interfaces. Figure 3.21 gives the 20 K PL spectrum of a sample with four *1.3-nm thick AlGaN/GaN QWs that were formed by growth interruption and nitridation of the Ga-rich AlGaN surface after every 10 nm of AlGaN growth. The duration of the growth interruption-nitridation determined directly the thickness of the thin GaN layer of the well.

3.3.4.4 Conclusions

To conclude, we have investigated the role of substrate temperature (TS) in the RFMBE growth of (0001) AlGaN/GaN heterostructures. The step-flow growth mechanism occurs in the “Ga-droplet” regime and results in the best AlGaN/GaN interfaces. The material properties change gradually with TS and layers with smooth surface without Ga-droplets can be grown very close to the “Ga-droplet” regime (TS = 700 8C in these experiments). However, we can grow layers with the ideal morphology of the “Ga-droplet” regime using periodic growth interruption and nitridation to consume periodically the accumulated Ga. Such nitridation of Ga-rich AlGaN surfaces can be used to grow very thin AlGaN/GaN QWs with high-quality interfaces and intense photoluminescence.

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3.3.5

Doping of GaN

In order to fabricate semiconductor devices, doping with impurity atoms is required to alter the conductivity of the semiconductor. For GaN in general, a number of dopants have been investigated including Si [126, 127], Ge [128], and O [129] for n-type conductivity and Mg [130, 131], Be [132], and C [133] for p-type conductivity. However, for PAMBE-grown GaN, the most commonly used dopants are Si and Mg for n- and p-type doping, respectively. Silicon has been the dopant of choice to obtain n-type GaN by PAMBE. Unintentionally doped GaN is typically n-type with very high resistivity that stems from compensation. It is still open to debate whether impurities or defects dominate the background compensation. However, with the introduction of Si impurities, the electron concentration in GaN films can be controlled between 1017 and 1021 cm–3 by varying the Si flux arriving at the growth surface. Based upon variable temperature Hall effect measurements of the net carrier concentration, the activation energy of Si donors was found to be in the range of 13 to 15 meV [126, 127]. In general, the carrier concentration in the 1016 cm–3 range is difficult to obtain reproducibly. Using migration-enhanced epitaxy (MEE) with a combination of AlN intermediate layers, Sugihara et al. reported electron mobilities as high as 668 cm2 V–1 s–1 for a carrier concentration of 9.5 ´ 1016 cm–3 [134].

Fig. 3.22 Electron mobility versus net carrier concentration of n-GaN films. The curves in the low carrier concentration regions are theoretical curves fitted to Eqs. (1) and (2) in Ref. [126] with the indicated dislocation densities. The dislocation densities of samples A and B were measured by TEM and found to be 8 ´ 109 and 2 ´ 1010 cm–2, respectively [126] (Fig. 1 from [126], reprinted with permission from Ng et al., Appl. Phys. Lett. 73, 821 (1998). Copyright 1998, American Institute of Physics).

3.3 Fundamentals of the GaN (0001) Epitaxial Growth by PAMBE

It has been widely observed by many research groups that the electron mobility first increases when the free electron concentration is decreased, and then decreases after a critical electron concentration is reached. This threshold value is typically in the low 1017 cm–3 range and is dependent upon the threading dislocation density. This phenomenon was first reported by Ng and coworkers [126, 135, 136] and a model of electron scattering by charged dislocations was proposed. In this model, it was suggested that dislocations with an edge component (which has dangling bonds) would capture electrons and become negatively charged centers. As a result, the lateral mobility of the remaining free electrons will be reduced due to scattering from these charged dislocations. The room-temperature electron mobility as a function of the net carrier concentration, as determined by Hall effect measurements, is shown in Fig. 3.22. It should be noted that this trend of electron mobility versus carrier concentration is independent of the growth technique and has also been observed for MOCVD GaN : Si films. The incorporation of Si was found to be independent of the polarity of GaN, i.e., Si incorporation levels were found to be equivalent for both N- and Ga-polarities based on secondary ion mass spectrometry (SIMS) measurements [137]. However, the incorporation of background impurities such as C and O was found to be higher for N-polarity GaN. Comparing the two different polarities of GaN, the resulting net electron concentration was found to be higher for N-polarity compared to Ga-polarity GaN for a given Si-doping level. In addition, the Si dopant profile was found to be less abrupt for the N-polarity films. Although direct measurements have not been made, a higher dislocation density for the N-polarity films is probable based on the lower mobility. It is also possible that the large number of threading dislocations act as diffusion pathways for the Si atoms. Early attempts to obtain p-type conductivity in GaN films were not successful until the discovery by Amano et al. [138] that the Mg-doped GaN films changed from highly resistive to p-type after electron beam irradiation. This was followed by the observation of Nakamura et al. [139] that thermal annealing is also effective to convert the MOCVD-grown GaN : Mg films to p-type. For Mg-doped GaN films grown in the presence of hydrogen, which is the case in MOCVD, the asgrown films are highly resistive due to the passivation of Mg atoms by H. Electron-beam irradiation or thermal annealing provides the necessary energy to dissociate the Mg–H complexes and thus activating the Mg dopants. However, post-growth annealing is not necessary for Mg-doping of GaN by MBE due to absence of H in the growth environment. The first observation of p-type conduction in MBE-grown GaN was reported by Moustakas and Molnar [140], where the room temperature hole concentration was up to 7 ´ 1018 cm–3. However, the reproducibility of such high hole concentrations remains difficult. The typical range of doping levels obtained range between 1 ´ 1017 to 2 ´ 1018 cm–3 with hole mobilities that are usually less than 10 cm2 V–1 s–1. The activation energy of the Mg acceptor level has been reported to be in the range of 140 to 180 meV [130, 141, 142]. Consequently, only about 1 to 2% of the Mg atoms are ionized at room temperature and two orders of magnitude higher Mg incorporation is required to obtain the desired hole concentration. However, there is an upper limit to the amount of Mg that can

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be incorporated as high levels of Mg can result in diminished structural quality of the film. There is also evidence that there exists a narrow window of optimal growth conditions for efficient p-type doping with Mg [143]. Since the vapor pressure of Mg is relatively high, there is competition between thermal desorption and incorporation into the GaN lattice at the typical growth temperature of about 700 to 750 8C. The incorporation of Mg was found to be relatively independent of the arriving Mg flux (for higher fluxes) at a growth temperature of 750 8C [144]. Higher Mg incorporation can be achieved by lowering the growth temperature as well as reducing the Ga/N ratio to increase the availability of Ga sites for Mg incorporation [145]. Smorchkova et al. [131] have observed the increase of Mg incorporation with the Mg arrival rate growing at a temperature of 650 8C. The doping profile was shown to be abrupt with no observable memory effect. In a different study, the resistivity of the Mg-doped films for a given growth temperature displayed a parabolic behavior with increasing Mg flux [130]. For a given growth temperature, there exists a minimum point for which the resistivity of the doped films is lowest. It was proposed that too high a dose of Mg can induce lattice distortions and disorder in the film. The annealing of the films up to 850 8C resulted in the reduction of the hole concentration with an increase in the mobility of the holes. The activation energy before and after annealing was 140 and 176 meV, respectively. This change in activation energy accounts qualitatively for the reduction in the hole concentration and the increase in mobility consistent with the removal of disorder due to annealing [130]. Other attempts have been made to try different dopant atoms to obtain p-type GaN. Doping with Be has met with little success [132] although there is evidence from theoretical calculations that involving hydrogen in the process may aid the incorporation of Be into the Ga substitutional site rather than an interstitial site [146]. At higher fluxes of Be, the formation of Be3N2 will occur which will degrade the quality of GaN [147]. Carbon doping has been attempted using NH3 gas-source MBE with the resulting films being highly resistive and showing no ptype conduction [133]. 3.4

Heteroepitaxial Growth 3.4.1

Substrates for PAMBE GaN Heteroepitaxy

GaN bulk crystal growth [148] exhibits a slow development and it has not been possible until now to produce practically useful GaN wafers. Thus, the entire IIInitrides technology is developed by epitaxial growth on a variety of substrates, such as Al2O3, SiC, Si, GaAs, and LiGaO2. An extensive review of the alternative substrates and their effects on the III-nitride epilayer material properties has been published recently by Liu and Edgar [149]. Several substrate-related aspects of the heteroepitaxial III-nitride growth on sapphire, SiC, GaAs, and oxide substrates have been also discussed in Refs. [150–153].

3.4 Heteroepitaxial Growth

Depending on the crystal symmetry and the orientation of the substrate surface, it is possible to grow hexagonal (wurtzite) or cubic (zincblende) III-nitride epilayers. Hexagonal GaN is grown on Al2O3 (0001), SiC (0001), Si (111), GaAs (111) and LiGaO2 (001) substrates, but only the first three have provided material quality enabling device applications. Cubic GaN is grown on GaAs (001), Si (001), and SiC/Si (001) substrates but its quality is far from being adequate for technological applications. The PAMBE method has been used, similarly to the other epitaxial methods, with all the alternative substrate types. The growth problems encountered in each heteroepitaxial system are, however, material specific and it would be practically impossible to address all the alternative cases in a comprehensive way within the limited extent of this chapter. We will thus refer the reader to some recent works for the PAMBE growth of GaN on SiC [154–158], Si [159–161], SiC/Si [162], GaAs [163–171], LiAlO2 [172], LiGaO2 [173], r-plane Al2O3 [174] and a-plane Al2O3 [175], and the following discussion will be limited to heteroepitaxy on c-plane sapphire. 3.4.2

Important Issues in the Heteroepitaxy of GaN-on-Al2O3 (0001)

C-plane-oriented sapphire (Al2O3) is the most commonly used substrate for the growth of GaN films. The lattice mismatch between sapphire and GaN, the difference in thermal expansion coefficients and the nonequilibrium conditions of growth lead to the formation of interfacial as well as other defects. The main defects are misfit dislocations (MDs), threading dislocations (TDs), translation domain boundaries on prismatic planes (TDBs) or otherwise prismatic stacking faults (PSFs), stacking faults on the basal plane (BSFs), low-angle domain boundaries (LADBs) and nanopipes. Most of them emanate from the heterostructure interface and propagate through the whole film thickness. Moreover, depending on the conditions of growth and given that GaN is a polar material it can grow with two different polarities. As a result, defects called inversion domain boundaries (IDBs) are also formed emanating from the GaN/Al2O3 interface. HRTEM observations showed that interactions between IDBs and BSFs lead to the structural transformation of IDBs from the low-energy and electrically nonactive IDB* type to the high-energy and electrically active Holt type [176]. Using the topological theory and the circuit-mapping technique, a detailed analysis of the different types of defects that are observed in epitaxial nitride thin films and interfaces are given in [177] and elsewhere in this handbook. The important role of the GaN/Al2O3 interface in device performance is due to the fact that it is a source of defects that may change dramatically the device properties. Whatever the deposition technique is, the microstructure of GaN thin films and their surface morphology strongly depend on the growth conditions. Important parameters of growth are the substrate surface pretreatment-nitridation, type (AlN or GaN) – thickness and deposition temperature of the buffer layer, growth temperature – growth rate and III/V flux ratio for the deposition of the main GaN

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epilayer [51, 112, 178]. These parameters affect the microstructure of the materials and thus the properties of the different devices. In a previous section of this chapter, we have presented analytically the fundamentals of the GaN (0001) PAMBE growth. It was pointed out that the III/V flux ratio and substrate temperature determine the Ga-adatom surface mobility and thus the GaN growth mode and the quality of the crystalline epilayers. Layer-bylayer growth by the step-flow mode occurs under Ga-rich conditions, when the GaN surface is covered by at least a Ga bilayer. The material properties of a thick epilayer will certainly depend on the surface kinetics, but in the case of highly lattice-mismatched heteroepitaxy the most important role belongs to the structural quality of the epilayer/substrate interface. The structure of a highly mismatched epilayer/substrate interface is determined by the properties of the substrate surface (cleanliness, smoothness) and the mechanisms of nucleation (wetting) and strain relaxation of the epilayer. Some pretreatments of the substrate surface are usually employed in order to favor the 2D character of the nucleation process and to facilitate the strain relaxation process. In the case of GaN-on-Al2O3, substrate surface nitridation and buffer layer play a key role in the microstructure configuration of the interface and the overgrown GaN thin films by MOCVD [179–186] or MBE [21, 87, 178, 187–198]. It is thus important to acquire a clear understanding of the nitridation process and its effects, since several reported results have not been sufficiently conclusive [87, 190, 192, 193, 195, 196]. An investigation aiming to provide further insight into the RF-plasma nitridation of (0001) sapphire was recently reported by Georgakilas et al. [178] and Mikroulis et al. [198]. Emphasis was placed on the temperature and time dependencies of the nitridation process and the effect of the nitridation temperature on the polarity and the microstructure of GaN films grown using a two-step growth process; an initial 16 nm GaN or 20 nm AlN nucleation layer was grown at 350 8C (LT: low temperature) and then annealed at 700 8C, which was also the growth temperature for the overgrown *0.3 lm GaN film. The sapphire surface was subjected to nitridation treatments of duration up to 100 min, by a nitrogen RF plasma source mostly operated at 500 W and a N2 pressure of 1.5 ´ 10–5 Torr. Two extreme substrate nitridation temperatures have been used: *700 8C (HNT: high nitridation temperature) and *165 8C (LNT: low nitridation temperature). Another series of samples in which a 20 nm AlN buffer layer was grown at 700 8C (HT: high temperature) on LNT (0001) sapphire followed by the growth of the main GaN epilayer at the same temperature was also investigated. The nitridation effect on the sapphire surface was studied in situ by RHEED and ex situ by AFM and AES. The local atomic structure of the interfaces was studied by HRTEM on cross-sectional specimens whereas XTEM was used for the investigation of the structural properties of GaN epilayers. RHEED data showed a substantial inplane lattice relaxation for nitridation at either *700 8C (HNT) or *165 8C (LNT). However, AES and HRTEM (see below) revealed that a substantial surface nitride layer, with average thickness of 1.5 nm, was formed only during 100 min nitridation at HNT. The N/Al AES peak ratio in-

3.4 Heteroepitaxial Growth

creased linearly with the time during 100 min nitridation at HNT. According to RHEED and AFM observations, 3D nitride islands were formed by 100 min nitridation at HNT, while the smoothness of the substrate surface improved after nitridation at LNT. In the following sections, electron microscopy investigation of the significance of sapphire nitridation processes, the amount of nitridation and its effect on the interfacial structures and the polarity of GaN epilayers grown on LT GaN or AlN buffer layers will be presented. A comparison of the microstructure of GaN films grown with the two different polarities will also be presented.

3.4.3

Electron Microscopy Investigation of Nitridated Al2O3 Interfaces 3.4.3.1 Experimental

The samples for TEM-HRTEM observations were cut in the cross-section orientation and thinned to electron transparency by the standard procedure of mechanical grinding followed by appropriate Ar ion milling. The TEM observations were carried out in a JEOL 120CX electron microscope operated at 100 kV. HRTEM observations were performed in a Topcon 002B and a JEOL 2010 electron microscopes operated at 200 kV, with a point-to-point resolution of 0.18 nm and 0.19 nm (Cs = 0.4 mm and Cs = 0.5 mm) respectively. The convergent beam electron diffraction (CBED) experiments were carried out in the JEOL 2010 electron microscope with a probe diameter of 10 nm.

3.4.3.2 Observation and Analysis of Interfacial Defect Content

HRTEM in cross-section geometry is a very powerful technique to investigate the effect of nitridation on sapphire surface, the local atomic structure of the interface between sapphire and buffer layer as well as the microstructure of the overgrown GaN thin films. The interfaces of the LT GaN buffer layer/Al2O3 and the LT AlN buffer layer/ Al2O3 observed in different samples, that all have undergone 100 min nitridation of sapphire surface at 165 8C, appeared to have remarkable structural quality. The two cross-sectional HRTEM images that are illustrated in Fig. 3.23 a, b, viewed along h1120i GaN//h1010i Al2O3 and h1120iAlN//h1010i Al2O3 zone axes, respectively, reveal that both interfaces are sharp and atomically smooth indicating that LNT nitridation of sapphire appeared to be limited to a surface atomic plane. On the contrary, a significant difference on the interfacial structure of the HNT specimen was observed. This is evident from the HRTEM image of Fig. 3.23 c taken along h1120i GaN//h1010i Al2O3 zone axes. The LT GaN buffer layer/Al2O3 interface of the HNT specimen is rough and cannot be clearly located. A bright, strong contrasted interfacial zone is observed having an average thickness of 1.5 nm. This interfacial zone corresponds to a surface nitride transition layer formed during the 100 min nitridation of the sapphire surface at 700 8C.

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Uchida et al. [182] reported the uniform formation of an initial amorphous aluminumoxynitride (AlNxO1–x) over the sapphire surface upon nitridation with NH3 in an MOCVD reactor. Such an amorphous layer was not observed in the sample shown in Fig. 3.23 c. The results presented here also differ from those reported by Widmann et al. [192] who investigated the effects of the nitridation temperature by comparing specimens that were subjected to sapphire nitridation up to 90 min at 200 8C, 500 8C, and 750 8C. They used a 25 nm AlN buffer layer grown at 550 8C and ob-

Fig. 3.23 Cross-sectional HRTEM images of interfaces, viewed along h1120iGaN (AlN)// h1010i Al2O3 zone axes. a LT GaN buffer layer/LNT Al2O3; b LT AlN buffer layer/LNT Al2O3; c LT GaN buffer layer/HNT Al2O3. The sharp and atomically smooth interfaces corre-

sponding to the LNT samples a and b, indicated by the white lines, are clearly visible. The thin interfacial layer formed on sapphire surface due to high-temperature nitridation is depicted between the two white lines in c.

3.4 Heteroepitaxial Growth

served by RHEED and HRTEM that, whatever the temperature and duration of nitridation used, the same surface phase was obtained. For their samples, sapphire nitridation was as efficient at low temperatures as at high temperatures. However, better structural quality of the interface region between sapphire and AlN was obtained for LNT. Heinlein et al. [190, 193] also investigated the time dependence of sapphire nitridation by RF plasma, using XPS, LEED, and AFM. They reported the formation of one monolayer of surface nitride after *300 min nitridation at 400 8C [190] and *200 min at 600 8C [193] and the growth of protrusions afterwards [190]. Nevertheless, the nitridation treatment did not have any clear effect on the properties of the GaN films. Sonoda et al. [195] using in situ RHEED observed diffraction spots corresponding to the formation of an AlN thin layer during 210 min of sapphire surface nitridation at 600 8C by supplying nitrogen plasma. The interfacial nitridation layer depicted in Fig. 3.23 c is also attributed to a very thin AlN interlayer as it will be demonstrated in the following. The interfaces depicted in Fig. 3.23 a, c are both formed between a LT GaN buffer and Al2O3. However, their interfacial structure is significantly different owing to the different amount of nitridation at LNT and HNT, respectively. In contrast, the interfaces shown in Fig. 3.23 a, b, formed between two different heterostructures, are sharp and atomically smooth given that both have been subjected to the same nitridation treatment (LNT) prior the deposition of the buffer layer. Due to the difference in the lattice mismatch between the two heterostructures their interfacial defect content is expected to be different. Conversely, the thickness of the interfacial nitridation layer observed in the HNT specimen is very low. Hence, the only way to come across the nature of this interlayer is the investigation of its defect content. Therefore, a structural analysis of the three interfaces illustrated in Fig. 3.23 has been performed and it was used for the characterization of the nitridation layer observed in Fig. 3.23 c [199]. The natural or lattice inplane misfit between GaN and Al2O3, taking GaN as the reference crystal, is given by the formula [200–203] m = (ds – de)/de,

(7)

where de{1010GaN} = 0.276 nm and ds{1120Al2O3} = 0.2379 nm are the interplanar spacing of {1010} planes of GaN and {1120} planes of Al2O3 respectively, which results in m = –13.8%. Considering the AlN/Al2O3 interface, with de{1010AlN} = 0.2695 nm, the corresponding lattice misfit is calculated to equal –11.73%. Thus, a compressive strain is exerted on the thin GaN and AlN buffer layers whereas the substrate, due to its large thickness, is considered to be unaffected and its lattice parameters to be constant. Since the thickness of the deposited buffer layers is larger than the critical thickness necessary for plastic relaxation [204], the mismatch between the two hexagonal crystals is expected to be accommodated by a network of three equivalent sets of perfect 60o misfit dislocations introduced in the plane of the interface. The Burgers vector of the misfit dislocations is b = 1/3

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h1120i in terms of the GaN or AlN lattices or b = 1/3h1010i in terms of the Al2O3 lattice. The edge component of one set of misfit dislocations is visualized in experimental HRTEM images as terminating fringes of the corresponding substrate lattice planes when they are viewed along h1120i GaN or AlN//h1010i Al2O3 zone axes [205]. Figure 3.24 a–c are Fourier-filtered images taken from the images of Fig. 3.23 a–c respectively, using only the inplane Fourier spatial frequencies. In Fig. 3.24 a, which corresponds to the GaN/Al2O3 interface of the LNT case, the {1120} Al2O3 lattice fringes terminate at the interface in a variation of seven or eight fringe intervals whereas in Fig. 3.24 b, which corresponds to the AlN/ Al2O3 interface also of the LNT case, the equivalent lattice fringes terminate in nine fringe intervals. As is clearly visible in Fig. 3.24 c, {1120} lattice fringes of Al2O3 terminate at the interface between Al2O3 and the thin interfacial layer formed during nitridation of the sapphire surface at 700 8C for 100 min. Terminating lattice fringes are observed in every nine fringe intervals as in the interface of the LNT sample (Fig. 3.24 b), giving evidence that the thin nitridated interlayer corresponds to an AlN layer. These experimental observations are discussed in the following. The spacing between edge misfit dislocations is given by the formula Dd = | b |/m,

(8)

where b is the Burgers vector. To calculate the theoretical spacing between the edge components of 60o misfit dislocations introduced in the interfaces shown in Fig. 3.24, | b | in Eq. (8) should be replaced by | b | cos 308, the edge component pof b along the corresponding <1120> direction in the Al2O3 lattice, | b | = a/ 3 = 0.2747 nm [205]. Taking this into account, the dislocation spacing is found to be Dd = 1.724 nm in the GaN/Al2O3 interface and Dd = 2.028 nm in the AlN/Al2O3 interface. Estimating the dislocation spacing in terms of the d-spacing of {1120} planes of Al2O3 that remains unaffected, for a stress-free GaN/Al2O3 interface one additional {1120} atomic plane of Al2O3 should be expected every 6.25 atomic planes of GaN. This practically means that misfit dislocations should be introduced in a successive sequence of 6-6-6-7 atomic planes of GaN or 7-7-7-8 atomic planes of Al2O3. Similarly, for a stress-free AlN/Al2O3 interface one additional {1120} atomic plane of Al2O3 should be expected every 7.5 atomic planes of AlN. Thus, a successive variation of 7-8 atomic planes of AlN or 8-9 atomic planes of Al2O3 should be expected. The effective spacing of one family of misfit dislocations introduced in the LT GaN/Al2O3 interface is directly measured on the filtered image shown in Fig. 3.24 a. It is seen that {1120} Al2O3 lattice fringes terminate at the interface, i.e., misfit dislocations are introduced in a succession of 8-8-7-7-7-8-8-7 fringe intervals corresponding to 14.27 nm in length. This is consistent with a local effective misfit dislocation spacing of Ddeff = 1.784 nm or 7.5 atomic planes of Al2O3 and consequently to an effective misfit relief d equal to –13.33%. Furthermore,

3.4 Heteroepitaxial Growth

Fig. 3.24 Fourier-filtered images taken from the images of Fig. 3.23 a–c respectively, using only the inplane Fourier spatial frequencies. Terminating {1120} Al2O3 lattice fringes at the interfaces, revealing the position of a regular array of one family of misfit dislocations, are

denoted by the white T symbols. c A misfit dislocation at the interface between the thin interfacial nitridation layer and GaN is also visible. Horizontal white lines indicate the interfaces.

this means that 96.6% of the compressive strain on the LT GaN buffer layer is relaxed through the introduction of the misfit dislocation network. Since the effective misfit d has a smaller absolute value than the lattice misfit m, a compressive (–0.74%) residual strain is exerted on the LT GaN buffer layer. For the LT AlN/Al2O3 interface the effective spacing of one set of misfit dislocations is measured on the Fourier-filtered image illustrated in Fig. 3.24 b. The {1120} Al2O3 lattice fringes are seen to terminate at the interface in nine fringe intervals leading to an effective spacing of nine atomic planes of Al2O3 or

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Ddeff = 2.14 nm. Consequently, the effective misfit relief equals to –11.12% or 94.76% of the compressive strain is relaxed through the misfit dislocation network introduced in the interface. As is measured in the image of Fig. 3.24 c, the local effective misfit dislocation spacing in the interface of the HNT sample equals that of the AlN/Al2O3 interface measured in Fig. 3.24 b, i.e., Al2O3 lattice fringes terminate in every nine fringe intervals. Thus, Ddeff = 2.14 nm and the corresponding effective misfit d = –11.12%. Based on the above it is deduced that the thin interfacial zone formed during the 100-min nitridation of the sapphire surface at 700 8C is a thin AlN interlayer. The effective misfit d in a relaxed configuration is given by the formula [202, 203, 206] d = (ds – deeff )/de

(9)

where deeff is the average experimental d-spacing of the epilayer planes measured after relaxation and ds, de the d-spacings of {1120} Al2O3 and {1010} epilayer atomic planes, respectively. Using the calculated value of the effective misfit d and taking deeff = 0.2678 nm measured on the experimental image of Fig. 3.24 c, the value of de is estimated from the above formula being equal to 0.2688 nm, in good agreement with de{1010 AlN} = 0.269 nm. Therefore, it is concluded that nitridation of the sapphire surface for 100 min at high temperature leads to the transition of few surface layers to AlN layers and thus to the formation of an AlN/Al2O3 structural interface. It should be noted that experimental observations in III-nitrides have shown that in low misfit thin layered heterostructures [207] the basic theories for equilibrium critical thickness calculations [204, 208–210] are not experimentally verified. On the contrary, in highly mismatched systems, as those reported in this work, the critical thickness of the epilayers above which misfit strain relief occurs is consistent with the values calculated from the theories [204, 209, 210]. The thin AlN interlayer formed due to HNT of sapphire has an average thickness of 1.5 nm. As was shown experimentally, this thickness slightly exceeds the value of the critical thickness and thus a regular array of misfit dislocations is being introduced in the interface to partially accommodate the lattice mismatch. 3.4.4

Effect of Al2O3 Nitridation on the Polarity and Microstructure of GaN Epilayers

In this section, XTEM and HRTEM investigation on the microstructure of GaN or AlN buffer layers grown on LNT and HNT Al2O3 substrates as well as of the overgrown GaN epilayers is summarized with respect to the Al2O3 nitridation process. Results from CBED experiments confirming the polarity control of the grown epilayers are also given. Micrographs taken from a LNT sample are shown in Fig. 3.25. The bright field (BF) XTEM images of Fig. 3.25 a, b show a low defect density compared to the usual structure of RFMBE GaN [51]. The region above the nitridation layer

3.4 Heteroepitaxial Growth

Fig. 3.25 a, b BF XTEM micrographs showing the microstructure of the LT GaN buffer layer and the overgrown GaN film of the LNT sample. The highly perturbed region near the interface and the low defect density of the epilayer are depicted; c HRTEM image, viewed along h1120i GaN //h1010iAl2O3 zone axes, illustrating the sharp interface as well as cubic GaN “pockets”, embedded into the hexa-

gonal matrix and BSFs; d CBED pattern recorded along [1010] zone axis on the matrix of the top GaN layers of the sample shown in a; e Corresponding simulated CBED pattern where the 0002 reflection is indicated pointing towards the free surface of the GaN revealing the N-polarity of the layers (specimen thickness 76 nm).

appeared highly perturbed, indicating irregular stacking of layers at the first stages of GaN growth [51]. This area corresponds to the LT GaN buffer and the first layers of the GaN overlayer and consists of cubic GaN “pockets”, embedded in the wurtzite GaN buffer, and high density of BSFs. The sharp buffer/substrate interface and embedded cubic phase material are clearly depicted in the HRTEM image of Fig. 3.25 c, viewed along h1120iGaN//h1010iAl2O3 zone axes. The majority of the defects observed in the main GaN epilayer are threading dislocations, with a density of the order of 1 ´ 1010 cm–2, and BSFs that are formed within the whole film thickness. The polarity of the overgrown GaN layers was revealed in situ by RHEED [64] and ex situ by KOH etching [211] results and confirmed by CBED observations. Following growth interruption and substrate cooling, the characteristic 3 ´ 3 reconstruction RHEED patterns [64, 198] were always obtained indicating that Nface material is grown on low-temperature nitridated sapphire by nitrogen RF

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plasma, using a GaN buffer layer. Anisotropic etching [211] in a solution of KOH : H2O (1 : 3.5) at 300 K for 30 min, followed by AFM observations was applied to all GaN thin films and confirmed the conclusion reached by RHEED. Significant etching occurred, resulting in a pyramidal surface morphology, indicating that the material grown was of the N-polarity [198]. RHEED and KOH etching results were further confirmed by CBED observations carried out on the GaN matrix of the LNT samples. Figure 3.25 d illustrates the experimental CBED pattern recorded on the matrix of the top GaN layers of the sample shown in Fig. 3.25 a, along the [1010] zone axis. The experimental CBED pattern was compared with simulated patterns calculated using the EMS software package [212], for thicknesses ranging from 50 to 120 nm with steps of 1 nm. A good match was obtained for a specimen thickness of 76 nm and the corresponding simulated CBED pattern is depicted in Fig. 3.25 e. The orientation of the c-axis was determined by comparison of the orientation of the CBED pattern with respect to the substrate/buffer direction in the XTEM images. The 0002 reflection that is indicated pointing towards the free surface reveals the N-polarity of the layers. Micrographs taken from a HNT sample are shown in Fig. 3.26. The BF XTEM image of Fig. 3.26 a illustrates the interface, the defected buffer layer and the whole overgrown GaN film. The crystalline quality of this sample is lower than that of the LNT one since the density of IDBs and threading dislocations, which propagate through the whole film thickness, is higher. However, the surface of the GaN film is relatively smooth [51]. IDBs that are observed to emanate from the thin AlN transition layer and propagate through the GaN buffer layer towards the top surface, are illustrated in the HRTEM image of Fig. 3.26 b taken with the electron beam along h1120i GaN// h1010i Al2O3 zone axes. By using HRTEM image simulations and comparison with the experimental HRTEM images, the majority of them have been characterized as being of the IDB* character. HRTEM observations showed that, following the growth direction, IDBs of IDB* type are transformed to those of the Holt-type structure. It was proved that these transitions are due to the interaction of two distinct planar defects, IDB-BSF, and can be attributed to the different growth rates of adjacent domains of inverse polarity [176]. No cubic phase GaN embedded in the hexagonal phase buffer layer was monitored in these specimens. RHEED patterns obtained from all specimens grown on nitridated sapphire surfaces up to 600–700 8C and a GaN buffer layer, showed the characteristic 2 ´ 2 reconstruction in agreement with the previous reports for Ga-face material [64]. The Ga-polarity of the materials was also revealed by anisotropic etching in a KOH : H2O solution, since their surfaces remained essentially intact [138]. The RHEED and KOH etching results were further confirmed by CBED patterns taken on the GaN matrix near the free surface of the films. The experimental CBED pattern, recorded along [1010] zone axis and the corresponding simulated one for a specimen thickness of 83 nm, are illustrated in Fig. 3.26 c, d. The 0002 reflection pointing towards the growth direction reveals the Ga-polarity of the material.

3.4 Heteroepitaxial Growth

Fig. 3.26 a BF XTEM micrograph where the LT GaN buffer/Al2O3 interface, the buffer layer, and the whole overgrown GaN epilayer of the HNT case are illustrated. High densities of IDBs and TDs propagating through the whole film thickness are depicted; b HRTEM image, taken with the electron beam along h1120iGaN//h1010iAl2O3 zone axes, illustrating the thin AlN transition layer formed on

sapphire and two IDB walls, emanating from the interface, that bound an inversion domain boundary. A mixed type threading dislocation (TD) is also depicted; c Experimental CBED pattern, taken along [1010] zone axis; d the corresponding simulated one for a specimen thickness of 83 nm. The 0002 reflection pointing towards the growth direction reveals the Ga-face of the material.

XTEM and HRTEM micrographs from a sample consisting of 1.2 lm GaN grown on LNT (0001) sapphire with a 20 nm LT AlN buffer layer are shown in Fig. 3.27. The overall microstructure of the grown material is shown in the XTEM micrograph of Fig. 3.27 a. Predominant defects are threading dislocations that emanate from the AlN/Al2O3 interface and propagate through the whole film thickness. Their density is higher in the area of the buffer layer and the first GaN layers but it is reduced towards the top of the film where it was estimated being of the order of 5 ´ 1010 cm–2. Narrow IDBs were also detected but no SFs on the basal or pyramidal planes have been observed. The excellent quality of the AlN/ Al2O3 and GaN/AlN interfaces is evident in the HRTEM image of Fig. 3.27 b,

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viewed along h1120iAlN(GaN)//h1010iAl2O3 zone axes, while the sharp and atomically smooth structure of both interfaces is visible in the two enlarged parts of the image given as insets. A terminating Al2O3 lattice fringe at the AlN/Al2O3 interface revealing the edge component of a misfit dislocation is also indicated. The three XTEM micrographs shown in Fig. 3.28 were recorded from the same area of a 0.4 lm GaN layer grown on LNT (0001) Al2O3 with a 20 nm HT AlN. As is demonstrated in the images, the crystalline quality of this film is improved compared to that shown in Fig. 3.27. The main defects present in the GaN epilayer are threading dislocations that are observed to originate from the substrate/buffer interface though a decrease of their density above the buffer layer is detected. Figure 3.28 a was taken along h1120iGaN, whereas Fig. 3.28 b, c were recorded in weak-beam dark field (DF) conditions with g = 1010 (g(3g)) and g = 0002 (g(5g)), respectively. Dislocations exhibiting a-type component are visible in Fig. 3.28 b while all c-type dislocations are out of contrast. In Fig. 3.28 c only dislocations with a c-component are revealed since under the imaging conditions all a-type dislocations are extinguished. A mixed type (a+c) dislocation, visible in all three images, is indicated by the white

Fig. 3.27 a XTEM micrograph illustrating the overall microstructure of a 1.2 lm GaN film grown on LNT (0001) Al2O3 with a 20 nm LT AlN buffer layer; b HRTEM image, viewed along h1120iAlN (GaN)//h1010iAl2O3 zone axes, where the AlN/Al2O3 and the GaN/AlN

interfaces are shown. The sharp and atomically smooth structure of both interfaces is evident from the two insets of the image. The edge component of a misfit dislocation in the AlN/Al2O3 interface is also indicated.

3.4 Heteroepitaxial Growth

arrow. From the diffraction contrast experiments the density of threading dislocations was estimated as 2 ´ 1010 cm–2 and 9 ´ 109 cm–2 for the a- and c-type respectively. The significant surface roughness of the film, ranging from 10 nm to 20 nm, is also depicted in the images. It should be noticed here that these GaN films were grown under slightly Ga-rich or N-rich conditions and thus presented higher surface roughness in comparison to other films grown under optimum RFMBE growth conditions (Ga-rich growth). A decrease of the structural imperfections is also expected in smooth GaN layers that have been grown under the optimum conditions, following a layer-by-layer growth mode. RHEED patterns obtained from all specimens grown on nitridated sapphire surfaces at 165 8C up to 100 min with a LT or HT AlN buffer layer revealed the Gaface polarity of the materials. KOH etching followed by AFM observations confirmed the (0001) polarity of the materials for all the samples studied.

Fig. 3.28 a XTEM image of a GaN film grown on LNT (0001) Al2O3 with a 20 nm HT AlN buffer layer, viewed along h1120iGaN; b, c weakbeam DF images of the same area as in a taken with g = 1010 (g(3g)) and g = 0002 (g(5g)), respectively. Dislocations with a-type component are visible in b while in c only ctype dislocations are in contrast.

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3.4.5

Conclusions

XTEM and HRTEM techniques were used for the microstructural characterization of films consisting of GaN layers grown on LNT and HNT (0001) Al2O3 substrates with LT GaN or AlN buffer layers. The effect of nitridation temperature on Al2O3 surface, the amount of nitridation, the microstructure of the films and the control of the polarity of overgrown GaN epilayers were investigated. The results indicated that, using nitrogen RF plasma, a significant Al2O3 nitridated zone was formed only at high temperatures due to the transformation of few surface Al2O3 layers to AlN. Moreover, this favors the Ga-face polarity of the overgrown materials. Conversely, the low temperature of (0001) Al2O3 nitridation always leads to the growth of N-face material when the growth starts with a LT GaN buffer layer. This N-face material exhibits improved crystalline quality. Sonoda et al. [213] also reported the Ga-face polarity for GaN layers grown with sapphire nitridation by NH3. Therefore, it is con-

Fig. 3.29 Models for AlN thin films on cplane sapphire. Small dots represent O atoms, small circles represent N atoms, large thick circles represent Al atoms. All the Al–N bonds drawn are within 10% of the bulk bond length for AlN (1.86 Å). Similarly, all the Al–O bonds drawn are within 10% of the bulk bond lengths for Al2O3, which are between 1.82 and 1.93 Å. The dashed bonds are out of these ranges. a 1 bilayer of AlN with (0001) polarity

and an Al monolayer decorating the surface; b 1 bilayer of AlN with (0001) polarity and N(H3) adatoms on the surface; c 1 bilayer of AlN with (0001† polarity and Al(T4) adatoms on the surface; d 1 bilayer of AlN with (0001† polarity and an Al monolayer decorating the surface (Fig. 1 from [215], reprinted with permission from R. Di Felice and J.E. Northrup, Appl. Phys. Lett. 73, 936 (1998). Copyright 1998, American Institute of Physics).

3.5 III-Nitride Alloys and Device Heterostructures

cluded that sufficient sapphire nitridation, either by nitrogen RF plasma or NH3 gas, should favor the growth of Ga-polarity material. However, Ga-face material also occurred when an AlN buffer layer on a weakly nitridated Al2O3 surface was used, in agreement with other reports [192, 213, 214]. The common characteristic of the two cases resulting in Ga-face polarity (high Al2O3 nitridation temperature with a GaN buffer layer and low Al2O3 nitridation temperature with an AlN buffer layer) is the existence of an AlN interfacial layer, as has been shown by HRTEM observations. Apparently, AlN nuclei islands of “Ga-face” polarity, formed either by high-temperature Al2O3 nitridation or AlN deposition, dominate the initial growth stages and are responsible for the eventually dominating Ga-face polarity of the overgrown films. This result is in good agreement with the theoretical work of Di Felice and Northrup [215], which predicts the lowest formation energy for an AlN/sapphire structure. The authors considered four different configurations for the AlN/Al2O3 (0001) interface, as shown in Fig. 3.29. The lowest formation energy was calculated for the Al2/3-NAl-N1/3 structure, shown in Fig. 3.29 b, which corresponds to the (0001) orientation of the AlN film. However, they also noticed that the AlN-Al1/3 structure of Fig. 3.29 c, which corresponds to (0001† AlN film orientation, could be also favorable if strain relaxation is included. This predicts a difficulty to nucleate a film without any IDBs. Our experiments [178, 198, 199] have shown that the temperature of Al2O3 (0001) nitridation is a critical parameter for the nucleation of the III-nitride layers on (0001) Al2O3. The substrate temperature during the nitridation by nitrogen RF plasma differentiates the strength of the nitridation effect and controls the polarity of the overgrown GaN films. The results suggest that a convenient method to obtain high-quality Ga-face epilayers is the combination of low-temperature sapphire nitridation with a low or high temperature AlN buffer layer.

3.5

III-Nitride Alloys and Device Heterostructures 3.5.1

Growth Model for Ternary III-Nitrides

The growth kinetics of III-nitrides grown by plasma-assisted MBE are significantly different compared to more traditional III–V compound semiconductors such as GaAs. Therefore, an understanding of the various parameters that affect the growth of III-nitride alloys is critical in order to optimize the quality and reproducibility of these alloys. The optimum conditions for the growth of GaN seem to be in a near-stoichiometric regime or a slightly Ga-rich regime. The condition of stoichiometry is determined by setting a constant N-flux and increasing the Ga-flux until the growth rate saturates. The point at which saturation is reached is thus defined as the “stoichiometric” condition. Under conditions where the Ga flux is far in excess of the active N species, Ga accumulation on the growth surface results in Ga droplets.

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Fig. 3.30 a In content; b InN loss for InGaN layers grown with different material fluxes as a function of growth temperature. Open symbols represent N-flux = 4.7 nm min–1, full symbols N-flux = 12 nm min–1, squares: Ga/ N = 0.75, diamonds: Ga/N = 0.5, triangles:

Ga/N = 0.25. All samples were grown under excess In. Broken lines show theoretical prediction for 4.7 nm min–1, solid lines for 12 nm min–1 (Fig. 1 from Ref. [216], reprinted courtesy of the authors and of Wiley-VCH).

Fig. 3.31 Variation of InN composition as a function of the film thickness determined by EDX (Fig. 3 from Ref. [217], reprinted with permission from Bottcher et al., Appl. Phys. Lett. 73, 3232 (1998). Copyright 1998, American Institute of Physics).

Averbeck and Riechert [216] have developed a quantitative model for the incorporation of Al and In into AlxGa1–xN and InxGa1–xN, respectively. They found that, for temperatures below where significant decomposition takes place and in the group-III-limited growth regime, the incorporation is determined mainly by the bond strengths between the group-III elements and N such that the more weakly bound species is completely displaced. The significance of this finding is that for the growth of AlGaN, the AlN mole fraction is determined primarily by adjusting the Al flux without changing the Ga flux. For InGaN growth, the scenario is a little more complicated since the typical substrate temperature (600–700 8C) for growing high-quality InGaN is usually above the decomposition temperature of InN. The above-mentioned quantitative model can only be applied for InGaN at growth temperatures below 500 8C, in which case the Ga atoms completely dis-

3.5 III-Nitride Alloys and Device Heterostructures

place the In atoms and the InGaN composition is mainly determined by the Ga flux. As shown in Fig. 3.30 a, the InN mole fraction depends strongly on the growth temperature and approaches zero above 700 8C. Figure 3.30 b shows the amount of InN loss as a function of growth temperature. It is clear from the different reports in the literature by various workers that the behavior of In incorporation is much more complicated than that of Al [217–222]. Bottcher et al. observed that the InN mole fraction in thick InGaN films (800 nm) gradually decreased from 0.16 to 0.08 in the first 400 nm of an 800 nm epilayer as shown in Fig. 3.31 [217]. It should be noted that although this is significant for the growth of thick InGaN films, it might not be an issue for InGaN quantum wells. However, their results hinted that excess In on the surface caused a selfblocking mechanism for In incorporation. For growth under group-III-rich conditions, significant surface segregation of In atoms has been observed by examining the sample surface with scanning tunneling microscopy [218]. For the (0001† surface of InGaN, it was found that a monolayer of In was bonded to a GaN bilayer underneath [219]. On the other hand, the (0001) surface is terminated by two monolayers of metal atoms, the topmost layer being entirely In and the layer below being a mixture of In and Ga atoms depending on the ratio of In/Ga fluxes [218]. Indium-incorporation studies based on reflection high-energy electron diffraction (RHEED) intensity oscillations have been reported by Adelmann et al. [220] who also observed a surfactant effect for low coverages of In on the growth surface. 3.5.2

InGaN

From a research standpoint, growing InGaN by MBE provides a number of advantages. Firstly, the growth parameters, such as group-III and nitrogen flux, can be independently varied. This allows a range of parameter space to be studied such as III/V ratio and growth temperature. In addition, in situ characterization tools such as RHEED allow studies of surface structure and desorption of group-III species from the growth surface. Recently, more progress has been made towards obtaining high-quality InGaN by PAMBE. However, the effort still lags behind in terms of optical devices such as LEDs, which is still dominated by material grown using MOCVD. With better understanding of the factors controlling the In incorporation into InGaN using PAMBE, the performance of LEDs grown by MBE should continue to improve. Shen et al. showed [223] In0.08Ga0.92N films with thickness on the order of 0.36 lm to have PL FWHM of 128 meV at a peak wavelength of 435 nm. The InN mole fraction of InGaN films shows a strong dependence on the growth temperature, as discussed previously. The authors found that the InN mole fraction was reduced by about a factor of 3 when raising the growth temperature from 560 to 610 8C. Others have reported a decrease in the InN mole fraction from 0.6 to 0.12 when the growth temperature was increased from 600 to 680 8C [224]. When the growth conditions are optimized, good optical properties can be obtained for InGaN

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3 Plasma-Assisted Molecular Beam Epitaxy of III–V Nitrides Fig. 3.32 Room-temperature cathodoluminescence spectrum of an In0.08Ga0.92N/GaN MQW structure with 25 periods (Fig. 6 from [225], reprinted with permission from Ng et al., J. Vac. Sci. Technol. B 18, 1457 (2000). Copyright 2000. American Institute of Physics).

films and MQWs. For example, Fig. 3.32 shows the cathodoluminescence spectrum for In0.08Ga0.92N/GaN MQWs, where a single luminescence peak at 397 nm with a narrow linewidth of 86 meV has been observed at room temperature [225]. Due to the low thermal stability of InN, a low growth temperature is required for high InN mole fraction alloys. In this respect, plasma-assisted MBE is well suited for high In content alloys compared to processes using ammonia since the pyrolysis of ammonia requires temperatures higher than the dissociation temperature of InN. Binary InN has been grown by MBE at growth temperatures of 350 to 600 8C on either InN [226] or AlN buffer layers [227]. However, the crystal quality remains poor (X-ray diffraction (XRD) rocking curve 50–60 arcmin) and the background electron concentration is in the range of 1018 to 1019 cm–3, leaving room for improvement.

3.5.2.1 Phase Separation and Ordering of InGaN

Phase separation in InGaN alloys was first observed in MBE-grown InGaN films [228, 229]. This is not surprising given that InN and GaN are immiscible at the typical MBE growth temperatures (600–750 8C). X-ray diffraction data for an In0.37Ga0.53N layer shows a peak due to InN in addition to the In0.37Ga0.53N and GaN peaks as shown in Fig. 3.33. The phenomenon of phase separation is independent of the growth technique and has also been observed in MOCVD-grown InGaN films [230, 231] as well as LEDs [232]. The highest achievable InN mole fraction for InGaN films before phase separation sets in is on the order of 0.15 to 0.2. However, strain may play a role in stabilizing the InGaN alloys [233] for thin layers in heterostructures such as quantum wells where an InN mole fraction of up to 0.81 has been observed without any detectable phase separation [228]. In addition to phase separation, ordering has also been observed in InGaN alloys where the In and Ga atoms are no longer randomly located on the metal HCP sublattice but each set of group III atoms occupy a preferred metal HCP sublattice. Evidence of ordering can be seen by the appearance of superlattice

3.5 III-Nitride Alloys and Device Heterostructures Fig. 3.33 XRD data for an In0.37Ga0.53N film that shows evidence of phase separation (Fig. 1 from [228], reprinted with permission from Singh et al., Appl. Phys. Lett. 70, 1089 (1997). Copyright 1997, American Institute of Physics).

Fig. 3.34 Cross-sectional SAD pattern along the [1120] zone axis from the InGaN film, showing the presence of (0001) spots (Fig. 7 from [229], reprinted with permission from Doppalapudi et al., J. Appl. Phys. 84, 1389 (1998). Copyright 1998, American Institute of Physics).

spots in selected area diffraction (SAD) [229, 231]. One example is shown in Fig. 3.34, which displays the selected area diffraction (SAD) image for an In0.09Ga0.91N film with the (0001) diffraction spots visible [229]. Although this issue is gaining the interest of researchers, thus far, it is not clear how the degree of ordering affects device performance such as in InGaN LEDs.

3.5.2.2 Effect of Atomic Hydrogen on the Incorporation of In

The presence of atomic H during plasma-assisted MBE has been found to increase the incorporation of In [234] and the degree of ordering [235]. Figure 3.35

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3 Plasma-Assisted Molecular Beam Epitaxy of III–V Nitrides Fig. 3.35 Dependence of growth rate and In incorporation on hydrogen flow rate (Fig. 1 from Ref. [234], reprinted courtesy of the Japan Society of Applied Physics).

Fig. 3.36 Degree of ordering as a function of the InN mole fraction with and without atomic hydrogen (Fig. 3 from Ref. [235], reprinted courtesy of Wiley-VCH).

shows the increase in InN mole fraction and overall InGaN growth rate when the hydrogen flow and hence the amount of atomic hydrogen is increased. Figure 3.36 shows that the ratio of the (0001)/(0004) Bragg peaks that are related to InGaN is increased in the presence of atomic hydrogen. However, the same authors found that increasing the flow rate of H2 without cracking into atomic H does not vary the incorporation of In. Circumstantial evidence points to the effect of H increasing the nitrogen species available for growth [236] as the growth rate of GaN increases with the presence of H. However, the mechanism of the enhancement of growth rate of GaN in the presence of H is not known at present.

3.5 III-Nitride Alloys and Device Heterostructures

The enhancement of In incorporation in the presence of H has been used to form InxGa1–xN/InyGa1–yN multiple quantum wells solely by modulating the hydrogen flow rate, while keeping all other growth parameters constant [234]. 3.5.2.3 InGaN LEDs

The progress of developing InGaN LEDs by MBE has been slow compared to the MOCVD technique. This is in part due to the spectacular results achieved by growing InGaN LEDs using MOCVD and the subsequent commercialization of such devices. Output powers of up to 7, 5, and 1.4 mW have been obtained for blue, green, and amber LEDs, respectively [237]. The output power of LEDs grown by MBE have yet to match those grown by the MOCVD technique. The high efficiency of InGaN LEDs has been attributed to compositional inhomogeneity in the InGaN quantum wells resulting in exciton localization [238]. It may well be that under the right set of growth conditions, such an effect can also be achieved by the MBE process. InGaN/GaN double heterostructure LEDs were grown by plasma-assisted MBE and showed electroluminescence at 425 nm with a 78 nm thick In0.2Ga0.8N active region [239]. To isolate the effect of nucleation using MBE, the device structure was grown on a template GaN layer grown using MOCVD. However, the EL intensity of the LED is still a factor of five to ten lower than MOCVD-grown LEDs. Another effort to grow InGaN LEDs by PAMBE on HVPE templates resulted in emission at 447 nm and a FWHM of 37 nm with no significant shift in peak wavelength with injected current of 20 to 120 mA, as shown in Fig. 3.37 [240]. However, the output power was only 20 lW, which is about two orders of magnitude lower than reported commercial InGaN LEDs. InGaN LED structures fully grown by PAMBE without any template layers grown by other growth techniques have also been investigated [224]. The reported emission wavelength was as long as 550 nm, which is in the green spectral region [224]. The LED emission exhibited a red-shift along with a narrowing of the full width at half maximum with increasing temperature. This is contrary to blue LEDs grown by MOCVD where a small (*20–40 meV) blue-shift is observed with increasing temperature from 20 K to room temperature. The blue-shift was interpreted by a band-tail filling model with a Gaussian density of states distribution [241]. In-free GaN p-n junctions were also fabricated by ECR-MBE and the emission wavelength was found to be around 400 nm [242]. The radiative transition was attributed to donor–acceptor pair recombination. Interestingly, annealing of the LED wafer before processing resulted in lower reverse leakage current and lower series resistance under forward-biasing conditions, pointing to a reduction of leakage paths. 3.5.3

AlGaN

AlxGa1–xN alloys in the entire composition range have been grown by plasma-assisted MBE [243, 244]. The typical growth temperature for AlGaN alloys lies between

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700 and 800 8C. Despite the progress in optoelectronic devices utilizing AlGaN as one of the layers composing the overall device, the properties of AlxGa1–xN, especially for x > 0.5 have not been widely investigated. A number of roadblocks are in the way for the realization of optoelectronic devices using AlxGa1–xN alloys with large AlN mole fraction. One of the most severe is the difficulty of doping AlGaN either n-type or p-type as x increases. Nevertheless, progress has been made in the structural characterization of these alloys. Atomic long-range ordering was first discovered in AlGaN alloys grown by PAMBE [245]. Ordering occurs along the c-axis, which is also the direction of growth. The ordering consists of alternating Al- and Ga-rich layers with the maximum ordering occurring at an AlN mole fraction of 0.5. In X-ray diffraction measurements, odd-order peaks, such as the (0001) and (0003), which are normally forbidden in a random alloy can be observed due to ordering. Figure 3.38 shows the ratio of the intensity of (0001)/(0004) peaks where the experimental data points follow the trend predicted by calculations using the kinematical model. In addition, spontaneously formed superlattices with 7 ML and 12 ML periods have also been observed in AlGaN alloys [246]. AlGaN alloys are important for optoelectronic devices such as LEDs and photodetectors operating in the UV spectral region between the range of 200 to 365 nm, which can be tuned according to the band gap of AlGaN. UV photodetectors are desirable for applications such as flame-sensing and solar-blind detection. UV LEDs and lasers are useful for applications such as biological agent detection, underwater communications, and a variety of medical applications. However, one of the most exciting opportunities is in the area of solid-state lighting, whereby UV LEDs exciting an appropriate phosphor can produce white light.

Fig. 3.37 Electroluminescence spectra of InGaN LED grown by PAMBE (Fig. 4 from Ref. [240], reprinted courtesy of Elsevier).

3.5 III-Nitride Alloys and Device Heterostructures

3.5.3.1 UV LEDs

The progress in UV LEDs has lagged behind the visible LEDs emitting in the blue and green. Mukai et al. [247] reported on an InGaN double heterostructure LED emitting at 371 nm with 7.5% efficiency and 5 mW output. However, in order to achieve shorter wavelength (k < 365 nm) emission, AlGaN quantum wells will have to be used as the active light-emitting layers. It has been noted that the efficiency of LEDs with GaN QWs degrades as a function of the threading dislocation density in the device [248] whereas InGaN QW LEDs are relatively unaffected by the high dislocation density. The speculation is that excitons in InGaN QWs can be highly localized due to In composition inhomogeneities. Kinoshita et al. [249] reported on an Al0.03Ga0.97N/Al0.25Ga0.75N MQW LED with peak emission around 333 nm. However, the efficiency of light-emission in AlGaN QWs is greatly reduced due to the built-in electric field causing a spatial separation of the electron and hole wavefunction and thus, reducing the overlap integral. It is unclear whether the mechanism of compositional inhomogeneity and clustering occurs in AlGaN-based QWs the way it occurs in InGaN-based QWs. AlxGa1–xN/AlyGa1–yN MQWs exhibit higher PL intensity compared to bulk AlxGa1–xN layers [250]. Interestingly, when In is introduced into the QW to form AlxGa1–x–yInyN wells, the PL efficiency is increased, possibly due to InGaN clusters within the well [251].

3.5.3.2 UV Detectors

Most of the work in the literature is concentrated on GaN detectors, so this part will focus more on the work in that area. However, the results should apply to AlGaN-based devices as well, in order to extend the working wavelength deeper into the UV. Photoconductive UV detectors have been fabricated on n-GaN on sapphire [252] and p-GaN on (111) Si [253] by PAMBE. In the work by Stevens et al. [253], the high photoconductive gain (12 A W–1 at 4 V for optical intensities below 1 W m–2) was attributed to free electrons and trapped holes. The linear dependence of the photocurrent on the optical intensity supports the model of a uniform distribution of traps within the band gap. Initial studies of photoconductive detectors formed on partially ordered AlxGa1–xN with up to x = 0.45 showed increased mobility-lifetime products compared to their GaN counterparts [254]. This was attributed to spatial separation and indirect recombination of the photogenerated electron-hole pairs as a result of the band gap misalignment of ordered and disordered domains. In addition to photoconductive detectors, Schottky MSM GaN photodetectors grown by PAMBE have been reported. These devices were found to have very low dark current (<1 pA at 30 V) and high external quantum efficiency (>70%) [255]. Figure 3.39 shows the current-voltage characteristics of the Schottky MSM detector with and without UV illumination. For higher Al content alloys, Schottky-type photodetectors are currently more practical from a contact-formation standpoint, as ohmic contacts are more difficult to form on the higher band gap AlGaN. The performance compares well with the best Schottky MSM photodetectors grown by

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Fig. 3.38 Ratio of (0001)/ (0004) Bragg peaks for AlxGa1– xN indicating the amount of ordering in the films (Fig. 3 from Ref. [245], reprinted with permission from Korakakis et al., Appl. Phys. Lett. 71, 72 (1997). Copyright 1997, American Institute of Physics).

Typical reverse bias I-V characteristics of 4 lm finger and 5 lm spacing MSM photodetectors grown by PAMBE (Fig. 3 from Ref. [255], reprinted courtesy of the IEEE).

Fig. 3.39

MOCVD [256]. Reference [256] also provides a good review of GaN Schottky MSM photodetectors, including characterization of reverse-bias degradation mechanisms that are attributed to interface-related traps. Kishino et al. [257] fabricated resonant-cavity-enhanced MSM photodetectors with a monolithically grown bottom DBR consisting of 20 pairs of Al0.06Ga0.94N/ AlN and a GaN absorbing layer. The top DBR was formed by two pairs of ZrO2/ SiO2 deposited after the MBE growth of the III-nitride layers. The detection responsivity showed an enhancement at 363 and 352 nm due to the resonant cavity effect as shown in Fig. 3.40. The third class of photodetectors includes p-n and p-i-n junction photodiodes [258, 259]. Compared to Schottky-barrier detectors, these devices have lower noise and faster response time. The peak responsivity at 360 nm is 0.11 A W–1 which

3.5 III-Nitride Alloys and Device Heterostructures Fig. 3.40 Comparison of the responsivity of GaN MSM photodetectors with and without the top DBR (Fig. 2 a from Ref. [257], reprinted courtesy of Wiley-VCH).

corresponds to an internal quantum efficiency of approximately 48%. However, the responsivity decreases by about an order of magnitude approaching 250 nm [258]. In comparison, photoconductive GaN detectors have a relatively flat response above the band gap energy. This may indicate that significant surface recombination takes place at the surface of Mg-doped GaN. For a device that is illuminated from the side of the n-GaN layer through the sapphire substrate, the responsivity curve does not show drastic degradation as compared to illumination from the p-GaN side [260]. Since the 1/e absorption length is *0.1 lm for energies above the GaN band gap using an absorption coefficient of 105 cm–1, most of the incident light is absorbed in the p-type layer if the thickness is larger than 0.1 lm. As reported by Torvik et al. [261], the photoconductivity spectrum of Mg-doped GaN compared to unintentionally doped GaN shows a less abrupt cutoff at wavelengths below the band gap, indicating that the high-level of Mg incorporation required for reasonable activated hole concentration generates defects states within the band gap. Therefore, the rejection ratio between above and below band gap detection will be reduced. An alternative solution to overcome the problem of coupling the light into the intrinsic layer is to use an AlGaN p-type layer that will be transparent to the desired detection wavelength [262]. However, AlGaN-based p-i-n diodes have not been investigated as widely as GaN ones. The improvement of the quality of AlGaN layers as well as p-type doping of AlGaN alloys is therefore crucial for all applications related to the UV spectral region. The advantage of MBE is that AlGaN alloys with large AlN mole fraction can be grown. The control of the Al content is relatively easy, as discussed in the earlier section on growth kinetics of III-nitride alloys. Improvements of the crystal quality of AlGaN alloys are still needed. The threading dislocation density has been found to have a profound effect on the visible rejection in UV detectors based on (Al)GaN [261]. Therefore, the availability of

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native GaN substrates will be eagerly anticipated in order for the MBE technique to be truly exploited for all its strengths in layer thickness control, interface abruptness and in situ monitoring. 3.5.4

GaN/AlGaN MQWs for Intersubband Transitions

In the area of III-nitride optoelectronics, the general focus has been on the development of devices based on interband transitions. The area of intersubband photonics utilizing the III-nitrides has been largely unexplored until recent times. A number of devices such as quantum well infrared photodetectors (QWIPs) and quantum-cascade lasers (QCLs) are based on intersubband transitions between quantum confined states in the conduction band [263]. The material system that is most explored is GaAs/AlxGa1–xAs or InxGa1–xAs/InyAl1–yAs, which can be lattice-matched to GaAs and InP substrates, respectively. Due to the limitations of the conduction-band offsets in these material systems, the operational wavelengths of practical devices are in the mid-infrared spectral region (k > 3 lm). Intersubband transitions in GaN/AlxGa1–xN quantum wells have unique advantages compared to other material systems. First, the large conduction-band offset in the GaN/AlxGa1–xN system allows for intersubband transitions in the near infrared (k = 1–3 lm) spectral region to be accessible. This would be of great interest for telecommunications applications where the minimum absorption region for silica-based fibers is around 1.55 lm. Furthermore, ultrafast intersubband transitions are possible in GaN/AlxGa1–xN quantum wells due to the large electron effective mass (0.2 m0) and large longitudinal optical (LO) phonon energy of *90 meV. This will be attractive for ultrafast switching or wavelength-conversion applications. Due to the lack of suitable lattice-matching substrates, the most challenging aspect of realizing GaN-based intersubband devices lies in the arena of thin film growth. Initial feasibility studies of ultrafast nonlinear optical properties of 1.55 lm intersubband transitions in AlGaN/GaN quantum wells were carried out by Suzuki and Iizuka [264]. The authors calculated that 1.55 lm intersubband transitions would be possible in 6 monolayers (MLs) or 15.6 Å GaN quantum wells (QWs) with Al0.7Ga0.3N barriers or 7 MLs (18.2 Å) GaN QWs with Al0.93Ga0.07N barriers without the presence of a built-in electrostatic field. In the presence of a built-in field, the conduction band profile of the MQW is modified. Rather than a rectangular conduction band profile, it is now a triangular profile with opposite slopes. For the thin wells necessary to achieve intersubband transitions at 1.55 lm, the first subband is relatively unaffected by the triangular profile of the QW. However, the second subband is surrounded by triangular-shaped barriers and electrons in this subband can tunnel out to the continuum states. This decreases the “effective” barrier height for quantum confinement. The same authors observed 3 and 4 lm intersubband transitions for GaN MQWs with thicknesses of 3 and 6 nm, respectively, and Al0.65Ga0.35N barriers using MOCVD [265]. The MBE technique provides excellent control of growth rates and interfaces between thin semiconductor layers. Therefore, using plasma-assisted MBE, multiple

3.5 III-Nitride Alloys and Device Heterostructures

Intersubband absorption at 1.52 lm for a sample with 13 Å GaN wells and 60 Å Al0.85Ga0.15N barriers (10 periods) (Fig. 6 from Ref. [266], reprinted courtesy of Elsevier). Fig. 3.41

quantum wells of GaN/AlxGa1–xN have been grown and evaluated for intersubband transitions [266]. Using multiple-pass-polarized absorption measurements, intersubband transitions around 1.55 lm have been observed for the first time [266, 267]. Figure 3.41 shows the absorption spectrum for a 10-period GaN/AlGaN MQW with the peak intersubband absorption at 1.52 lm and a FWHM of 124 meV. The spectrum shown is normalized by taking the ratio of the P-polarized to S-polarized absorption spectra and subtracting the background absorption from the sapphire substrate. Due to polarization selection rules, only light with an electric field component perpendicular to the plane of the quantum wells will be absorbed. Therefore, the fact that strong P-polarized absorption was observed compared to S-polarization confirms that the transition is indeed taking place between conduction subbands. By varying the GaN well thickness and the AlN mole fraction of the barriers, the peak absorption wavelength can be varied from 1.5 to 4.5 lm as shown in Fig. 3.42. In order to compensate for the effect of the built-in electrostatic field in the barriers, GaN/AlGaN MQWs have been grown on AlxGa1–xN template layers rather than GaN template layers. In the case where the GaN/AlGaN MQWs are grown on thick GaN, the AlGaN barriers are under tensile strain. The tensile strain in the barriers can be eliminated by growing the superlattices on a thick AlxGa1–xN layer with composition matched to that of the barrier. As a proof of concept, two sets of samples with identical MQWs on top of either thick GaN or AlGaN layers have been grown [266]. Reciprocal space mapping of the (105) Bragg peaks indicated that the MQWs are coherently strained to the underlying GaN or AlGaN template layer [268]. In Fig. 3.42, the two data points marked by closed and open triangles are for GaN/Al0.85Ga0.15N MQWs (10 periods) grown on Al0.65Ga0.35N and GaN/Al0.65Ga0.35N MQWs (10 periods) grown on Al0.5Ga0.5N, respectively. A

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Fig. 3.42 Dependence of the intersubband absorption wave length as a function of the GaN well width. The various symbols represent samples with different AlxGa1–xN composition in the barriers (open circle: x = 0.45, solid squares/open triangle: x = 0.65, solid circles: x = 0.80, open square/solid triangle: x = 0.85). All the MQWs were grown on thick GaN layers except those represented by triangles, which were grown on thick Al0.5Ga0.5N (open triangle) and Al0.65Ga0.35N (solid triangle) (Fig. 7 from Ref. [266], reprinted courtesy of Elsevier).

shift to a shorter intersubband transition wavelength is observed for both sets of samples compared with similar MQWs grown on GaN. A second technique of achieving better confinement for the upper electron state is to use the concept of Bragg reflection. This is achieved by creating a minigap that is aligned with the energy level of the upper subband. Using short-period superlattice barriers in place of regular thick barriers, minibands and minigaps are created in the barrier region. The XTEM image of a quantum well structure with GaN/AlGaN short-period superlattice barriers is shown in Fig. 3.43. All the individual layers of the short-period superlattice can be clearly resolved, indicating good interfaces between the GaN and AlGaN layers. As a result of better confinement of the upper state, intersubband absorption at shorter wavelengths can be achieved at a particular AlN mole fraction for SL barriers compared to thick barriers. For example, the intersubband absorption peak occurs at 1.65 lm for MQWs with GaN/Al0.65Ga0.35N (3/5 ML) short-period superlattice barriers compared to 1.75 lm for MQWs with 60 Å Al0.8Ga0.2N barriers. Therefore, for achieving shorter-wavelength intersubband transitions, the AlN mole fraction can be reduced, which reduces the lattice mismatch and strain between the layers. Another advantage of utilizing SL barriers lies in the ability to dope only the GaN layers in the SL barriers rather than in the “active QWs”. Intersubband absorption was observed in such “modulation-doped” structures, indicat-

3.5 III-Nitride Alloys and Device Heterostructures

SL barrier

SL barrier

active GaN QW

Fig. 3.43 XTEM image of GaN quantum wells with GaN/ Al0.65Ga0.35N short-period superlattice barriers. The lighter and darker layers are Al0.65Ga0.35N and GaN, respectively. The inset shows a conduction band schematic of the structure with the arrow indicating the intersubband transition (Fig. 3 from Ref. [270], reprinted courtesy of Wiley-VCH).

ing that electron transfer has occurred from the SL barriers to the main QW [269]. In addition, the FWHM of the transition is reduced, the improvement is probably due to the reduction of impurity scattering as the donor ions are now absent in the main QW. In order to determine the structural quality of these structures, X-ray diffraction has been performed on a sample with double quantum wells separated by SL barriers [270]. The results of X-ray diffraction around the (0002) Bragg peak are shown in Fig. 3.44 a together with the simulated curve. The (0002) GaN peak and (0006) sapphire peaks are present along with the primary SL peak and satellite peaks up to the 7th order. The relative intensity of the satellite peaks is modulated by the fact that there are two different periodicities (see Fig. 3.44 b): (A) due to a single period of the SL barrier (23 Å/period) and (B) due to the sum of the SL barrier plus the coupled quantum wells (126 Å/period). From the measured separation of the satellite peaks, values of 20 Å (e.g., between 0 and +1) and 105 Å (be-

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Fig. 3.44 a XRD intensity versus diffraction angle of a coupled quantum well structure with short-period SL barriers. The black and gray solid lines represent the data and simulated curves, respectively; b schematic of the conduction band profile of the sample structure used for the XRD measurement. The per-

iodicities A and B correspond to the satellite peak spacings labeled similarly and shown in a. The sample consists of 15 repeats of the SL barrier plus the coupled QWs (B) and capped with an additional SL barrier (Fig. 6 from Ref. [270], reprinted courtesy of WileyVCH).

tween 0 and –5) were deduced for the former and latter periodicities, respectively. The simulated curve generated using 7.8/10.1 Å GaN/Al0.65Ga0.35N for each period of the SL barrier and 15.6/10.6/10.4 Å GaN/Al0.65Ga0.35N/GaN for the coupled quantum wells provided an excellent fit to the experimental data. 3.5.4.1 Electron Scattering Time between Subbands

The electron scattering time between the conduction subbands has been measured at k * 1.55 lm [271, 272]. Using a sample with peak absorption at 1.67 lm and a full-width at half-maximum (FWHM) of *200 meV, a pump and probe

3.5 III-Nitride Alloys and Device Heterostructures

Fig. 3.45 DT/T photomodulation dynamics in the GaN/AlGaN MQW structure for P-polarization (solid line) and S-polarization (broken line); the dotted line is the biexponential fit: 0.0002 exp (–s/0.37) + 0.00003 exp (–s/1.8), with s being the time. Inset: Sample orientation in the setup (Fig. 3 from Ref. [271], reprinted courtesy of IEE).

photomodulation technique was utilized. The pump and probe wavelengths were 1.55 and 1.7 lm, respectively. The results of the photomodulation dynamics for both S- and P-polarizations are shown in Fig. 3.45. A time constant of 370 fs was extracted from the initial fast decay, which is due to the intersubband relaxation time. There is a second longer time constant of 1.8 ps that could be due to the thermalization of the electron distribution following the intersubband relaxation. There has been only one other previous report for intersubband relaxation time of GaN/AlGaN MQWs where a time constant of 150 fs was reported [273]. However, in that case, the transition wavelength was at a longer wavelength of 4.5 lm. In Sb-based heterostructures, similar measurements for wavelengths around 1.55 lm gave scattering times of *800 fs [274]. Therefore, for the GaN/AlGaN MQWs, the scattering time is the fastest observed so far.

3.5.5

AlGaN/GaN Heterostructures for Electronic Devices

PAMBE has been quite successful and competitive to MOVPE in the development of AlGaN/GaN heterostructures for electronic devices. Three types of electronic devices have been fabricated by PAMBE material: (a) heterostructure field-effect transistors (HFETs), heterostructure bipolar junction transistors (HBTs), and resonant tunneling diodes (RTDs). We will now overview the progress achieved for each type of device.

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3.5.5.1 AlGaN/GaN HFETs

Two-dimensional electron gas (2DEG) densities exceeding 1 ´ 1013 cm–2 may be realized without doping at AlGaN/GaN heterojunctions, as a consequence of differences in the spontaneous and piezoelectric polarization of GaN and AlGaN [275]. Several reports have indeed shown the formation of a polarization-induced 2DEG with the predicted high electron density at AlGaN/GaN heterojunctions grown by PAMBE [109, 214, 276–286]. Electron densities from *1012 cm–2 to 3.65 ´ 1013 cm–2 were realized by changing the thickness and the Al mole fraction (x) of the AlxGa1–xN layer. The maximum 2DEG density of 3.65 ´ 1013 cm–2 was achieved at an AlN/GaN heterojunction, with AlN barrier width of 4.9 nm [278]. The 2DEG mobility depends on the carrier concentration (NS) and the type of substrate. Typical mobility values for NS&1013 cm–2 are *1300 cm2 V–1s–1 at 300 K, *4500 cm2 V–1 s–1 at 77 K and *20,000 cm2 V–1 s–1 at 10 K. A record mobility of 75,000 cm2 V–1 s–1 at 4.2 K has been reported by Manfra et al. [282] for a 2DEG density of 1.5 ´ 1012 cm–2 in an Al0.05Ga0.95N/GaN structure grown on a HVPE-GaN template. Zervos et al. [284, 285] have investigated the formation of 2DEG at an AlxGa1–x N/GaN/AlyGa1–yN/GaN double heterostructure (DH). It was shown that the behavior of an AlGaN/GaN DH is completely different from what is known for a cubic III–V DH (no polarization fields). The GaN QW is not occupied by a 2DEG when the lower AlGaN barrier thickness and/or composition exceed those of the top barrier. On the contrary, the 2DEG in the GaN QW can be increased by increasing the thickness of the GaN QW and reducing the thickness and Al mole fraction (y) of the bottom AlyGa1–yN layer. A significant barrier height then appears at the lower interface of the GaN QW that may provide isolation from the substrate [284]. A very interesting advantage of PAMBE compared to MOVPE is the possibility to select the epilayer’s polarity during growth on Al2O3 (0001). Murphy et al. [214] controlled the epilayer’s polarity by using an AlN or GaN buffer layer and demonstrated the formation of 2DEG at a “normal” (Ga-polarity) or “inverted” (N-polarity) AlGaN/ GaN heterostructure, respectively. Stutzmann et al. [287] discussed the possibility to form lateral polarity heterostructures for basic studies and novel devices. The excellent 2DEG properties of the PAMBE-grown HFET structures have been implemented into the fabrication of HFET devices [214, 282, 283, 288–294], which have exhibited similar characteristics to those achieved with MOVPE-grown material. Murphy et al. [288] reported a unity current gain frequency fT = 50 GHz and a unity power gain frequency fmax = 97 GHz for devices of 0.28 lm gate length. In particular, excellent results for the power and low-noise capabilities of AlGaN/GaN HFETs grown on semi-insulating (0001) 4H-SiC substrates have been reported by Micovic et al. [291, 292]. An output power of 10.5 W was measured for transistors with 0.25 lm gate length and 2 mm gate width. The continuous wave output power density was 4 W mm–1 at 20 GHz [291]. A single-stage power amplifier built by combining four 1-mm devices exhibited continuous wave output power of 22.9 W with associated power added efficiency (PAE) of 37% at 9 GHz.

3.6 Conclusions and Perspectives

3.5.5.2 AlGaN/GaN HBTs

HBT devices have also been fabricated from PAMBE-grown AlGaN/GaN structures [294, 295]. Cao et al. [295] reported current densities up to 2.55 kA cm–2 at temperatures up to 250 8C and room-temperature dc current gains of 15–20. The IC was equal to IE, indicating high emitter injection efficiency. Xing et al. [294] reported that PAMBE-grown AlGaN/GaN HBT devices exhibited common emitter current gain cutoff frequency of 2 GHz with an input current density of over 2.7 kA cm–2. The Mg doping profile was much sharper in the MBE sample in comparison to a MOVPE one. 3.5.5.3 AlGaN/GaN RTDs

Resonant tunneling diodes (RTDs) of either an AlN/GaN double barrier type [296, 297] or an AlN/GaN superlattice barrier type [296] have been reported. The RTD devices exhibited clear negative differential resistance at room temperature. A peak-to-valley current ratio as high as 32 was obtained for double barrier RTDs [297], while it was 9.7 in a superlattice barrier RTD [296].

3.6

Conclusions and Perspectives

A judgment of the plasma-assisted MBE (PAMBE) capabilities and perspectives should always keep in mind that MBE is supposed to be a highly accurate growth method with in situ monitoring features that provides excellent thickness control and abrupt interfaces. MBE is a far from equilibrium epitaxial growth method aiming at the production of ultrathin heterostructures and, of course, is not an epitaxial growth method that could substitute for bulk crystal growth. The PAMBE of III-nitrides satisfies all the general characteristics of MBE, with its only weakness until now being the failure of earlier attempts to demonstrate light emitting devices comparable to MOVPE. It is a very exciting method for fundamental studies in thin film growth and can be used very effectively in basic research of quantum heterostructures and the R&D of heterojunction devices. Currently, PAMBE is also able to develop highly mismatched III-nitride heteroepitaxial material that performs competitively to MOVPE for all types of devices excluding light emitters. A significant advantage of PAMBE is its capability for growth at low substrate temperatures. This becomes important for In-containing III-nitrides and substrates decomposing at relatively low temperatures. The PAMBE of III-nitrides is particularly sensitive to both the III/V flux ratio as well as the substrate temperature. This implies that for large scale production even more demanding specifications are needed for the uniformity of the material sources. However, this is a technically solvable equipment problem. The surface morphological peculiarities are related to defects and could disappear when high quality GaN substrates become available. Vicinal (0001) GaN substrates would be normally the best choice for GaN PAMBE growth.

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3.7

Acknowledgments

During the course of our research in III-nitrides we have worked closely with many colleagues, whose contribution was valuable in the establishment of our current understanding. Their numerous names appear in the cited works we have coauthored. We also express our thanks to Dr. P. Ruterana for a critical reading of the manuscript. A. Georgakilas would additionally like to acknowledge the valuable support of Nikos Papadakis who constructed the gas line system and maintains the MBE system at FORTH and Georgia Papadaki who committed her best effort in the preparation of this document. He also acknowledges funding from several programs of the General Secretariat for Research and Technology (GSRT) that made it possible to acquire a GaN MBE system and carry out research in IIInitrides, with the most important RTD project being the PENED 99ED 320 “GANFET”. An internal grant of the University of Crete is also acknowledged. Ph. Komninou is grateful to Th. Karakostas, Th. Kehagias, and G. Nouet for their valuable collaboration. She also greatly acknowledges the EU for financial support under contract No. HPRN-CT-1999-00040. 3.8

References 1 2 3 4 5 6 7

8 9 10 11 12 13

14

A. Y. Cho, J. Cryst. Growth 202, 1 (1999). L. Leung, J. Cryst. Growth 227, 143 (2001). T. R. Block, J. Vac. Sci. Technol. B 16, 1475 (1998). J. M. Fastenau, Infrared Phys. Technol. 42, 407 (2001). I. Shibasaki, J. Cryst. Growth 175, 13 (1997). MBE products of PICOGIGA: http:// www.picogiga.com/marketsframe.html. MBE is key for Coherent’s production of InGaAsP-based laser diodes: http:// www.vgsemicon.com/products/MBEiskey.html. J. Franklin, J. Vac. Sci. Technol. B 18, 1645 (2000). A. Y. Cho, Surf. Sci. 17, 494 (1969). A. Y. Cho, J. Appl. Phys. 41, 2780 (1970). A. Y. Cho, J. Appl. Phys. 42, 2074 (1971). A. Y. Cho, Molecular Beam Epitaxy (AIP Press, 1997). E. H. C. Parker, The Technology and Physics of Molecular Beam Epitaxy (Plenum Press, 1985). L. L. Chang and K. Ploog, Molecular Beam Epitaxy and Heterostructures

15

16 17 18

19 20

21 22 23

24

(Martinus Nijhoff Publishers, 1985), NATO ASI Series E – No 87. M. A. Herman and H. Sitter, Molecular Beam Epitaxy, Fundamentals and Current Status (Springer-Verlag, 1989). E. Kasper and J. C. Bean, Silicon-Molecular Beam Epitaxy (CRC Press, 1988), Vol. I. E. Kasper and J. C. Bean, Silicon-Molecular Beam Epitaxy (CRC Press, 1988), Vol. II. Z. Sitar, M. J. Paisley, D. K. Smith, and R. F. Davis, Rev. Sci. Instrum. 61, 2407 (1990). Z. Sitar, L. L. Smith, and R. F. Davis, J. Cryst. Growth 141, 11 (1994). T. Lei, M. Fanciulli, R. J. Molnar, T. D. Moustakas, R. J. Graham, and J. Scanlon, Appl. Phys. Lett. 59, 944 (1991). T. D. Moustakas, T. Lei, and R. J. Molnar, Physica B 185, 36 (1993). R. J. Molnar and T. D. Moustakas, J. Appl. Phys. 76, 4587 (1994). S. Strite, J. Ruan, Z. Li, A. Salvador, H. Chen, D. J. Smith, W. J. Choyke, and H. Morkoc, J. Vac. Sci. Technol. B 9, 1924 (1991). M. E. Lin, B. N. Sverdlov, and H. Morkoc, J. Appl. Phys. 74, 5038 (1993).

3.8 References 25

26 27

28 29 30

31

32

33

34

35 36

37

38 39

40 41 42

A. Ohtani, K. S. Stevens, M. Kinnigburgh, and R. Beresford, J. Cryst. Growth 150, 902 (1995). Z. Y. Fan and N. Newman, J. Vac. Sci. Technol. A 16, 2132 (1998). K. Iwata, H. Asahi, S. J. Yu, K. Asami, H. Fujita, M. Fushida, and S. Gonda, Jpn. J. Appl. Phys., Part 2 35, L289 (1996). W. E. Hoke, P. J. Lemonias, and D. G. Weir, J. Cryst. Growth 111, 1024 (1991). H. Liu, A. C. Frenkel, J. G. Kim, and R. M. Park, J. Appl. Phys. 74, 6124 (1993). J. M. Van Hove, G. J. Cosmini, E. Nelson, A. M. Wowchak, and P. P. Chow, J. Cryst. Growth 150, 908 (1995). S. E. Hooper, C. T. Foxon, T. S. Cheng, L. C. Jenkins, D. E. Lacklison, J. W. Orton, T. Bestwick, A. Kean, M. Dawson, and G. Duggan, J. Cryst. Growth 155, 157 (1995). O. H. Hughes, D. Korakakis, T. S. Cheng, A. V. Blant, N. J. Jeffs, and C. T. Foxon, J. Vac. Sci. Technol. B 16, 2132 (1998). R. C. Powell, N.-E. Lee, Y.-W. Kim, and J. E. Greene, J. Appl. Phys. 73, 189 (1993). M. Rubin, N. Newman, J. S. Chan, T. C. Fu, and J. T. Ross, Appl. Phys. Lett. 64, 64 (1994). Z. Q. He, X. M. Ding, X. Y. Hou, and X. Wang, Appl. Phys. Lett. 64, 315 (1994). M. S. H. Leung, R. Klockenbrink, C. Kisielowski, H. Fujii, J. Kruger, G. S. Sudhir, A. Anders, Z. Liliental-Weber, M. Rubin, and E. R. Weber, Mater. Res. Soc. Symp. Proc. 449, 221 (1997). A. Sellidj, B. A. Ferguson, T.J. Mattord, B. G. Streetman, and C. B. Mullins, Appl. Phys. Lett. 68, 3314 (1996). B. A. Ferguson and C. B. Mullins, J. Cryst. Growth 178, 134 (1997). D. C. Jordan, I. S. T. Tsong, D. J. Smith, B. J. Wilkens, and R. B. Doak, Appl. Phys. Lett. 19, 3030 (2000). H. Morkoc, IEEE J. Selec. Top. Quantum Electron. 4, 537 (1998). K. Ohkawa, A. Ueno, and T. Mitsuyu, J. Cryst. Growth 117, 375 (1992). Sung-Hwan Cho, Hajime Okumura, and Katsuhiro Akimoto, Appl. Phys. Lett. 76, 3861 (2000).

43

44

45

46

47

48

49

50

51

52

53

54

55 56 57

R. P. Vaudo, J. W. Kook Jr, and J. F. Schetzina, J. Vac. Sci. Technol. B 12, 1232 (1994). W. C. Hughes, W. H. Rowland Jr, M. A. L. Johnson, Shizuo Fujita, J. W. Cook Jr, J. F. Schetzina, J. Ren, and J. A. Edmond, J. Vac. Sci. Technol. B 13, 1571 (1995). V. Kichner, H. Heinke, U. Birkle, S. Einfeldt, D. Hommel, H. Selke, and P. L. Ryder, Phys. Rev. B 8, 15749 (1998). M. A. L. Johnson, Z. Yu, C. Boney, W. C. Hughes, J. W. Cook Jr, J. F. Schetzina, H. Zhao, B. J. Skromme, and J. A. Edmond, Mater. Res. Soc. Symp. Proc. 449, 215 (1997). A. V. Blant, O. H. Hughes, T. S. Cheng, S. V. Novikov, and C. T. Foxon, Plasma Sources Sci. Technol. 9, 12 (2000). A. J. Ptak, K. S. Ziemer, M. R. Millecchia, C. D. Stinespring, and T. H. Myers, MRS Internet J. Nitride Semicond, Res. 4S1, G3.10 (1999). A. J. Ptak, Mr. Millecchia, T. H. Myers, K. S. Ziemer, and C. D. Stinespring, Appl. Phys. Lett. 74, 3836 (1999). T. H. Myers, M. R. Millecchia, A. J. Ptak, K. S. Ziemer, and C. D. Stinespring, J. Vac. Sci. Technol. B 17, 1232 (1999). Ph. Komninou, Th. Kehagias, Th. Karakostas, G. Nouet, P. Ruterana, K. Amimer, S. Mikroulis, and A. Georgakilas, Mater. Res. Soc. Symp. Proc. 639, G3.47.1 (2001). R. Langer, J. Simon, O. Konovalov, N. T. Pelekanos, R. Andre, A. Barski, and M. Godlewski, MRS Internet J. Nitride Semicond. Res. 4S1, G3.19 (1999). K. Kimura, S. Miwa, C. G. Jin, L. H. Kuo, T. Yasuda, A. Ohtake, K. Tanaka, and T. Yao, Appl. Phys. Lett. 71, 1077 (1997). A. N. Wright and C. A. Winkler, Active Nitrogen (Academic Press, New York, 1968). N. Newman, J. Cryst. Growth 178, 102 (1997). M. Cengher and A. Georgakilas, unpublished. D. R. Lide, CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, 1992), pp. 10–66.

183

184

3 Plasma-Assisted Molecular Beam Epitaxy of III–V Nitrides 58 59 60

61 62 63

64

65

66

67

68

69

70

71

72

N. I. S. T. Atomic Spectra Database at: http://nvl.nist.gov/. H. P. Summers, Mon. Not. R. Astron. Soc. 169, 663 (1974). A. Krtschil, H. Witte, M. Lisker, J. Christen, U. Birkle, S. Einfeldt, and D. Hommel, Appl. Phys. Lett. 74, 2032 (1999). S. J. Chua, H. W. Choi, J. Zhang, and P. Li, Phys. Rev. B 64, 205302 (2001). E. Hellman, MRS Internet J. Nitride Semicond. Res. 3, 11 (1998). A. R. Smith, R. M. Feenstra, D. W. Greve, J. Neugebauer, and J. E. Northrup, Phys. Rev. Lett. 79, 3934 (1997). A. R. Smith, R. M. Feenstra, D. W. Greve, M.-S. Shin, M. Skowronski, J. Neugebauer, and J. E. Northrup, Appl. Phys. Lett. 72, 2114 (1998). A. R. Smith, V. Ramachandran, R. M. Feenstra, D. W. Greve, M.-S. Shin, M. Skowronski, J. Neugebauer, and J. E. Northrup, J. Vac. Sci. Technol. A 16, 1641 (1998). R. M. Feenstra, H. Chen, V. Ramachandran, A. R. Smith, and D. W. Greve, Appl. Surf. Sci. 166, 165 (2000). V. Ramachandran, C. D. Lee, R. M. Feenstra, A. R. Smith, J. E. Northrup, and D. E. Greve, J. Cryst. Growth 209, 355 (2000). A. R. Smith, R. M. Feenstra, D. W. Greve, M. S. Shin, M. Skowronski, J. Neugebauer, and J. E. Northrup, Surf. Sci. 423, 70 (1999). A. R. Smith, R. M. Feenstra, D. W. Greve, M. S. Shin, M. Skowronski, J. Neugebauer, and J. E. Northrup, J. Vac. Sci. Technol. B 16, 2242 (1998). A. R. Smith, V. Ramachandran, R. M. Feenstra, D. W. Greve, A. Ptak, T. Myers, W. Sarney, L. Salamanca-Riba, M. Shin, and M. Skowronski, MRS Internet J. Nitride Semicond. Res. 3, 12 (1998). H. Chen, R. M. Feenstra, J. E. Northrup, T. Zywietz, J. Neugebauer, and D. W. Greve, J. Vac. Sci. Technol. B 18, 2284 (2000). V. Ramachandran, C. D. Lee, R. M. Feenstra, A. R. Smith, and G. W. Greve, Phys. Rev. Lett. 84, 4014 (2000).

73

74

75

76

77

78

79

80

81 82

83

84

85 86

87

J. E. Northrup, J. Neugebauer, R. M. Feenstra, and A. R. Smith, Phys. Rev. B 61, 9932 (2000). R. Held, G. Nowak, B. E. Ishaug, S. M. Seutter, A. Parkhomovsky, A. M. Dabiran, P. I. Cohen, I. Grzegory, and S. Porowski, J. Appl. Phys. 85, 7697 (1999). Q. K. Xue, Q. Z. Xue, S. Kuwano, T. Sakurai, T. Ohno, I. S. T. Tsong, X. G. Qiu, and Y. Segawa, Thin Solid Films 367, 149 (2000). Q. K. Xue, Q. Z. Xue, R. Z. Bakhtizin, Y. Hasegawa, I. S. T. Tsong, T. Sakurai, and T. Ohno, Phys. Rev. Lett. 82, 3074 (1999). Q. K. Xue, Q. Z. Xue, S. Kuwano, K. Nakayama, T. Sakurai, I. S. T. Tsong, X. G. Qiu, and Y. Segawa, J. Cryst. Growth 229, 41 (2001). K. Papcewicz, M. B. Nardelli, and J. Bernholc, Phys. Rev. B 20, R12725 (1997). C. Adelmann, J. Brault, E. MartinezGuerrero, G. Mula, H. Mariete, Le Si Dang, and B. Daudin, Phys. Stat. Sol. (a) 188, 575 (2001). G. Mula, C. Adelmann, S. Moehl, J. Oullier, and B. Daudin, Phys. Rev. B 64, 195406-1 (2001). J. Neugebauer, Phys. Stat. Sol. (b) 227, 93 (2001). C. T. Foxon, T. S. Cheng, S. V. Novikov, D. Korakakis, N. J. Jeffs, I. Grzegory, and S. Porowski, J. Cryst. Growth 207, 1 (1999). O. H. Hughes, T. S. Cheng, S. V. Novikov, C. T. Foxon, D. Korakakis, and N. J. Jeffs, J. Cryst. Growth 201/202, 388 (1999). C. T. Foxon, T. S. Cheng, S. V. Novikov, N. J. Jeffs, O. H. Hughes, Yu. V. Melnik, A. E. Nikolaev, and V. A. Dmitriev, Surf. Sci. 421, 377 (1999). E. Dimakis and A. Georgakilas, unpublished results. P. Hacke, G. Feuillet, H. Okumura, and S. Yoshida, Appl. Phys. Lett. 69, 2507 (1996). K. K. Lee, W. A. Doolittle, T.-H. Kim, A. S. Brown, G. S. May, S. R. Stock, Z. R. Dai, and Z. L. Wang, J. Cryst. Growth 231, 1 (2001).

3.8 References 88

89 90

91

92

93

94

95

96

97

98 99

100 101

102

103 104 105

T. Zywietz, J. Neugebauer, M. Scheffler, J. Northrup, and C. G. Van de Walle, MRS Internet J. Nitride Semicond. Res. 3, 26 (1998). O. Janzen, Ch. Hahn, T. U. Kampen, and W. Mönch, Eur. Phys. J. B 7, 1 (1999). V. M. Bermudez, D. D. Koleske, and A. E. Wickenden, Appl. Surf. Sci. 126, 69 (1998). F. Peiro, A. Cornet, A. Herms, J. R. Morante, A. Georgakilas, and G. Halkias, J. Vac. Sci. Technol. B 10, 2148 (1992). M. A. Khan, J. N. Kuznia, D. T. Olson, and R. Kaplan, J. Appl. Phys. 73, 3108 (1993). K. Prabhakaran, T. G. Andersson, and K. Nozawa, Appl. Phys. Lett. 69, 3212 (1996). S. W. King, J. R. Barnak, M. D. Bremser, K. M. Tracy, C. Ronning, R. F. Davis, and R. J. Nemanich, J. Appl. Phys. 84, 5248 (1998). I. Shalish, Y. Shapira, L. Burnstein, and J. Salzman, J. Appl. Phys. 89, 390 (2001). V. K. Gupta, C. C. Wamsley, M. W. Koch, and G. W. Wicks, J. Vac. Sci. Technol. B 17, 1249 (1999). T. K. Zywietz, J. Neugebauer, and M. Scheffler, Appl. Phys. Lett. 74, 1695 (1999). Ph. Komninou and A. Georgakilas, unpublished. C. T. Foxon, presentation in IPAM Workshop on Group-III Nitride Based Materials and Devices, Berlin, January 12–14, 2002. S. Guha, N. A. Bojarczuk, and D. W. Kisker, Appl. Phys. Lett. 69, 2879 (1996). N. Grandjean, J. Massies, F. Semond, S. Yu. Karpov, and R. A. Talalaev, Appl. Phys. Lett. 74, 1854 (1999). J. M. Myoung, O. Gluschenkov, K. Kim, and S. Kim, J. Vac. Sci. Technol. A 17, 3019 (1999). E. Iliopoulos and T. D. Moustakas, Appl. Phys. Lett. 81, 295 (2002). J. R. Arthur, J. Appl. Phys. 39, 4032 (1968). H. Riechert, R. Averbeck, A. Graber, M. Schienle, U. Strauß, and H. Tews, in Mater. Res. Soc. Symp. Proc. 449, 149 (1997).

106 M. Kamp and H. Riechert, in Proper-

107

108

109

110 111

112

113

114

115

116

117

118 119

120

ties, Processing and Applications of Gallium Nitride and Related Semiconductors, edited by J. H. Edgar et al. (INSPEC, IEE, UK, 1999), EMIS Datareview Series No. 23, pp. 426–440. B. Heying, R. Averbeck, L. F. Chen, E. Haus, H. Riechert, and J. S. Speck, J. Appl. Phys. 88, 1855 (2000). B. Heying, I. Smorchkova, C. Poblenz, C. Elsass, P. Fini, S. Den Baars, U. Mishra, and J. S. Speck, Appl. Phys. Lett. 77, 2885 (2000). C. R. Elsass, C. Poblenz, B. Heying, P. Fini, P. M. Petroff, S. P. DenBaars, U. K. Mishra, and J. S. Speck, J. Cryst. Growth 233, 709 (2001). T. D. Moustakas, Mater. Res. Soc. Symp. Proc. 395, 111 (1996). E. J. Tarsa, B. Heying, X. H. Wu, P. Fini, S. P. DenBaars, and J. S. Speck, J. Appl. Phys. 82, 5472 (1997). K. Amimer, A. Georgakilas, M. Androulidaki, K. Tsagaraki, M. Pavelescu, S. Mikroulis, G. Constantinidis, J. Arbiol, F. Peiro, A. Cornet, M. Calamiotou, J. Kuzmik, and V. Yu. Davydov, Mater. Sci. Eng. B 80, 304 (2001). D. Lederman, Z. Yu, T. H. Myers, and M. R. Richards-Babb, Appl. Phys. Lett. 71, 368 (1997). T. Zywietz, J. Neugebauer, and M. Scheffler, Appl. Phys. Lett. 73, 487 (1998). B. Heying, E. J. Tarsa, C. R. Elsass, P. Fini, S. P. DenBaars, and J. S. Speck, J. Appl. Phys. 85, 6470 (1999). C. Kruse, S. Einfeldt, T. Böttcher, D. Hommel, D. Rudloff, and J. Christen, Appl. Phys. Lett. 78, 3827 (2001). A. Parkhomovsky, A. M. Dabiran, B. Benjaminsson, and P. I. Cohen, Appl. Phys. Lett. 78, 2315 (2001). K. Tsagaraki and A. Georgakilas, unpublished. L. X. Zheng, M. H. Xie, S. M. Seutter, S. H. Cheung, and S. Y. Tong, Phys. Rev. Lett. 85, 2352 (2000). L. X. Zheng, M. H. Xie, S. J. Xu, S. H. Cheung, and S. Y. Tong, J. Cryst. Growth 227, 376 (2001).

185

186

3 Plasma-Assisted Molecular Beam Epitaxy of III–V Nitrides 121 M. H. Xie, S. M. Seutter, W. K. Zhu,

122

123

124 125

126

127

128

129

130

131

132

133

134

135

L. X. Zheng, H. Wu, and S. Y. Tong, Phys. Rev. Lett. 82, 2749 (1999). M. H. Xie, S. H. Cheung, L. X. Zheng, Y. F. Ng, H. Wu, N. Ohtani, and S. Y. Tong, Phys. Rev. B 61, 9983 (2000). M. V. Ramana Murty, P. Fini, G. B. Stephenson, C. Thompson, J. A. Eastman, A. Munkholm, O. Auciello, R. Jothilingam, S. P. DenBaars, and J. S. Speck, Phys. Rev. B 62, R10661 (2000). H. Liu, J. G. Kim, M. H. Ludwig, and R. M. Park, Appl. Phys. Lett. 71, 347 (1997). K. Tsagaraki, A. Georgakilas, E. Dimakis, G. Kittler, M. Androulidaki, G. Constantinidis, and N. Pelekanos, presented in IWN 2002, International Workshop on Nitride Semiconductors, Aachen, Germany, 22–25 July 2002. H. M. Ng, D. Doppalapudi, T. D. Moustakas, N. G. Weimann, and L. F. Eastman, Appl. Phys. Lett. 73, 821 (1998). W. Götz, N. M. Johnson, C. Chen, H. Liu, C. Kuo, and W. Imler, Appl. Phys. Lett. 68, 22 (1996). X. Zhang, P. Kung, A. Saxler, D. Walker, T. C. Wang, and M. Razeghi, Appl. Phys. Lett. 67, 1745 (1995). R. Y. Korotkov and B. W. Wessels, MRS Internet J. Nitride Semicond. Res. 5S1, W3.80 (2000). H. M. Ng, D. Doppalapudi, D. Korakakis, R. Singh, and T. D. Moustakas, J. Cryst. Growth 190, 349 (1998). I. P. Smorchkova, E. Haus, B. Heying, P. Kozodoy, P. Fini, J. P. Ibbetson, S. Keller, S. P. DenBaars, J. S. Speck, and U. K. Mishra, Appl. Phys. Lett. 76, 718 (2000). A. J. Ptak, L. Wang, N. C. Giles, T. H. Myers, L. T. Romano, C. Tian, R. A. Hockett, S. Mitha, and P. Van Lierde, Appl. Phys. Lett. 79, 4524 (2001). H. Tang, J. B. Webb, J. A. Bardwell, S. Raymond, J. Salzman, and C. Uzan-Saguy, Appl. Phys. Lett. 78, 757 (2001). D. Sugihara, A. Kikuchi, K. Kusakabe, S. Nakamura, Y. Toyoura, T. Yamada, and K. Kishino, Jpn. J. Appl. Phys., Part 2 39, L197 (2000). H. M. Ng, D. Doppalapudi, D. Korakakis, R. Singh, and T. D. Moustakas, in Proceedings of the 2nd International

136

137 138

139

140

141

142

143

144 145

146

147 148

149 150

151

Conference for Nitride Semiconductors, Tokushima, Japan (1997), pp. 10–12. N. G. Weimann, L. F. Eastman, D. Doppalapudi, H. M. Ng, and T. D. Moustakas, J. Appl. Phys. 83, 3656 (1998). H. M. Ng and A. Y. Cho, J. Vac. Sci. Tech. B 20, 1217 (2002). H. Amano, M. Kito, K. Hiramatsu, and I. Akasaki, Jpn. J. Appl. Phys., Part 2 28, L2112 (1989). S. Nakamura, T. Mukai, M. Senoh, and N. Iwasa, Jpn. J. Appl. Phys., Part 2 31, L139 (1992). T. D. Moustakas and R. J. Molnar, Mater. Res. Soc. Symp. Proc. 281, 753 (1993). W. Kim, A. Salvador, A. E. Botchkarev, O. Aktas, S. N. Mohammad, and H. Morkoc, Appl. Phys. Lett. 69, 559 (1996). W. Götz, N. M. Johnson, J. Walker, D. P. Bour, and R. A. Street, Appl. Phys. Lett. 68, 667 (1996). M. C. Yoo, M. Y. Park, S. K. Kang, H. D. Cho, and J. W. Lee, J. Cryst. Growth 175/ 176, 100 (1997). S. Guha, N. A. Bojarczuk, and F. Cardone, Appl. Phys. Lett. 71, 1685 (1997). J. W. Orton, C. T. Foxon, T. S. Cheng, S. E. Hooper, S. V. Novikov, B. Ya. Ber, and Yu. A. Kudriavstev, J. Cryst. Growth 197, 7 (1999). C. G. Van de Walle, S. Limpijumnong, and J. Neugebauer, Phys. Rev. B 63, 245205 (2001). F. Bernadini, V. Fiorentini, and A. Bosin, Appl. Phys. Lett. 70, 2990 (1997). I. Grzegory and S. Porowski, in Properties Processing and Applications of Gallium Nitride and Related Semiconductors, EMIS Datareviews Series, edited by J.H. Edgar et al. (INSPEC, UK, 1999), No. 23, pp. 359–366. L. Liu and J. H. Edgar, Mater. Sci. Eng. R 37, 61 (2002). Y. Takeda and M. Tabuchi, in Properties Processing and Applications of Gallium Nitride and Related Semiconductors, EMIS Datareviews Series, edited by J. H. Edgar et al. (INSPEC, UK, 1999), No. 23, pp. 381–385. A. D. Hanser and R. F. Davis, in Properties Processing and Applications of Gal-

3.8 References

152

153

154

155

156

157

158

159

160

161

162

163

lium Nitride and Related Semiconductors, EMIS Datareviews Series, edited by J. H. Edgar et al. (INSPEC, UK, 1999), No. 23, pp. 386–390. H. Okumura, in Properties Processing and Applications of Gallium Nitride and Related Semiconductors, EMIS Datareviews Series, edited by J. H. Edgar et al. (INSPEC, UK, 1999), No. 23, pp. 402– 408. E. S. Hellman, in Properties Processing and Applications of Gallium Nitride and Related Semiconductors, EMIS Datareviews Series, edited by J. H. Edgar et al. (INSPEC, UK, 1999), No. 23, pp. 396– 401. G. Kobmuller, P. Pongratz, R. Averbeck, and H. Riechert, Appl. Phys. Lett. 80, 2281 (2002). C. D. Lee, R. M. Feenstra, O. Shigiltchoff, R. P. Devaty, and W. J. Choyke, MRS Internet J. Nitride Semicond. Res. 7, 2 (2002). K. H. Ploog, O. Brandt, R. Muralidharan, A. Thamm, and P. Waltereit, J. Vac. Sci. Technol. B 18, 2290 (2000). P. Waltereit, O. Brandt, A. Trampert, M. Ramsteiner, M. Reiche, M. Qi, and K. H. Ploog, Appl. Phys. Lett. 74, 3660 (1999). Z. P. Guan, A. L. Cai, H. Porter, J. Cabalu, S. Huang, and R. E. Giedd, Appl. Surf. Sci. 165, 203 (2000). M. Androulidaki, A. Georgakilas, K. Amimer, M. Zervos, K. Tsagaraki, M. Dimakis, F. Peiro, and A. Cornet, Phys. Stat. Sol. (a) 188, 515 (2001). E. Calleja, M. A. Sanchez-Garcia, F. J. Sanchez, F. Calle, F. B. Naranjo, E. Munoz, S. I. Molina, A. M. Sanchez, F. J. Pacheco, and R. Garcia, J. Cryst. Growth 201/202, 296 (1999). H. P. D. Schenk, G. D. Kipshidze, V. B. Lebedev, S. Shokhovets, R. Goldhahn, J. Krausslich, A. Fissel, and W. Richter, J. Cryst. Growth 201, 359 (1999). A. Philippe, C. Bru-Chevallier, M. Vernay, G. Guillot, J. Hubner, B. Daudin, and G. Feuillet, Mater. Sci. Eng. B 59, 168 (1999). B. Pecz, L. Toth, Z. Czigany, K. Amimer, and A. Georgakilas, in Inst. Phys. Conf. Ser. 169, 293 (2001).

164 A. Georgakilas, K. Amimer, P. Tzaneta-

165

166

167

168

169

170

171

172

173

174 175

176

177

178

kis, Z. Hatzopoulos, M. Cengher, B. Pecz, Zs. Czigany, L. Toth, M. V. Baidakova, A. V. Sakharov, and V. Yu. Davydov, J. Cryst. Growth 227/228, 410 (2001). K. Amimer, A. Georgakilas, K. Tsagaraki, M. Androulidaki, D. Cengher, L. Toth, B. Pecz, and M. Calamiotou, Appl. Phys. Lett. 76, 2580 (2000). A. Georgakilas, Zs. Czigany, K. Amimer, V. Yu. Davydov, L. Toth, and B. Pecz, Mater. Sci. Eng. B 82, 16 (2001). A. Georgakilas, K. Tsagaraki, E. Makarona, G. Constantinidis, M. Androulidaki, M. Kayambaki, E. Aperathitis, and N. T. Pelekanos, Mater. Sci. Semicond. Proc. 3, 511 (2000). A. Georgakilas, M. Androulidaki, K. Tsagaraki, K. Amimer, G. Constantinidis, N. T. Pelekanos, M. Calamiotou, Zs. Czigany, and B. Pecz, Phys. Stat. Sol. (a) 176, 525 (1999). H. Okumura, H. Hamaguchi, G. Feuillet, Y. Ishida, and S. Yoshida, Appl. Phys. Lett. 72, 3056 (1997). D. J. As, T. Simonsmeier, B. Schoettker, T. Frey, D. Schikora, W. Kriegseis, W. Burkhardt, and B. K. Meyer, Appl. Phys. Lett. 73, 1835 (1998). O. Brandt, H. Yang, A. Trampert, W. Wassermeier, and K. H. Ploog, Appl. Phys. Lett. 71, 473 (1997). P. Waltereit, O. Brandt, M. Ramsteiner, R. Uecker, M. Reiche, and K. H. Ploog, J. Cryst. Growth 227, 437 (2001). W. A. Doolittle, S. B. Kang, and A. Brown, Solid State Electron. 44, 229 (2000). H. M. Ng, Appl. Phys. Lett. 80, 4369 (2002). D. Doppalapudi, E. Iliopoulos, S. N. Basu, and T. D. Moustakas, J. Appl. Phys. 85, 3582 (1999). G. P. Dimitrakopulos, Ph. Komninou, J. Kioseoglou, Th. Kehagias, E. Sarigiannidou, A. Georgakilas, G. Nouet, and Th. Karakostas, Phys. Rev. B 64, 245325-1 (2001). G. P. Dimitrakopulos, Ph. Komninou, and R. C. Pond, Phys. Stat. Sol. (b) 227, 45 (2001). A. Georgakilas, S. Mikroulis, V. Cimalla, M. Zervos, A. Kostopoulos,

187

188

3 Plasma-Assisted Molecular Beam Epitaxy of III–V Nitrides

179 180 181

182

183

184 185

186

187

188 189

190

191

192

193

194

M. Androulidaki, Ph. Komninou, Th. Kehagias, and Th. Karakostas, Phys. Stat. Sol. (a) 188, 567 (2001). H. Amano, N. Sawaki, I. Akasaki, and Y. Toyoda, Appl. Phys. Lett. 48, 353 (1986). S. Nakamura, Jpn. J. Appl. Phys., Part 2 30 L1705 (1991). C. Y. Hwang, M. J. Schurman, W. E. Mayo, Y. Li, Y. Lu, H. Liu, T. Salagaj, and R. A. Stall, J. Vac. Sci. Technol. A 13, 672 (1995). K. Uchida, A. Watanabe, F. Yano, M. Kouguchi, T. Tanaka, and S. Minagawa, J. Appl. Phys. 79, 3487 (1996). B. Pécz, M. A. di Forte-Poisson, L. Tóth, G. Radnóczi, G. Huhn, V. Papaioannou, and J. Stoimenos, Mater. Sci. Eng. B 50, 93 (1997). B. Daudin, J. L. Rouviere, and M. Arlery, Mater. Sci. Eng. B 43, 157 (1997). M. Sumiya, T. Ohnishi, M. Tanaka, A. Ohtomo, M. Kawasaki, M. Yoshimoto, H. Koinuma, K. Ohtsuka, and S. Fuke, MRS Internet J. Nitride Semicond. Res. 4S1, G.6.23 (1999). J.-S. Paek, K.-K. Kim, J.-M. Lee, D.-J. Kim, M.-S. Yi, D.Y. Noh, H.-G. Kim, and S.-J. Park, J. Cryst. Growth 200, 55 (1999). T. D. Moustakas, R. J. Molnar, T. Lei, G. Menon, and C. R. Eddy Jr, Mater. Res. Soc. Symp. Proc. 242, 427 (1992). N. Grandjean, J. Massies, and M. Leroux, Appl. Phys. Lett. 69, 2071 (1996). N. Grandjean, M. Leroux, M. Laügt, and J. Massies, Appl. Phys. Lett. 71, 240 (1997). C. Heinlein, J. Grepstad, T. Berge, and H. Riechert, Appl. Phys. Lett. 71, 341 (1997). N. Grandjean, J. Massies, P. Vennéguès, M. Leroux, F. Demangeot, M. Renucci, and J. Frandon, Appl. Phys. Lett. 83, 1379 (1998). F. Widmann, G. Feuillet, B. Daudin, and J. L. Rouvière, J. Appl. Phys. 85, 1550 (1999). C. Heinlein, J. K. Grepstad, H. Riechert, and R. Averbeck, Mater. Sci. Eng. B 58, 270 (1999). P. Vennéguès, N. Grandjean, J. Massies, and F. Semond, J. Cryst. Growth 201/202, 423 (1999).

195 S. Sonoda, S. Shimizu, Y. Suzuki, K.

196

197

198

199 200

201

202

203

204 205

206

207

208

Balakrishnan, J. Shirakashi, and H. Okumura, Jpn. J. Appl. Phys., Part 2 39, L73 (2000). E. C. Piquette, P. M. Bridger, R. A. Beach, and T. C. McGill, MRS Internet J. Nitride Semicond. Res. 4S1, G3.77 (1999). G. Namkoong, W. A. Doolittle, S. Kang, H. Sa, A. S. Brown, and S. R. Stock, MRS Internet J. Nitride Semicond. Res. 5, 1 (2000). S. Mikroulis, A. Georgakilas, A. Kostopoulos, V. Cimalla, E. Dimakis, and Ph. Komninou, Appl. Phys. Lett. 18, 266 (2002). Ph. Komninou, unpublished results. J. W. Matthews, in Epitaxial Growth, Materials Science Series, edited by J. W. Matthews (Academic Press, New York, 1975), Part B, Chap. 8, pp. 560–607. J. H. Van Der Merwe and C. A. B. Ball, in Epitaxial Growth, Materials Science Series, edited by J. W. Matthews (Academic Press, New York, 1975), Part B, Chap. 6, pp. 494–527. P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley, and M. J. Whelan, Electron Microscopy of Thin Crystals (Butterworths, London, 1965), pp. 343– 378. R. Scholtz and J. Woltersdorf, in Electron Microscopy in Solid State Physics, Materials Science Monographs, edited by H. Bethge and J. Heydenreich (Elsevier, Amsterdam, 1987), Vol. 40, Chap. 20, pp. 471–495. J. W. Matthews and A. E. Blakeslee, J. Cryst. Growth 27, 118 (1974). Th. Kehagias, Ph. Komninou, G. Nouet, P. Ruterana, and Th. Karakostas, Phys. Rev. B 64, 195329-1 (2001). S. Kaiser, H. Preis, W. Gebhardt, O. Ambacher, H. Angerer, M. Stutzmann, A. Rosenauer, and D. Gerthsen, Jpn. J. Appl. Phys., Part 1 37, 84 (1998). Ph. Komninou, Th. Kehagias, J. Kioseoglou, G. P. Dimitrakopulos, A. Sampath, T. D. Moustakas, G. Nouet, and Th. Karakostas, J. Phys. Condens. Matter 14, 13277 (2002). F. C. Frank and J. H. Van Der Merwe, Proc. R. Soc. A 198, 216 (1949).

3.8 References 209 C. A. B. Ball and J. H. Van Der Merwe,

210 211

212 213

214

215 216 217

218

219

220

221 222 223

224

225

226

in Dislocations in Solids, edited by F. R. N. Nabarro (North Holland, Amsterdam, 1983), Chap. 27, pp. 122–141. S. C. Jain, A. H. Harker, and R. A. Cowley, Phil. Mag. A 75, 1461 (1997). J. L. Weyher, S. Muller, J. Grzegory, and S. Porowski, J. Cryst. Growth 182, 17 (1997). P. A. Stadelmann, Ultramicroscopy 21, 131 (1987). S. Sonoda, S. Shimizu, X.-Q. Shen, S. Hara, and H. Okumura, Jpn. J. Appl. Phys., Part 2 39, L202 (2000). M. J. Murphy, K. Chu, H. Wu, W. Yeo, W. J. Schaff, O. Ambacher, J. Smart, J. R. Shealy, L. F. Eastman, and T. J. Eustis, J. Vac. Sci. Technol. B 17, 1252 (1999). R. Di Felice and J. E. Northrup, Appl. Phys. Lett. 73, 936 (1998). R. Averbeck and H. Riechert, Phys. Stat. Sol. (a) 176, 301 (1999). T. Bottcher, S. Eindfeldt, V. Kirchner, S. Figge, H. Heinke, D. Hommel, H. Selke, and P. L. Ryder, Appl. Phys. Lett. 73, 3232 (1998). H. Chen, R. M. Feenstra, J. Northrup, J. Neugebauer, and D. W. Greve, MRS Internet J. Nitride Semicond. Res. 6, 11 (2001). H. Chen, A. R. Smith, R. M. Feenstra, D. W. Greve, and J. E. Northrup, MRS Internet J. Nitride Semicond. Res. 4S1, G9.5 (1999). C. Adelmann, R. Langer, G. Feuillet, and B. Daudin, Appl. Phys. Lett. 75, 3518 (1999). D. F. Storm, J. Appl. Phys. 89, 2452 (2001). Y. Li, A. Koukitu, and H. Seki, J. Appl. Phys. 88, 571 (2000). X. Shen, T. Ide, M. Shimizu, S. Hara, and H. Okumura, Jpn. J. Appl. Phys., Part 2 39, L1270 (2000). R. Averbeck, A. Graber, H. Tews, D. Bernklau, U. Barnhofer, and H. Riechert, in Proc. SPIE 3279, 28 (1998). H. M. Ng, T. D. Moustakas, and K. F. Ludwig, Jr, J. Vac. Sci. Technol. B 18, 1457 (2000). Y. Saito, N. Teraguchi, A. Suzuki, T. Araki, and Y. Nanishi, Jpn. J. Appl. Phys., Part 2 40, L91 (2001).

227 H. Lu, W. J. Schaff, J. Hwang, H. Wu,

228

229

230

231 232

233 234

235

236

237

238

239

240

241 242

243

244

W. Yeo, A. Pharkya, and L. F. Eastman, Appl. Phys. Lett. 77, 2548 (2000). R. Singh, D. Doppalapudi, T. D. Moustakas, and L. T. Romano, Appl. Phys. Lett. 70, 1089 (1997). D. Doppalapudi, S. N. Basu, K. F. Ludwig, Jr, and T. D. Moustakas, J. Appl. Phys. 84, 1389 (1998). N. A. El-Masry, E. L. Piner, S. X. Liu, and S. M. Bedair, Appl. Phys. Lett. 72, 40 (1998). P. Ruterana and F. Deniel, Mater. Sci. Eng. B 59, 186 (1999). T. Mukai, M. Yamada, and S. Nakamura, Jpn. J. Appl. Phys., Part 1 38, 3976 (1999). S. Y. Karpov, MRS Internet J. Nitride Semicond. Res. 3, 16 (1998). K. Takahashi, Y. Okada, and M. Kawabe, Jpn. J. Appl. Phys., Part 2 40, L502 (2001). Y. Okamoto, K. Takahashi, H. Nakamura, Y. Okada, and M. Kawabe, Phys. Stat. Sol. (a) 180, 59 (2000). T. H. Myers, L. S. Hirsch, L. T. Romano, and M. R. Richards-Babb, J. Vac. Sci. Technol. B 16, 2261 (1998). T. Mukai, M. Yamada, and S. Nakamura, Jpn. J. Appl. Phys., Part 1 38, 3976 (1999). S. Chichibu, T. Azuhata, T. Sota, and S. Nakamura, Appl. Phys. Lett. 69, 4188 (1996). H. Sakai, T. Koide, H. Suzuki, M. Yamaguchi, S. Yamasaki, M. Koike, H. Amano, and I. Akasaki, Jpn. J. Appl. Phys., Part 2 34, L1429 (1995). P. Laukkanen, S. Lehkonen, P. Uusimaa, M. Pessa, A. Seppala, T. Ahlgren, and E. Rauhala, J. Cryst. Growth 230, 503 (2001). P. G. Eliseev, P. Perlin, J. Lee, and M. Osinski, Appl. Phys. Lett. 71, 569 (1997). R. P. Vaudo, I. D. Goepfert, T. D. Moustakas, D. M. Beyea, T. J. Frey, and K. Meehan, J. Appl. Phys. 79, 2779 (1996). D. Korakakis, H. M. Ng, M. Misra, W. Grieshaber, and T. D. Moustakas, MRS Internet J. Nitride Semicond. Res. 1, 10 (1996). H. Angerer, D. Brunner, F. Freudenberg, O. Ambacher, M. Stutzmann, R.

189

190

3 Plasma-Assisted Molecular Beam Epitaxy of III–V Nitrides

245

246

247 248

249

250

251

252

253

254

255

256

257

258

259

Höpler, T. Metzger, E. Born, G. Dollinger, A. Bergmaier, S. Karsch, and H.-J. Körner, Appl. Phys. Lett. 71, 1504 (1997). D. Korakakis, K. F. Ludwig, Jr, and T. D. Moustakas, Appl. Phys. Lett. 71, 72 (1997). E. Iliopoulos, K. F. Ludwig, Jr, T. D. Moustakas, and S. N. G. Chu, Appl. Phys. Lett. 78, 463 (2001). T. Mukai, D. Morita, and S. Nakamura, J. Cryst. Growth 190, 778 (1998). S. Nagahama, N. Iwasa, M. Senoh, T. Matsushita, Y. Sugimoto, H. Kiyoku, T. Kozaki, M. Sano, H. Matsumura, H. Umemoto, K. Chocho, T. Yanamoto, and T. Mukai, Phys. Stat. Sol. (a) 188, 1 (2001). A. Kinoshita, H. Hirayama, J. S. Kim, M. Ainoya, A. Hirata, and Y. Aoyagi, Phys. Stat. Sol. (a) 180, 397 (2000). H. Hirayama, Y. Enomoto, A. Kinoshita, A. Hirata, and Y. Aoyagi, Phys. Stat. Sol. (a) 180, 157 (2000). C. H. Chen, L. Y. Huang, Y. F. Chen, H. X. Jiang, and J. Y. Lin, Appl. Phys. Lett. 80, 1397 (2002). M. Misra, T. D. Moustakas, R. P. Vaudo, R. Singh, and K. Shah, Proc. SPIE 2519, 78 (1995). K. S. Stevens, M. Kinniburgh, and R. Beresford, Appl. Phys. Lett. 66, 3518 (1995). M. Misra, D. Korakakis, H. M. Ng, and T. D. Moustakas, Appl. Phys. Lett. 74, 2203 (1999). S. Wang, T. Li, J. M. Reifsnider, B. Yang, C. Collins, A. L. Holmes, Jr, and J. C. Campbell, IEEE J. Quantum Electron. 36, 1262 (2000). J. C. Carrano, T. Li, P. A. Grudowski, C. J. Eiting, R. D. Dupuis, and J. C. Campbell, J. Appl. Phys. 83, 6148 (1998). K. Kishino, M. Yonemaru, A. Kikuchi, and Y. Toyoura, Phys. Stat. Sol. (a) 188, 321 (2001). J. M. Van Hove, R. Hickman, J. J. Klaassen, P. P. Chow, and P. P. Ruden, Appl. Phys. Lett. 70, 2282 (1997). A. V. Sampath, M. Misra, K. Seth, Y. Fedyunin, H. M. Ng, E. Iliopoulos, Z. Feit, and T. D. Moustakas, Mater. Res. Soc. Symp. Proc. 595, W11.1.1 (2000).

260 A. Osinsky, S. Gangopadhyay, R. Gas-

261

262

263

264 265 266 267 268

269 270

271

272

273

274

275 276

ka, B. Williams, M. A. Khan, D. Kuksenkov, and H. Temkin, Appl. Phys. Lett. 71, 2334 (1997). J. T. Torvik, J. I. Pankove, S. Nakamura, I. Grzegory, and S. Porowski, J. Appl. Phys. 86, 4588 (1999). G. Y. Xu, A. Salvador, W. Kim, Z. Fan, C. Lu, H. Tang, H. Morkoc, G. Smith, M. Estes, B. Goldenberg, W. Yang, and S. Krishnankutty, Appl. Phys. Lett. 71, 2154 (1997). H. C. Liu and F. Capasso, Intersubband Transitions in Quantum Wells: Physics and Application I and II (Academic Press, 2000), Vols. 62 and 66. N. Suzuki and N. Iizuka, Jpn. J. Appl. Phys., Part 2 36, L1006 (1997). N. Suzuki and N. Iizuka, Jpn. J. Appl. Phys., Part 2 38, L363 (1999). H. M. Ng, C. Gmachl, S. N. G. Chu, and A. Y. Cho, J. Cryst. Growth 220, 432 (2000). C. Gmachl, H. M. Ng, S. N. G. Chu, and A. Y. Cho, Appl. Phys. Lett. 77, 334 (2000). H. M. Ng, C. Gmachl, S. N. G. Chu, A. Y. Cho, R. L. Forrest, E. D. Meserole, and M. S. Goorsky, presented in 19th North American Molecular Beam Epitaxy (NAMBE) Conference, Tempe, Arizona (2000). C. Gmachl, H. M. Ng, and A. Y. Cho, Appl. Phys. Lett. 77, 3722 (2000). H. M. Ng, C. Gmachl, T. Siegrist, S. N. G. Chu, and A. Y. Cho, Phys. Stat. Sol. (a) 188, 825 (2001). C. Gmachl, S. V. Frolov, H. M. Ng, S. N. G. Chu, and A. Y. Cho, Electron. Lett. 37, 378 (2001). H. M. Ng, C. Gmachl, S. V. Frolov, S. N. G. Chu, and A. Y. Cho, IEE Proc. Optoelectron. 148, 215 (2001). N. Iizuka, K. Kaneko, N. Suzuki, T. Asano, S. Noda, and O. Wada, Appl. Phys. Lett. 77, 648 (2000). T. Mozume, H. Yoshida, A. Neogi, N. Georgiev, K. Akasawa, and M. Kudo, in Proc. 25th International Symposium on Compound Semiconductors, Nara, Japan (IOP Publishing, 1998), p. 131. Y. Zhang and J. Singh, J. Appl. Phys. 85, 587 (1999). C. R. Elsass, I. P. Smorchkova, B. Heying, E. Haus, P. Fini, K. Maranowski,

3.8 References

277

278

279

280

281

282

283

284

285

286

J. P. Ibbetson, S. Keller, P. M. Petroff, S. P. DenBaars, U. K. Mishra, and J. S. Speck, Appl. Phys. Lett. 74, 3528 (1999). I. P. Smorchkova, C. R. Elsass, J. P. Ibbetson, R. Vetury, B. Heying, P. Fini, E. Haus, S. P. DenBaars, J. S. Speck, and U. K. Mishra, J. Appl. Phys. 86, 4520 (1999). I. P. Smorchkova, S. Keller, S. Heikman, C. R. Elsass, B. Heying, P. Fini, J. S. Speck, and U. K. Mishra, Appl. Phys. Lett. 77, 3998 (2000). A. Saxler, P. Debray, R. Perrin, S. Elhamri, W. C. Mitchel, C. R. Elsass, I. P. Smorchkova, B. Heying, E. Haus, P. Fini, J. P. Ibbetson, S. Keller, P. M. Petroff, S. P. DenBaars, U. K. Mishra, and J. S. Speck, J. Appl. Phys. 87, 369 (2000). I. P. Smorchkova, L. Chen, T. Mates, L. Shen, S. Heikman, B. Moran, S. Keller, S. P. DenBaars, J. S. Speck, and U. K. Mishra, J. Appl. Phys. 90, 5196 (2001). M. J. Manfra, L. N. Pfeiffer, K. W. West, H. L. Stormer, K. W. Baldwin, J. W. P. Hsu, D. V. Lang, and R. J. Molnar, Appl. Phys. Lett. 77, 2888 (2000). M. J. Manfra, N. G. Weimann, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, S. Syed, H. L. Stormer, W. Pan, D. V. Lang, S. N. G. Chu, G. Kowach, A. M. Sergent, J. Caissie, K. M. Molvar, L. J. Mahoney, and R. J. Molnar, J. Appl. Phys. 92, 338 (2002). M. J. Manfra, N. G. Weimann, J. W. P. Hsu, L. N. Pfeiffer, K. W. West, and S. N. G. Chu, Appl. Phys. Lett. 81, 1456 (2002). M. Zervos, A. Kostopoulos, G. Constantinidis, M. Kayambaki, and A. Georgakilas, J. Appl. Phys. 91, 4387 (2002). M. Zervos, A. Kostopoulos, G. Constantinidis, M. Kayambaki, S. Mikroulis, and A. Georgakilas, Phys. Stat. Sol. (a) 188, 259 (2001). A. Jimenez, E. Calleja, E. Munoz, M. Varela, C. Ballesteros, U. Jahn, K.

287

288

289

290

291

292

293

294

295

296 297

Ploog, F. Omnes, and P. Gibart, Mater. Sci. Eng. B 93, 64 (2002). M. Stutzmann, O. Ambacher, M. Eickhoff, U. Karrer, A. Lima Pimenta, R. Neuberger, J. Schalwig, R. Dimitrov, P. J. Schuck, and R. D. Grober, Phys. Stat. Sol. (b) 228, 505 (2001). M. J. Murphy, K. Chu, H. Wu, W. Yeo, W. J. Schaff, O. Ambacher, L. F. Eastman, T. J. Eustis, J. Silcox, R. Dimitrov, and M. Stuzmann, Appl. Phys. Lett. 75, 3653 (1999). A. Vescan, R. Dietrich, A. Wieszt, H. Tobler, H. Leier, J. M. Van Hove, P. P. Chow, and A. M. Wowchak, J. Cryst. Growth 201, 327 (1999). J. W. Johnson, A. G. Baca, R. D. Briggs, R. J. Shul, J. R. Wendt, C. Monier, F. Ren, S. J. Pearton, A. M. Dabiran, A. M. Wowchack, C. J. Polley, and P. P. Chow, Solid State Electron. 45, 1979 (2001). M. Micovic, A. Kurdoghlian, P. Janke, P. Hashimoto, D. W. S. Wong, J. S. Moon, L. McCray, and C. Nguyen, IEEE Trans. Electron Devices 48, 591 (2001). M. Micovic, J. S. Moon, T. Hussain, P. Hashimoto, W. S. Wong, and L. McCray, Phys. Stat. Sol. (a) 188, 31 (2001). S. Nozaki, H. Feick, E. R. Weber, M. Micovic, and C. Nguyen, Appl. Phys. Lett. 78, 2896 (2001). H. Xing, S. Keller, Y. F. Wu, L. McCarthy, I. P. Smorchkova, D. Buttari, R. Coffie, D. S. Green, G. Parish, S. Heikman, L. Shen, N. Zhang, J. J. Xu, B. P. Keller, S. P. DenBaars, and U. K. Mishra, J. Phys. Condens. Matter. 13, 7139 (2001). X. A. Cao, G. T. Dang, A. P. Zhang, F. Ren, J. M. Van Hove, J. J. Klaasen, C. J. Polley, A. M. Wowchak, P. P. Chow, D. J. King, C. R. Abernathy, and S. J. Pearton, Electrochem. Solid State Lett. 3, 144 (2000). A. Kikuchi, R. Bannai, and K. Kishino, Phys. Stat. Sol. (a) 188, 187 (2001). A. Kikuchi, R. Bannai, K. Kishino, C.M. Lee, and J.-I. Chyi, Appl. Phys. Lett. 81, 1729 (2002).

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4

Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy Agnès Trassoudaine, Robert Cadoret and Eric Aujol

Abstract

A complete study of the growth of gallium nitride is developed. A synthesis of major results on the growth of GaN by HVPE is presented. The principle and the use of the HVPE method are introduced. Thermodynamical and kinetic studies lead to a good understanding of the physics of the GaN growth by hydride vapor phase epitaxy. The two mechanisms involved in the growth of (00.1) GaN HVPE have been deduced from the numerous experiments performed on (001) GaAs by the chloride method. They include a desorption of adsorbed Cl in HCl by H2 for the first mechanism and a desorption of two Cl in GaCl3 by GaCl for the second one. Theoretical curves have been computed by taking into account the interactions between the mass transfer, approximated by a simple model, the parasitic GaN deposition, and the kinetics. They give a good approximation of the expected and observed growth rate values. A new domain of growth experimentally observed in conditions of the expected fast etching by HCl, ensures growth rates of 50–60 lm h–1 without a parasitic GaN deposit by using a suitable temperature profile. This profile is computed by considering a combined mechanism of Cl desorption by GaCl into GaCl2 and of etching by HCl. The GaCl2 produced has to be assumed to be rapidly decomposed with respect to the mass transfer velocity. Its formation rate in the vapor phase is assumed to be very slow with respect to the reverse reaction. These assumptions are in agreement with the difficulty of observing this species and the well-known doubt of its existence.

194

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

4.1

General Points on HVPE 4.1.1

Introduction

HVPE (hydride vapor phase epitaxy) is a growth method widely used in the silicon and III–V semiconductors technology. At the beginning of the 1960s, the development of the halide precursor techniques applied to Si and Ge allowed great strides to be made in the spread of GaAs. Since then, HVPE has always played an important role in the growth of III–V semiconductors and it was the first [1] and until the early 1980s the only method for growing epitaxial layers of gallium nitride [2–9]. The advantage of this technique was to grow thick buffer layers at high growth rates on available substrates. The first single-crystalline, colorless, HVPE GaN was obtained by Maruska et al. [1] in 1969 on sapphire substrates. Typical thicknesses for these deposits were in the range of 50–150 lm. In 1971, Wickenden et al. [2] grew GaN on a-SiC and a-Al2O3. Then, Ilegems [4] obtained single-crystal layers of GaN 100–200 lm thick on sapphire substrates in 1972. In 1974, Shintani and Minagawa [5] studied the effects of the growth parameters, the position of the substrate, the reactant gas flow rate and the substrate temperature, upon the epitaxial growth rate of GaN on (0001) sapphire substrates. Sano and Aoki [6] demonstrated the influence of the surface sapphire orientation on the growth rate in 1976. In 1977, Madar et al. [7] and Jacob et al. [8] grew intentionally n-doped GaN on sapphire substrates. Seifert et al. [9] led a study on the growth rate in VPE of GaN in a hydrogen as well as in an inert gas ambient in 1981. They obtained growth rates up to 800 lm h–1. But this technique was largely abandoned in the early 1980s because of an apparent inability to reduce the native defect concentration to nondegenerate levels and thus enable p-doping. When, in the 1990s, it appeared that interesting applications of GaN-based materials may be developed, HVPE returned [10–13] because of its ability to grow thick GaN films without too many defects at relatively low cost. Thick hexagonal GaN layers were widely obtained on sapphire substrates and cubic GaN has been grown on (001) GaAs [14–16]. The best quality epilayers were achieved by coalescence of selectively grown GaN on patterned SiO2 masks [17–20]. Free-standing GaN substrates were prepared for the first time by Kim et al. [21] and Melnik et al. [22]. Despite these remarkable achievements, the nitride materials still suffer from a very high defect density due to the lattice mismatch between the nitrides and all the available foreign substrates. Recent two-step processes employing low-temperature GaN buffer layers [23, 24] and techniques for substrate removal [25–30] have shown good quality materials with very promising characteristics. Development of the HVPE technique combined with other techniques for producing GaN templates may become the key to resolve the high density defect issue in III-nitride device technology.

4.1 General Points on HVPE

4.1.2

Principle of HVPE

In this growth method, the quartz walls of the reactors are heated in order to secure the stability of the group-III element precursors. These precursors are chlorides formed by flowing hydrogen chloride gas over a source of a liquid metal contained in a quartz tube. The elemental group-V precursors are hydrides fed into the reaction chamber by a separate quartz line. For the GaN, the chloride and hydride precursors are respectively GaCl and NH3. The vapor phase is transported to the deposition zone by a carrier gas, which can be hydrogen and/or an inert gas. The pressure inside the reaction chamber is kept at atmospheric pressure. The reactor is a very high purity quartz tube. The gases are of electronic quality that is to say with a purity better than one ppm for contaminant species. For nitrogen or hydrogen, each impurity is in concentration under 1 ppm. For the other gases, the total concentration of all the impurities is under 1 ppm. The metallic sources employed have a purity of 99.99999% (7N). Generally, the heating system is constituted of a multiple zone furnace. In particular, a source zone, where the quartz tube containing the metallic gallium, is placed, the central zone where the gases are homogeneously mixed, and the deposition zone where the sample is located during the growth. A schematic of a HVPE reactor is given in Fig. 4.1. The possibility to separately set the partial pressure of each species, the chlorides and hydrides being independently produced, allows a systematic approach for searching the growth conditions. The study of the influence of the variations of the vapor-phase composition on the growth rate is then easier. The different physical mechanisms, which occur during a growth, are also easier to understand. The vapor-phase composition depends on the metallic source efficiency, the am-

NH3 N2 NH3 GaCl HCl

Fig. 4.1

Schematic of the HVPE system.

195

196

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

monia decomposition and the flow of the different gases introduced in the reactor. The vapor-phase composition, the partial pressures of the different gaseous species and the temperature of the different zones of the reactor determine the growth rate and the solid composition of the epitaxial layer. The main characteristic of the HVPE is that the growth can be accomplished in a wide range of conditions around the thermodynamical equilibrium of the deposit reactions. If a large flow of HCl is not introduced in the reactor, the use of NH3 leads to initial conditions far from the thermodynamical equilibrium. Low (1 lm h–1) or high (more than 100 lm h–1) growth rates can be achieved with HVPE. 4.1.3

Use of HVPE

Many semiconductor devices have been fabricated from epitaxial wafers grown by the vapor transport method. Although highly controlled epitaxial technologies such as molecular beam epitaxy and vapor phase epitaxy have become popular, HVPE still has a significant position in semiconductors device fabrication. Most silicon VLSI (very large-scale integrated) circuits based on bipolar transistors are fabricated from epitaxial wafers grown by hydride or chloride method carried out in the SiCl4/H2, SiHCl3/H2, SiH4/H2 or Si/H2Cl2/H2 system. Some MOS (metaloxide semiconductor) logic LSI is also fabricated from epitaxial wafers grown by these methods. Light emitting diodes are fabricated from GaP or GaAsP epitaxial wafers grown by the Ga/HCl/AsH3/PH3/H2 system. GaAs microwave devices are produced from wafers grown by the Ga/AsCl3/H2 process. The strength of the HVPE is easy to demonstrate. First, unlike in the nonequilibrium processes (MOVPE or MBE), very high growth rates (>20 lm h–1) can be easily achieved in HVPE. Secondly, the group III chloride adsorption on the dielectric mask is extremely low with respect to the semiconductor surface. Consequently, selective growth [31] is an inherent property in HVPE at routine operating temperatures. One of the possible applications for the selective growth in HVPE is ‘conformal growth’. This technique has been developed to reduce the density of dislocations for monolithic integration of III–V and Si devices on Si. Conformal growth of III-V materials (either GaAs or InP) on Si consists of a confined lateral selective epitaxy of the III–V on a silicon substrate from III–V oriented seeds, and the vertical growth being stopped by an overhanging dielectric mask (see Fig. 4.2). Note that the conformal growth technique allows then for an independent control of the vertical and lateral extensions of the conformal III–V film, which represents a huge advantage with respect to conventional epitaxial lateral overgrowth (ELO). The dislocations initially present in the seeds can not propagate far through the conformal growing layer, as they are rapidly blocked either by the cap layer or by the substrate surface. Cross-sectional high-resolution TEM has shown that dislocations did not propagate beyond 1 to 2 lm from the seed sidewall layers [32, 33]. As no direct nucleation takes place between Si and the III–V material, conformal layers present dislocation densities ranging between 104

4.1 General Points on HVPE

Fig. 4.2

Schematic principle of conformal growth applied to GaAs.

and 105 cm–2, as they are not detected by TEM [32, 34, 35]. This result is in agreement with the data extrapolated from the efficiency of LEDs regrown on conformal buffer layers [36, 37]. The conformal growth method allows growth of highquality submicrometer-thick III–V layers up to 50 lm wide irrespective of the substrate and the seed orientation. Conformal epitaxy was also applied to the making of laterally modulated structures, both in composition and doping [38]. 4.1.4

Problems Associated with GaN Growth

The growth of GaN is complicated by the absence of a lattice-matched bulk substrate. This lack of a suitable bulk substrate has led to the use of a variety of nonlattice-matched substrates, with sapphire and SiC becoming the substrates of choice. The choice of a suitable substrate relies on many factors, such as the lattice parameter, coefficient of thermal expansion, chemical and structural similarity, cost and available diameter. Sapphire is the most widely used because of its low cost compared with SiC. For all the foreign substrates, many defects appear in the epitaxial layer thickness, typically consisting of dislocations. The initial nucleation of GaN on sapphire substrates can determine the material properties of the subsequent epitaxial layer [11, 13, 39, 40]. GaCl or NH3 pretreatment consisting of flowing GaCl or NH3 over the sapphire surface prior to the initiation of growth at high temperatures, or the use of a ZnO buffer layer, have been successfully applied to promote the initial nucleation and growth of improved material and properties [10, 11, 44, 45]. Sapphire nitridation has been mentioned as a means to improve HVPE materials by several groups [43–46]. There are other drawbacks, however, to the growth of GaN by HVPE, which limit its usefulness for devices. Perhaps, the most important is the nature of the chemistry involved in the GaN growth by this technique, which differs from other III–V semiconductors. For instance, in GaAs growth by HVPE thermal dissociation of the arsenic compounds results in the formation of As2 or As4 molecules [47, 48], which typically remain volatile and chemically reactive and thus participate in the film growth. In GaN HVPE, NH3 is used as the source of nitrogen rather than a nitrogen halide, NCl3, which is highly explosive. In this process, the thermal dissociation of NH3 results in the formation of N2 molecules that are extremely stable and essentially unreactive at the temperature of interest. In fact,

197

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4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

the viability of HVPE GaN growth lies in the relatively low dissociation of NH3, which enables the effective transport of reactive nitrogen to the growth surface [3]. Another difference in the growth of GaN by HVPE, as compared with other III–V compounds, is the strong thermodynamic propensity for GaN to form, leading to undesirable gas-phase reactions and wall-deposition problems. The composition of the vapor phase is thus not easy to control and the growth mechanism is difficult to understand. The HVPE process also tends to create copious amounts of NH4Cl, GaCl3 and GaCl3-NH3 that can condense in and eventually clog exhaust lines unless they are heated to sufficiently high temperatures (>150 8C). Finally, due to exchange reactions with the hot quartz walls of the reactor, aluminum- or magnesium-bearing compounds (which are required for AlGaN growth and efficient p-doping, respectively) are difficult to use by HVPE.

4.2

Thermodynamical Study

By the HVPE method, Ga precursors are obtained according to the following reactions: Galiq + HClg Û GaClg + 1/2 H2g,

(1)

GaClg + 2 HClg Û GaCl3g + H2g,

(2)

where subscript g is used for gas-phase species and liq for liquids. The efficiency of the first reaction had been estimated by Ban [3] to be equal to 99.5%. The group-V precursor is ammonia, which is thermodynamically unstable at high temperatures, but no more than 3% is decomposed in N2 and H2 at temperatures as high as 950 8C [3]. By analogy with GaAs deposition [49], one can postulate two thermodynamic reaction pathways, which might lead to the deposition of GaN [50]: GaClg + NH3g Û GaN + HClg + H2g,

(3)

3 GaClg + 2 NH3g Û 2 GaN + GaCl3g + 3 H2g.

(4)

The main gaseous species in GaN growth are GaCl, GaCl3, HCl, NH3, H2 and the carrier gas. In this work, Barin’s [51] thermodynamical data is used for the calculations related to reactions (1) to (4). The equilibrium constants calculated from the Van‘t Hoff’s second law should be in agreement with the equilibrium constants calculated from the partition functions of the involved molecules.

4.2 Thermodynamical Study

4.2.1

Thermodynamical Characteristics

We consider that all the reactions are at thermodynamical equilibrium. For the reactions (1) to (4) of the type a1A1 + a2A2 + . . . Û b1B1 + b2B2 + . . . ,

(5)

the equilibrium constant Kp can be written as follows:  Kp …T† ˆ exp

 DG…T† ; RT

…6†

where DG(T) is the variation of the Gibbs free energy between the products and the reacting species, calculated by taking into account the thermodynamical data DH0f(298) (enthalpy of formation at 298 K), S0298 (entropy at 298 K), and Cp (heat capacity) [51]. The Cp values of the gaseous species are fitted as a function of the temperature with the formula Cp = a + bT + cT2 + dT3 + eT4.

(7)

The variation of the Gibbs free energy is calculated as follows: DG(T) = DH(T) – TDS(T).

(8)

Calculation of the enthalpy of formation, DH(T): Z DH…T† ˆ

T

TX

Z DCp dT ˆ

298

298

So : DH…T† ˆ A ‡ DaT ‡

bj Cpj

j

X

 ai Cpi dT:

…9†

i

Db 2 Dc 3 Dd 4 De 5 T ‡ T ‡ T ‡ T ; 2 3 4 5

…10†

where A is a constant of integration. The convention for the notation of Da, Db, Dc, Dd, and De is Da ˆ

X j

bj aj

X

ai ai :

…11†

i

Knowing that (at standard pressure) DH…298† ˆ DHf0 …298† ˆ

X p

bp Hf0 …298†

X

br Hf0 …298†;

r

the expression of the free enthalpy of the reaction becomes

…12†

199

200

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

DH…T† ˆ DHf0 …298† ‡ Da…T ‡

Dd 4 …T 4

2984 † ‡

298† ‡ De 5 …T 5

Db 2 …T 2

2982 † ‡

Dc 3 …T 3

2985 †:

2983 † …13†

Calculation of the entropy, DS(T): Z DS…T† ˆ

DCp dT 298 T T

…14†

DS…T† ˆ B ‡ Da ln…T† ‡ DbT ‡

Dc 2 Dd 3 De 4 T ‡ T ‡ T ; 2 3 4

…15†

where B is a constant of integration. Knowing that DS…298† ˆ DS0298 ˆ

X

bp S0298

p

X

br S0298 ;

…16†

r

we obtain 

 T Dc ‡Db…T 298† ‡ …T 2 298 2 De 4 3 4 298 † ‡ …T 298 †: 4

DS…T† ˆ DS0298 ‡ Da ln ‡

Dd 3 …T 3

2982 † …17†

Finally, we can write DG…T† ˆ T

DH…T† ‡ DS…T†: T

…18†

Then     DHf0 …298† 298 T ‡ ln 1 ‡ DS0298 ‡ Da T 298 T       2 298 298 T 298 298 1 T 2 3 ‡ Db ‡ 2 ‡ Dc ‡ 3 2 T 298 T 2 298 2       4  3 3 4 298 298 1 T 4 298 298 1 T 5 ‡ Dd ‡ ‡ ‡ De : …19† 4 5 T 3 298 3 T 4 298 4

DG…T† ˆ T

The equilibrium constant Kp, for the temperature T, is then calculated with the characteristics expressed in the following units: DH0f(298) and DS0298 in cal mol–1, the temperature T in K, the numerical data used for Cp calculation in cal mol–1 K–1, R = 1.9872 cal mol–1 K–1.

–70542 0 –92312 –431580 –45940 –109621

GaCl H2 HCl GaCl3 NH3 GaN

240.25 130.41 186.6 325.148 192.451 29.706

S0298 ( J (K mol)–1) 29.585 28.3 30.9 56.5 26.1 38.1

a ( J (K mol)–1) 0.0329 0.00301 –0.011 0.0679 0.0304 0.009

b ( J (K2 mol)–1)

d ( J (K4 mol)–1) 3.3938 ´ 10–8 4.72 ´ 10–9 –1.06 ´ 10–8 4.13 ´ 10–8 –9.95 ´ 10–9 3.94 ´ 10–12

c ( J (K3 mol)–1) –5.0142 ´ 10–5 –4.56 ´ 10–6 2.04 ´ 10–5 –8.03 ´ 10–5 7.80 ´ 10–6 –7.35 ´ 10–9

K1(T)=exp[–(–17.92+(2326.53/T)+1.80 ´ ln(T)–2.73 ´ 10–3 ´ T+1.46 ´ 10–6 ´ T2 –4.70 ´ 10–10 ´ T3 +5.84 ´ 10–14 ´ T4)]. K2(T)=exp[–(15.48+(–21243.17/T)+0.79 ´ ln(T)–3.61 ´ 10–3 ´ T+1.51 ´ 10–6 ´ T2 –3.34 ´ 10–10 ´ T3–8.26 ´ 10–14 ´ T4)]. K3(T)=exp[–(41.93+(–11498.27/T)–5.01 ´ ln(T)+3.74 ´ 10-–3 ´ T–1.17 ´ 10–7 ´ T2+2.99 ´ 10–10 ´ T3–5.65 ´ 10–14 ´ T4)]. K4(T)=exp[–(49.67+(–22119.86/T)–4.61 ´ ln(T)+1.94 ´ 10–3 ´ T–4.09 ´ 10–7 ´ T2+1.33 ´ 10–10 ´ T3–9.78 ´ 10–14 ´ T4)].

DH0f(298) (kJ mol–1)

Gas

study.

–8.48 ´ 10–12 1.22 ´ 10–12 1.84 ´ 10–12 7.71 ´ 10–12 2.15 ´ 10–12 –6.46 ´ 10–16

e ( J (K5 mol)–1)

Tab. 4.1 Values of the parameters a, b, c, d, e, DH0f (298), and S0298, and equations of the thermodynamical constants, Ki(T) for the reaction (i), used in this

4.2 Thermodynamical Study 201

202

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

The parameters a, b, c, d, and e are reported in Table 4.1 together with the DH0f (298) and S0298 values, and with the equation of the thermodynamical constants used in this study for the various species involved. Koukitu et al. [52] and Przhevalskii et al. [53] have already published thermodynamical analysis of HVPE of GaN. Our polynomial form for the thermodynamical constants provides an accurate approximation according to their results.

4.2.2

Partition Functions of the Molecules

The ammonia molecule is pyramidal with a moment of inertia equal to 3.265 ´ 10–47 kg m2 [54]. The symmetry factor of the molecule is equal to 3 and the vibration frequencies are the following: m1 m2 m3 m4

= = = =

3506 cm–1 1022 cm–1 3577 cm–1 1691 cm–1

(1) (1) (2) (2)

[54], [54], [54], [54].

The degeneracy degree of the vibrational frequencies is indicated in brackets in the exponent. The potential energy of gaseous NH3, eNH3, was calculated to be equal to –280.1 kcal mol–1 from the thermodynamical data of Barin [51]. The GaCl3 molecule is planar with a D3h symmetry. The interatomic Ga–Cl distances are equal to (2.100 ± 0.005) Å and the angles Ga–Cl are equal to (120 ± 5)8 [55], which give a moment of inertia equal to 3.401 ´ 10–45 kg m2. The symmetry factor of the molecule is equal to 9 and the vibrational frequencies are: m1 m2 m3 m4

= = = =

381 cm–1 144 cm–1 457 cm–1 128 cm–1

(1) (3) (1) (1)

[56, 57], [58, 59], [56], [56, 58, 59].

The vibrational frequencies of the diatomic molecules GaCl and HCl are respectively equal to 365.3 cm–1 [60] and 2889.59 cm–1 [54]. The vibration partition function of the hydrogen molecule is taken equal to 1 because of its very high vibrational frequency. The solid GaN partition function is deduced from the Debye approximation with the solid GaN Debye temperature equal to 600 K [61]. This value matches the equilibrium constant calculated with the use of the thermodynamical data. All the partition functions of this work are collected in Table 4.2. Using these partition functions, the equilibrium constants of the deposition reactions in SI units can be written as follows: K3 …T† ˆ

ZGaNc ZHClg ZH2g ; ZNH3g ZGaClg

…20†

†…1

†

1

TD T

†‡

†…1

1

†…1

658:0 T

1470 T

exp

exp

exp

0:0093

TD T


‡ 0:27

4:65T

5:74  10 3 T

GaCl(g)

H2(g)

GaN(c)

4:83T 2

3

3

3

V4:39  1029 T 2

V6:61  1017 T 2

3

V3:45  1019 T 2

3

V4:14  1028 T 2

V1:32  1028 T 2

3:26  10 2 T

GaCl3(g)


TD 2 T ‡ 0:18

Partition function of translation

0:29

†3

†2

207:3 T

2430 T

HCl(g)

3 

exp

exp

3

3

T TD

†…1

†2 …1

548:6 T

5150 T

1:22  10 2 T 2



exp

exp

NH3(g)

Partition function of rotation

 6 1:2 ln …1

184:3 T

525:6 T

†

†…1

4157:5 T

5044 T

(b) Molecule



exp

exp

1

exp

1

exp

exp

…1

1

…1

…1

…1

Partition function of vibration

GaN(c)

GaCl3(g)

H2(g)

GaCl(g)

HCl(g)

NH3(g)

(a) Molecule

partition function. T is the growth temperature and V the volume


TD 3 T


TD 4 T

‡ 0:0046


TD 5 T



Electronic partition function   3 exp 14110 T   3 exp 51:8710 T   3 exp 55:710 T   3 exp 52:4710 T   3 exp 131:610 T   3 exp 104:110 T

0:058

Tab. 4.2 (a) Vibration partition functions. T is the growth temperature and TD, the Debye temperature of GaN; (b) rotation, translation and electronic

4.2 Thermodynamical Study 203

204

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

K4 …T† ˆ

2 3 ZGaN ZGaCl3g ZH c
2g ; kT 3 2 ZNH Z GaClg V 3g

…21†

where subscript c is used for crystalline species, T is the temperature, V is the volume, k the Boltzmann constant. Figures 4.3 and 4.4 display the equilibrium constants calculated from the thermodynamical data and the partition functions of the molecules. Both show a good

Comparison of the equilibrium constant for the reaction (3). K(3) (—–) is calculated from the thermodynamical data and K3(z) (– – –) from the partition function. Fig. 4.3

Comparison of the equilibrium constant for the reaction (4). K(4) (—–)is calculated from the thermodynamical data and K4(z) (– – –) from the partition function. Fig. 4.4

4.2 Thermodynamical Study

agreement between the equilibrium constants calculated from Van’t Hoff’s second law and from statistical physics. 4.2.3

Calculation of the Partial Pressures

For the pressure and the temperature kept constant, one can write the n relations representing the thermodynamical equilibrium constant of the n reactions of the type of reaction (5): Ki ˆ

‰B1 Šb1 ‰B2 Šb2


‰A1 Ša1 ‰A2 Ša2




…22†

with i varying from 1 to n and [X] being the partial pressure of the X species. The partial pressures of the gaseous species are calculated by solving a system of equations including the conservation of the gaseous species, the total pressure of the gaseous species equal to one atmosphere, and the equilibrium constants. Figures 5.5 and 5.6 represent the partial pressures versus temperature for 0 sccm and for 200 sccm of additional HCl, respectively. All the other growth parameters were kept constant and equal to the values reported in Table 4.3. The obvious difference between the two cases is the partial pressure of GaCl3 which is four orders of magnitude higher in the second case for a temperature equal to 1000 8C. For 0 sccm of additional HCl, the reaction for the formation of the GaCl3 species is therefore negligible and the impoverishment of GaCl and HCl can be ignored, which is not the case for 200 sccm of additional HCl.

Variation of the partial pressures versus temperature for 0 sccm of additional HCl.

Fig. 4.5

205

206

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy Variation of the partial pressures versus temperature for 200 sccm of additional HCl.

Fig. 4.6

HCl3 GaCl3

Tab. 4.3 Values of the gas flows used for the HVPE growth of GaN

Gas

Flows in sccm

HCl source N2 source Additional HCl N2 Carrier gas NH3

20 to 30 * 83 to 73 * 0 to 200 * 1480 to 2000 * 300

*) With (HCl + N2 source flow) = constant (103 sccm). **) With (additional HCl + N2 carrier gas flow) = constant (2000 sccm).

4.2.4

Thermodynamical Study of the GaN Deposit

For the thermodynamical study we consider the equilibrium of the deposition reactions (3) and (4). The equality of the chemical potential for each of them leads to the calculation of the thermodynamical constant. We obtain – for the reaction (3): 

lGaN ‡

l0HClg

‡

l0H2g

l0GaClg

l0NH3g

PGaCl PNH3 ˆ kT ln PHCl PH2

 …23† eq

(l0ig are the standard potentials of the gaseous species i; for each species considered at its equilibrium the corresponding potential is written with the ‘0’ exponent) – for the reaction (4):

4.3 Kinetic Study

2lGaN ‡ l0GaCl3g ‡ 3l0H2g

3l0GaClg

2l0NH3g ˆ kT ln

 3  2 PGaCl PNH 3 : 3 PGaCl3 PH eq 2

…24†

We can then define the equilibrium constant of the GaN deposit – for the reaction (3) as   PGaCl PNH3 eq ; K3 …T† ˆ PHCl PH2 eq

…25†

– for the reaction (4) as eq

K4 …T† ˆ

 3  2 PGaCl PNH 3 : 3 PGaCl3 PH eq 2

…26†

By analogy to the single condensation of one species, we define the state of advancement relative to a reaction Ag ‡ Bg , Cg ‡ Dsolid

…27†

having an equilibrium constant K eq …T†, by the expression as follows: 1‡cˆ

PA PB ; PC K eq …T†

…28†

where c is the relative supersaturation. The equilibrium between the vapor phase and the condensed one is represented by a c value equal to zero. If c > 0, the deposit occurs and if c < 0 the epilayer is etched by the Cg species. The expressions of the relative supersaturation for the GaN deposit by the reactions (3) and (4) are, respectively: c3 ˆ

PGaCl PNH3 1
PHCl PH2 K3eq

1;

…29†

c4 ˆ

3 2 PGaCl PNH 1 3
eq 3 PGaCl3 PH K 4 2

1:

…30†

4.3

Kinetic Study 4.3.1

Introduction

The surface kinetics depends on the adsorption and desorption kinetics of the gaseous species present at the crystal surface and on the diffusion kinetics of the adatoms or admolecules to the incorporation sites termed half-crystal or K site (see Fig. 4.7). To simplify the problem we consider that the growth results from two

207

208

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

Fig. 4.7

Microscopic events occurring in the growth by vapor

phase.

superficial diffusion flows, one from the NGa admolecules and the other from the NGaCl admolecules. Close to the step edge, only the NGa flow is directly incorporated when the NGaCl required the chlorine desorption before its incorporation. 4.3.2

Relations Between the {001} GaAs and (00.1) GaN Epitaxy

The growth rates of III–V compounds deposited by HVPE or the chloride methods generally present an increasing then a decreasing part with decreasing substrate temperature. Shaw [62–64] was the first to measure systematically the growth rate of GaAs on {001}, {111}A, {111}B, and {110} substrates, with hydrogen as carrier gas and by using the chloride method, as a function of temperature and, for {001} substrates, as a function of the GaCl partial pressure. He was the first to propose that a Langmuir GaCl adsorption isotherm could explain the decreasing part of the experimental curves with decreasing substrate temperature. Later a kinetic model based on GaCl adsorption [65, 66] was developed. A term of lateral interaction between GaCl adsorbed molecules was considered to take into account the slight decrease of the GaAs growth rate observed at low temperature, by increasing the GaCl partial pressure. In the model, the Cl desorption by hydrogen of adsorbed GaCl molecules was considered to compute the growth rate. This desorption mechanism is labeled by the H2 mechanism. Surface diffusion was introduced and computed by fitting the experimental measures of Hollan et al. [67–69] as a function of the substrate orientation, and of Gentner and coworkers

4.3 Kinetic Study

[70, 71] on 68 off {001} GaAs substrates, carried out at atmospheric and reduced pressures in hydrogen and helium. A second mechanism was evidenced by the possibility to grow in He by the chloride method without HCl, therefore without H2 at all. This mechanism also appears in H2 at low temperature and high AsCl3 molar fraction values. The GaCl surface coverage value computed in the H2 mechanism was close to one just before the appearance of this second mechanism. A desorption mechanism of two adsorbed chlorine atoms by GaCl in GaCl3 was therefore considered with an intermediate GaCl3 adsorption step [49]. This mechanism is called the GaCl3 mechanism. The only experimental curves available for computing the model parameters in the GaN HVPE system were the (00.1) curves reported by Seifert et al. [9]. In hydrogen as well in helium the decreasing part of the growth rate as a function of the reverse temperature was also observed. Furthermore the coaxial arrangement of the gas inlet tubes and the orientation of the substrate with respect to the flow prevented extraneous deposition on the quartz walls before the substrate. The measured growth rates reached very high values with respect to the highest values reported in recent years, 800 lm h–1 against 100–120 lm h–1 [72, 73]. This large difference indicates an important effect of the mass transfer and of the parasitic GaN deposition, always observed on the quartz walls in most reactors. Therefore, many of the results published in the last ten years could not be used to understand and model the (00.1) GaN HVPE. The {001} GaAs model has therefore been applied to the (00.1) GaN HVPE. Its parameters have been deduced from the two experimental curves of Seifert et al. [9]. With respect to the GaAs model an intermediate HCl adsorption step was added, as suggested by the quantum-chemical study of Seifert et al. [74]. Furthermore, adsorption of NH3 with an adsorption energy value of –24.8 kcal mol–1 has been considered. Such an adsorption was reported to occur in MOCVD [75], but the experimental data were not clearly reported as a function of the NH3 partial pressure. We have therefore considered an NH3 adsorption energy value, which could be in agreement with the MOCVD results without being competitive in the HVPE process. 4.3.3

Statistical Treatment of the Dynamic Equilibrium Surface-Vapor Phase

The growth process considered in the model developed by Cadoret [50] is a surface process involving the following adsorption steps: adsorption of NH3 molecules, adsorption of N atoms resulting from NH3 decomposition and finally adsorption of GaCl molecules on N atoms, according to the reactions: V ‡ NH3g , NH3 ;

…R1†…31†

3 NH3 , N ‡ H2g ; 2

…R2†…32†

N ‡ GaClg , NGaCl;

…R3†…33†

209

210

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

where subscript g is used for gas-phase species and V is a vacant site. As in the GaAs model [49] two desorption mechanisms of chlorine were considered, desorption in HCl vapor molecules following a surface reaction with H2 and desorption in GaCl3 vapor molecules following an absorption of GaCl on two GaCl underlying molecules (Fig. 4.8), according to the reactions: 2 NGaCl ‡ H2g , 2 NGa NGa

ClH , NGa ‡ HClg ;

2 NGaCl ‡ GaClg , 2 NGa 2 NGa

ClH;

…R4†…34† …R5†…35†

GaCl3 ;

GaCl3 , 2 NGa ‡ GaCl3g :

…R6†…36† …R7†…37†

The two mechanisms will be labeled as H2 and GaCl3 mechanisms. They are approached by means of a one-monolayer model of adsorption on a (00.1) Ga surface. The adsorbed species are then NH3 molecules, N atoms, NGaCl, NGa-ClH and 2 NGa-GaCl3 molecules. The one-monolayer adsorption model and the BraggWilliams approximation are used to simplify the problem, by reducing the aver-

Fig. 4.8 Schematic steps of adsorption and desorption processes involved in the a H2 mechanism; b GaCl3 mechanism.

4.3 Kinetic Study

age numbers of adsorbed molecules to the surface coverages hi of one underlying Ga atom. We have hv ˆ 1

Ri6ˆv hi ˆ 1

hNH3

hN

hNGaCl

hHCl

hGaCl3

hNGa ;

…38†

subscript v is used for the vacant sites, underlying Ga atoms. The admolecules NGa-HCl and 2 NGa-GaCl3 are denoted as HCl and GaCl3. The concentration Ci of i molecules per unit area is the product of the number Ns of surface sites per unit area by the surface coverage, Ci ˆ Ns hi : The number of activated molecules involved in the reactions (R1)–(R7) as well as possible intermediate states of hydrogen desorption from NH3 are ignored. GaCl adsorption on a Ga adatom [76, 77] is assumed to be negligible because it would lead to antisite positions after chlorine desorption, or would act as a simple inhibitor of the deposition process, which seems not to have been observed in GaAs. The two overall reactions corresponding to the H2 and GaCl3 growth mechanisms can be written as V ‡ NH3g ‡ GaClg , NGa ‡ HClg ‡ H2g ;

…R8†…39†

2 V ‡ 2 NH3g ‡ 3 GaClg , 2 NGa ‡ GaCl3g ‡ 3 H2g :

…R9†…40†

The net adsorption flux of molecules i, relative to the reaction Ri, per unit area, can be written as Ji ˆ J‡i

J

i

ˆ m‡i Ci

1

m i Ci :

…41†

The values of the reaction frequencies mi are calculated from the partition functions of the molecules in the initial or final and activated states using the Eyring’s theory [78]. One can consider that the surface is formed by Ns, per unit area, potential wells having a depth of ead. In the vapor phase, the interaction potential energy for one molecule is em. In Eyring’s theory crossing from an initial state to a final one occurs through an activated state having an energy e* (Fig. 4.9) higher than the initial and final potential energies. For their adsorption, the molecules must overcome a potential barrier with a height equal to (e*–em), which defines the adsorption activation energy. Passing from the crystal to the vapor phase, the molecules pass through a potential barrier with a height equal to (e*–ead), which defines the desorption activation energy. The adsorption and desorption flows can then be written as J‡ ˆ N‡ and

y‡ d

…42†

211

212

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy Variation of the potential energy of molecules in the growth direction.

Fig. 4.9

J ˆ N

y ; d

…43†

where d is the width of the potential barrier, y+ and y– are the mean rates of the activated molecules crossing through the potential barrier. N*+ and N*– correspond, respectively, to the number of the adsorbed and desorbed molecules. The total flows for the adsorption of the molecules i, relative to the reaction Ri, per unit area are expressed as follows J1 ˆ J‡1

J

1

ˆ m‡1 CV

m 1 CNH3

…44†

J2 ˆ J‡2

J

2

ˆ m‡2 CNH3

m 2 CN

…45†

J3 ˆ J‡3

J

3

ˆ m‡3 CN

m 3 CNGaCl

…46†

J4 ˆ J‡4

J

4

ˆ m‡4 CNGaCl

J5 ˆ J‡5

J

5

ˆ m‡5 CNGa-ClH

J6 ˆ J‡6

J

6

ˆ m‡6 CNGaCl

J7 ˆ J‡7

J

7

ˆ m‡7 C2NGa-GaCl3

m 4 CNGa-ClH

…47†

m 5 CNGa

…48†

m 6 C2NGa-GaCl3 m 7 CNGa

…49† …50†

with mi ˆ mi0 exp… eai =kT†

…51†

and Ci ˆ Ns hi :

…52†

  zGaCl3g =zGaCl3 kT a7 p 2pmGaCl3 kT V

R7

with eH2 ˆ eNGaCl-H2 -NGaCl eGaCl ˆ eNGaCl-GaCl-NGaCl

a6 PGaCl hNGaCl p 2pmGaCl kT hV

R6

eH2g

eNGa-GaCl

eGaClg

eNGa-HCl

2 eNGaCl

eNGa-GaCl3

eGaCl

eN

2 eNGaCl

eGaClg

eNH3g

eNH3g

eNGa-HCl

a4 PH2 hNGaCl p 2pmH2 kT hV

R4

  zHClg =zHCl kT a5 p 2pmHCl kT V

eH2

a3 PGaCl p 2pmGaCl kT

R3

R5

eNGaCl

a2

R2

eNH3

eNH3

a1 PNH3  p NS 2pmNH3 kT

R1

  zNH3g =zNH3 kT p NS 2pmNH3 kT V

e+ai

m+i0

Ri

Tab. 4.4 Expression of the kinetic coefficients for the expressions (44)–(50)

  zNH3g =zNH3 kT p NS 2pmNH3 kT V

a7 PGaCl3 hNGa  p 2pmGaCl3 kT hV

  zGaClg =zGaCl kT a6 p 2pmGaCl kT V

a5 PHCl p 2pmHCl kT

  zH2g =z2H kT hNGa-ClH a4 p hV 2pmH2 kT V

  zGaClg =zGaCl kT a3 p 2pmNGaCl kT V

3  1 zNH3g =zN z2H2g 3 kT 2 2 a2 p PH 2pmNH3 kT 2 V

a1

m–i0

2 eNGa

eGaCl3g

eHClg

2 eNGa-GaCl3

eNGa

2 eNGa-ClH

eNGa-GaCl3

eGaCl

3 2 eH2g

eNGaCl

eN

eNH3g

eNGa-HCl

eH2

eNGaCl

eNH3

eNH3

e–ai

4.3 Kinetic Study 213

214

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

The different values of mi0 and eai for the reactions R1 to R7 are given in Table 4.4. Pi is the partial pressure of the gaseous molecules ig: NH3g, GaClg, H2g, HClg, and GaCl3g. e+i, e–i, and e*i are the energies of the initial, final and activated state of the reaction Ri. k is the Boltzmann constant, Ns the site number per unit area and zi represents the partition function of the molecule i without the energetic term. Then, the condensation coefficient ai represents the ratio between the real partition function and the one calculated from the relation (51), without the term representing the activation energy. The partition functions of the admolecules GaCl3, GaCl and HCl can be written as follows: zGaCl3

  z2NGa-GaCl3 eGaCl3 2 ; ˆ ˆ zvNGa exp kT z2NGa

zGaCl ˆ

zHCl

  zNGaCl eGaCl ; ˆ zvNGa exp zN kT

…53† …54†

  zNGa-ClH eHCl : ˆ ˆ zvNGa exp zNGa kT

…55†

The vibration partition function of NGa, zvNGa, is deduced from the relation between the equilibrium constants of the reaction R8 calculated from the statistical physics and the classical thermodynamics. Then it can be written: zvNGa ˆ 565 exp…3:5  10 3 …T

1000††;

b eGaCl ˆ eadGaCl ‡ ahGaCl ‡ hGaCl3 2

114:5

…56† …57†

and eNH3 ˆ eadNH3 eHCl ˆ eadHCl

eNH3g ;

…58†

eHClg ;

b eGaCl3 ˆ eadGaCl3 ‡ chGaCl3 ‡ hNGaCl 2

…59† eGaCl3g ;

…60†

a, b, and c are, respectively, the potential energies of the lateral interactions between the admolecules GaCl-GaCl, GaCl-GaCl3, and GaCl3-GaCl3. eig and eadi are respectively the interaction energies of the gaseous and adsorbed molecules i.

4.3 Kinetic Study

4.3.4

Mass-Transfer Phase

The mass transfer has been numerically computed [79] with the 2D finite element method. In the usual experimental conditions of GaAs and InP epitaxy by chloride or hydride methods, the computed results have shown that the Pi partial pressure values over the substrate could be approximated by the relation: Pi ˆ Pi0 

VG ; 2kt

…61†

+ and – signs are relative to produced and depleted species, Pi0 is the inlet value, VG is the crystal growth rate, kt is the mass-transfer coefficient defined by the relation kt ˆ

2Dig X ; dkTm

…62†

X is the volume of a crystalline molecule and d the distance substrate-wall. Dig is the diffusion coefficient of ig in the vapor phase at the average value Tm of the reactor temperature. The Dig value is deduced from the following relation: Dig ˆ D0i …T=T0 †1:83 ;

…63†

where D0i is the coefficient of the molecule i for T0 = 273 K. Table 4.5 gives the values of the coefficient D0i in a nitrogen and an hydrogen atmosphere for the different gaseous species considered for the deposition reaction [80]. The two relations (61) and (62) are not to be applied in all cases. They give a good approximation of the mass transfer at the scale of growth rates measured on substrates of 1–4 cm2 area, in a hot wall reactor, with a horizontal main flow approximately parallel to the substrate, and a mean gas velocity high enough to reduce the diffusion layer thickness to the velocity gradient thickness, d/2, of the Poiseuille regime. The gas outlets are to be located at a distance from the substrate large enough to set the homogeneity of the vapor before the substrate zone. At the scale of the homogeneity of the substrate thickness and of its composition, for ternary and quaternary alloys, a fluid dynamic software is required.

Tab. 4.5 Diffusion coefficient for 273 K from Watanabe [80]

Species

H2

N2

GaCl

GaCl3

HCl

NH3

D0i in N2 (cm2 s–1) D0i in H2 (cm2 s–1)

0.355 0.518

0.122 0.355

0.098 0.351

0.071 0.261

0.119 0.369

0.152 0.396

215

216

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

4.3.5

Crystal Growth Phase

The equilibrium between surface and vapor of the species i is deduced from the conservation equation: Ji ˆ div…Jdi † ‡ Ji‡1 ;

…64†

with J5 ˆ div…Jd5 †;

…65†

J7 ˆ 2 div…Jd7 †;

…66†

@Ci ; @y

…67†

Jdi ˆ

Di

Jdi is the superficial flow of the diffusion of the molecule i towards the step edge. The surface structure is considered as formed by steps with a monomolecular height and a width Y0 coming from a misoriented surface or a spiral growth [81]. Di is the diffusion coefficient of the molecule i on the surface. At a distance very large with respect to the mean free paths of admolecules, the surface coverage, h1i and hV , are deduced from the relations (44) to (51) with Ji = 0. h1NH3 m‡1 PNH3 ˆ ˆ zNH3 ; hV m 1 kTzNH3g h1N m‡2 zN ˆ ˆ h1NH3 m 2 zNH3



kTzH2g PH2

32

…68†

;

…69†

h1NGaCl m‡3 PGaCl ˆ ˆ zGaCl ; h1N m 3 kTzGaClg

…70†

h1NGa-ClH m 5 PHCl ˆ ˆ zHCl ; h1NGa m‡5 kTzHClg

…71†

h1GaCl3 m 7 h1NGa PGaCl3 ˆ ˆ zGaCl3 : h1NGa m‡7 hV kTzGaCl3g

…72†

The zig partition functions of the molecules are expressed per unit volume and are given in Table 4.2. The surface coverage of NGa molecules is written as

4.3 Kinetic Study

h1NGa PNH3 PGaCl exp ˆ hV PH2 PHCl K8 …T†

De ˆ …1 ‡ c† exp kT

De : kT

…73†

K8(T) is the equilibrium constant of the overall reaction R8 corresponding to the H2 mechanism, c is the relative supersaturation of the vapor phase. The homogeneous equilibrium between GaCl3g, GaClg, H2g, and HClg is supposed to be set up over the substrate. Consequently, relation (73) holds for the two growth mechanisms, H2 and GaCl3. The surface coverage of vacant sites at surface-vapor equilibrium is assumed to be constant all over the surface. When the terrace width is small enough to prevent any limitation of the growth process to surface diffusion, the only parameters of the model are the adsorption energies of GaClg, HClg, GaCl3g, the a, b, and c lateral interaction terms, D e and the two condensation coefficients, a5 for the H2 mechanism and a7 for the GaCl3 mechanism.

4.3.5.1 H2 Growth Mechanism

The surface flux of NGa molecules is the solution of the balance equation deduced from (41), (65) and (67), written as m‡5 CNGa-ClH

m 5 CNGa ˆ

DNGa

@ 2 CNGa : @y2

…74†

The balance equation of NGaCl molecules deduced from (41), (64), (65) and (67) can be written as m‡3 CN

m 3 CNGaCl

m‡4 CNGaCl ‡ m 4 CNGa-ClH ˆ

DNGaCl

@ 2 CNGaCl @y2

…75†

with J4 = J5, the HCl surface diffusion being overlooked in the model. (m 3 ‡ m‡4 † is the overall NGaCl frequency of GaCl evaporation and chlorine hydrogenation. The agreement with the experimental results of GaAs [49] was obtained in a simple way by considering separate balance equations. In the GaN system these balance equations are written:  C1NGa CNGa

 1 m 5 CNGa ˆ

 C1NGaCl CNGaCl

DNGa

@ 2 CNGa ; @y2

 1 …m‡4 ‡ m 3 †CNGaCl ˆ

DNGaCl

…76† @ 2 CNGaCl : @y2

…77†

The solution of these equations given by Burton et al. [81] can be written:  J0NGa ˆ

C1NGa C0NGa

    Y0 ; 1 C0NGa m 5 XdNGa tanh 2XdNGa

…78†

217

218

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

J0NGaCl ˆ

 C1NGaCl C0NGaCl

    Y0 1 C0NGaCl …m‡4 ‡ m 3 †XdNGaCl tanh ; 2XdNGaCl

…79†

with

XdNGa

r DNGa ˆ ; m 5

XdNGaCl

Di ˆ a20

…80†

s DNGaCl ˆ ; m‡4 ‡ m 3

…81†

  kT=h Udi ; h exp V kB T …zVNGa † 16

…82†

a0 is the parameter of the GaN hexagonal mesh, Udi is the activation energy of surface diffusion of molecules i, h is the Planck constant. Equation (82) results from the application of the Eyring theory [78] by considering the activated molecule as having a vibration freedom degree changed into a translation one located over the diffusion potential barrier. We will assume that the NGa molecules adsorbed on the surface close to a step are in equilibrium with the kink sites of the step, which means a high value of the incorporation frequency with respect to the dechlorination frequencies in HCl and GaCl3. This surface coverage is written:   De h0NGa ˆ hV exp ; kT

…83†

subscript 0 is used for molecules adsorbed close to a step. The dechlorination condition of NGaCl molecules before their incorporation in kink sites is written as …m‡4 ‡ m 3 †

 C1NGaCl C0NGaCl

  C1NGa 1 C0NGaCl ˆ m 5 C0NGa

 1 C0NGa :

…84†

From (73) and (83) we obtain: h1NGa ˆ 1 ‡ c: h0NGa

…85†

The treatment of NGaCl and NGa surface diffusion ignores their interdependence, the resulting flux will be computed by averaging the added two separate fluxes. Assuming, moreover, that the surface fluxes towards the step from the upper terrace equals that from the lower terrace, the growth rate can be written as

4.3 Kinetic Study

2X …J0NGa ‡ J0NGaCl † ; Y0 2

VG ˆ

…86†

where X is the molecular volume,  VG ˆ VGMax

    XdNGaCl Y0 XdNGa Y0 tanh tanh ‡ ; Y0 2XdNGaCl Y0 2XdNGa

…87†

with VGMax ˆ Xm 5 C0NGa c; Y0 ˆ

…88†

a0 : 2 tan a

…89†

In micrometers per hour, with PHCl in Pascal and the HCl molecular mass in kg; we obtain VGMax

 a5 PHCl e ˆ 0:93357 hV p c exp Ns 2pmHCl kT

 ‡ De : kT

a4

…90†

The value of m+4, deduced from the expression given in Table 4.4, is computed by considering the NGaCl surface coverage, as equal to its value at a distance from steps higher than the mean free paths of molecules. The growth rate relative to a surface misoriented enough to have a terrace width much higher than the mean free paths of NGaCl and NGa molecules is expressed by (90).

4.3.5.2 GaCl3 Growth Mechanism

The growth rate of a surface misoriented enough not to be limited by surface diffusion, can be deduced from the expression of m–7 given in the Table 4.4 and (83). In micrometers per hour, with the GaCl3g pressure in Pascal and the molecular mass in kg, it can be written: VGMaxGaCl3 ˆ 2

   0:93357 hV e 2 PGaCl3 e p a7 PGaCl …1‡c† exp e 3 PGaCl Ns 2pmGaCl3 3

a7

 ‡ 2De ; kT

…91†

e is the homogeneous GaCl3g equilibrium partial pressure. The following rePGaCl 3 lations define the degree of excess of the deposition reaction in the H2 and GaCl3 mechanism:

PNH3 PGaCl ˆ 1 ‡ c; PH2 PHCl K8 …T†

…92†

e 2 PNH P3 2 PGaCl3 3 GaCl ; ˆ …1 ‡ c† 3 PGaCl3 PH P K9 …T† 2 GaCl3

…93†

219

220

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

with e ˆ PGaCl 3

2 PGaCl PHCl : PH2 K10 …T†

…94†

K10(T) is the equilibrium constant of the reaction GaClg ‡ 2 HClg , GaCl3g ‡ H2g :

…R10†…95†

Surface diffusion is approximated in the same way as in the H2 mechanism. The growth rate is therefore expressed by (87). In (80)–(82), m–5 and (m–3 + m+4) will be replaced by m–7 and (m–3 + m+6). These frequencies have been computed with the same approximations as in the H2 mechanism. In both mechanisms the mass-transfer effect was taken into account for HClg, GaClg, NH3g and H2g.

4.3.5.3 Spiral Growth of an Exact (00.1) Face, Burton-Cabrera-Frank Mechanism

Spiral growth is initiated by nucleation of a critical 2D nucleus at the surface intersection of a dislocation, having a screw component of the Burgers vector normal to the interface [81]. A stationary spiraling sequence of equidistant steps results from the critical nucleus growth. The growth rate can be expressed as for a misoriented surface with a distance between steps given by Y0 ˆ 19 rc :

…96†

The radius of the critical nucleus is written as rc ˆ

p rM a0 3 ; 2kT ln…1 ‡ c†

…97†

rM is the molecular ledge energy. The value of 51.3 kcal mol–1 resulting from the averaged ledge energies of rough and dense steps has been used in the model. 4.3.6

Search for the Model Parameters

The values of the adsorption activation energies, e+a3, e–a5, and e–a7, of GaClg, HClg, and GaCl3g molecules, required to calculate the mean free paths of molecules diffusing on surface, will be set to 11.3 kcal mol–1, the value of the adsorption activation energy of GaCl on As in GaAs [49]. Values in the range 10–15 kcal mol–1 are generally encountered in simple chemical-adsorption processes. This choice, which is close to expected values, was made to reduce the number of the model parameters. The adsorption of H2g molecules leading to their dissociation, the adsorption activation energy will be considered as equal to the dissociation energy, e+a4 =

4.3 Kinetic Study

104.2 kcal mol–1. The adsorption activation energy of GaClg on two underlying chlorine atoms, e+a6, leading to the adsorption of GaCl3 in a dual site will be a parameter of the surface-diffusion model. The parameter De is defined as the difference between the interaction potential energies of NGa admolecules adsorbed on (00.1) and in kink sites. The last value, –206.75 kcal mol–1, is deduced from the standard enthalpy of formation of NGa, and Gag, –26.2, and 68 kcal mol–1 [51, 54, 82] and from the N2g interaction energy [83]. N atoms will be assumed to be bound to the surface by one NGa bond whose value will be approximated to the average NGa interaction energy by bond, –51.69 kcal mol–1. The interaction potential energy of a NGaCl molecule, in kcal mol–1, is taken as equal to the N atom one, increased by the GaCl molecule energy defined by b eGaCl ˆ eadGaCl ‡ ahGaCl ‡ hGaCl3 2

114:5;

…98†

where –114.5 kcal mol–1 is the interaction potential energy of GaClg [84]. a is twice the lateral interaction energy between NGaCl molecules and b is the lateral interaction energy between GaCl and GaCl3 molecules. eadGaCl is then the adsorption energy of an isolated GaCl molecule. The interaction potential energies of molecules in the vapor phase are, in kcal mol–1, –279.83 for NH3g, –103, –104.2 and –269.85 for HClg, H2g, and GaCl3g [83, 85]. The potential energies of NH3, HCl, and GaCl3 molecules in kcal mol–1 can also be written as eNH3 ˆ eadNH3 eHCl ˆ eadHCl

…99†

279:83;

…100†

103;

b eGaCl3 ˆ eadGaCl3 ‡ hNGaCl ‡ chGaCl3 2

269:85;

…101†

c is the double of the lateral interaction energy between GaCl3 molecules. According to the equations (98) to (101), the partition functions of GaCl3, GaCl, and HCl molecules can be written: zGaCl3 ˆ

  z2NGa-GaCl3 eGaCl3 2 ˆ z exp ; vNGa kT z2NGa

…102†

zGaCl ˆ

  zNGaCl eGaCl ˆ zvNGa exp ; zN kT

…103†

zHCl ˆ

  zNGa-ClH eHCl ; ˆ zvNGa exp zNGa kT

…104†

with zvNGa ˆ 565 exp…3:5  10 3 …T

1000††:

…105†

221

222

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

NH3 adsorption is reported as to occur in MOCVD [75]. Having not found clear data to determine the adsorption energy we have chosen the value of –24.8 kcal mol–1. This leads to a Langmuir isotherm with a surface coverage varying from 0.04 at 1450 K to 0.63 at 917 K, without competitive adsorption of other species. Such a value could be in agreement with MOCVD results without being competitive in our model of HVPE process. The only experimental curves that could be used to match the theoretical model were the curves published by Seifert et al. [9] relative to a face misoriented 38 from the (00.1) orientation. Attempts to find a competitive NH3 adsorption failed to match these experimental curves. The experimental geometry and the high growth rate values obtained, 800 lm h–1 for the highest value measured in H2 carrier gas, suggested that the depletion of the vapor phase in source species and the related enrichment in produced species due to extraneous deposition and mass transfer effects, could be ignored. Moreover, two curves were drawn versus 1/T (Figs. 4.10 and 4.11) with helium and hydrogen as carrier gas, in the same experimental conditions. The source conversion efficiency of HCl was reported to be between 94 and 96%. In the model we have chosen the average 95% value, with a value of 1% for the rate of NH3g decomposition. Both experimental curves were necessary

Fig. 4.10 Experimental growth rates in lm min–1 measured by

Seifert et al. [9] with He as carrier gas, on substrates misoriented 38 from the (00.1) orientation. The flow rates in slm are source HCl flow, 0.015, NH3 flow, 1 and total flow, 3. The Ga source was held at 850–900 8C. The corresponding theoretical growth rate is drawn as a full line. At the extreme left, the abrupt increase of the curve with increasing temperatures, illustrates the beginning of the predominance of the H2 mechanism over the GaCl3 one, due to a slight decrease of GaCl surface coverage and to NH3 gas phase decomposition. The theoretical growth rate of substrates exactly (00.1) oriented is drawn as a dotted line.

4.3 Kinetic Study

Fig. 4.11 Experimental growth rates in lm/min measured by

Seifert et al. [9] with He as carrier gas, on substrates misoriented 38 from the (00.1) orientation. The flow rates in slm are: source HCl flow, 0.015, NH3 flow, 1 and total flow, 3. The Ga source was held at 850–900 8C. The corresponding theoretical growth rate is drawn as a full line. The H2 mechanism prevails over the GaCl3 in all the temperature range used. The theoretical growth rate of substrates exactly (00.1) oriented is drawn as a dotted line.

to calculate the parameters of the model in a single way. The results obtained are drawn in full line in Figs. 4.10 and 4.11. With hydrogen and helium used as carrier gas respectively, only the H2 and the GaCl3 mechanisms govern the growth. In helium, the occurrence of the H2 mechanism is very sensitive to the rate of NH3g decomposition. The high-temperature flat part of the curve (Fig. 4.10) corresponds closely to one value of the GaCl surface coverage, at a distance from steps higher than the mean free paths of molecules. A slight decrease of this coverage obtained by slightly decreasing the intensity of the GaCl lateral interaction results in the H2 mechanism predominance. The value of this last parameter has been chosen in order to reject the prevailing of the H2 mechanism over the GaCl3 one, at the higher limit of the temperature field used in the experiments (see Fig. 4.10). Changing the value of the GaCl adsorption energy eadGaCl, to obtain the same agreement, results in a change of the slope of the decreasing part of the curve drawn with H2 as carrier gas. The decreasing part of the Fig. 4.10 curve comes from the increasing of the GaCl3 surface coverage. With hydrogen as carrier gas the increasing of the HCl and GaCl surface coverages explains the decreasing part of the experimental curve (Fig. 4.11). Not considering the HCl adsorption leads to a bell shape curve, as in GaAs [49], matching

223

224

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

the experimental results in all points but the maximum that reached a value of 1600 instead of 800 lm h–1. The apparent activation energy (e–a5 + De) is positive but decreases with temperature. At high temperature, 1300 8C, its value is 18.26 kcal mol–1. Considering the 11.3 kcal mol–1 value for the adsorption activation energy of HClg, leads to De = 6.95 kcal mol–1. Using the same value for the adsorption activation energy of GaCl3g, leads to an apparent activation energy (e–a7 + 2 De) = 25.2 kcal mol–1 in the GaCl3 mechanism. The values of the adsorption energies and the expressions of the condensation coefficients required to match theoretical and experimental curves with these choices are: eadGaCl = –130.86 kcal mol–1, a = –8.14 kcal mol–1, b = 2.4 a, eadGaCl3 = –71.49 kcal mol–1, c = 0, eadHCl = –67.51 kcal mol–1, a5 = 35 exp(1.01 ´ 10–2(1223 – T)), a7 = 3 ´ 104 exp(6.5 ´ 10–3(1230 – T)). The potential energy value of GaN molecules deduced from De is –199.85 kcal mol–1. This corresponds to a GaN bond energy of –149.89 kcal mol–1 against –155.06 kcal mol–1 for the GaN bond energy in a kink site, assuming all bonds have the same energy. The GaCl adsorption energy exceeds only by 24.2 kcal mol–1 the energy of three N–Ga and one Ga–Clg bonds. This difference may partly come from a lower intensity of the Ga–Cl bond than the Ga–Clg one. So it appears that, statistically, most of GaCl molecules and therefore most of the GaN molecules resulting from chlorine desorption are bound to three underlying N atoms. The variation of the condensation coefficients with temperature may partly arise from entropy corrective terms of the adsorption-activated molecules. We used the surface-diffusion model to predict the substrate growth rates of the exact (00.1) orientation. The lack of experimental data led us to determine the diffusion activation energy of NGa in the H2 mechanism, by assuming a variation maximum of the growth rate with the misorientation angle similar to that observed in GaAs [49]. The third of the lateral interaction energies was added to this value to obtain the diffusion activation energy of NGaCl molecules. The value of the diffusion potential barrier of GaN molecules so calculated, 39.7 kcal mol–1, is 26.5% of the energy required to break off a molecule from the surface. Using the values of the diffusion potential barriers of GaN and NGaCl determined in the H2 mechanism, the prediction of the growth-rate variation with the misorientation angle in the GaCl3 mechanism, required the knowledge of e+a6. A value of 44.68 kcal mol–1 gives the right variation. The growth rates so obtained for an exact (00.1) orientation are drawn in dotted lines in Figs. 4.10 and 4.11. 4.3.7

Search for the Mass Transfer and Parasitic Nucleation Effects

When the degrees of excess of the deposition reactions are high, the ratios between the relative supersaturations and the corresponding degrees of excess are very close to one. The kinetics are then proportional to the vacant surface site cov-

4.3 Kinetic Study

erage, to the source species concentrations and to the reverse of the hydrogen concentration as deduced from (90)–(94). The equilibrium constants, the activation terms and the value of hV mainly govern the kinetic variations with the substrate temperature. The H2 concentration in neutral-gas transport systems mainly depends on the rates of NH3 decomposition and of hydrogen produced by the GaN parasitic deposition before the substrate, and on the mass transfer. The mass transfer reduces the partial pressures of the source species and increases the partial pressures of the produced species. These two effects can induce a H2 mechanism in a neutral carrier gas. The mass of GaN deposited before the substrate can reduce the degrees of excess up to a value close to one if high. The mass-transfer effect is approached by considering a diffusion layer thickness equal to the velocity-gradient thickness of an established Poiseuille regime, providing that the substrate is parallel to the flow and that the total flow is not too low. When the substrate makes an angle with respect to the horizontal plane, the mass transfer effect can be approached by varying the wall-substrate distance. Such an approach does not replace the fluid dynamic study for optimizing the working conditions of a reactor. On the other hand, a fluid-dynamic study is unable to determine the growth law, which are the boundary conditions to be known to solve the fluid-dynamic equations.

Fig. 4.12 Experimental growth rates in lm h–1 measured by

Seifert et al. [9] in H2 and He carrier gases, on substrates misoriented 38 from the (00.1) orientation, are represented by full circles and empty triangles. The kinetics and the growth rates computed with the mass transfer and wall-substrate distances of 1.5 cm, without and with a parasitic GaN deposition of 2 g h–1 are drawn as dashed curves 1, 2, and 3 in He and as full curves 4, 5 and 6 in H2. The dash-dotted curve 7 shows the GaCl2-HCl mechanism in the conditions of curve 6.

225

226

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

Fig. 4.13 Theoretical kinetics and growth rates taking into account the mass transfer and a wall-substrate distance of 1.5 cm are drawn in dashed and full lines, without and with parasitic GaN deposition of 1 and 2 g h–1 before the substrate, as a function of the source HCl concentration. The parts 1, 2, and 3 correspond to the GaCl2-HCl, H2, and GaCl3 prevailing mechanisms. The experimental conditions of Paskova et al. [88], empty triangles, have been used.

The mass transfer and parasitic deposition effects are illustrated in Figs. 4.12 and 4.13. The experimental points measured by Seifert et al. [9] in He and H2 atmospheres are reported as empty triangles and full circles in Fig. 4.12. The dashed curves 1, 2, and 3 represent, in He, the theoretical kinetic results, the curve computed by assuming a mass transfer corresponding to a substrate-wall distance of 1.5 cm, the curve computed by adding a GaN parasitic deposition of 2 g h–1 to this mass transfer. The full curves 4, 5, and 6 represent the same theoretical results computed with H2 as gas carrier. In H2 atmosphere the growth rate increases slightly with 1/T up to about 1220 K. At lower temperatures the kinetic slope arising from the surface saturation by HCl and GaCl adsorptions appears progressively. The mass transfer effect reduces the growth rate by about an order of magnitude for kinetic values higher than 100 lm h–1. Adding the GaN parasitic deposition cancels the supersaturation c at 988 K. Above this temperature value GaN etching by HCl vapor molecules is expected, but the experiments we carried out [86, 87] showed that growth rates up to 50 lm h–1 could be obtained in the HCl etching field. The mechanism involved in this field is developed in the next section. The dash-dotted curve 7 shows the corresponding theoretical results. In He atmosphere the growth rate variation with temperature is lower than in H2. This comes from the fact that the GaCl3 mechanism requires a high GaCl surface coverage. By decreasing temperature the GaCl3 adsorption progressively replaces

4.3 Kinetic Study

the GaCl one without drastically changing the hV value. The H2 vapor-concentration enhancement resulting from the mass-transfer effect, induces the H2 mechanism at temperatures higher than 1210 K. This transition point between the H2 and GaCl3 mechanisms is shifted from 1210 K to 1120 K by adding a GaN parasitic deposition rate of 2 g h–1. The kinetic theoretical curves obtained in the experimental conditions of Paskova et al. [88] without and with parasitic deposition rates of 1 g h–1 and 2 g h–1 are drawn as dashed lines in Fig. 4.13, as a function of the ratio of the Ga source HCl flow to the total flow. The H2 mechanism prevailing field, which appears only at values of this ratio lower than 0.0015, is extended up to 0.015 then up to a value higher than 0.034 by adding a parasitic deposition rate of 1 g h–1 and 2 g h–1. The corresponding curves drawn by considering a substrate-wall distance of 1.5 cm for the mass transfer are drawn as full lines. The H2 mechanism prevails over a value of 0.015 of the source HCl vapor concentration input. At 0.0034 and 0.0068 values the effect of the GaN parasitic deposition cancels the relative supersaturation. By increasing the source HCl concentration input beyond this point the growth rate increases drastically up to becoming almost constant. The parts 1, 2, and 3 of the 2 g h–1 full curve correspond to the mechanism developed in the next section and to the H2 and GaCl3 mechanisms. The three experimental points are reported as small triangles. The first point is located in a domain where the growth rate is very sensitive to the GaN parasitic deposition rate and to the source HCl concentration input. The second point is located in a domain where the growth rate is practically independent of these experimental parameters, which is in agreement with the constant value observed by the authors for different experiment times. The last point is the only one that seems to correspond to the GaCl3 mechanism. The drastic change of the experimental slope can be related to the H2-GaCl3 mechanism transition. 4.3.8

New Mechanism of Growth at Negative Values of c 4.3.8.1 Experimental Results

The experimental research of the zero supersaturation point with H2 and N2 as gas carriers has led us to find an unexpected new mechanism in a mixed N2/H2 gas carrier. The source, central, and substrate zones were kept at 1123, 1293–1313, and 1253 K, respectively. In pure H2 or N2 systems the zero growth rate point was obtained by adding HCl in the main flow, with a reasonable accuracy, at the vapor-crystal equilibrium [86, 87]. In N2, the results suggested that the GaCl3 vapor concentration was below but not too far from its homogeneous equilibrium value, which was around 10–3 atm. The large amount of HCl added in the main flow, 200 sccm, explains this high value. A parasitic GaN deposition was obtained even without growth on GaN substrates, which probably comes from the times required for reaching the homogeneous equilibrium GaCl3 vapor concentration. In H2, this problem was not encountered but if the reduction of the relative supersaturation effectively decreases the parasitic GaN deposition it also reduces the growth rate. Below a degree of excess of about 4 no growth occurs on sapphire substrates.

227

228

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

In a range of N2/H2 mixing varying with the experimental conditions, the growth rate did not depend on the additional HCl flow and values of 50–60 lm h–1 could be obtained with very negative values of supersaturation c, then in expected conditions of fast etching by HCl. A first set of experiments was performed with 2000 sccm of N2, 300 sccm of NH3, 20 sccm of HCl mixed with 83 sccm of nitrogen on the gallium source and without additional HCl. The hydrogen added in the main flow was varied from 0 to 2000 sccm, the total amount of the gas carrier flow staying constant at 2000 sccm. In the 0–650 sccm H2 flow range growth and extraneous deposits were observed upstream of the substrate. For 800, 1000, and 2000 sccm of H2 flows no growth nor parasitic deposition occur. The experiments showed that the nucleation-critical relative supersaturation value of GaN was close to 4 on sapphire substrate and higher than this value on quartz. Therefore there is a small domain of relative supersaturation values available to get the highest possible growth rate with a reduced GaN parasitic deposition. This domain seems not to exist with pure N2 as gas carrier. A second set of experiments was performed with the same total and NH3 flows, HCl and N2 flows on the gallium source, and with 20 sccm of additional HCl. The hydrogen added in the main flow was varied from 0 sccm to 1200 sccm. The parasitic deposit observed in the mixing zone decreased with increasing hydrogen flow, and finally completely disappeared for 500 sccm of hydrogen. The experimental points are reported and the growth rates, computed in the H2 and GaCl3

Fig. 4.14 In the experimental conditions reported in Sect. 4.3.8 the measured growth rates are represented by empty squares, as a function of the H2 concentration. The theoretical results are drawn as dashed curves for the H2, GaCl3, and GaCl2-HCl mechanisms. The prevailing mechanism, GaCl3, H2 then GaCl2HCl is drawn as a full curve. The mass transfer is taken into account with a wall-substrate distance of 1.5 cm.

4.3 Kinetic Study

mechanisms, are drawn as dashed lines in Fig. 4.14. The third theoretical mechanism, labeled GaCl2–HCl is also drawn as a dashed line. The prevailing mechanism is drawn as a full line. The mass transfer was calculated with a substratewall distance of 1.5 cm. By increasing the H2 flow the theoretical curves show that the prevailing mechanism is GaCl3 up to 30 sccm, then H2 up to 96 sccm and the third mechanism up to 1330 sccm, with the total flow of 2403 sccm. The zero point of the relative supersaturation c occurs with a H2 flow value of 175 sccm, at the decrease of the H2 and GaCl3 curves. At a H2 flow of 500 sccm, c = –0.63, the experimental growth rate reached a value of 60 lm h–1. Above 500 sccm the growth rate measured on GaN substrates drops drastically. Its zero value is reached at 1330 sccm of H2. A third set of experiments was performed at 500 sccm of H2 with additional HCl flow values of 20, 30, 40, 60, and 65 sccm. The experimental points are reported and the growth rates computed in the H2 and GaCl3 mechanisms are drawn as dashed lines in Fig. 4.15. At 40 sccm the growth rate value is 40 lm h–1 on GaN and 10 lm h–1 on sapphire substrates. At 65 sccm the 10 lm h–1 value was measured on a GaN substrate. The zero c value corresponds to an additional HCl flow of 6.5 sccm. For 20, 30, 40 and 65 sccm the c values are –0.63, –0.75, –0.81, and –0.89. The theoretical GaCl2–HCl mechanism is drawn as a full line.

Fig. 4.15 In the experimental conditions reported in Sect. 4.3.8 the measured growth rates are represented by empty squares, as a function of the additional HCl concentration. The theoretical results are drawn as dashed curves for the GaCl3 and H2 mechanisms. The prevailing mechanism drawn as a full curve is GaCl2-HCl. The mass transfer is taken into account with a wall-substrate distance of 1.5 cm.

229

230

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

4.3.8.2 Third Growth Mechanism

The first computations made using the software, without changing its parameters, reveals that the drop of the growth rate at 1330 sccm of H2 comes from the etching by HCl. A new dechlorination mechanism was to be considered and therefore its reverse reaction was also to be taken into account. The criterion to select between the etching of NGa by the reverse reaction of the new dechloruration mechanism and by HCl had to be the ratio between these two etching fluxes. For values lower than the combined mechanism with etching by HCl had to be considered. The theoretical curve matching the experimental points reported in Fig. 4.14 at negative c values was obtained by considering a dechloruration of NGaCl by GaClg in GaCl2g and a chloruration of NGa by HCl followed by H2g desorption for the reverse reaction. The involved reactions are: NGaCl ‡ GaClg ) NGa ‡ GaCl2g ; NGa

…R11†…106†

HCl ( NGa ‡ HClg ;

2 NGaCl ‡ H2g ( 2 NGa

…R12†…107† …R13†…108†

HCl;

NGaCl ‡ GaClg ( NGa ‡ GaCl2g ;

…R14†…109†

and for the equilibrium vapor reaction: 1 HClg ‡ GaClg ( GaCl2g ‡ H2g : 2

…R15†…110†

By assuming a simple adsorption process for reactions R11 and R12, the GaN growth flux is written PGaCl JGaN ˆ p exp 2pmGaCl kT



 eaGaCl hNGaCl kT Ns

PHCl p exp 2pmHCl kT



 eaHCl hNGa : kT Ns …111†

The curves drawn in Figs. 4.14 and 4.15 for this combined mechanism, labeled GaCl2-HCl, were computed with an apparent activation energy of the dechloruration reaction by GaCl into GaCl2g, exceeding only by 1.49 kcal mol–1 the activation energy of the etching reaction by HCl. This additional parameter was the only modification of the model parameters. The maximal velocity is given by the same relation (90) as in the H2 mechanism with in place of c, a relative supersaturation cmix given by 1 ‡ cmix ˆ …1 ‡ c†

r   r zH2g zNGaCl mHCl PGaCl 1:49
103 p ; exp mGaCl kTPH2 zGaCl zNGa 1:9857 T

…112†

where zi and zig are the partition functions of the adsorbed molecule i and of the vapor molecule ig in a unit volume.

4.3 Kinetic Study

4.3.9

Discussion

The relation (112) shows the variation of the growth rate with the H2 and GaCl partial pressures. The variation with the H2 partial pressure is governed by cmix, which cancels at 1330 sccm of H2 flow in our experimental conditions. The variation with the HCl partial pressure mainly comes from cmix/(1+c). The variation with temperature coming from the partition functions is illustrated in Fig. 4.16, where the curves computed with the H2, GaCl3 and GaCl2-HCl mechanisms are drawn as dashed lines as a function of 1/T, with 500 sccm of H2 and 20 sccm of additional HCl flows. The c value is negative at T >1087 K. The prevailing mechanism, drawn as a full line, is the H2 one at T <1010 K and the GaCl2-HCl one over this value. The growth rate drops drastically at T = 1333 K at cmix = 0. The curve shows that a growth rate of 50–60 lm h–1 can be obtained without any parasitic GaN deposition with central and substrate temperature values of 1060 and 980 8C, in these experimental conditions. In our conditions, where these values were 1020–1040 and 980 8C, we observed only a very slight parasitic GaN deposition. With only hydrogen in the main line, 1980 sccm, the dashed-dotted curve of Fig. 4.16 represents the growth-rate variation with the reverse temperature. The prevailing mechanism is GaCl2-HCl. The relative supersaturation of this mecha-

Fig. 4.16 In the experimental conditions reported in Sect. 4.3.8 the theoretical results are drawn as dashed curves for the GaCl3, H2, and GaCl2-HCl mechanisms. The prevailing mechanism, GaCl2, HCl then H2 is drawn as a full curve. The dashed-dotted curve represents the theoretical results obtained with only H2 in the main line; the only available mechanism is GaCl2-HCl. The mass transfer is taken into account with a wall-substrate distance of 1.5 cm.

231

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4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

nism, cmix cancels at T = 950 8C, while the c relative supersaturation is negative at T = 654 8C. The growth-rate maximum of 90 lm h–1 is reached at 863 8C with a cmix value of about 25, which is too high to avoid parasitic GaN deposition. At 895–890 8C the growth rate is about 50 lm h–1 and the range of cmix values, 4.1– 5.6, ensure nucleation on sapphire and not on quartz. Therefore in hydrogen, a growth rate of 50 lm h–1 can be obtained without any parasitic GaN deposition with central and substrate temperature values of 950 and 895 8C. According to the theoretical curve 7 of Fig. 4.12 a growth rate of 20 lm h–1 could be obtained without parasitic GaN deposition with central and substrate zone temperatures of 915 and 855 8C. The prevailing of the combined GaCl2-HCl mechanism over the GaCl2 one supposes that the ratio between the etching flux by HCl and by GaCl2 is higher than one. According to the curve drawn in full line in Fig. 4.14 as a function of the H2 vapor concentration this occurs at 95 sccm of H2 flow. This agreement with the experimental results can only be obtained by considering that the partial pressure of GaCl2 is lowered to its heterogeneous or homogeneous equilibrium value, depending on whether the first or the second value is the smallest. Moreover the GaCl2 partial pressure input has to be less than 10% of its homogeneous equilibrium value. This means: (i) the GaCl2 produced is rapidly transformed into HCl and GaCl; (ii) the GaCl2 homogeneous decomposition is much faster than its reverse reaction. This is in agreement with the fact that this species was not observed by Ban [3]. Without this hypothesis the pure GaCl2 mechanism would prevail at negative c values up to about 300 sccm of H2, in the experimental conditions of Fig. 4.14. The agreement with the experimental results could not be obtained. Indeed the mass transfer reduces the growth rate of the GaCl2 mechanism to a small value even by assuming that the GaCl2 partial pressure is lowered to its homogeneous equilibrium value. We used the GaCl diffusion coefficient in vapor to calculate this mass transfer, having no data on the GaCl2 molecule. The GaCl2 equilibrium pressures have been calculated with the thermodynamic data of Chatillon and Bernard [89], which are in better agreement with the mass spectrometry analysis [3] than the thermodynamic data of Barin [51]. The last data lead to values about three orders of magnitude higher than the first data. The theoretical curve of the GaCl2-HCl mechanism, drawn as a function of the additional HCl concentration inputs seems to drop at higher values than observed. At high additional HCl flows the produced GaCl2 may be not totally decomposed down to its heterogeneous equilibrium partial pressure. This hypothesis assumes that the decomposition rate is much higher than the mass transfer. A slight enhancement of the GaCl2 partial pressure would lead to a drop of the curve at lower additional HCl flow than observed on the theoretical GaCl2-HCl curve, by increasing the GaCl2 etching over the HCl one.

4.4 Results

4.4

Results

In the experimental conditions described in the third set of experiments of Sect. 4.3.8.1, HVPE GaN layers were grown on MOCVD GaN layers having a thickness of 2 lm grown on sapphire substrates. Different thicknesses, from 8 to 52 lm, of HVPE GaN layers were obtained on different samples varying only the time of growth, for otherwise identical conditions. Optical and morphological properties of these layers were investigated. The different samples studied are labeled: S1, which is a piece of the MOCVD template, and VPE8, VPE10, VPE18, and VPE52, which, respectively, correspond to the 8, 10, 18, and 52 lm of the HVPE GaN thick grown on different pieces of the MOCVD template. Optical properties are deduced from reflectivity experiments performed under normal incidence at 4 K. A halogen lamp was used and the modulated signal was dispersed through a HR640 monochromator and detected with a photomultiplier using a standard lock-in amplification. Scanning electron microscopy (SEM) images were used to observe the morphological quality of the surface of the HVPE layers. Three excitonic features, labeled A, B, and C, appear in the reflectivity spectra as shown in Fig. 4.17. They correspond to excitons involving holes from the three upper valence band of GaN. From the position of these features, it appears that they shift in energy. This behavior is attributed to the variation of the residual

Fig. 4.17 Reflectivity spectra of wurtzite GaN layers grown by HVPE. The excitonic transition energies are deduced from the adjustment of the experimental data with a multipolaritonic model. Sample S1 is a piece of the MOCVD template. Samples VPE8, VPE10, VPE18, and VPE52 are, respectively, the 8, 10, 18, and 52 lm of the HVPE GaN thick grown on different pieces of this template.

233

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4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

Fig. 4.18 Dependence of the transition energies of the A, B, and C excitons versus the inplane biaxial stress in the epilayers [90]. The experimental data (dots) correspond to the value reported in Fig. 4.3.

stress in the layer, which was demonstrated for the first time by Gil et al. [90]. In order to observe the thickness influence on the stress in the layers, theoretical curves are used that show the dependence of the transition energies of the A, B, and C excitons versus the inplane biaxial stress. This procedure requires a precise knowledge of the excitonic transition energy. In this way, each reflectivity spectrum is fitted using a multipolaritonic model including the spatial dispersion. This reflectivity model, based on the nonlocal dielectric behavior, uses a set of three oscillators to model the dielectric constant, more details can be found in Ref. [91]. The deduced values of the excitonic transition energies EA, EB, and EC are reported in Fig. 4.18. It appears that (i) whatever the thickness of the HVPE layer the residual stress is always lower than that of the MOCVD template; (ii) the behavior of the residual stress versus the thickness of the HVPE layer does not allow to deduce any obvious relationship between these two parameters. Indeed, the VPE8 is less strained than the VPE52 but more strained than the VPE18. Figure 4.19 displays the SEM images of the surface of the samples. Different densities of cracks appear on each grown sample. In this case it is also very difficult to define a suitable relationship between the thickness of the HVPE layer and the density of the cracks. The sample VPE10 that presents the lowest residual stress in the optical characterization is the sample, which presents no crack in SEM observations. We can conclude that there is a decrease of the residual stress in the HVPE layers in comparison with the MOCVD templates. A correlation appears between the residual stress and the crack density versus layer thickness, but complementary experiments must be performed in order to confirm this. Nevertheless, we have demonstrated the possibility of obtaining thick HVPE GaN layers exhibiting no cracks over 200 lm of the inplane area. Moreover, an improvement of the optical quality of the HVPE layers grown without parasitic deposition is demonstrated compared to the layers obtained with parasitic deposit. In fact, the layers obtained

4.4 Results

Fig. 4.19 SEM images of the surface of the different samples grown with various thicknesses of HVPE layers. Sample S1 is a piece of the MOCVD template. Samples VPE8, VPE10, VPE18, and VPE52 are, respectively, the 8, 10, 18, and 52 lm of the HVPE GaN thick grown on different pieces of this template.

with parasitic deposition on the quartz walls of the reactor upstream the substrate present a high level of unintentional residual doped GaN (1019–1020 at cm–3) and cannot present excitonic transitions due to its quasimetallic character. The hypothesis that the parasitic deposit on the quartz walls of the reactor leads to a high rate of Si-doped GaN seems to be supported by these present results.

235

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4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy

4.5

Conclusions

A complete study of the growth of gallium nitride by HVPE has been developed. The general points of the HVPE have been presented. The growth of GaN by HVPE was analyzed by means of thermodynamical and kinetic studies. Barin’s thermodynamical data were used. The equilibrium constants calculated from Van’t Hoff’s second law were found to be in good agreement with the equilibrium constants calculated from statistical physics. The numerous measurements of the growth rate of exact and misoriented {001} GaAs substrates, using the chloride method and the measures of Seifert et al. [9] in He and H2 on 38 off (00.1) GaN by HVPE, enabled us to model and understand the physics involved in the growth processes. As the GaN kinetics is about one order of magnitude higher than the GaAs kinetics, the mass transfer is larger for the first than the second system. Moreover the high supersaturation usually imposed leads to an important parasitic GaN deposition before the zone substrate that reduces and can even cancel the relative supersaturation. The method used to understand and model the GaAs and GaN growth processes can be applied to other III-N compounds. The first requirements are to measure the growth rate in controlled conditions, and to study the thermodynamic of the system. The modeling of the results obtained in expected conditions of fast HCl etching explains the physics involved in this process. It enables us to research, by computing, all the possibilities of growing at rates of 50–100 lm h–1 and more, without GaN parasitic deposition, by setting the central zone at higher and the substrate zone at lower temperatures than the temperature of cmix canceling.

4.6

References 1 2

3 4 5 6 7 8

H. P. Maruska and J. J Tietjen, Appl. Phys. Lett. 15, 327 (1969). D. K. Wickenden, K. R. Faulkner, and R. W. Brander, J. Cryst. Growth 9, 158 (1971). V. S. Ban, J. Electrochem. Soc. Vol 119, 761 (1972). M. Ilegems, J. Cryst. Growth 13/14, 360 (1972). A. Shintani and S. Minagawa, J. Cryst. Growth 22, 1 (1974). M. Sano and M. Aoki, Jpn. J. Appl. Phys. 15, 1943 (1976). R. Madar, D. Michel, G. Jacob, and M. Boulou, J. Cryst. Growth 40, 239 (1977). G. Jacob, M. Boulou, and M. Furtado, J. Cryst. Growth 42, 136 (1977).

9 10

11 12

13

14

W. Seifert, G. Fitzl, and E. Butter, J. Cryst. Growth 52, 257 (1981). K. Naniwae, S. Itoh, H. Amano, K. Itoh, K. Hiramatsu, and I. Akasaki, J. Cryst. Growth 99, 381 (1990). T. Detchprohm and K. Hiramatsu, Appl. Phys. Lett. 61, 2688 (1992). K. Hiramatsu, T. Detchprohm, and I. Akasaki, Jpn. J. Appl. Phys. 32, 1528 (1993). R. J. Molnar, K. B. Nichols, P. Maki, E. R. Brown, and I. Melngailis, in Mater. Res. Soc. Symp. Proc. 378, 479 (1995). A. Kimura, A. A. Yamaguchi, A. Sakai, H. Sunakawa, M. Nido, and A. Usui, Jpn. J. Appl. Phys. 35, L1480 (1996).

4.6 References 15

16

17

18

19

20

21

22

23

24

25

26

27

28

A. A. Yamaguchi, T. Manako, A. Sakai, H. Sunakawa, A. Kimura, M. Nido, and A. Usui, Jpn. J. Appl. Phys. 35, L873 (1996). H. Tsuchiya, K. Sunaba, T. Suemasu, and F. Hasegawa, J. Cryst. Growth 189/ 190, 395 (1998). A. Usui, H. Sunakawa, A. Sakai, and A. Yamaguchi, Jpn. J. Appl. Phys. 36, L899 (1997). K. Hiramatsu, H. Matsushima, T. Shibata, N. Sawaki, K. Tadatomo, H. Okagawa, Y. Ohuchi, Y. Honda, and T. Matsue, Mater. Res. Soc. Symp. Proc. 482, 257 (1998). T. Shibata, H. Sone, K. Yahashi, M. Yamaguchi, K. Hiramatsu, N. Sawaki, and N. Itoh, J. Cryst. Growth 189/190, 67 (1998). G. Nataf, B. Beaumont, A. Bouillé, S. Haffouz, M. Vaille, and P. Gibart, J. Cryst. Growth 192, 73 (1998). S. T. Kim, Y. J. Lee, D. C. Moon, C. H. Hong, and T. K. Yoo, J. Cryst. Growth 194, 37 (1998). Y. Melnik, A. Nikolaev, L. Nikitina, K. Vassilevski, and V. Dimitriev, in Mater. Res. Soc. Symp. Proc. 482, 269 (1998). P. R. Tavernier, E. V. Etzkom, Y. Wang, and D. R. Ckarke, Appl. Phys. Lett. 77, 1804 (2000). W. Zang, H. R. Alves, J. Bläsing, D. M. Hofmann, A. Krost, and B. K. Meyer, in Proc. IWN2000 Conference, Nagoya, p. 46. J. S. Speck, B. Heying, C. Elsass, P. Fini, D. Green, E. Haus, C. Poblenz, Y. Smorchkova, U. K. Mishra, and S. P. DenBaars, in Mater. Res. Soc. Symp. Proc. G7.4 (2000). W. S. Wong, T. Sands, and N. W. Cheung, Appl. Phys. Lett. 72, 588 (1998). M. K. Kelly, R. P. Vaudo, V. M. Phanse, L. Görgens, O. Ambacher, and M. Stutzmann, Jpn. J. Appl. Phys. 38, L217 (1999). R. P. Vaudo, G. R. Brandes, J. S. Flynn, X. Xu, M. F. Chriss, C. S. Christos, D. M. Keogh, and F. D. Tamweber, in Proc. IWN2000 Conference, Nagoya, p. 15.

29

30 31

32

33

34

35

36

37 38

39 40 41

42

43

44

S. S. Park, I. W. Park, and S. H. Choh, in Proc. IWN2000 Conference, Nagoya, p. 60. H. M. Kim, J. E. Oh, and T. W. Kang, Mater. Lett. 47, 276 (2001). E. Gil-Lafon, J. Napierala, D. Castelluci, A. Pimpinelli, R. Cadoret, and B. Gerard, J. Cryst. Growth 222, 482 (2001). O. Parillaud, E. Gil-Lafon, B. Gerard, P. Etienne, and D. Pribat, Appl. Phys. Lett. 68, 2654 (1996). B. Gerard, D. Pribat, R. Bisaro, E. Costard, J. Nagle, J. Ricciardi, and M. Dupuy, Mater. Res. Soc. Symp. Proc. 280, 675 (1998). O. Parillaud, N. Piffault, E. GilLafon, R. Cadoret, in Proc. Sixth Int. Conf. On Indium Phosphide and Related Materials, Santa Barbara (IEEE, 1994), p. 547. D. Pribat, B. Gerard, M. Dupuy, and P. Legagneux, Appl. Phys. Lett. 60, 2144 (1992). B. Gerard, X. Marcadet, P. Etienne, D. Pribat, D. Friedrich, J. Eichholz, H. Bernt, H. Hanssen, J. F. Carlin, and M. Ilegems, Mater. Res. Soc. Symp. Proc. 535, 139 (1999). B. Gerard and D. Pribat, Inst. Phys. Conf. Ser. 166, 23 (2000). E. Gil-Lafon, A. Videcoq, J. Napierala, D. Castelluci, A. Pimpinelli, B. Gerard, J. Jimenez, and M. Avella, Opt. Mater. 17, 267 (2001). S. Nakamura, Jpn. J. Appl. Phys. 30, L1705 (1991). I. Akasaki and H. Amano, J. Cryst. Growth 163, 86 (1996). A. Trassoudaine, E. Aujol, P. Disseix, D. Castelluci, and R. Cadoret, Phys. Stat. Sol. (a) 176, 425 (1999). R. J. Molnar, W. Götz, L. T. Romano, and N. M. Johnson, J. Cryst. Growth 178, 147 (1997). R. J. Molnar, P. Maki, R. Aggarwal, Z. L. Liau, E. R. Brown, I. Melngailis, W. Götz, L. T. Romano, and N. M. Johnson, in Mater. Res. Soc. Symp. Proc. 395, 189 (1996). K. Uchida, A. Watanabe, F. Yano, M. Kouguchi, T. Tanaka, and S. Minagawa, J. Appl. Phys. 79, 3487 (1996).

237

238

4 Growth of Gallium Nitride by Hydride Vapor Phase Epitaxy 45

46

47

48

49 50 51

52 53

54 55 56 57 58 59 60

61

62 63 64

B. Arnaudov, T. Paskova, E. M. Goldys, R. Yakimova, S. Evtimova, I. G. Ivanov, A. Henry, and B. Monemar, J. Appl. Phys. 85, 7888 (1999). S. Gu, R. Zhang, Y. Shi, Y. Zheng, L. Zhang, F. Dwikusuma, and T. F. Kuech, J. Cryst. Growth 231, 342 (2001). F. Lassalle, A. Porte, J. L. Laporte, C. Pariset, and M. Cadoret, Mater. Res. Bull. 13, 1285 (1988). A. Porte, F. Lassalle, C. Pariset, M. Cadoret, L. Chaput, and R. Cadoret, Rev. Phys. Appl. 24, 143 (1989). R. Cadoret, and E. Gil-Lafon, J. Phys. I France 7, 889 (1997). R. Cadoret, J. Cryst. Growth 205, 123 (1999). I. Barin, Thermodynamical Data of Pure Substances (VCH Weinheim, Basel, Cambridge, New York, 1993). A. Koukitu, S. Hama, T. Taki, and H. Seki, Jpn. J. Appl. Phys. 37, 762 (1998). I. N. Przhevalskii, S. Yu. Karpov, Yu. N. Makarov, Internet J. Nitride Semicond. Res. 3, Art. 30 (1998). JANAF Thermodynamical Data, Vol 14, (1985), 3rd edn. R. G. Pong, R. A. Staachnik, and A. E. Shirk, J. Chem. Phys. 63, 1525 (1975). M. C. Drake, and G. M. Rosenblatt, J. Chem. Phys. 65, 4067 (1976). I. R. Beattie, and J. H. Horder, J. Chem. Soc. A 3, 2655 (1969). C. E. Sjorgren, P. Klaeboc, and E. Rytter, Spectrochem. Acta 40, 457 (1984). G. K. Selivanov and A. A. Mal’Tsev, Zh. Strukt. Khim. 14, 943 (1973). K. P. Huber and G. Herzberg, Molecular spectra and molecular structure IV, Constant of diatomic molecules (van Nostrand Reinhold Co., New York, 1980). Landolt Bornstein, Numerical Data and Functional Relationships in Science and Technology, New Series, III 17a, O. Madelung (ed.) (Springer, Berlin 1982). D. W. Shaw, J. Electrochem. Soc. 115, 405 (1968). D. W. Shaw, J. Electrochem. Soc. 115, 777 (1968). D. W. Shaw, J. Electrochem. Soc. 117, 683 (1970).

65

66

67 68 69 70 71 72

73 74

75 76 77

78

79 80 81

82 83 84 85

R. Cadoret, in Current Topics in Materials Science, E. Kaldis (ed.) (North-Holland, Amsterdam, 1980), Vol 5. J. B. Theeten, L. Hollan, and R. Cadoret, in Crystal Growth and Materials, E. Kaldis and H.J. Scheel (eds.) (NorthHolland, Amsterdam, 1977). L. Hollan and C. Schiller, J. Cryst. Growth 13/14, 319 (1972). L. Hollan and C. Schiller, J. Cryst. Growth 32, 175 (1974). L. Hollan, J. M. Durand, and R. Cadoret, J. Electrochem. Soc. 124, 135 (1977). J. L. Gentner, C. Bernard, and R. Cadoret, J. Cryst. Growth 56, 332 (1982). J. L. Gentner and R. Cadoret, J. Phys. Colloq. France 43, C5 (1982). Y. Golan, X. H. Wu, J. S. Speck, R. P. Vaudo, and V. M. Phanse, Appl. Phys. Lett. 73, 3090 (1998). R. Zhang and T. F. Kuech, in Mater. Res. Soc. Symp. Proc. 482, 709 (1998). W. Seifert, S. Swchatlick, J. Reinhold, and E. Butter, J. Cryst. Growth 66, 333 (1984). O. Briot, S. Chur, and R. L. Aulombard, Appl. Phys. Lett. 71, 1990 (1997). J. Korec and M. Heyen, J. Cryst. Growth 60, 297 (1982). H. Jurgenssen, J. Korec, M. Heyen, and P. Balk, J. Cryst. Growth 66, 73 (1984). S. Glastone, K. J. Laidler, and H. Eyring, The Theory of the Rate Processes (Mc Graw-Hill, New York, 1965). H. Banvillet, Ph.D. thesis, University of Clermont II, 1992. H. Watanabe, in Handbook of Crystal Growth (1994). W. K. Burton, N. Cabrera, and F. C. Franck, Philos. Trans. Soc. 243, 299 (1951). D. Richman, J. Phys. Chem. Solids 33, 147 (1970). D. Herzberg, J. Mol. Spectrosc. 33, 147 (1970). R. F. Barrow, Trans. Faraday Soc. 56, 952 (1960). A. G. Gaydon, in Dissociation Energies and Spectra of Diatomic Molecules, 3rd edn.

4.6 References 86

E. Aujol, A. Trassoudaine, L. Siozade, A. Pimpinelli, and R. Cadoret, J. Cryst. Growth 230, 372 (2001). 87 R. Cadoret and A. Trassoudaine, J. Phys. Condens. Mater. 13, 6893 (2001). 88 T. Paskova, E. B. Svedberg, L. D. Madsen, R. Yakimova, I. G. Ivanov, A. Henry, and B. Monemar, MRS Internet J. Nitride Semicond. Res. 4S1, G3.16 (1999).

C. Chatillon and C. Bernard, J. Cryst. Growth 71, 433 (1985). 90 B. Gil, O. Briot, and R. L. Aulombard, Phys. Rev. B 52, R17028 (1995). 91 L. Siozade, S. Colard, M. Mihailovic, J. Leymarie, A. Vasson, N. Grandjean, M. Leroux, and J. Massies, Jpn. J. Appl. Phys. 39, 20 (2000). 89

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5

Growth and Properties of InN Valery Davydov, Albert Klochikhin, Sergey Ivanov, Jochen Aderhold, and Akio Yamamoto

Abstract

This chapter briefly reviews the most recent achievements in the growth of singlecrystalline InN and new data on fundamental properties of this material. Different aspects of growth of hexagonal InN layers by plasma-assisted molecular beam epitaxy and metalorganic molecular beam epitaxy are considered. The effects of initial growth stages, growth temperature, III/N flux ratio, layer thickness, and nitrogen-plasma components on the properties of InN layers are discussed. A detailed analysis of morphological, structural and electrical properties of hexagonal InN epilayers grown by molecular beam epitaxy on Al2O3 substrates is presented. High-quality InN layers with a carrier concentration of 8 ´ 1018 cm–3 and electron mobility of 1900 cm2 V–1 s–1 at 300 K were successfully grown by molecular beam epitaxy. The growth of InN by conventional metalorganic vapor phase epitaxy using trimethylindium and ammonia as source materials is described in detail, and the influence of growth temperature, growth pressure, reactor design, and gas flow rate on surface morphology, growth rate, and electrical properties of InN are considered. A carrier concentration of 6 ´ 1018 cm–3 and electron mobility of 730 cm2 V–1 s–1 were achieved in the InN films grown by metalorganic vapor phase epitaxy. Results of recent experimental and theoretical studies of lattice dynamics of single-crystalline hexagonal InN are presented. A survey of the most recent optical absorption, photoluminescence, photoluminescence excitation, and photomodulated reflectance studies of InN layers with electron concentrations between 6 ´ 1018 and 4 ´ 1019 cm–3 grown by all these techniques is given. Optical

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5 Growth and Properties of InN

measurements have revealed that the true band gap of InN is close to 0.7 eV, which is much lower than the band gap of 1.89 eV cited in the literature. This finding is supported by optical studies of In-rich InxGa1–xN alloys. The influence of oxygen and the Burstein-Moss effect on the InN optical absorption edge is considered. Possible mechanisms of transformation of the crystal structure and the band-gap variation are discussed using the results of postgrowth treatment of InN.

5.1

Introduction

Despite its practical importance [1–3], InN still remains the least studied material among III-nitride semiconductors. Synthesis and studies of physical properties of InN films were initiated in the early 1970s. In the first stage, the main technique to deposit InN films on quartz, sapphire or glass substrates was the reactive sputtering of an In-anode target heated by an electron beam and reacting with a nitrogen flux activated by a dc discharge in a hollow cathode [4–6]. Poor vacuum conditions, low growth rates and the use of cold substrates (room temperature) resulted in growth of polycrystalline wurtzite films with high electron concentrations (in excess of 1020 cm–3) and the band gap of *1.9 eV. Later a dramatic reduction of the carrier concentration (down to 2 ´ 1016–1017 cm–3) in InN grown by the radiofrequency (RF) sputtering of prenitridated In targets was obtained [7]. As a result, the highest ever reported electron mobility of 2700 cm2 V–1 s–1 at RT was achieved, retaining the band gap at 1.89 eV [8]. Magnetron sputtering at higher substrate temperatures (200–525 8C) yielded hexagonal InN films consisting solely of epitaxial grains with the c-axis nearly parallel to that of a sapphire substrate, although with n > 1020 cm–3 and mobility as low as 80 cm2 V–1 s–1 [9]. Slow and intricate progress of the epitaxial growth technology of InN was caused by several basic difficulties. These are (i) the low dissociation temperature of InN (500 8C [10], 550 8C [11], 630 8C [12]), possibly depending on the N overpressure; (ii) steep rise of equilibrium N2 pressure with a growth temperature (TS), starting at 470–500 8C, as was predicted theoretically [13] and established experimentally by a study of InN evaporation in vacuum [14], which causes a fast nitrogen escape from the film surface, and, finally, (iii) poor pyrolysis efficiency of ammonia reactant (NH3) at low growth temperatures, which is especially critical for metalorganic vapor phase epitaxy (MOVPE). In addition, at these temperatures the surface mobility of adatoms decreases making the growth of high-quality epitaxial films problematic. As for other III-N materials, due to a lack of suitable substrate materials matched to the InN lattice constant and thermal expansion coefficient, the InN films are grown on foreign substrates. In this case the substrate nitridation procedure, buffer layers and initial growth sequence along with the growth parameters (TS, In/N flux ratio, growth rate, etc.) can dramatically affect the crystal perfection of InN heteroepilayers. Al2O3 (0001) substrates are typically used for the InN het-

5.1 Introduction

eroepitaxy due to its wide availability and hexagonal symmetry. Si (111) and Si (100) substrates were also employed, but give a much worse structural quality due to mixture of hexagonal and cubic InN phases [15]. Growth of the cubic InN films on GaAs (001) substrates with an InAs buffer layer has also been reported [16]. Even when using the well-developed GaN templates, the lattice mismatch is not small enough (*12%) to avoid defect formation due to stress relaxation. The growth of InN by MOVPE was not realized until 1989, when the microwave plasma was used to activate N2 gas and the InN deposition on sapphire at TS < 500 8C by MOVPE was accomplished for the first time [17]. Later, this technique was modified and better structural quality of InN epilayers was achieved by postgrowth annealing at 450–550 8C and improvements in the nitridation technology [18–20]. However, the electrical and optical parameters of these layers, such as residual electron concentration 5 ´ 1019 cm–3 and fundamental absorption edge *1.97 eV, did not show any essential difference from those commonly displayed by InN films obtained by the sputtering techniques. The growth of single-crystalline InN by conventional MOVPE was first reported in [21]. The use of a high NH3 partial pressure in either low-pressure or atmospheric-pressure MOVPE reactors made it possible to increase TS (up to 550 8C) and, hence, the NH3 pyrolysis efficiency and to obtain the InN MOVPE films on sapphire without any external nitrogen excitation [22, 23]. The epitaxial InN films demonstrated slightly reduced electron concentrations (*5 ´ 1019 cm–3) and enhanced carrier mobility (up to 270 cm2 V–1 s–1 at RT). Further increase in TS resulted in higher homogeneity of InN epilayers [24], while the use of high-temperature GaN templates grown on sapphire provided the electron mobility as high as 700 cm2 V–1 s–1 at RT at the same carrier concentration of *5 ´ 1019 cm–3 due to improved structural quality [25]. Despite the relatively late start [26], plasma-assisted molecular beam epitaxy (PAMBE) has made a significant progress in growing InN films. Several groups using different nitrogen activators: electron cyclotron resonance (ECR) [27, 28], RF inductively coupled [29, 30], and even the combination of metalorganic In precursor with RF N2-activator [31], have reported on InN epilayers growth on sapphire with the electron concentration lowered to (3–9) ´ 1018 cm–3 and enhanced RT mobility, comparable with or exceeding that obtained by MOCVD, namely 500 cm2 V–1 s–1 [31], 800 cm2 V–1 s–1 [29], 820 cm2 V–1 s–1 [30], and 1700 cm2 V–1 s–1 [28]. Different buffer layers (AlN [29] and InN [27, 28, 30]) and nitridation procedures were used, demonstrating a great potential of the low-temperature PAMBE technique operated within 470–550 8C. The improvement in electrical characteristics was accompanied by an improvement in the structural quality, as follows from Raman and X-ray data [32, 33]. Due to advances in the growth of high-quality single-crystalline InN layers, new information on the electronic structure of InN has been obtained. Optical measurements on InN epilayers, both MBE and MOVPE grown, have revealed that the fundamental absorption edge of these layers lies around 1 eV or even below [28, 34, 35]. In addition, photoluminescence, which has never been observed in polycrystalline InN with a band gap of 1.89 eV, was observed in single-crystalline

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epilayers for the first time [34]. This photoluminescence was found to correspond to the lower-energy absorption edge revealed in single-crystalline InN [35–37]. It has been concluded from experiments [35] that hexagonal InN is a narrow-gap semiconductor with a band gap of about 0.7 eV, which is much smaller than the values of 1.8 eV to 2.1 eV reported previously [6–8]. This finding was supported by optical studies of In-rich InxGa1–xN alloys [35, 38]. An improved theory with the fixed pd repulsion [39] gives the band gap of hexagonal InN of about 0.8 eV, close to the experimental value. This chapter describes how the high-quality single-crystalline hexagonal InN layers can be grown by MBE and MOVPE techniques. It also presents the results of investigations of the lattice dynamics and electronic structure of the layers. The chapter is organized as follows: Sects. 5.2, 5.3, and 5.4 deal with the growth of InN layers by the PAMBE, metalorganic molecular beam epitaxy (MOMBE), and MOVPE techniques, respectively. Different aspects of InN growth are considered, and the effects of technological parameters on morphological, structural, and electrical properties are discussed. In Sect. 5.5, experimental and theoretical data on the lattice dynamics of hexagonal InN are presented. In the same section information on the electronic structure of single-crystalline InN obtained in the most recent optical studies is given. Optical properties of In-rich InxGa1–xN alloys (0.36 < x < 1) are also described. Section 5.6 contains the conclusions.

5.2

Growth of InN by Plasma-Assisted Molecular Beam Epitaxy 5.2.1

Introduction

PAMBE, being the most nonequilibrium epitaxial growth technique, possesses basic properties that become advantageous in the case of InN and InN-rich alloys epitaxy. The first factor is that the intensity of an activated nitrogen flux does not depend on the growth temperature TS, owing to N2 activation by plasma discharge, which can easily supply the active nitrogen flux high enough to achieve a 1 monolayer s–1 growth rate, using available RF activators (see below). In other words, TS can by chosen independently to provide the necessary adatom surface diffusion and stoichiometry conditions corresponding to optimal film quality at given group III atom and excited nitrogen fluxes. Secondly, it is expected that, despite the general conviction that the influence of ions on epilayer properties is negative, at low temperatures (as for InN MBE growth) and moderate ion energies, the ions can enhance the adatom surface mobility, improving epilayer quality. Finally, the MBE technique facilitates the growth kinetics control by using welldeveloped in situ analytical tools. In the following sections we consider different aspects of the PAMBE growth of InN and present a detailed analysis of morphological, structural and electrical properties of wurtzite InN epilayers grown by MBE on Al2O3 by using ECR N2-

5.2 Growth of InN by Plasma-Assisted Molecular Beam Epitaxy

plasma source (ASTeX). The effects of initial growth stages, growth temperature, III/N flux ratio, layer thickness, and nitrogen plasma components on the properties of InN layers are discussed, using the data of scanning electron microscopy (SEM), transmission electron microscopy (TEM), secondary ion mass spectroscopy (SIMS) and XRD. 5.2.2

InN PAMBE Growth Peculiarities 5.2.2.1 Role of Different Nitrogen Species in PAMBE

The PAMBE growth of III-N compounds employs a nitrogen flux activated by different types of low-pressure gas discharge. Aside from the chemically inert ground-state nitrogen molecules N2(X1å+g , v = 0) (the usual activation efficiency does not exceed a few percent), this flux consists of activated species including: neutral molecules in different vibrationally and electronically excited states (N2(X1å+g , v=0) and N2* = N2(A3å+u, a'1 å–u) etc., respectively), neutral atoms in different states, ionized molecules N+2 = N+2 (X2å+u, w) and atoms [40]. These species possess a quite different energy (up to tens of eV), which is distributed between translation (kinetic) energy component and internal degrees of freedom. Therefore, standard equilibrium thermodynamic approaches cannot be used alone to describe the PAMBE process depending essentially on the kinetics of interaction of the active nitrogen species with a growth surface, proceeding through different mechanisms. Unfortunately, quantitative information on the kinetic processes remains quite scarce despite their practical importance. A complex character of such interactions can be explained by a combined action of chemical (bond breaking) and physical (billiard-ball-like collisions) effects, which are closely related, yielding a subtle intertwinning of activated beam characteristics with growth parameters (surface temperature, III/N flux ratio, etc.). Nitrogen atoms, having three valence electrons and bonding with all group III elements without any potential barriers [41, 42], as well as N*2-excited molecules interacting with a solid state surface through the less exothermic dissociative chemisorption mechanism [43–45] are generally recognized as the most advantageous species for III-N epitaxial growth. In contrast, ionic species of plasma-activated nitrogen flux (N+2 , N+) responsible for such ion-surface processes as adatom-vacancy pair generation, displacement of atoms, embedding of N2-molecules, surface atoms sputtering and others [46, 47] are believed to cause most harmful consequences for epitaxial film quality (up to a transition to polycrystalline growth). In accordance with published data [48], the damage threshold of GaN can be estimated as 18–24 eV. However, such important parameters as threshold ion density and doses of the energetic species needed for the generation of both point defects and dislocations are not available. To our knowledge, no such studies have been reported for InN, but one can qualitatively suppose the same behavior and the value of threshold energy to be even less than that for GaN due to the weaker In-N binding energy. However, careful analysis of previously reported results gives evidence of a not necessarily negative role of ions in the epitaxy. The possibility of using N+2 ions to

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5 Growth and Properties of InN

grow GaN epitaxial films with good enough structural quality (xh (0002) = 300 arcsec) was demonstrated in early 1990s [49]. Moreover, a positive influence of NH+3 ions with an energy of 30 eV and a current density 3 ´ 1014 ions cm–2 s–1 on the two-dimensional character of the GaN growth was found in studies of ion-enhanced gas-source MBE [50]. Considering the complex composition of an activated nitrogen flux and the interaction of various nitrogen species with a semiconductor surface during epitaxial growth, one can suppose in the zero approximation that PAMBE with a certain growth rate (up to *1 lm h–1) is provided by an effective integral nitrogen flux (1014–1015 cm–2 s–1) comprising such species as N*2, N, N+2 with energy less than *20 eV. However, even a small flux (*1012 cm–2c–1) of relatively high-energy N+2 ions (> 20 eV) can cause both surface damage generation and enhancement of adatoms surface mobility. The most commonly employed methods of generating a low-temperature N2plasma for MBE applications use either RF (13.56 MHz) or microwave (with electron cyclotron resonance ECR) discharges. In the former case the cylindrical inductively coupled plasma (ICP) can be sustained only at relatively high working pressure (Pd*0.5 Torr) and powers (W*several hundreds of watts). In contrast, ECR discharge can be operated at the Pd starting from a few mTorr and W from several watts. One can establish from numerous publications that the ECR activator is characterized by lower intensity of the activated nitrogen flux (maximum growth rate achieved is limited to 0.2–0.4 lm h–1) and higher ion content in the flux compared to the ICP activators. It is due to many factors, including a difference in the type of plasma kinetic processes dominating in these activators, design of the end-plate aperture, existence of divergence magnetic field in ECR activators, which accelerates ions to the substrate and so on [51, 52]. The parameters of a N2-plasma drift near the growth position in an MBE chamber equipped with ECR activator (ASTeX Compact) were measured, and a rather low ion current density (*0.5 lA cm–2) and ion energy (*10–20 eV) at the typical discharge parameters (N2 mass-flow and power are within 1–4 sccm and 100–200 W, respectively) were revealed in [52]. At present, different ICP activators (EPI Uni-Bulb, OAR CARS-25, etc.) are commonly used for PAMBE. Indeed, during the high-temperature growth of GaN and AlN films these activators provide higher growth rate and a lower damage level compared with the ECR activators. However, taking into account the necessity of low-temperature growth regimes for InN (*500 8C) and some positive role of ions to enhance surface mobility of the adatoms, one can expect some advantages of ECR activators (or other ones with high enough ion content in the N2-activated flux) for MBE of In-rich nitrides.

5.2.2.2 Maintenance of Stoichiometric Conditions During InN Growth by PAMBE

The highest-quality epilayers can be obtained by PAMBE under group III-stabilized conditions providing a maximum surface diffusion of adatoms at moderate TS values, keeping the III/N flux ratio close to 1 : 1 (see [53] and references therein). Otherwise, (under N-stabilized conditions), a large binding energy between

5.2 Growth of InN by Plasma-Assisted Molecular Beam Epitaxy

group-III atoms and nitrogen significantly suppresses adatom diffusion, which results in a rough surface morphology [54]. Figure 5.1 summarizes the available experimental data on the temperature dependences of Ga, In, and N evaporating fluxes from elemental materials and binary compounds (GaN and InN), as well as their reference working fluxes corresponding to different growth rates (horizontal lines). In the case of GaN MBE the situation is quite favorable because the onset temperature of fast Ga evaporation from liquid Ga droplets on the GaN surface (*680–700 8C at the growth rates used) is much lower than the GaN dissociation temperature corresponding to a fast N escape from GaN, accompanied by a decrease in the GaN growth rate governed by a nitrogen flux under Ga-stable growth conditions (*780 8C [55]). In other words, a Ga pressure over liquid Ga is much higher than a N pressure over GaN over a wide TS range of interest until *780 8C (compare curves 4 (3) for Ga and 5 for N in Fig. 5.1). The experimental temperature dependence of the evaporation rate of excessive Ga in GaN MBE, proportional to exp (–2.8 eV/kT) [53], fits perfectly with that of a Ga flux from Ga-melt (curve 3 in Fig. 5.1). This enables one to grow droplet-free GaN under Garich conditions at constant growth rate in the TS = 680–760 8C range [54], neglecting a certain Ga overpressure that governs just point defect density in the epilayer.

Experimental temperature dependences of Ga, In, and N fluxes evaporating from the elemental group III metals or binary compounds. Line 1 is related to the total pressure during InN vacuum evaporation, governed mostly by N [56]. Lines 2 and 3 correspond to In and Ga evaporation, from elemental metals, respectively. Line 4 is the Ga evaporation from Ga on the GaN surface, while line 5 is a N escape from GaN [55]. Line 6 plots experimental data on N evaporation from InN obtained in this work. The solid horizontal line shows effective nitrogen flux corresponding to 1 ML s–1 growth rate.

Fig. 5.1

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5 Growth and Properties of InN

In contrast to GaN, InN MBE proceeds similarly to all other III–V compounds, i.e., the In pressure over liquid In is much smaller than the N pressure over InN in the temperature range of interest (up to *780 8C) (compare curves 2 for In and 6 for N in Fig. 5.1). In other words, the nitrogen escape from InN (InN dissociation) is faster than the evaporation of excessive In from the surface, as was experimentally confirmed in [56] during vacuum evaporation of an InN film. Curve 1 demonstrates the total pressure (in flux units) in the chamber obtained in [56], which is mostly determined by nitrogen. However, it is assumed to be much lower than the N pressure over the InN surface, which should be determined relatively to the InN surface conditions (using e.g., RHEED or visual control of In droplet appearance) as in the case of GaN [57]. Curve 6 was plotted with the same slope as 1, taking as a reference point the average temperature of the onset of the InN surface depletion by N under the nitrogen flux corresponding to a typical growth rate (at 450–470 8C) of droplet-free InN in our experiments –0.1 ML s–1. It shows approximately one order of magnitude higher N pressure over InN than in [56]. Using curve 6, one can predict that an InN layer can be grown at a growth rate of 0.5 ML s–1 at TS = 540–550 8C, having the activated N flux as high as 1 ML s–1. In general, this means that in the whole temperature range of interest the boundary between N-stable and In-stable regions in an InN PAMBE phase diagram is abrupt and all excessive In accumulates on the growth surface. This makes it difficult to keep In/N = 1 : 1 growth conditions, avoiding the In accumulation. The problem may be simplified by incorporation of some surfactant impurity, e.g., Mg, which due to the surface segregation effect can influence the In and N equilibrium pressures over the three-component system, establishing an equilibrium between gaseous, solid, and quasiliquid phases at the growth surface. The other possibility is to exploit a positive surfactant role of nitrogen ions that can increase the surface mobility of adatoms even under the N-rich conditions, as was discussed above. 5.2.3

Undoped InN Growth by PAMBE with Different Initial Stages 5.2.3.1 Growth and Epilayer Morphology

InN epilayers were grown by PAMBE on (0001) and (1102) sapphire substrates with the c-axis normal and parallel to the surface, respectively [27]. The custom-designed MBE chamber having ultimate background pressure *10–10 Torr was equipped with a turbomolecular pump with an effective pumping rate of *350 l/s. Elemental In was supplied by a standard effusion cell at a temperature varied within the 750– 850 8C range in a series of experiments. An ASTeX ECR plasma source was used for supplying activated nitrogen with a flow rate of about 1–5 sccm, allowing growth rates of 0.02–0.2 lm h–1. The back side of substrates was coated with Ti and mounted on In-free molybdenum holders. Before loading, sapphire substrates were rinsed in acetone only and then thermally cleaned and nitridated at 1000– 1100 8C for 30 min, finally demonstrating a streaky RHEED pattern. For the main InN layer growth TS was varied between 350 to 500 8C. Its calibration procedure

5.2 Growth of InN by Plasma-Assisted Molecular Beam Epitaxy

provided an approximately 10 8C accuracy and employed infrared (IR) pyrometer indications and a temperature versus heater power dependence adjusted to indium (157 8C) and tin (232 8C) melting points, as well as to the temperature of an onset of fast InN re-evaporation from sapphire (*630 8C [58]), registered by RHEED. The latter is most probably governed by the In evaporation from the Inrich melt depleted by nitrogen rather than InN decomposition that occurs much earlier (see Fig. 5.1 and data in [56]). Surface reconstruction of the InN epilayers during growth was monitored by RHEED as well. The film thicknesses were between 0.4 and 1.5 lm. Three different growth initiation regimes were used (see Fig. 5.2). In the first one (I), the growth of the main InN layer starts immediately after high-temperature substrate annealing and nitridation, when TS has been reduced to the working value under the nitrogen flux. In the second regime (II), a 15-nm thick InN buffer layer was first grown at *300 8C, followed by increasing TS to the value of the main InN growth. One should note that after the low-temperature buffer layer deposition, the RHEED pattern usually corresponds to a polycrystalline or textural three-dimensional (3D) growth (spots, circles and strokes on the circles) with rough growth surface. This picture does not change significantly on increasing TS to the temperature of the main InN layer growth (*470–500 8C), indicating no pronounced transformation of crystalline structure. The third regime (III) differed from regime II only by high-temperature (*800–900 8C) annealing of the low-

Schematic diagrams of three studied growth regimes of InN epilayers on Al2O3 substrates by PAMBE.

Fig. 5.2

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5 Growth and Properties of InN

temperature InN buffer under the activated nitrogen flux, resulting in nearly complete decay of RHEED pattern features related to the InN buffer. It is expected that after the sapphire nitridation an AlN or AlOxN1–x layer [12, 57, 59] arises on the surface, presumably relaxed with respect to the sapphire substrate. Having an epitaxial relationship [21 10]AlN//[1010]Al2O3 (see [18, 60] and references therein), it may reduce the lattice mismatch of the successive InN layer ([1010]InN//[1010]AlN) to *12% from 25.9% (for the [1010]InN//[1010]Al2O3 epitaxial relationship) or from 28.4% (for [21 10]InN//[1010]Al2O3 one). Nevertheless, MBE growth of continuous InN layer in regime I turns out to be possible only up to TS*350 8C under the chosen nitridation conditions. This may be explained by still high lattice mismatch causing a strain-induced enhancement of N re-evaporation at the initial InN monolayer growth [61] that requires an approximately 100– 150 8C decrease in TS with respect to the growth of unstrained InN film to avoid liquid In droplet formation followed by a columnar structure growth. On the other hand, the nitridation conditions could not be well optimized to provide high-quality buffer-free growth, as in Refs. [23, 62]. As a result, from the very be-

SEM images of InN epilayers grown by PAMBE on sapphire: a surface and cross section in the regime I (W258); b and c surfaces in regimes II (W254) and III (W239), respectively; d cleavage with cavities in the regime II, e featureless cleavage in the regime III.

Fig. 5.3

5.2 Growth of InN by Plasma-Assisted Molecular Beam Epitaxy

ginning of the growth at such low TS the RHEED pattern for the epilayer W258 (regime I) is practically the same as that observed after the buffer layer deposition. SEM images show a rough surface and columnar structure at the cleavage (Fig. 5.3 a). In contrast, regimes II (W254) and III (W239) allow the main InN layer to be grown at maximal possible TS*470 8C, when the In/N flux ratio is close to 1 : 1, at a given N flux, and In droplets do not occur. This temperature agrees well with our estimate of the onset of fast N escape from InN, resulting in an excess of In on the surface (see curve 6 in Fig. 5.1). RHEED for both InN layers demonstrates (1 ´ 1) streaky pattern corresponding to 2D-growth. SEM plan-view images (Figs. 5.3 b and c) show flat surface without columnar structure for both regimes. However, in cross-sectional SEM images the InN layer grown in the regime II reveals cavities at the InN/Al2O3 interface (Fig. 5.3 d), whereas only the regime III layers (W239) have a flawless interface with sapphire (Fig. 5.3 e). Regime III was used to grow InN layers of different thickness (W269 and W280) as well as different surface orientation (1102) (W294). As a possible explanation of the obvious advantage of the regime III over II, we suggest that the high-temperature annealing of a thin InN buffer up to its decomposition and complete evaporation, results in the formation under the nitrogen flux of a thin (around one ML) equilibrium surface layer of InAlN alloy with rather high In content determined by TS and incident active nitrogen pressure. An existence under the surface segregation conditions of such a surface alloy monolayer, with equilibrium composition governed by group V molecules overpressure and TS, was predicted theoretically for AlGaAs MBE growth [63] and experimentally shown later for InGaAs MBE. This flat continuous InAlN nucleation layer, relaxed with respect to the sapphire substrate due to huge lattice mismatch, provides flat growth front and much lower mismatch for the following InN layer, preventing the stress-induced In droplet formation. Contrary to this, the rough surface of the InN nucleation layer in the II regime strongly suppresses adatom diffusion during the main InN layer growth initiation, resulting in numerous separated nucleation centers and, thus, in formation of cavities at the InN/substrate interface. In contrast to GaN, where a low-temperature buffer resulted in improvement of the subsequent high-temperature GaN layer quality [64, 65], due to the low InN dissociation temperature it seems to be impossible to improve the structural quality of the InN low-temperature buffer by annealing, keeping unchanged its stoichiometry and surface integrity. Similar results with InN buffer were obtained in [23, 66].

5.2.3.2 Interface with Sapphire, XRD Characterization and Hall Measurements

Figure 5.4 a presents a typical dark-field [0002] TEM image of an InN/Al2O3 interface region of an InN epilayer grown in regime III, taken by using a Philips EM420 microscope at 100 kV. The TEM image demonstrates a single-crystal layer without misfit and threading dislocations generated at the InN/Al2O3 interface for a region of more than 0.5 lm wide. No columnar structure is observed. Using [0002] reflections allows one to display another intricate feature of the near-inter-

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5 Growth and Properties of InN

a Cross-sectional dark-field TEM (0002) image of an InN/Al2O3 heterostructure with a spontaneously formed AlInN interface layer. Regions I, II, and III correspond to InN,

Fig. 5.4

AlInN, and sapphire, respectively. Dark lines are nonidentified extended defects propagating from the sapphire substrate; b In, N, and Al depth distributions measured by SIMS.

face region, namely, rather thick (*70 nm) layer of different composition with sharp interfaces. Such a layer is observed practically in all the samples grown in regime III. Its thickness is in good agreement with the Al penetration depth into InN (*100 nm), measured by SIMS using a CAMECA IMS 3F instrument (Fig. 5.4 b). These observations allow us to suggest spontaneous formation of a thick quite uniform AlInN layer, which cannot be explained by a thermal diffusion of Al due to the low growth temperature. A possible reason for this phenomenon could be a nitrogen-plasma-induced Al diffusion from the sapphire substrate during the following InN growth [67]. The diffracted X-ray intensities of the InN epilayers were measured by doubleand triple-crystal diffractometers (DCD and TCD, respectively) using CuKal radiation (Bragg geometry) and MoKal radiation (Laue geometry). High-quality Ge (220) crystals were used as a monochromator and an analyzer. The x (FWHM) values of the TCD curves for the symmetrical reflections (0002) and (0004) were measured in the Bragg geometry in two directions: parallel and normal to the diffraction vector (H–2H and H scan modes, respectively). The DCD curves were measured with a wide open detector window also for symmetrical Laue diffraction from the (1010) planes normal to the sample surface, asymmetrical reflections in the Bragg geometry at a glancing angle of the (1124) incident and (112 4) reflected X-rays (the normal to the surface lies in the scattering plane), and the (101 1) symmetrical reflections in the Bragg geometry from the planes forming angles n with the (0001) surface in the range from 178 to 728 (the “out-of-plane” (op) curves, i.e., the normal to the surface does not lie in the scattering plane). The studied samples with the respective thicknesses (t), growth initiation regimes (I, II, III), and x of the XRD rocking curves detected under different reflections and scanning modes are summarized in Table 5.1. One should note that the XRD study reveals only hexagonal InN phase for all the samples. Figure 5.5 shows variations in the H-TCD curves for the (0002) reflection versus the growth

5.2 Growth of InN by Plasma-Assisted Molecular Beam Epitaxy

regime (W258, W254, and W269) and the thickness of layers grown in the regime III (W269, W239, and W280). As was expected from a previous analysis, the halfwidths of the diffraction curves considerably decrease when shifting consequently from regime I through regime II to regime III. For the H-2 H-scan mode, xH-2H is proportional to tan HB. For the three samples differing in the growth regime, the following observations can be made: xH (0002) > xH (0004), the ratios xH (0002)/xH (0004) being approximately equal to unity. The ratio between the half-widths of the Bragg curves for the asymmetrical (1124) and (112 4) reflections becomes less than unity, when going from the regime I sample (W258) to the layers grown on an InN buffer layer. As follows from these results, the scattering region changes its location with respect to the diffraction vector and the surface of the sample but remains strongly asymmetrical in shape for all three layers (xHxH-2H). For sample W258, xH (1124)&xH (112 4)&xH (0002); i.e., the halfwidth does not depend on HB or the recording geometry; and the scattering region (the long ellipse axis) is extended along the normal to the diffraction vector. For the samples with an InN buffer layer xH (1124) < xH (112 4), i.e., the scattering region does not contain the normal to the diffraction vector.

Tab. 5.1 Half-widths of the XRD reflection curves for undoped InN epilayers

Sample no. – regime

W258 W254 W269 W239 W280

– – – – –

I II III III III

t (lm)

1.50 0.45 0.40 0.65 1.00

ra (GPa)

~0 ~0 –0.58 –1.23 –1.3

The H-TCD rocking curves for the (0002) reflection of different undoped InN epilayers (1-W280, 2W239, 3-W269, 4-W254, and 5-W258).

Fig. 5.5

xH 0002 (arcsec)

xH-2H 0002 (arcsec)

xH 1124 (arcsec)

xtilt 1010 (arcsec)

xtwt (arcsec)

2140 777 698 350 336

174 80 75 55 43

2164 755 628 566 472

1100 680 638 571 513

12,000 8386 7555 6672 5560

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5 Growth and Properties of InN

The sizes of the coherent scattering region (CSR) along the growth axis (sz) are approximately equal to the layer thickness (see Table 5.2), which means that the contribution of the size effect to the xH (1010) broadening of the Laue curves is negligible. Since vertical screw (VSD) and vertical edge (VED) dislocations do not affect xH (1010), and the probability for horizontal screw dislocations to occur is low, the xH (1010) Laue broadening is determined only by the tilt component xtilt and horizontal edge (or misfit) dislocations with the Burgers vector parallel to the interface, the latter affecting the diffraction curve only in the case of thin layers. For the 0002 symmetrical Bragg curve, VED do not affect xH (0002), because their Burgers vector is perpendicular to the diffraction vector. Consequently, by subtracting the contribution of the size effect and the tilt contribution (identical for the Bragg and Laue geometries) from xH (0002), the only broadening component remains, reflecting the presence of VSD in the layers. For sample W258 (with t = 1.5 lm that allows us to ignore the disturbed region at the interface), the calculation according to [68] gives a VSD density of qvs = 4.9 ´ 109 cm–2. For the samples grown in regimes II and III, the qvs calculated under the assumption that xH (1010) = xtilt are equal to 0.51 ´ 108 and 0.65 ´ 108 cm–2, respectively. Surprisingly, qvsW269 > qvsW254, because all the half-widths measured for sample W254 are larger than those for sample W269. The possible explanation is that for thin (t < 0.5 lm) samples, the near-interface defect layer contributes strongly to the broadening of xH (1010) measured in the Laue geometry, making xH (1010) > xtilt. Indeed, as was derived from SEM and TEM studies, the growth in regime II (directly on the low-temperature InN buffer) causes the formation of a thicker defective layer near the interface, which contributes to xH (1010) (W254). As a result, the analysis of the broadenings for sample W254 leads to an overestimated contribution of xtilt and underestimated qvs values, whereas for sample W269 this effect is less pronounced. Therefore, the qvs densities given in Table 5.2 for samples W254 and W269 should be considered as minimum values. A gradual decrease in the half-widths measured for the samples grown in regime III as their thickness increases from 0.4 to 1.0 lm reflects an improvement of the crystal perfection. An analysis of the ratios xH (0002)/xH (0004) and

Tab. 5.2 Grain sizes along (sx) and normal (sz) to the layer surface, the densities of vertical

screw (qvs) and vertical edge (qve) dislocations, as well as Hall measurement data at 300 K of all the InN layers under study Sample no. – regime

t (lm)

W258 – I W254 – II W269 – III

1.50 0.45 0.40

W239 – III W280 – III

0.65 1.00

sx (lm) 0.08 0.17 0.26 > 0.5 1.1

sz (lm)

qvs qve n300 K l300 K (108 cm–2) (1011 cm–2) (1020 cm–3) (cm2 V–1 s–1)

1.5 0.41 0.49

48.8 > 0.51 > 0.65 (2.20) 2.04 1.88

0.54 1.15

6.21 3.03 2.46

4 2 2

1.92 1.33

1 0.5

93 160 132 600 1700

5.2 Growth of InN by Plasma-Assisted Molecular Beam Epitaxy

xH (112 4)/xH (112 4), the latter demonstrating strong reduction with the t increase, shows that at higher thickness the location of the ellipse scattering region in the reciprocal space changes from being extended along the normal to the diffraction vector (the tilt effect) to being extended along the surface (owing to the micro-misorientations of the diffraction planes around VSD). Since the size effect is rather small, the xH (0002) half-width measured for samples W239 and W280 is determined primarily by VSD typical of III-nitrides. Their calculated densities qvs are listed in Table 5.2 as well. By assuming the linear dependence qvs = f(t), one can obtain qvs = 2.2 ´ 108 cm–2 for sample W269, which is considerably larger than its qvs value calculated on the assumption of xH (1010) = xtilt. This is indirect evidence for the essential contribution of the component associated with misfit dislocations to the xH (1010) value measured for thin samples in the Laue geometry, in addition to the tilt component. The dependencies of the half-widths xoop for a series of the symmetrical Bragg reflections on the n angle between the basal plane (0001) and the planes of diffraction are depicted in Fig. 5.6. As can be seen, all the samples, except for sample W258, have a similar dependence xoop = f(n), indicating that the disordering in the layer plane and the mosaic spread contribute independently to the measured half-widths xoop. The approximation of the experimental values of xoop as in [69] results in the half-widths xtwt, which are governed only by the degree of layer disordering in the sample plane (twist). The obtained xtwt values were used to calculate qve, assuming a random dislocation arrangement (see Table 5.2). It can be seen that qve decreases when changing the growth regimes from I to III (W258– W269) and with an increase in t (W269-W280). It is worth noting that the difference in the densities of VSD and VED is rather large (three orders of magnitude). A similar difference was observed earlier for GaN layers grown by MOVPE [69]. The data obtained for single-crystal samples W239 and W280 characterize the den-

Dependences of FWHM – xoop – of the diffraction curves for the (1011) reflection of InN at the angle n(1-W280, 2W239, 3-W269, 4-W254, and 5-W258).

Fig. 5.6

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sity of randomly distributed VED, whereas a columnar structure with low-angle boundaries formed by the VED is characteristic of samples W258 and W254 and, in a lesser degree, W269. Samples W254 and W258 are fully relaxed as a result of layer fragmentation to small blocks, while the layers grown in regime III remain compressively strained even at a thickness of 1 lm, as follows from the sign and value of biaxial stress ra (see Table 5.1). To conclude, the asymmetry of diffraction scattering is characteristic of all the studied samples. The scattering region is extended along the surface of the samples grown in the regime III at t > 0.5 lm, which is associated with the dislocation arrangement along the c-axis and the anisotropy of deformation fields around them. It was confirmed that the structural quality of the InN layers drastically improves with high-temperature annealing of the LT InN buffer layer and with an increase of the InN layer thickness. The defect structure of the layers is characterized by large VSD and VED densities, the latter being three orders of magnitude larger. The VSD and VED densities decrease to 1.9 ´ 108 cm–2 and 1.3 ´ 1011 cm–2, respectively, away from the interface (by *1 lm). Carrier concentration and mobility determined by conventional Hall-effect measurements provide additional evidence for improvement of structural quality with variation of the initial growth stage from regime I to III and film thickness. It is reflected in a significant reduction of electron concentration, though remaining in the 1020 cm–3 range, which indicates presumably a defect origination of the electrons (see Table 5.2). The InN layer W280 grown in the regime III and having maximal thickness demonstrates electron concentration decrease to 5 ´ 1019 cm–3 at 300 K and the mobility as high as 1700 cm2 V–1 s–1 [28]. 5.2.4

Summary

To summarize, the strongly nonequilibrium nature of PAMBE has been employed to overcome technological puzzles of growing perfect InN films. Taking into account the necessity of low-temperature growth regimes for InN (*500 8C) and a positive role of nitrogen ions in enhancement of surface mobility of the adatoms, one can expect some advantages of ECR activators (or others with high enough ion content in the N2-activated flux) for PAMBE of In-rich nitrides. The highestquality InN epilayers can be obtained by PAMBE under group III-stabilized conditions providing a maximum surface diffusion of adatoms at moderate substrate temperatures, keeping the III/N flux ratio close to 1 : 1. By optimizing the initial stages of InN growth on (0001) and (1102) sapphire substrates, where intermediate high-temperature annealing of InN is used, continuous epilayers with smooth surfaces can be obtained. Analysis of XRD data reveals decreases in the densities of the vertical screw and vertical edge dislocations to 1.9 ´ 108 and 1.3 ´ 1011 cm–2, respectively, for the best films having a maximal thickness of *1 lm. These films demonstrate an electron concentration decrease to 5 ´ 1019 cm–3 at an electron mobility of 1700 cm2 V–1 s–1 at 300 K.

5.3 Growth of InN by Metalorganic Molecular Beam Epitaxy

5.3

Growth of InN by Metalorganic Molecular Beam Epitaxy 5.3.1

Introduction

In this section, the growth of InN by MOMBE will be described in detail. After a short review of the MOMBE technique and its implications for InN growth, the various stages of the growth process will be reported. Finally, the influence of important growth parameters on layer quality will be discussed. 5.3.2

MOMBE as a Growth Technique for InN

MOMBE combines the use of metalorganic vapor sources (in this case, triethylindium, TEIn), as in MOVPE, with the beam nature of MBE. Basically, a MOMBE system is a conventional MBE system with the effusion cells for elemental precursors replaced by gas injectors for metalorganic gases. The gas fluxes are limited to a few sccm so that growth under ultrahigh vacuum conditions is possible. This enables the use of analytical instruments, such as reflective high-energy electron diffraction (RHEED), quadrupole mass spectroscopy, etc. Furthermore, plasma sources for the activation of nitrogen can be used as in PAMBE. This is important for InN growth since the dissociation temperature of InN is in the range of 550 8C, constituting an upper limit for the growth temperature. At this temperature, the pyrolysis of ammonia, which is a key step in the MOVPE growth of nitrides, is not very efficient, so that plasma sources are an interesting alternative. The beam nature of MOMBE implies that the TEIn beam and the nitrogen beam reach the substrate without any interaction, avoiding parasitic gas-phase reactions. The dissociation of TEIn into ethyl radicals and elemental indium is a surface catalytic process that involves a number of intermediate steps. Competing processes, such as the re-evaporation of TEIn or the desorption of intermediate reaction products, also exist [70]. Consequently, the growth rate, the layer quality, and, in the case of ternary compounds, even the layer composition are a delicate balance between competing surface processes, so that they can change drastically under different growth conditions. This makes process optimization a tedious task. The ethyl radicals formed by the dissociation of TEIn can react to ethene (C2H4) and atomic hydrogen. Thus, a contamination of the InN layers with hydrogen is possible. Recent studies suggest that hydrogen acts as a donor in InN [71]. Another possible contamination is carbon. It is known from MOMBE growth of GaAs that appreciable amounts of carbon can be incorporated in an epitaxial layer, with triethylgallium (TEGa) giving better results than trimethylgallium (TMGa) [70]. This is why TEIn instead of triethylindium (TMIn) is used as the In precursor in this work. The vapor pressure of TEIn is much lower than that of TMIn, so that TEIn is less suited under MOVPE conditions, but for MOMBE the

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use of TEIn is possible. Finally, oxygen has been made responsible for the frequently observed unintentional n-type doping of InN layers [72]. The oxygen content of the TEIn used for this work is specified to be of the order of 1 ppm, with diethylether, (C2H5)2O, being the most important impurity [73]. This means that there is no oxygen-hydrogen bond. However, an analysis of the residual gas in the growth chamber after a growth run by mass spectroscopy shows the presence of oxygen-hydrogen bonds in species such as H2O or CH3OH. Therefore, one may speculate that the abundant atomic hydrogen in the growth ambient binds to free oxygen, thus preventing the incorporation of oxygen into the growing layer. 5.3.3

Growth Process 5.3.3.1 Growth System

InN films were grown by MOMBE on c-plane sapphire under ultrahigh vacuum conditions in a Riber 32 system. Activated nitrogen was generated with a CARS25 plasma source from Oxford Applied Research. The nitrogen source was equipped with an optical emission detector (OED), which is basically a photodiode, which detected the intensity of the nitrogen plasma lines. Thus, the OED signal can be used to measure the flux of active nitrogen. TEIn and TEGa (for some nucleation layers) were used as the group-III precursors.

5.3.3.2 Substrate Preparation

The back sides of the substrates were coated with 1 lm of titanium by RF sputtering to ensure efficient radiation heating. After this step the substrates were cleaned using standard degreasing procedures. Immediately before transferring into the UHV system, they were rinsed with ultrapure ethanol and then blown dry with nitrogen. The samples were subsequently baked at 750 8C for one hour and then transferred into the growth chamber. Inspection of the samples by reflective high-energy electron diffraction (RHEED) evidenced a good surface quality, showing a thin, streaky diffraction pattern.

5.3.3.3 Nitridation

As a first process step, the substrates were exposed to the nitrogen plasma for 45 min at a temperature of 500 8C to get a more reactive surface. All given temperatures were measured by a pyrometer, assuming an emissivity of e = 1 for the titanium-coated back sides of the samples. RF power and nitrogen flux were 440 W and 0.9 sccm, respectively. Afterwards, additional RHEED patterns corresponding to AlN could be observed, proving a partial nitridation of the surface. A complete nitridation could not be achieved, even at much longer nitridation times.

5.3 Growth of InN by Metalorganic Molecular Beam Epitaxy

5.3.3.4 Nucleation Layer Growth

Subsequently, the nitrogen flux was reduced to 0.6 sccm, and an additional flux of either 0.35 sccm TEIn or 0.32 sccm TEGa was directed onto the surface, resulting in the growth of an InN or a GaN nucleation layer. The fluxes of the metalorganic precursors were controlled by regulating the pressure on the upstream side of a calibrated leak. Growth time was 15 and 12 min for InN and GaN nucleation, respectively, leading to a nominal thickness of 20 nm as deduced from the growth rate. During this step the RHEED pattern became more and more spot-like, indicating three-dimensional growth. After growth, the substrate temperature was increased until the RHEED pattern became streaky again and kept at that value for ten minutes. After cooling to the selected growth temperature the deposition of InN was performed. 5.3.4

Influence of Growth Parameters on Surface Morphology

InN films were grown at different growth temperatures (TGrowth), TEIn fluxes (qTEIn), nitrogen fluxes (qN2), and RF powers of the plasma source (PCARS). A marked dependence of surface morphology on growth temperature and V/III ratio was observed. The V/III ratio RV/III is defined as the ratio between OED signal and TEIn flux. The OED signal combines the influence of nitrogen flux and RF power. Surface morphology of the grown InN layers was measured by atomic force microscopy (AFM) in the semicontact mode. The root-mean-square (RMS) roughness rq was estimated for different area sizes, namely for 5 lm ´ 5 lm and for 1 lm ´ 1 lm.

5.3.4.1 Influence of Growth Temperature

Figure 5.7 shows the dependences of the growth rate and the RMS roughness for two different area sizes on growth temperature for the case of InN nucleation. As stated previously, the growth rate is strongly dependent on growth temperature and drops to zero for growth temperatures above 550 8C due to InN dissociation. The RMS roughness for the smaller area size decreases with increasing growth temperature, whereas the RMS roughness for the larger area increases drastically when the growth temperature reaches 540 8C. The reason for this behavior is obvious from Fig. 5.8, which shows an AFM image of the sample grown at 540 8C: the layer consists of single, loosely connected hexagonal columns with very smooth tops. Here, as on all the AFM images given below, the left side (a) shows the 3-dimensional view and the right side (b) presents the 2-dimensional view.

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5 Growth and Properties of InN

Influence of growth temperature on growth rate and RMS roughness. qTEIn = 0.35 sccm, qN2 = 1.8 sccm, PCARS = 440 W. InN nucleation.

Fig. 5.7

Fig. 5.8 AFM image of sample CUI 572. Tgrowth = 540 8C, qTEIn = 0.33 sccm, qN2 = 1.8 sccm, PCARS = 440 W.

5.3.4.2 Influence of V/III Ratio

Figure 5.9 shows the RMS roughness for two different areas as a function of V/III ratio for the case of GaN nucleation. In both cases, the roughness decreases only slightly with increasing V/III ratio. The appearance of the surface, however, is quite different for different V/III ratios. The AFM images of two samples with different V/III ratios are shown in Figs. 5.10 and 5.11. For low V/III ratios, one obtains hexagonal columns again. For the case of InN nucleation the picture is somewhat different (Fig. 5.12). There is considerable scatter in the data, but it seems that optimum surface quali-

5.3 Growth of InN by Metalorganic Molecular Beam Epitaxy

Fig. 5.9

Influence of V/III ratio on RMS roughness. Tgrowth = 500 8C.

Fig. 5.10 AFM image of sample CUI 294 with RV/III = 0.2. Tgrowth = 500 8C, qTEIn = 0.6 sccm, qN2 = 0.6 sccm, PCARS = 440 W.

ty can be obtained for a V/III ratio of 0.53 with an RMS roughness as low as 0.29 nm. Figure 5.13 shows the AFM image of the optimized sample. Still, an hexagonal structure can be seen.

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5 Growth and Properties of InN

Fig. 5.11 AFM image of sample CUI 312 with RV/III = 0.98. Tgrowth = 500 8C, qTEIn = 0.2 sccm, qN2 = 1.8 sccm, PCARS = 440 W.

Fig. 5.12

Influence of V/III ratio on RMS roughness. Tgrowth = 500 8C.

Fig. 5.13 AFM image of sample CUI 486 with RV/III = 0.53. Tgrowth = 500 8C, qTEIn = 0.2 sccm, qN2 = 1.05 sccm, PCARS = 440 W.

5.3 Growth of InN by Metalorganic Molecular Beam Epitaxy

5.3.5

Dependence of Structural and Electrical Properties of InN Grown by MOMBE on V/III Ratio

InN films were grown with different V/III ratios and subsequently characterized by Raman spectroscopy, X-ray diffraction (XRD), and Hall-effect measurements. All samples were grown with an InN nucleation layer at 500 8C. It was found that the structural, electrical, and luminescence properties of InN grown by MOMBE show a marked dependence on V/III ratio. In general, an improvement of layer quality with increasing V/III ratio was observed.

5.3.5.1 Raman Measurements

x (E2) [cm–1]

FWHM [cm–1]

Room-temperature Raman spectra were recorded in a backscattering geometry in which E2 (high) and A1 (LO) symmetry modes are allowed. An Ar+ laser with a photon energy of 2.54 eV was used as the excitation source. Figure 5.14 shows the frequency x (E2) and the full width at half maximum (FWHM) of the E2 line as a function of V/III ratio. For unstrained InN, x (E2) has a value of 488 cm–1 [74]. Lower or higher values indicate tensile or compressive strain, respectively. It can be seen from Fig. 5.14 that the strain in the layers under strain changes from tensile to compressive with increasing V/III ratio. At a V/III ratio of 0.53 the linear fit curve for xE2 reaches the strain-free value, indicating that the growth of unstrained layers is possible. At exactly this V/III ratio the optimum surface morphology was obtained (Fig. 5.13). The low FWHM values for the E2 line suggest a high crystal quality of the layers. Increasing the V/III ratio leads to an increase in the line widths.

Fig. 5.14

Influence of V/III ratio on position and FWHM of the Raman E2 line.

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5 Growth and Properties of InN

5.3.5.2 XRD Measurements

XRD measurements were done in two different ways. A one-crystal CDMAX/RC diffractometer based on a high-brightness source was used to record H-2 H scans of the (0002) peak. A three-crystal spectrometer was used to obtain rocking curves (xH scans) of the (0002) peak. The FWHM of this line gives the deviation of the crystallites from the surface normal. Figure 5.15 shows the FWHM values for both the H-2 H scan and the xH scan. In both cases, the line widths drop with increasing V/III ratio, pointing to improved crystal quality. This seems to contradict the Raman results. However, one has to keep in mind that the X-rays penetrate the whole layer under study, whereas the penetration depth of the Ar+ laser does not exceed 200 nm.

FWHM (x-h) [']

264

Fig. 5.15

Influence of V/III ratio on the FWHM of the XRD scans.

5.3.5.3 Hall Measurements

Electron concentration and electron mobility of the samples were estimated by Hall measurements using the Van der Pauw geometry at room temperature (Fig. 5.16). The electron mobility increases with increasing V/III ratio, reaching a maximum value as high as 1900 cm2 V–1 s–1, indicating an improved crystal structure. The obtained maximum mobility is among the best values ever reported for InN. For the carrier concentration, a general improvement with increasing V/III ratio is found as well. However, whereas the improvement is very marked for V/ III ratios below 0.5, it seems to saturate at a value around 1019 cm–3 for higher V/ III ratios.

5.4 Metalorganic Vapor Phase Epitaxy of InN

Fig. 5.16

Influence of V/III ratio on the electrical properties of the samples under

study.

5.3.6

Summary

To summarize, this section has presented the growth of InN layers by metalorganic molecular beam epitaxy on nitridated c-plane sapphire. A thin nucleation layer of either InN or GaN was used in order to improve surface morphology, with InN giving better results. The growth temperature and the V/III ratio were identified as the most important growth parameters. For an appropriate choice of growth procedure, continuous and smooth films could be obtained. Both tensile and compressive strain was observed by Raman spectroscopy, depending on V/III ratio. Even strain-free layers with excellent surface morphology could be grown. In general, improvements in structural and electrical properties with increasing V/III were stated. InN layers with a carrier concentration of 8 ´ 1018 cm–3 and electron mobility of 1900 cm2 V–1 s–1 at 300 K were successfully grown.

5.4

Metalorganic Vapor Phase Epitaxy of InN 5.4.1

Introduction

In this section, the conventional MOVPE of InN using TMIn and NH3 as source materials is described. The effects of major growth parameters, such as growth temperature, growth pressure, reactor design and gas flow rate, on the growth rate, surface morphology and electrical properties of MOVPE InN are studied. Surface morphology and growth rate are found to be strongly dependent on

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growth temperature. Surface morphology is also affected by the reactor design. Electrical properties of the grown InN are shown to depend on growth temperature, growth pressure, and NH3/TMIn molar ratio. The enhanced NH3 decomposition during growth seems to be essential in improving electrical properties. As a result, InN films with a carrier concentration of the order of 1018 cm–3 and with an electron mobility of 730 cm2 V–1 s–1 were successfully grown for the first time by using atmospheric pressure growth. 5.4.2

Experimental

Using an MOVPE system with a horizontal reactor, InN was grown on a-Al2O3 (0001) substrates at 450–650 8C under a pressure of 76 and 760 Torr. As sources, TMIn (10 8C, 200 sccm) and NH3 (6–9 slm) were used, and N2 was the carrier gas. Two different designs of the horizontal reactor were used. Figure 5.17 shows the cross-sectional views of the horizontal reactors used [75]. Both reactors consist of a quartz tube (with a diameter of 54 mm), but the reactant-gas flow-spacing between the susceptor and the ceiling of the quartz chamber are different. Compared with the Type A reactor, Type B has a smaller flow-spacing (14 mm for Type B and 31 mm for Type A). TMIn is introduced with the N2 carrier gas through the lower entrance of the reactor, and NH3 is introduced through the upper one.

N2 +TMIn

Fig. 5.17 Cross-sectional views of the horizontal reactors used in the study.

Fig. 5.18 Temperature distributions in the susceptor along the gas flow direction.

5.4 Metalorganic Vapor Phase Epitaxy of InN

An 18-cm long susceptor with a 4.6-cm width is used. Figure 5.18 shows the temperature distribution in the susceptor along the gas flow. The temperature is highest at a distance of 3–5 cm from the upstream end, and then it decreases with increasing distance from the upstream end. The growth temperature Tg corresponds to the highest value in the susceptor temperature distribution shown in Fig. 5.18. 5.4.3

Surface Morphology and Growth Rate of MOVPE InN

Surface morphology of the grown InN strongly depends on the growth temperature. Figure 5.19 shows the AFM images of InN films grown at different temperatures using the Type A reactor [76]. When the InN film is grown at a temperature less than 550 8C, three-dimensional growth is observed with many small grains on the surface, as shown in Fig. 5.19 a. This is a characteristic feature of InN films with a columnar fibrous structure. At 630–650 8C, a continuous film with enhanced two-dimensional growth is obtained, as shown in Fig. 5.19 b and c. For the film grown at 650 8C, many pits are formed on the enlarged grain surface. Such pits seem to be formed by thermal etching during the growth at such a high temperature. Thus, high-temperature growth is efficient in enhancing grain growth and/or two-dimensional growth of InN. Surface morphology of MOVPE InN has also been found to be markedly dependent on the reactor design. Figure 5.20 shows the AFM images of InN films grown at 500 or 600 8C using the Type A or Type B reactor [75]. It has been found

Fig. 5.19 Surface morphology (AFM image) for InN films grown using the Type A reactor

at a different temperature. Growth pressure is 0.1 atm a 500 8C; b 600 8C; c 650 8C.

Fig. 5.20 AFM images for InN films grown at 500 or 600 8C using the Type A or Type B re-

actor. a Type A, 500 8C; b Type A, 600 8C; c Type B, 500 8C; d Type B, 600 8C.

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5 Growth and Properties of InN

that the Type B reactor brings about a larger grain size of grown InN than does the Type A reactor. When growth takes place at 600 8C, differences in the morphology of grown films between the two reactors are emphasized. As can be seen from Fig. 5.20 d, the film grown at 600 8C using the Type B reactor has very large grains with a smooth surface, showing that 2D growth is extremely enhanced. It should be noted that, at 600 8C, 2D growth is enhanced in spite of the increase in growth rate. As described below, the reason for the enhanced 2D growth in the Type B reactor can be understood through the investigation of the NH3/TMIn molar ratio dependence of the surface morphology of films for each reactor. Figure 5.21 shows the surface morphology of InN films grown using the Type A reactor with different NH3/TMIn molar ratios. As can be seen in the figure, 2D growth is enhanced even with the Type A reactor as the NH3/TMIn is decreased. When the NH3/TMIn ratio is reduced to 1.8 ´ 104, a film with grains as large as those for the Type B reactor (Fig. 5.20 d) is obtained, as seen in Fig. 5.21 c, although many pits are formed on the surface. Thus, even with the Type A reactor, enhanced 2D growth of InN can be attained by reducing the NH3/TMIn ratio. In Ref. [77] it was reported that the Ga-rich condition brought about a 2D growth mode in the MBE growth of GaN. Therefore, it is reasonable to consider in this case that the 2D growth of InN under the low NH3/TMIn ratio condition is due to the realization of an In-rich growth condition. An NH3 flow with a higher velocity is heated less effectively and then decomposes less effectively. Therefore, the mechanism for the less effective NH3/TMIn ratio in the Type B reactor is a reduced NH3 decomposition rate, which occurs because the smaller spacing results in a higher gas velocity. The data given below were obtained for the films grown with the Type A reactor. The growth rate is also markedly dependent on the growth temperature. Figure 5.22 shows the TMIn supply dependence of growth rate of InN at different growth temperatures [78]. One can see that the growth rate in the temperature range of 500–600 8C increases with increasing growth temperature even when the TMIn supply is constant, and shows a saturation against the increase in TMIn supply. At around 650 8C, on the other hand, the growth rate increases with increasing TMIn supply up to at least 28 lmol min–1. In this case, the growth rate seems to be lower than that expected from those at low temperatures (500–

Fig. 5.21 Surface morphology of InN films grown at 600 8C using the Type A reactor with

different NH3/TMIn molar ratios: a 7.5 ´ 104; b 4.5 ´ 104; c 1.8 ´ 104.

5.4 Metalorganic Vapor Phase Epitaxy of InN

600 8C). The dotted line in Fig. 5.22 shows the relationship between the growth rate and TMIn supply, which is obtained by extrapolating the low-temperature growth rates. The difference between the dotted line and the values at 650 8C is thought to be due to the decomposition of grown InN at this high temperature. For the quantitative discussion of the growth rate, the data given by the dotted line will be used as growth rates at 650 8C. The increase in the growth rate at 650 8C with increasing TMIn supply means that InN growth is limited by TMIn supply. The growth-rate saturation in the temperature range 500–600 8C shows that the growth rate is governed by NH3 supply rather than by TMIn supply in this temperature range. This seems to be due to a considerably lower decomposition rate of NH3 at 500–600 8C, and the growth-rate saturation is to be attributed to deficiency of active nitrogen. The increase in the growth rate with temperature at 500–600 8C is due to the increase in NH3 decomposition rate. In Fig. 5.23, saturated growth rate at each temperature is plotted against reciprocal temperature (1/T) [78] together with data on thermal decomposition of NH3 reported in Ref. [79]. Since no saturation of growth rate occurs at 650 8C for a TMIn supply up to

Fig. 5.22 Growth rate of InN at a different growth temperature as a function of TMIn supply. Growth pressure is 0.1 atm.

Fig. 5.23 Growth rate of InN as a function of 1/Tg. Signal intensity of N2 produced by thermal cracking of NH3 reported in Ref. [79] is also shown.

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5 Growth and Properties of InN

28 lmol min–1 (see Fig. 5.22), a tentative value of 1000 nm h–1, which may be underestimated, is used as a saturated growth rate at 650 8C. From these plots, activation energies of 0.7 and 0.8 eV are obtained for growth rate and thermal decomposition rate of NH3, respectively. Both are in good agreement with each other, and also with the data for NH3 decomposition on a tungsten surface (*0.9 eV) [12, 80]. Thus, it can be concluded that the growth rate at 500–600 8C is NH3 limited, and its saturation is due to a deficiency of active nitrogen even at the NH3/ TMIn ratio of 104. It is also pointed out that, by choosing growth conditions where the growth is limited by indium source supply, a growth rate as high as 0.8 lm h–1 or higher can be attained.

5.4.4

Electrical Properties of MOVPE InN

Figure 5.24 shows the growth-temperature dependence of carrier concentration and Hall mobility for InN films grown at 76 and 760 Torr [81]. As can be seen from the figure, the growth temperature has a marked effect on the electrical properties. As the growth temperature increases from 450 to 600 8C, the carrier concentration decreases appreciably and the Hall mobility increases. These improvements of electrical properties are believed to be due to the enhanced NH3 decomposition. At a temperature higher than 600 8C, electrical properties are somewhat deteriorated. Thus, the optimum growth temperature is found to be 600 8C. It can also be seen that atmospheric-pressure growth gives better electrical properties. This is due to the enhanced NH3 decomposition under the atmospheric pressure because of the low gas velocity. It should be noted that electrical properties are further improved when the dilution N2 gas flow rate is reduced from 2 to 0.5 slm, and a carrier concentration of the order of 1018 cm–3 is successfully obtained. Better electrical properties for samples grown with a low N2 dilution gas flow rate indicate that a reduced gas speed due to the reduced N2 dilution gas flow rate causes an enhanced NH3 decomposition rate, which results in a lower nitrogen vacancy concentration in InN. As shown in Fig. 5.24 a, the difference in the carrier concentration at 76 and 760 Torr becomes smaller with increasing growth temperature. This indicates that the difference in the effective NH3 decomposition rate becomes smaller as the growth temperature increases. Although the carrier concentrations for InN grown at 600 and 650 8C are comparable for 76 and 760 Torr, the Hall mobility at 650 8C is lower than that at 600 8C. This may be related to the pit formation on the InN surface, as shown in Fig. 5.19 c. For MOVPE InN films, it was reported that the carrier concentration reduces and Hall mobility increases with increasing NH3/TMIn ratio in the growth atmosphere [82]. Figure 5.25 shows the NH3/TMIn ratio dependence of carrier concentration for InN films grown at different temperatures [11]. For a growth temperature lower than 600 8C, a marked NH3/TMIn ratio dependence of the carrier concentration is found. This shows that the increase in the NH3/TMIn ratio brings about the reduction of nitrogen vacancies in InN by increasing active nitrogen in the growth atmosphere, which results in the improvement of electrical properties.

5.4 Metalorganic Vapor Phase Epitaxy of InN

Fig. 5.24 Growth temperature dependence of a carrier concentration; b electron mobility for InN films grown at 76 and 760 Torr with dif-

ferent N2 dilution gas flow rates. Data are for the samples grown at the center position of the susceptor.

Fig. 5.25 Carrier concentration of InN grown at a different temperature as a function of NH3/TMIn (V/III) ratio. Growth pressure is 0.1 atm.

Note that carrier concentration for the InN films grown at a temperature around 650 8C is independent of the NH3/TMIn ratio. This fact suggests that another mechanism governs electrical properties of InN films grown at such a high temperature. As described above, both surface morphology and growth rate for InN clearly demonstrate the change in growth reaction of InN at 600–630 8C. The growth reaction is limited by NH3 decomposition at temperatures lower than 600 8C, where electrical properties of the grown InN are governed by the active nitrogen concentration in the growth atmosphere. At temperatures higher than 630 8C, on the other hand, the growth is limited by TMIn supply, where active nitrogen concentration in the growth atmosphere is not a critical factor. At such high temperatures, however, thermal decomposition of the grown InN layer can govern its electrical properties, showing no NH3/TMIn ratio dependence of the carrier concentration. The data shown in Figs. 5.24 and 5.25 are for the samples grown at the center position of the susceptor. Figure 5.26 shows the susceptor-position dependence of electrical properties of InN films grown at different temperatures [81]. It can be

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5 Growth and Properties of InN

seen that the carrier concentration reflects the temperature distribution in the susceptor. For example, a marked increase in the carrier concentration along the susceptor for the 550 8C-grown sample is due to the temperature decrease in the susceptor (see Fig. 5.18). For the samples grown at 600 and 620 8C, a similar explanation can be given. Generally, one can say that a sample with a lower carrier concentration has a higher mobility. It is obvious from Fig. 5.26 that other parameters also affect electron mobility of InN films. Figure 5.27 shows the carrier concentration versus Hall mobility for the InN films obtained in the present study [81]. Also shown in the figure are the typical data reported for MBE and MOVPE-

Fig. 5.26 a Carrier concentration; b Hall mobility of InN films grown at different temperatures as functions of susceptor position.

Fig. 5.27 Carrier concentration versus Hall mobility for InN films in this study. Typical data reported for MBE- and MOVPE-grown InN are also shown in the figure for comparison.

5.4 Metalorganic Vapor Phase Epitaxy of InN

AFM observation of surface morphology for three samples with a different carrier concentration and electron mobility Fig. 5.28

a l = 730 cm2 V–1 s–1; b l = 700 cm2 V–1 s–1; c l = 280 cm2 V–1 s–1.

grown InN [25, 29, 83–85] for comparison. The carrier concentration of 5.8 ´ 1018 cm–3 obtained in this work is the lowest in the MOVPE-grown InN films ever reported. It should be noted that the samples of other authors (Refs. [25, 84]) and this work demonstrated a similar mobility 700–800 cm2 V–1 s–1 in spite of the difference in the carrier concentration by an order of magnitude (5 ´ 1018–5 ´ 1019 cm–3). To get information about this, AFM observations of the surface morphology were made for our samples. The surface morphologies of three typical samples are shown in Fig. 5.28. One can see that the samples with relatively smooth surfaces (Fig. 5.28 a and b) have a high mobility (700 cm2 V–1 s–1) in spite of the difference in the carrier concentrations, while the sample with a rough surface (Fig. 5.28 c) exhibits a low mobility. Thus, excellent morphology of InN is important for attaining a high electron mobility, as reported previously for MBE InN [83]. In order to minimize the residual carrier concentration, enhanced NH3 and reduced InN decompositions are needed to decrease the amount of nitrogen vacancies (which are donors). But these two parameters are a trade-off when the growth temperature is increased in the MOVPE InN using NH3. Therefore, from this viewpoint there should be an optimum growth temperature for both parameters to reduce carrier concentration, which is 600 8C. The reduced carrier concentrations of 1–2 ´ 1018 cm–3 for MBE-grown InN [29, 83] are attributed to the fact that active nitrogen can be supplied independently of the growth temperature in the MBE growth. Provided that active nitrogen is supplied independently of the substrate temperature in the MOVPE growth, further improvement of the electrical properties of grown InN will be possible. The ArF laser-assisted MOVPE, reported recently in Ref. [86], has such a potential, where NH3 is photolytically decomposed by an ArF laser (k = 193 nm) independently of the substrate temperature.

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5.4.5

Summary

To summarize, the conventional MOVPE of InN using TMIn and NH3 as source materials has been studied with an 18-cm long susceptor loaded in a horizontal reactor. Grain growth of InN has been found to be markedly enhanced by increasing growth temperature up to 630 8C and/or employing a reactor with a higher reactant-gas flow speed. From the temperature dependence of growth rate, it can be concluded that the growth rate at 500–600 8C is NH3 limited, and its saturation against the increase in the TMIn flow rate is due to deficiency of active nitrogen even at a NH3/TMIn molar ratio of 104. By choosing the growth conditions where the growth is limited by indium source supply at a temperature higher than 630 8C, a growth rate as high as 0.8 lm h–1 or more can be attained. An increase in the active nitrogen concentration in the growth atmosphere by increasing NH3 flow rate and/or by enhancing NH3 decomposition rate is effective for reducing the background carrier concentration in InN. The increase in growth temperature enhances not only the NH3 decomposition rate but also the thermal decomposition rate of the grown InN. Thus, the optimum growth temperature for InN is determined to be 600 8C for both reduced-pressure and atmospheric-pressure MOVPE. InN films with a carrier concentration of the order of 1018 cm–3 and an electron mobility of 730 cm2 V–1 s–1 were successfully grown at 600 8C for the first time by using atmospheric-pressure MOVPE.

5.5

Physical Properties of Hexagonal InN 5.5.1

Introduction

Development of new high-quality group-III-nitride-based devices requires information on fundamental properties of the materials used. The fundamental physical properties of InN have not been investigated thoroughly enough because of difficulties encountered in the growth of the layers with good characteristics. In particular, little is known about the vibrational, optical, and electronic properties of InN. Even a key parameter of InN – the band gap (EG) – has not been firmly established; so far EG values of 1.8 eV to 2.1 eV have usually been derived from the absorption spectra obtained for polycrystalline and nanocrystalline hexagonal InN [4–6, 87, 88]. No reliable data on the band-to-band photoluminescence (PL) of InN are available in the literature. Owing to recent progress in the growth techniques, perfect single-crystalline InN layers have been grown. Optical measurements on these InN layers allowed new valuable information on fundamental properties of the phonon spectrum of InN and electronic structure of this material to be obtained.

5.5 Physical Properties of Hexagonal InN

5.5.2

Lattice Dynamics of Single-Crystalline InN Layers 5.5.2.1 First-Order Raman Scattering

The knowledge of the phonon spectrum is necessary for a deeper insight into transport and thermal properties, as well as phonon-assisted optical transitions. Information on long-wavelength phonons is typically obtained by Raman scattering and IR spectroscopy, which are accurate and convenient techniques. Hexagonal InN crystallizes in the wurtzite structure with four atoms in the unit cell and belongs to the C46v (C63mc) space group. According to the factor group analysis at the C point, phonon modes in hexagonal InN belong to the irreducible representations: Cac + Copt = (A1 + E1) + (A1 + 2 B1 + E1 + 2 E2). Among the optical phonons, the A1 and E1 modes are both Raman and IR active, the E2 modes are only Raman active, and the B1 modes are silent [89]. There are six optical modes A1(TO), A1(LO), E1(TO), E1(LO), E2 (high), and E2 (low) active in the first-order Raman scattering. In order to obtain detailed information from Raman and IR measurements, samples with different orientations of the InN optical axis with respect to the substrate plane were prepared by PAMBE. When the basal or c-plane (0001) of sapphire was used, the optical axis of the InN layer was normal to the substrate surface. However, when InN was deposited on the r-plane …1102† of sapphire, the layer hexagonal axis was parallel to the substrate plane and had a fixed orientation. The availability of two sets of samples was important for the observation of all allowed optical phonons and their symmetry assignment both in Raman and IR measurements. Only InN films with hexagonal structure, showing no traces of other polymorphs, as determined by X-ray measurements, were investigated. Raman scattering was measured at room and cryogenic temperatures in a backscattering configuration using excitation energies from 1.83 eV to 2.54 eV. The scattering geometries used in the experiment are listed in Table 5.3. The z direction is parallel to the hexagonal axis, and x and y are mutually orthogonal and oriented in an arbitrary manner in the substrate plane. The spectral resolution was typically 3 cm–1. The IR reflection spectra were measured in the 200–4000 cm–1 range at an incidence angle of 208. The data were analyzed using the Kramers-Kronig procedure. Room temperature-polarized first-order Raman spectra at an excitation energy of 2.54 eV for nominally undoped InN layers grown on sapphire substrates of two orientations are shown in Figs. 5.29 and 5.30. As shown by analysis of these spectra, the measured first-order Raman spectra were consistent with the selection rules for the wurtzite structure [89]. It is seen that, in addition to two E2 and A1(LO) modes allowed by polarization selection rules in the z…xx†z configuration (Fig. 5.29), the Raman spectrum in this

Tab. 5.3 Raman selection rules for optical phonons in wurtzite-type crystals

Scattering configuration Allowed modes

z…yy†z E2, A1(LO)

z…xy†z E2

y…zz†y A1(TO)

y…xz†y E1(TO)

y…xx†y E2, A1(TO)

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5 Growth and Properties of InN Fig. 5.29 Room temperaturepolarized Raman spectra for the nominally undoped InN layer grown on (0001) sapphire substrate. The inset shows the second-order Raman spectrum.

Fig. 5.30 First order-polarized Raman spectra for InN recorded at room temperature for the nominally undoped InN layer grown on (1102) sapphire substrate. The inset shows the imaginary part of the dielectric function for A1(TO) and E1(TO) phonons obtained by the Kramers-Kronig analysis of the IR reflectivity data in different geometries: E||c (A1(TO)) and E^c (E1(TO)).

geometry has a pronounced feature at 445 cm–1. The temperature dependence shows that this line definitely belongs to the first-order spectrum. Examination of Mg-doped InN samples with different carrier concentrations [90] has shown that this feature shifts toward lower frequencies with decreasing carrier concentration (Fig. 5.31 a). This feature can be assigned to the lower coupled plasmon-LO-phonon mode (PLP–) arising in polar semiconductors due to interaction of longitudinal optical modes through the macroscopic field with collective excitations of free carriers [91]. The shift of the IR reflection line caused by plasma oscillations from 3500 cm–1 to 800 cm–1 with increasing acceptor concentration supports this interpretation (Fig. 5.31 b).

5.5 Physical Properties of Hexagonal InN Fig. 5.31 a Raman spectra; b IR reflectivity spectra for InN : Mg epilayers with different carrier concentrations: 1– 2 ´ 1020 cm–3; 2–1 ´ 1020 cm–3; 3–5 ´ 1019 cm–3; 4–1 ´ 1019 cm–3.

The IR reflectivity for InN samples grown on (0001) and (1102) substrates was also measured. Our IR data for A1(TO) at 448 cm–1 and E1(TO) at 476 cm–1 correlate well with the Raman measurements (see the inset in Fig. 5.30). Thus, all the six Raman-active modes in the spectra of InN have been measured and assigned. The fact that five of them were observed in the same InN sample grown on the …1102† sapphire substrate is extremely important for obtaining a self-consistent picture of the behavior of optical phonons in InN. A good agreement of the polarized Raman spectra with the selection rules for the wurtzite structure demonstrates the high quality of the InN samples. The high quality is also evidenced by small widths of all the Raman lines (6.2 cm–1 for E2 (high) and 11.6 cm–1 for A1(LO)). The lattice dynamics of hexagonal InN has been studied experimentally by several groups using Raman scattering [92–96] and infrared spectroscopic ellipsometry [97]. Table 5.4 summarizes the data on the Brillouin zone-center phonons. Our experimental data are in satisfactory agreement with the published data for the zone-center modes detected by other authors. The difference in the positions of our peaks and those reported in Refs. [92, 93, 95] can be explained by different strains of InN thin films grown on foreign substrates. It is interesting to note that the position of the strain-sensitive E2 (high) mode measured in oriented platelets of InN [96] coincides exactly with that in our InN samples. This suggests that our epilayers are strain relaxed. Theoretically, the phonon frequencies for hexagonal InN were studied by using a modified valence-force model, state-of-the-art density-functional perturbation theory, and first-principles calculations [95, 96, 98, 99]. Theoretical calculations of phonon frequencies in InN show good agreement with experimental data (see Table 5.4). Assuming that the dielectric constant at frequencies much higher than the lattice vibration frequencies, e1 , is isotropic and equals 8.4 [100], we estimated static dielectric constants of InN using the Lyddane-Sachs-Teller relation (e0 =e1 ˆ x2LO =x2LO ). The constants were found to be e?0 ˆ 13:1 and e==0 ˆ 14:4 for the ordinary and extraordinary directions, respectively. Note that a different val-

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5 Growth and Properties of InN Tab. 5.4 Frequencies and FWHM of optical phonons obtained from Raman and IR reflection

measurements Phonon mode Experiment Our studies [32] Ref. [92] Ref. [93] Ref. [94] Ref. [95] Ref. [96] Ref. [97] Calculations Ref. [95] Ref. [96] Ref. [98] Ref. [99]

E low 2

A TO 1

E TO 1

E high 2

A LO 1

E LO 1

B low 1

B high 1

87

447

475

220

565

480 440 445 443

476

570

200

540

472 477

586 596 590 580 590 588 590

593

87 88

488 495 491 488 490 488 491

443 440 443 449

470 472 467 457

492 483 483 485

589

605

586 587

595 596

202 270 225 217

568 530 576 566

93 104 83 85

ue of e1 ˆ 5:8 for InN can be found in the literature [94]. This means that at present the absolute values of e==0 and e?0 are not firmly established. However, the ratio between the static dielectric constants is independent of e?, and it was estimated to be e?0 =e==0 ˆ 0:91 in our experiments.

5.5.2.2 Phonon Dispersion in InN

To simulate the lattice dynamics of InN, a phenomenological model based on the pair-wise interatomic potentials and rigid-ion Coulomb interaction was invoked [101]. The ionic charges were chosen to reproduce the observed LO–TO splitting. The short-range potentials also accounted for the second-neighbor contributions. The potential parameters were determined by fitting the calculated C point frequencies and elastic constants to the experimental values. The calculated phonon dispersion curves along the major symmetry directions of the Brillouin zone and phonon density-of-states (DOS) function are plotted in Fig. 5.32. It can be seen that the InN phonon spectrum consists of two regions separated by a wide gap. The lower region (0–230 cm–1) includes acoustic and low-frequency B1 and E2 optical branches, while the upper region (450–600 cm–1) is associated with high-frequency optical vibrations. On the whole, the phonon spectrum of InN, in contrast to AlN, is similar to that of GaN [101–103]. This is not surprising since the dynamics of both lattices, due to a large difference between the cation and anion masses, is mainly governed by the motion of nitrogen atoms. Recently it has been shown that the phonon DOS functions of GaN and AlN can be extracted from Raman spectra of strongly disordered samples [101]. The same approach was used to check the correctness of the model calculations for InN. To this end, N+-irradiated (energy of

5.5 Physical Properties of Hexagonal InN Fig. 5.32 Calculated phonon dispersion curves and phonon DOS function for hexagonal InN. The disorder-induced Raman spectrum obtained at 7 K for N+-implanted InN is also shown.

ions – 30 keV, dose – 5 ´ 1014 ion cm–2) InN samples were investigated. The spectra were recorded at T = 7 K to suppress the phonon occupation effect. As seen from Fig. 5.32, the major features of the calculated DOS function for InN and the experimental DOS extracted from the Raman spectra of N+-irradiated InN sample correlate well in the entire spectral region, thus proving the validity of our model calculations. In a more recent paper [98] state-of-the-art density-functional perturbation theory was employed to calculate the phonon dispersion relations and DOS function for wurtzite InN. The results obtained by our phenomenological model [32] and ab initio calculations [98] correlate extremely well. The lifetime of LO phonons is a governing factor in the hot-phonon-related effects, and, hence, the knowledge of this parameter is of crucial importance for development of high-speed devices. The decay processes of LO phonons in III-nitrides have been studied insufficiently. An analysis of the calculated phonon dispersion curves leads to the conclusion that three-phonon channels of decay of LO phonons into two LA (TA) phonons with equal energies are forbidden in InN due to the fact that xLO > 2 xLA, TA in the entire spectral range [98]. This may affect the lifetimes of LO phonons, and hence determine the hot-phonon-associated processes, which play an important role in transport properties of hot carriers. Using the calculated phonon DOS, the lattice specific heat of InN at constant volume Cv was evaluated. Figure 5.33 shows the calculated temperature dependence for Cv, together with the measured specific heat at a constant pressure Cp taken from [104]. It should be noted that, according to [104], the difference Cv–Cp under normal pressure can be neglected. Our calculations agree perfectly with the experimental data reported in [104]. The Debye temperature hD as a function of temperature (see the inset in Fig. 5.33) was calculated in a similar manner to that done for GaN [103]. Our estimate hD ˆ 580 K at 150 K is in excellent agreement with hD ˆ 610 K derived from the measured specific heat [104]. It has been found that the Debye temperature hD of InN at 0 K is 370 K. (Note that hD ˆ 800 K for AlN and hD ˆ 570 K for GaN [103]).

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5 Growth and Properties of InN Fig. 5.33 Calculated (solid line) and measured (full circles) lattice-specific heat for InN. The inset shows the calculated temperature dependence of the Debye temperature.

5.5.3

Electronic Structure of Single-Crystalline InN Layers

The electronic structure of single-crystalline InN layers was carefully studied by means of optical absorption, photoluminescence (PL), photoluminescence excitation (PLE), and photomodulated reflectance spectroscopy.

5.5.3.1 Characterization of Samples

Undoped InN epilayers were grown on (0001) sapphire substrates by PAMBE, MOMBE, and MOVPE techniques [24, 27, 31, 105]. A set of InxGa1–xN layers (0.36 < x < 1) was grown by PAMBE [35]. The composition and crystalline structure of the samples were characterized by a large number of techniques. Only InN and InxGa1–xN films with hexagonal structure, showing no traces of other polymorphs, as determined by X-ray and Raman measurements were investigated. From symmetric (0002) and asymmetric …1124† Bragg reflections, lattice parameters c and a were found to be c = 5.7039 Å and a = 3.5365 Å, respectively. In the most perfect InN samples, the FWHMs for x and H-2 H scans at the (0002) reflection were typically in the ranges 250–300 arcsec and 50–60 arcsec, respectively. Polarized Raman spectra of InN and related alloys showed good agreement with the selection rules for the hexagonal symmetry. The phonon line widths of InN samples corresponded to that of a well-ordered crystal lattice. Atomic force microscopy measurements did not reveal any pronounced columnar structure of the samples studied. According to the Auger spectroscopic and Rutherford backscattering data, the oxygen concentration in the samples was about 1%. The Hall concentration of electrons n ranged from 6 ´ 1018 to 4 ´ 1019 cm–3, and the highest electron mobility l was found to be *1900 cm2 V–1 s–1 (for MOMBE-grown InN with n = 8 ´ 1018 cm–3).

5.5 Physical Properties of Hexagonal InN

5.5.3.2 Absorption and Luminescence in InN

The absorption coefficients a (x) for MOVPE, MOMBE, and PAMBE-grown InN samples at 300 K are shown in Fig. 5.34 a. The a (x) spectra were calculated from the transmission spectra with corrections for multiple reflections. The layer thickness was measured by means of scanning electron microscopy. It can be seen that a (x) for InN samples measured at 300 K rapidly reaches values of the order of a (x) > 4 ´ 104 cm–1 at the photon energy close to 1 eV. This high value of the absorption coefficient is typical of an interband absorption in direct band gap semiconductors. From measurements of the absorption edges, it can be concluded that the band gap (EG) value of hexagonal InN is in the range of 0.8–1.0 eV. Possible reasons for the strong difference in EG observed for the samples may be the Burstein-Moss shift associated with different doping levels and/or strains in the samples. Figure 5.34 b shows PL spectra at 77 K for the samples discussed above. The spectra display asymmetric bands with FWHMs ranging from 60 meV to 110 meV. The maxima of these bands are shifted toward lower energies relative to the EG values estimated from the absorption data. The luminescence bands were found to be wider in the samples with a higher carrier concentration. Analysis of the PL spectra in the temperature range 300–4.2 K (Fig. 5.35) showed that, as temperature decreases, the PL band narrows, its high-energy edge becomes steeper, and the intensity substantially grows. The observed behavior of the PL band is typical of radiative interband recombination in heavily doped semiconductors.

Fig. 5.34 a Absorption edge; b photoluminescence spectra of InN samples with different electron concentrations: 1 – MOVPE-grown

sample J702; 2, 3 – MOMBE-grown samples CUI 308 and CUI 489; 4 – PAMBE-grown sample W251.

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Fig. 5.35

Temperature dependences of the luminescence band parameters.

5.5.3.3 Luminescence and Absorption of Crystals with High Electron Concentrations

The high-energy PL band in n-type heavily doped semiconductors results from recombination of degenerate electrons with photoholes near the top of the valence band. The shape of this PL band has two characteristic features. The first is a high-energy wing that exhibits an exponential decrease in the region of (x– EG(n)) ³ EF due to a decrease in the electron population in accordance with the Fermi function f(x–EG(n)–EF) = 1/[exp {(x–EG(n)–EF)/kT} + 1]. Here, EG(n) is the carrier-concentration-dependent parameter that approaches the band gap EG(n) ? EG at vanishing concentration n ? 0, and EF is the Fermi energy of the degenerate electrons. The second feature is a low-energy wing of the PL band at x < EG(n), which typically shows the Urbach tail. This tail can overlap with the PL bands related to recombination of electrons with holes in deeper localized states. Figure 5.36 shows the experimental and calculated luminescence bands in GaAs, GaN, and InN crystals with free electron concentrations of about 1 ´ 1019 cm–3. The valence-conduction band diagram given in Ref. [106] leads to the following shape of the PL band in the energy region x > EG(n) I…x†  ‰x

EG …n†Šc=2 f …x

EG …n†

EF †

…1†

where c = 1 if only vertical interband transitions are allowed, and c = 4 if the momentum conservation law is completely broken as a result of the influence of defects and/or impurities on the hole or electron states. The experimental band shape for GaAs can be described well with c = 1, whereas for GaN crystals c equals 4. For InN, c increases from 2 to 4 with increasing concentration of free carriers.

5.5 Physical Properties of Hexagonal InN

High doping levels cause changes in the interband absorption coefficient due to the Burstein-Moss effect. In analogy with Eq. (1), the interband absorption coefficient can be expressed as a‰…x†  ‰x

EG …n†Šc=2 ‰1

f …x

EG …n†

EF †Š :

…2†

The experimental luminescence spectrum and absorption coefficient of the InN sample with n = 6 ´ 1018 cm–3 at T = 300 K are presented in Fig. 5.37 a together with corresponding curves calculated through Eq. (1) and (2). The same parameters are used in both expressions. It is seen that there is a good agreement between experimental and calculated data. Therefore, it can be concluded that the optical ab-

Fig. 5.36 Experimental and calculated luminescence bands in a heavily doped GaAs; bGaN; c InN crystals with charge carrier concentrations of 1.1 ´ 1019, 0.9 ´ 1019, and 0.9 ´ 1019 cm–3, respectively. Points show experimental data; the solid lines are calculations.

Fig. 5.37 a Experimental and calculated luminescence bands and absorption coefficients in InN (n = 6 ´ 1018 cm–3) at T = 300 K. Experimental and calculated luminescence bands at 77 (curves 1) and 300 K (curves 2); b in InN (n = 6 ´ 1018 cm–3); c in GaAs (n = 4.3 ´ 1018 cm–3). Points show experimental data; the solid lines are calculations.

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5 Growth and Properties of InN

sorption and luminescence bands of InN crystals have characteristics typical of interband transitions. Note that at high electron concentrations the absorption edge is well above the fundamental band gap (approximately by a value equal to the Fermi energy).

5.5.3.4 Temperature Dependence of the Luminescence Band Shape

Modifications of the luminescence band shape with varying temperature are caused by redistribution of electrons over the energy levels in accordance with the Fermi function and also by the temperature shift of EG(n). The PL bands of InN and GaAs at 77 and 300 K are presented in Fig. 5.37 b and c. A comparison of experimental spectra with calculated shapes allows one to find the temperature variation of parameter EG(n). The obtained temperature shift of EG(n) for the GaAs crystal is about 70 meV, consistent with the band-gap narrowing in this temperature interval. For the InN crystal, the shift is about 23 meV, which can also be related to the temperature-dependent band-gap narrowing. No anomalous temperature behavior of the PL band similar to that described in Ref. [36] was observed in our InN experiments.

5.5.3.5 Concentration Dependence of PL Band and Absorption Coefficient

The PL bands obtained at 77 K for the samples with different electron concentrations and the fitting curves obtained from Eq. (1) are shown in Fig. 5.38. According to Hall measurements, the free carrier concentrations in samples 1–4 are 6 ´ 1018, 9 ´ 1018, 1.1 ´ 1019, and 2.2 ´ 1019 cm–3, respectively. The temperature estimated from the exponential slope of the high-energy wing of the PL band is close to the measured temperature, except for InN sample 4. This discrepancy is probably due to a strong layer inhomogeneity for the sample with the highest carrier concentration.

Fig. 5.38 Semilog PL spectra of InN layers with different charge carrier concentrations: (1) 6 ´ 1018 cm–3; (2) 9 ´ 1018 cm–3; (3) 1.1 ´ 1019 cm–3; (4) 2.2 ´ 1019 cm–3. Points show experimental data; the solid lines are calculations. The inset shows the shift of the optical absorption edge due to the BursteinMoss effect for the same samples.

5.5 Physical Properties of Hexagonal InN

The Fermi energies EF estimated from these PL spectra are 95, 147.5, 167.5, and 245 meV in samples 1–4, respectively. Assuming an isotropic electron band, EF as a function of electron concentration n/n0 (n0 = 1 ´ 1018 cm–3) is given by EF ˆ 3:58…m0 =m †…n=n0 †2=3 meV :

…3†

Comparison of the Fermi energies of GaAs, InN, and GaN crystals leads to the conclusion that the electron effective mass in InN lies between those in GaAs and GaN. The electron concentrations for InN samples calculated from the Fermi energies (Eq. (3)) on the assumption of an effective mass of m* = 0.1 m0 are in good agreement with the Hall data. The shift of the optical absorption edge due to the Burstein-Moss effect for the same samples is shown in the inset in Fig. 5.38. It is seen that the shifts are considerable in this concentration range due to large values of EF. As follows from Eq. (1), the low-energy onset of the PL fitting curves defines EG(n). It has been found that EG(n) weakly depends on the electron concentration and is close to 0.65 eV. An extrapolation of EG(n) to n ? 0 gives the estimate of the true band gap of InN as EG = 0.69 eV [107]. The value of EG*0.69 eV is slightly smaller than EG*0.8 eV suggested by recent calculations with the fixed pd repulsion [39].

5.5.3.6 Photoluminescence Excitation and Photomodulated Reflectance Spectra

The PLE spectrum measured at the PL band maximum together with the PL and absorption spectra for one of the samples are shown in Fig. 5.39 a. It can be seen that the PLE spectrum behaves similarly to the absorption spectrum up to energy xmax. However, at the energy xmax, far from the absorption saturation, it displays an abrupt kink, and its intensity starts to fall. Such a behavior of the PLE spec-

Fig. 5.39 a PLE spectrum measured at the PL band maximum on one of the samples, together with the PL and absorption spectra;

b PL and photomodulated reflectance spectra obtained on one of the InN samples.

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trum can be understood if one takes into account that at energies E < xmax the photons create holes in the localized states, and at E > xmax the production of mobile holes dominates. When two mobile particles – an electron and a hole – are produced, the probability of formation of a separated e–h pair and, hence, the probability of nonradiative relaxation of each particle sharply increases. As a result, the PLE efficiency substantially decreases. The PLE results correlate with those obtained in absorption and PL studies. All three spectroscopic techniques give nearly the same band gap energies. Figure 5.39 b displays the PL and photomodulated reflectance (PR) spectra obtained for one of the InN samples. The zero point of the PR spectrum is close to the energy (x–EG(n)) = EF, and the shape of the PR spectrum indicates that the Fermi distribution of electrons is affected by photomodulation.

5.5.3.7 Optical Spectra of InxGa1–xN Layers

The InN band gap can also be estimated from optical spectra of InxGa1–xN alloys in the limit x ? 1. Figure 5.40 shows the PL and absorption spectra for some Inrich alloys (0.36 < x < 1). It is seen that the PL bands and the absorption edge shift toward higher energies as x decreases. As in InN, the maximum of the PL band in the alloys is red-shifted from the absorption edge by the value of about one half of the FWHM of the PL band. This shift is consistent with the estimate of the Burstein-Moss effect in our alloys with electron concentrations in the 4–7 ´ 1019 cm–3 range. A considerably larger Stokes shift of the PL bands in Inrich alloys was observed in Ref. [108]. EG(n) for alloys was derived by analyzing the PL band shape through Eq. (1), similar to InN. Figure 5.41 depicts EG(n) for In-rich alloys studied in this work as a function of alloy composition. The composition was estimated, according to the Vegard’s law, from the lattice constant c obtained from X-ray measurements. This

Fig. 5.40 PL spectra and absorption edges in In-rich InxGa1–xN layers ((1) x = 1; (2) 0.96; (3) 0.85; (4) 0.75; (5) 0.60; (6) 0.36).

5.5 Physical Properties of Hexagonal InN Fig. 5.41 EG(n) estimated for the In-rich alloys studied in this work (circles), and the positions of PL band maxima in Ga-rich alloys taken from Refs. [109] (diamonds), [110] (triangles), and [111] (squires) as a function of composition. The inset shows semilog PL spectra and calculated curves, obtained using Eq. (1) for the most perfect alloys: (1) x = 0.96; (2) x = 0.85; (3) x = 0.75.

figure also presents the position of the PL band maxima taken from the literature for Ga-rich InxGa1–xN alloys. The experimental points in Fig. 5.41 are fitted by a smooth curve EG = 3.493–2.843 x–bx(1–x) with the bowing parameter b = 2.5 eV. Nearly the same value of the bowing parameter (b*2.3 eV) has recently been reported in [38]. Therefore, the data obtained from PL spectra of In-rich InxGa1–xN layers confirm the small value of the InN band gap.

5.5.3.8 Wide-Gap InN-based Samples

To understand the reasons for the striking discrepancy between our data on the band gap with those cited in the literature, several samples, which were claimed to be hexagonal InN with band gaps in the region of 1.8–2.1 eV, were studied. The samples were grown by different techniques on different substrates, but all the samples had common features. The transmission spectra of these samples were strongly affected by plasma reflection in the IR region, pointing to very high charge carrier concentrations, up to 6 ´ 1020 cm–3. The samples were polycrystalline, as deduced from very wide Xray rocking curves. The broad features of Raman spectra reproducing the phonon density-of-states function (DOS) were observed, in contrast to the sharp polarized lines in our single crystalline samples (see Fig. 5.42). Therefore, both X-ray and Raman data suggest the presence of structural defects in high concentrations. Chemical composition analysis by Auger spectroscopy and the Rutherford backscattering technique revealed very high oxygen contents in wide-gap samples, up to 20 at%, much higher than in our samples. It can be supposed that it is oxygen that is responsible for high defect concentrations. In this case an increase of the band gap in wide-gap samples can be caused by formation of oxynitrides, which have much larger band gaps than that of InN. However, the Burstein-Moss effect in polycrystalline samples with high charge carrier concentrations may also be responsible for sizable changes in the band gap.

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5 Growth and Properties of InN Fig. 5.42 Raman spectra of single crystalline InN (1) before; (2) after implantation by N+; (3) calculated phonon DOS function for InN; (4) Raman spectra of “wide-gap” InN with EG*1.8 eV; (5) EG*1.95 eV.

Fig. 5.43 PL spectra in InN samples before (curve 1) and after (curve 2) annealing in vacuum; points show experimental data; the solid lines show fitting curves obtained using Eq. (1). nH – Hall data, nC – calculations.

5.5.3.9 Postgrowth Treatment of InN Samples

(a) Some of the samples were subjected to annealing at 490 8C for 5 h in vacuum. As can be seen from Fig. 5.43, treatment results in a substantial decrease in the PL band FWHM and increase in the high-energy wing slope. This transformation suggests that the electron concentration decreases, and the distribution of the electron density over the sample becomes more uniform. As revealed by Hall measurements, annealing results in a decreasing charge carrier concentration, too. (b) Annealing in an oxygen environment leads to formation of optically transparent oxynitrides whose band gap depends on the oxygen concentration in the

5.5 Physical Properties of Hexagonal InN

sample and approaches 2 eV at oxygen concentrations of about 20%. The absorption and luminescence spectra in such samples demonstrate a wide Urbach-like tail of localized states spreading over the entire region below the band edge. X-ray and Raman measurements revealed formation of alloys of the InN-In2O3 type. It can be inferred from the luminescence spectra that the samples saturated partially with oxygen still contain mesoscopic-size InN fragments. The InN PL band in such samples is slightly shifted towards higher energies, which can be attributed to the size quantization effect. The final stage of oxidation is the formation of In2O3 crystals.

5.5.3.10 Proton Irradiation

Information on point defects in n-InN has been obtained in radiation experiments [112]. Irradiation of n-InN layers with protons at 150 keV results in a substantial increase in the charge carrier concentration due to production of point defects with shallow donor states. The characteristic features of defect production suggest that these defects, which are stable at temperatures up to 200 8C, are native. They can be tentatively identified as vacancies on the nitrogen sublattice. This conclusion agrees well with theoretical predictions [113]. 5.5.4

Summary

To summarize, this section has presented data for all long-wavelength optical phonons in hexagonal InN. Results of calculations of phonon dispersion curves along the major symmetry directions of the Brillouin zone and phonon DOS in this material have been given. The ratio between the static dielectric constants of InN for ordinary and extraordinary directions has been estimated. Results of calculations of the lattice specific heat of InN over a wide temperature range have been presented. It has been inferred from analysis of optical absorption, PL, PLE and photoreflectivity data obtained on single-crystalline hexagonal InN, that the true band gap of InN is EG*0.7 eV, which is much lower than the value of 1.89 eV reported in the literature. This finding is supported by optical studies of In-rich InxGa1–xN alloys. Studies of InN samples with EG of 1.8–2.0 eV have indicated that the increased band gap may be due to the formation of oxynitrides, which have much larger band gaps than that of InN. The Burstein–Moss effect in polycrystalline samples with high charge carrier concentrations can also be responsible for sizable changes in the band gap. We also discuss the influence of postgrowth treatment of InN crystals in order to reveal possible mechanisms of transformation of the crystal structure and the band-gap variation.

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5.6

Conclusions

In this chapter we have demonstrated that high-quality single-crystalline hexagonal InN layers with electron concentrations of 1018 cm–3 can be grown by the PAMBE, MOMBE, and MOVPE techniques. Based on the study of the effects of different growth parameters, the InN layers with superior structural, optical, and electrical properties have been obtained. The results presented form the basis for a predictive growth of high-quality InN. Some important aspects of the growth have been clarified, however, many questions still remain unclear. Excellent transport properties of InN have been confirmed. New exciting developments may result from the discovery of photoluminescence never reported before for InN. This makes this material a promising candidate for optical devices operating in the near IR region. Due to advances in the growth of InN layers, new important information on fundamental physical properties of InN has been obtained. Analysis of the optical data for a large set of single-crystalline InN samples grown by different techniques has yielded a band gap close to 0.7 eV, which is much smaller than the values reported before. Several reasons for observation of band gaps higher than 0.7 eV can be suggested. One of them is the formation of oxynitrides or alloys of the InN-In2O3 type during the layer growth due to a low efficiency of the nitrogen source. Another possible reason is a blue-shift of the absorption edge caused by a large Burstein-Moss effect due to a small InN effective mass. A combined effect of the two factors mentioned above is possible. There is no doubt that the problem of the previously overestimated band gap values for InN requires further investigations. The present review is limited mostly to the growth and properties of InN. Another area where considerable progress in the near future can be expected is related to the In-rich alloys the information on the physical properties of which is scarce at present.

5.7

Acknowledgments

The authors from Ioffe Institute would like to express their gratitude to V. Jmerik, V. Mamutin, V. Vekshin, V. Ratnikov, T. Shubina, A. Sakharov, V. Kapitonov, M. Baidakova, A. Smirnov, D. Kurdyukov, B. Andreev, and H. Feick for the fruitful cooperation in PAMBE growth and various characterization experiments, and V. Emtsev, R. Seisyan, A. Mudryi, F. Bechstedt„ E. Haller, H. Harima R. Suris, S. Permogorov, B. Novikov, M. Willander, P. Kop’ev, T. Inushima and Y. Nanishi for valuable discussions. J. Aderhold wishes to thank J. Graul and O. Semchinova for their support. A. Yamamoto would like to thank A. Hashimoto and A.G. Bhuiyan for helpful discussions and M. Adachi, K. Koide and Y. Murakami for their contributions in performing growth and characterization experiments of MOVPE InN. All the authors would like to acknowledge the invaluable help of A. Smirnov and N. Nazina in preparation of the manuscript for publication. This work was partly supported by the Russian Foundation for Basic Research and Programs of Russian Ministry of Industry, Science and Technology.

5.8 References

5.8

References 1 2 3

4 5

6

7 8 9

10 11 12

13

14 15

16

17 18

S. N. Mohammad and H. Morkoc, Prog. Quant. Electron. 20, 361 (1996). S. Nakamura and G. Fasol, The Blue Laser Diodes (Springer, Berlin, 1997). S. K. O’Leary, B. E. Foutz, M. S. Shur, U. V. Bhapkar, and L. F. Eastman, J. Appl. Phys. 83, 826 (1998). J. Hovel and J. J. Cuomo, Appl. Phys. Lett. 20, 71 (1972). K. L. Westra, R. P. W. Lawson, and M. J. Brett, J. Vac. Sci. Technol. A 6, 1730 (1998). V. A. Tyagai, A. M. Evstigneev, A. N. Krasiko, A. F. Andreeva, and V. Ya. Malakhov, Sov. Phys. Semicond. 11, 1257 (1977). T. L. Tansley and C. P. Foley, Electron. Lett. 20, 1066 (1984). T.L. Tansley and C. P. Foley, J. Appl. Phys. 59, 3941 (1986). T. J. Kistenmacher, W. A. Bryden, J. S. Morgan, and T. O. Poehler, J. Appl. Phys. 68, 1541 (1990). J. W. Trainor and K. Rose, J. Electron. Mater. Res. 3, 821 (1974). Q. Guo, O. Kato, and A. Yoshida, J. Appl. Phys. 73, 7969 (1993). O. Ambacher, M. S. Brandt, R. Dimitrov, T. Metzger, M. Stutzmann, R. A. Fisher, A. Miehr, A. Bergmaier, and G. Dollinger, J. Vac. Sci. Technol. B 14, 3532 (1996). S. Y. Karpov, Y. N. Makarov, and M. S. Ramm, Internet J. Nitride Semicond. Res. 2, Art. 45 (1997). J. Ambacher, J. Phys. D.: Appl. Phys. 31, 2653 (1998). T. Yodo, H. Ando, D. Nosei, and Y. Harada, Phys. Stat. Sol. (b) 288, 21 (2001). A. P. Lima, A. Tabata, J. R. Leite, S. Kaiser, D. Schikora, B. Schottker, T. Frey, D. J. As, and K. Lischka, J. Cryst. Growth 201/202, 396 (1999). A. Wakahara and A. Yoshida, J. Appl. Phys. 54, 709 (1989). Q. Guo, N. Yamamura, and A. Yoshida, J. Appl. Phys. 75, 4927 (1994).

19

20

21

22

23

24

25

26 27

28

29

30

31

32

A. Yamamoto, M. Tsujino, M. Ohkubo, and A. Hashimoto, J. Cryst. Growth 137, 415 (1994). T. Tsuchiya, H. Yamano, O. Miki, A. Wakahara, and A. Yoshida, Jpn. J. Appl. Phys. 38, 1884 (1999). T. Matsuoka, H. Tanaka, T. Sasaki, and A. Katsui, Inst. Symp. GaAs and Related Compounds, Karuizawa, Japan, 25–29 Sept. 1989; Inst. Phys. Conf. Ser. 106, 141 (1990). A. Yamamoto, M. Tsujino, M. Chkubo, and A. Hasimoto, Sol. Energy Mater. 53, 53 (1994). Y.-C. Pan, W.-H. Lee, C.-K. Chu, H.-C. Lin, C.-I Chiang, H. Chang, D.-S. Lin, M.-C. Lee, and W.-K. Chen, Jpn. J. Appl. Phys. 38, 645 (1999). A. Yamamoto, Y. Murakami, K. Koide, M. Adachi, and A. Hashimoto, Phys. Stat. Sol. (b) 228, 5 (2001). S. Yamaguchi, M. Kariya, S. Nitta, T. Takeuchi, C. Wetzel, and I. Akasaki, J. Appl. Phys. 85, 7682 (1999). W. E. Hoke, P. J. Lemonias, and D. G. Weir, J. Cryst. Growth 111, 1024 (1991). V. V. Mamutin, V. A. Vekshin, V. Yu. Davydov, V. V. Ratnikov, T. V. Shubina, V. V. Emstev, S. V. Ivanov, and P. S. Kop’ev, Phys. Stat. Sol. (a) 176, 247 (1999). T. Inushima, V. V. Mamutin, V. A. Vekshin, S. V. Ivanov, T. Sakon, M. Motokawa, and S. Ohoya, J. Cryst. Growth 227, 481 (2001). H. Lu, W. J. Schaff, J. Hwang, H. Wu, G. Koley, and L. F. Eastman, Appl. Phys. Lett. 79, 1489 (2001). Y. Saito, T. Yamaguchi, H. Kanazawa, K. Kano, T. Araki, Y. Nanishi, N. Teraguchi, and A. Suzuki, J. Cryst. Growth 237, 1017 (2002). J. Aderhold, V. Yu. Davydov, F. Fedler, H. Klausing, D. Mistele, T. Rotter, O. Semchinova, J. Stemmer, and J. Graul, J. Cryst. Growth 222, 701 (2001). V. Yu. Davydov, V. V. Emtsev, I. N. Goncharuk, A. N. Smirnov, V. D. Petrikov, V. V. Mamutin, V. A. Vekshin, S. V.

291

292

5 Growth and Properties of InN

33

34

35

36

37

38

39 40

41

42

43 44

45

Ivanov, M. V. Smirnov, and T. Inushima, Appl. Phys. Lett. 75, 3297 (1999). V. V. Ratnikov, V. V. Mamutin, V. A. Vekshin, and S. V. Ivanov, Phys. Solid State 43, 949 (2001). V. Yu. Davydov, A. A. Klochikhin, R. P. Seisyan, V. V. Emtsev, S. V. Ivanov, F. Bechstedt, J. Furthmüller, H. Harima, A. V. Mudryi, J. Aderhold, O. Semchinova, and J. Graul, Phys. Stat. Sol. (b) 229, R1 (2002). V. Yu. Davydov, A. A. Klochikhin, V. V. Emtsev, S. V. Ivanov, V. V. Vekshin, F. Bechstedt, J. Furthmüller, H. Harima, A. V. Mudryi, A. Hashimoto, A. Yamamoto, J. Aderhold, J. Graul, and E. E. Haller, Phys. Stat. Sol. (b) 230, R4 (2002). J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager III, E. E. Haller, H. Lu, W. J. Schaff, Y. Saito, and Y. Nanishi, Appl. Phys. Lett. 80, 3967 (2002). T. Matsuoka, H. Okamoto, M. Nakao, H. Harima, and E. Kurimoto, Appl. Phys. Lett. 81, 1246 (2002). M. Hori, K. Kano, T. Yamaguchi, Y. Saito, T. Araki, Y. Nanishi, N. Teraguchi, and A. Suzuki, Phys. Stat. Sol. (b) 234, 750 (2002). F. Bechstedt, J. Furthmüller, J. Cryst. Growth 246, 315 (2002). D .I. Slovetskii, Mechanism of Chemical Reactions in Nonequilibrium Plasma (Moscow, 1980). C. T. Foxon, T. S. Cheng, S. E. Hooper, L. C. Jenkins, J. W. Orton, D. E. Lacklison, S. V. Novikov, T. B. Popova, and V. V. Tret’yakov, J. Vac. Sci. Technol. B 14, 2346 (1996). W. C. Hughes, W. H. Rowaland Jr, M. A. L. Johnson, S. Fujita, J. W. Cook Jr, J. F. Schetzina, J. Ren, and J. A. Edmond, J. Vac. Sci. Technol. B 13, 1571 (1995). N. Newman, J. Cryst. Growth 178, 102 (1997). A. J. Ptak, M. R. Millecchia, T. H. Myers, K. S. Ziemer, and C. D. Stinespring, Appl. Phys. Lett. 74, 3836 (1999). D. C. Jordan, I. S. T. Tsong, D. J. Smith, B. J. Wilkens, and R. B. Doak, Appl. Phys. Lett. 77, 3030 (2000).

46 47

48

49

50

51

52 53

54

55 56

57

58

59

60 61

62

A. Keudell, Plasma Sources Sci. Technol. 9, 455 (2000). Y. Lifshitz, S. R. Kasi, J. W. Rabalais, and W. Ekstein, Phys. Rev. B 41, 10468 (1990). R. F. Davis, M. J. Paisley, Z. Sitar, D. J. Kester, K. S. Ailey, K. Linthicum, L. B. Rowland, S. Tanaka, and R. S. Kern, J. Cryst. Growth 178, 87 (1997). R. C. Powell, N. E. Lee, Y.-W. Kim, and J. E. Greene, J. Appl. Phys. 73, 189 (1993). R. L. Headrick, S. Kycia, A. R. Woll, J. D. Brock, and M. V. Ramana Murty, Phys. Rev. B 58, 4818 (1998). Z. Sitar, M. J. Paisley, D. K. Smith, and R. F. Davis, Rev. Sci. Instrum. 61, 2407 (1990). A. Ohtani, K. S. Stevens, and R. Beresford, Appl. Phys. Lett. 65, 61 (1994). B. Heying, R. Averbeck, L. F. Chen, E. Haus, H. Riechert, and J. S. Speck, J. Appl. Phys. 88, 1885 (2000). T. Zywietz, J. Neugebauer, and M. Scheffler, Appl. Phys. Lett. 73, 487 (1998). O. Brandt, H. Yang, and K. H. Ploog, Phys. Rev. B 54, 4432 (1996). W. L. Chen, R. L. Gunshor, J. Han, K. Higashimine, and N. Otsuka, MRS Internet J. Nitride Semicond. Res. 5S1, W3.30 (2000). W. A. Bryden, J. S. Morgan, R. Fainchtein, and T. J. Kistenmacher, Thin Solid Films 213, 86 (1992). K. Uchida, A. Watanabe, F. Yano, M. Kouguchi, T. Tanaka, and S. Hinagawa, J. Appl. Phys. 79, 3487 (1996). R. A. Fisher, A. Miehr, O. Ambacher, T. Metzger, and E. Born, J. Cryst. Growth 170, 139 (1997). Q. X. Guo, H. Ogawa, and A. Yoshida, Appl. Phys. Lett. 66, 715 (1995). S. Ivanov and P. Kop’ev, Antimonide-related strained-layer heterostructures, M.O. Manasreh (ed.) in Ser. “Optoelectronic Properties of Semiconductors and Superlattices” (Gordon & Breach, 1997), Chap. 4, p. 95. K. Uchida, A. Watanabe, F. Yano, M. Kouguchi, T. Tanaka, and S. Minagawa, J. Appl. Phys. 79, 3487 (1996).

5.8 References 63

64 65 66

67

68

69 70

71

72

73 74

75

76

77

S. V. Ivanov, P. S. Kop’ev, and N. N. Ledentsov, J. Cryst. Growth 104, 345 (1990). A. Akasaki, Jpn. J. Appl. Phys. 29, L205 (1990). S. Nakamura, Appl. Phys. Lett. 58, 2021 (1991). N. Muira, H. Ishii, A. Yamada, M. Konagai, Y. Yamauchi, and A. Yamamoto, Jpn. J. Appl. Phys. 36, L256 (1997). V. V. Mamutin, T. V. Shubina, V. A. Vekshin, V. V. Ratnikov, A. A. Toropov, S. V. Ivanov, M. Karlsteen, U. Sodervall, and M. Willander, Appl. Surf. Sci. 166, 87 (2000). R. N. Kyutt, V. V. Ratnikov, G. N. Mosina, and M. P. Shcheglov, Phys. Solid State 41, 25 (1999). `O. Metzger, R. Hopler, and E. Bot, Phil. Mag. A 77, 1013 (1998). J. S. Foord, in Chemical Beam Epitaxy and Related Techniques , edited by J. S. Foord, G. J. Davies, and W. T. Tsang (John Wiley & Sons Ltd., Chichester, UK, 1997), p. 73. S. Limpijumnong and C. G. Van de Walle, Phys. Stat. Sol. (b) 228, 303 (2001). C. Stampfl, C. G. Van de Walle, D. Vogel, P. Krüger, and J. Polmann, Phys. Rev. B 61, R7846 (2000). S. Rushworth, EpiChem Ltd., private communication. V. V. Mamutin, V. A. Vekshin, V. Yu. Davydov, V. V. Ratnikov, V. V. Emtsev, A. N. Smirnov, S. V. Ivanov, and P. S. Kop’ev, Proceedings of The 7th International Symposium “Nanostructures: Physics and Technology”, Ioffe Institute, (1999) p. 521. A. Yamamoto, M. Adachi, and A. Hashimoto, J. Cryst. Growth 230, 351 (2001). A. Yamamoto, Y. Murakami, K. Koide, M. Adachi, and A. Hashimoto, in Proceedings of the 4th International Conference on Nitride Semiconductors, Denver, USA, 2001, p 21.8. H. Okumura, K. Balakrishnan, H. Hamaguchi, T. Koizumi, S. Chichibu, H. Nakanishi, T. Nagatomo, and S. Yoshida, J. Cryst. Growth 189/190, 364 (1998).

78

79

80 81

82

83 84

85

86

87

88 89

90

91

92

M. Adachi, Y. Murakami, A. Hashimoto, and A. Yamamoto, Proc. Int. Workshop on Nitride Semiconductors, Nagoya, (IPAP Conf. Series 1, 2000) pp. 339. C. R. Abernathy: GaN and related materials, edited by S. J. Pearton (Gordon and Breach Science Publishers, 1997), Vol. 2, Chap. 2, p. 11. M. Mesrine, N. Grandjean, and J. Massies, Appl. Phys. Lett. 72, 350 (1998). A. Yamamoto, T. Tanaka, K. Koide, and A. Hashimoto, International Workshop on Nitride Semiconductors, 22–25 July, 2002, Aachen, Germany, 170-P, 2002. (To be published in Phys. Stat. Sol.) A. Yamamoto, T. Shin-ya, T. Sugiura, and A. Hashimoto, J. Cryst. Growth 189/190, 461 (1998). M. Higashiwaki and T. Matsui, Jpn. J. Appl. Phys. 41, L540 (2002). Y. Saito, N. Teraguchi, A. Suzuki, T. Araki, and Y. Nanishi, Jpn. J. Appl. Phys. 40, L91 (2001). H. Lu, W. J. Schaff, J. Hwang, H. Wu, W. Yeo, A. Pharkya, and L. F. Eastman, Appl. Phys. Lett. 77, 2548 (2000). A. G. Bhuiyan, T. Tanaka, A. Yamamoto, and A. Hashimoto, Internatinal Workshop on Nitride Semiconductors, 22–25 July, 2002, Aachen, Germany, 165-P, 2002. (To be published in Phys. Stat. Sol.). K. Osamura, K. Nakajima, and Y. Murakami, Solid State Commun. 11, 617 (1972). K. Ikuta, Y. Inoue, and O. Takai, Thin Solid Films 334, 49 (1998). C. A. Arguello, D. L. Rousseau, and S. P. S. Porto, Phys. Rev. 181, 1351 (1969). V. V. Mamutin, V. A. Vekshin, V. Yu. Davydov, V. V. Ratnikov, Yu. Kudriavtsev, B. Ya. Ber, V. V. Emtsev, and S. V. Ivanov, Phys. Stat. Sol. (a) 176, 373 (1999). G. Abstreiter, M. Cardona, and A. Pinczuk, in Light Scattering in Solids, edited by M. Cardona and G. Guntherodt, Vol. IV), (Springer, Berlin, 1984) p. 5. H. J. Kwon, Y. H. Lee, O. Miki, H. Yamano, and A. Yoshida, Appl. Phys. Lett. 69, 937 (1996).

293

294

5 Growth and Properties of InN 93 M. C. Lee, H. C. Lin, Y. C. Pan, C. K.

94

95

96

97

98 99 100

101

102 103

104

Shu, J. Ou, W. H. Chen, and W. K. Chen, Appl. Phys. Lett. 73, 2606 (1998). T. Inushima, T. Shiraishi, and V. Yu. Davydov, Solid State Commun. 110, 491 (1999). G. Kaczmarczyk, A. Kaschner, S. Reich, A. Hoffmann, C. Thomsen, D. J. As, A. P. Lima, D. Schikora, K. Lischka, R. Averbeck, and H. Riechert, Appl. Phys. Lett. 76, 2122 (2000). J. S. Dyck, K. Kim, S. Limpijumnong, W. R. L. Lambrecht, K. Kash, and J. C. Angus, Solid State Commun. 114, 355 (2000). A. Kasic, M. Schubert, Y. Saito, Y. Nanishi, and G. Wagner, Phys. Rev. B 65, 115206 (2002). C. Bungaro, K. Rapcewicz, and J. Bernholc, Phys. Rev. B 61, 6720 (2000). H. M. Tütüncü, G. P. Srivastava, and S. Duman, Physica B 316/317, 190 (2002). T. L. Tansley, in Properties of Group III Nitrides, edited by J. H. Edgar (INSPEC, London, 1994), p. 39. V. Yu. Davydov, Yu. E. Kitaev, I. N. Goncharuk, A. N. Smirnov, J. Graul, O. Semchinova, D. Uffmann, M. B. Smirnov, A. P. Mirgorodsky, and R. A. Evarestov, Phys. Rev. B 58, 12899 (1998). K. Karch and F. Bechstedt, Phys. Rev. B 56, 7404 (1997). J. C. Nipko, C.-K. Loong, C. M. Balkas, and R. F. Davis, Appl. Phys. Lett. 73, 34 (1998). S. Krukowski, A. Witek, J. Adamczyk, J. Jun, M. Bockowski, I. Grzegory, B. Lucznik, G. Nowak, M. Wroblewski, A. Presz, S. Gierlotka, S. Stelmach, B.

105

106 107

108

109 110

111

112

113

Palosz, S. Porowski, and P. Zinn, J. Phys. Chem. Solids 59, 289 (1998). E. Kurimoto, H. Harima, A. Hashimoto, and A. Yamamoto, Phys. Stat. Sol. (b) 228, 1 (2001). E. Burstein, Phys. Rev. 93, 632 (1954). V. Yu. Davydov, A. A. Klochikhin, V. V. Emtsev, D. A. Kurdyukov, S. V. Ivanov, V. A. Vekshin, F. Bechstedt, J. Furthmüller, J. Aderhold, J. Graul, A. V. Mudryi, H. Harima, A. Hashimoto, A. Yamamoto, and E. E. Haller, Phys. Stat. Sol. (b) (2002), to be published. J. Wu, W. Walukiewicz, K. M. Yu, J. W. Ager III, E. E. Haller, H. Lu, and W. J. Schaff, Appl. Phys. Lett. 80, 4741 (2002). M. H. Kim, J. K. Cho, I. H. Lee, and S. J. Park, Phys. Stat. Sol. (a) 176, 269 (1999). K. P. O’Donnell, J. F. W. Mosselmans, R. W. Martin, S. Pereira, and M. E. White, J. Phys. Condens. Mater. 13, 6977 (2001). A. Klochikhin, A. Reznitsky, L. Tenishev, S. Permogorov, W. Lundin, A. Usikov, S. Sorokin, S. Ivanov, M. Schmidt, H. Kalt, and C. Klingshirn, Nanostructures: Physics and Technology, Ioffe Institute, St. Petersburg, 2001, p. 554. V. V. Emtsev, V. Yu. Davydov, E. E. Haller, A. A. Klochikhin, V. V. Kozlovskii, G. A. Oganesyan, D. S. Poloskin, N. M. Shmidt, V. A. Vekshin, and A. S. Usikov, Physica B 308, 58 (2001). C. Stampfl, C. G. Van de Walle, D. Vogel, P. Krüger, and J. Pollmann, Phys. Rev. B 61, R7846 (2000).

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Surface Structure and Adatom Kinetics of Group-III Nitrides Jörg Neugebauer

Abstract

Recent results based on density-functional theory calculations concerning the structure and stability of group-III nitride surfaces are discussed. An analysis of the thermodynamically stable surface structures for this materials system reveals that the driving mechanisms behind surface reconstructions are fundamentally different to those in “traditional” (i.e., arsenic- or phosphorus-based) III–V semiconductors. Specifically, surfaces are always metal-rich and nitrogen atoms on and in the surface layer are thermodynamically unstable. This feature will be shown to have important consequences on surface morphology, adatom kinetics, growth, reactivity, and alloy formation.

6.1

Introduction

GaN and its alloys with AlN and InN exhibit some unique properties among semiconductors, such as a large band gap, strong interatomic bonds, and a high thermal conductivity. Because of these properties, group-III nitrides have been considered a promising materials system for optoelectronic devices in the blue/ UV region of the optical spectrum and for high-temperature/high-power devices. Group-III nitrides are now successfully being used for producing white, green, blue, and ultraviolet (UV) light emitters [1, 2] and for high-temperature or highpower electronic devices [3–5]. In addition, group-III nitrides are a very promising materials system for high-frequency and for solar-blind detectors [3].

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6 Surface Structure and Adatom Kinetics of Group-III Nitrides

A major obstacle in improving and optimizing GaN-based devices is the rather poor morphology of the epilayers: compared to “traditional” semiconductors where low impurity and dislocation densities are standard, for GaN even devicequality material contains huge concentrations of extended defects [6]. An important step to improve surface morphology is a detailed understanding of surface structure and growth processes on the atomic scale. For the technologically relevant surfaces (the wurtzite (0001), (0001), (1101), and (1100) and the cubic (001) and (110)) various experimental and theoretical studies over recent years have led to considerable understanding of the atomic geometry, the driving forces leading to their reconstructions, and their effect on adatom kinetics. In this chapter a review of these studies is presented with a focus on the theoretical methods and results. In the first part, a brief overview about the methods and terminology is given (Sect. 6.2). The second part (Sect. 6.3) summarizes our present knowledge regarding surface reconstructions and driving forces for all relevant cubic and hexagonal surfaces. Both polar and nonpolar surfaces are considered. Finally, we discuss consequences of the specific surface structures on adatom kinetics (Sect. 6.4) and growth (Sect. 6.5).

6.2

Method

The morphology of surfaces can be described by two principal approaches: (i) in a thermodynamic picture that applies if all atoms on the surface can find their energetically most stable site, and (ii) in a kinetic model where energetic barriers exist that prevent the atoms from finding their most stable configuration. Whether a thermodynamic or kinetic model has to be applied depends on the specific growth conditions. Generally, high temperatures and low growth rates during growth will bring the system closer to thermodynamic equilibrium. It also depends on the specific material: a system with lower diffusion barriers (as expected for a system with a low melting temperature) will be closer to thermodynamic equilibrium. 6.2.1

Thermodynamic Equilibrium

In thermodynamic equilibrium the surface morphology does not depend on the specific reaction path by which the surface has been created but only on the formation energy of the surface, which has to be a minimum. The surface energy is commonly defined as the energy necessary to cut a crystal on some plane. It is important to keep in mind that cutting a crystal means creating two surfaces: an upper and a lower surface that are not necessarily identical. If the two surfaces are nonequivalent, this definition gives only the sum of the two surface energies but not an absolute energy for each individual surface.

6.2 Method

To be more specific let us consider a zinc blende crystal. An example where two identical surfaces are created are cuts along nonpolar {110} surface planes. The two resulting planes are obviously identical (see Fig. 6.1). Cutting along {001} gives two inequivalent surfaces: one is terminated by cations and the other by anions. We can obtain two identical surfaces by adding a cation layer on the anionterminated surface or vice versa. Thus, although cutting gives two inequivalent surfaces it may still be possible by adding/removing atoms to obtain two equivalent surfaces and thus an absolute surface energy (which is just one half of the energy needed to cut the crystal). There exist, however, orientations where this is not possible. For example, cutting along {111} gives two surfaces, (111) and (1 1 1), that are inequivalent and where one surface cannot be transformed into the other by adding/removing additional atoms (see Fig. 6.1). For a zinc blende crystal it is possible to define a physically meaningful absolute surface energy. One uses the fact that planes pointing in different directions may have the same crystallographic surface structure. The (111) surface, e.g., is only one out of four possible {111} facets. The absolute surface energy can then be obtained by constructing a finite crystal limited by only one type of facets, e.g., (111). If the crystal is sufficiently large, edge effects can be neglected and the energy difference between the finite crystal and the corresponding bulk system defines unambiguously the surface energy. For practical calculations this approach would be rather inefficient since large cells would be needed and alternative schemes based on calculating the energy density have been developed [7, 8]. For a wurtzite crystal the symmetry is too low to allow the determination of an absolute surface energy for all possible facets. The simplest example is the analog to the (111) surface – the (0001) surface, which has no equivalent facets pointing in other directions. For this surface, none of the above definitions can be applied: to construct a finite crystal this surface occurs always in combination with other surfaces. Thus, only a relative surface energy can be defined [9]. For the wurtzite (0001) surface this means that only the sum of the (0001) and (0001) surface energies is unambiguously defined. An absolute surface energy for each individual surface is physically meaningless. Following the above definition, and keeping in mind that atoms between the surface and the chemical reservoirs can be exchanged, the surface formation energy is

Fig. 6.1 Schematic side view of the (110) [left], (001) [middle], and (111)/(1 1 1) [right] surfaces of zinc blende GaN.

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6 Surface Structure and Adatom Kinetics of Group-III Nitrides

Gsurf ˆ 12 …G…fnA ; nB g†

n A lA

n B lB Š ;

…1†

where G…fnA ; nB g† is the Gibb’s free energy of the structure used to model the surface. The structure consists of nA, nB atoms of species A and B, respectively. In a supercell approach, as has been used by most theoretical investigations on semiconductor surfaces, it is a slab consisting of an upper and a lower surface that is taken into account by the factor 1/2. The periodic boundary conditions we have in such an approach correctly reproduce the two-dimensional translational symmetry of the surface. lA and lB are the chemical potentials of species A and B, respectively. Since the surface energy is, by definition, referenced with respect to the bulk energy we have lA ‡ lB ˆ lAB…bulk† :

…2†

Using the definition of the Gibb’s free energy the surface energy can be equivalently written as Gsurf …p; T; lB † ˆ 12 …G…fnA ; nB g; p; T†

nA lAB…bulk† …p; T†

DnlB …p; T†† ;

…3†

with Dn ˆ nB nA . In the above equation we have explicitly included the dependence of the various quantities on the external parameters p, T, and l. Formally, we can write nA lAB…bulk† …p; T† ˆ Gbulk …fnA ; nB g; p; T† where Gbulk is the Gibb’s free energy of a bulk cell consisting of nA and nB atoms A and B. The difference in the Gibb’s free energy of the bulk and surface system can be separated into various energy contributions: G…nfnA ; nB g; p; T† ˆ DE0el ‡ DE0ion

Gbulk …fnA nB ˆ nA g; p; T† TDSion

TDSel

pDV :

…4†

The main contribution is the first term (i.e., the difference in the electronic total energy). All other parts are significantly smaller for realistic systems and will be neglected for the following discussion. Using the above approximation the surface energy can be expressed as Gsurf …lB † ˆ 12 …DE0el

DnlB …p; T†† :

…5†

Since the electronic energy is independent of the pressure and the temperature the explicit pressure and temperature dependence of the surface formation energy disappears. The surface energy depends only implicitly on p, T via the temperature and pressure dependence of the chemical potentials. Thus, neglecting entropy effects and changes in the volume, the surface energy is unambiguously expressed by the chemical potentials. In thermodynamic equilibrium, a surface will be realized that has a minimum surface energy. This surface structure is commonly called an equilibrium surface

6.3 Bare GaN Surfaces

structure. A major obstacle in calculating the equilibrium structure is the large number of possible surface structures. In principle, an infinite number of structures with varying geometries and stoichiometry would have to be considered. A major reduction of possible structures can be made if the symmetry of the surface unit cell is known, which can be obtained experimentally, e.g., by STM (scanning tunneling microscopy), LEED (low-energy electron diffraction), or RHEED (reflection high-energy electron diffraction). Indeed, the combination of these techniques with first-principles calculations has proved to be a powerful tool to identify surface structures. Still, even if the symmetry of the surface unit cell is known, a large number of possible structures is possible. It is therefore crucial to understand the driving mechanisms behind surface reconstructions. While these principles are well known for traditional semiconductors it will be shown that for group-III nitrides very different rules apply (see Sect. 6.3.4). 6.2.2

Kinetics

As has been pointed out in the previous section, in thermodynamic equilibrium the surface morphology is solely defined by identifying the structure with the lowest energy. If kinetic processes become important, e.g., if barriers prevent atoms from going into the most stable configuration, the knowledge of the surface structure is only the starting point. In order to theoretically study kinetic effects, the adsorption and desorption processes, the kinetics of adatoms (diffusion barriers, migration paths) and island nucleation have to be computed. Adatom kinetics will be discussed in Sect. 6.4 and will be shown to have dramatic consequences for the stability and structure of surfaces (see Sect. 6.5). Studies on nucleation processes and desorption/adsorption mechanisms are desired.

6.3

Bare GaN Surfaces 6.3.1

Nonpolar Surfaces

Although wurtzite and cubic GaN are typically grown along polar directions (mainly along the (0001) and (001) directions) other possible growth directions have been examined, such as nonpolar surfaces. Nonpolar surfaces have been observed as side facets, they also form the inner surface of nanotubes [10, 11] and open-core dislocations [12]. Nonpolar GaN surfaces have been studied theoretically by several groups applying density-functional theory calculations [13–15] and Hartree-Fock calculations [16]. For wurtzite GaN the (1100) and the (1120) surfaces have been investigated, for cubic GaN the (110) surface. While for traditional semiconductors the nonpolar surfaces have been extensively studied both experimentally and theoretically

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(see, e.g., Ref. [17]) for group-III nitrides mainly theoretical studies have been performed. However, specifically for group-III nitrides, growing along a nonpolar direction might be technologically very appealing: in contrast to polar surfaces these structures are intrinsically free of electric fields as caused by piezoelectricity and spontaneous polarization. However, only very recently it became possible to grow GaN layers along the [1100] nonpolar direction [18].

6.3.1.1 Wurtzite GaN (1100)

A schematic model of the GaN (1100) surface is shown in Fig. 6.2. On the surface there are equal numbers of three-fold-coordinated Ga and N atoms in the top surface layer, thus allowing charge neutrality to be obtained without changes in stoichiometry or reconstruction. The Ga and N atoms form an array of Ga–N dimers. The GaN (1100) surface has been studied by Northrup and Neugebauer [13] and Filippetti et al. [15] employing density-functional theory calculations. The two main relaxation mechanisms are a contraction of the Ga–N bond (by 6%) and a slight buckling rehybridization with N atoms tending to adopt p3 coordination and Ga atoms adopting an sp2 configuration. The bond rotation angle is 78 and the surface energy is 118 meV Å–2. It is interesting to note that the bond rotation is by more than a factor of 2 smaller and the surface energy by more than a factor of 2 larger than for the GaAs surface. These trends hold also for other group-III nitrides [15] and will be discussed in more detail in Sect. 6.3.1.4. Electronic-structure calculations show two surface states: a N-derived surface state lies just below the valence-band maximum (and thus is completely occupied) and a Ga-derived state lies above the conduction-band minimum (and thus is empty) [13]. Thus, if the quasiparticle self-energy corrections correspond primarily to a rigid shift of the unoccupied states relative to the occupied states, then there should be no surface states in the band gap on GaN (1100). Since it is possible to prepare this surface by an epitaxial growth process rather than by cleaving (see, e.g., Ref. [19]) the possibility of nonstoichiometric surfaces has been investigated [13]. In structures where Ga was replaced by N and vice ver-

Fig. 6.2 Schematic (top) view of the (1100) surface of wurtzite GaN. Larger circles mark atoms in the first layer, smaller ones are those in the second layer. The dashed lines outline the boundary of a unit cell (5.179 Å by 3.171 Å).

6.3 Bare GaN Surfaces

sa, it has been found that a surface having Ga–Ga dimers instead of Ga–N dimers in the top surface layer may be stable under very Ga-rich conditions. Such a surface should be more reactive than the Ga–N dimer-terminated surface, and could be a useful intermediate stage in atomic layer epitaxial growth processes.

6.3.1.2 Wurtzite GaN (1120)

The structure of the (1120) surface corresponds to a chain of three-fold-coordinated Ga and N atoms, as indicated in Fig. 6.3. In each unit cell there are four surface atoms: two Ga and two N atoms. This surface has been studied employing density-functional theory calculations [13]. The calculated Ga–N bond lengths in the surface chain are 1.85 Å (cis) and 1.87 Å (trans), corresponding to contractions of 4–5% compared to the bulk value. Similar to the (1100) surface, the Ga atoms relax towards an sp2 configuration with bond angles of 1198, 1168, and 1158. It therefore moves inwards by 0.17 Å. The N atom exhibits a small outward displacement (0.05 Å; bond angles 1078, 1068, and 1018). The bond rotation angle is 78, the surface energy is slightly higher than for the (1100) surface (123 meV Å–2). Contrary to the (1100) surface, the structure formed by replacing surface N atoms with Ga atoms is not energetically favorable, even under Ga-rich conditions.

Schematic (top) view of the (1120) surface of wurtzite GaN. The dashed lines outline the boundary of a unit cell (5.493 Å by 5.179 Å). The smaller circles denote atoms in the second layer. Fig. 6.3

6.3.1.3 Cubic GaN (110)

The cubic GaN (110) surface consists of one cation and one anion in the surface unit cell. The surface atoms are arranged in zigzag chains along the [110] direction. This surface has been studied by Jaffe et al. [16] based on Hartree-Fock calculations and by Grossner et al. [14] and Filippetti et al. [15] employing a plane-wave pseudopotential method. Similar to the nonpolar wurtzite surfaces (see Sect. 6.3.1) the relaxation is described by a significant bond contraction and a bond rotation (see Table 6.1). While the value of the bond contraction given in the different reports varies only slightly (4.9–7%), the bond rotation angle is not well defined: values reported give values between 18 and 168. With their calculated value of 18,

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Jaffe et al. [16] even suggested that the bond-rotation model should be replaced by a model that is determined by surface-bond contraction. Density-functional theory calculations, on the other hand, show that the relaxation has to be described by a combination of bond contraction and bond rotation [14, 15]. The rather large variation of the bond rotation angle might be related to a soft phonon mode connected with this relaxation. Further calculations and experimental studies are called for. Similar to the nonpolar surfaces two surface states are found: a fully occupied state below the valence band edge (related to N p-orbitals) and an empty state close to or within the conduction band (related to Ga dangling bond states). The surface is semiconducting.

6.3.1.4 General Trends

The relaxation of all nonpolar GaN surfaces is similar: it is characterized by a significant bond contraction and rotation. The values are summarized in Table 6.1. Grossner et al. [14] studied the relaxation of the BN, AlN, and InN (110) surfaces and Filippetti et al. [15] that of the AlN, InN (110), and (1100) surfaces. The relaxation is again characterized by bond contraction and rotation. Compared to the (110) surface of traditional III–V semiconductors all calculations exhibit a significantly smaller bond rotation angle and a much stronger bond contraction. This behavior has been explained in terms of the high ionicity of group-III nitrides [14, 15]. The surface energy of the two main nonpolar surfaces is about 120 meV Å–2. This is larger (by a factor of 2) than the surface energy of (110) GaAs (Table 6.1). For wurtzite GaN the (1100) surface is energetically slightly more favorable than the (1120). Generally we can conclude that the nonpolar surfaces of group-III nitrides exhibit only quantitative differences compared to nonpolar surfaces of traditional semiconductors: the values for the relaxation (bond contraction and angle) are different and the surface energy is higher. Qualitatively, however, nonpolar surfaces all behave alike: they have a large surface band gap (making the surface semiconducting) and the bulk-terminated 1 ´ 1 translational symmetry is conserved.

Tab. 6.1 Surface energy r, bond rotation angle h, and relative bond contraction e for nonpolar

GaN surfaces as calculated in Refs. [14–16, 20]. For comparison, the values for the GaAs (110) surface are also shown [21]

r (meV Å–2) h (8) e (%)

GaN (110)

GaN (1100)

GaN (1120)

GaAs (110)

118 [14], 118 [15] 1 [16], 14.3 [14], 7.3 [15] 7 [16], 5.3 [14], 4.9 [15]

118 [20], 120 [15] 7 [20], 11.5 [15] 6 [20], 6 [15]

123 [20] 7 [20] 5 [20] (cis), 4 [20] (trans)

57 16.7 0.9

6.3 Bare GaN Surfaces

6.3.2

Polar Cubic GaN Surfaces

The technologically most common growth surfaces are the (0001) and (0001) surfaces of wurtzite GaN and the (001) of cubic GaN. All of these surfaces are polar, i.e., an ideal truncated surface consists either of cations or anions. Experimentally it has been found that both surface and bulk properties depend sensitively on the surface orientation [3]. It is now generally accepted that growing on (0001) leads to a smoother surface, a better morphology and lower impurity concentrations. Thus, the surface orientation and reconstruction have a large impact on the material quality. In the following, we will discuss the structural and energetic properties of the relevant polar surfaces. In this section we will focus on the metastable cubic phase of cubic GaN, for which the (001) surface is preferred for the epitaxial growth process. Growing along [111] leads to the formation of the wurtzite phase since only the stacking sequence “cubic: ABCABC ?wurtzite: ABABAB” has to be changed.

6.3.2.1 GaN (001) Surface

Cubic (zinc blende) GaN can be grown epitaxially on cubic SiC or GaAs substrates [22–24]. The ideal GaN (001) surface consists of one atom in the 1 ´ 1 surface cell (Fig. 6.4, left) and each surface atom has two dangling bonds. For cations (anions) each dangling bond is occupied with 3/4 (5/4) electrons. The surface has been studied employing first-principles calculations [25]. The atomic geometry for the unreconstructed Ga-terminated surface is characterized by small vertical relaxations: the top layer (Ga) relaxes 0.08 Å outward; the relaxation of the second layer (N) is already negligible. The calculated surface band structure is shown in Fig. 6.5 a. For the unreconstructed surface two surface states (S1, S2) are found. The energetically lower state is a bonding state between neighboring surface Ga atoms. It is partially occupied with 3/2 electrons rendering it metallic. In GaAs, the unreconstructed Ga-terminated (001) surface shows a qualitatively similar band structure [26]. The main difference is a significantly larger dispersion (more than 1 eV) of the surface bands on the GaN surface. The larger dispersion indicates the formation of significantly stronger Ga–Ga bonds on GaN compared to the analogous GaAs surface (see also Sect. 6.3.4).

Schematic (side) view of the ideal (left) and reconstructed (right) (100) surface of cubic GaN. The numbers give the bond

Fig. 6.4

lengths in Å. The ovals mark the dangling bonds.

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6 Surface Structure and Adatom Kinetics of Group-III Nitrides

Band structure calculated within the local-density approximation for the relaxed Ga-terminated a (1 ´ 1); b (4 ´ 1) surface of GaN. The shaded region corresponds to the bulk projected band structure for zinc blende GaN. The dashed lines are surface states. In a the energetically lower surface state (S1) is

Fig. 6.5

partially occupied with 3/2 electrons. The upper surface state (S2) is empty. The dashdotted line marks the position of the Fermi energy. In b the lower three surface states are doubly occupied; the upper surface states are empty. From Ref. [25].

The strong dispersion along the CJ 0 direction and the metallic character suggest that the Ga-terminated (1 ´ 1) surface might be Peierls unstable along the [110] direction. Electron-counting considerations indicate that the smallest unit cell that allows an energy gap is a (4 ´ 1) structure. In fact, first-principles calculations showed that the (1 ´ 1) surface is unstable against lowering its symmetry and forming a (4 ´ 1) reconstruction [25]. The reconstructed surface is semi-insulating with a LDA band gap of 1.2 eV (see Fig. 6.5 b). The three bonds in the tetramer give rise to three almost dispersionless surface states close to the valence band that are each doubly occupied. The two dangling bond orbitals (see Fig. 6.4) are unoccupied and give rise to the two upper surface states (Fig. 6.5 b). It should be noted that a surface consisting of linear tetramers is unique and has not been observed experimentally nor studied theoretically for other III–V (001) surfaces. First-principles calculations performed by Zywietz et al. [27] showed indeed that on the corresponding GaAs surface the tetramers are unstable and spontaneously form dimers. The very different stability of tetramers on the two materials originates from the sizable mismatch of the covalent radii of Ga and N: in order to form a tetramer on GaN, breaking of back bonds is not required and the Ga–N bond length remains unchanged (< 0.1 Å; Fig. 6.4, right). On (001) GaAs, however, forming a tetramer is not possible without breaking back bonds. Studying a large number of possible surface reconstructions with different stoichiometries and starting from very different initial geometries and symmetries it has been found that the above-described linear tetramer structure is thermodynamically stable [25]. Figure 6.6 shows the surface energy of a selected set of the struc-

6.3 Bare GaN Surfaces

Surface energies for clean GaN (001) surfaces as a function of the Ga chemical potential lGa. Only the thermodynamically allowed range is shown. The 2 ´ 2 Ga adatom structure consists of a Ga atom in the four-fold hollow site; the surface-labeled 2 ´ 2 Ga dimer consists of two Ga atoms bonded in a Ga-bridge position. After Ref. [25]. Fig. 6.6

tures with the lowest energy. Indeed, the energetically preferred surface is the Gaterminated (4 ´ 1) structure. Growing GaN layers on GaAs (001), Brandt et al. [22] observed a reversible sequence of reconstructions exhibiting (1 ´ 1), (2 ´ 2), and c(2 ´ 2) reflection high-energy electron diffraction (RHEED) patterns when going from N-rich to Ga-rich conditions. The c(2 ´ 2) and (2 ´ 2) structures have also been reported by Schikora et al. [24]. According to STM measurements by Wassermeier et al. [28] the (2 ´ 2) surface consists of one dimer per surface unit cell. First-principles calculations, however, showed all possible dimer structures to be higher in energy than the tetramer structure [25]: starting with N dimers results in the formation of N2 molecules that are bound in a physisorbed state and are unstable against desorption. Ga dimers are energetically most stable on a Ga-terminated surface. However, the energy gain is too small to make them favorable (see Fig. 6.6). We can therefore exclude a (2 ´ 2) reconstruction as a stable structure on clean GaN (001) surfaces. This conclusion is consistent with recent experimental results: growing GaN (001) on cubic SiC Feuillet et al. observed a (4 ´ 1) (N-rich) and a (1 ´ 1) (Ga-rich) reconstruction [29]. Only when exposing these surfaces to an arsenic background pressure were the two surface reconstructions commonly found for GaN on GaAs [(2 ´ 2) and c(2 ´ 2)] observed, implying that these surfaces are arsenic induced. In fact, as has been shown in Ref. [25] the (2 ´ 2) structure is induced by a submonolayer of arsenic. Thus, the tetramer structure is a strong candidate to explain the (4 ´ 1)

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6 Surface Structure and Adatom Kinetics of Group-III Nitrides

RHEED pattern observed by Feuillet et al. when growing GaN on SiC, i.e., in the absence of any arsenic [29]. 6.3.3

Polar Wurtzite Surfaces

Although the cubic form of GaN has some potentially interesting features for device applications (it has a smaller band gap (by 0.2 eV) and can be easily cleaved) all devices produced so far are based on wurtzite GaN. The common growth direction of wurtzite GaN is normal to the hexagonal {0001} basal plane, where the atoms are arranged in bilayers consisting of two closely spaced hexagonal bilayers (see, e.g., Ref. [3]). One side of the bilayer consists of anions, the other of cations, i.e., the bilayers have polar faces (see side view in Fig. 6.7). Thus, in the case of GaN we have to distinguish between two growth orientations: the Ga-face [or (0001)] orientation where Ga is in the top position of the bilayer and the N-face [or (0001)] orientation with N in the top position. Both surface orientations are inequivalent, i.e., once the first bilayer has been grown the orientation is fixed. It is important to note that Ga-face does not mean Ga-terminated; termination is a surface property determining which species is in the top surface layer. A nitrogenface surface, as will be shown later, can be Ga-terminated. Experimentally it has been found that bulk and surface properties (defect and impurity concentrations, type and concentration of extended defects, morphology) can sensitively depend on whether growing on a Ga- or N-face surface: Ponce et al. [30] observed that bulk GaN exhibits smooth surfaces on the (0001) (i.e., Gaface) surface and rough facets correspond to (0001) (i.e., N-face) surfaces. It has been further reported that on sapphire substrate high-quality MOCVD-grown GaN is commonly achieved when growing in the (0001) direction (see, e.g., Ref. [30]), while MBE growth commonly occurs in the (0001) direction [31, 32]. In the following, we will focus on the Ga- and N-face surfaces and discuss our present understanding about surface structure and energetics. In addition, we will discuss the (1101) surface that has been often observed when growing on patterned substrates.

Schematic top and side view of the ideal truncated GaN (0001) surface. The dashed lines outline the boundary of a (2 ´ 2

Fig. 6.7

unit cell. High-symmetry adsorbate sites are marked by H3 (hollow) and T4 (on top of second layer atom).

6.3 Bare GaN Surfaces

6.3.3.1 GaN (0001) Surface

The experimentally most commonly observed reconstruction on GaN (0001) is (2 ´ 2). The (2 ´ 2) reconstruction corresponds to a stable growth front that yields high-quality thin films [33, 34]. Since this reconstruction has not been observed on GaN (0001) the presence of it is regarded as a fingerprint of GaN (0001). Other reconstructions observed by RHEED and STM on this surface are: (1 ´ 2), (4 ´ 4), (5 ´ 5), and (6 ´ 4) (see, e.g., Refs. [35, 36] and references therein). Under very Ga-rich conditions a pseudo- (1 ´ 1) structure has been reported [35]. The ideal truncated GaN (0001) surface with Ga in the top surface layer is shown in Fig. 6.7. Each Ga surface atom has one dangling bond and is bonded to three N atoms in the second layer. It is common to start from the ideal surface to denote the reconstructed surface: adding a Ga or N layer on this surface would be called a Ga or N adlayer structure and adding/removing a Ga atom would be called Ga adatom/vacancy, respectively. This surface has been studied theoretically by several groups employing plane wave pseudopotential methods [31, 36, 37] and ab initio tight-binding methods [38, 39]. All studies focused on (1 ´ 1) and (2 ´ 2) structures. Structures that have been investigated were adatoms on the H3 and T4 site, trimers, and Ga adlayers on various sites. The relative formation energies, as calculated by Smith et al. [31], are shown in Fig. 6.8. Under N-rich conditions a (2 ´ 2)-H3 N-adatom model is energetically most stable (with a (2 ´ 2) Ga-vacancy model only slightly higher in energy), while under Ga-rich conditions a (2 ´ 2)-T4 Ga-adatom structure is favored. Similar results have been also found by other groups [36–39]: under N-rich conditions the Ga-vacancy and N-adatom (on a H3 site) are the stable surfaces and close in energy, under Ga-rich conditions the Ga-adatom (on a T4 site) is preferred. Only Elsner et al. [38] find under Ga-rich conditions a Ga-monolayer and a Ga-trimer model to be more stable than a Ga-adatom structure. The reason for this deviation might be an insufficient description of the metallic Ga–Ga bond in a tight-binding approach. Electron diffraction measurements by Smith et al. [35] showed under very Garich conditions a rather unusual pseudo-(1 ´ 1) reconstruction. This structure contains at least two monolayers of Ga residing on top of the Ga-terminated bilayer and is found to be highly metallic. Furthermore, low-energy electron diffraction (LEED) measurements showed this structure to be incommensurate, while STM measurements exhibited a clear (1 ´ 1) periodicity. This discrepancy has been explained in terms of a discommensuration fluid phase, similar to that observed on Au (111) [40]. Recent model calculations employing density-functional theory confirm that a laterally contracted overlayer of Ga atoms bonded to a 1 ´ 1 Ga adlayer is energetically favorable in the Ga-rich limit [41]. The calculations also show that the energy of this structure is very insensitive to the lateral position of the contracted layer with respect to the underlying Ga layer. The flatness of the energy surface suggests the presence of rapidly moving domain boundaries separating regions of the surface having different registries. This type of motion may lead to the (1 ´ 1) corrugation pattern seen in STM. Except for the Ga double layer structure [41] all energetically favorable (0001) surfaces obey the electron-counting rule, i.e., these surfaces are semi-insulating

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The relative energies calculated for possible models of the GaN (0001) surface are shown as a function of the Ga chemical potential. The reconstructions are named following the convention in Sect. 6.3.3.1. The energy zero is arbitrary (see Sect. 6.2.1).

Fig. 6.8

and the surface band gap is open. Calculations by Fritsch et al. [39] show electronic surface states in the band gap that are related to the dangling bonds of the adatoms and to the back bond of first-layer atoms.

6.3.3.2 GaN(0001) Surface

STM measurements combined with LEED and RHEED observed four dominant reconstructions on GaN (0001). They are: (1 ´ 1), (3 ´ 3), (6 ´ 6), and c(6 ´ 12) listed in order of increasing surface coverage [31, 42]. Based on the experimentally observed reconstructions ab initio calculations have been performed for a large number of (1 ´ 1) and (2 ´ 2) candidate systems [35]. The resulting surface energies are shown in Fig. 6.9. For N-rich conditions a (2 ´ 2)-H3 Ga-adatom model is found to be most stable, while for Ga-rich conditions a (1 ´ 1) adlayer structure is preferred. In the stable (1 ´ 1) model a full monolayer of Ga atoms sits directly atop the N atoms, with the Ga–N bond length equal to 1.97 Å (compared to 1.94 Å in bulk GaN). The Ga–Ga separation in the adlayer (3.19 Å) is considerably larger than a typical Ga–Ga separation of 2.7 Å in bulk Ga. It is interesting to note that this is a completely novel structure with no known analogue among other semiconductor surfaces. In fact, this structure violates most of the empirical rules used to describe semiconductor surfaces (see Sect. 6.3.4.1): it clearly disobeys electron counting and it maximizes the number of dangling bonds. One immediate conse-

6.3 Bare GaN Surfaces

The relative energies calculated for possible models of the GaN (0001) surface are shown as a function of the Ga chemical potential. The energy zero is arbitrary. AOA (adatom on adlayer) denotes a Ga adatom on a Ga adlayer. Fig. 6.9

quence of the breaking of the electron-counting rule is that the surface must be metallic; this has been indeed observed by scanning tunneling spectroscopy (STS) [35]. The stability of this unusual structure can be explained in terms of the very different atomic size and chemical character of Ga and N (see Sect. 6.3.4.2). (2 ´ 2)-reconstructed surfaces have been also investigated in Refs. [37–39]. Elsner et al. [38] find a Ga adatom (on H3) and a Ga-adlayer structure under N- and Garich conditions, confirming the results by Smith et al. [31]. Rapcewicz et al. [37] find a Gaadatom (on H3), and Fritsch et al. [39] a vacancy complex to be stable over the entire range of thermodynamically allowed chemical potentials. The differences from the calculations given by Refs. [31] and [38] might be due to not considering a Ga-adlayer structure (which has been regarded as energetically very unfavorable due to the existence of three dangling bonds per surface atom) or due to the approximate nature of tight-binding methods [39]. Calculations have also been performed for several possible models of the (3 ´ 3) surface [31]. Structural models having one, two or three additional Ga adatoms on (or in) the Ga adlayer had been considered and it has been found that one additional Ga adatom is the best model for the observed (3 ´ 3) reconstruction. In this structure, the extra Ga atom resides only 0.9 Å above the adlayer plane. In the absence of lateral relaxation, the Ga adatom must be positioned 1.8 Å above the adlayer to preserve a reasonable Ga–Ga distance. The extremely large inward relaxation of the adatom in the (3 ´ 3) structure is enabled by a 0.5-Å lateral relaxation of the nearest-neighbor Ga-adlayer atoms, which allows the adatom to move much

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closer to the adlayer plane, thereby stabilizing the structure. It is therefore called an inplane adatom model. All stable structures identified by first-principles calculations exhibit a metallic character. The metallic character has also been confirmed by experiment: STS measurements on the (1 ´ 1) and (3 ´ 3) structures showed a nonvanishing density of states around the Fermi level [35]. The electron-counting rule is thus violated but they nonetheless form minimum-energy structures.

6.3.3.3 GaN (1101) Surface

The GaN (1101 surface has been observed as a sidewall facet in lateral epitaxial overgrowth, which is used for threading-defect reduction [43, 44]. These surfaces have been also found as sidewalls in the inverted pyramid defects [45, 46], which form at the termination of some threading dislocations at the GaN surface during growth of In-containing alloys. Theoretically this surface has been studied by Northrup et al. [47] employing first-principles calculations. The schematic structure that is stable under Ga-rich conditions is shown in Fig. 6.10. It consists of Ga atoms in two distinct types of sites in the surface layer. These sites have been called B2 and T1 sites. The atoms in B2 are bonded to two N atoms in the layer below. This is similar to the bonding configuration of Ga atoms on the (001) ideal surface of cubic GaN (see Sect. 6.3.2.1). The atoms in the T1 sites are bonded to one N atom in the layer below, as in the (1 ´ 1) Ga-adlayer structure existing on the (0001) surface (see Sect. 6.3.3.2). The structure stable under N-rich conditions contains one Ga atom per cell bonded in an H3 site. This adatom is bonded to three N atoms in the layer below. The Ga-adlayer structure stable under Ga-rich conditions (which is the preferred growth mode) has some interesting features: (i) low-coordinated surface atoms with only one or two bonds exist and (ii) the two surface atoms have different coordination numbers. For traditional semiconductors, surface atoms always prefer to have the highest possible coordination number, i.e., to form three bonds.

Fig. 6.10 Schematic representation of the GaN (1101) Gaadlayer surface. Surface sites T1 and B2 are sites in which Ga makes one or two bonds with N atoms. Filled circles mark Ga atoms, open circles show N atoms.

6.3 Bare GaN Surfaces

This tendency not only holds for surface atoms but has been also observed for atoms at the edge of steps [48]. The existence of low-coordinated surface atoms has been shown to have dramatic effects on alloys such as chemical ordering or pit formation [47].

6.3.4

General Trends and Comparison with Traditional Semiconductors 6.3.4.1 General Trends

A remarkable feature of polar GaN surfaces is the existence of novel structures that are very different from the well-established structures of III–V semiconductor surfaces. On conventional semiconductor surfaces the specific structure of surface reconstructions can be explained on the basis of a small number of guiding principles. First, surfaces tend to reduce the number of dangling bonds (e.g., by forming dimers [on the open (001) surfaces], trimers, by adding adatoms or creating vacancies [mainly on close-packed surfaces]). Second, surfaces minimize their electronic energy (this is commonly formulated as the electron-counting rule; all energetically low-lying anion dangling-bond states are doubly occupied, all cation dangling-bond states are empty) [49]. Finally, they tend to minimize the electrostatic energy by optimizing the arrangement of the charged surface atoms. Despite their simplicity and their empirical character these rules have been very successful in explaining the structure of polar and nonpolar surfaces for a wide variety of semiconductors. However, as has been shown in the previous sections, reconstructions on GaN do not always follow these principles. One example is the tetramer structure found on cubic GaN (001) (see Sect. 6.3.2.1): commonly, the preferred building block on (001) surfaces of conventional semiconductors are dimers. Another example is the Ga-adlayer structure on GaN (0001) which violates several rules: It disobeys electron counting, atoms in the top surface layer sit on singly coordinated sites (i.e., only one bond per surface atom is formed), and each surface atom has the highest possible number of dangling-bond states. An analysis of all stable GaN surfaces reveals an interesting similarity: almost all stable surfaces are characterized by the complete absence of N adatoms or even of N in the top surface layer. In most structures N atoms prefer a four-fold-coordinated (i.e., bulk-like) position. Exceptions include the nonpolar surfaces (Sect. 6.3.1) and the (2 ´ 2)-H3 N-adatom reconstruction on GaN (0001), which is only stable under extreme N-rich conditions. The trend to prefer only Ga atoms (cations) in the surface layer has not been observed for traditional III–V or II–VI semiconductors. Judging from the preference of unusual structures on GaN, the tendency to form Ga-stabilized surfaces appears to override all conventional rules. In the following we will identify the properties of GaN that give rise to these unusual surface reconstructions and show that the tendency to form cation-stabilized surfaces is a feature of all group-III nitrides.

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6.3.4.2 Comparison with Traditional Semiconductors

In order to compare the stability of GaN surfaces with those of traditional semiconductors Neugebauer et al. [25] calculated and analyzed the energy of several unreconstructed (001) GaAs and GaN surfaces. The results are shown in Fig. 6.11. For GaAs both the Ga- and As-terminated (1 ´ 1) surfaces are energetically highly unfavorable with the Ga-terminated surface slightly higher in energy than the Asterminated surface. For GaN a strikingly different behavior is found: while the Nterminated surface is close in energy to the As-terminated GaAs surface the Gaterminated surface is more than 3.5 eV per (1 ´ 1) cell lower in energy than the corresponding GaAs surface. In fact, the energetically most stable tetramer structure is only slightly more stable (&0.27 eV per (1 ´ 1) cell) than the ideal Ga-terminated surface. Thus, on GaN we have a large energy difference between the cation- and anion-terminated surface that is not observed on GaAs. A more detailed analysis revealed that two properties unique to group-III nitrides are responsible for the unusual stability. First, Ga atoms on GaN form stronger Ga–Ga bonds than on GaAs. The origin of the stronger bonding lies in the sizeable mismatch of the covalent radii of Ga and N. Because of the small radius of the N atoms the Ga atoms in GaN have approximately the same distance as in Ga bulk. The Ga atoms on the surface can form metallic bonds similar to those in Ga metal even without any relaxation, thus stabilizing the Ga-terminated surface. A second mechanism stabilizing metal surfaces on group-III nitrides with respect to N-terminated surfaces is the very different cohesive energies of the bulk phases of Ga and N: the cohesive energy of bulk Ga is 2.81 eV/atom while that of the N2 molecule is 5.0 eV/atom. The N–N bond in the N2 molecule is one of the

Fig. 6.11 Surface energies for cubic (1 ´ 1) GaN (solid lines) and GaAs (dot-dashed lines) (001) surfaces as a function of the Ga chemical potential lGa. Only the thermodynamically allowed range is shown. Also, the reconstructed surfaces with the lowest energy have been included: for GaAs the b2-(4 ´ 2) and for GaN the (4 ´ 1) tetramer structure (dashed lines). Note that the thermodynamically allowed range is different for GaAs and GaN.

6.4 Adatom Kinetics

strongest bonds found in nature. In contrast, the cohesive energy of bulk As (2.96 eV/atom) is only slightly larger than that of bulk Ga. Because of this asymmetry between the Ga and N reservoir, more energy is needed to transfer N atoms from its reservoir to the surface than to transfer Ga atoms to the surface.

6.3.4.3 Conclusions

From the above discussion we can replace the three main mechanisms governing surface reconstructions on traditional semiconductor surfaces by the following rules: group-III nitride surfaces have the tendency to (i) stabilize metal-rich structures, (ii) obey electron counting, and (iii) reduce the number of dangling bonds. The latter two rules only apply if the first rule is fulfilled. It should be noted that the first rule is related to the chemical properties of the two different species, while (ii) and (iii) are driven by the electronic structure. For conventional compound semiconductors, the properties of the two constituents are rather similar and there is no preference for either cations and anions. This explains why surface reconstructions on these systems are exclusively guided by the electronic principles, while for group-III nitrides the chemical nature of the surface atoms is crucial. It should be noted that these rules are, of course, too simplistic to derive surface structures a priori, i.e., without input from experiment or without performing realistic calculations. However, they help to explain why group-III nitrides behave in many respects so different from conventional semiconductors. Furthermore, the strong tendency to stabilize metal-rich surfaces is not only a new property but also has important and unexpected consequences on the stability of adsorbate-covered surfaces, the choice of optimum growth conditions, and the formation of extended defects, as will be discussed in the following sections.

6.4

Adatom Kinetics

In order to improve growth in a systematic way it is essential to understand the underlying kinetic processes such as adsorption, desorption, and surface diffusion (see also Sect. 6.2). In particular, adatom diffusion is considered to be a key parameter controlling the growth rate, the material quality, and the surface morphology. Experimentally, an analysis of surface diffusion is difficult. So far, only effective diffusion barriers can be derived [23, 50]. Effective parameters average over a large area including not only the clean surface but also steps, impurities, dislocations, etc. Since the effective diffusion barrier is usually dominated by the process with the highest barrier, these parameters give no insight into the microscopic processes. Theoretically, adatom diffusion has been studied at GaN (0001)/(0001) [51] and at the cubic (001) surface [52] employing density-functional theory. We will start our discussion with diffusion at equilibrium GaN surfaces.

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6.4.1

Diffusion of Adatoms on Equilibrium GaN Surfaces

An important tool to study adatom kinetics is the calculation of the potential energy surface (PES). The potential energy surface Etot …Rad k † is calculated by fixing the adatom laterally at different positions Rad and allowing all other atoms and k the adsorbate height to relax. The local minima of Etot …Rad † give all possible adk sorption sites. The PES also gives immediate insight into diffusion barriers and migration paths. For GaN (0001) and (0001), Zywietz et al. [51] calculated the PES for Ga and N adatoms. The (0001) surface has been described by a Ga-terminated bilayer model; the (0001) surface by a Ga-adlayer structure. The results are listed in Table 6.2. As can be seen, Ga and N adatoms show a very different diffusivity. The diffusion barriers of Ga adatoms are in the range between 0.2 and 0.7 eV (depending on the surface) while for N adatoms significantly higher barriers (between 1.1 and 1.5 eV) are found. An important consequence of these results is that Ga adatoms will be orders of magnitude more mobile than N atoms at typical growth temperatures. The low diffusion barrier is a direct consequence of the fact that GaN equilibrium surfaces are Ga-stabilized (see Sect. 6.3.4.3). For Ga atoms the adsorbate-surface interaction is predominantly realized by Ga–Ga bonds. Since Ga bulk melts already slightly above room temperature (Tmelt = 30 8C), the Ga–Ga bonds are weak and the adatoms behave almost like a liquid film on the surface. A similar effect has not been reported at “traditional” III–V semiconductor surfaces like, e.g., GaAs where the surfaces do not exhibit a metallic-like character. The diffusion barrier on these surfaces is thus mainly characterized by breaking strong cation-anion bonds. As a consequence, a significantly higher Ga diffusion barrier is found on these surfaces: for the polar GaAs (111) surface the barrier is 1.1 eV [54].

Tab. 6.2 Diffusion barriers of Ga and N adatoms on GaN (001), (0001), and (0001). The calcu-

lations have been performed for the unreconstructed Ga-terminated surface using a (2 ´ 2) surface unit cell [26, 53] Surface orientation

Adatom

Ediff (eV)

(001) (0001) (0001)

Ga Ga Ga

0.2 0.7 0.2

(001) (0001) (0001)

N N N

1.5 1.3 1.1

6.5 Consequences for Growth

6.4.2

Diffusion on Nonequilibrium Surfaces

The significantly larger diffusion barrier for N adatoms compared to Ga adatoms has important consequences: although N adatoms on equilibrium surfaces are unstable against evaporation as N2 molecules (see Sect. 6.3.4), they can be kinetically stabilized during growth at the surface. In order to evaporate, two N atoms have first to form a N2 molecule. Since migration of N adatoms is a highly activated process (but necessary to form molecules), under more N-rich growth conditions the nitrogen desorption rate may become smaller than the adsorption rate: extended regions in which the surface is primarily covered by N atoms may be formed. These N adatoms are likely to influence the migration path and the diffusion barrier of Ga adatoms. Zywietz et al. [51] also studied the diffusion of Ga adatoms on N-terminated (0001) and (0001) surfaces. Only Ga adatoms have been considered: putting N adatoms on N-terminated surfaces always resulted in the formation of weakly bound N2 molecules desorbing at typical growth temperatures. For both surface orientations the diffusion barrier of Ga adatoms is strongly affected: for (0001) the migration barrier increases from 0.6 to 1.8 eV, while for (0001) it increases from 0.2 to 1.0 eV. Based on the above discussion we can understand how N adatoms can be incorporated on the surface although they are thermodynamically unstable: to grow GaN the incoming N-flux must be larger than the N-desorption rate, which is mainly governed by the N adatom diffusion barrier. We can further conclude that excess N at the surface (which can be formed under N-rich conditions) significantly reduces the mobility of Ga adatoms. The reason is the formation of strong Ga–N bonds, which have to be broken during the migration of the adatoms. The reduction in surface diffusivity when going towards more N-rich conditions is consistent with a recent MBE growth study by Tarsa et al. [55]: under Ga-rich conditions step flow is observed (implying low diffusion barriers) while under more N-rich conditions island formation is found.

6.5

Consequences for Growth

In the previous sections we have summarized our present knowledge about surfaces (structure, energetics) and adatom kinetics on GaN. In the following we will use this information to derive consequences for growth (see also Ref. [52]). It should be noted that the following discussions are kept rather qualitative: to obtain quantitative growth information further studies (e.g., concerning steps, step diffusion, dissociation of molecules, etc.) are needed. For growth models based on empirical parameters see, e.g., Refs. [56, 57]. Let us first focus on kinetic effects. The very different mobility of Ga and N adatoms and the formation of excess N have important consequences for the growth

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of GaN. In the Ga-rich regime, where the amount of N on the surface is small, the Ga adatoms are highly mobile and a step-flow mode resulting in 2D growth is expected. As a consequence, the surface morphology should be improved and a low density of defects is expected. Furthermore, if excess Ga adatoms are present on the surface (as expected for Ga-rich growth conditions), N adatoms can be efficiently incorporated: the probability that fast-moving Ga adatoms capture N atoms is much higher than the other process where N atoms form molecules and desorb from the surface. Under N-rich conditions nitrogen-terminated surfaces can be kinetically stabilized. These surfaces exhibit higher diffusion barriers (see Sect. 6.4.2), and hence a significantly reduced Ga diffusion length. Once the diffusion length is shorter than the mean distance between the binding sites a statistical roughening of the surface can be expected. Furthermore, the adatom might be trapped at sites not corresponding to the ideal bulk positions. For example, if a Ga atom is trapped at the T4 site, a fcc nucleation center is formed. Thus, the higher adatom mobility under more Ga-rich conditions will also significantly reduce the density of stacking faults. From a kinetic point of view we therefore expect Ga-rich conditions to be optimal for the growth of GaN. From a thermodynamic point of view, growth conditions are preferred where the formation of rough surfaces or facetting is energetically unfavorable. For polar GaN surfaces (which are the relevant surfaces for growth), the surface stability is highest under Ga-rich conditions; the reason is the preference of cation-stabilized surfaces (see Sect. 6.3.4). Nonpolar surfaces (which might be formed as facets) are stoichiometric (see Sect. 6.3.1): the surface energy is independent of the specific chemical potential. Consequently, the difference in surface energies increases and the stability of the polar surfaces decreases when going towards more N-rich conditions; facetting might occur. This behavior casts severe doubts on the old paradigm of pushing growth towards extreme N-rich conditions in order to avoid a N deficiency and the formation of N vacancies. Instead, from a thermodynamic and a kinetic point of view we expect best growth conditions under more Ga-rich conditions. Experimental observations [22, 23, 29, 58] support these conclusions: optimum surface morphology is achieved under more Ga-rich conditions, while under N-rich conditions surface roughening and inferior material quality have been observed. It should be mentioned that the extreme binding energy of N2 and the large mismatch in atomic radii, which drive polar surfaces to be Ga-rich, are general features of the III-nitride semiconductors. For AlN, InN, and their alloys with GaN we therefore expect a similar behavior.

6.6

Acknowledgments

This work has been done in close collaboration with John Northrup, Chris Van de Walle (both Xerox PARC), Randy Feenstra (Carnegie Mellon University), Matthias Scheffler and Tosja Zywietz (both Fritz-Haber-Institut). Many thanks also go to

6.7 References

Pierre Ruterana, Gerard Nouet (CRISMAT-CNRS), and Philo Komninou (Aristotle University of Thessaloniki) for critically reading the manuscript. Financial support by the Deutsche Forschungsgemeinschaft (Schwerpunktprojekt “Gruppe-III Nitride”) and the European Community under contract number HPRN-CT-199900040 are gratefully acknowledged. 6.7

References 1

2 3 4 5 6

7 8 9 10

11

12

13 14

15

16

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, and H. Kiyoku, Appl. Phys. Lett. 69, 1477 (1996). S. Nakamura, T. Mukai, and M. Senoh, Appl. Phys. Lett. 72, 2014 (1998). O. Ambacher, J. Phys. D 31, 2653 (1998). S. N. Mohammed, A. A. Salvador, and H. Morkoc, Proc. IEEE 83, 1306 (1995). F. A. Ponce and D. P. Bour, Nature 386, 351 (1997). S. D. Lester, F. A. Ponce, M. G. Craford, and D. A. Steigerwald, Appl. Phys. Lett. 66, 1249 (1994). N. Chetty and R. M. Martin, Phys. Rev. B 45, 6074 (1992). N. Moll, A. Kley, and M. Scheffler, Phys. Rev. B 54, 8844 (1996). K. R. B. Chen, B. Yakobson, and J. Bernholc, Phys. Rev. B 57, 7281 (1998). D. Cherns, W. Young, J. W. Steeds, F. A. Ponce, and S. Nakamura, J. Cryst. Growth 178, 201 (1997). W. Quian, G. Rohrer, M. Skowronski, K. Doverspike, L. B. Rowland, and D. Gaskill, Appl. Phys. Lett. 67, 2284 (1995). J. Elsner, R. Jones, P. Sitch, V. Porezag, M. Elstner, T. Frauenheim, M. Heggie, S. Oberg, and P. Briddon, Phys. Rev. Lett. 79, 3672 (1997). J. E. Northrup and J. Neugebauer, Phys. Rev. B 53, R10477 (1996). ¨ller, and F. U. Grossner, J. Furthmu Bechstedt, Phys. Rev. B 58, R1722 (1998). A. Filippetti, V. Fiorentini, G. Cappellini, and A. Bosin, Phys. Rev. B 59, 8062 (1999). J. E. Jaffe, R. Pandey, and P. Zapol, Phys. Rev. B 53, R4209 (1996).

17

18

19

20 21 22

23

24

25

26 27

28

29

30

W. Mo¨nch, Semiconductor Surfaces and Interfaces, Springer Series in Surface Sciences, Vol. 26 (Springer, Berlin, 1993). P. Waltereit, O. Brandt, M. Ramsteiner, R. Uecker, P. Reiche, and K. Ploog, J. Cryst. Growth 218, 143 (2000). P. Waltereit, O. Brandt, M. Ramsteiner, R. Uecker, P. Reiche, and K. Ploog, in Proc. Internat. Symp. on Blue Laser and Light Emitting Diodes, Seehotel Zeuthen, Germany, 2000. J. E. Northrup and J. Neugebauer, Phys. Rev. B 53, R10477 (1996). G.-X. Qian, R. Martin, and D. Chadi, Phys. Rev. B 38, 7649 (1988). O. Brandt, H. Yang, B. Jenichen, Y. Suzuki, L. Da¨weritz, and K.H. Ploog, Phys. Rev. B 52, R2253 (1995). H. Yang, O. Brandt, M. Wassermeier, J. Behrend, H. P. Scho¨nherr, and K. H. Ploog, Appl. Phys. Lett. 68, 244 (1996). D. Schikora, M. Hankeln, D. J. As, K. Lischka, T. Litz, A. Waag, T. Buhrow, and F. Henneberger, Phys. Rev. B 54, R8381 (1996). J. Neugebauer, T. Zywietz, M. Scheffler, J. E. Northrup, and C. G. Van de Walle, Phys. Rev. Lett. 80, 3097 (1998). T. Zywietz, PhD thesis, Technische Universität Berlin, 1999. T. Zywietz, J. Neugebauer, M. Scheffler, and J. Northrup, HCM Newsletter (Psi k Network) 29 (1998). M. Wassermeier, H. Yang, O. Brandt, A. Yamada, J. Behrend, and K. H. Ploog, Surf. Sci. 385, 178(1997). G. Feuillet, H. Hamaguchi, K. Ohta, P. Hacke, H. Okumura, and S. Yoshida, Appl. Phys. Lett. 70, 1025 (1997). F. A. Ponce, D. P. Bour, W. T. Young, M. Saunders, and J. W. Steeds, Appl. Phys. Lett. 69, 337 (1996).

317

318

6 Surface Structure and Adatom Kinetics of Group-III Nitrides 31

32

33

34

35

36

37

38

39

40

41 42

43

A. R. Smith, R. M. Feenstra, D. W. Greve, J. Neugebauer, and J. E. Northrup, Phys. Rev. Lett. 79, 3934 (1997). A. Kazimirov, G. Scherb, J. Zegenhagen, T.-L. Lee, M. J. Bedzyk, M. K. Kelly, H. Angerer, and O. Ambacher, Appl. Phys. Lett. 84, 1703 (1998). M. E. Lin, S. Stite, A. Agarwal, A. Salvador, G.aL. Zhou, N. Teraguchi, A. Rocket, and H. Morkoc, Appl. Phys. Lett. 62, 702 (1993). W. C. Hughes, W. H. Rowland, M. A. L. Johnson, J. W. Cook, J. F. Schetzina, J. Ren, and J. A. Edmond, J. Vac. Sci. Technol. B 13, 1571 (1995). A. R. Smith, R. M. Feenstra, D. W. Greve, M.-S. Shin, M. Skowronski, J. Neugebauer, and J. E. Northrup, J. Vac. Sci. Technol. A 16, 2242 (1998). Q.-K. Xue, Q. Z. Xue, R. Z. Bakhtizin, Y. Hasegawa, I. S. T. Tsong, T. Saurai, and T. Ohno, Phys. Rev. Lett. 82, 3074 (1999). K. Rapcewicz, M. B. Nardelli, and J. Bernholc, Phys. Rev. B 56, R12725 (1997). J. Elsner, M. Haugk, G. Jungnickel, and T. Frauenheim, Solid State Commun. 106, 739 (1998). J. Fritsch, O. F. Sankey, K. E. Schmidt, and J. B. Page, Phys. Rev. B 57, 15360 (1998). A. R. Sandy, S. Mochrie, D. M. Zehner, G. Grübel, K. G. Huang, and D. Gibbs, Phys. Rev. Lett. 68, 2192 (1992). J. Northrup and J. Neugebauer, Phys. Rev. B 60, R8473 (1999). A. R. Smith, R. M. Feenstra, D. W. Greve, J. Neugebauer, and J. E. Northrup, Appl. Phys. A 66, S947 (1998). S. Kitamura, K. Hiramatsu, and N. Sawaki, Jpn. J. Appl. Phys. 34, L1184 (1995).

44

45

46

47 48 49 50

51

52

53

54 55

56

57 58

O.-H. Nam, M. Bremser, T. Zheleva, and R. Davis, Appl. Phys. Lett. 71, 2638 (1997). Y. Chen, T. Takeuchi, H. Amano, I. Akasaki, N. Yamano, Y. Kaneko, and S. Wang, Appl. Phys. Lett. 72, 710 (1998). X. Wu, C. Elsass, A. Abare, M. Mack, S. Keller, P. Petroff, S. DenBaars, J. Speck, and S. Rosner, Appl. Phys. Lett. 72, 692 (1998). J. Northrup, L. Romano, and J. Neugebauer, Appl. Phys. Lett. 74, 2319 (1999). P. Kratzer, C. Morgan, and M. Scheffler, Prog. Surf. Sci. 59, 135 (1998). W. Harrison, J. Vac. Sci. Technol. 16, 1492 (1979). C. Kisielowski, Strain in GaN Thin Films and Heterostructures, Semiconductors and Semimetals, Vol. 57, Chap. 7 (Academic Press, New York 1999). T. Zywietz, J. Neugebauer, and M. Scheffler, Appl. Phys. Lett. 73, 487 (1998). T. Zywietz, J. Neugebauer, M. Scheffler, J. Northrup, and C. Van de Walle, MRS Internet J. Nitride Semicond. Res. 3, p 1 (1998). T. Zywietz, J. Neugebauer, and M. Scheffler, Appl. Phys. Lett. 74, 1695 (1999). A. Kley, P. Ruggerone, and M. Scheffler, Phys. Rev. Lett. 79, 5278 (1997). E. J. Tarsa, B. Heying, X. H. Wu, P. Fini, S. P. DenBaars, and J. S. Speck, J. Appl. Phys. 82, 5472 (1997). S. Y. Karpov, Y. N. Makarov, and M. S. Ramm, MRS Internet J. Nitride Semicond. Res. 2, 45 (1997). K. Wang, J. Singh, and D. Pavlidis, J. Appl. Phys. 76, 3502 (1994). R. Averbeck and H. Riechert, Phys. Stat. Sol. (a) 176, 301 (1999).

Part 2

Defects and Interfaces

321

7

Topological Analysis of Defects in Nitride Semiconductors Georgios P. Dimitrakopulos, Philomela Komninou, Theodoros Karakostas, and Robert C. Pond

Abstract

A review of the topological theory of defects and interfaces in crystalline materials is presented, aimed at demonstrating the usefulness of this method for the study of nitride films and interfaces. The review addresses both a priori and a posteriori topological defect characterization in a unified manner, showing their equivalence, the circumstances under which each approach is applicable, and practical aspects of their deployment. A number of experimental observations are illustrated, and it is demonstrated that the topological analysis leads to useful conclusions on admissible defects, structure-mechanism relations, and the influence of defects on properties. These given observations concern (i) dislocations (threading, stacking-fault, interfacial) in GaN epilayers, (ii) influences of the epitaxial interface on the systematic appearance of inversion and stacking disorder, (iii) structural transformations of inversion domain boundaries due to their intersections with stacking faults, (iv) double-positioning twinning, and (v) junction lines between hexagonal and cubic nitride interfaces.

7.1

Introduction

Defects in epitaxial films may degrade device performance (e.g., [1–5]), and innovative strategies have been devised to reduce defect content (e.g., [3, 6–8]). A variety of defects can arise during the growth, processing, and operation of devices, and it is important to identify the consequences of their introduction and their in-

322

7 Topological Analysis of Defects in Nitride Semiconductors

fluence on properties. A most potent origin of defects is the “mismatch” between epilayer and substrate that arises due to differences of symmetry, structure, and orientation. For example, it has long been appreciated that lattice mismatch (i.e., mismatch between the translation symmetry) must be accommodated by misfit dislocations, for epitaxial films with thickness greater than a critical value (e.g., [6, 9]). More recently, it has been shown that other forms of “mismatch”, such as the misalignment of symmetry axes and mirror planes, or the absence of particular such elements in one of the two adjoining crystals, may also lead to defect introduction [10, 11] in agreement with the Curie principle of symmetry compensation [12]. For example, in epitaxial GaAs on (001) Si (or Ge), the compensation of fourfold screw rotation symmetry along [001], that exists in the substrate but is suppressed in the epilayer, can induce inversion domain disorder [13, 14]. A similar mismatch between epitaxial NiSi2 and its Si substrate can promote interfacial dislocation formation [15]. We have indicated above that any structural mismatch or discrepancy between a substrate and an epilayer is a potential source of defects, either residing in the common interface, or emanating from the interface into one of the crystals. Using topological arguments, an expression that characterizes all the defects that may arise in this manner has been obtained [10, 16]. In the following, we shall review the methods of topological characterization and demonstrate their application to the characterization of defects in nitride films and interfaces. Defects between crystallographically equivalent, and hence energetically degenerate, interfacial structures can be determined a priori [10]. Such information is invaluable for substrate/epilayer selection, as well as for the interpretation of observations at microscopic level. The character of defects that separate nonequivalent regions is also incorporated into the topological formation and can be discussed a priori in certain instances, for example when inner unit-cell vectors are involved [16]. Defects in both classes will be considered here. Moreover, defects in the bulk of GaN layers, including partial dislocations, stacking-faults (SFs) and inversion domain boundaries (IDBs), will be discussed. Topological methods are again found to be helpful in the characterization of these defects and the analysis of their interactions. A posteriori topological characterization of defects on high-resolution transmission electron microscopy (HREM) micrographs is performed by circuit mapping [11]. The methods of a priori and a posteriori defect analysis will be presented in a unified manner and practical aspects of their deployment will be demonstrated. HREM observations in nitride epilayers and interfaces will be analyzed, and conclusions will be extracted concerning admissible defects and structuremechanism relations. GaN and other related epilayers have generated significant interest for use in optoelectronic device applications (e.g., [5, 17]), since the material’s large direct band gap can be employed for the production of blue and ultraviolet wavelengths. It is challenging that devices comprising such epilayers exhibit satisfactory performance despite a multiplicity of microstructural defects such as threading and misfit dislocations, nanopipes, IDBs, SFs on basal and prismatic crystallographic planes, twins, and grain boundaries (GBs) (e.g., [18–25]). Such defects appear in

7.1 Introduction

epilayers grown on a range of substrates (e.g., sapphire, SiC, Si, GaP, etc.) and by various deposition techniques (MBE, MOCVD, VPE) (e.g., [5, 25–28]). A comprehensive understanding of the topological properties of microstructural defects is required in order to interpret experimental observations, to appreciate their behavior and influence on material properties, and finally to improve the quality of GaN epilayers. In Sect. 7.2 we introduce the crystallographic tools and topological methods that are necessary for the characterization of defects in nitride epilayers. A derivation of the expression for predicting the topological character of interfacial defects is given using the notation of the International Tables for Crystallography [29]. When defects are observed experimentally by HREM, it is necessary to use an a posteriori method, such as circuit mapping, for their characterization. The method was initially introduced by Frank [30] and employed translation operations. However, in order to characterize all types of admissible defects, and to construct circuits that may cross faults or interfaces, a more generalized form of mapping is needed [11]. In Sect. 7.3 the structure of GaN is described, as well as the experimental conditions under which the presented observations have been obtained. In Sect. 7.4 we consider line defects, in particular dislocations, both as single crystal defects and as defects associated with faults and interfaces. In GaN epilayers, a multiplicity of dislocations, such as threading, partial, misfit, and grain-boundary dislocations (e.g., [19, 22, 31, 32]) exists. They are named in relation to the mechanism by which they are introduced, and valuable information is obtained by a thorough understanding of their topological properties. In Sect. 7.5, we examine planar defects, in particular IDBs and SFs on prismatic crystallographic planes, in relation to the structure of the epitaxial interface. IDBs are particularly important when growth proceeds along a polar direction, since they facilitate the coexistence of crystalline regions of inverse polarity, thus affecting physical and chemical properties such as surface structure and morphology, chemical etching behavior, crystal growth behavior, etc. [25, 27, 33, 34]. Section 7.6 is devoted to the junction lines of planar defects. By understanding the topology and defect character of such lines we can better comprehend the associated interactions. For example, one such interaction leads to the structural transformation of IDBs with a resultant influence of these defects on the electrical behavior. The conclusions are discussed in Sect. 7.7. The Appendix gives an account of Frank’s 4-vector method for crystallographic problems involving hexagonal and trigonal crystallography [35], and shows how the Miller-Bravais indexing scheme is related to a more general mathematical framework that facilitates crystallographic calculations in direct and reciprocal space.

323

324

7 Topological Analysis of Defects in Nitride Semiconductors

7.2

Defect Characterization 7.2.1

Defect Characterization by a Volterra-like Approach

The character of line defects in elastic continua was originally discussed by Volterra [36], and the admissible forms are referred to as dislocations, disclinations and dispirations. This approach is adapted to interfacial defects by considering initially a bicontinuum of two elastic half-spaces, designated white (k) and black (l), which are joined along a planar interface with no initial long-range stresses as depicted in Fig. 7.1 a. We then introduce a cut along the interface, and we modify the exposed surfaces by adding/removing material and/or by applying tractions, as shown schematically in Fig. 8.1 b and c. Finally we rejoin the exposed surfaces and, as a result, a line defect appears between the initial interface and the new. In agreement with Volterra, this defect is characterized by the operation required to bring the new surfaces together, which can be formulated in terms of the operations enacted on the initial surfaces. Assume the new k surface is obtained from the initial one by an operation V(k)j = (V(k)j, v(k)j) in Seitz notation [29] (where V(k)j is the orthogonal part and v(k)j the translation part), and, similarly, the new l surface is obtained by V(l)i. Then, by convention [10, 11], the defect is described topologically by the operation required to bring the exposed l surface onto the exposed k one, i.e., Z ij ˆ V…k†j V…l†i

1

…1†

Equation (1) is consistent with the RH/FS convention of the circuit mapping method (see Sect. 7.2.2) taking the line direction n of the defect to point outwards

a Schematic illustration of a portion of an elastic bicontinuum; b schematic illustration of the introduction of an interfacial dislocation by a Volterra-like process. The line sense n of the defect is defined in accordance with the RH/FS criterion for bicrystals [11]. The new k and l surfaces are obtained from the initial ones by translation operations; c schematic illustration of the introduction of an interfacial disclination; the new surfaces are obtained by rotation operations.

Fig. 7.1

7.2 Defect Characterization

from the page in Fig. 7.1. Z ij is an admissible description of a line defect if it represents a rigid-body operation. If it is a displacement Z ij = (I, zij), where I is the identity, then the defect is a dislocation with Burgers vector bij = zij (Fig. 7.1 b). If Z ij is a rotation (Rij, 0), the defect is a disclination of strength Rij (Fig. 7.1 c), and an operation with both translational and rotational components characterizes a dispiration. Crystals are discrete media that are left invariant only by the spacegroup symmetry operations, and, furthermore, the lattices introduce natural choices for coordinate frames. With respect to the coordinate frame issue, we choose to define Z ij in the k frame, and hence Eq. (1) takes the form Z ij ˆ V…k†j PV…l†i 1 P

1

;

…2†

where P = (P, p) is the transformation relating the l coordinate frame to the k one, describing their relative orientation and position (P is the matrix that transforms k vectors into corresponding l ones, expressed in the k frame – see Appendix – and p is the rigid-body translation, expressed in the k frame, of the l origin away from the k origin). Operations in the l crystal take the form PV(l)i P –1 when re-expressed in the k frame. With respect to the invariance issue, substitution of symmetry operations, designated W i = (Wi, wi) in [29], in the place of V i operations in Eq. (2), yields descriptions of defects between crystallographically equivalent, and hence energetically degenerate, regions. These can be obtained a priori since such operations are known, and Eq. (2) takes the special form Z ij = Qij where Qij ˆ W…k†j PW…l†i 1 P

1

;

…3†

The operations in this set characterize defects that separate energetically degenerate regions of interface, since the operations applied to the initial k and l surfaces create new surfaces that are crystallographically equivalent to the initial ones in the visualization presented in Fig. 7.1. Equation (3) can be used to predict the character of such defects, and this has been explored elsewhere [10]. The multiplicity of defects in this class depends on the extent to which k and l symmetry is suppressed by the formation of the initial bicrystal, and dissymmetrization provides a fundamental basis for classifying these defects [10]. In this manner, Eq. (3) is in agreement with the Curie principle of symmetry compensation according to which, when symmetry is suppressed at some structural level, it may reappear at another [12]. Treatments elsewhere (e.g., [10, 11, 37]) have used this approach and have also included the consideration of antisymmetry operations that interrelate the k and l crystals. If one (or both) of the rigid-body operations substituted in Eq. (2) is not a symmetry operation, then the defect separates crystallographically distinct regions. The arguments outlined above show that expressions (2) and (3) have similar forms, and that the operations Qij form a subset of the operations Z ij. Operations

325

326

7 Topological Analysis of Defects in Nitride Semiconductors

in the set Z ij that do not also belong to Qij characterize defects in the distinct category. However, if there are no constraints on the nature of rotational and displacive operations that can be substituted into Eq. (2), there is no means of predicting which operations in the distinct set characterize physically feasible defects. On the other hand, in certain instances, there are structural choices of V i operations, for example when inner unit-cell vectors are utilized, and Eq. (2) defines the rigorous framework in which to investigate such defects. 7.2.2

Defect Characterization by Circuit Mapping

The topological analysis of defects in crystals and interfaces that was presented in Sect. 7.2.1 has demonstrated that it is necessary to consider spacegroup symmetry in order to be able to characterize the complete range of admissible defects. This means that traditional defect characterization by contour mapping [30] needs to be generalized so that symmetry operations other than translations can be included. In this subsection, we outline the mathematical basis for such generalized mapping, and a detailed account can be found in [11]. We have chosen the hexagonal close-packed (hcp) structure to illustrate the principles involved, since a similar crystalline form can be considered as parent structure of GaN (see Sect. 7.3). Here we use the Miller-Bravais system for indexing (a review of crystallographic calculations and manipulations in hexagonal crystals is presented in the Appendix). The coordinate frame used is that of a hexagonal lattice with primitive translation vectors a1 = 1/3 [21 10], a2 = 1/3 [1210], a3 = 1/3 [1 120], and c = [0001]. The choice of the location for the origin of the coordinate system with respect to the atomic positions is arbitrary, and in the present work we choose a center of symmetry, as depicted schematically in Fig. 7.2. The two nonequivalent atoms in the structure’s basis, designated type A and type B, are located at uA = 1/12 [4043] and uB = 1/12 [4043]. The symmetry of any crystal is specified by its spacegroup, i.e., the group of operations that leave the crystal invariant with respect to a fixed coordinate frame. For hcp the set of such operations is concisely represented by the spacegroup

Schematic projection along [0001] of an hcp crystal (spacegroup P63/mmc) showing some of the principal symmetry elements, and A and B type atomic sites, at heights ± 1/4 [0001], distinguished by different shading. Small circles denote inversion centers. Dashed and solid lines denote the projections of {1100} glide mirrors and {21 10} mirrors, respectively. Arrows denote two-fold symmetry axes. The lattice translations a1 = 1/3 [21 10], a2 = 1/3 [1210], a3 = 1/3 [1 120] are also indicated. Fig. 7.2

7.2 Defect Characterization

327

Tab. 7.1 Matrices for the point symmetry operations in the space group 6/mmm

1 2 2 0

2 1 2 0

3 0 0 7 7 0 5 3

2 16 6 1 34 2 0

2 2 1 0

1 2 2 0

3 0 0 7 7 0 5 3

3 0 0 7 7 0 5 1

2 2 M…1100† 6 16 1 34 2 0

1 2 2 0

2 2 1 0

3 0 0 7 7 0 5 3

0 0 1 0

3 0 0 7 7 0 5 1

2 2 M…1010† 6 16 2 34 1 0

2 1 2 0

1 2 2 0

3 0 0 7 7 0 5 3

1 2 2 0

2 2 1 0

3 0 0 7 7 0 5 3

2 1 M…0110† 6 16 2 34 2 0

2 2 1 0

2 1 2 0

3 0 0 7 7 0 5 3

2 16 6 2 34 1 0

2 1 2 0

1 2 2 0

3 0 0 7 7 0 5 3

2 1 M…0001† 6 16 2 34 2 0

2 1 2 0

2 2 1 0

3 0 0 7 7 0 5 3

2 1 16 6 2 34 2 0

2 2 1 0

2 1 2 0

3 0 0 7 7 0 5 3

2 2 16 6 2 34 1 0

1 2 2 0

2 1 2 0

3 0 0 7 7 0 5 3

2 1 2 0

2 2 1 0

3 0 0 7 7 0 5 3

2 2 1 0

1 2 2 0

3 0 0 7 7 0 5 3

0 1 0 0

0 0 1 0

3 0 3 0 7 7 0 5 1

2

0 0 1 0

1 0 0 0

3 0 M…21 10† 0 7 7 5 0 1

2

0 60 6 41 0

1 0 0 0

0 1 0 0

3 0 M…1210† 0 7 7 5 0 1

2

2 1 2‰21 10Š 6 60 40 0

0 0 1 0

0 1 0 0

3 0 M…1 120† 0 7 7 0 5 1

2

2 0 2‰1210Š 6 60 41 0

0 1 0 0

1 0 0 0

3 0 2‰1100Š 0 7 7 0 5 1

2

2 0 2‰1 120Š 6 61 40 0

1 0 0 0

0 0 1 0

3 0 2‰1010Š 0 7 7 5 0 1

0 1 0 0

0 0 1 0

3 0 2‰0110Š 0 7 7 0 5 1

0 0 1 0

1 0 0 0

3 0 2‰0001Š 0 7 7 0 5 1

2

1 60 6 40 0

I

2 3+

0 61 6 40 0 2

3–

1

‡

3

2

1 6 0 6 4 0 0 2

0 6 1 6 4 0 0

0 6 0 6 4 1 0 1 6 0 6 4 0 0 0 6 0 6 4 1 0 0 6 1 6 4 0 0 2 16 6 1 34 2 0 2

2

1 16 6 2 34 2 0

1 0 0 0

0 1 0 0

3 0 0 7 7 0 5 1

0 0 1 0

0 1 0 0

3 0 0 7 7 0 5 1

0 1 0 0

1 0 0 0

1 0 0 0

6+

2

2 16 6 2 34 1 0 2

6–

‡

6

2

6

2 16 6 1 34 2 0

P63/mmm and is listed in Tab. 7.1. Some of the principal elements are indicated in Fig. 7.2; for example, mirror planes are present on {1 120} and (0001), and cglide mirror planes on {1010}. We note that the mirror planes relate A-type atoms to other A atoms, and B-type to other B, whereas the c-glide mirror planes interrelate A and B type atoms. The six-fold screw-rotation axis, 63, along [0001] also interrelates A and B type atoms.

328

7 Topological Analysis of Defects in Nitride Semiconductors

Symmetry operators are represented, using the notation of [29], in the form W = (W, w), where W is a rotation, mirror, inversion or the identity, and w is a displacement arising either due to a translation intrinsically associated with the operation or due to the location of the symmetry element with respect to the chosen origin, or both. In the case of pure translation operations, W = (I, t), where I is the identity and t the translation.

7.2.2.1 Circuits in Perfect Crystals

In order to introduce the mathematical formulation and to grasp the necessary concepts behind generalized mapping, it is convenient to discuss initially the formulation of circuits when there is no defect present. We imagine an observer who is transported on an excursion through the crystal (that is taken to be fixed), by a sequence of operations enacted on him alone. If these operations are restricted to being symmetry operations, each one takes the observer from one point to another, crystallographically equivalent one, and, from the observer’s point of view, the crystal appears unchanged at each stage. An origin, O, is chosen at some convenient center of symmetry. Next, the starting point of the excursion, S, is located by the vector s; this latter point may be a center of symmetry, or it may be more convenient sometimes to choose an atomic site. For example, in the analysis of HREM images obtained using a low-index incident beam direction, the two choices may correspond to projected locations of tunnels between atomic columns or atomic columns, respectively. Initially, the observer is taken to be in his starting orientation (say facing along a1 with –a2 front right, –a3 front left and c up). At the end of the sequence of operations, the observer reaches the point F, located by the vector f, and may also have been rotated and/or inverted. Imagine that the observer has reached some intermediate point in his excursion. The next operation in the sequence, the ith say, has to operate on the observer at this point. If this operation is a translation, we simply have W i = (I, t). However, in more general cases, the operation may involve rotation or reflection for example and, furthermore, this may act through some point, ri, other than the observer’s location. Thus, in the general case, we must re-express the ith operation as W i, where W i ˆ …I; ri †W i …I; ri †

1

…4†

and ri is the position vector of point ri. Such a redefinition does not modify the component Wi, but may change wi (although not in the case of translations). A complete excursion can therefore be expressed mathematically as the following sequence of operations C ˆ …C; c† ˆ W n . . . W 3W 2W 1 :

…5†

We refer to C as the circuit operator, and it relates the observer’s final status to his starting orientation and location (I, s). Thus

7.2 Defect Characterization

C…I; s† ˆ …C; Cs ‡ c† ;

…6†

where f = Cs + c is the final location of the observer, and C is the resultant rotation and/or inversion of the observer’s frame. When C = (I, 0), the circuit is closed in both the translational and orientational sense. To illustrate these procedures, three simple circuits depicted in Fig. 7.3 are described below. a) Circuit 1: SABCDS, Fig. 7.3 a This is a circuit comprising only translation operations. For simplicity we choose our origin to be coincident with the point S, i.e., s = 0. The sequence of symmetry operations, W1 to W5, making up the circuit, and the observer’s locations following each individual operation, are listed in Tab. 7.2. In this case the circuit is closed and C = (I, 0). b) Circuit 2: SHJKLMS, Fig. 7.3 b The chosen origin is indicated in Fig. 7.3 b, and the starting point of the circuit is the B-type atom S, i.e., s = uB. Listed in Tab. 7.2 are the six symmetry operations in the sequence. The first is a (1100) c-glide mirror operation taking the observer to the A-type atom, H. At this point the observer’s frame has been reflected in the (1100) plane and shifted to uA–a3. The next two operations are translations taking

Closed circuits in perfect crystals (see text for details). Shading indicates differ-

Fig. 7.3

ent levels along the projection direction. Small circles denote inversion centers.

329

330

7 Topological Analysis of Defects in Nitride Semiconductors Tab. 7.2 Circuits in perfect crystals

Circuit 1 (Fig. 7.3 a) Start

Finish Circuit 2 (Fig. 7.3 b) Start

Finish Circuit 3 (Fig. 7.3 c) Start

Finish

Symmetry operations

Observer location

(I, s) = (I, 0) W 1 = (I, –2 a1) W 2 = (I, 2 a3) W 3 = (I, –a2) W 4 = (I, a1) W 5 = (I, –3 a3) C = (I, 0)

S A B C D S

(I, s) = (I, uB) W 1 = (M(1100), 1=2 c) W 2 = (I, –2 a1) W 3 = (I, –2 a2) W 4 = (M(1100), –1=2 c) W 5 = (I, 2 a1) W 6 = (I, 2 a2) C = (I, 0)

S H J K L M S

(I, s) = (I, 3 a1 + uA) W 1 = (6+, –1=2 c) W 2 = (6+, 1=2 c) W 3 = (6+, –1=2 c) W 4 = (6+, 1=2 c) W 5 = (6+, –1=2 c) W 6 = (6+, 1=2 c) C = (I, 0)

S J K L M N S

the observer through J to K. Next, another (1100) c-glide mirror operation is applied taking the observer to L and reflecting his frame back into its initial orientation. Finally, two translations carry the observer through M to S. (Note that for the first and fourth operations W i = W i because the mirror operations are defined to act through the chosen origin, i.e., r = 0). This circuit is closed and it can be confirmed readily that C = (I, 0), i.e., C (I, s) = (I, s). c) Circuit 3: SJKLMNS, Fig. 7.3 c This closed excursion comprises six screw-rotation operations; the origin is O and S is chosen to be an A-type atom at s = 3 a1 + uA. The sequence of operations and observer locations are listed in Tab. 7.2. Note that the observer visits A- and B-type atomic sites alternately. Also, since all the operations act through the chosen origin, r = 0 in each case and hence W i = W i. It can be confirmed readily that C = (I, 0), i.e., that the circuit is closed in the general sense.

7.2 Defect Characterization

7.2.2.2 Circuits in Imperfect Crystals and Circuit Mapping

In the characterization of dislocations in single crystals that was pioneered by Frank [30], a closed circuit comprising translation operations is constructed, encircling the defect, and this circuit is subsequently mapped into perfect reference material. If a line direction n is attributed to the dislocation and the initial circuit is taken to be right-handed about this direction, then the closure failure from F to S, in the mapped circuit, is the Burgers vector, b, of the defect (i.e., the RH/FS convention). Expressing this procedure using our present terminology, we say that the observer makes a righthanded closed circuit about the dislocation. If the observer travels through “good” material where the strains are not too large, and the observer is “short-sighted”, the circuit appears to comprise a sequence of symmetry operations transporting him through a series of equivalent points. When this sequence is mapped into reference material, the circuit will fail. Since the circuit operator C transports the observer from S to F, the defect is characterized by the inverse operation C–1. In the case considered by Frank [30], where all the component symmetry operations are translation vectors, the circuit operator will take the form C = (C, c) = (I, t), where b = –t. A detailed analysis of circuit mapping for the simple case of a threading dislocation in GaN is given in Sect. 7.4.

7.2.2.3 Circuit Mapping of Interfacial Defects

The circuit mapping method can be extended readily to the case of interfacial defects. It is necessary, however, to consider the following additional features: – the existence of two adjoining crystals that may have different symmetries and orientations, – that a bicrystalline reference space must be defined, and – that closed circuits around interfacial line defects cross the interface at two places. These issues are discussed below. As in Sect. 7.2.1, we distinguish the two crystals by designating them as white (k) and black (l). Coordinate frames and origins are selected for each crystal, and these are interrelated by P = (P, p). The topological parameters of interfacial defects ultimately need to be expressed using one coordinate frame, and we choose the k frame in this capacity. Defects are defined with respect to some reference space, and, in the case of single crystal defects, the perfect crystal, as described by the crystal spacegroup, is the most convenient reference. In the case of interfacial defects, the appropriate reference space is the dichromatic complex [11]. This is the composite resulting from the two undistorted crystals if they are imagined to interpenetrate with the relative orientation and position defined by P. The dichromatic complex and its symmetry have been discussed in detail elsewhere [38]. To characterize an interfacial defect, a line direction n is first assigned. A righthanded circuit is then constructed that comprises a k and a l segment, and these are linked by two displacements, k-to-l and l-to-k, across the interface as depicted schematically in Fig. 7.4. A starting point, S, is chosen in the k crystal close to the

331

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7 Topological Analysis of Defects in Nitride Semiconductors

interface, and the observer is transported to another k point, U, near the interface, at the end of the k segment. The sequence of operations in the k segment is represented by the circuit operator C(k). Next the observer experiences a displacement (I, pkl) across the interface from U to the l point V. The observer’s excursion then proceeds by means of l symmetry operations until he reaches point Z. The l segment is represented by C(l), which becomes PC(l) P –1 when re-expressed in the l frame. Finally, the circuit is closed by another displacement (I, plk) across the interface from Z back to S. Both crossing displacements are also expressed in the k frame. The total circuit is now mapped into the bicrystalline reference space, i.e., the dichromatic complex. The circuit operator is given by C…kl† ˆ …I; plk †PC…l†P 1 …I; pkl †C…k† :

…7†

The defect is characterized by C(kl)–1, i.e., the inverse of the circuit operator for the total circuit, and this is the irreducible expression of the closure failure of the mapped excursion. It can be seen that C(kl) depends in part on the operations that transport the observer across the interface. In the important case of defects that separate crystallographically equivalent regions of interface, it is necessary for the observer to cross in correspondingly equivalent ways in order that no spurious defect content be included in the final expression. To fulfil this requirement, the observer should be oriented in an equivalent way at each crossing, relative to the local interface normal, n (which is taken to be a unit vector directed towards the k crystal). Under these circumstances, Eq. (7) can be re-expressed more simply as C…kl† ˆ PW…l†i P 1 W…k†j

1

;

Closed circuit around an interfacial defect illustrated schematically prior to mapping in a dichromatic complex. The defect has line direction out of the plane of the paper as represented by the unit vector n.

Fig. 7.4

…8†

7.3 Crystalline Structures and Experimental Details

where P = (P, p). The inverse of this expression is identical to the formulation obtained in the characterization of interfacial defects using a Volterra-like approach, i.e., Eq. (3), where W(k)j and W(l)–1 are the symmetry operations required to i bring equivalent k and l surfaces together after a cut is made along the interface and modifications are made to the exposed initial surfaces. One surface of the cut invoked in such a process is defined by an infinity of S points, and each one maps in the reference space to a corresponding F point related to it by C(kl). In circuit mapping, passive operations are used, i.e., operations that displace and/or change the orientation of the observer’s frame. On the other hand, in the Volterra approach, the operations are active, i.e., they are motions enacted on the medium while keeping the coordinate system invariant, and hence C(kl)–1 = Qij.

7.3

Crystalline Structures and Experimental Details

In its stable form, GaN exhibits the wurtzite structure (spacegroup P63mc, lattice parameters aa-GaN = 0.319 nm, ca-GaN = 0.518 nm) when deposited on substrates such as sapphire and 6H-SiC. Wurtzite is a hexagonal nonholosymmetric structure. The term nonholosymmetric denotes that the structure does not exhibit the highest possible order of symmetry for this particular crystal system [29], and can be considered as a daughter product of a holosymmetric structure. In our case, the parent structure is a hexagonal structure with atoms in the same fractional coordinates as in hcp (spacegroup P63/mmc). The parent-to-daughter dissymmetrization is due to the atomic motif (or basis) that is associated with each lattice point. In the holosymmetric parent the basis is composed of two atoms designated A and B type and located at uA and uB (see Sect. 7.2), whereas in wurtzite there are two additional atoms, a and b, at locations ua = 1/12 [4043] + 0.377 [0001] and ub = 1/12 [4043] + 0.377 [0001]. In the hexagonal GaN polytype (a-GaN), the locations A and B are occupied by one atomic species, while a and b are occupied by the other. The a-GaN structure can also be imagined as two interpenetrating hexagonal substructures, one of Ga and one of N; in each substructure, the fractional coordinates of atomic positions are the same as in hcp. The two substructures are relatively shifted by *3/8 [0001], and the stacking sequence along [0001] is . . .AaBbAaBb. . . . The a-GaN symmetry is depicted schematically in Fig. 7.5, and Tab. 7.3 lists the point-symmetry operations of spacegroups P63mc and P63/mmc in accordance with the International Tables [29]. Due to the polyatomic basis, half of the point symmetry operations that describe the parent structure are suppressed in a-GaN, including the center of symmetry. Therefore, a-GaN is noncentrosymmetric and the dissymmetrization can be expressed by the coset decomposition [29] P63 =mmc ˆ fP63 mcg [ 1fP63 mcg :

…9†

Using this crystallographic information, the [1 120] and [1100] projections of a-GaN can be determined and appear as depicted in Fig. 7.6, with d(1100) = 0.2739 nm,

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7 Topological Analysis of Defects in Nitride Semiconductors Schematic illustration of the a-GaN structure (spacegroup P63mc) in projection along [0001], with symmetry elements superimposed. Open and filled circles denote distinct atom types at height 0 and *1/8 [0001] respectively. Solid lines and dashed lines indicate projections of {1 120} mirror planes and {0110} glide mirror planes respectively. The lattice translations a1 = 1/3 [21 10], a2 = 1/3 [1210], a3 = 1/3 [1 120] are also indicated. Fig. 7.5

Tab. 7.3 Point-symmetry operations of spacegroups P63mc and P63/mmc. The former includes

only the first twelve operations while the latter all twenty-four symmetry operations Symmetry operation

Location

Glide component

P63mc, P63/mmc 1 3+ 3– 2 6+ 6– m m m c c c

0, 0, 0, w 0, 0, 0, w 0, 0, 0, w 0, 0, 0, w 0, 0, 0, w u, –u, 0, 0 0, v, –v, 0 u,0, –u, 0 –u, –u, 2u, 0 2u, –u, –u, 0 –u, 2u, –u, 0

P63/mmc 2 2 2 2 2 2 1 3+ 3– m 6+ 6–

–u, –u, 2u, 0 2u, –u, –u, 0 –u, 2u, –u, 0 u, –u, 0, 1=4 0, u, –u, 1=4 u, 0, –u, 1=4 0, 0, 0, 0 0, 0, 0, w, 0; 0, 0, 0 0, 0, 0, w, 0; 0, 0 u, v, –(u+v), 1=4 0, 0, 0, w; 0, 0, 0, 1=4 0, 0, 0, w; 0, 0, 0, 1=4

0, 0, 0, 1=2 0, 0, 0, 1=2 0, 0, 0, 1=2

0, 0, 0, 1=2 0, 0, 0, 1=2 0, 0, 0, 1=2

Seitz operator

Symmetry element

{I, 0} {3+, 0} {3–, 0} {2, 1=2 c} {6+, 1=2 c} {6–, 1=2 c} {M, 0} {M, 0} {M, 0} {M, 1=2 c} {M, 1=2 c} {M, 1=2 c}

– [0001] [0001] [0001] [0001] [0001] (1 120) (21 10) (1210) (1100) (0110) (1010)

{2, 0} {2, 0} {2, 0} {2, 1=2 c} {2, 1=2 c} {2, 1=2 c} {1, 0} {3+, 0} {3–, 0} {M, 1=2 c} {6+, 1=2 c} {6–, 1=2 c}

[1 120] [21 10] [1210] [1100] [0110] [1010] – [0001] [0001] (0001) [0001] [0001]

7.3 Crystalline Structures and Experimental Details

Projections along [1 120] and [1100] of a-GaN in a direct; b reciprocal space. In a the structure is illustrated schematically. Circles and rectangles denote atoms at distinct levels along the projection direction. Large

Fig. 7.6

and small symbols denote distinct atomic species. Crosses indicate the position of the origin. In b corresponding electron diffraction patterns are given (see text for details).

d(1120) = 0.1581 nm and d(1122) = 0.1347 nm. The angle # between the planes (1100) and (1101) is 28.04 8 and the angle a between the planes (1120) and (1122) is 31.59 8. Diffraction patterns obtained using transmission electron microscopy with the incident beam parallel to [1 120] and [1100] are also shown in Fig. 7.6. It is readily seen, and confirmed by calculations (in the manner prescribed in the Appendix), that the ratios |gi|/|gj| etc. are equal to dj/di etc., and that # and a are the angles gi^gj for the corresponding planes. Note that the reflection g = 0001 is kinematically forbidden but is observable in the [1 120] pattern due to double diffraction. In a metastable polytype, GaN crystallizes in the zinc blende cubic structure (ab-GaN = 0.451 nm, spacegroup F43m). As in the wurtzite case, the zinc blende structure is also nonholosymmetric and noncentrosymmetric. Zinc blende can be considered a daughter product of the diamond structure (spacegroup Fd3m), and

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7 Topological Analysis of Defects in Nitride Semiconductors

a coset decomposition similar to Eq. (9) applies. The zinc blende structure can also be described as two interpenetrating fcc substructures, one of Ga and one of N, that are separated by 1/4 [111]. The cubic polytype (b-GaN) has certain advantages over the hexagonal counterpart, in particular easy cleavage, direct band gap, and higher carrier mobilities. Extended efforts have recently been made to grow bGaN epilayers of good quality on a variety of substrates and by different techniques (e.g., [39–44]). However, such films commonly exhibit large densities of defects, mainly twins and SFs, and their overall quality currently requires further improvement. Due to the increased interest on such epilayers, we will also consider some of their characteristic defects. In the following sections, a number of experimental observations of defects in GaN epilayers will be studied based on the fundamentals that have been presented in Sect. 7.2 and the present section. For our purpose, specimens were obtained from a-GaN layers epitaxially deposited on (0001) Al2O3 by RF plasma MBE [27]. Prior to deposition, the sapphire surface had undergone high-T nitridation, followed by low-T deposition of an 8–20-nm AlN buffer layer. The buffer layer is employed in order to mediate misfit relief and improvement of epilayer quality [45]. Following a high-T anneal of the buffer, a-GaN epilayers were grown under various conditions. The epilayers exhibited the relative orientation relationship (0001)a-GaN//(0001)sapph., h1010ia-GaN//h1210isapph. with the substrate. Following deposition, some a-GaN epilayers were overgrown by stoichiometric TiN thin layers, deposited for Ohmic contact purposes by dc reactive magnetron sputtering at room temperature. The orientation relationship after this deposition was (0001)a-GaN//(111)TiN, h1120ia-GaN//h110iTiN, and details are given elsewhere [46, 47]. In addition to the a-GaN epilayers, specimens were obtained from b-GaN layers deposited on (0001) Al2O3 by low-T HVPE. The orientation relationship in this case was (111)b-GaN//(0001)sapph., h110ib-GaN//h1010isapph.. Sample preparation involved mechanical thinning followed by ion-milling to electron transparency. HREM micrographs were obtained using a Topcon 002B microscope, operated at 200 kV, with a point-to-point resolution of 0.18 nm and Cs = 0.4 mm. Where deemed necessary, image simulations for the identification of planar defects on HREM micrographs were performed and, for this purpose, the multislice algorithm in the EMS software [48] was employed; supercells of the defects were created in the appropriate projection, and a through focus-thickness series of simulated images were constructed. A defect model of nitride epilayers, should consider point defects, line defects such as dislocations, and planar defects such as faults and interfaces. In order to be comprehensive, the model should also consider the superpositions and interactions between defects in all categories. As a contribution to the development of such a model, we present in the following a number of applications of the topological theory to the characterization of defects, and their coexistence. In the manner outlined in the introduction, we begin with line defects, and continue with planar defects and defect interactions.

7.4 Dislocations in GaN Epilayers

7.4

Dislocations in GaN Epilayers 7.4.1

Threading Dislocations

Threading dislocations are introduced in the initial stages of island growth and they accommodate small deviations from the exact epitaxial orientation relationship between the epilayer and its substrate. Their Burgers vectors reflect the mechanism of their introduction; in [0001] growth of a-GaN, edge dislocations with Burgers vectors bi = ai = 1/3 h2110i (i = 1, 2, 3) are introduced in order to accommodate small angular deviations about the [0001] axis. Screw dislocations with b = c = [0001] are also introduced to accommodate deviations due to the overgrowth of substrate steps (e.g., [31, 32, 49]). Fig. 7.7 a is a plan-view HREM micrograph of an edge threading dislocation in wurtzite GaN. The defect can be characterized by circuit mapping as described in Sect. 7.2. Using the dark spots (atomic columns for the particular imaging conditions), a closed right-handed circuit SGHIJKLS has been drawn around the line direction n of the defect (taken to point into the page). The circuit is shown mapped into the reference space in Fig. 7.7 b, whereby it is seen that closure failure FS arises. The origin, O, has been chosen to be at a location corresponding to a center of symmetry of the holosymmetric parent structure (see Sect. 7.3). The

a Plan-view HREM micrograph of an edge threading dislocation in a-GaN with [0001] line direction. A closed right-handed Burgers circuit has been drawn around the line direction of the defect (defocus = –29 nm, thickness = 7.8 nm, atomic columns correspond to dark spots); b mapping of the Burgers circuit to the reference space. Closure Fig. 7.7

failure FS identifies the defect as an edge dislocation with Burgers vector b = 1/3 h21 10i ([0001] projection: large and small circles denote distinct atomic species. Open and filled circles denote atoms at heights 0 and *ca-GaN/8, respectively. n is the line direction of the defect pointing into the page).

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7 Topological Analysis of Defects in Nitride Semiconductors

starting point S is located at an A-type atomic site, at uA from the origin. The sequence of translations taking the observer from S through G, H, I, J, K and L to F are indicated and are listed in Tab. 7.4. It can be verified readily that the circuit operator is C = (I, 1/3 [2110]), and hence b = a1 = 1/3 [21 10]. Moreover, it is clear that C will be the same for any other right-handed circuit and hence b is independent of the circuit chosen. (In fact, C is found to be invariant with the circuit even if the component operations in the circuit sequence are visualized in terms of rotation or mirror operations.) Fig. 7.7 b also demonstrates the equivalence between circuit mapping and the Volterra approach as described in Sect. 7.2. The surface of a possible Volterra cut, indicated by a dashed line in Fig. 7.7 b, can be taken as being defined by an infinity of possible starting points, S, for circuits. Each such point will have a corresponding endpoint, F, related to it by C when mapped into reference material. In other words, the two surfaces so defined are those that must be brought together in order to introduce the defect. The choice of starting points defining the “cut” surface is arbitrary. The core structures of threading dislocations have been studied in order to understand their electronic behavior [2, 19], and it is interesting to consider these structures topologically. For this purpose, consider distortions of the 6-membered atom rings on the (0001) plane that are introduced through the addition or removal of atoms. These rings are composed of three atoms on the same level, alternating with another three at a level *ca-GaN/8 below the first. The removal/addition of one atom from the ring results in a line defect of rotational character. This is illustrated in Fig. 7.8; circuits for the characterization of this defect are shown

Tab. 7.4 Circuits around a-GaN line defects in the bulk

Dislocation circuit (Fig. 7.7) Start

Finish Dispiration circuit (Fig. 7.8) Start

Finish

Symmetry operations

Observer location

(I, s) = (I, uA) W 1 = (I, 3 a1) W 2 = (I, –8 a2) W 3 = (I, 8 a3) W 4 = (I, –8 a1) W 5 = (I, –8 a2) W 6 = (I, –8 a3) W 7 = (I, 4 a1) C = (I, –a1)

S G H I J K L F

(I, s) = (I, uA–2 a1) W 1 = (6–, 1=2 c) W 2 = (6–, –1=2 c) W 3 = (6–, 1=2 c) W 4 = (6–, –1=2 c) W 5 = (6–, 1=2 c) C = (6+, 1=2 c)

s a b c d f

7.4 Dislocations in GaN Epilayers

a Schematic illustration of a dispiration in the form of a pentagonal ring introduced in the basal plane. Concentric circuits sabcds and s'a'b'c'd’s' have been drawn around the defect; b mapping of the circuits Fig. 7.8

to the reference space. Closure failures fs and f 's' arise. The closure failure increases with distance from the core (the projection direction and symbols are as in Fig. 7.7).

in Fig. 7.8 a, and are mapped to the reference space in Fig. 7.8 b. The origin, o, is again chosen to be a symmetry center of the parent structure, and two concentric circuits are indicated. Consider first the case where the component symmetry operations are translations. It is clear that now C is not independent of the circuit chosen, but that c = f–s increases in magnitude for larger circuits. This implies that the defect encircled is not a dislocation, although, formally, it can be modeled as a wall of dislocations with b content increasing in proportion to |s|. It is actually simpler to model the defect as a dispiration, and to consider circuits comprising sequences of screw-rotation operations similar to circuit 3 in Sect. 7.2.2 and Fig. 7.3 c. Thus the observer is carried from s to a by the operation W 1 = (6–, 1=2 c), and from a to b by W 2 = (6–, –1=2 c), similarly alternating to f; this sequence is listed in Tab. 7.4, and Eq. (5) yields C ˆ …6‡ ;1=2 c† ˆ …6 ;1=2 c†…6 ;

=2 c†…6 ;1=2 c†…6 ;

1

=2 c†…6 ;1=2 c† :

1

…10†

In other words, the defect is a dispiration characterized by C–1, i.e., a disclination component 6– (60 8 clockwise rotation) about [0001] and a dislocation component with b = –1=2 c. Note that this characterization is independent of the circuit chosen since s' is carried to a' by W 1 in the same way that s is carried to a, and so on. As in the case of the dislocation depicted in Fig. 7.7 b, Fig. 7.8 b demonstrates the equivalence between the Volterra approach and circuit mapping. The cut surfaces can be visualized as being defined by an infinity of possible starting points s, and corresponding finishing points f, and C–1 is the operation required to bring the f surface onto the s surface, material having been removed (or added) as appropriate.

339

340

7 Topological Analysis of Defects in Nitride Semiconductors Schematic illustration of a pentagon-heptagon pair in a (0001) plane. The pair corresponds to a dipole of 60 8 positive and negative wedge dispirations. A closed circuit has been drawn around the line direction of the defect to identify its character. Mapping of the circuit to the reference space characterizes the defect as an edge dislocation with b = a1 (the projection direction and symbols are as in Fig. 7.7). Fig. 7.9

Defects such as those depicted in Fig. 7.8 require wrong bonds and would be electrically active, but they are unlikely to appear since they are associated with strain fields that increase parabolically with distance from the core. Similar defects, 60 8 wedge disclinations in particular, have been shown to be important in other structures, for example in fullerene molecules and nanotubes [50]. On the other hand, the strain field of a rotational-type line defect can be annihilated by that of another such defect of opposite sign. This is illustrated by the coexistence of a pentagon and a heptagon in Fig. 7.9. Mapping of the closed circuit that has been drawn around the defect configuration, characterizes this coexistence to comprise the core of an edge dislocation with Burgers vector b = nai, where n is an integer that increases proportionally with increasing distance between the two defected rings. This is in agreement with the modeling of dislocations as dipoles of two rotational-type line defects, as discussed by Eshelby [51]. Using our present – 1 terminology, a dispiration characterized by C–1 1 = (6 , – =2 c) is present at the origin –1 O, and an opposite dispiration, characterized by C2 = (6+, 1=2 c) is located at r. Thus, the circuit operator for the combined defect is C ˆ …I; 6 r ‡ r† ˆ …I; r†C2 …I; r† 1 C1

…11†

and hence the total configuration is a dislocation with b = 6–r–r. For example, if r = a2, then b = a1, which is consistent with Fig. 7.9. In the manner described above, the topological analysis results in the initial identification of plausible defect cores and an extensive analysis has been given by Potin et al. [19].

7.4 Dislocations in GaN Epilayers

7.4.2

Stacking-fault Dislocations

Basal-plane SFs are often observed in epitaxial a-GaN as a consequence of growth during which atoms may deposit either on Bb or Cc positions above an Aa layer. It has been shown that most basal SFs are of intrinsic character [20, 27], and that they do not introduce localized states in the band gap, although they can bound quantum-well-like regions of zinc blende GaN in the wurtzite-structured matrix [52]. Two intrinsic SFs can be distinguished in a manner similar to SFs in the hcp structure [53]; the first, I1, corresponds to one violation of the stacking rule, or, equivalently, to the introduction of one row of zinc blende stacking in the wurtzite-type stacking sequence along [0001]. This fault is formed crystallographically by the removal of one basal layer (e.g., Aa) followed by a 1/3 h0110i shear. This leads to the stacking . . . AaBbAaBbCcBbCc . . ., and the corresponding displacement vector is p = 1/6 h0223i. The I1 SF is a growth defect since it cannot be formed by dissociation of crystal dislocations with b = ai [53]. The second type of intrinsic SF, I2, comprises two rows of zinc blende stacking introduced by a 1/3 h0110i shear, and can be formed by dissociation of b = ai dislocations. Both intrinsic SFs are low-energy defects, since they do not disturb the nearest-neighbor packing, with I1 being more energetically favorable [52]. In addition, extrinsic (Etype) SFs having a 1/2 [0001] rigid-body translation are also possible. In the following, we illustrate two cases of dislocations related to the I1 SF. The first is the simple case of a partial dislocation that delineates the termination of the SF. The second case is that of a dislocation delineating the coexistence of energetically degenerate SF regions. Fig. 7.10 a illustrates schematically an I1 SF, and Fig. 7.10 b is a HREM micrograph of such a fault that is terminated by a partial dislocation. A closed righthanded circuit, SGHIJKLMS, has been drawn around the line direction of this partial in order to characterize its Burgers vector. The circuit maps to SGHIJKLMF in the reference space (Fig. 7.10 c), and closure failure FS arises. The sequence of operations is listed in Tab. 7.5, and the circuit operator is given by C ˆ …C; c† ˆ …I; p†W 6W 5W 4W 3W 2W 1 ;

…12†

which yields C = (I, 1/6 [2203]) and hence b = 1/6 [2203]. A subtle point is raised here; when moving from H to I, the observer seems to undergo a ca-GaN/2 shift from the reader’s perspective, in addition to moving rightwards by [0110]. However, when mapping this motion, the ca-GaN/2 shift does not appear. This is understood if we consider that, as mentioned in Sect. 7.2, the observer is “shortsighted” and seeks locations that appear crystallographically equivalent to him in order to continue his excursion. When he moves from H to I, he encounters the 1 =2 c component of the Burgers vector and so he “sees” a location with identical surroundings at a level ca-GaN/2 above; hence he perceives this motion as a [0110] lattice translation. This perception appears in the mapping of his motions. In closing the discussion of this defect, we note again the consistency with the

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7 Topological Analysis of Defects in Nitride Semiconductors

a Schematic illustration of an I1 SF in a-GaN ([21 10] projection: large and small circles indicate distinct atomic species. Open and filled circles denote atoms at height 0 and aa-GaN/2, respectively); b HREM micrograph of an I1 SF terminating at a partial dislocation. An image simulation of the fault is shown in the inset and stacking sequences have been indicated (defocus = –59 nm, thickFig. 7.10

ness = 3.2 nm, atomic columns correspond to white spots). A closed right-handed circuit has been drawn around the line of the defect using lattice translations and a closing displacement from M to S; c mapping of the circuit to the reference space. Closure failure FS appears, identifying the line defect as a partial dislocation with Burgers vector b = 1/6 [2203].

characterization of defects by the Volterra approach. The Burgers vector is obtained from Eq. (1) if we use V(k)j = (I, p)–1 and set V(l)i equal to the identity. Hence, this is a defect belonging to the ’distinct‘ category in the sense that it separates a region of perfect crystal, from a faulted region. In the following

7.4 Dislocations in GaN Epilayers Tab. 7.5 Circuits around SF dislocations in a-GaN

Symmetry operations

Observer location

Circuit around SF-terminating partial (Fig. 7.10): Start (I, s) = (I, uA) W 1 = (I, 3 ´ [0001]) W 2 = (I, 2 ´ [0110]) W 3 = (I, [0110]) W 4 = (I, [0110]) W 5 = (I, 7 ´ [0001]) W 6 = (I, 4 ´ [0110]) W 7 = (I, 3 ´ [0001]) Finish (I, p) = (I, 1/6 [2203]) C = (I, 1/6 [2203])

S G H I J K L M F

Circuit around dislocation between degenerate SF regions (Fig. 7.11) Start (I, s) = (I, uA) W…k†1 = (I, 3 ´ [0001]) W…k†2 = (I, 4 ´ [0110]) W…k†3 = (I, 2 ´ [0001]) W…k†4 = (M(0110), –1/2 [0001]) (I, pk,l) = (I, 1/3 [0110]) W…k†1 = (I, 3 ´ [0001]) W…k†2 = (I, 4 ´ [0110] + 1/3 [1120]) W…k†3 = (I, 2 ´ [0001]) W…k†4 = (M(0110), 1/2 [0001]) Finish (I, pk,l) = (I, 1/3 [0110]) C(kl) = (I, 1/3 [1010])

s g h i j k l m n p f

paragraph, we demonstrate a SF-dislocation delineating the coexistence of energetically degenerate SF regions. Fig. 7.11 a is a HREM micrograph depicting a disconnection, i.e., a defect with combined dislocation and step character between two SF regions. The step character is ca-GaN/2. It is observed that the SF-associated . . . AaBbCc . . . stacking adopts mirror-related orientations on either side of the defect and hence the two SF regions are energetically degenerate. This observation prompts an a priori analysis using the Volterra method that enables consideration of the dissymmetrization on account of the SF, and determination of its consequences in terms of defects delineating crystallographically equivalent regions. For this purpose, we designate the crystalline areas above and below the SF as k and l, respectively; we then follow the dissymmetrization procedure [10, 38] that yields the suppressed symmetry on account of the SF-associated displacement. These operations are employed in Eq. (3), and without going into an extensive analysis (the reader is referred to the relevant publications), we state that the {0110} c-glide mirrors are amongst the suppressed operations in this case. The associated step is obtained if we consider the effect of the c-glide mirror on the unit normal, n, to the SF plane, i.e.

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7 Topological Analysis of Defects in Nitride Semiconductors

Fig. 7.11 a HREM micrograph of a brokensymmetry dislocation with b = 1/3 [1010] that resides on an I1 intrinsic SF in epitaxial aGaN. The defect separates crystallographically equivalent regions on either side of a ca-GaN/2 demistep. Stacking sequences on either side of the defect are indicated, and image simulations of the mirror-related SF structures are shown as insets (defocus = –59 nm, thick-

…M…0110† ;

=2 c†n ˆ M…01100† n

1

=2 c ˆ n

1

ness = 3.8 nm, atomic columns correspond to white spots). A right-handed closed circuit sghijklmnps has been drawn around the line direction of the defect; b mapping of the circuit to the dichromatic complex. Closure failure fs arises. Note that the observer crosses crystallographically equivalent fault regions in correspondingly equivalent ways. ([21 10] projection: symbols are as in Fig. 7.10).

=2 c :

1

…13†

Hence the glide mirror conserves the orientation of the SF but shifts its location by ca-GaN/2. Using P = (I, p) = (I, 1/6 [0223]) in Eq. (3), we also substitute W(k)j = (M(0110), –1=2 c) for the k component, and W(l)i = (M(0110), –1=2 c–a2), for the l component. Then we obtain Qij = (I, b) = (I, 1/6 [1010]), i.e., the SF disconnection has dislocation character. The predicted Burgers vector is confirmed a posteriori by circuit mapping and it is useful to give a complete account of this characterization. For this purpose, we apply Eq. (7) where P = I. A closed right-handed circuit, sghijklmnps, has been indicated in Fig. 7.11 a around the line direction of the defect. The circuit is shown mapped to sghijklmnpf in the reference space in Fig. 7.11 b, and the motions of the observer are listed in Tab. 7.5. The observer is transported from s to i by translation operations, and, at i, the c-glide mirror is applied to him. The subtle point here is that the glide mirror operation changes the orientation of the observer’s frame and this must be taken into account. This is immediately reflected in the way the observer perceives his motions. Hence, when moving from location l to m, his surroundings appear the same as when he was moving from g to h. At n the observer is again operated upon by the c-glide mirror, and finishes his excursion by a translation back to the starting point. The closure failure fs is obtained

7.4 Dislocations in GaN Epilayers

in a straightforward manner if the circuit is formulated mathematically. Equation (7) yields C(kl) = (I, 1/3 [1010]) and hence b = 1/3 [1010] as predicted a priori. It is interesting to note that the {1010} c-glide mirror appears naturally in the circuit because it is necessary in order to move the observer from an A-type location to a B-type one and vice versa, and that C(kl)–1 = Qij, in agreement with the arguments presented in Sect. 7.2. To conclude this subsection, the topological analysis has resulted in the characterization of SF-dislocations arising as a result of suppressed symmetry. These defects have been distinguished from partials that delineate the coexistence between the SF and perfect crystal. 7.4.3

Interfacial Dislocations and Dislocation Models of Interfacial Structure

Interfacial structures can often be described in terms of line-defect arrays superimposed on some singular configuration so that they accommodate deviations from it. Such descriptions are useful at certain instances such as for descriptions of epitaxial interfaces, as well as low-angle grain boundaries (LAGBs) inside the epitaxial layer. The subject of this type of mesoscopic modeling has been reviewed in detail by Christian [54], and we recapitulate on its basic principles and limitations in relevance to experimental observations involving GaN epilayers. The characterization of isolated interfacial defects, both by the Volterra approach and by circuit mapping, was discussed in Sect. 7.2, and it was shown that the two methods are equivalent with the former giving a priori information and the latter being used for a posteriori study. When examining interfacial defect arrays, it is important to consider the singular starting configuration upon which the array is superimposed. This configuration constitutes the reference space for circuit mapping, or equivalently, for the Volterra approach, the initial elastic medium. Two principal cases can be distinguished; in one case, the singular configuration is a single crystal and the defect array accommodates small angular misorientations or lattice distortions. Such descriptions include LAGBs formed by series of threading dislocations inside the epilayer, as well as semicoherent epitaxial interfaces accommodated by misfit dislocations. In the second case, the singular configuration is a dichromatic complex, and the array accommodates small angular deviations from a special misorientation of two abutting crystals. Although there is no simple correlation between geometric parameters and interfacial free energy, considerable evidence has been found showing that two-dimensionally periodic boundaries are sometimes favorable [55]. In the following, we discuss both cases in turn. In the case of epitaxial interfaces and LAGBs, a circuit such as the one illustrated in Fig. 7.4 can be employed to identify the defect content of the interface. As discussed above, instead of mapping the k and l segments into a dichromatic complex, we map both into a single reference space, and it is often convenient to choose one of the component crystals for this purpose [54]. Taking the case where the interfacial structure at ZS is identical to the interfacial structure at UV, the circuit operator is given by

345

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7 Topological Analysis of Defects in Nitride Semiconductors

C…kl†r ˆ C…l†r C…k†r ;

…14†

where the superscript r signifies that the circuit is mapped in the reference frame. If we consider only translation operations in the circuit, as argued by Frank [56] and Bilby [57], we can write C(k)r = (I, t(k)r) and C(l)r = (I, –t(k)r), and hence C…kl†r ˆ …I; t…k†r

t…l†r † :

…15†

Equation (15) shows that the total interfacial dislocation content that is intersected by the circuit is equal to –t(k)r + t(l)r, which we designate br. In other words, the dislocation content is that which is necessary in order to accommodate the mismatch between two translations, one in each of the crystals (i.e., the vectors SU and ZV in Fig. 7.4), mapped into the reference space. In the Frank-Bilby formulation [56, 57], these vectors are represented by a probe vector, vr, lying along the interface. Equation (15) yields a multiplicity of equivalent descriptions since the k and l lattices can be invoked from that of the reference by a multiplicity of transformations, but one is consistent with the physical bicrystal; usually this is obtained if we consider the individual defects to be dislocations with Burgers vectors equal to lattice vectors of minimum magnitude, and are arranged so that their density is also minimum [55]. The circuit can be made small enough so that it encircles only one dislocation, and we illustrate the usefulness of such mapping by demonstrating the characterization of a misfit dislocation at a TiN/a-GaN epitaxial interface. Thin films of stoichiometric cubic TiN were deposited for ohmic contact formation on (0001) surfaces of a-GaN epilayers [23] with orientation relationship (0001)a-GaN//(111)TiN, h1120ia-GaN//h110iTiN, and arrays of dislocations at the interface accommodate the *5.8% misfit. When the interface is imaged by HREM in cross section along [1120]a-GaN, only one of the three sets of misfit dislocations is visible end-on. Such a micrograph is shown in Fig. 7.12 a where the TiN/a-GaN interface is clearly resolved as containing one misfit dislocation. In Fig. 7.12 a a right-handed closed circuit, SGHIJKLS, is indicated around the misfit dislocation, and an observer is imagined to make this excursion by undergoing a sequence of translation operations. The circuit comprises a segment, SGHI, in the TiN crystal (designated k) and a segment, IJKLS, in a-GaN (designated l). In order to obtain the Burgers vector, the two circuit segments are mapped in the reference space, i.e., one of the two crystals, and we choose the k crystal in this context. This mapping is illustrated graphically in Fig. 7.12 b; the circuit maps to SGHIJKLF, and a closure failure FS arises. The operator corresponding to the k circuit segment is C…k†k ˆ …I; t…k†k † ˆ …I; 9  1=2 ‰1 12Š† ˆ …I; 4  1=2 ‰1 10Š†…I; 9  1=2 ‰1 12Š†…I; 4  1=2 ‰110Š† : The operator corresponding to the l segment is

…16†

7.4 Dislocations in GaN Epilayers

(a)

(b) a Cross-sectional HREM micrograph of the TiN/a-GaN interface, viewed along [1120]a-GaN//[110]TiN, indicating a closed righthanded circuit SGHIJKLS around a misfit dislocation (defocus = –59 nm, white spots correspond to projected atomic columns); b mapping of the circuit to the reference space Fig. 7.12

(crystal k); closure failure FS arises. The probe vector vk is indicated. The line direction vector n of the defect is out of the page (open circles denote N atoms and shaded circles are Ti atoms. Large circles correspond to atoms at zero level, and small circles to atoms at height aa-GaN21/2/4, respectively).

C…l† ˆ …I; t…l†† ˆ …I; 1=3 ‰21 10Š ‡ 8  ‰1100Š† ˆ …I; 1=3 ‰21 10Š†…I; 2  ‰0001Š†…I; 8  ‰1100Š†…I; 2  ‰0001Š†

…17†

and it is mapped to operator C(l)k = (I, –t(l)k) = (I, 8 ´ 1/2 [112] + 1/2 [011]) in the k spacegroup. By substitution into Eq. (15) of the operators given in Eqs. (16) and (17), we obtain {C(kl)k}–1 = (I, FS) = (I, bk), where bk = 1/2 [011] is the Burgers vector expressed in the coordinate frame of crystal k. The advantage of the mathematical formulation over simple contour mapping is clear; a circuit based on a 2dimensional projection of the bicrystal would have given only the component of b that is perpendicular to the projection direction. In epitaxial systems of increased misfit, the spacing of misfit dislocations decreases and for high values of misfit the interface is incoherent. In a similar manner, by increasing the angular misorientation, a GB transforms from the low-an-

347

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7 Topological Analysis of Defects in Nitride Semiconductors

Fig. 7.13 a Plan-view HREM image of an interfacial disconnection at a (2310) symmetric tilt GB in GaN (the micrograph is a portion of a micrograph given in [18] and is reprinted courtesy of the authors and the American Physical Society). The defect exhibits dislocation as well as step character. A closed circuit SPQTUV has been drawn around its line direction to identify its Burgers vector; b map-

ping of the circuit to the reference space; closure failure FS arises identifying the Burgers vector to be b = 1/21 [1540]. Note that the bicrystal is depicted unrelaxed since reconstruction does not by itself introduce incompatibilities. The closure failure FS is consistent with the a priori characterization by the Volterra method ([0001] projection: symbols are as in Fig. 7.7).

gle to the high-angle regime, and the array of dislocations becomes so dense that the cores eventually overlap. In such cases, the Frank-Bilby equation yields a multiplicity of equivalent descriptions for the defect content, all of which are consistent with the same physical bicrystal [55]. Particular descriptions corresponding to low dislocation density may be more convenient for modeling purposes, but they are not more meaningful than alternative higher density ones since all lead to the same long-range displacement field (if any exists) in an elastic continuum model. At shorter range, the displacement field of an interface depends on the details of the way the defect content is distributed, rather than simply the total defect con-

7.5 Inversion and Stacking Disorder in Relation to Epitaxial Structure

tent as identified by the Frank-Bilby equation. Additionally, nonelastic contributions to the interfacial energy arise in the immediate vicinity of interfaces. Hence, the Frank-Bilby equation is a topological expression of interfacial defect content, and is not simply related to interfacial energy. Moving on to the second case where the interfacial defects are superimposed on a bicrystalline configuration, we illustrate in Fig. 7.13 a a HREM micrograph of a disconnection on a (2310) symmetric tilt GB in epitaxial a-GaN observed by Potin et al. [19]. A closed circuit SPQTUVS has been drawn around the defect in order to identify its character. The circuit maps to SPQTUVF in the reference space (Fig. 7.13 b) and closure failure FS = b = 1/21 [1540] appears (expressed in the k coordinate frame). Fig. 7.13 b is at the same time a Volterra diagram, illustrating that the defect is a dislocation arising due to the misorientation of lattice vectors, and b can also be obtained from Eq. (3) if we set W(k)j = (I, 1/3 [21 10]), W(l)i = (I, 1/3 [1 120]), and P equal to the 180 8 rotation matrix about [2310]. In the Volterra approach, this translates into considering the juxtaposition of two incompatible surface steps, corresponding to these vectors. The resulting disconnection separates crystallographically equivalent regions of interfacial structure, and, in addition to its dislocation character, it is associated with an interfacial step of height given approximately by the average of the steps on the abutting surfaces. Without going into an analytical discussion, we point the reader’s attention to two issues already discussed. One is the equivalence between Volterra and circuit mapping. The second issue is the need for crossing crystallographically equivalent interfacial regions in equivalent ways, so that the correct defect content arises as closure failure.

7.5

Inversion and Stacking Disorder in Relation to Epitaxial Structure

In this section we study the relationship between the structure of the epitaxial interface and IDBs or SFs on prismatic crystallographic planes that emanate from this interface into a-GaN epilayers. For this purpose, the Volterra method of the topological theory is employed. IDBs have been observed frequently in a-GaN deposited on (0001) sapphire, and they adopt {1010} habit planes (e.g., [25, 27, 58– 61]) (Fig. 7.14). The density of these defects is significantly reduced in layers deposited on (0001) 6H-SiC; on the other hand, films grown on such substrates usually exhibit SFs on {21 10} planes. Elucidation of the circumstances under which IDBs and SFs are systematically introduced is important since these defects of structure affect the crystalline quality and physical properties of the deposited layer. In the following, the crystallography of a-GaN epilayers is studied, and compared to another well-studied case of epitaxy, i.e., GaAs on (001) Si. As mentioned in Sect. 7.3, a-GaN is nonholosymmetric. Symmetry operations that are suppressed when going from the parent to the daughter structure characterize domain boundaries and are termed domain “exchange” operations, W e(k)j [10, 13]. When an exchange operation is substituted in Eq. (3), it describes the intersection

349

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7 Topological Analysis of Defects in Nitride Semiconductors

Fig. 7.14 Low-magnification cross-section HREM micrograph along [21 10]a-GaN of an a-GaN/sapphire bicrystal having the (0001)a-GaN// (0001)sapph., [21 10]a-GaN//[01 10]sapph. orientation relationship. The micrograph illustrates the epitaxial interface and emerging (0110) IDBs.

Fig. 7.15 Schematic illustration of a domain boundary emanating from the interface into crystal k. The new k surface is related to the initial one by an exchange operation W e(k).

of a domain boundary of crystal k with the interface as depicted schematically in Fig. 7.15. In the case of GaN epilayers, it is the suppression of inversion symmetry that leads to inversion domains. In some cases of epitaxy involving nonholosymmetric deposits (e.g., [13, 14]), the introduction of IDBs is required for the coexistence of crystallographically equivalent regions of the epitaxial interface, and it is interesting to examine when this is also the case for a-GaN epilayers.

7.5 Inversion and Stacking Disorder in Relation to Epitaxial Structure

As discussed in Sect. 7.2, the bicrystalline reference space is the dichromatic complex, i.e., the composite of interpenetrating crystals, and interfacial defects are described by operations that are suppressed with respect to the spacegroup of this composite. Such symmetry operations are given concisely by the coset decomposition of the crystal’s spacegroup, U(k), with respect to the spacegroup of the dichromatic complex U(c), i.e. U…k† ˆ fU…c†g [ W…k†1 fU…c†g [ . . . [ W…k†n fU…c†g :

…18†

At the same time, the coexistence of crystallographically equivalent regions of the epitaxial interface is constrained by the invariant orientation of the substrate. Hence only some of the coset representatives {W(k)1, . . ., W(k)n} are actually useful for the description of defects in epitaxial interfaces, in particular those for which W…k†j n ˆ n

…19†

and these are operations corresponding to mirrors and rotation axes perpendicular to the interface. Further to the interfacial variants arising from Eq. (18), additional variants are obtained if we consider the coset decomposition of the holosymmetric parent spacegroup U(k)p, and such variants coexist separated by domain boundaries. In the case of a-GaN, the decomposition of Eq. (9) applies, and, corresponding to Eq. (19), we now have We …k†j n ˆ …1W…k†k †n ˆ n

…20†

For Eq. (20) to be valid, W(k)k may represent a mirror plane coincident with the interfacial plane, a two-fold axis contained in the interfacial plane, or a roto-inversion axis perpendicular to the interface. Based on these arguments, we determine all possible interfacial orientations for which a-GaN may exhibit IDBs on account of the coexistence of crystallographically equivalent regions of epitaxial interface. Tab. 7.6 lists the layer groups of a-GaN surfaces and of its parent structure. For the cases where, by going from parent to a-GaN, the symmetry is reduced, Tab. 7.6 also lists the corresponding domain exchange operations. It can be seen that dissymmetrization occurs in general for {hki0} surfaces (with {1 120} and {0110} being particular subcases of higher symmetry). We also find that all dissymmetrized surfaces contain the vector 3/8 [0001] that relates the interpenetrating Ga and N substructures and hence they are composed of equal numbers of both atom types (i.e., the growth direction is nonpolar). The implications of Tab. 7.6 are demonstrated in the following using cases of aGaN epitaxy on sapphire. Sapphire is a centrosymmetric rhombohedral structure (spacegroup R3c, asapph. = 0.476 nm, csapph. = 1.2991 nm), with anions forming approximately an hcp-like structure, and cations in two-thirds of the octahedral interstices. The point-symmetry operations of spacegroup R3c are listed in Tab. 7.7.

351

352

7 Topological Analysis of Defects in Nitride Semiconductors Tab. 7.6 Layer groups of unrelaxed parent and a-GaN surfaces. For the cases where, by going

from parent to daughter, the symmetry is reduced, the corresponding domain exchange operations are also listed Surface orientation

Holosymmetric parent a-GaN

Domain exchange operation(s)

(0001) {1 120}

p3m p2mc

p3m pc

{0110}

p2mm

pm

{hh0l} {hki0} {hkil}

pm pm p1

pm p1 p1

– (0001) mirror, h1 120i two-fold axis (0001) mirror, h0110i two-fold axis – (0001) mirror –

Tab. 7.7 Point-symmetry operations in the spacegroup R3c

Symmetry operation 1 3+ 3– 2 2 2 1 3+ 3– c c c

Location

0, 0, 0, w 0, 0, 0, w –u, –u, 2 u, 1=4 2 u, –u, –u, 1=4 –u, 2 u, –u, 1=4 0, 0, 0 0, 0, 0, w; 0, 0, 0, 0 0, 0, 0, w; 0, 0, 0, 0 u, –u, 0, 0 0, v, –v, 0 u,0, –u, 0

Glide component

Seitz operator

Symmetry element

0, 0, 0, 1=2 0, 0, 0, 1=2 0, 0, 0, 1=2

{I, 0} {3+, 0} {3–, 0} {2, 1=2 c} {2, 1=2 c} {2, 1=2 c} {1, 0} {3+, 0} {3–, 0} {M, 1=2 c} {M, 1=2 c} {M, 1=2 c}

– [0001] [0001] [1 120] [21 10] [1210] – [0001] [0001] (1 120) (21 10) (1210)

Fig. 7.16 a illustrates schematically an a-GaN/sapphire bicrystal having the epitaxial relationship (1010)a-GaN//(1 120)sapph., [0001]a-GaN*//[1101]sapph. (angle 1.67 8) [62], i.e., the growth direction is nonpolar. The bicrystal is obtained by sectioning a dichromatic complex in which the oxygen sites of sapphire coincide with the Ga sites of a-GaN. An (0001) IDB is taken to intersect the epitaxial interface, and it is seen that the interfacial regions on either side are crystallographically equivalent and energetically degenerate. The IDB compensates for the two-fold rotational symmetry about [1010], which is suppressed when going from the parent to the a-GaN structure. The configuration of Fig. 7.16 a is described by Eq. (3), if we substitute W e(k)j = (2[1010], 1=2 c), and W(l)i = (2[1 120], 1=2 c). Taking into account the depicted relative orientation and position of the crystals this yields Qij = (I, 0), i.e., the particular IDB-interface junction line does not have defect character. The IDB structure corresponds to the Austerman-Gehman IDB model [63], i.e., one atomic species remains

7.5 Inversion and Stacking Disorder in Relation to Epitaxial Structure

a Schematic illustration of an aGaN/sapphire bicrystal having the epitaxial orientation relationship (1010)a-GaN// (1 120)sapph., [0001]a-GaN//[1101]sapph. The projection direction is [1210]a-GaN. An (0001) IDB emanates from the interface into the a-GaN epilayer. The interfacial structures on either side of the IDB are crystallographically equivalent; b schematic illustration of an atomic model of an a-GaN/sapphire bicrystal having the epitaxial orientation relationship Fig. 7.16

(0001)a-GaN//(0001)sapph., [21 10]a-GaN// [1010]sapph.. An (0110) IDB is shown emanating from a step at the interface; the IDB delineates the coexistence of nondegenerate interfaces. The misfit between the two crystals has not been taken into account in the figure. In GaN symbols are as in Fig. 7.10. In sapphire, cross-hatched and unhatched circles represent atoms of different species; different shadings represent different levels along the projection direction.

353

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7 Topological Analysis of Defects in Nitride Semiconductors

undeviated while the other switches its tetrahedral site upon crossing the boundary. The symmetry compensation illustrated in Fig. 7.16 a is in accordance with the Curie principle [12] but the introduction of this IDB is not imposed by the need for polarity conservation, since the (1010)GaN layers contain both atom types. The bicrystal of Fig. 7.16 a may be contrasted with the case of a bicrystal with the (0001)a-GaN//(0001)sapph., h21 10)a-GaN//h1010isapph. orientation relationship, for which the growth direction is polar. From Tab. 7.6 we see that the (0001)a-GaN surface is not dissymmetrized and hence there are no available domain exchange operations to facilitate the coexistence of crystallographically equivalent epitaxial regions through the introduction of an IDB. On the other hand, {1010} IDBs are frequently observed in such epilayers (Fig. 7.15), and other reasons must be sought for their systematic introduction, such as compensation of the misfit along the growth direction due to steps on the substrate surface, as proposed by Ruterana et al. [64]. Such a model is illustrated schematically in Fig. 7.16 b, where it can be seen that the structure of the epitaxial interface changes after the csapph./3 step in the substrate. The resulting structural arrangement of atoms in the unrelaxed model of the epitaxial interface on the right-hand side of the IDB is reminiscent of the Austerman-Gehman model that was illustrated in Fig. 7.16 a. To describe the defect character of such a configuration we can employ Eq. (2), if we set V(k)j = (I, v(k)j) where v(k)j = 1/3 [21 1(3KGaN)]4 and, for the l crystal, we employ a symmetry operation W(l)i = (I, t(l)i), where t(l)i = 1/3 [101(Ksapph.)]4, expressed in the Frank system (see Appendix). The relative orientation and location is described by P = (P, 0) where 2

p 1‡ 3 6 1 p P ˆ …asapph: =3aa-GaN †6 41 3 0

3 p 1p 1 p3  0 1 p3 1 ‡ 3 0 7 7: 1‡ 3 1 05 0 0 3

…21†

Hence Eq. (2) yields Zij = (I, bij) where 2 bij ˆ

2 1 1

3

p 6 7 7 asapph: 3 3 aa-GaN 6 6 p 7 6 7 9 aa-GaN 4 6…3 ca-GaN csapph: † 5 p asapph: 3 3 aa-GaN

…22†

and has magnitude equal to 0.09 nm. This Burgers vector may be further reduced if we also consider that the IDB exhibits a rigid-body translation as described in [64]. To enhance our understanding, we compare the models of Fig. 7.16 with the case of GaAs on (001) Si depicted schematically in Fig. 7.17. In this case, the introduction of the IDB accommodates the coexistence energetically degenerate interfacial structures on either side of a morphological feature, in particular a demistep of height equal to half the spacing of (001) lattice planes. GaAs exhibits the

7.5 Inversion and Stacking Disorder in Relation to Epitaxial Structure

Schematic illustration, along [110], of a (001) GaAs-on-Si epitaxial bicrystal. The two crystals are in parallel orientation. An IDB emanates from a demistep in the interface. This defect configuration accommodates the

Fig. 7.17

coexistence of two crystallographically equivalent regions of interfacial structure (large, small, and hatched circles denote Ga, As, and Si atoms respectively. Shading denotes atoms at level a/21/2/4).

zinc blende, structure while Si crystallizes in the diamond structure (see Sect. 7.3). The crystallographic equivalence of the interfacial regions on either side of the IDB is due to the existence of exchange operations that conserve the orientation of the epitaxial interface, for example the four-fold screw rotation along [001], W e(k) = (4+[001], 1/4 [111]). The translation part of this operation corresponds to the shift in the location of the interfacial plane leading to the demistep. The demistep is introduced in the epilayer due to a corresponding morphological feature in the substrate since the Si spacegroup includes a [001] four-fold screw, i.e., W(l) = (4+[001], 1/4 [111]). In a similar manner we may study the introduction of SFs on prismatic {21 10} planes (also termed stacking mismatch boundaries and translation domain boundaries) of a-GaN deposited on (0001) 6H-SiC (e.g., [28, 65, 66]). A structural model is depicted schematically in Fig. 7.18. The substrate has the same spacegroup symmetry as GaN and the two structures exhibit parallel orientation. The {21 10} SFs are introduced in order to accommodate SiC steps of partial character, in particular steps described by inner unit cell vectors. Since such vectors are not included in the spacegroup symmetry operations, the configuration is described by Eq. (2). Putting V(k)j = (I, v(k)j) = (I, 1/6 [0223]) (as in the Amelinckx SF model [67]) and V(l)i = (I, v(l)i) = (I, 1/6 [0221]), we find bij*0 for the junction line of the interface and the SF. To conclude this section, we have studied a priori the effect of IDBs on the structure of the epitaxial interface, and it has been shown that, when the growth direction of a-GaN is polar, the interfacial structure changes at junctions with IDBs. This conclusion is independent of local relaxations such as those required for the relief of misfit. The introduction of {21 10} SFs during growth on (0001)

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7 Topological Analysis of Defects in Nitride Semiconductors

Schematic illustration, along [21 10], of a prismatic SF emanating from a step of partial character on the (0001) surface of the 6H-SiC substrate. The SF plane is (1210) (i.e., inclined in this projection) and has been

Fig. 7.18

taken here to exhibit a rigid-body translation corresponding to the Amelinckx model [67] (in the GaN, symbols are as in Fig. 7.10. In SiC, distinct hatchings represent distinct atomic species).

6H-SiC is due to the accommodation of steps of partial character on the surface of the substrate.

7.6

Interface and Fault Junction Lines 7.6.1

Interactions of Inversion Domain Boundaries with Stacking Faults

As discussed in Sect. 7.5, in a-GaN epilayers grown on (0001) sapphire, IDBs appear on {1010} prismatic planes [24, 25, 27, 58–60, 66]. In their majority, such defects have been found to exhibit a particular relative displacement of the inverse polarity domains [24, 25, 27, 58, 59, 61], and it has also been shown that such IDBs are electrically inert and have modest energies [68]. These boundaries have been designated as IDB* type (Fig. 7.19 a). In a second configuration, termed Holt IDB [69], the atoms on either side of the boundary are located at interchanged positions in the crystalline structure (Fig. 7.19 b). Holt IDBs involve wrong bonds, and have been shown to be electrically active and to exhibit higher formation energy than IDB* ones [68]; they too have been observed experimentally (e.g., [24, 27, 58, 59]). In this subsection, a mechanism leading to the transformation of

7.6 Interface and Fault Junction Lines

Schematic illustration of {0110} IDB models: a IDB* (p = –c/8); b Holt IDB (p = 3c/8). (h21 10i projection: symbols are as in Fig. 7.10 and tetrahedra indicate polarity reversal). The rigid-body translations p are defined by reference to the Austerman-Gehman model [63]. Fig. 7.19

IDB* to Holt IDB, and vice versa, through interaction with I1 intrinsic basal SFs is predicted using the topological theory and is confirmed by HREM observations. In Sect. 7.2 it has been shown that interfacial line defects can have an associated step character, and that the Volterra-like approach takes into account the incompatibilities between steps on abutting surfaces. Taking our interface to be a {1010} IDB, we can examine a priori the defect character of line junctions with I1 SFs by using Eq. (2) and by considering SF-introducing V i operations and related steps. In an extensive analysis, Volterra diagrams of all the generic IDB-I1 SF interactions have been presented [24]. Here we confine ourselves to one example of such an interaction, and the corresponding Volterra diagram is depicted in Fig. 7.20. The step-introducing operation is V(l)i = (I, vi) = (I, 1/6 h2203i), and the corresponding step height is h(l) = (3)1/2aa-GaN/6. The 1/2 [0001] component of the SF displacement accommodates the transformation between the two IDB types, i.e., IDB* and Holt since the rigid-body translations of the inverse polarity domains are –1/8 [0001] and 3/8 [0001] respectively for the two IDB structures, taking as reference the Austerman-Gehman IDB model [63]. The orthogonal part of the transformation P in Eq. (2) is P = 1, the inversion operation, and the displacement p is defined by the IDB type prior to the Volterra cut. The k operation for the Volterra diagram of Fig. 7.20 is the identity, V(k)j = (I, 0). Then Eq. (2) yields Z ij = (I, 1/3 [1100]), i.e., the IDB structural transformation is accommodated by the I1 SF and a partial dislocation of mixed type with b = 1/3 [1100] expressed in the k coordinate frame. In the HREM micrograph of Fig. 7.21 a, an interaction between an I1 SF and an IDB is illustrated. The faults were characterized by comparison with corresponding simulated images shown as insets. For the particular imaging conditions (defocus corresponding to the second maximum of contrast) atomic columns are projected as white spots, and, for the Holt model, the stacking sequences on either side of the IDB appear to have opposite senses, whereas, for IDB*, the senses appear to be the same [59]. Also, in Fig. 7.21 a, it is observed that the IDB plane corresponds to dark spots which, for this defocus, represents IDB plane cutting single bonds as depicted in Fig. 7.19.

357

358

7 Topological Analysis of Defects in Nitride Semiconductors Volterra diagram of an IDB*-I1 SF interaction leading to a Holt IDB. The IDB and the SF are indicated by broken lines. On the SF, a sphalerite unit has been drawn to indicate its sense.

Fig. 7.20

Following the identification of the planar defects, we move on to study their junction line. In Fig. 7.21 a, a closed right-handed circuit SABCDEGHIJS has been drawn around the line direction of the junction line in order to determine its defect character. In Fig. 7.21 b, this circuit is shown to map to SABCDEGHIJF in the reference space, and closure failure FS arises. In this configuration, two interacting planar faults are involved, and circuit mapping can be extended to take into account such situations [70, 71]. We distinguish each crystalline area bounded by these faults as k, l1, and l2; the circuit comprises segments in all components, and the reference space is the complex formed if we imagine all components to interpenetrate. Let C(k)1 and C(k)2 be the circuit segments in the k domain, and C(l), the segment in the l domain. The circuit also comprises displacements, pSF, pkl, and plk, associated with crossing the interfaces. For this junction line, the composite circuit operator is then given by the expression C…kl† ˆ …I; plk †PC…l†2 …I; pSF † C…l†1 P 1 …I; pkl † C…k†1 :

a Cross-sectional HREM micrograph along [21 10], showing an I1 SF (indicated by the characteristic AaBbCc stacking) interacting with an IDB (indicated by a solid line). The SF induces a transformation of IDB structure. Image simulations of the IDB structural models, IDB* and Holt, are shown as insets (defocus = –59 nm, thickness = 3.2 nm, atoms are on white spots). A closed righthanded circuit SABCDEGHIJS has been drawn around the line direction of the IDB-SF junction line in order to determine its defect charFig. 7.21

…23†

" acter; b mapping of the circuit of a to the reference space; closure failure FS arises. Enlargements are used to illustrate the appropriate way to cross the IDBs using inversion through centers of the hexagonal parent structure (depicted as cross-hatched rectangles) and displacements in the complex of interpenetrating crystals (see text). The line defect accommodates the transition from IDB* to Holt ([21 10] projection: symbols are as in Fig. 7.10, and n denotes the line direction of the defect).

7.6 Interface and Fault Junction Lines

359

360

7 Topological Analysis of Defects in Nitride Semiconductors Tab. 7.8 Circuit around an SF-IDB junction line in a-GaN (Fig. 7.21)

Start

Finish

Symmetry operations

Observer location

(I, s) = (I, uA) W…k†1 = (I, 2 ´ [1010]) W…k†2 = (I, 4 ´ [0001]) W…k†3 = (I, 2 ´ [1010]) (1, pkl) = (1, 3/8 [0001]) W…k†4 = (I, 2 ´ [1010]) W…k†5 = (I, 2 ´ [0001]) (I, pSF) = (I, 1/6 [2023]) W…l†6 = (I, [0001]) W…l†7 = (I, 2 ´ [1010] + 1/3 [2110]) (1, pkl) = (1, 1/8 [0001]) C(kl) = (I, 1/3 [1100])

S A B C D E G H I J F

In Eq. (23), the composite circuit operator is expressed in the k coordinate frame, and P=1. Equation (23) takes into account any structural transformation of the IDB type and gives the irreducible expression of the closure failure. We note that care should be exercised when crossing the IDBs because, in the parent structure of a-GaN, the centers of inversion are not located at atomic sites (see Sect. 7.2). When crossing an IDB, inversion is performed using such a center, followed by the displacement of the corresponding IDB model. This is illustrated in Fig. 7.21 b at enlarged sections depicting the IDB crossing locations. Moreover, we need to consider that a-GaN is composed of two interpenetrating hexagonal substructures (see Sect. 7.3), and, when mapping the circuit, we need to exercise care in order to employ the inversion centers of the appropriate substructure, i.e., those of the substructure corresponding to the atomic sites that are used for mapping the circuit segments. The Burgers vector of the IDB-SF junction line is determined from the mathematical formulation of the circuit. The circuit segments are listed in Tab. 7.8, and substitution into Eq. (23) yields b = 1/3 [1100] in the k coordinate frame, in agreement with the characterization by the Volterra approach. Junctions of IDBs with I1 SFs may also lead to the introduction of screw partial dislocations with Burgers vector b = 1=2 c. This mechanism is illustrated schematically in Fig. 7.22 where an I1 SF is shown to impinge on a bounding IDB of an inverse polarity domain. Taking all the bounding IDBs of the domain to be initially of the IDB* type, the I1 SF induces an IDB*-to-Holt transformation on the particular domain boundary. Then, Frank’s node rule [30] requires that screw partials with b = 1=2 c are introduced between the Holt IDB and the other bounding IDBs. At this time, the existence of such partials remains to be verified experimentally. In conclusion, it has been observed that I1 SFs interact with IDBs thereby introducing structural transformations, from the electrically nonactive IDB* to the electrically active Holt IDB or vice versa. The IDB-SF junction lines have partial dislocation character. Such transformations should be induced by kinetics due to the

7.6 Interface and Fault Junction Lines Fig. 7.22 Schematic illustration of a prismatic inverse-polarity domain bounded by IDB*s. On one IDB, an I1 SF induces an IDB* to Holt structural transformation. This results in the introduction of screw partial dislocations with Burgers vector 1=2 c. The dislocation reaction, in agreement with Frank’s node rule [27], is b3 = 1/6 [2203] = b1 + b2 = 1/2 [0001] + 1/3 [1100].

different growth rates exhibited by adjacent domains [21, 25]. A growth defect such as an I1 SF could terminate on an IDB if an adjacent, unfaulted domain has already grown to a higher level, thus leading to an inevitable structural transformation of the IDB. Conversely, a faulted domain may have grown to a higher level and the IDB structure transformation occurs as the adjacent inverse domain reaches the SF. As discussed by Rouviere et al. [25], Ga-polarity domains grow faster than N-polarity ones, and these transformations could arise frequently. 7.6.2

Double-positioning Twinning

TiN epilayers have been shown to exhibit ohmic behavior on n-type a-GaN (e.g., [23, 47, 72–74]). On the other hand, structural defects in thin films strongly affect their electrical characteristics, and the HREM technique has been extensively employed for structural characterization. In this section, a topological analysis based on the Curie principle of symmetry compensation [12] is applied for TiN films on a-GaN. This theoretical approach predicts that twin boundaries that are usually termed double-positioning boundaries (DPBs) should invariably emanate from particular interfacial morphological features. DPBs have been observed in a number of epitaxial systems and can mediate a columnar growth of the deposit (e.g., [75–78]). In the TiN/a-GaN system, our prediction is verified by the experimental HREM observations. The circuit-mapping method is employed for the a posteriori characterization. The topological theory allows consideration of the coexistence of crystallographically equivalent, and hence energetically degenerate, regions of the interfacial structure through geometrically necessary disconnections, i.e., defects that exhibit combined interfacial dislocation and step character. In addition, a contribution pertinent to the emanation of twins and other extended defects from interfaces has been made by Dimitrakopulos and Karakostas [79]. The topological methodology comprises a dissymmetrization procedure involving the construction of a di-

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7 Topological Analysis of Defects in Nitride Semiconductors

chromatic complex whereby the epilayer (k) and the substrate (l) are imagined to interpenetrate at the required relative orientation and position. The ordinary symmetry operations of this composite satisfy the equation [10] W…c†j ˆ W…k†j ˆ PW…l†i P

1

:

…24†

In the epitaxial system under study, we designate the TiN contact layer as crystal k, and a-GaN as crystal l. The TiN spacegroup is Fm3m (rocksalt structure), and its orientation relationship with a-GaN has been given in Sect. 7.2. Through Eq. (24), we determine the dichromatic complex symmetry to be 3m, where the 3-fold axis is along [111]k//[0001]l, and there are three coincident mirror planes {110}k// {21 10}l. The symmetry analysis yields that the {0110} c-glide mirrors, (M(0110), 1=2 c), of crystal k are suppressed since there are no counterparts in crystal k (i.e., PW(l)i P –1 = P(M(0110), 1=2 c) P –1 = W(k)j). In addition, we notice that these operations conserve the orientation of the epitaxial interface, since M(0110)·n = n (where n is the unit normal to the epitaxial interface), but shift its location by ca-GaN/2 (see Eq. (13)). Hence, these suppressed operations interrelate variants of the interfacial structure that are separated by a demistep of height equal to ca-GaN/2 (or an odd multiple of that). The demistep separates an Aa- from a Bb-type layer in the . . . AaBbAaBb . . . wurtzite stacking sequence. Moreover, these operations can be used to predict the defect between such variants. Defect prediction has been addressed so far by using the Volterra approach, and geometrically necessary line defects between crystallographically equivalent interfaces are dislocations, disclinations, and dispirations, depending on the character of the suppressed symmetry [10]. Disclinations and dispirations are line defects of rotational and combined rotational-translational character, respectively, and are pertinent to the suppression of rotations, screw rotations, mirrors, and glide mirrors. The predictive arguments of [10] are made under the assumption of structural continuity in both abutting crystal components. In our case of variant coexistence, a twist dispiration is predicted by this assumption. However, line defects of rotational character are high-energy defects since their strain energy increases parabolically with the distance from the core. In a more energetically favorable configuration, it has been shown that continuity can be broken in the crystal not exhibiting the particular symmetry element, and the accommodation of the variants is achieved through the introduction of a twin or a GB in this crystal [79]. The resulting configuration is a 3-junction of interfaces that has been termed “variant-constituted” junction [79]. In this case, the orthogonal part of operator Qij of Eq. (3) describes the orientation relationship between components k and e (Fig. 7.23) while the translation part of this operator may be localized at the interface in the form of an interfacial dislocation or may express a rigid-body translation between k and e. It has been discussed above that the Curie principle can be employed to predict that twin boundaries should emanate into the TiN crystal from the epitaxial inter-

7.6 Interface and Fault Junction Lines Fig. 7.23 Schematic illustration of a variant-constituted 3-junction created due to the coexistence of two variants of an epitaxial interface. A twin boundary emanates into the epilayer in order to compensate for a suppressed mirror-symmetry operation of the substrate.

face with a-GaN due to the suppression of the c-glide mirror symmetry. This topological prediction is verified by observation. Fig. 7.24 shows a micrograph of a (112) DPB that is observed to emanate into TiN from a demistep on the a-GaN substrate. To fully confirm the topological prediction, we examine the defect character exhibited by the junction line of the three components. This characterization can be performed on the HREM micrograph by using circuit mapping for interface junction lines [70, 71]. The reference space, when more than two crystal components are involved, is the polychromatic complex formed by the interpenetration of all the constituents, and the circuit comprises segments in all components. For a 3-junction, such as illustrated in Fig. 7.25, the general expression is C…kel† ˆ …I; plk †fP l C…l†P l 1 g…I; pel †fP e C…e†P e 1 g…I; pke †fP k C…k†P k 1 g ;

…25†

where the circuit operator, C(kel), is expressed in an independent coordinate frame. In Eq. (25), P k = (Pk, pk) etc. are the transformations from the independent frame to the crystal coordinate frames, and the relative displacements of the three

Fig. 7.24 Cross-sectional HREM micrograph along [21 10]a-GaN of the TiN/a-GaN epitaxial interface. A DPB is observed to emanate into TiN from a demistep at the interface. A closed circuit SGHIJS has been drawn around

the junction line in order to characterize its defect character. The location of the interfacial plane is indicated by a solid line, and the locations of the mirrors and glide mirror by broken lines.

363

364

7 Topological Analysis of Defects in Nitride Semiconductors Fig. 7.25 Schematic illustration of a closed right-handed circuit employed in order to characterize the defect character of a 3-junction line. The circuit comprises segments in all three crystal components, as well as displacements from one crystal to the other.

crystals pke, pel, and plk are expressed directly in the independent frame. If the independent frame is chosen to be the coordinate frame of crystal k, Eq. (25) simplifies to C…kel† ˆ P lk C…l†P el C…e†P ke C…k† ;

…26†

where P lk = (Plk, plk) represents the transformation l-to-k, and so on. As mentioned in Sect. 7.2, the operations in the circuit segments can be other than translations (i.e., rotations, mirrors). However, in order for C(kel)–1 to be the irreducible expression of the closure failure of the mapped excursion, it is imperative that the observer regains both his initial location and orientation at the end of the circuit in real space. Additionally, it is necessary, as discussed in Sect. 7.2, that the observer crosses any crystallographically equivalent interfaces in correspondingly equivalent ways. For this purpose, the observer must be oriented in equivalent ways relative to the local interface normals. Following the above general remarks, we apply the methodology for our particular case. A closed right-handed circuit SGHIJS around the 3-junction line is shown in the experimental micrograph of Fig. 7.24. Starting from the epitaxial interface, the observer is transported, through crystal k, to a coincidence position on the twin boundary by a translation operation followed by a (001) mirror reflection (segment SGH); at H the mirror-twinning operation is applied to the observer’s frame. The excursion continues by a (001) mirror operation in crystal e (segment HI). From I the observer is transported through the wurtzite structure l back to S, by first being operated upon by the (0110) glide mirror operation, and then by a translation operation (segment IJS). This circuit maps to SGHIF in the polycrystalline complex, as shown in Fig. 7.26, and closure failure FS arises. In order to quantitatively determine the closure failure, we employ Eq. (26) whereby the circuit segments are C(k) = (M(001), 0) (I, [001]), C(e) = (M(001), 0), and C(l) = (I, 1/3 [1 120]) (M(0110), –1/2 [0001]). With respect to the interrelating trans-

7.6 Interface and Fault Junction Lines

Fig. 7.26 Mapping of the circuit depicted in Fig. 7.24 to the reference space. Closure failure FS arises. The positions of the mirrors and glide mirror are indicated by dashed lines. ([21 10]a-GaN projection: in GaN symbols are as in Fig. 7.10 and in TiN they are as in Fig. 7.12).

formations, we note from the experimental micrograph of Fig. 7.24 that the (001) mirrors of the twin-related crystallites and the (1010) c-glide mirror plane of the substrate intersect along a common line (note that the glide mirror does not pass through atomic positions). Hence we can consider plk = pel = 0 (although we note that a relative displacement along the projection direction is not discernible from the experimental micrograph). The matrices Plk and Pel have been described in detail elsewhere [80]; we also have P ke = (T, 0) where T is the twinning mirror operation. The analytical calculation yields C(kel) = (I, –b), identifying the junction line as a dislocation with Burgers vector 2

0

3

6 7 bˆ4 0 5 1

2

1

0

aa-GaN 6 4 1 aTiNp2 0

2 p aa-GaN 2 6 6 ˆ 4aTiN 4

1 1 K K

…K ‡ 2†

1 0 1

1

3

2

0

3

2

1

31

6 7 6 7C B 7 B 1 6 0 7 1 6 2 7C 15
B 6 7‡ 6 7C @ 2 4 0 5 3 4 1 5A 1 K 0 3

7 2 7 4aTiN 5 p aa-GaN 2

and magnitude equal to 0.17 nm.

0

…27†

365

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7 Topological Analysis of Defects in Nitride Semiconductors

Fig. 7.27 Cross-sectional HREM micrograph of the b-GaN/ sapphire epitaxial interface. A DPB is observed to emanate into b-GaN from a demistep at the interface (indicated by a black solid line). White lines indicate the orientation of {111} planes in crystals k and e. In e distortions to this line are introduced by the large number of SFs that terminate on the DPB.

The prediction that DPBs emanate from substrate demisteps in the TiN/a-GaN system has been confirmed by HREM, and the junction line of the DPB with the epitaxial interface has been characterized by circuit mapping and has been shown to exhibit dislocation character. Another similar case is that of DPBs observed in b-GaN epilayers deposited on (0001) sapphire. The orientation relationship was (111)b-GaN//(0001)sapph., h110ib-GaN//h1010isapph.. The structure of b-GaN is zinc blende and has been described in Sect. 7.3. In this case we find the {1210} c-glide mirrors of sapphire to be suppressed. Without going into an analytical discussion, we illustrate in Fig. 7.27 an HREM micrograph of such a DPB emanating from the b-GaN/sapphire epitaxial interface. The DPB delineates crystallographically equivalent regions of interfacial structure on either side of a demistep. The DPB itself is seen to be discontinuous and to consist of mixed segments of incoherent twin boundary perpendicular to the epitaxial interface, and coherent twins and SFs parallel to the interface. Such a structural configuration has also been reported for DPBs in other heteroepitaxial systems [81].

7.6 Interface and Fault Junction Lines

7.6.3

Junction Lines between Hexagonal and Cubic Nitride Phases

The technology of nitride epilayers includes ternary and quaternary alloys of the forms AlxGa1–xN and InxAlyGa1–x–yN. In the quaternary case, the employed technique (MBE) requires growth at low temperature [82]. This may result in the appearance of the metastable cubic phase thus leading to film areas that appear polycrystalline. However, the boundaries that appear are topologically limited, as will be shown below. The polycrystalline structure is modulated by interface junctions in which crystallographically equivalent variants participate. Such a case is presented in Fig. 7.28 a where a junction line of three crystallites, one of cubic phase and two of the hexagonal, is illustrated. The orientation relationship is {111}//(0001), h110i//h21 10i. The coherent interfaces between the hexagonal and the cubic phase are crystallographically equivalent orientation variants that are related by {110} mirror planes of the cubic phase (crystal l) when they subtend a dihedral angle of 70.53 8. This results in a variant constituted 3-junction in the manner discussed in Sect. 7.6.2. In the micrograph of Fig. 7.28 a it is seen that the boundary between the variants of the hexagonal phase (crystals k and e) deviates significantly from the exact twin plane. The structure of this boundary is clearly resolved and the continuity of lattice planes from the (0001) orientation in one variant to the {0110} orientation in the other can be observed. A closed circuit SGHIJKLMS has been indicated around the junction line in order to determine its defect character. To avoid any spurious defect content, the circuit follows the translation periodicity of the polychromatic complex. This reference space is depicted schematically in Fig. 7.28 b. We note that ternary and quaternary nitride alloys may exhibit ordering that may result in a modification of the spacegroup symmetry [83]. However, for the purposes of our present discussion

Fig. 7.28 a Cross-sectional HREM micrograph along [21 10]//[110] of a junction line between the cubic phase and two orientation variants of the hexagonal phase in InAlGaN alloy. A closed circuit SGHIJKLMS has been drawn around the junction line, following the translation periodicity of the polychromatic complex, in order to determine its defect character. The position of the (110) mirror plane interrelating the interface variants has been indicated by a solid line

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7 Topological Analysis of Defects in Nitride Semiconductors

Fig. 7.28 b schematic illustration of the reference space showing the mapped circuit. It is found that no closure failure appears

([21 10]//[110] projection: symbols are as in Fig. 7.10).

we consider the In and Al atoms to occupy random positions in the Ga substructure, i.e., the spacegroup symmetries are taken to be unaltered (P63mc and F43m for the hexagonal and cubic phase, respectively). The closed circuit of Fig. 7.28 a is shown mapped in the reference space in Fig. 7.28 b, and it is found that no closure failure appears, i.e., this 3-junction line does not exhibit defect character. To conclude this subsection, the compensation of the cubic mirror symmetry is shown to result in GBs in the hexagonal phase when the two coexist in InxAlyGa1–x–yN. Our observations show that junction lines leading to such GBs may appear frequently in these epilayers, and the GBs themselves have been observed to become incoherent when their length exceeds one or two translation periodicities of the polychromatic complex. Given that {111} planes may appear in eight crystallographically equivalent orientations, we may deduce the frequent occurrence of GBs in variant orientations, and such epitaxial films can be characterized topologically as variant-constituted polycrystals in the manner described in [79]. The influence of the GBs on the electrical properties of the epilayer requires further appreciation, especially if the GB structural units are associated with dangling bonds.

7.7 Conclusions

7.7

Conclusions

Through a number of experimental observations, we have covered extensively the applicability of the topological theory for the characterization of defects in nitride epilayers and have demonstrated the insight that can be gained about defects that arise following symmetry compensation or other structural reasons. The topological theory has been developed into a complete and rigorous tool that can be employed for a priori as well as a posteriori defect characterization [10, 11, 16, 38, 70, 71, 79]. In the former case, a Volterra approach is employed, while, in the latter, circuit mapping is used. We have given here a unified presentation of both methods, showing their equivalence, circumstances under which they are applicable, and practical aspects of their deployment. The presented observations lead to the realization that it is of technological importance to employ spacegroup symmetry and to consider the actual crystal structures for the prediction and characterization of defects, rather than mere translation symmetry. In this manner, complete information is obtained on parameters such as the Burgers vectors of dislocations, the strength of disclinations or the mirror matrices of twins, as well as on whether such defects induce a structural transformation. The method has been utilized here in a simple manner to illustrate a number of experimental observations of defects in GaN heteroepitaxy thus contributing towards the development of a defect model for these epitaxial layers. We have also considered the superposition and interactions between defects in a number of instances. In one section we have concentrated on threading, SF and misfit dislocations. The insight that has been gained on the influence of these defects on crystalline structure is valuable for ascertaining their effect on physical properties of the material. It has been demonstrated that, depending on the topological parameters, line defects may either conserve the crystalline structure in their surrounding space or they may accommodate a structural transformation (for example they may separate regions of “good” crystal from regions of faulted crystal). The topological theory offers a fundamental way of distinguishing between such cases on the basis of symmetry arguments. We have also considered the systematic appearance of inversion and stacking disorder in GaN films; such disorder degrades the crystalline quality of the epilayer with a resultant influence on properties, for example IDBs affect the polarity. It has been shown that the structure of the epitaxial interface can be responsible for the introduction of such disorder and this effect can be explained through appropriate topological analysis. In a-GaN this analysis has yielded that, when growth proceeds along a polar direction, the introduction of IDBs is not imposed by the coexistence of energetically degenerate interfacial regions. In another section we have examined structural transformations of IDBs due to their intersections with intrinsic SFs. HREM observations show that, for [0001] growth, IDBs are transformed from the low-energy and electrically nonactive IDB* type to the high-energy, electrically active, Holt-type structure. It has been proven that these transitions are due to the interaction of two distinct planar de-

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7 Topological Analysis of Defects in Nitride Semiconductors

fects, and can be attributed to the different growth rates of adjacent domains of inverse polarity. It has also been found that the resulting junction lines exhibit partial dislocation character. In the final section, the symmetry compensation principle was employed to predict that DPBs can emanate from demisteps in the TiN/GaN interface and this has been confirmed by HREM. In a manner that is similar in principle, grain boundaries emanate in the hexagonal phase of quaternary nitride alloys as a result of the coexistence of orientation variants of its interface with the corresponding cubic phase. In both cases, it is the compensation of mirror symmetry in one component that results in the appearance of these extended defects. In concluding, we remark that “symmetry theory offers necessary but not sufficient conditions for the realization of phenomena” [12]. Geometrically admissible defects may not be physically feasible, and this has to be kept in mind when striving for a priori defect determination. The Volterra approach offers the necessary conditions for a defect to delineate crystallographically equivalent regions but has to be combined with energetical considerations and a posteriori experimental observations employing circuit mapping, in order to lead to a comprehensive defect model for a given material system. On the other hand, in epitaxial systems, the symmetry and structure of the substrate both constrain as well as influence the defects that may appear in the epilayer and the predictive capacity of the topological theory attains increased technological importance.

7.8

Acknowledgments

This work was supported by the HPRN-CT-1999-00040 contract of the European Union. The authors are indebted to Professors T.D. Moustakas and G. Nouet for valuable discussions, Prof. T.D. Moustakas and Assist. Prof. A. Georgakilas for providing specimens used in this study, and Mr. J. Kioseoglou for HREM image simulations and processing.

7.9

Appendix: The Frank Coordinate System for Hexagonal and Trigonal Crystallography

The principal advantage of the Miller-Bravais indexing scheme is that indices of planes and directions reflect the symmetry of the crystal, and hence crystallographically equivalent planes or directions have similar indices. On the other hand, this advantage appears to have been gained at the expense of increased complexity in crystallographic calculations because the coordinate frame used is not orthogonal. However, by relating the Miller-Bravais scheme to the more general system of mathematics [35], these apparent complexities are removed and the commonly performed calculations can be carried out readily. The device exploited is a 4-dimensional (4D) orthogonal frame such that the Miller-Bravais symbols

7.9 Appendix: The Frank Coordinate System for Hexagonal and Trigonal Crystallography

can be interpreted as vectors confined to a 3-dimensional (3D) subspace of this 4space. A.1

Projection from a Higher Dimension

It is possibly the invocation of a 4D space that has discouraged the widespread use of Frank’s method by crystallographers. For this reason, we present here, in a slightly different manner to that in the original paper, Frank’s introduction to the use of a higher-dimensional frame for the representation of figures in a lower dimension. Imagine first that it is necessary to devise an indexing scheme for the hexagon AEBFCD illustrated in Fig. 7.A1. One choice would be to index the direction OA as [1,0], and OB as [0,1]. Clearly, this procedure would not reflect the symmetry of the figure because, for example, the index for OE would be [1,1]. A second possibility is to regard the hexagon as the 2D projection of a cube viewed along its body diagonal O'O, where O' is vertically above O in the figure. Now, making use of a 3D Cartesian frame, we can index O'A' as [100], O'B' as [010] and O'C' as [001] where A', B', and C' and represented vertices of the cube located vertically above A, B and C, respectively. Since the projection direction O'O is [111], the components of these primitive vectors, resolved parallel to the plane of the projection, are OA = 1/3 [21 1], OB = 1/3 [121] and OC = 1/3 [1 12], respectively. We note that the scalar product formed between any vectors in the 2D space and the projection direction, [111], must be zero or, in other words, the three indices of the projected vector must sum to zero. Thus, by exploiting the auxiliary dimension, a much more symmetrical algebraic representation is obtained, while still retaining the advantages of a Cartesian frame. We note that the 3-fold symmetry exhibited by the hexagon is also a “true” symmetry element of the cube, but the 6fold symmetry arises only in the 2D space. Now consider the analogous procedure of projecting a 4D hypercube, with edges indexed as [1000], [0100], [0010] and [0001], along the direction [1110]. The first three unit vectors projected into three dimensions along this direction are 1/3 [21 10], 1/3 [1210], and 1/3 [1 120], whereas the fourth, being perpendicular to [1110], remains

Fig. 7.A1 Schematic view of a cube viewed along a body diagonal, illustrating the hexagonal form in projection.

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7 Topological Analysis of Defects in Nitride Semiconductors

invariant, i.e., [0001]. Thus, we have obtained a 3D subspace comprising three vectors in a basal plane, and a fourth vector, [0001], that is perpendicular to this plane. As was the case for the previous example, the scalar product formed between vectors in the 3D subspace and the projection direction must be zero, and hence the first indices of vectors in the subspace must sum to zero. The relationship between the subspace cell, defined by the vectors 1/3 [21 10], 1/3 [1210], 1/3 [1 120], and [0001], and the conventional hexagonal unit cell is now apparent. However, it is necessary to scale this cell in order that its dimensions correspond to the lattice parameters, a and c, of a real hexagonal or trigonal crystal. Let the unit 4-space vectors have magnitude e. It follows that the magnitude of each of the vectors 1/3 h21 10i is equal to (2/3)1/2e, and therefore that the ratio of the magnitude of [0001] to 1/3 h21 10i is (3/2)1/2. In other words, the cell obtained by projection of a hypercube has a particular c/a ratio. Now, by increasing the length of 4-vector components parallel to [0001] by the appropriate factor, the three-dimensional cell will exhibit the c/a ratio required for a particular problem. The required factor is simply equal to c/e = (2/3)1/2c/a, and this was designated K by Frank. A.2

Crystallographic Calculations

It can be seen that a direction, symbolized by [uvtw] according to the Miller-Bravais system, corresponds to the Cartesian 4-vector [uvt(Kw)]4 where the subscript is used here to distinguish 4-vectors. Thus, for crystallographic directions the transformation between the Miller-Bravais symbolism and the 4-vector notation is very simple. Crystallographic calculations can be carried out in a straightforward manner using the latter formulation: (i) The magnitude of the vector [uvt(Kw)]4 is equal to (u2 + v2 + t2 + K2w2)1/2 in units of e (or, alternatively, (3/2)1/2a). (ii) The scalar product of [u1 v1 t1 (Kw1)]4 and [u2 v2 t2 (Kw2)]4 is equal to u1u2 + v1v2 + t1t2 + K2 w1w2 in units of e2. (iii) The angle between these two vectors is given by cos # ˆ

…u1 u2 ‡ v1 v2 ‡ t1 t2 ‡ K2 w1 w2 † …u21 ‡ v21 ‡ t21 ‡ K2 w12 †1=2 …u22 ‡ v22 ‡ t22 ‡ K2 w22 †1=2

:

…A1†

(iv) The vector product of these two vectors can be obtained by expanding the following determinant [84]: e1 u1 u2 p1 3

e2 v1 v2 1 p 3

e3 e4 t1 Kw1 t2 Kw2 ; 1 p 0 3

…A2†

7.9 Appendix: The Frank Coordinate System for Hexagonal and Trigonal Crystallography

where e1, e2, etc. are the Cartesian unit vectors in 4-space. We note that the resulting 4-vector can be regarded as that which is simultaneously perpendicular to [u1 v1 t1 (Kw1)]4 and [u2 v2 t2 (Kw2)]4 and is also perpendicular to 3–1/2 [1 1 10]4 and hence exists in the projected subspace. The resultant 4-vector can, of course, be transformed back into Miller-Bravais symbolism, if required, by simply dividing the final index by K. Calculations involving planes can also be performed readily. Frank [35] showed that the 4-vector perpendicular to the plane with Miller-Bravais index (hkil) is [hki(l/K)]4. (This can be proved, for example, by identifying two 4-vectors in the plane, and forming their vector product as described above.) It is then straightforward to determine the angle between this plane normal and any other crystal direction by using Eq. (A1). It can also be seen that the factor K will not appear in the scalar product of these two directions. Moreover, this formulation shows why the “zone law”, i.e., hu + kv + it + lw = 0, is valid for directions [uvtw] lying in the plane (hkil). It is also straightforward to show that the interplanar spacing, d, for the planes (hkil) is given by d ˆ ‰h2 ‡ k2 ‡ i2 ‡ …l2 =K2 †Š

1=2

…A3†

in units of e. (This can be shown, for example, by determining the angle, }, between [0001] and the plane normal, using Eq. (A1), and then using cos} = ld/c, where c/l is the intercept of the plane on the c axis.) A.3

Reciprocal Space

Conventional treatments do not appear to relate direct and reciprocal lattices for hexagonal crystals in the customary way. On the other hand, Frank’s method makes this connection in a straightforward and rigorous manner. The unit vectors of the direct, ei, and reciprocal, ej , 4-spaces are simply related by ei
ej ˆ dij …i; j ˆ 1; 2; 3; 4† ;

…A4†

where dij is the Kronecker delta. Thus, the reciprocal unit vectors are parallel to the direct ones and have magnitude e–1. It follows that the usual crystallographic notation for the reciprocal vector, g = hkil, associated with the planes (hkil), corresponds to the reciprocal 4-space vector g4 = hki(l/K). In other words, the MillerBravais symbol of a direction in direct space is transformed to the 4-vector by multiplying the last index by K, and in reciprocal space, the corresponding procedure is to divide the last index by K. Clearly, the magnitude of this latter vector is equal to [h2 + k2 + i2 + (l2/K2)]1/2 in units of e–1, and this is equal to d–1. Moreover, the vector g4 can be seen to be parallel to the normal to the plane, i.e., parallel to [hki(l/K)]4, as is required by definition. Students are frequently confused by the apparent rotation of 30o between the diffraction pattern, obtained when a beam is incident perpendicular to the basal plane of a hexagonal crystal, and the atomic

373

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7 Topological Analysis of Defects in Nitride Semiconductors

arrangement in that plane. The shortest reciprocal vectors have the form g = 1100, whereas the shortest translation vectors in the crystal have form 1/3 h21 10i. Frank clarified this point by explaining that the direct unit cell can be visualized as a projection from a higher-dimensional space, and hence fractional indices may arise, in contrast to the situation in reciprocal space where the diffraction pattern corresponds to a section of the reciprocal space, and hence nonintegral indices do not arise using the crystallographic notation. A.4

Matrix Algebra

The 4 ´ 4 matrices corresponding to the twenty-four point symmetry operations in the holosymmetric hexagonal spacegroup are shown in Tab. 7.1, and the method of their derivation has been described elsewhere [84]. It can be seen that the matrices have a particularly simple form and all elements are independent of K. Twelve of the operations comprise column vectors of the type h1000i exclusively, and the remaining twelve matrices involve columns of the form 1/3 h21 10i, which are 4-vectors of unit magnitude and include a component 2/3 [1110] parallel to the projection direction from 4D into 3D space. Symmetry matrices can be used to operate on a given 4-vector, expressed as a column vector, in order to find the symmetry-related 4-vector. In the present context, it is also necessary to define in the Frank system the transformation matrix between two crystals, designated k and l, that abut along an interface. Let P be such a matrix that relates the l coordinate frame to the k one. Then, assuming two hexagonal or trigonal crystals, the unit vectors are related by …e1 e2 e3 e4 †l ˆ …e1 e2 e3 e4 †k P

…A5†

and P is a 4 ´ 4 matrix. Hence, expressing all vectors as 4-vectors, the coordinate transformation from l to the k coordinate frame is 2 3 3 u x 6 7 6 y 7 6 7 ˆ P6 v 7 : 4 t 5 4 z 5 Kw l Kq k 2

…A6†

The derivation of matrix P is necessary in order to perform calculations, and the information that is usually provided for this purpose, in the case of epitaxial bicrystals, is in the form of pairs of parallel axes and/or planes. In addition, we have to take into account that, in the case of interphase interfaces, the crystals have different c/a ratios. For our purpose, the Frank coordinate system is most useful and easy to use, since it is 4-dimensionally cubic. Hence, we need a set of four pairs of parallel directions, in order to deduce P, each being perpendicular to the other three. Three pairs are given by the orientation relationship; the fourth

7.10 References

pair is the pair [1110]//[1110] since both crystals are obtained from the same projection of the 4D space. Hence if we have, say, the orientation relationship ‰x1 y1 z1 q1 Šk ==‰u1 v1 t1 w1 Šl ; ‰x2 y2 z2 q2 Šk ==‰u2 v2 t2 w2 Šl ; ‰x3 y3 z3 q3 Šk ==‰u3 v3 t3 w3 Šl in 4-vectors, we initially determine the corresponding unitary vectors, i.e., 1=2 ‰x10 y01 z01 q01 Šk ˆ ‰x1 y1 z1 Kq1 Šk =…x12 ‡ y21 ‡ z21 ‡ K2 q21 †k ; etc., and then calculate the matrix 2

x10 6 y0 6 1 4 z0 1 q01

x20 y02 z02 q02

x30 y03 z03 q03

p 3 2 0 1=p3 u1 6 v0 1=p3 7 76 1 1= 3 5 4 t01 0 w10

u02 v02 t02 w20

u03 v03 t03 w30

p 3 1=p3 1=p3 7 7 1= 3 5 0

1

:

…A7†

Finally we multiply this matrix with the ratio of magnitudes e for the two crystals, which reduces to the ratio of a lattice parameters. In the case of cubic-hexagonal epitaxial systems, the same methodology is applied, only the cubic is formulated to include a fourth axis [0001] instead of [1110].

7.10

References 1

2

3

4

5 6 7

F. Ponce, in Introduction to Nitride Semiconductor Blue Lasers and Light Emitting Diodes, edited by S. Nakamura and S. F. Chichibu (Taylor & Francis, London New York, 2000), p. 105. J. Elsner, A. Th. Blumenau, T. Frauenheim, R. Jones, and M. I. Heggie, Mater. Res. Soc. Symp.Proc. 595, w9.3.1 (2000). J.I. Pankove and Th. D. Moustakas (ed.), Gallium Nitride (GaN) I, Semiconductors and Semimetals (Academic Press, New York, 1998), Vol. 50. S. J. Rosner, E. C. Carr, M. J. Ludowise, G. Girolami, and H. I. Erikson, Appl. Phys. Lett. 70, 420 (1997). S. Nakamura, Science 281, 956 (1998). R. Beanland, D. J. Dunstan, and P. J. Goodhew, Adv. Phys. 45, 87 (1996). B. Beaumont, V. Bousquet, P. Vennegues, M. Vaille, A. Bouille, P. Gibart, S. Dassonneville, A. Amokrane, and B. Sieber, Phys. Stat. Sol. (a) 176, 567 (1999).

8

9 10

11 12

13 14

15

16

H. Lahreche, P. Vennegues, B. Beaumont, and P. Gibart, J. Cryst. Growth 205, 245 (1999). S. C. Jain, A. H. Harker, and R. A. Cowley, Phil. Mag. A 75, 1461 (1997). R. C. Pond, in Dislocations in Solids, F. R. N. Nabarro (ed.) (North Holand, Amsterdam, 1989), Vol. 8, p. 5. R. C. Pond and J. P. Hirth, Solid State Phys. 47, 288 (1994). A. V. Shubnikov and V. A. Koptsik, Symmetry in Science and Art (Plenum Press, New York London, 1974). R. C. Pond, J. P. Gowers, and B. A. Joyce, Surf. Sci. 152/153, 1191 (1985). Ph. Komninou, J. Stoemenos, G. P. Dimitrakopulos, and Th. Karakostas, J. Appl. Phys. 75, 143 (1994). A. C. Daykin, C. J. Kiely, and R. C. Pond, Acta Metall. Mater. 40, S195 (1992). G. P. Dimitrakopulos, Th. Karakostas, J. G. Antonopoulos, and R. C. Pond, Interface Sci. 5, 35 (1997).

375

376

7 Topological Analysis of Defects in Nitride Semiconductors 17

18

19

20 21 22

23

24

25

26 27

28

29

30 31

32

33

H. Morkoç, S. Strite, G.B. Gao, M. E. Lin, B. Sverdlov, and M. Burns, J. Appl. Phys. 76, 1363 (1994). X. H. Wu, L. M. Brown, D. Kapolnek, S. Keller, B. Keller, S. P. Den-Baars, and J. S. Speck, J. Appl. Phys. 80, 3228 (1996). V. Potin, P. Ruterana, G. Nouet, R. C. Pond, and H. Morkoç, Phys. Rev. B 61, 5587 (2000). V. Potin, P. Ruterana, and G. Nouet, J. Phys. Condens. Matter. 12, 10301 (2000). P. Ruterana and G. Nouet, Mater. Res. Soc. Symp. Proc. 595, w5.4.1 (2000). Th. Kehagias, Ph. Komninou, G. Nouet, P. Ruterana, and Th. Karakostas, Phys. Rev. B 64, 195329 (2001). Ph. Komninou, G. P. Dimitrakopulos, G. Nouet, Th. Kehagias, P. Ruterana, and Th. Karakostas, J. Phys. Condens. Matter. 12, 49 (2000). G. P. Dimitrakopulos, Ph. Komninou, J. Kioseoglou, Th. Kehagias, E. Sarigiannidou, A. Georgakilas, G. Nouet, and Th. Karakostas, Phys. Rev. B 64, 245325 (2001). J. L. Rouviere, M. Arlery, R. Niebuhr, K. H. Bachem, and O. Briot, Mater. Sci. Eng. B 43, 161 (1997). P. Vennegues, B. Beaumont, and P. Gibart, Mater. Sci. Eng. B 43, 274 (1997). Ph. Komninou, Th. Kehagias, J. Kioseoglou, E. Sarigiannidou, Th. Karakostas, G. Nouet, P. Ruterana, K. Amimer, S. Mikroulis, and A. Georgakilas, Mater. Res. Soc. Symp. Proc. 639, G3.47 (2001). Y. Xin, P. D. Brown, C. J. Humphreys, T. S. Cheng, and C. T. Foxon, Appl. Phys. Lett. 70, 1308 (1997). T. Hahn (ed.), International Tables for Crystallography (Reidel, Dordrecht, 1983). F. C. Frank, Phil. Mag. 42, 809 (1951). X. H. Wu, P. Fini, E. J. Tarsa, B. Heying, S. Keller, U. K. Mishra, S. P. DenBaars, and J. S. Speck, J. Cryst. Growth 189/190, 231 (1998). X. J. Ning, F. R. Chien, P. Pirouz, J. W. Yang, and M. Asif Khan, J. Mater. Res. 11, 80 (1996). E. S. Hellman, MRS Internet J. Nitride Semicond. Res. 3, 11, 1998.

34 35 36 37

38 39 40

41

42

43

44

45 46 47

48 49

50

51 52

B. Daudin, J. L. Rouviere, and M. Arlery, Mater. Sci. Eng. B 43, 157, 1998. F. C. Frank, Acta Crystallogr. 18, 862 (1965). V. Volterra, Ann. Sci. Ec. Norm. Sup. Paris 24, 401 (1907). R. C. Pond, D. J. Bacon, A. Serra, and A. P. Sutton, Metall. Trans. A 22, 1185 (1991). R. C. Pond and D. S. Vlachavas, Proc. R. Soc. A 386, 95 (1983). T. Araki, T. Minami, and Y. Nanishi, Phys. Stat. Sol. (a) 176, 487 (1999). J. Suda, T. Kurobe, T. Masuda, and H. Matsunami, Phys. Stat. Sol. (a) 176, 503 (1999). S. Oktyabrsky, K. Dovidenko, A. K. Sharma, J. Narayan, and V. Joshkin, Appl. Phys. Lett. 74, 2465 (1999). G. Feuillet, F. Widmann, B. Daudin, J. Schuler, M. Arlery, J. L. Rouvière, N. Pelekanos, and O. Briot, Mater. Sci. Eng. B 50, 233 (1997). H. Okumura, K. Ohta, G. Feuillet, K. Balakrishnan, S. Chichibu, H. Hamaguchi, P. Hacke, and S. Yoshida, J. Cryst. Growth 178, 113 (1997). F. R. Chien, S. R. Nutt, J. M. Carulli, Jr., N. Buchan, C. P. Beets, Jr., and W. S. Yoo, J. Mater. Res. 9, 2086 (1994). I. Akasaki, Mater. Sci. Eng. B 74, 101 (2000). S. Nakamura, T. Mukai, and M. Senoh, Appl. Phys. Lett. 64, 1687 (1994). P. Ruterana, G. Nouet, Th. Kehagias, Ph. Komninou, Th. Karakostas, M. A. Di Forte Poisson, F. Huet, and H. Morkoç, Phys. Stat. Sol. (a) 176, 767 (1999). P. A. Stadelmann, Ultramicroscopy 21, 131 (1987). H. Zhou, F. Phillipp, M. Gross, and H. Schröder, Mater. Sci. Eng. B 68, 26 (1999). G. P. Dimitrakopulos, V. P. Dravid, Th. Karakostas, and R. C. Pond, Acta Crystallogr. A 53, 341 (1997). J. D. Eshelby, Solid State Phys. 3, 79 (1956). C. Stampfl and C. G. Van de Walle, Phys. Rev. B 57, R15052 (1998).

7.10 References 53

54

55

56

57 58 59 60

61

62

63 64

65 66

67

68 69 70

71

J. P. Hirth and J. Lothe, Theory of Dislocations, 2nd edn (Wiley Intersciences, New York, 1982). J. W. Christian, The Theory of Transformations in Metals and Alloys (Pergamon Press, Oxford, 1981), p. 340. A. P. Sutton and R. W. Balluffi, Interfaces in Crystalline Materials (Oxford Science Publications, Oxford, 1995). F. C. Frank, in Symposium on the Plastic Deformation of Crystalline Solids (The Physical Society, London, 1950), p. 150. B. A. Bilby, Prog. Solid. Mech. 1, 329 (1960). V. Potin, G. Nouet, and P. Ruterana, Appl. Phys. Lett. 74, 947 (1999). V. Potin, G. Nouet, and P. Ruterana, Phil. Mag. A 79, 2899 (1999). B. Pécz, M. A. di Forte-Poisson, F. Huet, G. Radnóczi, L. Tóth, V. Papaioannou, and J. Stoemenos, J. Appl. Phys. 86, 6059 (1999). D. Cherns, W. T. Young, M. Saunders, J. W. Steeds, F. A. Ponce, and S. Nakamura, Phil. Mag. A 77, 273 (1998). T. Kato, P. Kung, A. Saxler, C. J. Sun, H. Ohsato, M. Razeghi, and T. Okuda, J. Cryst. Growth 183, 131 (1989). S. B. Austerman and W. G. Gehman, J. Mater. Sci. 1, 249 (1966). P. Ruterana, V. Potin, B. Barbaray, and G. Nouet, Phil. Mag. A 80, 937 (2000). S. Tanaka, R. S. Kern, and R. F. Davis, Appl. Phys. Lett. 66, 37 (1995). B. N. Sverdlov, G. A. Martin, H. Morkoç, and D. J. Smith, Appl. Phys. Lett. 67, 2063 (1995). H. Blank, P. Delavignette, R. Gevers, and S. Amelinckx, Phys. Stat. Sol. 7, 747 (1964). J. E. Northrup, J. Neugebauer, and L. T. Romano, Phys. Rev. Lett. 77, 103 (1996). D. B. Holt, J. Mater. Sci. 19, 439 (1984). G. P. Dimitrakopulos, Th. Karakostas, and R. C. Pond, Interface Sci. 4, 129 (1996). G. P. Dimitrakopulos, Ph. Komninou, Th. Karakostas, and R. C. Pond, Interface Sci. 7, 217 (1999).

72

73

74

75 76

77

78

79 80 81

82

83

84

C. A. Dimitriadis, Th. Karakostas, S. Logothetidis, G. Kamarinos, J. Brini, and G. Nouet, Solid-State Electron. 43, 1969 (1999). P. Ruterana, G. Nouet, Th. Kehagias, Ph. Komninou, Th. Karakostas, M. A. Di Forte, Poisson, F. Huet, M. Tordjman, and H. Morkoç, in Microscopy of Semiconducting Materials 1999, A. G. Cullis and R. Beanland (eds.), Inst. Phys. Conf. Ser. 164 (Institute of Physics Publishing, Bristol Philadelphia, 1999), p. 568. P. Ruterana, G. Nouet, Th. Kehagias, Ph. Komninou, Th. Karakostas, C. A. Dimitriadis, F. Huet, and M. A. Di Forte Poisson, Mater. Res. Soc. Symp. Proc. 595, w11.75.1. (2000). R. F. Davis, S. Tanaka, and R. S. Kern, J. Cryst. Growth 163, 93 (1996). Q. Wahab, L. Hultman, I. P. Ivanov, M. Willander, and J.-E. Sundgren, Thin Solid Films 261, 317 (1995). D. J. Smith, D. Chandrasekhar, B. Sverdlov, A. Botchkarev, A. Salvador, and H. Morkoç, Appl. Phys. Lett. 67, 1830 (1995). L. Hultman, H. Ljungcrantz, C. Hallin, Janzén, J.-E. Sundgren, B. Pécz, and L. R. Wallenberg, J. Mater. Res. 11, 2458 (1996). G. P. Dimitrakopulos and Th. Karakostas, Acta Crystallogr. A 52, 62 (1996). R. C. Pond, M. Aindow, and W. A. T. Clark, Scr. Metall. 21, 971 (1987). F. R. Chien, S. R. Nutt, J. M. Carulli, Jr, N. Buchan, C. P. Beetz, Jr, and W. S. Yoo, J. Mater. Res. 9, 2086 (1994). T. D. Moustakas, in Gallium Nitride (GaN) II, Semiconductors and Semimetals, J. I. Pankove and T. D. Moustakas (eds.) (Academic Press, New York, 1999), Vol. 57, p. 33. M. K. Behbehani, E. L. Piner, S. X. Liu, N. A. El-Masry, and S. M. Bedair, Appl. Phys. Lett. 75, 2202 (1999). R. C. Pond, N. A. McAuley, A. Serra, and W. A. T. Clark, Scr. Metall. 21, 197 (1987).

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8

Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms Pierre Ruterana, Ana M. Sánchez, and Gérard Nouet

Abstract

Using high-resolution electron microscopy, atomistic modeling and image simulations, typical contrast was identified for the a pure edge threading dislocations in GaN layers grown by MBE on sapphire or SiC. Their atomic structure was shown to exhibit 5/7, or 8 atom cycles. A topological analysis of high angle grain boundaries was carried out in order to determine the defect content at the interfaces. The reconstruction of some boundaries was only possible by taking into account the occurrence of structural units that exhibit 4 atom ring cycles for the dislocation cores. The pure edge threading dislocations were shown to be connected to misfit dislocations at the GaN/Al2O3 interface. The {1210} stacking fault has two atomic configurations in wurtzite (Ga, Al, In)N with 1/2 h1011i and 1/6 h2023i displacement vectors. It originates from steps at the SiC surface and it can form on a flat (0001) sapphire surface. These configurations have comparable energy in AlN, whereas the 1/2 h1011i {1210} is more stable in GaN and InN. In the investigated samples, the {1010} inversion domain boundaries exhibit two atomic configurations (Holt and V models) depending on the growth conditions. The samples containing Holt inversion domains have a flat surface morphology, whereas the V IDBs were observed in the centre of small pyramids (100 nm high) protruding at the sample surface. The Holt inversion domains were always smaller (< 20 nm), at higher densities (2.5 ´ 1010 cm–2), whereas the V ones reach 50 nm and one order of magnitude lower density. The two atomic configurations have now been shown to be able to coexist inside the same sample,

380

8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

mainly due to interactions with the basal stacking faults. The inversion domains were found to be generated mostly at surface steps where they minimized the large misfit along the c axis (20%).

8.1

Introduction

The GaN-based III–V semiconductors have large direct band gaps which make them excellent candidates for short wavelength opto-electronic applications [1]. Among these materials, GaN and AlN are of particular interest as their solid solutions or superlattice structures allow bandgap engineering in the range of 3.45– 6.28 eV. As bulk crystals or wafers of these materials are not available, GaN has to be epitaxially grown on a large variety of substrates. The wurtzite allotropic structure of GaN is thermodynamically the most stable, but cubic substrates have been used to stabilize the zinc blende phase since cubic semiconductors are more readily doped [2]. The most commonly used substrates are sapphire and a-SiC, which have hexagonal symmetry. SiC may be the most promising for its small thermal and lattice mismatch with GaN [3], although the majority of work that has been reported is on sapphire substrates which present a large lattice mismatch (16%). This was due to the good results obtained in deposition by metal organic chemical vapor deposition (MOCVD) on sapphire [4] and difficulties in surface preparation for SiC substrates. Recently, enhancement in the substrate cleaning procedure by addition of a hydrogen plasma step has allowed to overcome the latter problem and it is now possible to deposit GaN layers by electron cyclotron resonance (ECR) enhanced molecular beam epitaxy (MBE) [3]. The active GaN layers contain large densities of crystallographic defects, among which those that can cross the whole epitaxial layer and be detrimental to the electro-optical properties are the threading dislocations [5, 6], the nanopipes [7], the inversion domains [8, 9], and the prismatic planar defects [8, 10, 11]. As pointed out by many workers, the large majority of these defects is made of threading dislocations which originate from the particular growth mode of GaN on top of the (0001) sapphire or SiC substrates. This mosaic growth mode leads to islands that are rotated mostly around the c axis and therefore are bounded by mainly a edge dislocations [12, 13]. In a conventional semiconductor, such as silicon or GaAs, such defect densities in the order of 1010 cm–2 would result in nonusable layers. In GaN, commercial LEDs are made from such layers, this has led many workers to conclude that extended defects would have a negligible electro-optical activity, such as nonradiative recombination [14]. In the case of threading dislocations, the nonradiative activity was tentatively explained by the reconstruction of the core, which eliminates the dangling bond in the 8 atom cycles [15, 16]. Unfortunately, this explanation does not hold for the laser diodes in which it was possible to increase the lifetime to 10,000 hours [17] only by introducing new growth techniques in order to have areas where the dislocation density could be lower than 106 cm–2 [18].

8.1 Introduction

The {1210} planar defects have been called double positioning boundaries (DPBs) [10, 19], stacking mismatch boundaries (SMBs) [20] or inversion domain boundaries (IDBs) [8]. These faults have been investigated using high-resolution electron microscopy (HREM) and Convergent Beam Electron Diffraction (CBED), and it was shown that they are stacking faults on top of both sapphire and SiC [21, 22]. In fact, these planar defects have already been studied in the sixties and two displacement vectors have been measured by conventional microscopy [23, 24]. In ceramic AlN, Drum [24] investigated faults which intersected on the basal and prismatic {1210} planes, it was shown that the displacement vector was 1/2 h1011i and that they folded to the basal planes by leaving a 1/6 h1010i stair rod dislocation at the intersection. Almost at the same time, Blank et al. [23] were the first to study the planar defects which folded from basal to prismatic {1210} planes in wurtzite ZnS, and to interpret them as stacking faults whereas other authors considered them to be thin lamella of the sphalerite phase in CdS [25]. These prismatic faults were then shown to be growth domains and the displacement vector was found to be 1/6 h2023i which is the same as that of the I1 basal stacking fault in the hexagonal compact packed (hcp) structure. GaN is of wurtzite structure, which is noncentrosymmetric. In such structures, defects due to polarity were reported for the first time by Aminoff and Broome [26]. Since then, several terms have been used for them, such as inversion twins [27], or antiphase boundaries [28]. Westwood and Notis [29] discussed the confusion between antiphase and inversion domain boundary (IDB) and showed it to be due to a too general definition of antiphase boundary that includes IDB. For example, using the two-colour symmetry theory, Pond and Holt [30] showed that the antiphase boundary described by Holt [28] was in fact an IDB. Inversion domain boundaries have been analysed in several materials like wurtzite BeO [27] and sphalerite GaAs [31]. Two models for the atomic structure of IDBs were proposed by Austerman and Gehman [27] and by Holt [28], respectively. The Austerman model has the anion sublattice continuous across the boundary whereas the cations switch from one type of tetrahedral site to the other. This model was found to agree with HREM observations in ZnO [32] as well as in ZnSe [33]. In the Holt model, the cations and anions are exchanged across the boundary, leading to the formation of anti-sites or wrong bonds (A–A, B–B). Its occurrence was reported in SiC [34] as well as in GaAs epitaxially grown on Si [31]. During the last decade, many studies have been carried out in sintered AlN and essentially two morphologies were observed for the IDBs: a planar variant lying in the (0001) basal plane and a curved one [35–37]. In epitaxial GaN layers, the IDBs were observed on sapphire substrate and not on SiC as it was shown in layers grown in the same conditions on both substrates [38]. A detailed study of the polarity of GaN/SiC layers has shown that the layers are unipolar [22]. In the unique work which reported IDBs in GaN grown on SiC substrate, a thin amorphous layer was present at the interface with the substrate [39]. Various morphologies have been reported for IDBs in GaN layers grown on sapphire substrate: they can be either bounded by {1010} planes and cross the whole epitaxial layer [40], or be limited by {1010}, {1011} and {1012} planes and

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

form house-shaped domains buried near the interface with the substrate [41]. They have been observed for various growth techniques: MBE, MOCVD or hybrid vapor phase epitaxy (HVPE) [9]. Many reports are now available on the IDBs atomic structure: although a translation on the basal plane has been reported [41], the most recent investigations have excluded it. In their transmission electron microscopy (TEM) work, Cherns et al. [42] studied displacement fringes in GaN layers grown by MOCVD and confirmed the model with a c/2 translation, first proposed by Northrup et al. [9]. In a HREM work, on GaN layers grown by MBE, Potin et al. [43] reported the occurrence of Holt type IDBs. For the time being, there is still a controversy on the role of the defects on the device performances. The high efficiency of the light emitting diodes seems to indicate that most of the defects are inactive whereas the short lifetimes of laser diodes may be attributed to them. Anyway, it is clear that an improvement of the crystalline quality of the layers would allow higher performances of the devices. For the fabrication of GaN-based devices, an important step in the nitride growth progress was the use of AlN or GaN buffer layers by Akasaki et al. [44] who showed that it greatly improved the crystalline quality of GaN layers, especially those grown on sapphire substrates. In the present work, an extensive report is made on the atomic scale structural analysis of the extended defects in GaN and AlN layers. The results were obtained by the HREM technique on the core structure of threading dislocations, prismatic stacking faults and IDBs. Finally, the possible formation mechanisms for each type of crystallographic defects will be discussed.

8.2

Crystallographic Considerations 8.2.1

Substrates 8.2.1.1 Sapphire

The corundum form of Al2O3 belongs to the trigonal R3c spacegroup (167), taking the origin at 3c, as in the International Tables for Crystallography, the oxygen is located at (x, y, z) = (0.306,0,0.25). If this position is approximated to (x, y, z)&(1/3,0,1/4), the anion framework forms an hcp lattice (Fig. 8.1) with a = 0.476 nm and c = 1.299 nm. The Al3+ occupy 2/3 of the octahedral sites but is located at (x, y, z) = (0,0,0.352) instead of (0,0,1/3), thus the cations are shifted by ± 0.025 nm along the c axis from the ideal octahedral sites. The oxygen ion is larger than the aluminium ion (r–/r+&3), therefore the study of the steps on the substrate can be limited to the steps in the oxygen framework, leading to step heights which are multiples of c/6 (d(0006)&0.216 nm). The (0001) Al2O3 surfaces are oxygen terminated [45] and present steps along {1120} and {1010} planes [46]. Two crystallographically equivalent surfaces are connected by a symmetry operation of the space group; along the [0001] direction, A–A or B–B

8.2 Crystallographic Considerations A schematic diagram of the Al2O3 sapphire unit cell, there are 6 oxygen layers in the unit cell, the distances between the various atomic layers change as shown in the figure. The oxygen ions form a pseudohexagonal lattice. The small Al ions occupy the octahedral sites.

Fig. 8.1

surfaces are separated by c/3, 2c/3 and c steps. A step separating two “A” surfaces will be noted for instance (A–A,c/3). Steps of height c/6, c/2 or 5c/6 separate two surfaces related by a glide symmetry operator, such steps are called demisteps, they will be noted for example (A–B,c/6) [47].

8.2.1.2 Silicon Carbide

In contrast to most of the compound semiconductors, silicon carbide (SiC) is a IV-IV alloy which exhibits a large number of polytypes. Like the other compound semiconductor materials, it is tetrahedrally coordinated and its structure can be considered as a network of corner sharing tetrahedra [48]. SiC has a number of advantages over sapphire (Table 8.1): – In the basal plane, its mismatch to GaN is only 3.5% and an AlN buffer layer allows to decrease it to less than 2.5%. – Moreover, its thermal expansion coefficients are also closer to those of GaN. – It is a semiconductor and as such exhibits a good electrical conductivity which may be used for the backside ohmic contacts.

Tab. 8.1 Crystallographic data on wurtzite GaN, AlN and the substrates: sapphire and 6H-SiC

Material

a (nm)

a/aSiC (%)

a/asapph. (%)

c (nm)

c/cSiC (%)

c/csapph. (%)

Polytype

GaN AlN SiC Sapphire

0.3189 0.3112 0.308 0.476

3.54 1.04

16.09 13.29

0.5185 0.4982 1.512 1.2991

2.9 1.15

19.7 15.06

2H

SG

P63mc 6H R3c

383

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

The most used polytype is the 6H, but the 3C is also currently used mainly as a nucleation layer for the growth of cubic GaN on top of silicon. A comprehensive description of the tetrahedrally coordinated structures is very useful for the investigation of the interface defects. The bonds describe a tetrahedron denoted T which possesses one atom species at each corner and the other atom species in its center [48]. The basal plane of this structure is defined by one face of the tetrahedron and the bond perpendicular to this latter defines the c axis. A rotation of 1808 around c produces a twinned variant denoted T' (Fig. 8.2 a). The two variants are also related to each other by a mirror symmetry about a {1100} plane. A tetrahedron can occupy one of the three possible positions in the basal plane and layers of tetrahedra are then denoted T1, T2, T3, T1', T2', T3' (Fig. 8.2 b). The structure of these materials and their different polytypes can be completely described by stacking these six tetrahedra layers. All stacking sequences are not possible and two rules must be respected to keep a corner sharing structure: (i) A tetrahedron T can be followed by another one of the same kind with the following subscript: T1 T2 T3 and inversely for the twinned variant: T3' T2' T1'. (ii) A tetrahedron T1 must be followed by the twinned variant of the preceding subscript: T1T3' and inversely for its twinned variant: T1' T2. For example, the structures of the different polytypes, under the present study, are described by the following sequences: T1 T'3 or T2 T'1 or T3 T'2 for the wurtzite structure, which corresponds to the polytype denoted 2H in the Ramsdel notation, T1 T2 T'1 T'3 for the 4H polytype, T1 T2 T3 T'2 T'1 T'3 for the 6H polytype, T1 T2 T3 or T'3 T'2 T'1 for the 3C polytype.

Representation of the tetrahedrally coordinated materials: a the two possible tetrahedra; b the rules for stacking the tetrahedra.

Fig. 8.2

8.2 Crystallographic Considerations

8.2.2

Epitaxial Layers

GaN crystallizes in the cubic structure (sphalerite) or in the hexagonal structure (wurtzite). The latter is thermodynamically more stable and in conventional growth conditions on (0001) sapphire substrate, GaN is hexagonal (wurtzite: space group P63mc), with the lattice parameters a = 0.319 nm and c = 0.518 nm. The anions (N3–) form an hcp structure in which the cations (Ga3+) occupy half of the tetrahedral sites. The structure of a unit cell of GaN projected along [0001] is depicted schematically in Fig. 8.3. The open symbols represent c sites, which are occupied by nitrogen atoms, the Ga atoms are in the tetrahedral sites b. These latter sites can either be at heights 3/8c above (b1) or below (b2) each N site, depending on the crystal polarity.

Schematic diagram showing the b1 and b2 tetrahedral sites of GaN unit cell. If we supposed that N occupies the c sites, only one family of b sites can be simultaneously occupied by Ga atoms.

Fig. 8.3

8.2.3

Epitaxial Relationships

On top of the (0001) sapphire, the GaN layers have the well-known epitaxial relationship: (0001)substrate//(0001)GaN and [1120]substrate//[0110]GaN. This relation leads to the continuation of the anion compact stacking (O2– in the substrate, N3– in the thin film). The apparent 308 rotation between the two crystals is due to the choice of the crystallographic origin (in the substrate, the origin is related to the Al3+ lattice). At the interface, the cations switch from octahedral (Al3+ in Al2O3) to tetrahedral sites (Ga3+ in GaN). So, an important parameter could be the coordinate polyhedra of the cations that is between an oxygen plane and a nitrogen plane at the interface. There are three polyhedra to consider: each one corresponds to one of the three interstitial sites of the hcp structure (2 tetrahedral sites plus 1 octahedral site).

385

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

Furthermore, the hcp anion stacking does not have the same parameters in both materials. This leads to mismatch in the a and c directions of an hcp structure. In the basal plane, the mismatch is equal to: fa ˆ

asubstrate adeposit ˆ asubstrate

16:09%

p where a*sub. = asub./ 3, so as to respect the 308 rotation. It was shown, after Bragg filtering of HREM images, that this lattice misfit is largely relaxed in the first monolayer of GaN, with a network of regularly spaced 608 dislocations. A residual stress of –2.1% was evaluated near the interface and related to the high density of threading defects present in the epitaxial layers [49]. In the c direction, the difference of lattice parameters leads to an even larger mismatch: fc ˆ

 csubstrate cdeposit ˆ  csubstrate

19:7%

where c*sub. = csub./3. This mismatch may act at the substrate surface steps as the growth takes place at adjacent terraces. In the growth on 6 H-SiC, there is no rotation of the lattice, the misfits are shown in Table 8.1. Bicrystallographic Analysis of Interfacial Defects We now consider the symmetry of dichromatic complexes, i.e., configurations which can be visualized by allowing two crystals relatively rotated to interpenetrate. The configuration created by two lattices rather than two crystals is called dichromatic pattern [50]. We have used for symmetry operations and transformations the notation described in the International Tables for Crystallography. Moreover, let one crystal be designated white (k), and the other black (l). The relative orientation is defined by the operation P = (P, p) which transforms white vectors into corresponding black ones (expressed in the white coordinate frame). P may either be a rotation, thereby relating crystals of the same polarity, or a rotoinversion relating crystals of opposite polarity. The translation p represents the shift of the black crystal origin following the operation P. This formalism enables the symmetry of dichromatic complexes to be established for any relative orientation and position of the k and l crystals. Coincident symmetry operations in such complexes arise when black and white crystal symmetry operations coincide and correspond to the intersection of the crystal spacegroups, i.e., U…k† \ U…l†. Explicitly, the coincident operations in the complex, W, are the solutions to the following identity [51]: 8.2.4

W…k†j ˆ PW…l†i P

1

ˆ W…c†k

…1†

This set will include an infinite number of translations parallel to [0001] for all rotations, and a 3-dimensional set also known as the coincident site-lattices (CSLs)

8.2 Crystallographic Considerations

for special misorientations, independent of any translation p. Other coincident operations arising for any value of rotation about [0001] may be broken by translation p. In addition, colour reversing or anti-operations, which relate black features to white and vice versa will also arise. These can be identified by inspection of the multiplicity of equivalent description of P, i.e. P W(k)i. Those operations in this set which have the form of symmetry operations are antioperations in the spacegroup of the complex, W'(c)k, i.e. PW…k†j ˆ W 0 …c†k

…2†

The space group of a dichromatic complex is then given by the extension of the coincident translation groups by the set W…c†k [ W 00 …c†k [51]. In this work, grain boundaries with rotations close to the following special values have been observed (13.178, 21.798, 17.908) inside MBE GaN layers, the corresponding coincident site densities are R = 19, 7, 31, respectively. The matrices, P, corresponding to these rotations have been calculated elsewhere [52]. We note that the CSLs resulting from rotations h and h ± 608 are identical because the lattices of the k and l crystals exhibit the symmorphic symmetry P6/mmm which includes a six-fold rotation axis parallel to [0001]. For such rotations about [0001], there are six solutions to expression (1) as listed in Table 8.2 for the case where p = 0; these solutions are independent of h. Similarly, six anti-operations are solutions to expression (2) independent of h, as listed in Table 8.2. Thus, the space groups of dichromatic complexes for rotations about [0001] are always p63m'c' except when CSLs arise and the symmetry becomes P63m'c'. An illustration of the R = 7 dichromatic complex is given in Fig. 8.4. We note that complementary complexes, i.e. for rotations h and h ± 608, could be allocated the spacegroups P63m'c' (Fig. 8.4 a) and P63c'm' (Fig. 8.4 b) by appropriate choice of unit cells. In other words, the two complexes differ only in the disposition of their c' and m' planes. We also note that complementary complexes arise for the same rotation h, but with p = 0 in one case and p = 1/2 c in the other. Similarly, they also arise for roto and rotoinversion operations, h and h. Finally we note that a special case arises for the 608 rotoinversion operation; in this instance the spacegroup becomes P6'/m'mm with R = 1, i.e. inversion domains rotated relatively by 608 around [0001]. Interfacial defects arise when the black and white crystals surfaces are not complementary and exhibit incompatible steps [53]. Following the topological theory of line defects in interfaces [51], the Burgers vectors bij of the admissible interfacial dislocations are given by bij ˆ t…k†j

Pt…l†i

where t(k)j and t(l)i represent the jth and ith translations in the k and l crystals, respectively, and P is a matrix which re-expresses t(l)i in the k coordinate frame. Thus, bij is the difference between the two translations expressed in the same coordinate frame. Moreover, the vectors bij are vectors joining white to black sites in the dichro-

387

388

8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms Tab. 8.2 The twelve symmetry operations of the dichromatic complex P63m'c' representing two GaN crystals rotated about [0001]

Coincident operations Numbering 1 2 3 4 5 6

Symmetry operation 1 3+ 3– 2 6– 6+

Location

Glide or screw component

0, 0, 0, 0, 0,

0,0,1/2 0,0,1/2 0,0,1/2

Antioperations numbering 1 2 3 4 5 6

Symmetry operation

Location

Glide or screw component

m m m c c c

x, –x, z x, 2x, z 2x, x, z x, x, z x, 0, z 0, y, z

0,0,1/2 0,0,1/2 0,0,1/2

0, 0, 0, 0, 0,

z z z z z

matic pattern. The cores of such interfacial defects are associated with steps. The heights of the free surface steps are given by h(k)j = nk t(k)j and h(l)i = P–1 nk t(l)i = nl t(l)i, where n is the unit vector normal to the interface, it is orientated towards the k crystal. These heights are quantified in units of d(hkil), the interplanar spacing of the lattice planes parallel to the interface in the k and l crystals. The interfacial defects observed using HREM can be characterized by circuit mapping as proposed by Pond [54]. In this procedure, a circuit is constructed around an interfacial defect on the micrograph, with segments in the k and l crystals connected by displacements p1 and p2 across the interface. These circuit segments are designated by C(k) and C(l) and the complete circuit C(k, l), as expressed in the k coordinate frame, is given by C…k; l† ˆ …I; p2 † 1 PC…l†P 1 …I; p1 †C…k† In the simplest cases, the translations p1 and p2 are of opposite signs, so their contributions to the total circuit cancel. When the circuit is mapped into a reference space, any closure failure is equal to the total defect content. Using the RH/ FS convention, the defect is given by C(k, l)–1, where C(k, l) represents the irreducible expression of the closure failure. As C(k) = (I, c(k)), C(l) = (I, c(l)) and P = (P, p), we obtain C…k; l†

1

ˆ …I; c…k††…P; p†…I; c…l††…P 1 ; p† ˆ …I; c…k†

Pc…l†† for p ˆ 0 :

Thus, bij = –C(k, l) = –c(k)–P c(l). Moreover, the step heights can be determined experimentally from the above circuit and h(k)j = –nk c(k)/d(hkil)j whereas h(l)i =P–1

8.2 Crystallographic Considerations

Dichromatic complexes of R 7, open and filled circles represent k and l, respec-

Fig. 8.4

tively. The space groups of the unit cell are a P63m'c' (h), b P63c'm' (608–h).

nk c(l)/d(hkil)i = nl c(l)/d(hkil)i. In the following, we use the notation proposed by Braisaz et al. [55] and by Serra and Bacon [56] to write Burgers vectors as bp/q where p and q are defined as h(k)j = pd(hkil)j and h(l)i = qd(hkil)i. In theory, a multiplicity of step configurations can arise for a defect with b because translation vectors of the dichromatic pattern can be added to both t(k)j and t(l)i without modifying b. Therefore, in order to describe unambiguously the observed defect, it is necessary to determine the associated values of t(k)j and t(l)i characterizing the step. 8.2.5

Growth on SiC

In order to describe this growth, particularly along the c axis, we may concentrate on the 2H and 6H polytypes that correspond to AlN and a-SiC structures respectively. A projection of these structures (Fig. 8.5) along a h1120i direction parallel to the edge of the basis triangle of a tetrahedron results in triangles where the Si (or Al) atom is displaced to the right of the center for the direct variant and to the left for the twinned one. These two structures have different unit cells within the same space group P63mc. Unit cells are indicated by dashed lines in Fig. 8.5. The basic atomic pattern is different for the two structures. It corresponds, in the 2H polytype (Fig. 8.5 a), to one molecule of AlN per tetrahedra. For the 6H-SiC polytype, this pattern is more complex and consists of three molecules of SiC corresponding to the stacking of three tetrahedra in a cubic sequence: T1 T2 T3 (Fig. 8.5 b).

389

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

Fig. 8.5

Tetrahedral representation of the a 2H; b 6H polytypes of SiC.

8.2.5.1 Stacking Faults in 2H Polytype

The 2H polytype is the simplest one from which all the other polytypes can be described by introduction of periodic Stacking Faults (SFs). The tetrahedral notation is used in this paragraph to describe the structure of the three types of SFs (Fig. 8.6) existing in the wurtzite structure [57]. (i) Intrinsic SF denoted I1: the following stacking sequence is T1 T03 T1 T2 T01 T2 and the other possibility, I01 : T03 T1 T03 T02 T3 T02 , is related to I1 by a rotation of 1808 around the c axis (the faulted sequence is underlined). (ii) Intrinsic SF denoted I2: obtained by the dissociation of a 1/3 h1120i dislocation into two Shockley partials. Its sequence is T1 T03 T1 T2 T3 T02 T3 and for the twinned variant I02 : T03 T1 T03 T01 T02 T3 T02 . (iii)Extrinsic SF denoted E: this defect corresponds to the insertion of a complete sequence of the sphalerite structure, e.g.: T1 T2 T3 or T01 T02 T03 in T1 T03 ^ T1 T03 leading to T1 T03 T1 T2 T3 T1 T03 , or T1 T03 T01 T02 T03 T1 T03 which is the twinned variant. This defect is bounded by a Frank partial dislocation (b = 1/2 [0001]). These three different sequences constitute the possible stacking faults in the wurtzite structure.

8.2.5.2 Defects at Interface Steps

The (0001) or (111) interfaces in tetrahedrally bonded materials make particular cases for which defects due to interface steps can be predicted by a simple procedure described in the following. Since this section aims at predicting the defects

8.2 Crystallographic Considerations

Fig. 8.6 Atomic models of the basal stacking faults projected along [1120]. (*) represent nitrogen, (l) gallium, (–) in-plane and (=) out-of-plane bonds.

introduced by steps at the interface between two different polytypes, the lattice misfit and chemical nature of the atoms need not be taken into account. If we consider an interface step as shown in Fig. 8.7, it separates two different surface terminations 1 and 2 of the substrate. Two parameters are needed to characterize such steps: – the height of the step, – the position of the surface termination in the stacking sequence of the substrate. In order to take into account all the possible configurations, each position of surface termination is combined with the possible step height. The areas marked A in Fig. 8.7, in polytype I, can be always considered as a faulted stacking sequence of the polytype II of the deposited material. In this way, the two crystals grown on the surface terminations 1 and 2 can be related to each other by a displacement vector d. If the displacement d relating the two surface terminations does not correspond to a symmetry operation of the structure of the deposited material, a defect will be generated in the deposited layer, with a fault vector corresponding to

391

392

8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms Interface step and displacement vector at a (0001) SiC surface, the area marked A under terrace 1 faces a purely wurtzite portion on terrace 2, it is considered as a faulted wurtzite sequence.

Fig. 8.7

Wurtzite and sphalerite positions for the growth of GaN on (0001) SiC.

Fig. 8.8

the displacement d. The d vectors can be reduced to the fault vector of one of the possible SFs of the polytype II. Moreover, as shown in Fig. 8.8, the epitaxy of the polytype II can start at the wurtzite or sphalerite positions on the substrate surface and this position can change on both sides of the step. Taking both cases into account leads to four possibilities: two wurtzite interfaces, two sphalerite interfaces and two cases with one sphalerite and one wurtzite interface. The first two configurations do not modify d whereas the two latter ones add a twin component. Considering the area A as a faulted sequence of the 2H polytype, a combination of SFs of the 2H polytype is identified. The sum of their fault vectors can always be reduced to that of one of the three possible SFs: I1, I2 and E of the hexagonal structure (I1: 1/6 h2023i, I2: 1/3 h1010i or E: 1/2 h0001i). Therefore, the dislocation character of all steps can always be identified as one of these three vectors. If we consider that all the possible step configurations arise with the same probability, one can estimate the probability of the different defects to occur. The results when a 2H polytype is deposited on the 6H, 4H and 3C polytypes are summarized in Table 8.3. They are given in case of – wurtzite interfaces, – general interfaces (sphalerite and/or wurtzite).

8.2 Crystallographic Considerations Tab. 8.3 Possible displacement vectors at steps on (0001) SiC polytypes

Interface

2H/6H

2H/4H

2H/3C

Defect character

Wurtzite interfaces (%)

General configuration (%)

I1 I2 E –

45 22 – 33

42 25 8 25

I1 I2 E –

50 – – 50

47 19 3 31

I1 I2 E –

33 33 17 17

33 33 17 17

The 2H/6H interface. The results show that almost one step in two is of I1 type and 25% of the steps do not generate defects. The E type steps occur only when the sphalerite interface is taken into account; this probability is lower than 10%. The 2H/4H interface. In this case, only height steps ranging from 1 to 4 tetrahedra must be considered. For wurtzite interfaces, only I1 type steps occur and one step in two does not exhibit a dislocation character. The I2 and E type steps occur only when sphalerite interfaces are investigated. The 2H/3C interface. Step height of 6 tetrahedra is enough to attain coincidence between the two lattices. In this case, in contrast to the 4H or 6H substrates, the position of the step in the stacking sequence of the substrate is not critical for the defect type and the only height that does not lead to a dislocation character for the step is of 6 tetrahedra. In summary, although a substrate may present a good lattice match and same symmetry with the deposited material, numerous defects due to the structure difference can be generated at the interface. 8.2.6

Growth on Sapphire 8.2.6.1 Geometrical Modeling of the First Monolayers Growth

By studying the stacking of the anion framework as well as the cation location, while respecting the epitaxial relationship, it is possible to describe all the operators that link two crystallites grown on two adjacent areas with or without a step. First, all the stackings of GaN that lead to the continuation of the anion hcp structure on a stepless surface of sapphire are described. Afterwards, a translation induced by the step is added to the operator. This operator, denoted Wce (for crystal exchange), is compared to the observed defect operators. The diagram of this procedure is shown in Fig. 8.9 and is explained in the following.

393

394

8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms Exchange operators at the sapphire surface for the growth of wurtzite GaN, see text and Tables 8.4 to 8.8 for details.

Fig. 8.9

We use the A, B and C notation to locate the atom projections onto the basal plane; on a “A” terminated substrate surface (oxygen plane), there are two possibilities to stack the first nitrogen plane, plus two other possibilities for the second plane: ABA/BAB . . ., ABA/BCB . . ., ABA/CBC . . . and ABA/CAC . . . . These four nitrogen stackings are related by a translation noted Rstack, which is one of the three stacking fault vectors of the hcp structure (RI1, RI2, and RE). For each nitrogen stacking, there are two polarities (up and down) that differ by the occupation of the two tetrahedral sites by the cation Ga3+, and which are related by the mirror operator. Thus, the eight GaN stackings that respect the epitaxial relationship are related by an operator Wce = Rstack or Wce = Rstack + m. These stackings differ by the polyhedron defined by the N3– and O2– species in which the first Ga3+ is inserted at the interface. The polyhedra to take into account are: upward tetrahedron (3 O2––Metal3+–N3–), downward tetrahedron (O2––Metal3+–3 N3–) and octahedron (3 O2––Metal3+–3 N3–), which leads to down polarity, because the fourfold coordination of the N3– is supposed to impose the polarity of all the film. We do not take into account the case where the substrate is Al3+–terminated, because such a cation plane plays the same role as the first Ga3+ layer, except that its projection is located on 2/3 of the “C” positions. Thus a step between Al3+ and O2- on the substrate may change the interface polyhedra but is not supposed to introduce other situations than those described here.

8.2 Crystallographic Considerations

The eight configurations, with their operators (Rstack: translation and mirror) which relate them are shown in Fig. 8.10. The vectors Rstack that link two GaN crystallites grown on the same terrace of the substrate as a function of the interface polyhedra with or without the mirror operation are given in Table 8.4. It shows that if the interface is exclusively made of downward tetrahedra or octahedra, the vector Rstack is exclusively RI1 or RE, respectively. The combination of

Fig. 8.10 The 8 different possible stackings of GaN on (0001) sapphire, the starting positions are 4 upward tetrahedra, 2 octahedra, and 2 downward tetrahedra (one is drawn). The operator relating one configuration to the other corresponds either to a mirror or to one of the displacement vectors of the stacking faults in the hexagonal system.

395

8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms Tab. 8.4 Displacement vectors linking two GaN crystallites growing on a single terrace

Rstack

GaN 1 on A plane of substrate Tetrahedron down

Octahedron (down)

Tetrahedron up

RE

50% 50% 0% 0%

0% 50% 50% 0%

25% 50% 25% 0%

Octahedron (down)

0 RI1 RI2 RE

0% 50% 50% 0%

50% 0% 0% 50%

25% 25% 25% 25%

Tetrahedron up

0 RI1 RI2 RE

25% 50% 25% 0%

25% 25% 25% 25%

25% 37.5% 25% 12.5%

Tetrahedron down GaN 2 on A plane of substrate

396

0 RI1 RI2

downward tetrahedra and octahedra leads to the formation of RI1 and RI2 vectors in equal proportions. If the growth starts with upward tetrahedra, we obtain RI1, RI2, and RE vectors in proportion 3, 2 and 1, respectively. The interface can also contain up and down polyhedra. For instance, the occurrence of up and down tetrahedra on the same terrace of the substrate leads to the formation of Rstack = RI1 and RI2 (in 2 : 1 proportions) fault vectors, plus the mirror m. In order to deal with the demi-steps, for instance (A–B, c/6), it is necessary to examine the hypothetic case where the first area is “A” terminated and the second one is “B” terminated, but onto the same terrace. Between two crystallites, for a given polyhedron, a translation RI1 or RE has to be added to Rstack, using the relations: RI1 + RE = RI2, RI2 + RE = RI1 and RE + RE = 0. The Rstack as a function of the interface polyhedra for an A–B stepless surface is given in Table 8.5. Now, considering a step between the two terraces on which GaN crystallites are grown, one obtains a translation Tstep along [0001] between the two crystallites. This translation is calculated modulo RE = 1/2 [0001] in GaN as a residual translation Tres. In order to express Tres as a fraction of cGaN, we make the approximation cAl2O3&5/2 cGaN. Thus a step of 2c on the substrate is equivalent to 5c in GaN, and so does not introduce defects due to the mismatch along the c axis. For example, the step (A–B, c/6) induces a translation of 5/12 cGaN, which is equivalent to Tstep = RE + Tres, where Tres = –1/12 [0001]. Within the above approximation, there are four possible absolute values of Tres, which have to be considered as expressed in cGaN (Table 8.6): |Tres|&0 for the steps of height h = n cAl2O3, where n is an integer c |Tres|& , for the demi-steps (A–B, c/6), (A–B, 5c/6), (A–B, 7c/6) and (A–B, 11c/6). 12

8.2 Crystallographic Considerations

c |Tres|& , for the steps (A–A, c/3), (A–A, 2c/3), (A–A, 4c/3) and (A–A, 5c/3). 6 c |Tres|& , for the demi-steps (A–B, c/2) and (A–B, 3c/2) 4 It can be noticed that the operator relating two GaN crystallites grown on two areas, located or not on the same terrace, may contain: a mirror, a translation R (due to the several possibilities generated by the epitaxial relationship and to the growth on A and B planes of the substrate) and a residual translation Tres (due to the vertical mismatch). The operator Wce is given by the following expression: Wce = m + R + Tres.

Tab. 8.5 Displacement vector versus interface polyhedron at the GaN surface with steps

GaN «1» on A plane of substrate

GaN «2» on B plane of substrate

Rstack

Tetrahedron down

Octahedron (down)

Tetrahedron up

Tetrahedron down

0 RI1 RI2 RE

0% 25% 50% 25%

25% 25% 25% 25%

12.5% 25% 37.5% 25%

Octahedron (down)

0 RI1 RI2 RE

25% 25% 25% 25%

0% 50% 50% 0%

12.5% 37.5% 37.5% 12.5%

Tetrahedron up

0 RI1 RI2 RE

12.5% 25% 37.5% 25%

12.5% 37.5% 37.5% 12.5%

12.5% 31.25% 25% 18.75%

Tab. 8.6 Residual translation at (0001) surface steps

Step notation (in cAl2O3 unit)

Height (nm)

Step in cGaN unit

Tstep

Absolute value of Tres (in cGaN unit)

(A–B, c/6) (A–A, c/3) (A–B, c/2) (A–A, 2c/3) (A–B, 5c/6) (A–A, c) (A–B, c + c/6) (A–A, c + c/3) (A–B, c + c/2) (A–A, c + 2c/3) (A–B, c + 5c/6) (A–A, 2 c)

0.216 0.433 0.649 0.866 1.082 1.299 1.515 1.732 1.948 2.165 2.381 2.598

5/12 5/6 5/4 5/3 25/12 5/2 35/12 10/3 15/4 25/6 55/12 5

RE–1/12 [0001] –1/6 [0001] 1/4 [0001] RE + 1/6 [0001] 1/12 [0001] RE –1/12 [0001] RE–1/6 [0001] –1/4 [0001] 1/6 [0001] RE + 1/12 [0001] 0

1/12 1/6 1/4 1/6 1/12 0 1/12 1/6 1/4 1/6 1/12 0

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

8.2.6.2 Planar Defects

In order to investigate the formation of a planar defect, one can define it using an operator relating the two crystals on each side. In this work, we study translation domain boundaries (TDBs) and inversion domain boundaries (IDBs). As pointed out by Rouviere et al. [58], TDBs are planar defects where the two crystals across the boundary are related by an operator WTDB which contains exclusively a translation. These defects have been identified in basal and prismatic planes by Vermaut et al. [21]. The fault vectors were found to be RI1 = 1/6 [0223], RI2 = 1/3 [0110] and RE = 1/2 [0001] (basal stacking faults) and RA = 1/6 [0223] and RD = 1/2 [0111], which correspond to models proposed by Blank et al. [23] and Drum [24]. The inversion is the result of the crystal noncentrosymmetry. If we consider the hcp sublattice of anions, its spacegroup (P63/mmc) is centrosymmetric because the 63 axis is perpendicular to the (0001) mirror. This structure contains two groups of tetrahedral sites (b1 and b2) which are related by the (0001) mirror. The wurtzite structure is created by adding a cation in one tetrahedral site group of the anion framework, removing the mirror from the spacegroup which becomes P63mc. So, the loss of the mirror perpendicular to the 63 axis brings about two crystallographic variants related by this broken operator. Thus, a mirror located on the (0001) anion plane of the wurtzite can be used to create the inversion which changes the polarity, given by the cation-anion bond parallel to the c axis. In order to describe an IDB structure, a translation R may be needed in addition to the mirror. Thus, the operator of an IDB can be written: WIDB = m + R. Several models of inversion domain boundaries have been described and many of them were found in the basal and prismatic planes of wurtzite materials. In the basal plane, Austerman and Gehman [27] proposed a model in which the anion sublattice stays undeviated whereas the cations switch from b1 to b2 across the interface. It means that the two crystals are related by the mirror lying in the basal plane of the anion sublattice. The operator is noted: WAust = m. Kim and Goo [32] studied the basal IDBs in ZnO. They showed that the oxygen sublattice is not continuous but displaced by the vector R = 1/2 [1010]. So, the operator that describes this IDB is WKG = m + 1/2 [1010]. In the {1010} planes, the Austerman model operator is still WAust = m which leads to the continuation of the anion sublattice. Another model can be built, where the cation stacking stays undeviated across the boundary, the mirror operation lies in the cation basal plane, or a 1/4 [0001] translation is added after applying the mirror located at the anion basal plane: WB = m + 1/4 [0001]. In the model proposed by Holt [28], Ga and N atoms are exchanged across the interface. Using the mirror to create the inversion, a translation of 1/2 [0001] –1/8 [0001] must be added to generate this structure, its operator is WHolt = m + 1/2 [0001] –1/8 [0001]. This configuration leads to Ga–Ga and N–N bonds in the boundary plane. Another model, built by translating the crystal by –1/8 [0001] after the mirror operation, denoted “V” or IDB*, does not contain wrong bonds and may be energetically more favorable than the Holt model [9]. The possible IDB configurations are given in Table 8.7 along with the associated symmetry operators, the reference structure is the Austerman configuration, which is described by a mirror operation.

8.2 Crystallographic Considerations Tab. 8.7 Possible IDBs configurations and the associated symmetry operations

Models

Operators WIDB

Austerman B V or IDB* Holt IR1 IR2 IR3 IR4

WAust. = m WB = m + 1/4 [0001] WV = m–1/8 [0001] WHolt = m–1/8 [0001] + 1/2 [0001] WIR1 = m–1/8 [0001] + 1/2 [0 1 1 0] WIR2 = m–1/8 [0001] + 1/3 [0 1 1 0] WIR3 = m–1/8 [0001] + 1/2 [0 1 11] WIR4 = m–1/8 [0001] + 1/6 [0223]

In our samples, the inversion domain boundaries structure has been identified as Holt and V models [43, 59]. Such planar defects may form when adjacent islands coalesce, this may take place on stepless surface, or at steps.

8.2.6.3 Stepless Surface

On a stepless surface, the polarity of the layers may depend on the interface polyhedra whose choice is probably determined by energetical factors brought about for example by the substrate surface state, the deposition conditions, etc. . . . . At the growth onset, for a nitrogen polarity matrix, down polyhedra (octahedra and down tetrahedra) are favored, whereas, for a gallium polarity matrix, the favored polyhedra are up tetrahedra. In the case where only one polarity is found, without inversion domains, the operator that relates two crystallites grown on a stepless surface can be written: Wce = Rstack. At their coalescence, a translation domain boundary characterized by WTDB = Wce = Rstack forms. This is in agreement with observations of the numerous basal and prismatic stacking faults in GaN layers. If up and down polyhedra are found to initiate the growth, this would lead to the formation of inversion domain boundaries characterized by the Austerman model (Wce = m) which may also contain a translation (Wce = Rstack + m). It follows that on a stepless surface, TDBs may form, and IDBs of Austerman type can appear in prismatic planes in the case where up and down polyhedra coexist.

8.2.6.4 Steps

Let consider that the interface polyhedra are either up or down; the operator that links two crystallites grown on adjacent terraces can be written Wce = R + Tres. The residual translation Tres along [0001], due to the lattice mismatch, may be elastically relaxed or minimized by the formation of a planar defect. This defect will be characterized by an operator which is the closest to Wce. For each value of Tres, Wce is compared to the known WTDB and WIDB operators.

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

In the first case, Tres = 0, the defects are the same as a stepless terrace (TDBs or Austerman IDBs). If we suppose that polyhedra are either up or either down, such steps are in favor of TDBs formation, for instance prismatic stacking faults. For the second case (Tres&± 1/12 [0001]), no TDBs are found to compensate the Tres, but as shown above, most of the prismatic inversion domains are characterized by the operator WIDB = R–1/8 [0001] + m. Thus, the introduction of a mirror m in one 0 crystallite changes the operator Wce in Wce = R + Tres + m. It then becomes possible to divide by two the residual translation by introducing a mirror in Wce. For instance, for the (A–B, c/6) step, if Wce = Tstep = RE–1/12 [0001], the introduction of a mir0 ror in one crystallite leads to: Wce = RE–1/12 [0001] + m = RE–1/8 [0001] + m + 1/24 [0001] = WHolt + 1/24 [0001]. Therefore, such a step may favor the formation of an inversion domain boundary, because 1/24 [0001] is small (0.02 nm) and may be elastically relaxed. Schematically, this may imply the application of a mirror in one crystallite leading to a basal Austerman IDB; there appears then a prismatic IDB, which contains a 1/8 [0001] translation and allows to minimize Tres. In the same way, steps that create residual translations close to ± 1/6 [0001] lead to the same conclusions as the previous case. For example the (A–A, c/3) step, if Wce = Tstep = –1/6 [0001], the 0 introduction of a mirror in one crystallite leads to: Wce = –1/6 [0001] + m = –1/8 [0001] + m–1/24 [0001] = WIDB*–1/24 [0001].

Tab. 8.8 Exchange operations for the possible defects that form at (0001) surface steps due

residual translation and interface polyhedra on growth of GaN Tetrahedra down

Octahedra

Tetrahedra up

(A–B, c/6) (A–B, c + 5c/6)

0 = 25%(WIR2 + e) Wce +50%(WIR4 + e) +25%(WV + e)

0 Wce = 50%(WIR2 + e) +50%(WIR4 + e)

0 Wce = 12.5%(WHolt + e) + 31.25%(WIR2 + e) + 25%(WIR4 + e) + 18.75%(WV + e)

(A–A, c/3) (A–A, c + 2c/3)

0 Wce = 50%(WIR4 + e) +50%(WV + e)

0 = 50%(WHolt + e) Wce +50%(WV + e)

0 = 12.5%(WHolt + e) Wce + 25%(WIR2 + e) + 37.5%(WIR4 + e) + 25%(WV + e)

(A–B, c/2) (A–B, c + c/2)

0 Wce = 50%(WB + RI1) + 50%(WB + RI2) + 25%(WB + RE)

0 Wce = 50%(WB + RI1) +50%(WB + RI2)

0 Wce = 12.5%WB + 31.25%(WB + RI1) + 25%(WB + RI2) + 18.75%(WB + RE)

(A–A, 2c/3) (A–A, c + c/3)

0 Wce = 50%(WHolt + e) + 50%(WIR2 + e)

0 Wce = 50%(WHolt + e) +50%(WV + e)

0 Wce = 25%(WHolt + e) + 37.5%(WIR2 + e) + 25%(WIR4 + e) + 12.5%(WV + e)

(A–B, 5c/6) (A–B, c + c/6)

0 Wce = 25%(WHolt + e) + 50%(WIR2 + e) + 25%(WIR4 + e)

0 Wce = 50%(WIR2 + e) +50%(WIR4 + e)

0 Wce = 18.75%(WHolt + e) + 25%(WIR2 + e) + 31.25%(WIR4 + e) + 12.5%(WV + e)

8.3 Dislocations

In the case of demi-steps which create a residual translation of ± 1/4 [0001], the 0 operator Wce is Wce = Tstep = 1/4 [0001], the addition of the mirror gives Wce = m +1/4 [0001] = WB. It means that such steps could lead to the formation of inversion domain boundary in which the cation sublattice would stay undeviated. In the above examples, Wce is taken as Tstep, but the translation Rstack has also to be accounted for in order to compare Wce to the WIDB. It is possible to include 0 in Wce the proportion of Rstack as a function of the interface polyhedra (Table 8.8). 0 = Wce ± m, can When adding a mirror in the basal anion plane of a crystallite, Wce be written as a weighed sum of WIDB. For instance, if the interface polyhedra are 0 exclusively down tetrahedra, the (A–B, c/6) step leads to: Wce = Wce + m = Tstep +m + Rstack = RE–1/12 [0001] + m + Rstack = WHolt + 1/24 [0001] + Rstack. According to Table 8.8, Rstack can be written as: Rstack = 25% RI1 + 50% RI2 + 25% RE. Thus, the ex0 change operation Wce is: 0 ˆ 25% …WIR2 ‡ e† ‡ 50% …WIR4 ‡ e† ‡ 25% …WV ‡ e†; where e ˆ 1=24 ‰0001Š : Wce

All the steps that lead to a residual translation equal to c/12, c/6, and c/4 have been studied in the same way, by considering the three possible interface polyhedra, Table 8.8 summarizes the results. In conclusion, the shift along [0001] induced by the step may be minimized by the introduction of a mirror on one terrace of the step, at the coalescence of the adjacent crystallites. This leads to the formation of a basal and a prismatic IDB that contains a 1/8 [0001] translation.

8.3

Dislocations 8.3.1

Misfit Dislocations

The interfacial area of GaN/sapphire can exhibit zones without extended defects, but even then, it is not easy to locate the misfit dislocations at the interface on a high-resolution image. In order to visualize them one has to filter the images. A Fourier filtering shows that they are regularly spaced 608 dislocations. And, if we take the core to be located at the interface, the measured average distance of 2 nm shows that they define a stepless relaxed area (Fig. 8.11). 8.3.2

Threading Dislocations

Conventional TEM has shown that these dislocations originate at the interface and the large majority propagate to the sample surface. Their line is roughly parallel to the c growth axis and the large majority are edge type. It has been shown that c and a + c dislocations tend to bend and annihilate; the density of those that

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

Fig. 8.11

Misfit dislocations at the sapphire/GaN interface.

Fig. 8.12

5/7-atom ring threading dislocation.

reach the layer surface is only a few percent of that near the interface [58]. Calculations have shown that the low optical activity of the edge threading dislocations may be explained by the formation of dimer bonds inside an 8-atom ring core [15]. The most accurate observations published so far have shown that this is the case in MOCVD-grown samples [16]. However, our HREM observations suggest that this may not be the case, at least in MBE-grown GaN layers. In addition to the above atomic configuration, we have noticed typical contrast (Fig. 8.12) which is not explained by an 8-atom core. And from our observations, this configuration has more or less an equal frequency with the 8-atom ring core. Image simulations show that this core is compatible with a 5/7-atom ring configuration [60].

8.3 Dislocations

8.3.3

Nanopipes

Such defects are empty or filled holes that exhibit a dislocation character, they mostly have a regular shape. They can extend up to a few tens of nanometers and are usually limited by {1010} planes. They have been called nanopipes in analogy to SiC in which such features can measure more than 10 lm and are called macropipes. From our experience they can be classified into two classes, those which have an edge component and those which are pure screw dislocations. As shown in Fig. 8.13, as large as 2a edge component may be exhibited by such defects. In our specimens, it was noticed that the former class of nanopipes are confined inside the first 200 nm of the epitaxial layer [61]; they contain amorphous material in layers grown on 6 H-SiC, whereas they are empty on top of sapphire [38]. Other authors have shown that the pure screw nanopipes cross the entire epitaxial layer [7]. They may either keep the same section or close and open up a few times on their way to the surface.

Fig. 8.13 A nanopipe with a large edge component (2a).

8.3.4

Grain Boundaries

Grain boundary structures can often be described conveniently in terms of an array of line-defects superimposed on some singular configuration [62]. The function of the defect array is to accommodate small angular deviations from the special misorientation. Although there is no simple correlation between geometric parameters and interfacial free energy, considerable evidence has been found showing that two-dimensionally periodic boundaries are sometimes favorable. There is also some evidence that other one-dimensionally periodic structures are singular,

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

for example certain boundaries in ZnO [63]. In the present work it is helpful to identify misorientations corresponding to potentially singular values. Since the GaN films studied here grow with their basal plane parallel to the Al2O3 substrate, the most common type of misorientation encountered is relative rotation of one crystal with respect to an adjacent one about their common [0001] axis. Thus, we shall concentrate on the nature of singular configurations that can arise from such misorientations. This can be done using the method developed by Pond and Vlachavas, which identifies the symmetry of dichromatic patterns and complexes [50]. The following discussion is about grain boundaries with rotations close to the following special values (13.178, 21.798, 17.908), the corresponding coincident site densities are R = 7, 19, 31, respectively.

8.3.4.1 The R = 19 Boundary

Conventional TEM analysis shows that such grains have a regular shape with four straight boundaries linked together by angles of 608 or 1208, their size is about 120 ´ 150 nm2. The value of the rotation angle is very close to that of R = 19 (h = 13.178) in the CSL notation. The corresponding dichromatic pattern is shown in Fig. 8.14. The two lattices are rotated around their common 6-axis. For this di-

Fig. 8.14 Dichromatic pattern of R = 19, the CSL unit cell has been drawn as well as the smallest translation vector.

8.3 Dislocations

chromatic pattern, a CSL unit cell has been constructed and their basis vectors are 1/3 [7 1 8 0], 1/3 [7 1 8 0] and [0001] expressed in the k frame. A part of the boundary is shown in Fig. 8.15. By comparison with the dichromatic pattern, the interface plane was found to be along a side of the CSL unit cell. In Fig. 8.15 a, the SXF circuit was drawn with c(k) = SX = –6~ a1 + 9~ a3 = 1/3 [21 3 24 0]k and c(l) = XF = 9~ a1 –6~ a3 = 1/3 [24 3 21 0]l, corresponding to three periods of the CSL. The normal to the interface was determined by making the cross product of c(k) by [0001] and [0001] by c(l) leading to nk = [3 5 2 0]k and nl = [2 5 3 0]l, respectively. So, for these three periods of the interface, the interface plane is along (3 5 2 0)k/(2 5 3 0)l and it corresponds to a side of the CSL unit cell of R = 19. If the circuit SVF corresponding to one period (i.e. c(k) = SV = 1/3 [7 1 8 0]k and c(l) = VF = 1/3 [8 1 7 0]l) is reported in the k crystal, the closure failure FS is equal to 1/3 [1 2 1 0]. Thus, the primary dislocation for one period corresponds to one crystal dislocation b =~ a2 . If a circuit is mapped into the dichromatic pattern rather than into the lattice of a single crystal, secondary dislocations can be determined. In the previous case, this leads to c(k, l) = c(k) + P19 c(l) = 0, where P19 can be found in Potin et al. [52]. Therefore, in this part, the interface appears to be completely periodic without any additional defect. However, such defects have been detected in this boundary. For example, the area designated by YSZ was studied and c(k) and c(l) were found to be equal to c(k) = YS = 1/3 [8 2 10 0]k and c(l) = SZ = 1/3 [9 0 9 0]l = [3 0 3 0]l. After calculations, we obtained: c(k, l) = c(k) + P19 c(l) = 1/57 [8 7 1 0]k. By definition, the Burgers vector of this defect is the opposite of c(k, l) and is equal to 1/57 [8 7 1 0]k. This vector corresponds to an interfacial edge dislocation with the smallest magnitude and its angle with the interface plane is equal to 608. The step height was determined to be h(k)j = –nk c(k)/d(3 5 2 0) = 2 and h(l)i = nl c(l) = 3/d(2 5 3 0). For Burgers vector bij = 1/57 [8 7 1 0]k, the associated smallest translation vectors are t(k) = 1/3 [11 2 0]k and t(l) = 1/3 [11 2 0]l. These translation vectors are consistent with previous step heights as h(k) = nk t(k) = 2, h(l) = nl t(l) = 3 and t(k) + P19 t(l) = 1/57 [8 7 1 0]k. Moreover, these values are consistent with the experimental image. Six similar additional defects have been found along this interface boundary, regularly spaced of about eight periods of the CSL. The corresponding misorientation was calculated and found equal to h = 2 arcsin (b/d) = 0.198. This interface plane is symmetric, periodic with a period characterized by the presence of one primary dislocation and separated regularly by secondary dislocation corresponding to Burgers vectors b3/2 at 60 degrees of the interface. In order to reconstruct the core of the primary dislocations, we have used some configurations which had been generated for the study of pure edge isolated dislocations as discussed above. For the R = 19 studied boundary, a careful observation shows that different contrasts are exhibited by the primary dislocations. For example, as shown in Fig. 8.15 a, between V and S, the core of the dislocation exhibits an 8-atom ring whereas between S and Y, it is a 5/7 one. Similarly, the whole boundary has been reconstructed and it appears that it is made of eight or five/seven atom rings as it was already reported for isolated pure edge dislocations. In the experimental image (Fig. 8.15 b), the sequences of 5-, 6-, 7-, and 8-atom 7 rings are shown.

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

8.3.4.2 The R = 7 Boundary

A. The R = 7 Symmetric Boundary Unlike the R = 19 grains which had straight boundaries, those of this R = 7 meander in the matrix, and it is crossed by {1120} stacking faults previously characterized by Vermaut et al. [21]. Moreover, the boundaries are sometimes decorated with small voids. A diffraction analysis indicates a rotation angle equal to 228 ± 0.28. This value is very close to that of R = 7 in the CSL notation which is h = 21.798. The orientation of the experimental image according to the dichromatic pattern indicates that the studied boundary is along a side of the CSL unit cell. This was confirmed by mapping the circuit in the k and l frames (Fig. 8.16). We obtained c(k) = SX = 1/3 [4 1 5 0]k and c(l) = XF = 1/3 [5 1 4 0]l, leading to the normal at the interface equal to nk = c(k) ^ [0001] = 1/3 [6 9 3 0]k and nl = [0001] ^ c(l) = 1/3 [3 9 6 0]l. Therefore, the indices of the interface plane are (2310)k/(1320)l. This circuit has been reported in the k lattice and the Burgers vector was found to correspond to one dislocation core a2 for one period. We have studied seven adjacent

The atomic structure of R = 19 with a step: a circuit mapping; b the atomic struc-

Fig. 8.15

ture of the boundary showing 5/7- and 8atom ring dislocation cores.

8.3 Dislocations

periods and no additional defect was present. With c(k) = SX = 1/3 [28 7 35 0]k and c(l) = XF = 1/3 [35 7 28 0]l, we obtained: c(k, l) = c(k) + P7 c(l) = 0. This grain boundary has been reconstructed and the cores of the primary dislocations were found to contain 8- and 5/7-atom rings. Whereas for R = 19 boundary, the two configurations were alternated, for this R = 7 perfect boundary, we observed five 5/7 configurations followed by two 8-atom ring model (Fig. 8.16 b). In another area of the boundary, several additional defects were present, as shown by the presence of steps at the interface (Fig. 8.17 a). Four defects have been characterized and two of them were similar (defects 1 and 4). For these defects, the circuit mapping: c(k) = S1X1 = 1/3 [14 2 16 0]k and c(l) = X1F1 = 1/3 [17 4 13 0]l leads to: c(k, l) = c(k) + P7 c(l) = 1/21 [1 5 4 0]k. Therefore, the Burgers vector bij is the opposite of c(k, l) and we obtain bij = 1/21 [1 5 4 0]k. This Burgers vector is located at 608 of the interface plane and is parallel to another side of the CSL unit cell. It is a Burgers vector of a secondary dislocation with the smallest possible amplitude. The corresponding step heights were equal to h(k) = –nk c(k) = –2 and h(l) = nl c(l) = –1. For bij = 1/21 [1 5 4 0]k, the smallest cor-

Fig. 8.16 R = 7: a mapped circuits and reference in k frame; b the atomic structure of the boundary with the 5/7- and 8-atom cycles.

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responding translation vectors are t(k) = a1=1/3 [2 1 1 0]k and t(l) = a1=1/3 [2 1 1 0]l. For these values, the step heights are h(k) = nk t(k) = –2 and h(l) = nl t(l) = –1 and the corresponding Burgers vector is t(k) + P7 t(l) = 1/21 [1540]k. For the defect labeled 3, c(k) was equal to S3X3 = 1/3 [5 270]k and c(l) to X3F3 = 1/3 [6060]l, leading to bij = –c(k, l) = –c(k) + P7 c(l)] = 1/21 [5 4 1 0]k. The step heights were found to be equal to h(k) = –nk c(k) = 1 and h(l) = nl c(l) = 2. bij corresponds to a Burgers vector of the smallest amplitude and it is inclined by 608 to the interface plane and the corresponding shortest crystal translation vectors are t(k) = –a3 = 1/3 [1120]k and t(l) = –a3 = 1/3 [1120]l. For these values, the calculated corresponding step heights and Burgers vector are similar to those experimentally observed. The step configuration corresponding to this defect is shown in Fig. 8.17 b. The circuit around the defect labeled 2 is c(k) = S2X2 = 1/3 [2 2 4 0]k and c(l) = X2F2 = 1/3 [3030]l. The corresponding step heights and Burgers vector are equal to h(k) = 2, h(l) = 1 and bij = 1/21 [1 5 4 0]k, respectively. These would be consistent with the shortest crystal translation vectors t(k) = –a1 = 1/3 [2110]k and t(l) = –a1 = 1/3 [2110]l which lead to the same values of step heights and Burgers vector. But, the sign of the vectors implies re-entrant steps, as shown in Fig. 8.17 c and this is not consistent with the image. However, if a translation vector of the (2310)k interface, that is 1/3 [4 150]k is added to t(k) and t(l), the step configura-

Fig. 8.17 Steps of various configurations in a R = 7 grain boundary: a image of the area with circuits around the steps; b reconstruction of

steps 1 and 4; c re-entrant step 2 before reconstruction; d reconstruction of step 2.

8.3 Dislocations

tion illustrated in Fig. 8.17 d is obtained and this is consistent with the image. Thus, the steps are characterized by t'(k) = 1/3 [2240]k = X2S2 = –c(k) and t'(l) = 1/3 [3030]l = X2F2 = c(l). So, this defect is an interfacial edge dislocation, with bij at 608 of the interface plane and which exhibits a larger step than the other defects. B. The R = 7 Asymmetric Boundary Another grain has been observed with a similar rotation angle of 21.88 and therefore corresponding to a R = 7 boundary. Contrary to the previous, it was characterized by large straight facets. Besides a symmetric interface corresponding to a side of the CSL unit cell, an asymmetric straight boundary was present as well. In the l crystal, the interface plane corresponds to {1010} (Fig. 8.18). We determined: c(k) = 1/3 [13 2 11 0]k and c(l) = 1/3 [14 7 70]l leading to nk = [3850] and nl = 1/3 [0 21 21 0]l. Therefore, the interface plane was (3850)k/(0110)l choosing the lattice of the k crystal, this circuit SXF exhibits the closure failure FS = a1 + 3 a2. For the four periods we have determined that no secondary dislocation was present because: c(k) + P7 c(l) was equal to zero with c(k) = 1/3 [52 8 44 0]k and c(l) = 1/3 [56 28 28 0]l. The reconstruction of the boundary is shown for these four periods (Fig. 8.18). The periods 2 and 4 are completely similar and made of two neighboring 5and 4-atom cycles, one 8- and one 5/7-atom ring models. For defects 1 and 3, the neighboring 4- and 5-atom cycles are present as well and they form a characteristic pattern, which allowed us to determine without ambiguity the different periods. Between them, the two primary dislocation cores exhibit different features; for defect 1, two following 5/7-core models are present whereas for defect 3, it was two 8-atom ring models.

8.3.4.3 The R = 31 Symmetric Boundary

This grain has an irregular shape, but the corresponding diffraction pattern indicates a rotation angle equal to 188, close to that of R = 31 (17.908). The circuit mapped in the k and l frames (c(k) = SX = [5 1 6 0]k and c(l) = XF = [6 1 5 0]l) leads

Fig. 8.18

R = 7 asymmetric boundary, 8-, 5/7- and 4-atom ring cores dislocations are exhibited.

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to the normal at the interface equal to nk = [7 11 4 0]k, to nl = [4 11 7 0]l and therefore to the interface plane (7 11 4 0)k/(4 11 7 0)l. This corresponds to a diagonal of the CSL unit cell. When this circuit was reported in the k lattice, the Burgers vector was found to be equal to 3 a2. No additional defect was found in this part of the boundary (Fig. 8.19 a). However, the circuit mapped with c(k) = S1X1 = 1/3 [14 2 16 0]k and c(l) = X1F1 = 1/3 [17 4 13 0]l leads to c(k, l) = 1/31 [6 5 1 0]k. The corresponding Burgers vector is inclined by 608 to the interface plane and corresponds to another diagonal of the unit cell. The step heights were found to be equal to h(k) = –nk c(k) = –4 and h(l) = nl c(l) = –7, leading to b–4/–7 = 1/31 [6 5 1 0]k. The corresponding shortest crystal translation vectors are t(k) = a3 = 1/3 [1 120]k and t(l) = –a3 = 1/3 [1 120]l and they would be consistent with the values of step heights and Burgers vector. The sign of the vectors implies a re-entrant step, but this is not consistent with the image. However, if a translation vector of the [7 11 4 0]k interface, that is [5 1 6 0]k is added to t(k) and t(l). Thus, the steps are

Fig. 8.19 R = 31 boundary with one step and a 4-atom ring dislocation: a circuit mapping, and the different periods of the boundary; b reconstruction of the boundary showing the

step and the atom rings, the 4-atom ring is in period 2 (arrow), the Burgers vector of the step is b–4/–7 and lies at 608 of the interface plane.

8.3 Dislocations

characterized by t'(k) = 1/3 [14 2 16 0]k = X1S1 = –c(k) and t'(l) = 1/3 [17 4 13 0]l = X1F1 = c(l). So, this defect is an interfacial edge dislocation, with b–4/–7 inclined at 608 of the interface plane (Fig. 8.19 b). In this micrograph, four periods are present, they are made of three dislocation cores even the one which exhibits a defect character. The period labeled one has two dislocation cores made of 8-atom cycles separated by a 5/7-atom dislocation core. Moreover, we note that the first 8-atom cycle core is slightly shifted downwards. In period two, the two first dislocation cores are made of 5/7-atom cycle, the first is shifted downwards whereas the third dislocation core is made of a 4atom cycle. Period three exhibits a defect character, it is made of three dislocation cores separated by a downward step. Two 8-atom cycle cores are present with one 5/7 between them. In fact, this period is characterized by the withdrawal of one (1010) plane (normal to the interface). The last period labeled four is made of one 5/7-core shifted upwards, one 5/7- and one 8-atom cycle cores at the same level. 8.3.5

Formation

In our recent work [64], plan-view HREM observations revealed that pure edge threading dislocations are directly related to two extra prismatic AlN half-planes, whose missing parts are associated with two misfit dislocations of the interfacial network. The Burgers vector of the threading dislocation equals the sum of the Burgers vectors of the two misfit dislocations of a type. Therefore such threading dislocations are directly connected to the misfit dislocations, and the residual strain in the epitaxial layer may be used to explain their high density. These observations are in fair agreement with the idea of mosaic growth of GaN on top of the substrate. In contrast, Naranayan et al. [65] have shown that after 20 s of high temperature (HT) growth, GaN islands were free of threading dislocations (TDs). Then, after 75 and 120 s growth, most of the islands contained pure screw c type and pure edge a type TDs with an interspersion of mixed a type TDs. Most of the TDs originated from faulted regions located within nucleation layers. TDs move toward the island top surface for c type or curve toward island side facets for a type. Coalescence of HT GaN islands did not give rise to either a, c, or a+c type TDs. After 240 s of growth, most TDs were predominantly of a type and could result from climb and glide of basal plane dislocations that form by the dissociation of Shockley partials located within the faulted regions. They concluded that TDs form primarily by the coalescence of Frank partials near the GaN/sapphire interface. Therefore, it seems that the origin of the large densities of the threading dislocations which are present inside the GaN epitaxial layers has no yet been fully explained and more work is needed in order to understand their formation which seems to be also dependent to the growth conditions.

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8.4

Stacking Faults 8.4.1

Basal Stacking Faults

For the last decade, the III–V nitride semiconductors have been extensively investigated because of their potential opto-electronic applications in the whole part of the visible spectrum. However, problems still exist and are mostly due to the lack of suitable substrates. Until now, the best results have been obtained for GaN layers grown by MOCVD on the c-face of sapphire. But, the large mismatch close to 16% and the different thermal coefficients compared to GaN lead to the presence of densities of defects, up to five orders of magnitude higher than in other semiconductors. Among the different types of defects, the presence of stacking faults has been reported on sapphire and SiC substrates close to the interface, in GaN layers grown by molecular beam epitaxy or MOCVD, using an AlN buffer layer or not [66]. In bulk GaN grown under high nitrogen pressure, the three types of stacking faults were observed (I1, I2, and E) whereas in GaN layers grown over sapphire, the presence of faults I1 bounded by Frank-Shockley partials was reported [67, 68]. Recent work indicates that stacking faults may not induce defect states in the band gap, but that they can give rise to quantum-well-like regions of zinc-blende materials embedded in the wurtzite lattice that can bind electrons [69]. This was confirmed by photoluminescence and transmission electron microscopy experiments, indicating an excitonic transition at 3.4 eV due to the presence of stacking faults [70]. In the following, we present an analysis of basal stacking faults observed at the vicinity of the interface with the substrate. The AlN/GaN layers were grown on top of (0001) sapphire. At low magnification, we observed that a high density of defects is present near the interface, which are mostly dislocations and stacking faults. At the immediate vicinity with the sapphire substrate, the defects are long extended stacking faults whereas further from it (20 nm), we mainly observed short width faults with an extension less than few ten {1010} lattice spacings. The long extended stacking faults are mainly I1 and I2 faults even if segments of E fault were also observed [71]. We focus more particularly on the narrow basal stacking faults. Figure 8.20 shows a high magnification image, along the h1120i zone axis, of the GaN layer at 15 nm from the interface substrate. Two half {1010} planes are underlined, they are separated by about ten lattice planes. By referring to the perfect wurtzite structure, the wrong stacking sequences can be underlined and we determined that these faults are I2. These I2 faults may occur following the dissociation of a perfect dislocation (a = 1/3 h1120i) into two Shockley partials. However, the Burgers circuit drawn around these faults did not exhibit any closure failure. The two partial dislocations bounding these basal faults have opposite Burgers vectors (b = 1/3 h1010i). These faults I2 can be formed directly by shear and we note that their presence is related to the end of the buffer layer. Besides these I2 faults, I1 faults are also present (Fig. 8.21) and the Burgers circuit drawn around shows up a closure failure equal to 1/3 [1120]. At the left of this fault,

8.4 Stacking Faults

Fig. 8.20

I2 stacking fault loops, no closure failure.

Fig. 8.21

I1 stacking fault, closure failure: 1/3 [1010 ].

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additional (0002) and {1010} half planes may be shown whereas at its right, it is one half (0002) opposite plane. This I1 fault corresponds to a climb-dissociated perfect dislocation into two Frank-Shockley partials, following this reaction: 1=3h1120i ! 1=6h2023i ‡ 1=6h0223i

or a ! …p1 ‡ c=2 † ‡ …p2

c=2 † :

Figure 8.22 shows two neighboring basal stacking faults with a short extension and when a Burgers circuit is drawn around them, the closure failure appears to be equal to c. In fact, a careful examination indicates that there are two faults of I1 and I2 types. The I2 may be shown at the left of the figure, it is bounded by two opposite partial dislocations (b = 1/3 h1010i) similarly to those presented in Fig. 8.20. Thus, it is not due to the dissociation of a dislocation and does not contribute to the closure failure. On the right, a I1 fault is present bounding by two Frank-Shockley partials; this fault results from a climb-dissociation of a perfect c dislocation with this reaction: c ! …p1 ‡ c=2 † ‡ … p1 ‡ c=2 † ;

with

p1 ˆ 1=3h1 1 00i :

Previously, I1 stacking faults were reported to exist in GaN layers grown on sapphire substrate by MOCVD [41, 68] whereas I2 and E ones were not reported. In

Fig. 8.22

I1 and I2 stacking faults, closure failure, c.

8.4 Stacking Faults

our case, we report the presence of both I1 and I2 faults at the immediate vicinity to the interface with the substrate. The I2 fault can form directly by shear or after a dissociation of a pure edge dislocation into two Shockley partials. The extended faults are observed in the first 15 nm of the GaN layer, which corresponds to the thickness of the buffer layer. It was shown that the buffer layer is predominantly cubic and transformed in hexagonal GaN during heating [72]. Thus, these faults may be due to incomplete transformation from sphalerite to wurtzite structures. Besides, the formation of the extended faults may be due to the mosaic growth mode of GaN/sapphire layers. The presence of steps, due to the 38 misorientation, leads to the presence of defects because they create an additional shift between the epitaxial islands grown on adjacent terraces. The relaxation of the shift along [0001] is made by the insertion of stacking faults in the epitaxial layers [73]. 8.4. 2

Prismatic Stacking Faults 8.4.2.1 Morphology of the {1120} Stacking Faults Inside the Epitaxial Layers

In epitaxial layers, independent of the substrates, observations carried out in planview samples show {1120} defects which can either terminate by partial dislocations or form closed domains (Fig. 8.23). Along the [0001] direction, it is difficult to see them edge on (Fig. 8.23 b), due to the fact that they easily fold from the

Fig. 8.23 Prismatic stacking fault, [0001] view: a the fault is terminated by two partial dislocations; b the prismatic fault forms a

closed domain limited by {1120} planes. It often folds into the basal plane as shown in position A and arrow.

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

prismatic to the basal plane. For the closed domains, it is possible that these faults may limit inversion domains. Therefore, we recorded convergent beam diffraction patterns and for example the 1011 and 101 1 discs recorded inside the domains and in the matrix were always identical along the h10 12i zone axis [22]. Convergent beam electron diffraction is a very powerful technique for structure identification, thickness, and residual stress measurements. The contrast inside the discs, due to dynamical diffraction, reveals also the whole symmetry of the structure along the observed direction [74].

8.4.2.2 Identification of the Stacking Fault Atomic Structure

Two atomic models exist in the literature for the {1120} prismatic fault in wurtzite materials as originally characterized by conventional electron microscopy in the 1960s by Blank et al. [23] (Fig. 8.24 c) and Drum [24] (Fig. 8.24 a), respectively. For HREM characterization, a defect contained, for example, in the (1210) plane should be observed along the [10 10] direction, in order to be edge on. However, the projection of the 1/2 [10 11] fault vector should result in a 1/2 [0001] transla-

a)

b)

c)

d)

Fig. 8.24 Models of the prismatic stacking fault: a and b the Drum model: 1/2 [1011]; c and d the Blank model: 1/6 [2023].

8.4 Stacking Faults

tion vector which is not visible on a [1010] HREM image. Then, no information can be obtained on the fault vector. In [1120] zone axis images, the projection of the fault vector should exhibit one 1/4 [1100] and one 1/2 [0001] components. Therefore, observations of the inclined defects should bring information on the fault vector. Unfortunately, the core structure of the defect will not be directly observed. To confirm the similarity between our observations and the already reported defects, image simulations have been carried out. Sets of supercells have been generated to simulate the inclined planar defect. There are two ways possible to create the defect: – one can apply directly a 1/2 [1010] translation, – or one can remove a (1210) plane and apply a 1/6 [1210] translation operation to obtain the same defect which is compatible with the compression state of the AlN layer. The sides of these supercells are along the [1120], [1100] and [0001] directions respectively. Their stacking along the [1120] direction forms a particle in which the defect is contained in the (1210) plane. The translation operation of the defect leads to an overlay of the atomic columns which makes them appear double (Fig. 8.24 b, d) with a hexagonal-like projection for the Drum model (Fig. 8.24 b). The corresponding simulated images are shown in Fig. 8.25; it is shown that the two models can be clearly distinguished. In all the observations we carried out along the [0001] direction we found the Drum model atomic structure as shown in Fig. 8.26 a along with the simulated image (inset). In cross section observations we sometimes noticed a prismatic fault linking two I1 SFs which was found to exhibit a different contrast (Fig. 8.26 b). Inside the area defined by the projected image of the defect, the lattice fringes of the basal planes of AlN exhibit alternately a continuous fringe and high intensity spots (between points b and c in Fig. 8.26 b). This contrast matches the Blank model atomic configuration.

Fig. 8.25 Models of the prismatic stacking fault, simulated images: a and c Drum model; b and d Blank model.

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The displacement vector of these planar faults was confirmed in conventional as well as HREM experiments [21]. In the conventional weak beam technique, we made the g, ng experiment in order to extinguish the a fringes and we systematically found the 1/2 [1011] prismatic stacking fault corresponding to the Drum model.

Fig. 8.26 Experimental images of the prismatic stacking fault: a projection [0001], Drum model; b cross section, a–b: basal

stacking fault I1, b–c: Blank configuration, c–d: stacking fault I1, d–e: Drum configuration.

8.4 Stacking Faults

8.4.2.3 Formation Mechanisms

A. On (0001) 6H-SiC Surface Notwithstanding possible misorientation of the wafer, the [0001] SiC surface exhibits steps of various heights and it was necessary to make a close investigation in order to identify the different types of steps and determine their connection with the planar faults. In these tetrahedrally coordinated materials, if one ignores the mismatch along the c axis, the two compounds can be considered as polytypes. Therefore, a 6H-portion under a step can be decomposed into a faulted 2H stacking, and depending on the type of step, the decomposition may result in a displacement vector d as discussed previously. This gives rise to the only fault vec-

Displacement vectors at 6H-SiC/ GaN interface: a I2 type of step with no defect propagating in the epitaxial layer; b I2

Fig. 8.27

type of step with the formation of a prismatic stacking fault (D).

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tors of the hcp lattice (the intrinsic I1, RI1 = 1/6 h2023i, I2, RI2 = 1/3 h1010i and the extrinsic E, RE = 1/2 h0001i). Among them, I1 and E have 1/2 c component along the c axis and may lead to the formation of an extended defect in the epitaxial layer. The displacement vector identical to I2 is confined in the interface and may contribute to release the misfit strain (Fig. 8.27 a). When all the step heights are taken into account, it was found that the largest fraction of the faults that will be formed are I1 as shown in Table 8.3 and has been discussed in more details [21]. This explains the HREM observations in the layers grown over the (0001) 6H-SiC surface: the I1 steps were seen to give rise to the formation of extended prismatic stacking faults (Fig. 8.27 b), whereas no E step type has been observed. B. On (0001) Sapphire Growth on a Single Terrace The previous systematic analysis of the polyhedra combinations allows to determine the relative proportions of the planar defects induced by the operator Wce (see Sect. 8.2.6). For instance, if the interface polyhedra are exclusively downward tetrahedra, the RSF will be only RI1, and combinations of downward tetrahedra and octahedra lead to the formation of RI1 and RI2 faults in equal proportions (Table 8.5) which may explain the formation of stacking faults inside the epitaxial layers. Growth on Adjacent Terraces A step, between two terraces on which two GaN islands grow, introduces a translation TS between them. Its component along c axis can be reduced in RE = 1/2 h0001i and a residual translation Tres. The number of RE is calculated to minimize the absolute value of this residual translation. For instance, the step between two A terraces with a height of c/3 in Al2O3 (0.433 nm) is equivalent in GaN to 0.835 cGaN, or: TS = 2RE + Tres = Tres with Tres = –0.165 cGaN&cGaN/6. By considering all the steps between A or B terraces (A or B layers of the hcp stacking), the TS translation can be written as: TS = aRE + Tres with a = 0 or 1 and Tres may take four values with the approximation 2 cAl2O3*5 cGaN (Table 8.6). So, the operator relating adjacent terraces must involve this additional parameter, Tres:

Wce ˆ R ‡ m ‡ Tres

where

R ˆ RSF ‡ aRE :

As this residual translation is never equal to c/2, it cannot be simply accommodated by the formation of prismatic stacking faults. The operator describing IDBs can be written in order to point out the c/8 translation found inside some of the models in addition to the mirror operation (Table 8.7). When compared to the residual translation Tres, the introduction of the IDB containing the c/8 translation may help in minimizing the shift along c at most of the steps; it is reduced to 1/24 cGaN as seen in the last column of Table 8.9. Therefore, in the case of steps, the residual translation cannot be minimized by introducing a stacking fault. During epitaxial growth of GaN layers on (0001) sap-

8.4 Stacking Faults Tab. 8.9 Vertical displacement reduction by introduction of an IDB

Step notation in cAl2O3 unit

Wce = Tstep

0 Wce = Wce ± m

0 Wce = WIDB + e [0001]

(A–B, c/6) (A–A, c/3) (A–B, c/2) (A–A, 2c/3) (A–B, 5c/6) (A–B, c + c/6) (A–A, c + c/3) (A–B, c + c/2) (A–A, c + 2c/3) (A–B, c + 5c/6)

RE–1/12 [0001] –1/6 [0001] 1/4 [0001] RE + 1/6 [0001] 1/12 [0001] –1/12 [0001] RE–1/6 [0001] –1/4 [0001] 1/6 [0001] RE + 1/12 [0001]

RE–1/12 [0001] + m –1/6 [0001] + m 1/4 [0001] + m RE + 1/6 [0001]–m 1/12 [0001]–m –1/12 [0001] + m RE–1/6 [0001] + m –1/4 [0001]–m 1/6 [0001]–m RE + 1/12 [0001]–m

WHolt + 1/24 [0001] WV–1/24 [0001] WB –WHolt + 1/24 [0001] –WV–1/24 [0001] WV + 1/24 [0001] WHolt–1/24 [0001] WB –WV + 1/24 [0001] – WHolt–1/24 [0001]

phire, the occurrence of basal and prismatic stacking faults is not a straightforward result of the steps at the substrate surface. They form on coalescence of islands whose growth has been initiated with different polyhedra.

8.4.2.4 Relative Stability of the Atomic Configurations

As discussed above, during HREM experiments, all the observations carried out along [0001] zone axis took mainly place in the GaN layers and exhibited the Drum: 1/2 [1011] atomic configuration for the prismatic stacking fault. In cross section specimen, it was possible to make a detailed analysis of the AlN buffer layers as well and in a few instances the I1: 1/6 [2023] atomic configuration was also observed. However, even in those cases, it was limited to nanometric areas and it rapidly folded back to the basal plane. The I1 stacking fault passes from the basal to the prismatic plane continuously, whereas the occurrence of the Drum fault needs the formation of a stair rod 1/6 [1010] dislocation at the intersection. So in order to be able to form the Drum configuration, its energy has to be smaller than that of the I1 prismatic configuration. So, we have calculated the energy of the two stacking faults configurations for the GaN, AlN and InN alloys in order to try to explain the observations carried out in GaN and AlN layers. We applied the method of lattice relaxation to a set of 1984 atoms containing the defect for the two atomic models. As seen in Table 8.10, the formation energy of each configuration depends on the compound for AlN, GaN and InN. In AlN, the two atomic configurations of the {1120} stacking fault have a comparable value of formation energy. This is in complete agreement with the above HREM observations in which the two configurations could be observed inside the AlN buffer layers. The calculations indicate that, for InN and GaN, the atomic configuration corresponding to the Drum model could be more stable. These results are in agreement with the observations made in the GaN layers where all the analyzed cases gave the Drum model.

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms Tab. 8.10 Formation energy in meV Å2 for the relaxed atomic configuration of the {1120} stack-

ing fault Model

Amelinckx (1/6 h2203i)

Drum (1/2 h1101i)

AlN GaN InN

100 78 65

100 22 21

Fig. 8.28 Formation and propagation for the prismatic stacking fault.

The two configurations of the stacking fold easily from the basal to the prismatic plane of these wurtzite materials. In the basal plane both have the 1/6 h2023i displacement vector of the I1 stacking fault. In the {1120} plane, they differ by 1/6 h1010i, which is worth less than 4% in energetic balance between the two vectors (using the b2 criterion) in the three nitrides compounds. These faults are growth defects, as they cannot be generated by pure deformation, their occurrence and subsequent evolution inside the epitaxial layer can be sketched as in Fig. 8.28.

8.5

Inversion Domain Boundaries

AlN and GaN are of wurtzite structure, which is noncentrosymmetric, defects due to polarity can form, such defects were reported for the first time by Aminoff and Broome [26]. In this work, the atomic structure of the {1010} IDBs has been determined by several TEM methods. It was found that experimental micrographs recorded at specific defoci and thicknesses can be used in order to determine the atomic structure of the boundaries.

8.5 Inversion Domain Boundaries

8.5.1

Identification of the Inversion Domains

In multi-beam bright field images taken near h1120i zone axis, besides the threading dislocations, small vertical domains are present. They start at the interface and cross the whole epitaxial layer. In order to reveal the inversion character of these domains, we have carried out multi-beam dark field experiments with reflections exhibiting the noncentrosymmetric character of the crystal. Serneels et al. [75] have demonstrated that under these conditions, the inversion domains present a complementary contrast for +g and –g reflections. Friedel’s law states that the intensity diffracted in the direction ko + g for an incident beam ko equals the intensity diffracted in the direction –(ko + g) for an incident beam along –ko. However, in a noncentrosymmetric crystal like GaN, Friedel’s law fails as the structure factor of a reflection hkil is not necessary equal to that of hkil. All [hki0] zone axes can be used for these experiments as they are noncentrosymmetric. We have used [1100] zone axis and dark field images with g = 0002 and g = 0002 are presented in Fig. 8.29. The complementary contrast indicates that these domains are related to the bulk by an inversion operation. In plan-view observations along the [0001] zone axis (Fig. 8.30), the IDBs present hexagonal sections bounded by {10 1 0} planes. In cross-section images, we have identified typical inversion domains inside two types of samples grown using different conditions. For both these domains cross the whole epitaxial layer, but the size of the domains, their density and the surface morphology are different. In type grown without buffer layer by ECR-MBE, the size of the domains is in the range 5–20 nm with a large majority smaller

Fig. 8.29 Inversion character for the prismatic domains a 0002 dark field image, b 0002 image. Areas of inverted contrast are shown by arrows.

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms Fig. 8.30 A planar view micrograph along [0001] showing IDBs with hexagonal section and weak contrast.

than 10 nm. Their density was estimated (in plan-view specimens) to be equal to 2.5 ´ 1010 cm–2 and the surface appears to be completely flat. In contrast, for the ones grown with a low-temperature buffer layer, the surface morphology was characterized by small pyramids in the center of which are located the inversion domains. These pyramids are about 100 nm width and 75 nm height whereas the size of the domains can reach 50 nm; their density is about one order of magnitude less. One of the most powerful techniques in order to study inversion domains is convergent beam electron diffraction. The contrast within the disks of a CBED pattern, due to dynamical diffraction, reveals the symmetry elements of the investigated zone axis. Particularly, the noncentrosymmetry of a wurtzite crystal can be indicated by the absence of the mirror in the basal plane, leading to asymmetries between the two opposite diffraction disks of a CBED pattern (0002 and 0002). Therefore, the presence of an inversion domain can be demonstrated by CBED analysis carried out in the inversion domain and inside the neighboring matrix. For GaN layers, such experiments have been carried out for plan-view specimens along the h1102i zone axis, where there is an asymmetry between 1101 and 1101 diffraction disks [42, 76]. The two types of polarities (nitrogen and gallium) have been reported for homoepitaxial GaN [77], for GaN layers grown on sapphire substrate by MOCVD [78] as well as by MBE [43]. In all these cases, the layers that contain inversion domains have N-polarity, and therefore inversion domains present a Ga-polarity.

8.5 Inversion Domain Boundaries

In our case, the small size of our domains has prevented us from using CBED experiments in order to confirm the presence of the inversion operation. However, we have carried out CBED experiments for the determination of the absolute polarity of the GaN layers. The experimental CBED pattern recorded on the GaN matrix along the h1100i zone axis was compared to simulated patterns, calculated using the Bloch wave method for thicknesses ranging from 50 to 200 nm, with a step of 5 nm. A good match was obtained with the experimental pattern for a 90nm thickness. The asymmetry between the 0002 and 0002 diffraction disks is clearly shown for these patterns: the 0002 disk exhibits a black fringe whereas it is white inside the 0002. Afterwards, the orientation of the c axis was determined by comparison of the orientation of the CBED pattern and the substrate-layer direction TEM image. The microscope calibration has been verified by carrying out CBED experiments on 6 H-SiC layers for which the absolute polarity was previously known [22]. We found that the [0002] ? [0002] direction corresponds to the substrate ? GaN matrix one. Thus, the GaN matrix had always a nitrogen polarity and the inversion domains a gallium one, as previously observed [77, 78]. 8.5.2

Atomic Models of the Boundary

In the GaN wurtzite structure, one atom species occupies c positions whereas there are two possibilities for the second sublattice: the b1 or b2 tetrahedral sites, which cannot be simultaneously occupied. The Ga and N atoms are tetrahedrally coordinated and the c axis of a tetrahedron points upwards or downwards depending on the occupied b sites. Therefore, two crystallographic variants are possible and the c axis is polar, leading to nonequivalent [0001] and [0001] directions. Conventionally, the [0001] direction is chosen parallel to Ga ? N bond, along the c

Fig. 8.31 The two models of the prismatic IDB. H: Holt, V for the reconstructed model with a c/2 translation. The IDB position is shown by arrows.

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axis, and if the Ga–N bonds point upwards, the GaN layer has a Ga polarity whereas if the Ga–N bonds point downwards, the GaN layer has a N polarity. When the surfaces are formed by breaking the bonds parallel to the c axis, the former surface is gallium terminated, and the latter is nitrogen terminated. In Fig. 8.31 are shown the two typical models for the atomic structure of IDBs. The H model is based on the description of Holt that exchanges the two sublattices: atoms A in positions c and atoms B in positions b become atoms A in positions b and atoms B in positions c. The other model was proposed by Romano et al. [79] as IDB* and by Potin et al. [43] as V; compared to the Holt model, it is characterized by a c/2 translation in order to avoid the Ga–Ga and N–N bonds. For each model, two locations can be obtained for the {1010} boundary plane, by cutting the in-plane bond parallel to the projection plane or the two other bonds. 8.5.3

Atomic Structures of the Boundary

The TEM results indicate the presence of an inversion operation and of a possible translation along the c axis. The above models were used for image simulations and compared to experimental observations. But firstly, we studied the contrast exhibited by GaN matrix near the IDB in order to determine the thickness and defocus working conditions. Simulations were carried out along the h1120i zone axis for thicknesses from 1 nm to 25 nm and defocus from 0 to –100 nm. Typically, two maxima of contrast are exhibited: –25 to –35 nm and –50 to –60 nm defocus. Around –29 nm, the white spots coincide with the tunnels whereas around –54 nm, they are on the atomic column positions. For thicknesses < 4 nm, the spots are shifted towards the heaviest atomic species (Ga), whereas, for higher thicknesses, they are shifted towards the other atomic species (N) and, they quickly merge with them (8 nm): the Ga atoms are no more visible. As a consequence, the stacking sequence (ABAB) is underlined. The stacking sequences observed for the bulk are opposite for the two polarities [59, 76]. The simulated images of the two models are presented at 5 nm thickness for –29 and –54 nm defocus (Fig. 8.32). For the V model, the stacking sequences are the same on both sides of the IDB, in contrast with the Holt model at –54 nm defocus (Fig. 8.32 b and d). At –29 nm defocus, the tunnels are projected into white spots, they can be underlined for thicknesses ranging from 1 to 5.5 nm and from 10 to 15 nm. For the Holt model, the sequences are in the same direction whereas, for the V model, they are opposite (Fig. 8.32 a and c). Therefore, the two models can be discriminated. Typical HREM images recorded at –29 and –54 nm defocus are presented in Fig. 8.33. At –29 nm defocus (Fig. 8.33 a), the stacking sequences on both sides of the IDB are in the same direction for a given row, whereas for defocus equal to –54 nm (Fig. 8.33 b) they are opposite. Therefore, these micrographs represent the H model. In Fig. 8.33 c and d, the two stacking sequences are opposite and no shift exists at –29 nm defocus whereas at –54 nm a small shift appears downwards and the two stacking sequences are in the same direction. Therefore, this IDB corresponds to the V model.

8.5 Inversion Domain Boundaries

For these IDBs, the boundary plane can be obtained by cutting two or one bond per atom leading to different atomic structures. Therefore, one has also to distinguish between the models (H2, V2) and their counterparts. In this instance, we have undertaken comparative image simulations for H2, V2 and H1, V1 models. The H models are characterized by the presence of wrong bonds at the boundary plane whereas the IDBs of the V model are made of 4- and 8-atom rings. As seen above, the H and V models can be distinguished by considering the stacking sequences. Therefore, the argument about the boundary plane is between H1 and H2, V1 and V2, respectively. For H1 and V1 models, the boundary plane cuts only one bond per atom and {1010} interplanar distance is not modified. In V2, the projection of the boundary plane shows small 4 atom rings that are not separated in our microscope. The simulated images of the four models have been calculated at 5nm thickness, for two defoci (–29, –54 nm). At –29 nm defocus, the boundary plane of the H2 and V2 models is located between white spots whereas, for H1 and V1, it is located on a row of white spots. In the –54 nm defocus images, it is the opposite.

Fig. 8.32 The two models of the prismatic IDB, simulated images at –29 and –54 nm for 5 nm thickness; a and b Holt model; c and d V model.

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Fig. 8.33 Experimental images of inversion domain boundaries, the two observed configurations: a and b: the Holt model; c and d the V model.

Fig. 8.34 Position of the IDB inside closely and largely spaced {1010} planes, simulated images of H a and V b IDB models, atom

projections are shown in the upper part of the micrographs.

For the H2 model, clearly defined bright spots are coincident with the boundary plane at –54 nm defocus, so there is no possible confusion between the two models (Fig. 8.34 a). In the case of V1 and V2, the distinction is made at –29 nm defocus where also no confusion is possible between the two models: large elongated dark contrast is coincident with the boundary plane of the V2 model, whereas in the V1 model, bright spots which represent the 8 atom ring tunnels show up (Fig. 8.34 b).

8.5 Inversion Domain Boundaries

Fig. 8.35 Experimental images of the two cuts of the boundary plane of the a H IDB at 54 nm defocus, A–B: H1 configuration, B–C: H2 configuration and b V IDB at 29 nm defo-

cus, A–B, V2 closely space planes and two bonds per atom inside the boundary, B–C, V1 largely spaced atomic planes and one atom bond inside the boundary plane.

In the experimental micrographs of both models, we have observed the boundary plane and we have noticed that this plane moves from one configuration to the other of the same model. In Fig. 8.35 a, an Holt IDB is presented for –54 nm defocus. From A to B, the boundary plane is located between two rows of equivalent brighter spots indicating the H1 configuration, and as seen from B to C, only one row of brighter spots is present characterizing the H2 configuration. In Fig. 8.35 b, a V IDB is shown for –29 nm defocus, from A to B, the two brighter spots show the V2 configuration and from B to C, we have a unique row of brighter spots characterizing the V1 configuration. For the two types of samples, the change from one configuration to another one is indicated by the inclined arrows. 8.5.4

Atomic Structure of Boundary Plane and Epitaxial Layer Morphology

Many authors have related the occurrence of inversion domains inside the GaN epitaxial layer with its surface morphology. It is shown that such hexagonal prisms were necessary Ga polar domains inside a N matrix whose growth velocity is lower. The consequence was that such domains were usually found in the center of small pyramids [78]. However other types of morphologies were reported, although no connection was made with the atomic structure of the boundary plane [40]. Fairly recently, it was possible to analyze samples which contained inversion domains and exhibited either a flat surface, of pyramidal-like morphology. The GaN layers with flat surfaces were directly grown at 800 8C at a 40-nm h–1 rate, up to a 2-lm thickness by ECR-MBE. They contained nanometric domains

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Morphology of GaN layer containing inversion domains. a Holt IDBs high density of domains, flat layer surface; b larger V domains in center of surface pyramids.

Fig. 8.36

up to 1010 cm–2 (Fig. 8.36 a). The pyramidal topped layers were also deposited at 800 8C on a low temperature (550 8C) GaN buffer layer (40 nm thickness) by NH3-MBE (Fig. 8.36 b). A careful HREM investigation showed that the two types of samples exhibited different atomic configuration of the boundaries. The flat layers contained Holt type IDBs, whereas the domains that terminated in the centers of nanometric pyramids had exclusively the V configuration [59]. 8.5.5

Interaction with Basal Stacking Faults

As can be seen in Fig. 8.37 a, an I1 stacking fault arrives into an inversion domain and does not cross it, however, the inversion domain continues without any visible modification towards the layer surface. When stopped, the I1 stacking fault is terminated by a Shockley partial dislocation: 1=6 h2023i ˆ 1=3 h1010i ‡ 1=2 h0001i :

8.5 Inversion Domain Boundaries

Fig. 8.37 Interaction of an IDB and a basal stacking fault: a whole area showing the domain and the impinging I1 stacking fault; b the Burgers circuit with no closure feature

from the area of the white square in a; c the scheme of the interaction and switch from V to H configuration.

In this case, only the modification of the stacking sequence is visible but there is no additional c/2 plane, meaning that this component of the Shockley partial has been absorbed by the inversion domain boundary. Moreover, the Burgers circuit drawn around the area where terminates the I1 fault does not show any closure failure (Fig. 8.37 b) even in the basal plane, therefore the 1/3 h1010i component lies at 308 from the 1/3 h1120i zone axis.

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms

A possible mechanism, which can explain the above observations, is sketched in Fig. 8.37 c. From the left-hand side, an I1 fault arrives into the IDB which initially bears the V atomic configuration with 8- and 4-atom rings. In the intersecting plane, the basal stacking fault terminates. The termination of the stacking fault issues a c/2 translation which switches the IDB from the V atomic configuration to the Holt one, with Ga–Ga and N–N wrong bonds [80]. I1 ‡ V ! p1 ‡ H where p1 corresponds to the 1/3 h0110i partial dislocation at 308 from the observation zone axis, explaining why no additional lattice planes are visible at the stacking fault termination. For the last few years, it has been argued that due to energetic factors, the only atomic configuration of the {1010} inversion domain boundary would necessary be reconstructed in order to avoid the formation of Ga–Ga and N–N bonds inside the III-nitride ionic semiconductors. In our previous reports, it was shown that the Holt and the reconstructed atomic configuration were in GaN layers grown in different epitaxial conditions. The Holt configuration was found in very small domains (*20 nm) inside layers having a flat surface, whereas the V one bordered larger domains (> 50 nm) which terminated in the center of small pyramids. These domains were shown to form only in nitrogen polar GaN layers. The difference in their size was tentatively explained on the basis of the “ab initio” calculations that indicate that the Holt type configuration has a high formation energy. Now, it is clear that the two atomic configurations of inversion domain boundaries in GaN can coexist inside the same layer. Moreover, it is possible to switch from one configuration to the other by interacting with a basal stacking fault that has a c/2 component. 8.5.6

Formation

Observations at the interface with the substrate showed that Holt type (WHolt = m + 1/2 [0001] –1/8 [0001]) {1010} IDBs start at the interface where steps are present. Figure 8.38 illustrates these observations: steps forming 5–10 nm terraces, can be upwards or downwards, with c/3 and c/6 heights. This is in agreement with the geometrical analysis which showed that such steps introduce a shift along the c axis that may be minimized by the introduction of IDBs. Furthermore, these IDBs are effectively described by an operator which contains a 1/8 [0001] translation. In our observations, no inversion domain was seen to originate from a stepless surface. A quite interesting observation has been made, as illustrated in Fig. 8.39, large c/3 terraces were observed (> 20 nm). In this case, this does not give rise to the formation of an inversion domain. Actually, from both c/3 steps there form extended defects which create 1/2 [0001] partial dislocations (RE) located a few nanometers from the interface, as well as basal stacking faults (SFs) and deformation (D) inside the GaN epitaxial layer as can be seen in the figure.

8.6 Discussion and Conclusions Fig. 8.38 Connection of IDB to the sapphire (0001) surface, the IDB formed on top of a small hexagonal domain limited by c/3 steps.

Fig. 8.39 An area of the GaN/sapphire interface with largely spaced c/3 steps, no ID could form.

8.6

Discussion and Conclusions

The above results show that using the conventional means of HREM: observations in a 0.18 nm point to point resolution microscope, geometrical and atomistic modelling, and image simulations, it is possible to point out the main features of the atomic structure of the extended defects present in very high densities inside GaN epitaxial layers. Typically, some of the defects have now been completely

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elucidated and others that probably play a critical role on the properties of the layers need more research effort. The typical extended defects in GaN layers are stacking faults, threading dislocations and inversion domain boundaries. In good quality MOCVD and MBE GaN layers, the planar defects (stacking faults, inversion domain boundaries) are absent at the top of the layers where the devices are located. The above results have shown that the three stacking faults (I1, I2, E) of the hexagonal structure, which are always present, remain close to the buffer layers. The prismatic stacking faults have been extensively studied, their habit plane is {1120} in contrast to previous reports which indicated that domain boundaries without inversion character may be limited by {1010} boundaries [8, 10, 11, 19, 20]. They exhibit two atomic structures and fold easily from the basal to prismatic plane. In the basal plane, they take the 1/6 h2023i I1 atomic configuration and have been often found terminated by the associated partial dislocation [21, 81]. The two configurations differ by 1/6 h1010i, which is worth less than 4% in energetic balance between the two vectors (using the b2 criterion). Our observations and empirical potential calculations [82] are in agreement with the “ab initio” results carried out for GaN which showed the 1/2 h1011i atomic configuration to be more stable [83]. At the (0001) 6H-SiC surface, the deposition of AlN or GaN form a compound that has exactly the same P63mc wurtzite symmetry. However, in case of steps, the 6H-stacking faces the 2H polytype and depending on the step type and height, there may result a displacement vector, which was identified as I1, I2 or E, with highest probability for I1 and I2 [21, 22, 81]. As the steps on hexagonal surface are mainly along the {1120} planes and that the I1 displacement vector has a 1/2 (0001) along the c growth axis, the coalescing islands generate the prismatic stacking fault when they come into contact from adjacent steps. In fact, the shift along the c axis that may be introduced by a step is quite small: £ 3% in comparison with the case of sapphire where it is close to 20%. Whether this small misfit is confined to the interface, or if it contributes to a possible rigid body translation in the planar defect, has to be investigated in more detail [73]. At the (0001) sapphire surface, the epitaxial relationship comes from the continuation of the anion stacking. As in the case of (0001) SiC, the steps are along the {1120} planes. However, these lattice planes are parallel to {1010} of GaN; so the {1120} stacking faults in GaN layers grown over (0001) sapphire are not simply related to the substrate surface steps. Moreover, the shift due to the four types of steps that may be present on the anionic (0001) surfaces cannot be accommodated by the formation of {1120} stacking faults inside the GaN layer [73]. As already discussed by Blank et al. [23], these faults cannot be generated by deformation, they are to be considered as growth faults. In the above observations, they are equally found in wurtzite nitride layers grown on top of SiC and sapphire. Inside these layers of wurtzite AlN and GaN which have a noncentrosymmetric structure, it is possible to form inversion domains during growth of epitaxial layers. For GaN grown on sapphire substrate, two configurations are possible de-

8.6 Discussion and Conclusions

pending on the polarity: a Ga polarity for the GaN matrix leads to buried inversion domains and the occurrence of inversion domains crossing the whole epitaxial layer has been connected to a N polarity [58]. In this work, two different models have been found: the first is of Holt type characterized by the exchange of the cations and anions across the boundary. For the second, an additional c/2 translation is applied, which allows the wrong bonds (Ga–Ga, N–N) in the boundary plane to be avoided. The latter model appears to be energetically favored as shown by ab initio calculations [9], confirming why many authors [42, 58, 59, 79] have observed it. By comparing the AB sequences in the HREM micrographs recorded in adequate conditions, the two models have been shown to be present [59]. These results were confirmed by carrying out a fringes experiments that allow to determine the displacement vector [76]. It has also been found that the location of the boundary can shift from one {1010} plane to the next, thus cutting one or two bonds per atom. The two atomic structures of the boundary plane are probably formed under different growth conditions. As already noticed by Romano and Myers [40], the surface of a GaN layer with inversion domains can be either flat or exhibit small pyramids centred on the IDs. The samples with flat surfaces, we observed, contained very high densities of nanometric inversion domains. On the top of sapphire, their boundaries had predominantly a Holt atomic configuration. On the top of Si (111), the two configurations have been shown to coexist. Therefore, at the growth temperatures, it seems that the leading factor for the formation of the boundaries is not only the energy. Due to the mosaic structure of the layers, numerous edge dislocations are present with very high densities (1010 cm–2); they form low angle grain boundaries which are rotated about the c axis. As the rotation angles are small (< 1 8), the distance between the dislocations is quite large ³ 100 nm. Early work on the mosaic growth explained these densities by assuming that the small rotations around the c axis were due to growth errors [12]. The high angle grain boundaries observed in this work were found to extend from the GaN/sapphire interface to the GaN film surface. In such layers, the density of threading dislocations is not unusually high (1010 cm–2). It is therefore possible that the mosaic growth of GaN on top of (0001) sapphire does not only include the small angle rotations between adjacent grains which are due to growth errors, but also local arrangements of the threading dislocations into high angle grain boundaries. This high-resolution electron microscopy analysis presents evidence of multiple core structure for the a pure edge dislocation in GaN layers. Our observations show that mainly two atomic configurations are present with 5/7- and 8-atom cycles at a similar frequency in low angle boundaries. The topological theory formalism, which comprises the crystallographic analysis using dichromatic patterns and circuit mapping, has been used to characterize the interface structure of three different CSL tilt grains boundaries around [0001]. This has allowed us to determine the boundary planes and the various step risers that were found to have or not a dislocation character. The Burgers vectors of the primary dislocations have been found to correspond to a pure edge dislocations with

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the 5/7- and 8-atom ring cores. In some of the boundaries, we have pointed out the occurrence of the 4-atom ring core, with the formation of a more complicated configuration, 5/4/7-atom rings in asymmetric boundaries [52]. These observations are probably in agreement with the theoretical analysis of Wright et al. who showed that the core of the edge dislocation may exhibit various atomic configurations depending on the Fermi level [83]. Of course, our observations of the 8-atom ring configuration are also in agreement to the theoretical predictions of Elsner et al. [15], as it is not possible to image the reconstruction along the dislocation line direction using HREM. The technique used here does not show what happens along the dislocation line, so it is not possible to discuss cases such as dimer formation, which eliminates the dangling bonds in the 8-atom core. However, our results probably can assess that the a pure edge dislocation has more than one atomic configuration in contrast to other reports [15, 16]. However, the situation is probably more complicated and the simple cases we have discussed here should be analyzed in more details, taking into account that such configurations as the Ga and N vacancies can be present [84], which complicates the whole picture.

8.7

Acknowledgments

Part of this work was supported by the EU under contract number HPRN-CT1999-00040. This report would not have been written without the contributions of Dr. V. Potin, Dr. P. Vermaut, Dr. A. Béré and B. Barbaray.

8.8

References 1

2 3

4 5

6

7

H. Morkoç, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, and M. Burns, J. Appl. Phys. 76, 1363 (1994). J. Pankove, J. Luminescence 7, 114 (1973). M. E. Lin, S. Strite, A. Agarwal, A. Salvador, G. L. Zhou, N. Teraguchi, A. Rockett, and H. Morkoç, Appl. Phys. Lett. 62, 702 (1993). S. Nakamura, Y. Harada, and M. Senoh, Appl. Phys. Lett. 58, 2021 (1992). F. A. Ponce, D. P. Bour, W. Götz, N. M. Johnson, H. I. Helava, I. Grzegory, J. Jun, and S. Porowski, Appl. Phys. Lett. 68, 917 (1995). P. Vermaut, P. Ruterana, G. Nouet, A. Salvador, and H. Morkoç, Inst. Phys. Conf. Ser. 146, 289 (1995). D. Cherns, W. T Young, and F. A. Ponce, Mater. Sci. Eng. B 50, 76 (1997).

8

9 10 11

12

13 14

15

J. L. Rouviere, M. Arlery, A. Bourret, R. Niebuhr, and K. Bachem, Inst. Conf. Ser. 146, 285 (1995). J. E. Northrup, J. Neugebauer, and L. T. Romano, Phys. Rev. Lett. 77, 103 (1996). S. Tanaka, R. S. Kern, and R. F. Davis, Appl. Phys. Lett. 66, 37 (1995). Y. Xin, P. D. Brown, C. J. Humphreys, T. S. Cheng, and C. T. Foxon, Appl. Phys. Lett. 70, 1308 (1997). X. J. Ning, F. R. Chien, P. Pirouz, J. W. Wang, and M. A. Khan, J. Mater. Res. 3, 580 (1996). F. A. Ponce, MRS Bull. 22, 51 (1997). S. D. Lester, F. A. Ponce, M. G. Crawford, and D. A. Steigerwald, Appl. Phys. Lett. 66, 1249 (1995). J. Elsner, R. Jones, P. K. Sitch, V. D. Porezag, M. Elstner, T. Frauenheim,

8.8 References

16

17

18

19

20

21

22 23

24 25 26 27 28 29 30 31 32 33

34

M. I. Heggie, S. Oberg, and P. R. Briddon, Phys. Rev. Lett. 79, 3672 (1998). Y. Xin, S. J. Pennycook, N. D. Browning, P. D. Nellist, S. Sivanathan, F. Omnès, B. Beaumont, J. P. Faurie, and P. Gibart, Appl. Phys. Lett. 72, 2680 (1998). S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, Y. Sogimoto, T. Kozaki, H. Umemoto, M. Sano, and K. Chocho, Appl. Phys. Lett. 72, 211 (1998). T. S. Zheleva, O. K. Nam, M. D. Bremser, and R. F. Davis, Appl. Phys. Lett. 71, 2472 (1997). D. J. Smith, D. Chandrasekar, B. Sverdlov, A. Botchkarev, A. Salvador, and H. Morkoç, Appl. Phys. Lett. 67, 1803 (1995). B. N. Sverdlov, G. A. Martin, H. Morkoç, and D. J. Smith, Appl. Phys. Lett. 67, 3064 (1995). P. Vermaut, P. Ruterana, G. Nouet, A. Salvador, and H. Morkoç, Phil. Mag. A75, 239 (1997). P. Vermaut, P. Ruterana, and G. Nouet, Phil. Mag. A76, 1215 (1997). H. Blank, P. Delavignette, R. Gevers, and S. Amelinckx, Phys. Stat. Sol. 7, 747 (1964). C. M. Drum, Phil. Mag. A 11, 313 (1965). L. T. Chadderton, A. F. Fitzgerald, and A. D. Yoffe, Phil. Mag. 8, 167 (1963). G. Aminoff and B. Broome, Z. Kristallogr. 80, 355 (1931). S. B. Austerman and W. G. Gehman, J. Mater. Sci. 1, 249 (1966). D. B. Holt, J. Phys. Chem. Solids 30, 1297 (1969). A. D. Westwood and M. R. Notis, J. Am. Ceram. Soc. 74, 1226 (1991). R. C. Pond and D. B. Holt, J. Phys. C110, 43, 57 (1982). Z. Liliental-Weber, M. A. O’Keefe, and J. Washburn, Ultramicroscopy 30, 20 (1989). J. C. Kim and E. Goo, J. Am. Ceram. Soc. 73, 877 (1990). M. Shiojiri, C. Kaito, S. Sekimoto, and N. Nakamura, Phil. Mag. A 46, 495 (1982). D. R. Rasmussen, N. H. Cho, D. W. Susnitzky, and C. B. Carter, Ultramicroscopy 30, 27 (1989).

35

36 37 38

39

40 41

42

43 44

45

46 47 48 49

50 51

52

53 54 55

A. D. Westwood, R. A. Youngman, M. R. McCartney, A. N. Cormack, and M. R. Notis, J. Mater. Res. 10, 1270 (1995). Berger, J. Am. Ceram. Soc. 78, 153 (1995). Y. Yan, M. Tarauchi and M. Tanaka, Phil. Mag. A 75, 1005 (1997). P. Ruterana, P. Vermaut, V. Potin, G. Nouet, A. Botchkarev, A. Salvador, and H. Morkoç, Mater. Sci. Eng. B 50, 72 (1997). Z. Liliental-Weber, H. Sohn, N. Newman, and J. Washburn, J. Vac. Sci. Technol. B 13, 1578 (1995). L. T. Romano and T. H. Myers, Appl. Phys. Lett. 71, 3486 (1997). X. H. Wu, L. M. Brown, D. Kapolnek, S. Keller, B. Keller, S. P. DenBaars, and J. S. Speck, J. Appl. Phys. 80, 3228 (1996). D. Cherns, W. T. Young, M. Saunders, J.W. Steeds, F. A. Ponce, and S. Nakamura, Phil. Mag. A. 77, 273 (1998). V. Potin, P. Ruterana and G. Nouet, J. Appl. Phys. 82, 1276 (1998). I. Akasaki, H. Amano, Y. Koide, K. Hiramatsu, and N. Sawaki, J. Cryst. Growth 98, 209 (1989). P. Kung, C. J. Sun, A. Saxler, H. Ohsato, and M. Razeghi, J. Appl. Phys. 75, 4515 (1994). D. W. Susnitzky and C. B. Carter, J. Am. Ceram. Soc. 69, 217 (1986). R. C. Pond, J. P. Gowers, and B. A. Joyce, Surf. Science 152, 1191 (1985). P. Pirouz and J.W. Yang, Ultramicroscopy 51, 189 (1993). S. Kaiser, H. Preis, W. Gebhardt, O. Ambacher, H. Angerer, M. Stutzmann, A. Rosenauer, and D. Gerthsen, Jpn. J. Appl. Phys. 37, 84 (1998). R.C. Pond and D. S. Vlachavas, Proc. Roy. Soc. A 386, 95 (1983). R. C. Pond, in: Dislocations in Solids, Vol. 8, p. 1, edited by F. R. N. Nabarro (North Holland, Amsterdam, 1989). V. Potin, P. Ruterana, G. Nouet, R. C. Pond, and H. Morkoç, Phys. Rev. B 61, 5587 (2000). J. P. Hirth and R. C. Pond, Acta Mater. 44, 4749 (1996). R. C. Pond, Interface Science 2, 1 (1995). T. Braisaz, P. Ruterana, G. Nouet, and R. C. Pond, Mater. Sci. Forum 207, 113 (1996).

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8 Extended Defects in Wurtzite GaN Layers: Atomic Structure, Formation, and Interaction Mechanisms 56 57

58 59 60

61

62

63 64

65

66 67

68

69 70

A. Serra and D. J. Bacon, Phil. Mag. A 73, 333 (1996). J. P. Hirth and J. Lothe, in: Theory of Dislocations, 2nd ed, p. 354 (Wiley Interscience, New York, 1982). J. L. Rouviere, M. Arlery, and A. Bourret, Inst. Phys. Conf. Ser. 157, 173 (1997). V. Potin, P. Ruterana, and G. Nouet, Appl. Phys. Lett. 74, 947 (1999). P. Ruterana, V. Potin, and G. Nouet, Mater. Res. Soc. Symp. Proc. 482, 435 (1998). P. Vermaut, P. Ruterana, G. Nouet, and H. Morkoç, MRS Internet J.N.S.R. 1 art. 42. A. P. Sutton and R. W. Balluffi, Interfaces in Crystalline Materials (Clarendon, Oxford, 1995). F. Sarrazit, R. C. Pond, and N. A. Kisilev, Phil. Mag. Lett. 77, 191 (1998). Th. Kehagias, Ph. Komninou, G. Nouet, P. Ruterana, and Th. Karakostas, Phys. Rev. B, 64, 195329 (2001). V. Narayanan, K. Lorenz, W. Kim, and S. Mahajan, Appl. Phys. Lett. 78, 1544 (2001). V. Potin, P. Vermaut, P. Ruterana, and G. Nouet, J. Elect. Mater. 27, 266 (1998). Z. Liliental-Weber, C. Kisielowski, S. Ruvimov, Y. Chen, and J. Washburn, J. Electron. Mater. 25, 1545 (1995). N. E. Lee, R. C. Powell, Y. W. Kim, and J. E. Greene, J. Vac. Sci. Technol. A 13, 2293 (1995). C. Stampfl and C. G. Van de Walle, Phys. Rev. B 57, R15052 (1998). G. Salviatti, M. Albrecht, C. ZanottiFregonara, N. Armani, M. Mayer, Y. Shreter, M. Guzzi, Y. V. Melnik, K. Vassilevski, V. A. Dmitriev, and H. P. Strunk, Phys. Stat. Sol. A 171, 325 (1999).

71 72

73

74

75

76 77

78 79

80

81 82

83 84

V. Potin, P. Ruterana, and G. Nouet, J. Phys. Condens. Mater. 12, 10301 (2000). K. Lorenz, M. Gonzalves, W. Kim, V. Narayanan, and S. Mahajan, Appl. Phys. Lett. 77, 3391 (2000). P. Ruterana, V. Potin, B. Barbaray, and G. Nouet, Phil. Mag. A 80, 937 (2000). J. C. H. Spence and J. M. Zuo, Electron Microdiffraction (Plenum Press, New York, 1992). R. Serneels, M. Snykers, P. Delavignette, R. Gevers, and S. Amelinckx, Phys. Stat. Sol. (b) 58, 277 (1973). V. Potin, P. Ruterana, and G. Nouet, Phil. Mag. A 79, 2899 (1999). F. A. Ponce, D. P. Bour, W. T. Young, M. Saunders, and J. W. Steeds, Appl. Phys. Lett. 69, 337 (1996). B. Daudin, J. L. Rouviere and M. Arlery, Appl. Phys. Lett. 69, 2480 (1996). L. T. Romano, J. E. Northrup, and M. A. O’Keefe, Appl. Phys. Lett. 69, 2394 (1996). A. M. Sanchez, P. Ruterana, G. Nouet, S. I. Molina, F. Pacheco, and R. Garcia, Appl. Phys. Lett. 79, 3588 (2001). P. Vermaut, Ph. D. thesis, University of Caen, France, 1997. P. Ruterana, A. Béré, B. Barbaray, G. Nouet, A. Hairie, E. Paumier, A. Salvador, A. Botchkarev, and H. Morkoç, Phys. Rev. B 59, 15917 (1999). J. E. Northrup, Appl. Phys. Lett. 72, 2316 (1998). A. F. Wright and J. Furthmuller, Appl. Phys. Lett. 72, 3467 (1998).

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Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-based Epitaxial Layers Slawomir Kret, Pierre Ruterana, Claude Delamarre, Tarek Benabbas, and Pawel Dluzewski

Abstract

This chapter presents recent developments on techniques that can be used to determine the local strain, chemical composition or atomic structure retrieval in high-resolution electron microscopy (HREM). The source of noise in images and effective methods for improving the signal-to-noise ratio in direct or Fourier space are discussed. The artefacts of filtering are discussed. A detailed analysis of the thin-foil relaxation effect on the measured distortion fields is presented as well as the possibilities of using the finite element calculations for its modeling. The local composition measurement based on the chemically sensitive reflections, pattern recognition and the measurement of lattice parameters are described. Examples from semiconductor heterostructures are used to illustrate the different procedures. A particular emphasis is put on the latest results in GaN layers and its alloys with In or Al, where there are still high densities of defects and composition fluctuations inside quantum wells.

9.1

Introduction

During the last decade, gallium-based nitrides have been the subject of an important research effort due to their high potential for applications in optoelectronics, power devices, and detectors [1, 2]. On one hand these semiconducting materials

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

have a band gap that extend from red (InN: 0.8 eV) to the UV (AlN: 6.2 eV) and, therefore, they may cover a large range of the spectrum for emission and detection. On the other hand, they do not exist as bulk materials and they are essentially grown by epitaxy on a large variety of substrate, which exhibit large lattice and thermal mismatch. The active layers contain huge amounts of crystallographic defects of three types: the threading dislocations, the inversion domain boundaries, and the stacking faults. Using the conventional HREM of image simulation in combination with atomistic modeling, it was shown that many atomic configurations of these defects coexist inside the GaN epitaxial layers [3–5]. It is expected that the various configurations will affect the device properties in different ways. A quantitative assessment of these configurations would be of great importance in order to accurately know the mechanisms that underlie their influence on the performance of the devices [6]. Moreover, it is suspected that the high brightness of the ternary InGaN layers that constitute the emitting part of the lasers and electroluminescent diodes is due to high localization of the carriers inside In rich clusters. Although, strain [7] and QUANTITEM [8] measurements have already pointed out that segregation of In does take place in the ternary layer, the nature, size, and geometry of the elemental emitter is still the subject of controversy [9, 10]. This chapter briefly reviews methods of quantitative analysis and extraction of information from high-resolution electron microscopy (HREM) images. Our attention will be focused on the efficient ones, which are currently used for characterization of structure parameters and processes in semiconductor heterostructures at atomic scale such as: · chemical composition, diffusion, and segregation in ternary systems: InGaAs, CdZnTe, InGaN, etc. · atomic configuration of defects: dislocations, grain boundaries, stacking faults, etc. · mapping of localized distortion fields. Most of the presented methods were invented a few years ago. However, during the last decade, the availability of high-performance computers and the improvement in the point-to-point resolution of the microscopes have been leading factors for the development of practical tools and their use in material science laboratories as standard characterization tools. Currently, the local lattice distortion measurements are efficient in the study of quantum-well structures of II–VI and III– V semiconductors in particular for chemical profiles in ternary alloy systems [11– 13]. The atomic configurations of a number of defects and interfaces are resolved using approaches based on the optimization and matching between simulated and experimental images [14]. So far, the methods based on the exit-face wave reconstruction by focal series [15] or holography have been demonstrated in a number of experimental reports solving structure of perfect crystals, as well as for simulated and experimental images of defects [16, 17]. Most of the methods developed for III–V and II–VI semiconductors can be easily adopted to GaN-based semiconductors.

9.1 Introduction

The quantitative information that is made available by high-resolution electron microscopy (HREM), is mostly: atomic structure, lattice parameters/strain, and chemical composition. Of course, the high-resolution image is a two-dimensional intensity pattern coming from a complex interference of the electron beams exiting from the analyzed sample. The electron wave function at the exit face of the thin foil contains the required information: wexit (structure, composition, and thickness). The objective lens (spherical and chromatic aberration, etc.) of the microscope plays a critical role in the image formation process, along with the coherence of the incident electron beam. The amplitude of the wave function in the image plane can be written as:  T …imaging conditions) , wimage ˆ wexit where T is a function of the objective lens defocus df and of partial spatial and temporal coherence of the incident electron wave. In the image plane, the intensity is usually recorded either on negative films, or more recently by use of CCD cameras. Therefore, the HREM micrographs are made of maxima and minima of intensity due to interference:  jwimage j2 ˆ wimage
wimage ; which may or may not be coincident with lattice fringes or atomic positions. Depending mostly on the foil thickness, two types of interference images are formed: (i) the linear image corresponds roughly to the interference of the dominant transmitted beam and Bragg reflections, (ii) whereas the nonlinear image forms by that of the different reflections, complicating the pattern and the subsequent interpretation in terms of atomic structure. Until the 1990s, structural analysis of materials on the atomic scale had been limited to fundamental studies concerned mainly with the atomic configuration of extended defects. The consequence was the development of image-simulation softwares as soon as the point-to-point resolution of the microscopes became smaller than 0.3 nm [18], using the formalism of optical physics proposed by Cowley in the late 1950s [19]. This multislice formulation of the wave-function interaction and propagation through the thin foil is still basically used, as it is the only way to deal with the image simulation of the atomic structure of crystallographic defects. At the same time and mainly for optimization of computing time, Van Dyck [20] demonstrated that the exit phase wave function could be calculated by solving the electron Schrödinger equation in the real space. With the first microscopes approaching 0.2-nm resolution, it was possible to investigate a number of grain boundaries [21] using the dislocations models that had been proposed before [22]. Since then, the multislice and the Bloch wave formalism [23] were put into image simulation software [18, 24] and the first packages for digital image processing be-

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

came available [25]. From the start, it became clear that the construction of geometrical models for the investigated defect could not represent the real structure and there was a large effort on modeling in order to generate structures as close as possible to thermodynamic equilibrium. A number of results were reported for the core structure of defects and interfaces using nonlinear elasticity-calculated models in metals [26] and semiconductors [27]. It was possible to show that the anisotropic elasticity may describe the structure of a Lomer dislocation even inside the core [28]. However, apart from these particular cases, it was necessary to develop more robust tools for modeling the atomic structure of the defects and the grain-boundary community played a very important role in this work. The description of interfaces and defects needs to minimize the energy of a large number of atoms; therefore a large amount of work was done using empirical potentials. This led to a reasonable knowledge of atomic structure of defects, like twins [29–31], and more complex interfaces in metals [32] and oxides [33]. In the 1980s, with the advent of ultralarge-scale integration of circuits, the elemental semiconductor components were brought close to a few tens of nm and the interfaces begun to play an important role. In optoelectronics, the latest growth methods were pushed to allow the control of layer thickness and/or chemical composition within one atomic layer. From then on, quantitative characterization on the subnanometer scale has become a key issue for the future progress in device performance and reliability. In the last decade, a number of suitable methods were developed and the point-to-point resolution of the electron microscopes went below 0.2 nm. Today, the limit of information is approaching 0.1 nm for the latest field emission gun microscopes.

9.2

Suitable Images for Quantitative Analysis

Using latest high-resolution microscopes, for most of the semiconductor materials, it is always possible to find a zone axis that is suitable to study a particular problem and obtain the lattice fringe images (interference of two beams) or structural images (many-beam interference). Of course, a resolution better than 0.1 nm would give access to more zone axes, leading to possible reconstruction of the 3D structure of many defects. Due to complex dynamical diffraction, the foil thickness should be less than *15 nm for medium-voltage microscopes and less than *30 nm for high-voltage instruments (one extinction distance) when medium-range atomic number (Z) materials are observed. For thicker samples, interpretation of images is complicated, due to parameters, which are difficult to control and/or include in models (crystal or beam tilt, inelastic and thermal diffuse scattering, etc.). Most of the useful methods are based on the analysis of small numbers of images obtained in optimal conditions. This optimization is needed for methods based on analysis of difference of image templates due to chemical sensitive reflections [34]. In this case, the voltage, defocus, and thickness will be chosen for maximizing the contribution of chemically sensitive beams. For lattice-

9.2 Suitable Images for Quantitative Analysis

distortion mapping, structural-imaging conditions will be favorable [35], when the images have as simple as a possible template with maximum contrast and minimum contribution of chemically sensitive reflections. Möbus and Wagner [36] proposed a procedure that adapts voltage and thickness in order to provide maximum excitation of the main beams (structural beams at half of their extinction distances) for optimal accuracy in structural determination. Some methods use series of images taken with different defocus (exit-wave reconstruction from focus series [37]), but generally defocus values should be low to minimize the image delocalization. This effect becomes important at interfaces with sharp chemical transitions, as shown by Lichte [38] and Thust et al. [37]. A formal definition of delocalization as a property of contrast transfer (wave aberration) was introduced in Coene et al. [15] and Zandbergen et al. [39]: @v R ˆ ˆ jCs k3 g 3 ‡ kDfgj ; @g where Cs is the spherical aberration constant, k the electron wavelength, and Df the defocus. This equation represents a spatial delocalization imposed by the microscope on a certain spatial frequency g. The delocalization is minimized for a particular g at a defocus of Df ˆ

Cs k2 g 2 :

The delocalization causes atomic displacements in the real object structure, relative to a reference structure as investigated by Möbus and Wagner [36] using the geometrical-phase method [40] for a series of possible 0.1-nm resolution microscopes. Delocalization at abrupt interfaces (GaAs/AlAs) and microscopes with field emission guns was shown by Stobbs et al. [41] to take place in a few monolayers (1 to 2). The most important experimental factor for the image to be suitable for quantitative evaluation is the quality of TEM sample. Generally, samples with slow rise in thickness and very thin amorphous layer are necessary. It is therefore crucial to optimize the sample preparation for each studied material. There is no processing or filtering method that can give good results when the amorphous or contamination layers are thick. For quantitative analysis, the sample thickness must be known and during the image acquisition, it is important to have sufficiently large areas in order to clearly see the changes of image contrast with sample thickness. Indeed, most suitable methods for determination of thickness are based on the thin-foil geometry reconstruction at large scale (see Sects. 9.6 and 9.7).

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9.3

Digitization

The digitization of the image is the first step in quantitative evaluation, negative electron films and slow scan cameras are the most used media to record images in HREM, the image plates are not yet so widely used. In agreement with the Shannon sampling theorem, a minimum of two samples for the highest image periodicity is required. In practice, Seitz et al. [42] pointed out that the precision of contrast maxima localization could only be improved up to 60 pixels per lattice distance. A review of the literature shows that the sampling used for digitization is up to 20–25 pixel Å–1 in the study of atomic configurations and 4–10 pixel Å–1 for long-range lattice distortion mapping. Sampling should never be lower than 4 pixels per lattice period. The size of images is generally limited to 2048 ´ 2048 pixels. The relatively small dynamic of HREM images makes the electron films a good enough medium for recording. The digitalization of negatives can be done directly with densitometers as by Möbus and Rühle [43]. The comparison of the densitometer (Perkin-Elmer 1010GM PDS and professional CCD scanner LeafScan45) for electron microscopy application was made by Mitsuoka et al. [44]. In many cases, cheaper solutions can be used as CCD cameras with highquality optics or even desktop publishing scanners with resolution starting from 1200 dpi for lattice distortion measurement. Similar comparison of scanners can be found in Ref. [45]. When using a scanner, it is important to verify the uniform displacement rate of the CCD row. The optical density of the film is calculated from the transmitted data using the equation OD(x,y) = Log10(T(x,y)/T0), where T(x,y) is the transmittance of the digitizing device and T0 is the transmittance in the nonexposed border of the film. Some scanners introduce automatic correction on digitized data, which must be known, unfortunately it is not always easy to obtain such details from manufacturers. According to many investigations [36–38, 46–48], the relation between the optical density OD(x, y) and the electron density j(x, y) can be approximated by the nonlinear relation: OD…x; y† ˆ OD0 …1

e

ctj…x;y†

†;

where t is the exposure time and c (“speed”) is a coefficient characterizing the sensitivity of the photographic emulsion. If the measured transmitted intensity T(x, y) is used to determine j(x, y), then the nonlinearities as well as the “Callier effect”, must be taken into account, especially in the case of using films to record electron holograms [49]. If quantitative comparison of absolute image intensity with simulations is to be done, a linearization of the image is necessary; this can be done using calibration curves [50]. If only the position of image contrast maxima is required, such correction is not necessary. Some authors even consider the electron film negatives sufficiently linear in HREM density range and use them for direct atomic configuration retrieval [43].

9.3 Digitization

The spiral distortion of the projection lens introduces long-range distortion in the image. The magnitude of the distortion varies with distance from the center of the plate and depends on the instrument used [50]. This and other artificial distortions from the scanner or optical system of CCD camera used for digitization, which is specific of each device and magnification, can be corrected with the procedure that has been described in detail by Campbell et al. [51]. When investigating the short-range local distortion, the correction can be made at the end of processing. Formally, the transfer function of a digitizing device can be deconvoluted; however, it is not always easy to measure this transfer function with enough precision, and in practice, such deconvolution may introduce additional errors by subtracting useful information. It is useful to make normalization of optical density data between 0 and 1, especially if comparison with simulations has to be done. The 1 is attributed to the intensity of electron beam in the hole near the sample border and zero to the density level of the nonexposed area of the film [52]. A thorough discussion of the different normalization methods used in quantitative comparison of the experimental and simulated images can be found in Ref. [53]. For lattice distortion measurements such corrections are not really necessary, processing can be done directly on the raw data from the digitizer. In fact, this technique is based on the measurement of the contrast maxima position or local lattice periodicity. These parameters are not very sensitive to device nonlinearity. Moreover, after processing, the obtained maps of lattice distortion show all artificial distortion at large scale, thus such artefacts can be subtracted at the end of processing giving only the local lattice distortion that is of interest. In general due to different effects (sample thickness changes, amorphous layers, etc.) only localized lattice distortion in areas of about 50 ´ 50 nm2 can be measured precisely. Advantages of electron films · large area in one shot, possibility of taking border and region of interest on same image, · offline choice of areas adequate for analysis, · sufficient linearity for many HREM applications, · good resolution (up to 5 ´ 5 lm2 pixel, however, with low dynamic range), · information capacity up 500 Mb/film up to 12 000 ´ 18 000 image size, · use at relatively small magnification ´ (400–600) k. Disadvantages · digitization required, · not fast enough for image series, · development required, · possible noncontrolled deformation due to wet processing. Advantages of slow scan CCD cameras · linear response to electron dose, · automatic and fast image series, · direct image access, no intermediate operation.

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Disadvantages · large pixel 25 ´ 25 lm (but high dynamic range), · small image 1024 ´ 1024 (or 2048 ´ 2048), · high magnification required to obtain sufficient sampling > ´ 600 k. The image plates (IP) that have been introduced quite recently in the TEM field are an intermediate case, they have a larger area than CCDs (3760 ´ 3000), good linearity and dynamic, but like negatives, the gain variation cannot be normalized easily. In the case of the negatives, which may be digitized with high resolution, the grain nature of emulsion leads to reduced dynamic range and the signal-to-noise ratio is small. For similar sizes of pixel, the CCD and IP have better dynamics and signalto-noise ratio. In a near future due to progress of resolution, sensibility and larger surface, the CCD and CMOS detectors will probably dominate, eliminating the postprocessing necessary in the case of films and image plates.

9.4

Noise

On high-resolution images, the most important noise is due to thin-foil irregularities; ion-beam thinning gives rise to an amorphous layer of a few nanometers thickness [54]. The thickness ratio between the amorphous layer and the crystalline part varies locally and can lead to fluctuation in the image contrast [55]. Contamination and irradiation damage from the high-energy electrons during observation is another source for degradation of the image contrast. The irradiation damage leads to the formation of defects inside the thin foil and modifies the sample structure in a complicated way. Of course, such noise strongly depends on the observed area and for each analyzed image, the noise has to be determined locally. The various types of noise are difficult to separate and eliminate, for example, partially amorphized material gives a contribution to the spatial frequencies that is very close to that from nondefective but deformed areas of the sample. Other types of noise are: · Quantum noise (shot noise). Such noise gives rise to strongly localized large intensity variation in HREM images (1/10 of interatomic distance). In such areas, the intensity can be more than an order of magnitude larger than the mean value. Applying a median filter in the real space or a low-pass filter in the reciprocal space eliminates this noise. · The noise is due to the size and statistical distribution of the grains in the photographic emulsion. It is dependent on the film quality, exposure and development conditions, as well as on the ratio between the microscope and optical (during digitization of the negative) magnifications. There are two main approaches for improving the signal-to-noise ratio: (i) filtering in the reciprocal space, or (ii) averaging many images of identical motifs in the real space by translation and superposition on the image.

9.4 Noise

One may also use the filtering based on the principle of spatial signal continuity, i.e., using the value of neighbor pixels for the calculation of the value for a given pixel. This is done by convolution of the image by a small (Gaussian, spherical, linear, etc.) 2D kernel [56]. Other filters that can reduce noise in the real space are the so-called neighborhood ranking filters. Examples of such filters are median filter, Olympic filter, and “rolling ball filter” [56]. Application of this type of filters in HREM is limited to elimination of shot noise. The most effective procedures of filtering noise in real space are the averaging of periodic image motives. Cross-correlation is used to determine the corresponding position of the motives as shown in Fig. 9.1. From the 17 images of Fig. 9.1, the noise reduction is seen to improve as the number of averaged images increases (Fig. 9.1 b: 2, 5, 8, 11, and 14 images). This method was applied to zeolite images, which are usually noisy, in order to improve the signal-to-noise ratio for atomic structure retrieval, as well as to grain boundaries. In this noise p reduction, the random errors in the intensity distribution is proportional to 1 N (where N is the number of images). In fact, most filtering is done in Fourier space, where the information from crystal and amorphous layer is easy to separate. In amorphous layers, the noise coming from grains of the emulsion and detector noise is distributed all over the spatial frequencies, whereas the information coming from a crystal is located near Bragg spots. The straightforward way of noise reduction is to select circular regions around Bragg peaks in the Fourier amplitude image and use the inner pixels for inverse transform. This filtering is suitable for images of a perfect crystal and periodic windowing. However, in general, the areas of interest are arbitrarily chosen and the periodicity of the crystal is broken on the borders. This gives rise to streaks across the Bragg spots in the FFT. This effect can be damped if the image is multiplied by a circular, Hanning or other type of window that gradually reduce the intensity to a constant value (0, mean value, etc.). In the case of nonperiodic features like dislocations, interfaces or grain boundaries, characteristic “streaking” is present, applying small circular masks in Fourier space can delete this useful information. On the other hand, using large circular masks will reduce the efficiency of the filtering. One way of solving this problem is the “adaptive filter” proposed by Möbus et al. [57]. A filter is adaptive if it is characterized by the following three conditions: (i) the shape of the filter mask is adapted to the spectrum of the image, (ii) the mask is generated by the spectrum of the image, (iii) the windows of the mask are automatically placed at all positions, which allows an optimal separation of signal from noise. Another efficient filtering method in Fourier space is the Wiener-type filter, where the noise level is estimated locally in the FFT image and for each spatial frequency, the amplitude of the FFT is compared to the estimated noise level. A filter F acts on the image I to yield an estimate S of the true signal St contaminated by a certain noise g where:

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

A set of 17 elementary images extracted from a high noise image by crosscorrelation: a The 17 templates; b reduction of noise by averaging, with 2, 5, 8, 11, and 14 images. The raw HRTEM image used in this example was recorded by J. Y. Laval from a spin ladder compound SrCuO.

Fig. 9.1

FI ˆ S and I ˆ St ‡ g : The conventional Wiener filter is generated by looking for the filter, which minimizes:

9.4 Noise

X Wˆ …FI

St †2 ;

and assuming that the signal and noise are not correlated, the appropriate solution is: F ˆ jSe j2 =jIj2 ; where Se is an estimate of the signal. A conventional choice of this is:  jSe j2 ˆ

jIj2 0;

jgj2 ;

jIj > g : jIj < g

There are a number of methods for estimating the noise in the reciprocal space, the most used ones are those based on radial averaging of the amplitude without introducing the Bragg peaks in the calculation. The mean profile is approximated by a linear, Gaussian or exponential function and extrapolated by rotation of the obtained curve about the center of the calculated Fourier transform. Recently, Rosenauer et al. [58] proposed the following way for noise reduction: the power spectrum is divided in domains of equal size An (Fig. 9.2 a). This size has to be larger than the maximum extension of Bragg peaks. Next each area is subdivided into blocks Bm. For each block, the intensity IBm is calculated as the average over all pixels in the block. The mean value of intensity in domain An is calculated using the following equations: IAn ˆ

1 X wBm IBm ; wBm ˆ max…IBm † Bm W Bm

IBm ‡ 1; W ˆ

X

wBm :

Bm

The weight coefficient wBm insures that the blocks containing Bragg peaks (wBm  1) contribute negligibly to the calculation of the noise, in contrast to those of low intensity:   wBm  max …IBm † : Bm

The values IAn correspond to the estimated noise jgj2 in the centers of domains An …kx ; ky †, where kx ; ky are frequencies. The efficiency of this type of filtering is demonstrated in Fig. 9.2 c and d, which show the power spectrum along with the inset of a HREM image. As can be noticed in the original image (Fig. 9.2(b)), applying the Wiener filter dramatically reduces the noise in the generated power spectrum and image (Fig. 9.2 c). A review of the efficiency of other variants of the Wiener filter (parametric, parametric random-phase, Cannon) was given by Marks [59]. He estimated the improvement of the signal-to-noise ratio by a factor 3–7 (depending on how the estimated noise is related to the true noise). The comparison of the background subtracting filter and Wiener filter was given by Kilaas and Radmilovica [60].

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

Noise reduction by Wiener filtering: a) FFT of a HREM image of sphalerite structure along the [110] zone axis, b) 3d visualisation of part of FFT spectrum (white frame in a), c) spectrum and image before filtering, d) after filtering.

Fig. 9.2

Artefacts in Fourier filtering are connected with precise separation of the signal and noise. Here, the signal is proportional to the size of the area of particular periodicity. Small crystals inside a matrix or locally deformed zones produce signals below the noise level. Thus, some knowledge of the signal characteristics is needed in order to devise masks that conserve part of the noisy spectrum suspected to contain the signal. However, this procedure is dangerous as artificial structures from amorphous signal can be generated. In the geometric-phase methods the global averaging of information can reduce local fluctuations of the displacement field (see Sect. 9.5.4).

9.5 Strain Measurement

9.5

Strain Measurement 9.5.1

Domain of Application

The local stress fields play an important role in the formation of nanostructure materials, their mechanical and electronic properties. For example, the stress-induced diffusion and mass transport during growth is responsible for the self-organization and growth of quantum dots in epitaxy of ultrathin crystalline layers with large lattice mismatch. Fundamental research is of great importance in order to understand the mechanisms underlying defect formation, thin-film growth in semiconductor materials, and eventually to help to improve the quality of electronic devices. The stress can induce a band-gap modification in the semiconductor, thereby changing the transport and optoelectronic properties. On the other hand, too large a stress leads to defects nucleation inside the epitaxial layers, decreasing the carrier mobility and resulting in poor-quality devices. In TEM, the diffraction contrast is very sensitive to strain fields and, from the beginning, this strain field was visualized. It is possible to obtain quantitative information about the strain fields by simulation of diffraction contrast images; of course the resolution of this measurement is limited to a few nm [61]. 9.5.2

Assumptions

Attempts at measuring local crystal distortions on HREM images have been made for many years [62]. It is the development of larger-scale computing facilities that has allowed the possibility to build high-performance methods for HREM image analysis. Most of these methods are based on the assumption that there exists a direct relationship between the local maxima or minima of intensity and the local crystal structure [11]. In practice, the positions of the intensity maxima are used to obtain a lattice that represents the dimensions of the projected unit cells. The positions of the intensity maxima may correspond to the location of the atomic columns, the tunnel sites and sometimes to neither of them. This assumption is not always valid, it has long been known, for example, that in the case of off-axial imaging lattice fringes shift due to thickness variation and the measured lattice parameter depends on the gradient of the complex transfer function [63]. Image simulations for axial HREM show that the lattice spacing measured in thin multilayers depends on the imaging conditions [64, 65], particularly for noncentrosymmetric structures [35]. Hÿtch and Plamann [35] give practical rules for minimizing errors:

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

· choosing conditions (thickness and defocus) where the fringe contrast is maximal, this minimizes the symmetry-breaking effects and reduces the gradient of the effective lens transfer function, · avoiding regions where the fringe contrast changes rapidly. It is clear that near defects or abrupt interfaces these empirical rules must be verified carefully by image simulations. 9.5.3

Peak-finding Procedure 9.5.3.1 Overview

This approach is currently used in many laboratories to study localized strain fields in materials. It is similar to that proposed by Bierwolf et al. [11] who developed and applied image-processing techniques in order to analyze the strain state in semiconductor heterostructures along the [110] projection. It consisted of filtering out the frequencies below 2.0 nm–1 and above 4.5 nm–1, next they used a routine for reinforcing the contrast in order to determine the positions of the maxima. The deformation of the crystal was measured by generating a Moiré pattern after superimposition of an ideal lattice extrapolated from the nondeformed area. They measured the interfacial strain inside buried ultrathin layers of Si inside InAs and thick GaAs layers, where the misfits are 7.5% for GaAs/Si and 7.0% for GaAs/InAs. They determined the maxima within 0.5 pixel (0.0085 nm) and the lattice parameters of the reference lattice with an accuracy of better than 0.5%. They also showed that the average deformation over one monolayer (a fraction of one pixel) depends on the sampling. In the approach proposed by Jouneau et al. [66], the positions of the maxima were calculated directly on the images without any filtering, just by finding the center of mass around the pixel of highest intensity. They limited the search in a circle of a radius equal to half the distance between two peaks. The search was carried out recursively until attaining stable positions. They next measured the displacement between the ideal lattice and the calculated network. The local deformation was deduced as the derivative of the displacements. The signal-to-noise ratio was improved by averaging the local distortions along the row of atoms perpendicular to the growth direction. This was applied to pseudomorphic ZnTe/ CdTe and MnTe/CdTe multilayers where the average distance of the {002} lattice planes was measured within 0.002 nm accuracy. Another recursive algorithm allowing the centers of mass of intensity on a raw image to be found was proposed by Seitz et al. [67]. It was applied for the characterization of Inx1Al1–x1As/Inx2Al1–x2As (x1=x2) heterostructures along the [100] projection with a detection limit of 2.8% and a spatial resolution of 0.4–0.4 nm2. It was shown that the error along the interface could be reduced by averaging, then a deformation close to 0.2% could be measured with a resolution of 0.4 ´ 35 nm2. In the digital analysis of lattice images (DALI) algorithm developed by Rosenauer et al. [58], after using a Wiener filter, the maxima positions are de-

9.5 Strain Measurement

termined by calculating the intersection of four parabolas crossing the highest contrast pixel at 45 8. For each parabola, the position xn,yn (n = 1, 2, 3, 4) and root mean square rx, ry are determined. The value |r| is taken as the accuracy on the position of the contrast maxima. Typical values are |r| = 0.003 nm. However, the residual noise introduces an error of 0.01 nm. This error has been estimated by comparing the calculated and measured position inside nondeformed areas. DALI was used to characterize ZnSexTe1–x/ZnSe multiquantum wells [68], and to investigated diffusion of Cd in CdSe/ZnSe [69], as well as the relaxation of strain in Ga0.4In0.6As islands grown on GaAs [70]. Kret et al. [71] used a two-dimensional mapping of the distortion in a GaAs/InGaAs-coherent island coupled with finite element calculations to determine the distribution of indium in the island.

9.5.3.2 Procedure

The typical procedure of local lattice distortion measurement by the peak-finding procedure consists of: · · · ·

selection of the area of interest, noise reduction (optional), detection of the lattice sites, choice of a reference area and calculation of the basis vectors of the reference lattice, · extrapolation of the reference lattice to the deformed zones and calculation of the displacement vector of each experimental lattice sites, · calculation of the lattice distortion or local lattice parameter by derivation of the displacements. A. Selection of Area of Interest The main criteria are the foil thickness and the amount of the amorphous layer. It is recommended to avoid areas in which the thickness increases rapidly, especially if the thickness changes are perpendicular to interfaces or the quantum well of interest. The processed zone should be larger than the analyzed object in order to avoid confusion between the lattice distortions due to long-range variations of imaging conditions and the real localized strain. In the following paragraphs, we use an InGaAs island grown on a (001) GaAs surface (Fig. 9.3) to illustrate the different steps of this technique.

B. Noise Reduction The accuracy of the localization of the image maxima depends on the noise level that is determined mainly by the ratio between the amorphous layer and crystal thickness in the thin foil. As was shown by Seitz et al. [42], the detection limit of the maxima positions on nonfiltered images is r = 7% of lattice parameter for ionmilled samples and r = 2.4% for a cleaved Si sample. This level of noise is for many cases higher than the amplitude of the distortion to be measured. Some

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

A coherent, noncapped island GaAs/InGaAs, the nominal In composition is 35%: a reference area inside GaAs; b zone of interest for strain analysis.

Fig. 9.3

authors accept this and reduce the noise at the end of the processing by one-dimensional averagingpof  final distortion or displacements [67]. In this case, the error is reduced as r= N , where N is the number of averaged values. The shifts of the maxima positions of intensity due to noise in a perfect crystal lattice are random. If the average shift is r the lattice parameter a can be determined with high accuracy by measuring d = Ma, the mean value of the lattice parameter is then a ˆ d=M, within an error of Da ˆ r=M. In a crystal with deformation, the local measured aM i;j is attributed to the lattice site xi,j,yi,j. Obviously, if the lattice parameter changes at distances smaller than d ˆ Ma, its variations will not be precisely determined. This type of approach is adequate for the study of longrange strain fields and even small changes can be detected. Its extension to the local displacement field measurement is discussed in Sect. E. If local lattice parameters have to be measured, noise reduction is necessary. Paciornik et al. [72] applied the Gaussian filter in real space in order to reduce the shot noise prior to calculation of the center of gravity. Rosenauer et al. [58] used Wiener filters with the local noise-level estimation in Fourier space before maxima localization. Kret et al. [71] proposed to reduce the noise in two steps: i) start by using a parameterized Wiener type of filter in Fourier space, in order to reduce the effect of global averaging of information introduced by this type of filter; ii) reduce the fluctuations in the displacements by 2D local averaging in real space.

9.5 Strain Measurement

The reduction of the “force” of the Wiener filter protects from subtraction of the information coming from small highly deformed regions of the sample that produce small signal in Fourier space near high Bragg peaks and are often difficult to be separated from the noise. C. Detection of the Lattice Sites A number of methods can be used for the localization of the maxima of intensity in HREM images. After Fourier filtering, the pixel of maximum intensity can give this position within 0.5-pixel accuracy. This method has been applied by Bierwolf et al. [11]. In contrast, the pixel of maximum intensity can be far from the center of the features of maximum intensity in a raw high-resolution image, within 2–3 pixels. Much work has been devoted to finding techniques in order to accurately locate the centers of the maximum intensity in raw HREM images: C.1 Mass center The mass center ~ C of an image region is defined by

~ Cˆ

 X ~ ri † ri I…~ ~ ri 2 image region

X

I…~ ri † ~ ri 2 image region

ri † its intensity. To evaluate the positions of where ~ ri is the pixel position and I…~ maximum intensity, mass centers are calculated inside image regions that are frequently chosen with circular shapes. The results obtained by this technique are only meaningful when the probe circle encloses the real position. The choice of the circle radius is also very important: our tests show that the position of this center, when determined by different radii, may be located within 0.5–2 pixels depending on the quality of the image. A radius of 0.5 interatomic distance is the most frequently used. In order to minimize the error on the starting position, Jouneau et al. [66] successively used a recursive method, which calculated the starting position at each step until a stable position is obtained. Of course, this procedure does not eliminate the error due to the shot noise. Therefore, if a pixel located far from the center has a high intensity, the gravity center can be artificially displaced. C.2 Calculation of the mass center of a contour around the maxima of contrast Stenkamp and Jäger [73] preferred to calculate the center of mass within a contour around the maxima of intensity position. In order to draw this contour, they calculated the switch from positive to negative values for the curvature of all the intensity profiles through the maxima of intensity using a Laplacian operator. In the image, the Laplacian-based edge detection operator points out the geometrical centers of the bright dots above atomic or tunnel positions.

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

C.3 One-dimensional profiling Seitz et al. [67] used many one-dimensional profiles across the maxima of intensity, starting with the pixel of maximum intensity and taking it as the starting point for the next iteration. The process stops when the two last positions are coincident within the desired accuracy. Rosenauer et al. [58] used a similar approach: polynomial fitting along 4 different directions on a filtered image. C.4 Fitting a 2D function z = f(x,y) to the intensity distribution This method attempts to minimize the expression

X …f …x; y†

I…x; y††2

i

for all the pixels considered. The maximum of f(x, y) provides the desired center of mass. Various forms of two-dimensional functions can be used, for example, Gaussian, polynomial, or such as the intensity distribution obtained by image simulation and even by averaging inside a unit cell [42]. D. Reference Area and Calculation of the Base Vectors The reference area is chosen on the same image as the evaluated region, but outside of the deformed regions. Of course, this may be difficult to fulfil in practice due to relatively long-range propagation of the distortion fields and limited size of constant imaging conditions. Finally, the compromise must be made on the leastdeformed zones near the area of interest. Depending on the uniformity of the thickness, the optimal number of atomic columns inside the reference area can be from 1000 to 4000 [74]. The error in the reference will give a constant contribution to the measured distortion field quite simple to detect and subtract. Different types of lattices can be used for distortion measurement. In Fig. 9.4 a two sublattices are used in the [110] projection of a sphalerite crystal. In this case, there are 4 parameters of the reference lattice exx ; exy ; eyx and eyy (Fig. 4 b). These parameters are accurately calculated by the fit to the list of the maxima positions in the reference zone. In the fitting procedure the starting points x0 and y0 are additional parameters. In the frame shown in Fig. 9.3 (white frame inside GaAs) the precision of the determination of the basis vectors is better than 0.001 nm, however the systematic error due to the choice of the area can be 10 times higher. E. Lattice Distortion in Discrete and Quasicontinuum Form Using the fitted exx ; exy ; eyx and eyy reference basis vectors, the lattices are extrapolated on the whole image. In Fig. 9.5 only one of the reference sublattices is shown in red, green corresponds to the deformed network (white frame close to the surface, Fig. 9.3). The part of the island shown in this figure is highly strained so that the displacements between the two networks are clearly visible. For each experimental lattice site the displacement is simply calculated as the difference between the x, y coordinates of the corresponding node of the reference and deformed lattices.

9.5 Strain Measurement

Fig. 9.4 a The two sublattices of h110i zone axis in a sphalerite crystal used for lattice distortion evaluation superimposed on HREM;

b the exx,exy,eyx lattice basis vectors of one of the sublattices.

Deformed crystal. White: nodes of the lattice corresponding to the experimental maxima positions. Black: extrapolated lattice

from the reference nondeformed substrate, the image corresponds to frame a in Fig. 9.3.

Fig. 9.5

The displacement vectors are shown in Fig. 9.6 (the values have been amplified by 5 times for visibility). The components of the displacement vector give the discrete components of the distortion field uxi,j and uyij. Most authors use this discrete form of the displacement for derivative, local lattice parameter calculation [58] or averaging to reduce errors. In fact, it is interesting to generate a regular spaced grid by interpolation [71]. In this form, manipulation of data is easier, and the consequences of this projection are as follows:

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

Displacement vectors, ~ u…i; j; 1†, scale multiplied by 5. Only the vectors of one of the sublattices are shown.

Fig. 9.6

· The discrete displacements uxi,j and uyij are converted to the continuous displacement fields Ux(x,y) and Uy(x,y) which are easier to compare with results of the FE calculation. · The random shift of the maxima positions are transferred to local fluctuations of the displacement fields Ux(x,y), Uy(x,y). The data in quasicontinuous form is used to reduce this fluctuation by convolution of this 2D floating-point pixel image with small 2D kernel. This is equivalent to averaging the displacement values on a distance corresponding to the full width at half maximum (FWHM) of the kernel functions, which are 2D Gaussians or exponential decreasing functions [75]. The efficiency in the reduction of the fluctuation is easily visualized in one dimension [74]. Choosing an arbitrary starting point for averaging, the local displacement in point xi is: ‡ . . . ‡ ui ‡ . . . ‡ ui‡M=2 M di M=2 ‡ . . . ‡ di ‡ . . . ‡ di‡M=2 ˆ M

uM i ˆ

ui

M=2

M…i ‡ 1†aR

;

where aR is reference lattice parameter, with distances di measured between the starting point and lattice point i, M is the number of neighbor lattice sites used for the calculation. So the error on the uM i is: DuM i ˆ

Ddi

M=2

‡ . . . ‡ Ddi ‡ . . . ‡ Ddi‡M=2 ‡ M…i ‡ 1†DaR : M

9.5 Strain Measurement

Reduction of displacement field fluctuation amplitude by local averaging. Largest drop obtained for n = 5.

Fig. 9.7

where DaR is the error of the reference parameter, which is generally small (0.25 pm) and we can assume that Ddi

M=2

‡ . . . ‡ Ddi ‡ . . . ‡ Ddi‡M=2 ˆ r :

In the rows of atoms the random noise can not displace atoms by groups, so the Dd errors for successive lattice nodes will be statistically positive and negative and the final error will be compensated to the value r, which the average random shift for one lattice site. Therefore, uM i 

r : M

This assumption can be checked experimentally in a perfect crystal where the displacement oscillates around zero. The amplitude of this oscillation can be reduced by changing the averaging distance. Fig. 9.7 shows how the amplitude Dux can be reduced for increasing averaging distances. It is clear that, for example, the amplitude of this fluctuation drops to 0.6 pm, when the averaging distance corresponds to 5 neighbor maxima, confirming the above assumption that Du is proportional to 1/M. Two-dimensional averaging, which uses the convolution of the floating point images of the displacement components with 2D kernel, has a complicated mathematical formulation, but the effect on the displacement damping is proportional to 1/FWHM. Unfortunately, with such averaging, the resolution on the calculated displacement field drops to about FWHM.

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

Fig. 9.8 Maps of the displacement field. a ux ; b uz in pixels; c displacements in X and Z directions (amplified by 30). Colors correspond to values of ezz , the reference basis vectors are, ax: 13.25 and az: 18.66 in pixels.

Such continuous displacements (Fig. 9.8 a and b) are measured for the whole island of Fig. 9.3, with respect to a arbitrarily chosen origin shown by the cross, they are represented in pixels. Fig. 9.8 c shows the effect of the “continuous” displacements on the “discrete” reference lattice. Apart from curving of the lattice planes, one clearly notices an increase and a decrease of the lattice parameters on the top of the island and in the valleys, respectively. Similar distribution of the displacements in a GaAs/InGaAs island was obtained by Rosenauer et al. [76]. The shape of the displacement field depends highly on the chosen origin; therefore such data can hardly be used for comparative analysis. A more synthetic im-

9.5 Strain Measurement

The HREM image of the island from Fig. 9.3, 1-nm resolution contour plot of the strain field is superimposed, a exx; b ezz.

Fig. 9.9

age can be obtained by calculating the distortion, which is directly related to the local lattice parameter [75]. The two-dimensional distortion field is obtained by derivating the displacement field. If the displacements are very noisy or if the filtering in Fourier space is very strong important details of distortion fields will disappear. The fluctuation amplitude of the displacement field after filtering is typically between 10 to 15 pm, calculated from the image of Fig. 9.3. On the derivative, only distortions larger than 2% are clearly visible. A good compromise is to reduce the resolution of the distortion mapping to 1 nm. For this averaging distance, the amplitude of DU fluctuation is about 0.85 pm and variations of the distortion as small as 0.002 can be detected as shown by the separation of isolines in Fig. 9.9. The exx map shows clearly that in the valleys, the ax lattice parameter of the InGaAs epilayer is smaller than that of the GaAs substrate, which means that these areas are highly compressed.

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9.5.4

The Geometric-Phase Method

The geometric-phase method [77] performs the measurement of lattice distortion using the arithmetic of complex images in Fourier and real space. It consists of Fourier filtering the image with an asymmetric filter centered at a Bragg spot, which gives a complex image whose phase contains the position of the intensity maxima. By dividing this complex image by a reference complex image containing the perfect lattice frequency, the resulting complex image contains the phase difference at each pixel P~g …r†, which is the value for the local displacement along the direction determined by the selected Bragg spot (direction of the reciprocal lattice vector ~ g). The typical procedure is illustrated in Fig. 9.10 for a low-angle grain boundary in GaN. From this image recorded along the [0001] zone axis (Fig. 9.10 a), a FFT is calculated (Fig. 9.10 b), then phase images are deduced for the reflections of interest (Fig. 9.10 c and d). Another example is presented on Fig. 9.11 for the island of Fig. 9.3 using four different reciprocal vectors. Here, the Gaussian mask used in reciprocal space for the reconstruction of phase images introduces averaging and smoothing of information in real space. In Fig. 9.11 b, the size of the mask was chosen to obtain similar averaging as for the images of ux, uy from Fig. 9.8, one can see important artefacts on the top of the island. The dark line shows the approximate position of the border; contrary to real-space methods this information mixing between amorphous and crystal part of sample cannot be avoided. The phase images obtained for the ~ g220 and ~ g002 vectors are similar to those of ux and uy shown in Fig. 9.8. In the phase images the jump from white to black results from the restriction of the geometrical phase to the range of values ‰ p; pŠ and shows the change of the geometrical phase from –p to +p (and vice versa). A change of the geometrical phase of 2p corresponds to a displacement of one lattice fringe period in the GaAs substrate. The maximum displacement is at least twice that corresponding to the 220 and 002 lattice planes, respectively, because on the phase images an abrupt change of phase appears. The displacement field with respect to the two-dimensional lattice defined by the vectors ~ g1 and ~ g2 can be obtained by combination of information from two lattice periodicities by using two phase images P~g1 …r† and g1 and ~ g2 , and solving the following equations [77]: P~g2 …r† for nonparallel vectors ~ 

P~g1 …~ r† ˆ P~g2 …~ r† ˆ

2p~ g1
~ u…~ r† ˆ 2p~ g2
~ u…~ r† ˆ

2pfg1x ux …~ r† ‡ g1y uy …~ r†g 2pfg2x ux …~ r† ‡ g2y uy …~ r†g ;

where g1x and g1y are the kx and ky components (~ k being the variable in reciprocal space) of the vector ~ g1 and ux …~ r† and uy …~ r† are the x and y components of the displacement field at position ~ r ˆ …x; y† in the image. This equation can be rewritten in matrix form: 

P~g1 P~g2



 ˆ

2p

g1x g2x

g1y g2xy



ux uy

 ;

9.5 Strain Measurement

Fig. 9.10 Illustration of the geometrical phase procedure using a GaN low-angle boundary: a the HREM image of low angle boundary showing the edge dislocations; b FFT of a; c phase image for g: 0110; d geometric phase using g: 1010.

where the relationship between the phase and the displacement field as a function of position in the image has now been made explicit. We can now introduce vectors a1 and a2 that correspond to the lattice in real space defined by the reciprocal lattice vectors ~ g1 and ~ g2 , as was shown by Hÿtch et al. [77], the displacement field can be calculated using equation

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

Fig. 9.11 The phase images obtained for 4 reciprocal vectors and different size of the mask. The black line shows the border of the



ux uy

 ˆ

1 2p



a1x a2y

a1x a1y



P~g1 P~g2 :

island: a mask diameter corresponds to 15 pixels averaging distance in real space; b averaging distance of 40 pixels.



Next, the lattice distortion tensor b…x; y† is calculated as the numerical derivative of u…x; y† as in real space method. 0

 bˆ

b xx byx

b xy byy



@ux B @x B ˆB @ @uy @x

1 @ux @y C C C @uy A @y

The result ~ u…x; y† has apparent discontinuities due to the abrupt phase changes from –p to +p in phase images P~g1 and P~g2 . These produce discontinuities in the derivatives b usually without physical meaning (1–2 pixels). In the case of Fig. 9.10, the abrupt phase changes are due to additional lattice planes starting at the dislocations, however, the discontinuity lines are not parallel to lattice planes. This is due to the local misorientation, which is not constant, in such a defective area. The calculated strain maps can be used for automatic defect detection and calculation of the Burgers vectors as shown by Kret et al. [78]. In many cases the distortion field has continuous character and the undetermined values due to the above discontinuities can be recovered by interpolation. Another solution to this problem is, for example, to calculate the derivative using ¨ ytch et al. [77]. complex images as proposed by H

9.5 Strain Measurement

Further differentiation of the lattice distortion leads to the dislocation-core distribution tensor; the continuum theory defines it as ~a ˆ

curlb :

If before this operation, the values of core pixels of the b tensor are deleted and replaced by interpolation, then the tensor ~a is zero in the whole region except inside the core of the dislocations where it forms peaks. By integration of the „ aij …z1 ; z2 † values, the inplane Burgers vector components bi ˆ a ds (Sc: disloij Sc cation core surface) are calculated. The validity of distortion field extracted from HREM depends of the imaging parameters and general rules are given in paragraph 2. However, in the neighborhood of defects, the choice of imaging conditions is critical and must be checked against image simulations. In Ref. [79] examples are given for the edge threading dislocations with Burgers vector 1/3 h21 10i in GaN (see Fig. 9.12). The dislocation model was relaxed by total energy minimization using empirical potentials on large supercells. In the case of TOPCON 002B microscope, for a foil thickness in the range of t = 5–15 nm, and defocus df = –10 to –30 nm, the strain fields extracted from HREM images are in agreement with the distortion calculated by atomic relaxation. The useful window of thickness and defocus is larger in the case of the high voltage microscopes. Fig. 9.12 shows that the experimentally measured strain field in optimized conditions is in agreement with the simulated one. The slight differences can be explained by the fact that the dislocations are located in low-angle boundaries, where the left and right parts of the crystal are slightly misoriented, and this is not taken into account in the simulated images. The geometrical phase method has now been used for analysis of distortion fields around a defect or defect network as was shown for misfit dislocations in GaSb/GaAs [80] and in CdTe/GaAs [81] or for interaction of threading dislocations and prismatic stacking faults in GaN [82]. It also has been valuable for the calculation of strain fields in heteroepitaxial pseudomorphic multilayers like CdTe/ZnTe [83] and Co/NiO [84].

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

Fig. 9.12 [0001] zone axis: a simulated HRTEM image for foil thickness t = 10 nm

and defocus –20 nm obtained for a relaxed supercell with a 5/7-atom ring core; b experimental image of an edge dislocation (Topcon 002B); c 2D lattice distortion tensor b extracted from a; d experimental tensor b.

9.5.5

Peak Finding Versus Geometric Phase

The two methods are based on the same general assumption that the relation between the atom positions in the crystal and features in the image contrast is constant inside the analyzed area (phase shift between maxima and atoms is supposed to be zero or constant). But there are some fundamental differences: (i)

The geometric-phase method uses basically only two reflections to construct the distortion field (different pairs can be used and eventually the resulting strain fields compared). (ii) In distortion measurements based on peak-finding information from many beams is introduced simultaneously.

9.6 Foil-Thickness Effect

They also have two different procedures for noise reduction. (iii) In the geometric phase technique, global averaging is used. (iv) For the peak finding procedure, noise reduction can be made in real space, this provides the possibility to process localized features such as edges. (v) The reference in geometric phase can not be chosen very precisely. The determination of positions of Bragg peaks can have a large error due to averaging of information in Fourier space from deformed and reference zones. (vi) In the peak-finding procedure, the reference zone can have any shape and can be determined with high precision by fitting the network to a set of maxima. (vii) However, in geometric phase, the correct reference can be retrieved in real space after processing by choosing it and subtracting its phase components from the whole phase image of the analyzed area. (viii) An important advantage of the phase method, with respect to peak finding, is that the information is taken from a localized region in Fourier space, i.e., lens aberrations are minimized. Moreover, the geometric-phase method is simple to use for the measurement of distortion when defects are present in the area of interest.

9.6

Foil-Thickness Effect

In quantitative interpretation of HREM images, the determination of the thickness is a key problem for the interpretation of contrast features in the methods that try to fit atomic models of an unknown structure, as well as estimation of the thin-foil relaxation effect for lattice-distortion measurements. In some cases, when the thickness rise is slow and uniform, it is possible to choose the area of interest between the first extinction fringe and sample border; the average thickness can then be estimated by geometric criteria with a precision of about Dt = 5 nm. The general approach is to compare the observed pattern with image simulations for a known structure. The solution is to evaluate the thickness in many places around the area of interest and to construct the overall geometry of the thin foil. For many semiconductor materials, an effective method has been developed that gives a precision of Dt = 1.5 nm. This approach is based on quantitative analysis of information from the transmission electron micrographs (QUANTITEM) developed by Ourmazd’s group [85–87]. The QUANTITEM procedure has recently been discussed with regard to composition evaluation in ternary layers like InxGa1–xAs [88]. It detects the projected crystal potential that is proportional to the sample thickness. Kisielowski et al. [87] stated that the QUANTITEM analysis is valid to the extent that dynamical scattering in the investigated material can be described in terms of two Bloch waves. However, it was also shown that the procedure could be used for III–V semiconductors like GaAs or AlAs, where three Bloch waves are excited with substantial intensity [76, 87]. The QUANTITEM algorithm was also implemented into the DALI program as described by Rosenauer et al. [89, 90].

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

A second procedure to determine the sample thickness is based on the method of Stenkamp and Jäger [91], and Stenkamp and Strunk [92] who examined the amplitudes of appropriate Fourier coefficients Ji. The intensity distribution I(r) in the high-resolution image is derived from a Fourier sum I…r† ˆ

X

J…g†ei2pg
r ;

g

in which the complex Fourier coefficients J(g) depend on the beam amplitudes and phases and on the microscope parameters, as seen in [91, 92]. A fast Fourier transform algorithm is used to obtain the Fourier coefficients J(g) and to calculate the amplitude of the image unit cell: jJ…~ g†j ˆ

q Re2 …J…~ g†† ‡ Im2 …J…~ g†† :

Another approach, which does not require three template image vectors, uses the correspondence analysis (CA) [93], which is also implemented in the DALI program package. The CA procedure was demonstrated in a (Ni,Al) superalloy [93]. In transmission electron microscopy thin sections of investigated material are used and the thickness has a marked impact on image contrast, and the second important consequence is the relaxation effect. During the thinning process, free surfaces are introduced and the measured distortions are not from a bulk sample due to elastic relaxation at the surfaces. Of course, the aim is to obtain information about bulk properties. In many cases the consequences of the elastic relaxation can be predicted and good approximation of the real strain or stress fields in bulk can be obtained by finite elements calculations. The main application of strain analysis is the composition evaluation in pseudomorphologically grown thin layers. The sketch of Fig. 9.13 shows the elastic relaxation effect in the case of a strained heterostructure. The unit cells of the epitaxial layers are tetragonally distorted. Fig. 9.13 depicts the situation that applies for cross-sectional samples of quantum-well-type heterostructures. The strained layer is able to expand at the free surfaces of the thin foil (Fig. 9.13), where it is elastically relaxed at the maximum extent. This leads to a diminished tetragonal distortion. The lattice parameter a|| of a layer unit cell parallel to the interface plane and to the electron beam direction is defined by the lattice parameter as of the substrate. The lattice parameter a|| parallel to the interface plane and parallel to the electron beam direction as well as the parameter a^ perpendicular to the interface plane vary locally. It is assumed that an atomic distance measured from the HREM contrast pattern corresponds to a lattice parameter a^ that is averaged along the electron beam direction. Following Ref. [90], for a cubic crystal with the electron beam along a direction h110i or h100i if the reference is chosen inside the thick nondeformed substrate, the lattice parameter that corresponds to the measured lattice spacing along the growth direction is within two limiting cases of a thin or a bulk sample:

9.6 Foil-Thickness Effect

Fig. 9.13 Cross section sample geometry of quantum-well-type structure. Thin-foil effect on relaxation of the strain due to free surfaces and column bending.

as

a? as

ˆA

as

a as

;

 Athick h100i;h110i ˆ Athin h100i ˆ

 1‡

1‡2

C12 C11



C12 C11 ‡ C12

;  ;

where a is the (local) bulk lattice parameter and Ci,j are the elastic constants of the strained layer. The elastic relaxation effect was analytically studied by Gibson et al. [94], and Treacy and Gibson [95]. From the analytical solution for a modulated sinusoidal composition in a superlattice using linear elasticity, these authors proposed to use Fourier sums for finding the solution of any chemical profile. They demonstrated that the relaxation is dependent on the ratio of the superlattice wavelength and the local sample thickness. More complicated geometries as strained islands or local segregations as well as relaxation around defects need numerical computation. The strain in quantumwell structures can either be obtained using linear elasticity formalism [96] or by atomic modeling using empirical interatomic potentials [97]. Faux et al. [98] have

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

made a comparative study of the two methods on ultrathin layers (0.5 nm) embedded in a matrix with a misfit of 1%. Their results showed that, even for such low dimensions, the calculation based on linear elasticity is still valid. In contrast, Pryor et al. [99] obtained significant differences very close to the interfaces (2–3 lattice parameters), between atomistic modeling and linear-elasticity calculations for the strain in an imbedded quantum box of GaAs/InAs with a pyramidal shape. However, inside the island, both methods did not exhibit larger differences. Usually, the mismatch between the layers of different compounds is simulated within the thermo-elasticity formalism. The various layers take some expansion coefficients and the temperature is increased so that they are submitted to a strain corresponding to the mismatch. Then the nodes move following the laws of elasticity and the equilibrium is attained at the minimum of the elastic energy of the system. The strain state in a coherent Stranski-Krastanow island of GeSi/Si was calculated by the finite elements (FE) method by Christiansen et al. [100]. The authors of Ref. [75] used the 3D finite element calculation with TEM sample border conditions to explain the strain state in a cross-sectional sample of a noncapped InGaAs-coherent island. A similar calculation was carried out by Rosenauer et al. [76] for a vertical gradient of In in the island. 2D FE calculation was used by Tillman et al. [101] to study the impact of column bending in HREM on the strain evaluation of GaAs/InAs/GaAs QWs. Scheerschmidt et al. [102] used molecular dynamic simulations to generate relaxed models for a reliable interpretation of electron microscopy investigations in analyzing the size, shape, and strain fields of pyramidal quantum dots. In the example, the cross section of a coherently strained InGaAs/GaAs-noncapped island with homogeneous In composition and sinusoidal shape is used from Refs. [74, 75]. The 3D mesh used for the calculation of strain distribution of the thinned island is exhibited in Fig. 9.14. As shown in Fig. 9.15, the ezz component changes

Fig. 9.14 The geometry of the FE model of sinusoidal shaped island with uniform composition (a quarter of the island): a the layout at the substrate surface, l is the distance between the islands and t is the thickness for the TEM samples; b quarter of the island used for the FE calculation.

9.6 Foil-Thickness Effect

Fig. 9.15 Finite element calculation of ez for a thin foil of 10 nm and the whole island. The relaxation of the whole island takes place only at the top surface: a a 5-nm section of the island view of the strain calculated for the

whole island; b the strain field in the thin foil of the island, viewed from the external walls; c a section of the island showing the strain from the middle; d the strain in the inner part of the thin foil.

in an equivalent volume of the material due to thinning of the sample. The strain distribution on the external wall looks dramatically different for this ezz component. The differences observed for the exx (not shown) are smaller and their projection along the beam direction are very similar (Fig. 9.16). Strong lattice compression zones are observed in the valleys, the lattice parameter ax is smaller than in the GaAs (the equilibrium 30% In lattice parameter of InGaAs is 2.7% larger than that of GaAs). The shapes of the isodistortion lines are comparable to those obtained on the experimental micrograph (Fig. 9.9 a). The differences in the absolute value are due to lateral and vertical gradients of indium (center of island is rich in In), which has not been included in the modeling.

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

Fig. 9.16 Averaged ex for 10 nm along the zone axis: a the whole island; b the thin foil.

9.7

From Strain to Stress

In TEM experiments, the measured distortions are obtained from thin sections. In fact, the aim is to deduce information on the state of stress before the TEM sample preparation process. A solution was proposed by Dluzewski et al. [81] using the nonlinear modeling starting from the experimentally measured distortion field. This field is used as the initial data for the finite element calculation. The applied model for anisotropic behavior of the crystal takes into account the nonlinear geometrical effects related to configuration changes as well as the socalled constitutive nonlinearity of the stress-strain behavior of crystal lattice. This procedure is closely related to the problem of the third-order elastic constants being responsible for the asymmetry between the tensile and compressive response of a crystal lattice. During extension, real materials become softer, while under compression their elastic tangent stiffness dramatically increases. So, for instance, in order to balance the stress around an edge dislocation core, the tensile region which is more flexible, takes a large part of the elastic stain leading to the volume expansion of crystal lattice induced by a single edge dislocation. The constitutive equations [103] applied for anisotropic behavior of a crystal lattice take into account the volume effect and the elastic extension/compression asymmetry for dislocations. The volume effect induced by misfit dislocations in interfacial zones is responsible for the negative surface tension reported in multilayers [104] and confirmed by FE numerical calculations [81]. The FE approach was also applied to a network of threading dislocations in a GaN layer grown on sapphire. In this procedure, the phase images Pgi(x, y) are calculated for 1010; 0110, or 1100 lattice periodicity z is perpendicular to the image plane (Fig. 9.10). The Pij …x; y† distribution that is determined in this way in thin TEM samples shown in Fig. 9.17 was read by the finite element program as initial

9.7 From Strain to Stress

Fig. 9.17 a Lattice distortion tensor b extracted from experimental image.

values of the distortion. FE iteration with a border condition corresponding to the bulk sample material was performed to obtain a stable solution and finally the stress field was calculated as shown in Fig. 9.18. Due to the large values of the distortion, the finite deformation approach was used, i.e., the difference between the initial and deformed configurations is included in the algorithm. The authors use finite element calculation with Taylor’s FEAP program [105], which is modified to take into account the finite deformation of anisotropic crystals [106]. The details of the treatment of the core is given in [107]. All the dislocations in

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Fig. 9.18 a–d The 4 components of stress

fields obtained from the experimentally measured distortion by FE calculation in the case of the bulk material border condition calculated for HRTEM image from Fig. 9.12. The arrows show orientation of the Burgers vec-

tor; e the displacement uz in z (e-beam direction), the mesh deformation is multiplied by 10 to show the TEM sample surface deformation; (f) the rzz component calculated for the free surface boundary conditions.

Fig. 9.18 have the same Burgers vector 1/3 h21 10i, but for some of them, this vector is not parallel to the x axis. Only the dislocations marked: 1, 2, 3, 4, 5, 6 have a similar distribution of rij. For dislocations 12, 13, 14, 15, 17, which have Burgers vectors oriented in the opposite direction, the stress field has inverted positive and negatives lobes. For the other dislocations 7, 8, 9, 10, 16 it is necessary to rotate the coordinate system by 60 8 to obtain a corresponding stress field distribution. The maximal values of the calculated stress reach ± 7–8 GPa in the case of the rxx and ryy component and ± 4 GPa for rxy and rzz components. When the boundary conditions are changed to allow for the relaxation in the z direction, as a TEM sample, the calculated ryy is about 4 times smaller (Fig. 9.18 f). This relaxation is the result of the relatively small displacements in the z direction shown in Fig. 9.18 e. Therefore, the thin-film surface relaxation effect due to pure-edge dislocation is

9.8 Local Chemical Composition

small and the 2D distortion tensor can be obtained with good accuracy from HRTEM images. This kind of approach opens new perspectives in materials characterization by giving access to information in the z direction, which is out of reach when using only TEM studies. However, such stress values inside the core of a dislocation need some adjustment as well as theoretical consideration, as proposed in [81]. Especially, the significance of the continuum approach at distances smaller that one atomic spacing need to be closely investigated in this kind of calculation.

9.8

Local Chemical Composition

There are numerous methods in electron microscopy that can be used to show chemical information about the analyzed sample, although only a few are able to give a value of the composition within a certain accuracy. The spectroscopic techniques like EDS or EELS have a limited spatial resolution mainly due to the probe size (a few nm to 0.5 nm for the best field emission gun TEMs). Dark field images can exhibit strong contrast between layers of different composition when chemically sensitive beams are used (200 for sphalerite semiconductors). This technique was developed by Bithel and Stobbs [108] and applied to GaAs/(Ga, Al)As superlattices. The spatial resolution was estimated as 0.5 nm inside quantum wells of thickness above 2–3 nm. The Fresnel fringes method consists of analyzing the fringes that form at interfaces when the image is strongly defocused. The shape of these fringes is very sensitive to the chemical-composition profile; comparisons between calculated and experimental images have been used to characterize GaAs/GaAlAs interfaces [110]. In heterostructures based on ternary semiconductor compounds, HREM techniques can by used to determine the composition at near atomic scale, which is very difficult to obtain with spectroscopic methods. Three main effects are used for this analysis: (i) the presence of the chemical sensitive reflections in ternary semiconductor compounds, e.g., AlAs/GaAs [111], (ii) the difference of lattice parameter between two-layered materials, e.g., InAs/GaAs, CdTe/ZnTe, and (iii) the differences in the local image pattern due to dynamical interaction between diffracted beams, e.g., Si/Ge [87]. An algorithm of real-space pattern recognition based on vectorial representation of the image in elementary cells was proposed by Schwander et al. [86] for HREM images of GaAs/AlAs interface analysis. This works for optimal defocus and thickness conditions, which maximize the contribution of chemical sensitive 002 reflections along the [001] zone axis. This technique was extended to other systems and in conditions without a chemical sensitive reflection and was given the name of QUANTITEM [87]. With atomic resolution, it is possible to evaluate the chemical composition with an accuracy of 10%; it is also possible to determine the thickness of an area of known composition. For sphalerite semiconductors, the [100]

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zone axis gives the best results, along the [110] zone axis the contrast features are rather complicated and it may be difficult to calculate the chemical composition [88]. Using pattern recognition on cross-sectional HREM images taken in [1120] zone axis, Kisielowski et al. [8] have shown that In segregates in 1–3 nm areas inside a GaN/InxGa1–xN/GaN heterostructure. Other procedures for the extraction of chemical composition have been proposed, most of them rely on the reflections that allow different patterns as a function of the composition to be produced: Thoma and Cerva [112] used the amplitude Fourier component of the 200 reflection for the calculation of the chemical composition in each cell. This method was adapted by Stekamp and Strunk for centrosymmetric crystals without a chemical sensitive reflection [92]. The more successful method of chemical composition determination in ternary alloys is based on the measurement of the local lattice parameters. For ternary materials AxB1–xC the Vegard’s law: aAx B1

xC

ˆ xaAC ‡ …1

x†aBC

assumes a linear relationship between the lattice parameter and the chemical composition. One then uses the results of deformation measurement of Sect. 9.5 and, adding the correction for the thin-foil relaxation effect, the local composition is determined. The method can allow the use of nonchemical sensitive images, which may even contain noise, and would be completely useless in the case of algorithms based on pattern recognition. This technique has been successful for investigation of quantum wells layers such as CdTe/ZnTe and MnTe/CdTe [66] interface inter-diffusion in ZnxCd1–xSe/ZnSe [70], or CdTe/CdMnTe quantum wells with a trapezoidal shape of Mn distribution [113]. In such images, the two references can be chosen, one in the CdMnTe barrier with 75% Mn content and the second in a 15-ML thick pure CdTe layer [113]. More recently, Gerthsen et al. [7] applied these techniques to wurtzite InGaN. They used lattice-fringe images recorded close to the [1010] zone axis in two-beam conditions where only the transmitted and the two 0002 beams were used. They pointed out that small clusters of 3–5 nm with high In concentration (up to 70– 80%) might be present inside layers of 10–20% nominal composition. All the above methods suffer from the projection and averaging problem. In the case of the strain-state analysis, image simulations revealed that, in homogenous contrast conditions of white dots on the black background, the distortion profile can be extracted correctly [101]. Another image simulation taking into account the lattice plane bending was made by Rosenauer and Gerthsen [90]. It was found that lattice bending does not introduce noticeable errors in the displacement field along the growth direction, if the windows of defocus are chosen to avoid the half-spacing contrast in the h110i projection in GaAs and InGaAs layers. An additional interpretation problem comes when the studied object is made of small QDs with diameter comparable to or smaller that the thin-foil thickness. The comparison between the In clustering process occurring in MOCVD growth of InGaN QWs with nominal 15–17% In was investigated in [114]. The

9.8 Local Chemical Composition

Fig. 9.19 Indium composition evaluation for InGaN QWs grown by MOCVD: a Color-coded In distribution superimposed on HRTEM image. Black vertical and horizontal lines show the grid used for the calculation; b surface plot in perspective view. Numbers show the correspondence between a and b. The In composition scale was obtained after FE modeling.

authors used images taken along the [1120] zone axis and the peak-finding procedure to determine the strain along the growth direction. The finite element modeling was used to determine the In composition assuming a homogeneous In distribution (Fig. 9.19). It was clearly shown that in the case of the In-rich clusters this scaling gave an underestimation of the In content, and it was necessary to make FE modeling with nonhomogeneous composition to attain good agreement with the real In concentration inside the QWs [114]. This effect was also demonstrated by Kret et al. [83] in the case of the small Cd-rich CdZnTe islands embedded in a ZnTe matrix. In other reports, uncapped and capped InxGa1–xAs/GaAs-incoherently strained islands were studied and finite element calculation was used in order to take into

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

account the thin-foil relaxation effect. Vertical [76] as well as lateral [75] In composition gradients were detected. Quantum dots in ZnSe/CdSe [13] and CdZnTe [83] were also studied by this method. In this case, the Cd composition obtained using an intermediate parameter between the thin- and thick-foil limits lead to underestimated values. Inside thin areas, the evaluated Cd concentration could be as high as 85% [83]. The composition evaluation by lattice-fringe analysis (CELFA) using chemically sensitive reflections was recently developed by Rosenauer and Gerthsen [115]. It has been applied for chemical composition evaluation in InxGa1–xAs [76] and CdxZn1–xSe [116], so far this method has not been applied to an InxGa1–xN alloy.

9.9

Atomic-Structure Retrieval

The electron probe is one of the few experimental methods that are able to give access to direct observation of atomic structure of defects. A number of examples are now available in the literature, such as dislocation cores in Si or misfit dislocations at the CdTe/GaAs interface using Z-contrast imaging [117]. Recently, Z-contrast imaging was combined with maximum entropy analysis for the core structure of threading dislocation in GaN [118]. The determination of atomic configuration for defects is complicated in coherent imaging due to dynamical diffraction effects and nonlinear image formation with severe lens aberration; therefore, the interpretation needs extensive computation [119]. Close to the defects, the position of image features can be shifted from that inside the perfect crystal so the approaches developed in previous paragraphs for long-range distortion fields measurement can not be simply applied. Presumably, high-voltage electron microscopes would be quite efficient for this type of study. However, the new medium-voltage fields emission gun ones, with information limits near 0.1 nm and Cs correctors, are going to be interesting alternatives in the future. There exist many strategies to determine the atomic configurations in the coherent imaging conditions. The most popular methods are based on the visual comparison of the experimental and simulated images of the defect. The more sophisticated approach of this kind is based on the assumption of the pseudoweak phase object approximation (PWPOA) and deconvolution of the microscope transfer function. Using this method, the shuffle- and glide-type 60 8 dislocations were recently distinguished in silicon using a 200-kV field emission gun microscope [120]. However, this type of technique can only exclude some models and confirm a particular proposed configuration. Generally, more quantitative descriptions of atom positions in the cores are required by comparison of atomistic computation with experiment, in order to provide an accurate determination of defect structure. The promising approach is the reconstruction of the exit-wave function by focus variation methods [121] or by electron holography [122]. This approach is relative-

9.9 Atomic-Structure Retrieval

ly old as commented by Saxton [123] for focus variation methods; recording the amplitude and phase of the image wave by electron holography was proposed by Gabor [124]. These two methods were applied to perfect crystal structure images such as Ba2NaNb5O15, CaO [16], inter-metallic superconductors [39], and a perfect silicon crystal [125]. Recently, some authors presented application of these techniques to defects: the successful reconstruction of an edge dislocation core in GaAs from simulated images [37], characterization of interfaces in YBCO/CeO2 and CeO2/R-Al2O3 [126], and the R = 13 grain boundary in gold [127]. This kind of method can give aberration-free images and information about atomic structure close to the information limit of the microscope. However, the interest has been mostly to demonstrate the resolution improvement and not for the determination of the exact position of atomic columns, so far. The methods for refining the atomic-column positions in the defect cores use iterative structure retrieval and the strategy is a comparison of the simulated images from a series of model structures with experimental ones using a quality function. Advanced optimization schemes for parameter finding and quality function that have been developed up to now for iterative structure retrieval will be reviewed briefly. The general procedure goes as follows: · · · · ·

artefact-free image and signal-to-noise ratio, preprocessing of image data for quantitative comparison with simulated image, determination of imaging parameters, optimization of parameters of simulation in perfect crystal area, optimization of the position of atoms near the defect or interface to minimize the quality function.

9.9.1

Artefact-free Sample and Signal-to-Noise Ratio

The level of the noise in evaluated areas must be very low and sometimes, for periodic grain boundaries, averaging of a few periods has been used for noise reduction, however, this approach is very limited due to changes of thickness and it is impossible in the case of localized defects (dislocation, steps, etc.). So, the quality of the sample may be the limiting factor in many materials due to sample-preparation techniques. For example, the thinning rate must be uniform at interfaces and defect areas in order to avoid local variations of thickness. Nonuniform thickness in connection with stress fields around a defect and thin-foil relaxation can completely change the image pattern around the defect. In the case of grain boundaries, it is also often difficult to control the orientations of the zone axes of the grains, which need to be strictly identical on both sides of the boundary. Small misorientations can mislead the optimization process and in most cases they will need to be included in the process in order to have some chance of success. So far, quantitative studies of grain boundaries have been made on bicrystals where the misorientation was controlled by X-ray diffraction just before crystal bonding. Of course, the other important factor that influences the image quality

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is the ratio between the amorphous layer to the crystal thickness. In fact, this is in favor of the use of high-voltage microscopes for this kind of study because the TEM sample may be thicker than for the medium-voltage (200 kV) microscopes [36]. However, it is also clear that sample-preparation techniques have been improving rapidly during recent years and, for example, the tripod polishing method was shown to dramatically decrease the thickness of the amorphous layers, making it a good candidate for the above type of investigations [128]. Moreover, when carrying out this type of investigation, one is often faced with the choice of which defect to analyze and which criteria to use. It was very recently shown that in GaN layers, it is possible to use the dislocation core distribution measurements derived from the geometric-phase method [79]. This allows the strain fields around each dislocation and the minimum distance between the peaks point to those dislocations which are nondissociated and imaged edge on to be detected. Such dislocations are the only ones that can next be analyzed for the atomic-structure determination. 9.9.2

Defect-Structure Determination Strategies

Two main approaches exist: (i) First one tries to find an atomic model from geometrical considerations; next the atom positions are relaxed using suitable atomistic calculations such as molecular statics or molecular dynamics with many-body inter-atomic potentials that can handle large amounts of atoms [130]. Such generated supercells are then used for image simulation and the obtained images are compared with the experimental ones. (ii) In the second strategy, the initial model is generated from the experimental image for example by cross-correlation of the image with the projected potential of a structural motif of the perfect crystal. The optimization procedure is performed first in perfect crystal areas to find the imaging conditions in the neighborhood of the investigated defect. Then the imaging conditions can be extrapolated to the area with the defect of interest. 9.9.3

Preprocessing of Image Data and Image Simulations

This step depends on the recording method and is more complex in the case of electron films than the CCD slow scan cameras, as described in Sect. 9.2. The aim is to obtain the experimental data set that can be directly compared pixel by pixel with simulations (i.e., the spatial sampling as well as the intensity units of images must be the same). It is necessary to adjust the magnification, the orientation and the intensity units of the experimental image to match those of the corresponding values in the simulated images. For the alignment of the two images, one makes sure that the sampling distance of the experimental image corresponds to that in the simulated image. This

9.9 Atomic-Structure Retrieval

is done by first minimizing the image mismatch between the resampled experimental image of a bulk unit cell and the corresponding simulated image in an iterative way. And finally, the correct relative positions of the supercell images are found by cross-correlating the complete experimental image with a super cell that serves as a template. Another alignment procedure based on the phase spectrum of two shifted images was proposed by Suchay [131]. Independent of the chosen strategy, the simulation of an image for the supercell of a defect defined by the position x, y, z of each atom position is performed using the multislice algorithm. Most authors use the image simulation code of Stadelmann [24], which now includes the effect of three-fold astigmatism and anisotropic blurring function which can be used to account for effects such as sample vibration, or the modulation transfer function of the CCD array [132]. 9.9.4

Quality Functions (Goodness-of-Fit Criteria)

In order to compare the experimental to simulated images, various methods have been used, such as the normalized Euclidean distance [133] and the cross-correlation coefficient [134]. However, it was shown by King and Campbell [50, 51] that in order to take into account the uncertainties in experimental images, it is useful to calculate the Goodness-of-Fit. Neglecting these errors artificially weights the fit toward the highest intensity part of the image. They proposed to use a v2 statistics calculation in order to have more confident values of the imaging parameters [51]. Such analysis is valid when the probability distribution function has a symmetric form. It was then shown that this is the case for HREM images and they employed a nonlinear least-squares optimization method for their characterization of grain boundaries in Nb and Al. The cross-correlation coefficients are highly sensitive to the pattern of the image. The chi-squared (v2) goodness-of-fit parameter is a better indicator of the overall similarity of the images as it also takes into account the image contrast and the uncertainty of the experimental data. 9.9.5

Determination of the Imaging Parameters

For each working session, the imaging parameters that need to be determined include the local specimen thickness, the focus setting of the objective lens and the beam tilt in x and y directions. The optimum values of these parameters need to be determined by minimization procedures between simulated and experimental images of perfect crystal areas. The other microscope parameters such as the accelerating voltage, the aberration coefficient and defocus spread or the incident beam semiconvergence angle, which are known, can be kept constant. Many optimization methods were applied to determine imaging parameters in perfect crystal areas: thermal annealing [135] and optimization, which employs nonlinear least-squares methods [51]. It was found that the probability distribution function for HREM parameters are the simple Gaussian curves and this function can be used for optimization [51].

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9.9.6

Optimization Strategies

If the imaging conditions are determined in a perfect crystal area, the next step is to quantitatively retrieve the atomic structure of the defect by iterative comparison of the simulated images and the aligned experimental ones. Kienzle et al. [130] used preliminary structure models as a first guess, as for example the geometrical models of a R = 3 grain boundary in SrTiO3. The procedure is a structure refinement by iterative automatic generation of the model for which the simulated images are closer and closer to the experimental ones to within the desired accuracy. The most time-consuming part of the atomic structure retrieval is the optimization of the atomic column position near the defect cores. The movement of one atomic column influences not only contrast features directly connected it, but the image pattern is modified at distances larger than one unit cell. Therefore, movements of columns are not independent of the image pattern. The number of attempts is very large and it would be difficult to test all possible configurations. The solution lies in using optimization strategies that by atom movement improve the quality function and the optimization stops when the column-position changes by less than a given error value. So far, for the column position optimization in the defect core, a simplex algorithm was applied in the case of the R3 boundary in Cu [133]. The simulated evolution optimization technique proposed by Möbus [134] was successfully used for investigating the structure of the Cu/ sapphire interface, an edge dislocation in niobium [53], and a R3 (111) tilt boundary in SrTiO3 [136]. 9.9.7

Precision of the Structure Retrieval

The systematic structure refinement, which combines atomistic calculation, image simulation, and quantitative comparison with experimental images, has been now used to determine the atomic structure of mostly grain boundaries. Such quantities as the rigid-body translation and accurate atomic positions have been determined with an accuracy of 0.014 nm in SrTiO3 [130]. However, such grain boundaries are periodic features and in most studies the signal-to-noise ratio could be increased by averaging along the boundary plane. For localized defects like dislocations, it was shown that core structures are more difficult to retrieve using such methods due to the low signal-to-noise ratio [51]. Recently Möbus and Kienzle [137] investigated the precision of the location of the atom position in a crystal defect using the continuous probability functions and concluded that in order to actually improve the error bars of a Q-HREM experiment themselves, investments have to be directed towards improving signal-to-noise ratio (time series, focal series, etc.) or to reduce the systematic errors by more elaborate simulation schemes (including “real-world” specimen effects, such as column bending, surface reconstruction, compositional impurities). Moreover, a number of reports have shown that a comparison between the simulated and experimental images

9.10 Discussion and Conclusions

may be difficult as the simulations give an overestimation of the total contrast by typically a factor of 3 in Si or GaAs [52, 138]. However, other reports showed that for simple metals like Al or Nb, a good-quality fit could be obtained by including parameters for the background contrast or anisotropy blurring functions [51].

9.10

Discussion and Conclusions

As can be seen above, the recent progress in HREM has led to a number of methods for quantitative information retrieval. We have focused on those that directly apply to investigation of semiconducting materials where there is always a reference structure close to the area of interest. Therefore, the recent developments of electron crystallography were not dealt with (for information please see Ref. [139]). Our aim has been two-fold: to discuss methods that are suitable for local chemical composition evaluation as well as those able to determine the atomic structure of crystallographic defects. For the techniques that can be applied for chemical composition analysis, it is possible to work in real space using the peak-finding procedure. In reciprocal space, the geometrical phase method has proven to be efficient for strain measurements and it can also be used in investigation of layers containing defects, mainly as a first step for atomic-configuration retrieval [78, 79]. When using these methods, it is interesting to have a clear idea of their accuracy. In the peak-finding procedures, there is an error on location of the maxima of contrast and then on the corresponding distortions. On a good raw HREM image, when using a conventional 200-kV LaB6 microscope, and an ion-milled semiconductor sample, the displacement can be calculated within 1 unit cell resolution and accuracy of about DU = 30 pm, which allows an error of De = 0.075. The numbers are slightly improved when a Wiener filter is used: DU = 15–6 pm and De&0.035–0.02. If local averaging can be used in the case of slow variation of distortion or chemical composition, the noise can be dramatically reduced and the amplitude of the fluctuations are small: DU = 0.5–0.8 pm, De&0.001–0.002 are achieved with 1–1.5 nm averaging distance. However, this means that the spatial resolution for composition mapping is decreased and no variation of distortion field in distances smaller than 1–1.5 nm can be detected. Comparable accuracy is obtained by onedimensional averaging particularly useful for chemical profiles in QWs characterization (see Fig. 9.22 b). The accuracy on the relative lattice parameter can be even higher, it is only limited by the size of the zones with stable imaging conditions and in our estimation the averaged lattice parameter for GaN can be measured with a precision better than 0.05% (0.25 pm) in areas containing 2000–4000 atomic columns. But the angles and aspect ratio of the unit cells has relatively important errors due to directional nonuniformity of the microscope magnification. So, only a relative measurement is possible with internal reference. The noncorrected three-fold astigmatism can introduce shifts in the lattice fringe pattern leading to substantial errors

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9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

(5 pm) on the measured values for volume expansions for example in grain boundaries [140]. Composition fluctuations are then obtained within 5% [90] precision. In pattern recognition methods like QUANTITEM, it was claimed that, although the detection limit depends strongly on the quality of the sample, for the best-quality ones, in a foil of about 3 nm thickness, a single atom may be detected with 60% confidence level and a double-atom change with 90% confidence [34]. For the atomic structure retrieval methods, it was shown that the precision will strongly depend on the average Z number of the column [133] and it is worse for light atoms (18 pm for a O column) than for heavier atoms (4 pm for Al column) as shown in a R = 11 grain boundary by King and Campbell [50]. In these investigations, one uses a 2D image of a 3D object. The thin foil often has an irregular surface covered with an amorphous layer of unknown thickness and geometry due to the preparation procedures. Of course, one needs to extract the information of the detail (the defect, the interface, and the chemical composition changes) that is often imbedded in a perfect crystal matrix. As is shown above, there is always a need for the first guess, a model. This has to be as close as possible to thermodynamic equilibrium, which is why the structural investigation has to be carried out in conjunction with modeling. Of course, in many cases, it may be enough to minimize the elastic energy of the system and FE calculations have proven to be efficient in modeling the strains for chemical-composition determination. This multidisciplinary approach is even more important for the retrieval of the atomic structure of the defects. In this instance, statistical analysis is necessary for confidence tests along with the atomistic modeling of the defect by total-energy minimization. Finally, more accurate analysis will be possible when higher-quality data is available. This development is now on the way, in fact a number of cases which have not been discussed above have been investigated by focus series or electron holography methods, which allow images with a resolution close to 0.1 nm by reconstruction of the exit electron wave to be obtained. Such images will have a good signal-to-noise ratio and thus will be easier to quantify with highest accuracy.

9.11

Acknowledgments

Part of this work was supported by the EU under contract number HPRN-CT1999-00040. The authors would like to thank J. Y. Laval and A. Dubon of LPS-ESPCI in Paris for contribution of some of the HRTEM images used as examples in image processing. Thanks also go to Y. Androussi and A. Lefebvre of LSPES Villeneuve d’Ascq France, as well G. Maciejewski and G. Jurczak of IPPT-PAS, for valuable contributions to modeling of stress relaxation in TEM samples. Dr. Potin and G. Nouet are gratefully acknowledged for their contribution to the HREM work. The authors also acknowledge M. A di Forte Poisson of Thales for providing InGaN samples and for fruitful discussions.

9.12 References

9.12

References 1

2

3

4 5

6 7

8

9

10

11

12 13

14 15

16 17 18 19

B. Gil, Group III Nitride Semiconductors, Physics and Applications (Oxford Science Publications, 1998). H. Morkoç, Nitride Semiconductors and Devices, Springer Series in Materials Science, Vol. 32 (1999). P. Ruterana, A. Béré, B. Barbaray, G. Nouet, and H. Morkoç, Phys. Rev. B 59, 15917 (1999). V. Potin, G. Nouet, and P. Ruterana, Phil. Mag. A 79, 2899 (1999). V. Potin, P. Ruterana, G. Nouet, R. C. Pond, and H. Morkoç, Phys. Rev. B 61, 5587 (2000). A. F. Wright and J. Furthmuller, Appl. Phys. Lett. 72, 3467 (1998). D. Gerthsen, E. Hahn, B. Neugebauer, A. Rosenauer, O. Schön, M. Heuken, and A. Rizzi, Phys. Stat. Sol. (a) 177, 145 (2000). C. Kisielowski, Z. Liliental-Weber, and S. Nakamura, Jpn. J. Appl. Phys. 36, 6932 (1997). L. Bellaiche, T. Mattila, L.W. Wang, S.H. Wei, and A. Zunger, Appl. Phys. Lett. 74, 1842 (1999). K. P. O’Donnell, R. W. Martin, and G. P. Middleton, Phys. Rev. Lett. 82, 237 (1999). R. Bierwolf, M. Hohenstein, F. Phillipp, O. Brandt, G. E. Crook, and K. Ploog, Ultramicroscopy 49, 273 (1993). P. H. Jouneau, PhD thesis, Institut Polytechnique de Grenoble, 1993. D. Litvinov, A. Rosenauer, D. Gerthsen, and N. N. Ledentsov, Phys. Rev. B 61, 16819 (2000). A. Thust and K. Urban, Ultramicroscopy 45, 23 (1992). W. Coene, G. Jansen, M. Op de Beeck, and D. van Dyck, Phys. Rev. Lett. 69, 3743 (1992). M. Op de Beeck and D. Van Dyck, Ultramicroscopy 64, 153 (1996). A. Orchowski and H. Lichte, Ultramicroscopy 64, 199 (1996). M.A. O’Keefe, Acta Crystallogr. A 29, 349 (1974). J.M. Cowley and A.F. Moodey, Acta Crystallogr. 10, 609 (1957).

20 21 22 23

24 25 26 27

28

29 30 31

32 33

34

35 36 37

38 39

D. van Dyck, Phys. Stat. Sol. (a) 52, 283 (1975). A. Bourret, L. Billard, and M. Petit, Inst. Phys. Conf. Ser. 76, 23 (1985). J. Hornstra, J. Phys. Chem. Solids 5, 129 (1957). P. B. Hirsch, A. Howie, and M. J. Whelan, Phil. Trans. Roy. Soc. A 252, 449 (1960). P. Stadelmann, Ultramicroscopy 21, 131 (1987). W. O. Saxton, T. J. Pitt, and M. M. Horner, Ultramicroscopy 4, 343 (1979). M. J. Mills and P. A. Stadelmann, Phil. Mag. A 60, 355 (1989). A. Catana, M. Hentzie, P. E. Schmid, and P. Stadelmann, J. Phys. Condens. Matter. 1, 3999 (1989). A. Vila, A. Cornet, J. R. Morante, P. Ruterana, M. Loubradou, R. Bonnet, Y. Gonzales, and I. Gonzales, Phil. Mag. A 71, 85 (1995). A. Serra and D. J. Bacon, Phil. Mag. A 54, 793 (1986). M. Igarashi, M. Kantha, and V. Vitek, Phil. Mag. B 63, 603 (1991). T. Braisaz, P. Ruterana, B. Lebouvier, and G. Nouet, Phys. Stat. Sol. (b) 191, 267 (1995) K. L. Merkle, Ultramicroscopy 40, 281 (1992). D. X. Li, P. Pirouz, A. H. Heuer, S. Yadavalli, and C. P. Flynn, Phil. Mag. A 65, 403 (1992). A. Ourmazd, F. H. Baumann, M. Bode, and Y. Kim, Ultramicroscopy 34, 237 (1990). M. J. Hÿtch and T. Plamann, Ultramicroscopy 87, 199 (2001). G. Möbus and T. Wagner, J. Microsc. 194, 124 (1999). A. Thust, W. M. J. Coene, M. Op de Beeck, and D. Van Dyck, Ultramicroscopy 64, 211 (1996). H. Lichte, Ultramicroscopy 38, 13 (1991). H. W. Zandbergen, D. Tang, J. Jansen, and R. J. Cava, Ultramicroscopy 64, 231 (1996).

485

486

9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers 40 41 42 43 44

45

46 47 48 49 50 51

52 53

54 55 56 57 58

59 60 61 62 63

M. J. Hytch, Micros. Microanal. Microstruct. 8, 41 (1997). S. H. Stobbs, K. Sato, and W. M. Stobbs, Ultramicroscopy 58, 275 (1995). H. Seitz, K. Ahlborn, M. Seibt, and W. Schröter, J. Microsc. 190, 184 (1998). G. Möbus and M. Rühle, Ultramicroscopy 56, 54 (1994). K. Mitsuoka, K. Murata, Y. Kimura, K. Namba, and Y. Fujiyoshi, Ultramicroscopy 68, 109 (1997). P. Bron, J. P. Rolland, and D. Thomas, Microsc. Microanal. Microstruct. 8, 11 (1997). H. Frieser, E. Klein, and E. Zeitler, Z. Angew. Phys. 1l, 190 (1959). H. Frieser and E. Klein, Z. Angew. Phys. 10, 337 (1958). E. Zeitler, Ultramicroscopy 46, 405 (1992). E. Völkl, F. Lenz, Q. Fu, and H. Lichte, Ultramicroscopy 55, 75 (1994). W. E. King and G. H. Campbell, Phys. Stat. Sol. (a) 166, 343 (1998). G. H. Campbell, D. Cohen, and W. E. King, Microsc. Microanal. Microstruct. 3, 299 (1997). M. J. Hÿtch and W.M. Stobbs, Ultramicroscopy 53, 191 (1994). G. Möbus, R. Schweifest, T. Gemming, T. Wagner, and M. Rühle, J. Microsc. 190, 109 (1998). N. G. Chew and A. G. Cullis, Ultramicroscopy 23, 175 (1987). R. Kilaas and R. Gronsky, Ultramicroscopy 16, 193 (1985). J. C. Russ, The Image Processing Handbook (CRC Press, 1995). G. Möbus, G. Necker and M. Rühle, Ultramicroscopy 49, 46 (1993). A. Rosenauer, S. Kaiser, T. Reisinger, J. Zweck, W. Gebhard, and D. Gerthsen, Optik 101, 1 (1996). L. D. Marks, Ultramicroscopy 62, 43 (1996). R. Kilaas and V. Radmilovica, Ultramicroscopy 88, 63 (2001). J. M. Cowley, Diffraction Physics (Plenum Press, 1976). G. J. Wood, W. M. Stobbs, and D. J. Smith, Phil. Mag. A 50, 375 (1984). J. C. H. Spence, J. M. Cowley, and R. Gronsky, Ultramicroscopy 4, 429 (1979).

64 65 66

67

68

69

70

71

72 73 74 75

76

77 78

79

80

81

T. Walther and C. J. Humphreys, Inst. Phys. Conf. Ser. 147, 103 (1995). P. Bayle, and J. Thibault, Microsc. Microanal. Microstruct. 8, 125 (1997). P. H. Jouneau, A. Tardot, G. Feuillet, H. Mariette, and J. Cilbert, J. Appl. Phys. 75, 731 (1994). H. Seitz, M. Seibt, F. H. Baumann, K. Ahlborn, and W. Schröter, Phys. Stat. Sol. (a) 150, 625 (1995). A. Naumov, H. Stanzl, K. Wolf, A. Rosenauer, S. Lankes, and W. Gebhard, J. Cryst. Growth 138, 595 (1994). A. Rosenauer, T. Reisinger, E. Steinkirchner, J. Zweck, and W. Gebhardt, J. Cryst. Growth 152, 42 (1995). K. Tillman, A. Thust, M. Lentzen, P. Swiatek, A. Forster, W. Laufs, D. Gerthsen, T. Remmele, and A. Rosenauer, Phil. Mag. Lett. 74, 309 (1996). S. Kret, C. Delamarre, J. P. Laval, and A. Dubon, Phil. Mag. Lett. 77, 249 (1998). S. Paciornik, R. Kilaas, and U. Dahmen, Ultramicroscopy 50, 255 (1993). D. Stenkamp and W. Jäger, Ultramicroscopy 50, 321 (1993). S. Kret, PhD thesis, University Paris, 1998. S. Kret, T. Benabbas, C. Delamarre, Y. Androussi, A. Dubon, J. Y. Laval, and A. Lefebvre, J. Appl. Phys. 86, 1988 (1999). A. Rosenauer, W. Oberst, D. Litvinov, D. Gerthsen, A. Forster, and R. Schmidt, Phys. Rev. B 61, 8276 (2000). M. J. Hytch, E. Snoeck, and R. Kilaas, Ultramicroscopy 74, 131 (1998). S. Kret, P. Ruterana, J. Chen, and G. Nouet, Mater. Res. Soc. Symp. Proc. 639, art. G11.54 (2000). S. Kret, J. Chen, P. Ruterana, and G. Nouet, Proc. Inst. Phys. Conf. Ser. 169, 319 (2001). E. Snoeck, B. Warot, H. Ardhuin, A. Rocher, M. J. Casanove, R. Kilaas, and M. J. Hytch, Thin Solid Films 319, 157 (1998). P. Dluzewski, G. Maciejewski, G. Jurczak, and S. Kret, to be published.

9.12 References 82

83

84

85

86

87

88

89

90 91 92 93

94

95 96

97

98

S. Kret, P. Dluzewski, P. Dluzewski, and E. Sobczak, J. Phys. Condens. Mater. 12, 10313 (2000). S. Kret, P. Dluzewski, E. Sobczak, A. Szczepanska, S. Mackowski, T. Wojtowicz, G. Karczewski, J. Kossut, and P. Ruterana, Mater. Res. Soc. Symp. Proc. 642, paper J3.8 (2000). B. Warot, E. Snoeck, P. Baulés, J.-C. Ousset, M.-J. Casanove, S. Dubourg and J. F. Bobo, J. Appl. Phys. 89, 5414 (2001). A. Ourmazd, D. W. Taylor, J. Cunningham, and C. W. Tu, Phys. Rev. Lett. 62, 933 (1989). P. Schwander, C. Kisielowski, M. Seibt, F. H. Baumann, Y. Kim, and A. Ourmazd, Phys. Rev. Lett. 71, 41 (1993). C. Kisielowski, P. Schwander, F. H. Baumann, M. Seibt, Y. O. Kim, and A. Ourmazd, Ultramicroscopy 58, 131 (1995). J.-L. Maurice, P. Schwander, F. H. Baumann, and A. Ourmazd, Ultramicroscopy 68, 149 (1997). A. Rosenauer, T. Remmele, D. Gerthsen, K. Tillmann, and A. Förster, Optic 105, 99 (1997). A. Rosenauer and D. Gerthsen, Adv. imag. electron. Phys. 107, 121 (1999). D. Stenkamp and W. Jäger, Inst. Phys. Conf. Ser. 134, 15 (1993). D. Stenkamp and H. P. Strunk, Appl. Phys. A 62, 369 (1996). J. F. Aebersold, P. A. Stadelmann, and J. L. Rouviere, Ultramicroscopy 62, 171 (1996). J. M. Gibson, R. Hull, J. C. Bean, and M. M. J. Treacy, Appl. Phys. Lett. 46, 649 (1985). M. M. J. Treacy, and J. M. Gibson, J. Vac. Sci. Technol. B 4, 1458 (1986). S. Christiansen, M. Albrecht, H. P. Strunk, P. O. Hanson, and E. Bauser, Appl. Phys. Lett. 64, 3617 (1994). C. Priester, I. Lefebvre, G. Allan, and M. Lannoo, Mater. Res. Soc. Symp. Proc. 317, 131 (1993). D. A. Faux, G. Jones, and E. P O’Reilly, Modeling. Simul. Mater. Sci. Eng. 2, 9 (1994).

99 C. Pryor, J. Kim, L. W. Wang, A. J. Wil-

100

101 102

103 104 105

106 107

108 109 110 111 112 113

114 115 116

117 118

liamson, and A. Zunger, J. Appl. Phys. 83, 2548 (1998). S. Christiansen, M. Albrecht, H. P. Strunk, P. O. Hansson, and E. Bauser, Appl. Phys. Lett. 66, 574 (1995). K. Tillmann, M. Lentzen, and R. Rosenfeld, Ultramicroscopy 83, 128 (2000). K. Scheerschmidt, D. Conrad, H. Kirmse, R. Schneider, and W. Neumann, Ultramicroscopy 81, 289 (2000). P. Dluzewski, J. Elasticity 60, 119 (2000). F. Spaepen, Acta Mater. 48, 31 (2000). O. C. Zienkiewicz and R. J. Taylor, The Finite Element Method, Vol. 1 (McGrawHill, London, 1989). P. Dluzewski, G. Jurczak and H. Antunez, CAMES 10, 1 (2003). S. Kret, P. Dluzewski, G. Maciejewski, V. Potin, J. Chen, P. Ruterana, and G. Nouet, Diam. Relat. Mater. 11, 910 (2002). E. G. Bithel and W. M. Stobbs, Philos. Mag. A 60, 39 (1989). E. G. Bithel and W. M. Stobbs, J. Appl. Phys. 69, 2149 (1991). F. M. Ross and W. M. Stobbs, Ultramicroscopy 32, 219 (1990). T. Walther and D. Gerthsen, Appl. Phys. A 57, 393 (1993). S. Thoma and H. Cerva, Ultramicroscopy 38, 265 (1998). S. Kret, G. Cywinski, T. Wojtowicz, J. Kossut, C. Delamarre, J. Y. Laval, A. Dubon, and G. Schiffmacher, X Conference on Electron Microscopy of Solids, Warsaw-Serock, Poland, September 20– 23, 1999. P. Ruterana, S. Kret, and M. A. Poisson, Mater. Sci. Eng. B 93, 185 (2002). A. Rosenauer and D. Gerthsen, Ultramicroscopy 76, 49 (1999). N. Peranio, A. Rosenauer, D. Gerthsen, S. V. Sorokin, I. V. Sedova, and S. V. Ivanov, Phys. Rev. B 61, 16015 (2000). A. J. McGibbon, S. J. Pennycook, and D. E. Tesson, J. Microsc. 195, 44 (1999). Y. Xin, E. M. James, I. Arslan, S. Sivananthan, N. D. Browning, S. J. Pennycook, F. Omnes, B. Beaumont, J.-P.

487

488

9 Strain, Chemical Composition, and Defects Analysis at Atomic Level in GaN-Based Epitaxial Layers

119 120 121 122 123 124 125 126

127 128

130

Faurie, and P. Gibart, Appl. Phys. Lett. 76, 466 (2000). J. H. Spence, Mater. Sci. Eng. Rep. 26, 49 (1999). D. Wang, F. H. Lj, and J. Zou, Ultramicroscopy 85, 131 (2000). D. Van Dyck, M. Op de Beeck, and W. Coene, Optik 93, 103 (1993). H. Lichte, Ultramicroscopy 47, 223 (1992). W. O. Saxton, Ultramicroscopy 55, 171 (1994). D. Gabor, Nature 161, 777 (1948). R. Bierwolf and M. Hohenstein, Ultramicroscopy 56, 32 (1994). H. W. Zandbergen, E. Connolly, I. E. Graboy, V. L. Svetchnikov, and A. R. Kaul, Physica C 29, 37 (2000). A. Orchowski and H. Lichte, Ultramicroscopy 64, 199 (1996). R. Anderson, S. Klepeis, J. Benedict, W. G. Vandygrift, and M. Orndorff, Inst. Phys. Conf. Ser. 100, 491 (1989). O. Kienzle, F. Ernst, and G. Möbus, J. Microsc. 190, 144 (1998).

131 H. Suchay, PhD thesis, University of

Paris, 1999. 132 W. E. King, G. H. Campbell, S. M.

133 134 135 136 137 138 139

140

Foiles, D. Cohen, and K. M. Hanson, J. Microsc. 190, 131 (1998). D. Hofmann and F. Ernst, Ultramicroscopy, 53, 205 (1994). G. Möbus, Ultramicroscopy 65, 205 (1996). A. Thust, M. Lentzen, and K. Urban, Ultramicroscopy 53, 375 (1994). O. Kienzle, M. Exner, and F. Ernst, Phys. Stat. Sol. (a) 166, 57 (1998). G. Möbus and O. Kienzle, Ultramicroscopy 85, 183 (2000). C. B. Boothroyd, J. Microsc. 190, 99 (1998). X. Zou, M. Sundberg, M. Larine, and S. Hovmöller, Ultramicroscopy 62, 103 (1996). K. L. Merkle, R. Csencsits, K. L. Rynes, J. P. Withrow, and P. A. Stadelmann, J. Microsc. 190, 204 (1998).

Part 3

Processing and Devices

491

10

Ohmic Contacts to GaN Philip J. Hartlieb, Robert F. Davis, and Robert J. Nemanich

Abstract

The Schottky-Mott, Bardeen, and metal-induced gap state models of the formation of the Schottky barrier at a metal-semiconductor contact interface and the relative importance of each model to ohmic contact behavior on GaN are described. The underlying principles regarding the development of stable, Ti-based ohmic contacts to n-type GaN for optoelectronic applications has been subsequently addressed. The specific contact resistivity for these contacts has been reported to be as low as 8.9 ´ 10–8 X cm2. By contrast, achieving ohmic contacts to p-type GaN with a specific contact resistivity < 10–5 X cm2 continues to be a challenge due to the inherent difficulties involved in acceptor doping with Mg and the existence of an *2-nm thick tenacious layer of native contamination on the as-grown surface that can add an additional 0.2 eV to the barrier height. The results of various plasma-, directed ion beam- and chemical-based in situ and ex situ surface preparation methods to remove contaminants, and/or modify the surface electronic properties, and/or achieve epitaxy of large grain size contacts with the underlying GaN are detailed. For the majority of studies the mechanism through which the ohmic behavior is improved is complex. The investigators of the present research have used an NH3-based chemical vapor clean to achieve ordered, stoichiometric, ptype GaN (0001) surfaces without detectable C and a significantly reduced O concentration. The resultant significant reduction in the downward band bending is attributed to the removal of contamination-induced surface states located in the lower portion of the band gap. Ni- and Pd-based contact structures on these cleaned surfaces are significantly less rectifying than identical contact structures

492

10 Ohmic Contacts to GaN

on conventional HCl-treated surfaces, which is consistent with the removal of surface contamination and a reduction in the Schottky barrier height. Significant differences in structure and morphology were also observed for contacts on chemical-vapor-cleaned and HCl-treated surfaces following a postmetallization anneal. These results are compared and contrasted with the reported results of electrical, chemical, and structural characterization by numerous other investigators.

10.1

Introduction

GaN (Eg = 3.4 eV) [1] is a relatively new direct band gap III–V semiconductor, which taken together with InN (Eg = 1.9 eV) [1] and AlN (Eg = 6.2 eV) [1] form an alloy system with the partially realized and the future potential for optoelectronic devices operating from the red to the deep UV. The high critical breakdown field of GaN is approximately an order of magnitude greater than both Si and GaAs. As such, this material is well suited for high-power applications. The achievement of p-type GaN has allowed the development of blue and green light emitting diodes (LEDs), blue emitting laser diodes, as well as nitride-based heterojunction bipolar transistors and field effect devices [2–6]. A strict definition for an ohmic contact assumes that the resistance across the metal-semiconductor interface is independent of the applied voltage. Many practical contacts exhibit limited voltage dependence; thus, Rhoderick and Williams [7] suggested that an ohmic contact be defined as one in which the voltage drop across the contact is negligible compared to the voltage drop across the remainder of the device. The small electron affinity of n-type GaN (*3.2 eV) makes it relatively easy to achieve ohmic contacts with low specific contact resistivity (qc). The Ti-based ohmic contacts to the n-GaN epilayer in the aforementioned device structures routinely achieve specific contact resistivities between 8 ´ 10–5 and 9 ´ 10–8 X cm2 [8–19]. However, a scientific understanding of the mechanism(s) through which ohmic behavior is achieved, as well as the effects of metal interlayer thickness, surface preparation, annealing ambient, and interfacial reaction products, is yet to emerge. A considerably larger obstacle to the future improvement of GaN-based devices incorporating a ptype epilayer, which include LEDs, HBTs, and laser diodes, involves a detailed understanding of the metal/p-GaN interface and the development of approaches to reduce the specific contact resistivity (qc), which has been consistently reported between 1 ´ 10–4 and 1 X cm2 [20–38]. Large qc values proceed directly from the inherent difficulties involved in acceptor doping with Mg, which is the most common method for achieving p-type-conducting GaN. The current limitation in the maximum concentration of Mg that can be incorporated during growth (*1 ´ 1020 cm–3) [39–41] as well as the large acceptor ionization energy (*300 meV) [1] limit the percentage of the atomic concentration that is ionized at room temperature to < 2.0% [38, 39]. Both limitations make it difficult to fabricate a tunneling ohmic contact to p-GaN in a manner similar to that used in other metal-semiconductor systems [42]. Addition-

10.2 Principles of Metal-Semiconductor Contacts

ally, there is a tenacious layer of native contamination on the as-grown surface that is *2 nm thick, which can add an additional 0.2 eV to the barrier height [43, 44]. The large ionization potential, doping limitations, and native surface contamination associated with p-type GaN results in large Schottky barrier heights and wide depletion regions at the metal/semiconductor interface regardless of the contact metal that is deposited. The deficiencies noted above also suggest that the current-conduction mechanism across the metal/p-GaN interface should be limited to the thermionic and/or thermionic field emission regimes. Trexler and coworkers [45] have shown that Ni/Au, Pd/Au, and Cr/Au contacts on p-GaN (p = 9.8 ´ 1016 cm–3) have a combination of thermionic and thermionic field emission as the dominant current-conduction mechanism. The expressions for the specific contact resistivity [46] associated with metal-semiconductor contacts operating either in the thermionic or in the thermionic field emission regimes indicate that a change in the barrier height by a few tenths of an eV will result in a reduction and/or increase in qc by at least an order of magnitude. In light of this sensitivity to the barrier height, the mechanism through which the metal-semiconductor contact forms and the resulting Schottky barrier height are of paramount importance. The Schottky–Mott, Bardeen, and metal-induced gap state (MIGS) models for metal-semiconductor contact formation have each been considered to explain the experimental results of ohmic contact formation on GaN. The first section of this chapter will briefly address the underlying principles of each model. The relative importance of each model will be considered in the individual sections that describe the experimental studies of ohmic contacts to both n- and p-type GaN. The description of studies of ohmic contacts to n-GaN will focus on Ti-based metallizations, which constitute the majority of work conducted in this area. The remainder of this review will be dedicated to experimental studies of ohmic contacts to p-type GaN, which will include selected studies conducted by the present authors.

10.2

Principles of Metal-Semiconductor Contacts

The earliest model for metal-semiconductor contact formation developed by Schottky and Mott (1938) [7] assumes that the barrier at the metal/semiconductor interface is a strict function of the difference between the work function of the metal and the electron affinity of the semiconductor. Expressions for the Schottky barrier [7] at the metal/semiconductor interface for contacts on n- and p-type semiconductors are shown in Eqs. (1) and (2), respectively, where Um, vs, and Eg are the metal work function, electron affinity, and semiconductor band gap, respectively. Ubn ˆ Um Ubp ˆ Eg

vs ; Um ‡ vs :

…1† …2†

493

494

10 Ohmic Contacts to GaN

Implicit in these two equations is the fact that the magnitude of the Schottky barrier should exhibit a 1 : 1 correspondence with changes in the metal work function. However, early experimental evidence consistently revealed a weak dependence of the Schottky barrier on the work function of the metal. In some cases there was no dependence. To explain the discrepancy, Bardeen (1947) [47] later proposed the surface/interface state model for metal-semiconductor contact formation. This model assumes that the metal and semiconductor are separated by a thin insulating layer, which in turn gives rise to a continuous band of states within the forbidden gap characterized by a neutral level (U0). The sign of the charge contained within what are assumed to be donor-like states is determined by the position of the semiconductor Fermi level at the surface with respect to the neutral level of the band of surface/interface states. When the neutral level lies above, below, or coincides with the Fermi level the sign of the charge contained in the states is positive, negative or neutral, respectively. The band of surface/interface states essentially screens the semiconductor from the metal when the two materials are brought together and the Fermi levels align. This screening effect subsequently overshadows the inherent difference in work function between the two materials. In the limiting case where the density of states is sufficiently high, the Fermi level is said to be “pinned” and the Schottky barrier height is completely independent of the work function of the metal. Note that 1012 states cm–2 is sufficient to pin the Fermi level at the semiconductor surface. The magnitude of the Schottky barrier is subsequently expressed as the Bardeen limit shown in Eq. (3). UB  Eg

U0 :

…3†

The Bardeen model was later refined by Cowley and Sze [48], wherein the expression for the Schottky barrier height is that shown in Eq. (4) and ei, d, q, and Ds are the interfacial layer permittivity, interfacial layer thickness, elementary charge, and density of interface states, respectively. U0b ˆ c…Um cˆ

ei : ei ‡ dDs

vs † ‡ …1

c†…Eg

U0 † ;

…4† …5†

This model takes into account the situation wherein the Schottky barrier still exhibits some dependence on the metal work function even in the presence of surface/interface states. Note that the Schottky barrier approaches the Schottky-Mott (Eqs. (1) and (2)) and the Bardeen (Eq. (3)) limits as the density of surface/interface states (Ds) approaches zero and infinity, respectively. Persistent scatter in the experimental data, as described by Eqs. (3) and (4), led to additional models for metal-semiconductor contact formation. Heine (1965) [49] proposed a model that emphasized the effects of metal-induced gap states (MIGS) or tailing of the quantum-mechanical wave functions from the metal into the for-

10.2 Principles of Metal-Semiconductor Contacts

bidden gap of the semiconductor. In this case, the tailing was sufficient to perturb the intrinsic states at the semiconductor surface to create additional states located in the forbidden gap [7]. In their unified defect model Spicer et al. [50, 51] proposed that defects formed at the interface during metal deposition give rise to interface and/or surface states that are assumed to be primarily responsible for the formation of the Schottky barrier. A more detailed description of the previously mentioned models is provided in Ref. [7]. More recently, Bermudez [52] has taken a phenomenological approach wherein the Schottky barrier is described in terms of the contribution from the bare surface barrier height (BSBH) as well as a Schottky–Mott term, which is dependent on the work function of the metal. The nature and origin of the surface states that leads to band bending at the prepared surface and constitutes the BSBH contribution are not yet well understood. Bermudez notes that regardless of the primary mechanism through which interface/surface states are formed, the fundamental idea of a band of states characterized by a neutral level and the subsequent effects on Fermi level alignment and Schottky barrier formation, as described by Cowley and Sze, is applicable. Regardless of the mechanism through which the Schottky barrier forms, ohmic contact formation hinges on either eliminating the Schottky barrier altogether or making it sufficiently thin such that a tunneling contact with linear current-voltage (I-V) characteristics is achieved. For metal-semiconductor contacts wherein the Schottky barrier exhibits a pronounced dependence on the metal work function, selecting a contact metal based on matching the work functions of the materials may eliminate the barrier. Similarly, large barriers can be overcome through the use of an intermediate semiconductor layer with graded stoichiometry that gradually reduces the work function to the appropriate value for the given contact metal. However, most ohmic contacts are routinely achieved by creating a highly doped region in the near surface of the semiconductor that significantly reduces the depletion width and results in a tunneling ohmic contact. There are several possible approaches to generating a highly doped, near-surface region that includes the incorporation of large quantities of dopant during growth as well as the intentional introduction of defects with the appropriate donor and/or acceptor-like properties. In this case the electrical properties of the defect and the corresponding contribution to the conduction process are the same as that for an intentionally introduced dopant. This is entirely different from the contribution of electrically active defects to a “hopping” conduction process. The former is usually achieved using a dry etch process that damages the near-surface region of the semiconductor and removes the appropriate component. A similar effect may be achieved via a high-temperature postmetallization anneal wherein the metal contact reacts with the underlying semiconductor and selectively removes one or more of the constituent atoms from the near surface of the semiconductor. These interfacial reactions may be tailored so as to achieve the desired defect type and concentration. In addition to modifying the electronic properties in the near-surface region the resulting morphology at the reacted interface may also result in a thinning of the Schottky barrier. In cases where the high-temperature anneal results in metal protrusions that spike into the semiconductor, large

495

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10 Ohmic Contacts to GaN

field concentrations may result. The large fields at the tip of each protrusion act so as to exaggerate the band bending at the interface and subsequently thin the Schottky barrier [53]. Note that several of the aforementioned processes may occur simultaneously. That is, an annealing temperature, time, and ambient may be chosen such that an ohmic contact is achieved through defects created in the near-surface region, and/or interfacial roughening, and/or the formation of a new phase with the appropriate work function in direct contact with the semiconductor. The remainder of this chapter addresses contact measurement techniques as well as experimental studies of ohmic contacts to both n- and p-type GaN. For each section the appropriate models for both the formation and elimination of the Schottky barrier will be highlighted.

10.3

Measurement Techniques

The specific contact resistivity (qc) at the metal/semiconductor interface provides a quantitative measure of the ohmic properties for a given contact scheme. This quantity is expressed in units of X cm2 and is independent of the size of the contact measured. A comprehensive treatment of the techniques used to measure qc is provided in Ref. [54]. Two of the techniques for qc measurement will be briefly addressed here, the first of which is the transfer length method (TLM) [55]. This technique rests on the assumption that the entire area of the contact is not active during the charge transfer process. The transfer length, which is considered to be the active area of the contact, is expressed in Eq. (6), where qc and qs are the specific contacts resistivity and semiconductor sheet resistance, respectively. LT ˆ

r qc : qs

…6†

Strictly defined, the transfer length is the distance wherein the voltage due to charge transfer from the metal to the semiconductor or vice versa has dropped to 1/e of the maximum value [54]. For this method, a set of identical rectangular-shaped contacts, which are horizontally and vertically aligned, is deposited and/or photolithographically patterned on the semiconductor substrate at various contact spacings. The total resistance is measured between successive sets of contacts over a finite voltage range and plotted according to the expression in Eq. (7), where d (cm) is the contact spacing, Rc (X) is the contact resistance, and Z (cm) is the contact width.   qs
d qs
d qs
LT RT ˆ : ‡ 2
Rc ˆ ‡2
Z Z Z

…7†

In this case the voltage and current are measured across the same set of contacts and is referred to as a front-contact resistance measurement. As the contact width

10.4 Experimental Studies of Ohmic Contacts to n-Type GaN

and spacing are known the slope, x-intercept, and y-intercept from a linear fit of the data provides values for qs, Rc, and LT, respectively. The specific contact resistivity is then calculated according to Eq. (6). For the TLM technique a MESA etch is often used to isolate the set of contacts and reduce the contribution from current flowing around the edges of each contact. This additional step results in a more accurate measurement of the specific contact resistivity. The circular transfer length method (CTLM) [56, 57] technique eliminates the contribution from edge currents without using an additional MESA etch. This method uses a large-area rectangular contact with circular cutouts of radius r0. The cutouts are horizontally and vertically aligned. A circular contact with radius r is placed at the center of each cutout region such that the gap spacing between the concentric cutout and contact is varied in the same way as the contact spacing in the rectangular model above. In this case the current is forced to flow perpendicular between the center contact and the cutout edge without an additional MESA etch. The expression for the total resistance measured between the center contact and edge as a function of gap spacing (d) is shown in Eq. (8). RT ˆ

     qs r0 1 1
ln ‡ LT
‡ : 2
p r0 d r0 d r0

…8†

In the limit where 2pr0  d the expression in Eq. (8) reduces to that shown in Eq. (9). RT 

qs
…d ‡ 2
LT † : 2
p
r0

…9†

In this case the specific contact resistivity may be extracted in the same way as that for the rectangular model.

10.4

Experimental Studies of Ohmic Contacts to n-Type GaN

An appropriate introduction to the experimental approaches used to overcome the barrier at the metal/n-GaN interface to achieve an ohmic contact includes a discussion of the relevant models that address the formation of the Schottky barrier itself. Although the Ti-based metallizations were initially explored as low work function contacts that would minimize the Schottky barrier according to the Schottky–Mott model, the role of MIGS in forming metal contacts to n-GaN has received considerable attention to date [58–61]. Kampen and Monch [58] measured the Schottky barrier of Ag and Pb contacts on n-GaN surfaces prepared using a Ga deposition and desorption technique. The samples were heated to 800 8C and subsequently exposed to a Ga flux for 10 min. Clean and ordered surfaces were achieved after heating for an additional 30 min at the same temperature in the absence of a Ga flux. The upward band bending at the clean surface has been mea-

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10 Ohmic Contacts to GaN

sured to be approximately 0.5 eV [59]. Barrier heights of 0.82 eV and 0.73 eV were measured for Ag and Pb contacts, respectively, which was in good agreement with the predictions of the MIGS-and-electronegativity model as shown in Fig. 10.1. Similarly, Dumont et al. [61] measured Schottky barriers of 1.15 eV and 0.85 eV for Au and Cu contacts, respectively, on n-GaN, which is also in good agreement with the same model. The clean n-GaN surfaces, prepared using an in situ, hightemperature (700 8C) H-plasma treatment followed by Ga deposition and desorption at 950 8C, exhibited upward band bending of 0.9 eV. This value is significantly larger than that measured in the previous study [59]. The MIGS-and-electronegativity model assumes that the barrier heights at ideal metal/semiconductor interfaces are primarily determined by the continuum of metal-induced gap states. It is important to note that ideal interfaces are defined as being intimate, abrupt, free of structural defects and foreign atoms, and laterally homogeneous [58]. Numerous experimental studies [62–65] have explored different methods to obtain clean, ordered, and stoichiometric n-GaN surfaces prior to contact deposition to understand the behavior of intimate metal-semiconductor contacts. The surface preparation prior to contact deposition largely determines the degree to which the n-GaN surface and the resulting metal/semiconductor interface may be assumed to be ideal. Bermudez et al. [63] investigated the effects of N-ion sputtering followed by a high-temperature anneal (ISA). The C and O contamination were both reduced below the detectable limits of Auger electron spectroscopy (AES), and ordered (1 ´ 1) surfaces were obtained. However, low-energy electron diffraction (LEED) revealed surface imperfections, which were attributed to N-vacancy formation. More

Fig. 10.1 Barrier heights of n-GaN (0001) Schottky contacts as a function of the electronegativity difference vm–vGaN [58].

10.4 Experimental Studies of Ohmic Contacts to n-Type GaN

importantly, surface state emission was identified at or near the valence band maximum (VBM) using the difference spectrum from the valence band spectra acquired from the clean n-GaN surface prior to and immediately following a controlled O2 exposure. The same study showed a decrease in the intensity of the surface state feature in the difference spectrum when the N-ion-sputtered surface was cleaned in an NH3 flux. In this case the NH3, which was readsorbed from the UHV background during the cooling process, effectively annihilated a portion of these surface states. The inherent variation in the surface electronic properties due to differences in surface preparation methods was underscored in a study by Wu et al. [64] that explored the effects of multiple cycles of ISA cleaning. In this study an additional band of surface states located at or near the VBM was observed on surfaces wherein residual O and C contamination was detected even after 2 ISA cycles. This emission was effectively eliminated with additional ISA cycles. Although the features observed by Bermudez and Wu et al. are located at similar binding energies, the physical origin, electronic properties, and corresponding effects on Schottky barrier formation are not necessarily the same. This must be assumed in light of the fact that the surface feature observed by Bermudez is effectively eliminated by a controlled O2 exposure, while that observed by Wu et al. persists in the presence of both O and C surface contamination. The studies above suggest that the degree to which extrinsic and/or intrinsic surface states contribute to Schottky barrier formation is a strong function of the surface-preparation method. Whether or not the MIGS-and-electronegativity model may be applied to metal contacts deposited on nonideal n-GaN surfaces containing intrinsic and/or extrinsic surface states remains to be determined. However, Kampen et al. [58] has suggested that interface dipoles due to foreign atoms or structural defects can be considered as secondary mechanisms in addition to MIGS. The effects of the n-GaN surface preparation method on the mechanism through which the Schottky barrier is finally overcome to form ohmic contacts will be addressed in the next section. The majority of successful ohmic contacts to n-type GaN have included a Ti layer in direct contact with n-GaN as part of either a bi- or a multilayer metallization scheme [8–19]. Values of qc as low as 8.9 ´ 10–8 (X cm2) [8] have been achieved; however, there continues to be considerable debate regarding the mechanism(s) by which the ohmic contact is formed. Multiple experimental studies indicate that the predominant mechanism is a strong function of ex situ and/or in situ n-GaN surface preparation methods, the constituent metals included in the contact structure and the corresponding atomic ratios, and postmetallization annealing ambients. Both reactive ion (RIE) [8–10] and inductively coupled plasma (ICP) [11] etching techniques have been successfully employed in fabricating ohmic contacts to n-type GaN. Fan et al. [8] investigated the effects of treating the n-GaN (n = 2 ´ 1017 cm–3, n = 4 ´ 1017 cm–3) surface with an RIE process prior to the deposition of (Ti 15 nm/ Al 20 nm/Ni 40 nm/Au 50 nm) contact structures. A minimum qc value of 3.3 ´ 10–6 X cm2 was achieved for nonalloyed contact structures on RIE-processed surfaces. The subsequent ohmic behavior of the contact was attributed to the re-

499

500

10 Ohmic Contacts to GaN

moval of native surface contamination and/or the creation of N vacancies in the near-surface region as a result of the RIE process. The creation of a substantial number of N vacancies, which have been previously shown to act as donor-like defects, effectively increases the doping in the near-surface region, decreases the width of the Schottky barrier and forms a tunneling ohmic contact. Wang et al. [9] have also demonstrated a reduction in qc for Ti 30 nm/Al 100 nm/Ti 30 nm/Au 30 nm contact structures deposited on RIE-processed n-GaN (n = 1.4 ´ 1020 cm–3, n = 5.2 ´ 1017 cm–3) surfaces. A minimum qc value of 5.2 ´ 10–6 X cm2 was achieved for the as-deposited contacts. Similarly, Sheu et al. [11] was able to achieve nonalloyed ohmic contacts by depositing a Ti 20 nm/Al 320 nm scheme on an n-GaN (n = 7 ´ 1017 cm–3) surface that had been exposed to a Cl2-based inductively coupled plasma and subsequently annealed at 600 8C for 5 min in N2. In this case the ohmic behavior was again attributed to N vacancy formation in the near-surface region. Lin and Lee [12] successfully fabricated nonalloyed ohmic contacts to n-GaN (n = 5 ´ 1017 cm–3) using an (NH4)2Sx ex situ surface pretreatment prior to the deposition of Ti 50 nm/Al 150 nm contact structures and achieved a minimum qc value of 5.0 ´ 10–5 X cm2. The chemical treatment effectively removed the native oxide and protects the surface from oxidation prior to contact deposition. To further reduce qc, an ex situ and/or in situ surface pretreatment is often used in conjunction with a high-temperature postmetallization anneal. There are currently two mechanisms that have been proposed to explain ohmic contact formation during annealing of Ti-based metallizations. The first mechanism attributes the improved ohmic behavior to the formation of a thin TiN layer during the high-temperature anneal and the subsequent formation of N vacancies in the near-surface region of the n-GaN. The manner in which N vacancy formation results in ohmic contact formation has been outlined above. The second mechanism suggests that during the high-temperature anneal the Ti effectively reduces the native oxide at the surface and alloys with additional metals included in the contact structure to form a low work function material in direct contact with the underlying n-GaN. The predominant mechanism through which the ohmic contact is formed via high-temperature postmetallization annealing is specific to both the constituent metals in the contact structure as well as the corresponding atomic ratios. Smith et al. [13] investigated the ohmic contact formation mechanism for Ti 100 nm, TiN 100 nm, and Ti 25 nm/Au 190 nm contact structures on n-GaN (n = 1.2 ´ 1018 cm–3) annealed between 500 and 900 8C in N2. The n-GaN films were cleaned ex situ using a HCl : H2O (1 : 1) solution and then thermally desorbed in vacuum at 700 8C for 15 min prior to contact deposition. After annealing the contact structures through 900 8C, the qc value for Ti, TiN, and Ti/Au contacts reached minimum values of 9.9 ´ 10–3 X cm2, 1.1 ´ 10–2 X cm2, and 1.2 ´ 10–6 X cm2, respectively. X-ray photoelectron spectroscopy (XPS) measurements made on thin (1.5 nm) Ti overlayers annealed at 800 8C confirmed the formation of TiN. The Ti 2p core level spectra shown in Fig. 10.2 exhibits a significant shift to higher binding energy and pronounced shouldering, which is consistent with the formation of TiN. Fig. 10.3 shows cross-sectional transmission electron microscopy (TEM) micrographs of Ti/

10.4 Experimental Studies of Ohmic Contacts to n-Type GaN

Fig. 10.2 Evolution of the Ti2p XPS peak as a function of annealing, showing the binding energy shift and high binding energy shoulder indicative of TiN formation [13].

Au contact structures annealed through 900 8C in N2. TiN formation at the metal/ semiconductor interface is again clearly indicated. The decreased qc in coincidence with TiN formation at the reacted interface is consistent with N vacancy formation and subsequent thinning of the Schottky barrier, as described in mechanism one above. Additional evidence for this mechanism was provided in a study [14] that explored Ti 150 nm, TiN 200 nm, and Ti 5 nm/TiN 200 nm contact structures on nGaN (n = 7 ´ 1017 cm–3) annealed between 400 and 900 8C in N2 or Ar2 ambients. Prior to contact deposition the n-GaN films were cleaned ex situ using a HCl : H2O (1 : 1) solution. Depth-profiling XPS revealed a thin layer of TiN at the interface for Ti contacts annealed at 700 8C in N2. The Ti contacts reached a minimum qc value of 4.0 ´ 10–6 X cm2 when annealed at 800 8C for 1 min in N2. The reasons for which a lower qc was achieved as compared to that for Smith et al.

501

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10 Ohmic Contacts to GaN

Fig. 10.3 Cross-sectional TEM images representative of the Au/Ti/GaN samples: RTA annealed at 900 8C. As-deposited Ti is finely polycrystalline; after annealing the Ti layer has transformed almost completely to TiN. The annealed TiN is oriented with TiN (111) planes parallel to the GaN (0002) basal plane [13].

[13] will be discussed at the end of this section. Ti/TiN contacts reached a minimum qc value of 6.0 ´ 10–6 X cm2 after annealing at 800 8C for 1 min in Ar2. The absence of a temperature-dependent value of qc for both the Ti and the Ti/TiN contact structures suggests a field emission conduction mechanism, which is consistent with N vacancy formation and the thinning of the Schottky barrier as described for mechanism one. The temperature-dependent qc observed for TiN contacts deposited directly on n-GaN indicates that conduction occurs via thermionic emission and suggests that the interface remained abrupt and unreacted during subsequent annealing. A similar mechanism has been suggested by additional studies that investigated the electrical and structural properties of Ti/Al metallizations on n-GaN. Ruvimov et al. [10] observed a thin TiN layer at the metal/semiconductor interface for as-deposited Ti 20 nm/Al 100 nm contacts on an RIE-processed n-GaN (n = 5 ´ 1018 cm–3) film. The thickness of the TiN layer increased to *5 nm after a rapid thermal anneal at 900 8C for 30 s in a N2 ambient. This mechanism is further evidenced by the fact that Fan et al. [8] observed a decrease in the qc value by approximately two orders of magnitude when Ti/Al contacts that were previously deposited on RIE-processed n-GaN are annealed at 900 8C for 30 s. Ruterana et al. [15] achieved a qc value of 1 ´ 10–5 X cm2 for Ti 20 nm/Al 80 nm contacts deposited on an n-GaN (n*1018 cm–3) surface previously treated using a low-energy (*5 eV) Ar ion etch

10.4 Experimental Studies of Ohmic Contacts to n-Type GaN

and annealed at 500 8C for 10 s. TEM micrographs of the annealed contact structure shown in Fig. 10.4 reveal a 2-nm thick, polycrystalline TiN layer at the metal/ semiconductor interface. Papanicolaou et al. [16] investigated the ohmic contact formation mechanism for Ti 25 nm/Al 100 nm contact structures on n-GaN (n = 1.1 ´ 1018 cm–3) annealed between 500 and 1200 8C under vacuum. Prior to contact deposition the n-GaN films were descummed in an O2 plasma and then etched in a NH4OH : H2O (1 : 10) solution followed by a deionized water rinse. The contacts exhibited rectifying behavior after isochronal anneals (2 min) at 500, 600, and 700 8C. The as-deposited I-V characteristics returned after an 800 8C anneal and achieved a minimum qc value of 5.4 ´ 10–5 X cm2 when annealed at 900 8C. In stark contrast to the studies above the initial degradation in the I-V characteristics was attributed to the formation of TiN at the interface. It was suggested that the offset due to the formation of a TiN/GaN heterojunction resulted in a larger Schottky barrier height regardless of the effects of N vacancy formation. The improvement in the ohmic behavior after annealing at higher temperatures (900 8C) is attributed to the diffusion of Al to the metal/semiconductor interface, where it forms stable AlN and/or Al-Ti-N phases. In this case the role of Al is critical to the formation of a low qc contact. An additional study by Luther et al. [17] investigated the electrical and structural properties of Ti 35 nm/Al 115 nm contacts annealed between 400 and 600 8C in Ar2. The results of this investigation suggested an equally important yet somewhat different role for the Al interlayer. Ohmic contacts with a qc value of

Fig. 10.4 A Ti/Al layer after 10 min anneal at 500 8C, the TiN crystallites are small, and amorphous patches (A) may exist [15].

503

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10 Ohmic Contacts to GaN

*7 ´ 10–6 X cm2 were achieved after annealing at 400 8C for 5 min. The diffusion of the Al to the GaN surface is evidenced by the XPS depth profiles shown in Fig. 10.5. However, in light of the fact that the interface remained abrupt, Luther et al. proposed that ohmic-contact formation occurred via a reduction of the native oxide by the Ti overlayer and the formation of a low work function Al-Ti intermetallic phase in intimate contact with the n-GaN. The contradictory results and the marked differences between the proposed mechanisms for Ti/Al ohmic contact formation in particular are not surprising in light of the results of Pelto et al. [18] and Kwak et al. [19] that showed that small differences in the Ti : Al layer thickness ratios can lead to significant differences in the morphology and electrical properties of the contact. Pelto et al. [18] also suggested that differences in layer thickness ratios will result in substantial differences in the reaction products formed within the metallization and ultimately the final phase that contacts the underlying GaN. This may indeed explain the contrast in the experimental evidence presented for the two mechanisms that have been proposed to date. This study also addressed the effects of an O-gettered postmetallization annealing ambient. The qc values for contacts annealed in a gettered ambient are 2.6 times lower than those annealed in a nongettered ambient. The

Fig. 10.5 XPS depth profiles of Ti/Al (35/ 115 nm) contacts on GaN: a as-deposited and annealed at 400 8C for b15 s; c 45 s;

d 3 min. Atomic per cents of Al, Ti, O, Ga, and N are shown as a function of sputter time [17].

HCl : H2O (1 : 1) HCl : H2O (1 : 1) HCl : H2O (1 : 1)

HCl : H2O (1 : 1) HCl : H2O (1 : 3) (NH4)2Sx dilute HCl ICP etching/600 8C anneal/HCl : H2O (1 : 1) HCl : H2O (1 : 1) Ar ion etching NR O2 plasma, NH4OH : H2O (1 : 10) NR Reactive ion etching (RIE) HCl : H2O (1 : 1) desorption 700 8C 15 min NR HCl : H2O (1 : 1)

NR 1 ´ 1018 d) 1.2 ´ 1018 a)

5 ´ 1016 c) 2.5 ´ 1017 a) 5 ´ 1017 a) 7 ´ 1017 a) 7 ´ 1017 a)

1 ´ 1018 d) 1.1 ´ 1018 a)

5 ´ 1018 a)

1.2 ´ 1018 a)

NR

TiN TiN TiN

Ti/Al Ti/Al Ti/Al Ti/Al Ti/Al

Ti/Al Ti/Al

Ti/Al

Ti/Au

Ti/TiN

NR desorption 700 8C 15 min NR Ar ion etching desorption 700 8C 15 min NR NR NR NR NR

HCl : H2O (1 :1) HCl : H2O (1 : 1)

NR 1.2 ´ 1018 a)

Ti Ti

In situ treatment

Ionized charge (cm–3)

Contact

Ex situ treatment

NR NR NR NR NR

NR NR NR

4 ´ 10–5 NR 1.1 ´ 10–2 2 ´ 10–5 9.6 ´ 10–6 5 ´ 10–5 1 ´ 10–5 7.2 ´ 10–5

500 8C/10 s 1 ´ 10–5 1100 8C/2 min 1.2 ´ 10–5 NR 1.2 ´ 10–6 6 ´ 10–6

600–1150 8C 550 8C/1 min NR 400 8C/3 min 500 8C/5 min

900 8C/30 s 900 8C 800 8C/1 min

NR

NR

NR NR NR

[

[

[

[ [

NR NR [ [ [

[ [ [

NR

[

[

[ [

[ [ NR NR NR

NR [ [

NR [

800 8C/1 min NR 900 8C

[ [

4 ´ 10–6 9.9 ´ 10–3

800 8C/1 min 900 8C NR NR

Specific contact Surface and/or interface analysis resistivity Electronic Chemistry Structure/ (X cm2) states morphology

Thermal treatment

14

13

10

15 16

19 18 12 17 11

14 15 13

14 13

Ref.

Tab. 10.1 Reported Ti-based ohmic contact schemes for n-type GaN. Specific contact resistivity values are reported for room temperature. Ionized charge is reported prior to surface pretreatment

10.4 Experimental Studies of Ohmic Contacts to n-Type GaN 505

Reactive ion etching (RIE) Reactive ion etching (RIE) Reactive ion etching (RIE) Reactive ion etching (RIE) NR

NR

NR

NR

NR

5.2 ´ 1017 b)

1.4 ´ 1020 b)

NR

NR

1.1 ´ 1018 a)

Ti/Al/Ti/Au

Ti/Al/Ti/Au

Ti/Al/Ni/Au

Ti/Al/Ni/Au

Ti/Al/Ni/Au

NR = not reported, ICP = inductively coupled plasma a) carrier conc. b) ND-NA c) unintentionally doped d) Si concentration

NR

In situ treatment

Ionized charge Ex situ treatment (cm–3)

Contact

Tab. 10.1 (cont.)

(6.0 ± 1.7) ´ 10–7 NR

NR NR

1.19 ´ 10–7 8.9 ´ 10–8

750 8C/30 s 900 8C/30 s 900 8C/30 s 1100 8C/2 min 1.3 ´ 10–5

NR

5.08 ´ 10–5 NR

[

NR

NR

NR

NR

[

NR

NR

NR

NR

Specific contact Surface and/or interface analysis resistivity Electronic Chemistry Structure/ (X cm2) states morphology

900 8C/30 s

Thermal treatment

16

8

8

9

9

Ref.

506

10 Ohmic Contacts to GaN

10.5 Experimental Studies of Ohmic Contacts to p-Type GaN

effect of a gettered annealing ambient is underscored by a comparison of the studies by Smith et al. [13] and Luther et al. [14], which explored single Ti layers on nGaN. Luther et al. were able to achieve a qc value *3 orders of magnitude lower than that of Smith et al. using a gettered N2 annealing ambient. Note that the Ti thickness and the annealing temperatures were comparable, while the doping level in the gettered study was slightly lower. The contact structures, experimental conditions, and corresponding qc values from the studies above are shown in Tab. 10.1. The effects of in situ and/or ex situ surface pretreatment, contact metals and corresponding atomic ratios, and postmetallization annealing conditions on the minimum qc values achieved have been briefly addressed. A considerable amount of experimentation is still required to fabricate device-quality ohmic contacts to n-GaN with consistent electrical, chemical, and structural properties.

10.5

Experimental Studies of Ohmic Contacts to p-Type GaN

A few studies have addressed the relative importance of each of the models for Schottky barrier formation at metal p-GaN interfaces. Koide et al. [66] investigated the electrical properties of Ni, Ta, Au, Ti, Al, Cu, Pd, and Pt contacts on p-GaN (p < 1 ´ 1018 cm–3), which had been previously treated using a buffered hydrofluoric acid solution (BHF). A resistance value was determined from the current at an applied voltage of ± 0.1 V. This value is defined as the total resistance between sets of contacts spaced 8 lm apart. The exponential decrease in the resistance at the metal/semiconductor interface with increasing metal work function shown in Fig. 10.6 suggests that the Schottky barrier height is somewhat sensitive to the work function of the metals used in the study. To distinguish between the effects of several competing processes on the final Schottky barrier height a number of studies have investigated the chemical and electrical properties of metal contacts deposited on clean p-type GaN surfaces. Wu et al. [64] and the present authors [70] observed distinct bands of surface states located at and approximately 1.0 eV above the VBM, respectively, for clean p-GaN surfaces. In both cases the nature and origin of the surface states was unknown. Wu et al. [64] suggested that although the barrier height exhibited some dependence on the metal work function, the final Schottky barrier height at the metal/semiconductor interface is a result of several competitive processes including the effects of the metal work function, interface states due to defects, reaction products, and states that are induced by the metal deposition itself. The position of Wu and Khan [69] is further supported by the fact that the present authors [70] have experimentally measured the Schottky barrier height at the Pd/p-GaN interface to be 1.3 ± 0.1 eV. Compared to the barrier height predicted by the Schottky-Mott model, an interface dipole contribution of 0.4 ± 0.1 eV is suggested. Note that even though the Schottky barrier exhibits a limited dependence on the metal work function, the large ionization potential of p-GaN (6.5 eV*v+Eg), as well as the absence of any metal with a work

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10 Ohmic Contacts to GaN

Fig. 10.6 R0 values as a function of metal work functions for var-

ious contact metals [66].

function greater than 5.8 eV, makes it impossible to select a contact metal based solely on matching the work functions of the materials. Although the primary mechanism responsible for the formation of the Schottky barrier is unclear, a significant obstacle to ohmic contact formation is the tenacious layer of native surface contamination, which adds an additional 0.2 eV to the barrier height [44]. In light of this challenge, research concerned with multiple in situ and ex situ surface preparation methods has been conducted in an attempt to remove contaminants [27, 28, 30–32, 34, 44, 64–73], and/or modify the surface electronic properties [27, 30, 32, 34, 44, 64, 65, 68–74], and/or improve the epitaxial microstructure of the metallization [70, 75]. A dilute HCl bath, which is the most common ex situ cleaning technique [27, 28, 30, 34, 67, 68, 72, 73], has been shown to only slightly reduce O and C contamination at the surface. Analyses of the results of similar ex situ treatments that used room temperature aqua regia (HCl : HNO3 1 : 1) [27], boiling aqua regia [27–30, 32, 72, 73], boiling KOH [34, 68], BOE [44], dilute HF [74], or a sequential dip in multiple chemical baths [32, 67, 73] have also revealed limited success in cleaning and/or modifying the properties of the p-type GaN surface. For the majority of studies the mechanism through which the ohmic behavior is improved is somewhat speculative. However, several authors have suggested that ex situ chemical cleaning in boiling aqua regia [30, 72], boiling KOH [68], or successive treatments in boiling aqua regia and (NH4)2Sx solution [73] partially removes GaOx and subsequently leaves behind a large concentration of Ga vacancies in the near-surface region. As Ga vacancies have been predicted to behave as shallow acceptors [76], the Fermi level would be shifted towards the valence band edge following the wet chemical process. As a result, the depletion region would be reduced and a lower specific contact resistivity subsequently achieved. How-

10.5 Experimental Studies of Ohmic Contacts to p-Type GaN

ever, the same study [76] has indicated that N vacancies are the thermodynamically favored defect in p-type GaN. Therefore, it is unlikely that a Ga-deficient surface would be maintained for an extended period of time. Additional studies that also investigated the effects of ex situ cleaning in boiling aqua regia [27] and successive treatment in boiling aqua regia and (NH4)2Sx [32] suggest that the mechanism through which contact properties are improved involves a change in surface termination and/or suppression of the reformation of the oxide after pulling the film from solution. Still other authors [31, 34, 44] postulate that rather than changes in surface termination or significant changes in defect concentrations, a more probable mechanism involves a partial removal of the surface contamination and corresponding reduction in the Schottky barrier height. The latter mechanism assumes that prior to any ex situ cleaning process the asgrown surface contains a significant number of contamination-induced interface states located within the forbidden gap. It is not unreasonable to assume that the density of these contamination-induced interface states is directly proportional to the thickness of the native contamination. It further assumes that in equilibrium the Fermi level lies below the neutral level of the distribution of interface states. In the case above, positive charge would accumulate at the interface and increase the downward band bending and subsequently increases the Schottky barrier height following metallization. Ex situ chemical treatment prior to contact deposition results in a reduction in the thickness of the native contamination and subsequently reduces the density of contamination-induced interface states as well as the net charge contained within them. As a result, both the downward band bending and the Schottky barrier height at the metal/semiconductor interface are ultimately reduced. The difficulties involved in achieving clean, stoichiometric p-type GaN surfaces using ex situ chemical treatments is underscored by the fact that there is a finite time between pulling the sample from solution and loading into ultrahigh vacuum (UHV). The rapid reformation of the contamination layer has been confirmed in a study that investigated the effects of Ar ion sputtering on the surface properties of ptype GaN [44]. Although there are obvious limitations to the ex situ cleaning methods described above, these studies provide valuable insight into the effects of contamination removal on the electronic properties at the p-type GaN surface. In situ surface preparation methods, which included UHV annealing [67, 68], ion bombardment [44, 64, 65], plasma techniques [20, 77], Ga metal deposition and desorption [59], and NH3 chemical vapor cleaning (CVC) [70] have been explored to overcome the deficiencies of the ex situ techniques outlined above. UHV annealing, which in some cases has been used in conjunction with one of the ex situ methods described above, has been shown to only partially remove oxygen and carbon contamination. Waki et al. [67] showed a significant reduction in the O1s/Ga2p3/2 and C1s/Ga2p3/2 XPS photoelectron peak intensity ratios by combining an ex situ wet chemical clean in successive 36% HCl and 96% H2SO4 : 30%H2O2 solutions with UHV annealing at 600 8C for 10 min. Au electrodes subsequently deposited on the cleaned p-GaN (p = 1.5 ´ 1017 cm–3) surface

509

510

10 Ohmic Contacts to GaN

exhibited improved ohmic behavior compared to identical electrodes deposited on an as-grown surface, although the qc values on the cleaned surface still measured as high as 20 X cm2. Ar or N ion bombardment of surfaces effectively removes native surface contamination although considerable nonstoichiometries in the near-surface region result. Ishikawa et al. [44] investigated Ar and N ion sputtering of both as-grown and buffered hydrofluoric acid (BHF) treated p-GaN (p = 1.0 ´ 1017–1.0 ´ 1018 cm–3) surfaces. Both Ar and N ion-sputtered surfaces exhibited a significant decrease in both the O1s and C1s XPS photoelectron peak intensities. However, following either Ar or N ion sputter treatments the N/Ga ratio was subsequently decreased and increased, respectively, which suggests a nonstoichiometric p-GaN surface. Significant deterioration in the electrical properties was observed by Ishikawa and his coworkers [44] for Ni contacts deposited on ion-sputtered surfaces previously treated with BHF compared to identical contacts deposited on p-GaN surfaces treated with BHF only. Therefore, although sputtering the p-type GaN surface with N or Ar ions significantly decreases both C and O contamination, the surface is subsequently damaged, and a highly nonlinear contact results. A similar observation was made by Wenzel et al. [77] wherein a degradation in the linearity of Ni/Au contacts was observed when a glow discharge was used to treat the p-GaN (p = (1.5–3.0) ´ 1017 cm–3) surface prior to contact deposition. As has been suggested in previously mentioned studies, N vacancies are the dominant defect in ptype GaN. A large number of donor-like N vacancies created at the ion-sputtered surface would compensate the Mg acceptors in the near-surface region, increase the depletion region and produce the observed degradation in ohmic behavior. Wu et al. [64, 65] showed that the ISA cleaning previously used by Bermudez et al. [63] on n-GaN surfaces, was equally effective for obtaining clean and ordered p-type GaN surfaces. In this case a large portion of the damage induced by N-ion sputtering was subsequently recovered by high-temperature annealing. The downward band bending at ISA-cleaned p-GaN surfaces was measured to be 0.75 and 1.2 eV, respectively, via X-ray and ultraviolet photoelectron spectroscopies. The latter study also accounted for a band of surface states that extended approximately 0.6 eV above the VBM on the cleaned p-GaN surface. Bermudez et al. [63] also observed a similar band of surface states on ISA-cleaned n-GaN surfaces. The I-V characteristics of contacts deposited on these ISA-cleaned surfaces have not been reported. Eyckeler et al. [59] have obtained clean and well-ordered p-GaN (p = 1.2 ´ 1017 cm–3) surfaces using a Ga deposition and desorption technique. The samples were initially heated to 800 8C and exposed to a Ga flux of 1 ´ 1018 Ga atoms cm–2 s–1 for 10 min. The samples were subsequently annealed at the same temperature for an additional 30 min in the absence of the Ga flux. Assuming an Ea of *300 meV, the downward band bending at the clean p-GaN surface was approximately 2.9 eV. To our knowledge this is the largest band bending reported for p-GaN to date. The present authors have employed an NH3-based high-temperature CVC process to achieve clean, ordered, and stoichiometric p-GaN surfaces. Fig. 10.7 shows the XPS photoelectron peaks from both the HCl-treated (as-loaded) and CVC-treated surfaces. Following the CVC process the C signal was reduced below the detectable -

10.5 Experimental Studies of Ohmic Contacts to p-Type GaN

Fig. 10.7 XPS a C 1s; b O 1s and core level photoelectron peaks from the as-loaded and chemical vapor cleaned p-GaN surface. The

O 1s and C 1s spectra were acquired using MgKa (hm = 1253.6 eV) and AlKa (hm = 1486.6 eV) radiation, respectively.

limit of the XPS, which is approximately 0.3 at%. The O concentrations and Ga/N ratios on the as-loaded and CVC-treated surfaces were 15 and 2 ± 1 at%, respectively, 1.5 and 1.0, as calculated using the integrated intensities and corresponding sensitivity factors (O1s = 0.660, N1s = 0.420, Ga3d = 0.310). The ultraviolet photoelectron spectroscopy (UPS) valence band spectra shown in Fig. 10.8 shows a significant reduction in the downward band bending and a corresponding downward movement of the surface Fermi level following the CVC process. This is attributed to the removal of contamination-induced surface states located in the lower portion of the band gap. The band bending and effective electron affinity at the clean surface appears to be dependent on the surface roughness value (RMS) and/or crystallinity of the as-grown p-type GaN. The band bending at the clean p-GaN surfaces with RMS roughness values of 8.0 ± 1.5 nm and 2 ± 1 nm was measured to be 0.8 ± 0.1 eV and 1.4 ± 0.1 eV, respectively. The effective electron affinity at the clean p-GaN surface was measured to be 2.6 ± 0.1 eV and 3.1 ± 0.1 eV for p-GaN surfaces with as-grown RMS roughness values of 8.0 ± 1.5 nm and 2 ± 1 nm, respectively. The inset to the valence band spectra for the smoother p-GaN surface shown in Fig. 10.8 reveals a shoulder at the VBM as well as a previously unidentified band of surface states centered at approximately 1.0 eV below the Fermi level. The subsequent effects of the CVC process described above on the ohmic properties of as-deposited and annealed Pd/Au and Ni/Au contact schemes will be addressed below. The Ni/Au contact scheme in particular has achieved widespread use in both commercially produced LEDs as well as other GaN-based devices that contain a ptype GaN epilayer [4, 6]. The Ni-based contact schemes have been previously employed in making ohmic contacts to GaAs [78, 79] due in part to their ability to penetrate the native oxide at the semiconductor surface. A large number of stud-

511

512

10 Ohmic Contacts to GaN Fig. 10.8 UPS valence band spectra from the: a as-loaded; b chemical vapor-cleaned p-GaN surface. The dashed lines indicate the shift of the core level feature. A linear fit of the high kinetic energy side of spectra b and the subsequent position of the valence band maximum on the clean surface are shown within the inset. The vertical arrow labeled SS2 indicates surface-staterelated emission. All spectra were acquired using the He I photon line (hm = 21.2 eV). The binding energy is measured with respect to the Fermi level (EF = 0 eV).

ies have used either in situ [20, 74, 77] or ex situ [20–23, 25, 26, 29, 33, 36, 44, 81– 88] surface pretreatments as described above, prior to fabricating the Au/Ni/pGaN contact structure. The majority of these studies report rectifying contacts in the as-deposited condition; however, there are a few reports of as-deposited qc values within the reported range of 5 ´ 10–3–1 ´ 10–1 X cm2 [25, 26, 29, 33, 36, 84]. To overcome the deficiencies of both in situ and ex situ surface-preparation methods numerous studies [20–26, 29, 36, 84, 87–93, 95] have investigated the effects of annealing Au/Ni/p-GaN contact structures between 350 and 850 8C in a N2 ambient from 30 s to 30 min. Values for qc have been reported in the range of 3.8 ´ 10–1 X cm2–3.6 ´ 10–4 X cm2. The dispersal of the native contamination [44, 94] and/or the formation of reaction products either within the contact metallization or at the metal/semiconductor interface [22, 23, 25, 26, 29, 84, 88–91, 95] have been proposed as possible mechanisms for the reduction of qc. Although most studies report a decrease in qc following a postmetallization anneal at temperatures between 450 and 600 8C, there is still considerable disagreement regarding the temperature at which specific interfacial reactions occur, the products of those reactions, and the mechanism through which newly formed phases subsequently reduce qc. Prior to examining the temperature dependence in the annealing studies below it is important to note the difficulty involved in comparing temperatures from one study to the next. For most annealing studies, the contact structure is placed in touching contact with a heated support whose temperature is independently determined using a welded thermocouple that is subsequently bonded to the support. As the nature of the sample itself precludes temperature

10.5 Experimental Studies of Ohmic Contacts to p-Type GaN

determination via optical pyrometer (GaN, SiC, and sapphire are all transparent in the IR), the temperature of the sample is often taken to be the same as that which is measured for the heated support. However, the nature of the thermal contact that is made between the sample and the support has a significant effect on the actual sample temperature that is achieved during the annealing process. These thermal effects have led to temperature differences between the sample and the support that are as large as 100 8C. This effect may be partially responsible for the large temperature ranges that are reported below. Several studies report that annealing between 450 and 600 8C results in the formation of Au-Ga [25] and/or Au-Ni-Ga [26, 29] solid solutions and subsequently leaves behind a significant number of Ga vacancies in the near-surface region of p-GaN. The mechanism through which Ga vacancies would decrease the specific contact resistivity has been outlined above. The dissolution of both Ni and Ga in Au-rich solid solutions is consistent with the fact that the solubility limits of both Ni and Ga in Au at 450 8C have been reported to be *10%. Another study [23] suggests the formation of GaAu2 and/or Ga7Au2 compounds, which would also lower qc via Ga-vacancy generation. It is also important to note that several authors [88, 90, 91] report Ni-N phases for contact structures annealed between 500 and 550 8C which apparently contradicts work by Venugopalan et al. [95], which suggests that Ni will not form any stable nitrides. This disagreement is further evidenced by the fact that Koide et. al. [84] observed the formation of a Au-Ni solid solution in intimate contact with an unreacted p-GaN surface following a 500 8C anneal in N2, while Sheu et al. [88] have reported that both Ni-Ga and Ni-N phases form without postmetallization annealing. Koide et al. [84] were able to achieve qc values as low as 7 ´ 10–3 X cm2 after annealing at 500 8C for times longer than 5 min. Note that Koide et al. [84] and Sheu et al. [88] prepared the p-GaN surface using BHF and HCl : H2O (1 : 1) solutions, respectively. King et al. [43] have previously shown that n-GaN surfaces exposed to UV/O3 oxidation and then subsequently etched in either HCl : H2O (1 : 1) or BHF (10 : 1) result in significantly different levels of O and C contamination. As the dispersal of native contamination is accompanied by additional reactions within the contact structure [84] and/or at the metal/semiconductor interface, the effects of contamination removal alone on the ohmic behavior have not been assessed. In order to draw a distinction between these two effects the present authors [71] used an NH3-based high-temperature CVC process to prepare clean, ordered and stoichiometric p-GaN (p = 2 ± 1 ´ 1018 cm–3) surfaces onto which the Ni/Au metallization was deposited. The details of this cleaning process have been outlined above. The band bending and electron affinity at the prepared p-GaN surface were measured to be 0.8 ± 0.1 eV and 2.6 ± 0.1 eV, respectively. Fig. 10.9 shows that as-deposited contacts on CVC-treated surfaces are significantly less rectifying in the low-voltage region (< 2 V) compared to identical contact structures on the as-loaded surface, which is consistent with the removal of surface contamination and a reduction in the Schottky barrier height. In this case, the effects of surface contamination have been assessed without using a postmetallization anneal. Following a high-temperature postmetallization rapid thermal anneal at 450 8C for

513

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10 Ohmic Contacts to GaN

Fig. 10.9 Current voltage (I-V) plots for as-deposited Ni/Au contacts on as-loaded (triangle) and CVC (circle) p-type GaN surfaces.

The low-voltage region has been magnified in b. The contact spacing was 5 lm.

30 s in N2, there is a significant improvement in the ohmic behavior for contacts on as-loaded surfaces. There is virtually no change in the I-V characteristics for contacts on CVC-treated surfaces, which is again consistent with the removal of surface contamination prior to contact deposition. The qc values for contacts on as-loaded and CVC surfaces following the high-temperature anneal were 4 ± 2 X cm2 and 3 ± 2 X cm2, respectively, and are equivalent to within the experimental error. Although the contacts are electrically equivalent, there are significant differences in the interfacial-reaction products observed at the metal/semiconductor interface. The formation of Au : Ga (90 : 10) and Au : Ni (90 : 10) solid solutions was observed for contacts on as-loaded surfaces following the 450 8C anneal. There were significantly less interfacial reactions for annealed contacts on chemical vapor-cleaned surfaces. Therefore, although the effects of surface contamination may be overcome via postmetallization annealing, there are significant differences in the thermal stability of the interface for contacts on CVC and contaminated surfaces. If the degree to which surfaces are cleaned is varied from one study to another, the effects observed by the present authors may explain the appearance of a particular reaction product in one case and its absence in another. Annealing in N2/O2 [33, 84], air [82, 85, 86, 91, 93, 96–98], O2 [83, 85, 92, 93], N2/ H2 [99], and Ar2/H2 [38] have also been explored in an attempt to further reduce the as-deposited qc values for the Au/Ni/p-GaN contact structure. The most significant reductions in qc have been recently observed for Ni/Au contact structures annealed in O2-containing ambients. Chen et al. [86] reported qc values as low as 4 ´ 10– 6 X cm2 for Ni (5 nm)/Au (5 nm) contacts following an anneal at 500 8C for 10 min in air. However, as with the N2-based annealing studies there is little understanding regarding the mechanism through which the reduction occurs.

10.5 Experimental Studies of Ohmic Contacts to p-Type GaN

Several studies by the same group [85, 86, 96, 98] have shown that annealing Ni/Au contacts in an O2-containing ambient at *500 8C leads to the formation of a NiO phase in intimate contact with the p-GaN surface. The authors of the above studies suggest that the low qc value is a result of a reduction in the Schottky barrier height due to the favorable band line up between NiO, which has been reported to be a p-type conducting oxide, and p-GaN. However, Maeda et al. [83] have fabricated Au/NiO/p-GaN (p = (4–5) ´ 1017 cm–3) contact structures, wherein the p-type conducting NiO was deposited directly on p-GaN via rf sputtering, and obtained contradictory results. The qc value for these Au/NiO contacts annealed at 500 8C in O2 remained several orders of magnitude larger than that of Ni/Au contacts, which have been previously annealed at 500 8C in N2. This suggests that the intermediate NiO layer is not responsible for the improvement in contact properties. Maeda et al. and others [82–84] have speculated that the mechanism through which the qc value is lowered involves both the breaking of Mg–H bonds in the near-surface region and the formation of H2O that subsequently removes the H from p-GaN. This mechanism is supported by a separate study [100] that investigated the effects of annealing ambient on the Mg acceptor activation process for p-type GaN. The introduction of O into the annealing gas led to a significant reduction in resistivity compared to films annealed at the same temperature in N2. The reduction in resistivity was also accompanied by a decrease in the atomic concentration of H measured via secondary ion mass spectroscopy SIMS. Hall measurements indicated an increase in the hole concentration and a decrease in mobility for samples annealed in O2-containing ambients. Many studies have investigated Pt- [21, 28, 30, 35, 37, 38, 44, 81, 84, 98, 101] and Pd- [7, 27, 31–34, 38, 44, 70–73, 75, 77, 84, 87, 101, 102] based metallization as a means to further reduce the specific contact resistivity. Pd and Pt are ideal candidates for ohmic contacts to p-type GaN in light of the large work function of each as well as the ability to dissolve and store large quantities of H in solid solution. Kim et al. [73] investigated Pd (20 nm) contacts on p-GaN (p = 1.9 ´ 1017 cm–3) surfaces pretreated with either HCl : H2O (1 : 1), boiling aqua regia HCl : HNO3 (3 : 1), or successive treatment in boiling aqua regia and (NH4)2Sx. The atomic concentrations of Ga, N, O, and C as well as the FWHM of the Ga 2p core-level spectrum following each surface pretreatment are shown in Tab. 10.2. Note that the O and C concentrations are lowest for the sample that was treated in succession with boiling aqua regia and (NH4)2Sx. The decrease in native contamination following the HCl, boiling aqua regia, and boiling aqua regia + (NH4)2Sx pretreatments was observed in coincidence with a decrease in the qc values which were measured to be 3.6 ´ 10–1 X cm2, 7.0 ´ 10–3 X cm2, and 2.9 ´ 10–4 X cm2, respectively. The significant decrease in the qc value following the successive pretreatment in boiling aqua regia and (NH4)2Sx is attributed to both a partial removal of native surface contamination and the subsequent passivation of the surface via the formation of Ga–S bonds. The author suggests that the Ga–S bonds suppress the formation of the native oxide prior to contact deposition. Kim et al. [27] investigated Pd/Au contact structures on p-GaN (p = 4.4 ´ 1016 cm–3) surfaces previously treated with either HCl : H2O, aqua regia,

515

516

10 Ohmic Contacts to GaN Tab. 10.2 The change of atomic concentrations of elements and FWHM of Ga 2p spectrum with the type of surface treatment on p-type GaN. Ref. [73]

Ga N C O FWHM of Ga2p

HCl (%)

Aqua regia (%)

(NH4)2Sx (%)

17.7 67.9 10.1 4.3 1.7530 eV

21.6 69.4 6.5 2.5 1.6708 eV

22.4 71.8 4.3 1.5 1.6482 eV

or boiling aqua regia. A qc value of 1.99 ´ 10–4 X cm2 was achieved for as-deposited contacts on p-GaN surfaces previously treated with boiling aqua regia, which was approximately one order of magnitude lower than that for contacts on aquaregia or HCl : H2O-treated surfaces. The AES depth profiles shown in Fig. 10.10 for contacts deposited on aqua-regia-treated surfaces annealed at 700 8C indicates the outdiffusion of Ga into the Pd layer. These reactions continue with subsequent annealing through 800 8C. In direct contrast to these results, the depth profiles for contacts on boiling aqua regia-treated surfaces shown in Fig. 10.11 do not reveal extensive interfacial reactions even after annealing at 800 8C. Although there is a reduction in the native surface contamination following the boiling aqua regia pretreatment, the author attributes the low as-deposited qc value as well as the high-temperature interfacial stability to a change in surface termina-

Fig. 10.10 AES depth profiles of Au/Pd/pGaN (aqua regia treated) before and after annealing at 600 8C, 700 8C, and 800 8C [27].

10.5 Experimental Studies of Ohmic Contacts to p-Type GaN Fig. 10.11 AES depth profiles of Au/Pd/p-

GaN (boiling aqua regia treated) before and after annealing at 600 8C, 700 8C, and 800 8C [27].

tion following the pretreatment. That is, following the boiling aqua regia pretreatment angle-resolved XPS shows a change from Ga- to N-surface termination. A number of the Pd-based contact studies noted above have investigated the effects of various ex situ surface pretreatments [27, 31, 32, 34, 44, 72, 73, 75, 77]. An improvement in the as-deposited ohmic behavior is most often attributed to a partial removal of the native surface contamination prior to contact deposition. The manner in which the Schottky barrier is reduced and the ohmic behavior improved via contamination removal has been discussed in a previous section. To access the effects of in situ surface pretreatment, the present authors [89] investigated Pd/Au contacts on p-GaN surfaces previously treated using a high-temperature NH3-based CVC process. Stoichiometric p-GaN surfaces with no detectable C and a significantly reduced O concentration were achieved. As-deposited contacts on the CVC surface passed a greater current at an equivalent voltage compared to the corresponding contact structures on the as-loaded surface. These results are consistent with the removal of native surface contamination. Fig. 10.12 shows a consistent decrease in resistance as well as improved ohmic behavior for contacts on the CVC surface annealed through 800 8C. A modest improvement in the ohmic behavior of contacts on the as-loaded surface is observed with successive annealing through 800 8C. Fig. 10.13 shows that contacts on the CVC surface maintain significantly smoother surface morphologies following 600 and 700 8C anneals compared to identical contact structures on as-loaded surfaces. The smoother surface morphologies for contacts on the cleaned surface may be attributed to a reduction of the metal/semiconductor interfacial energy as a result of the CVC process. These observations suggest that the improvement in the as-deposited I-V characteristics as well as the high-temperature microstructural stability may be at-

517

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10 Ohmic Contacts to GaN

Fig. 10.12 Current- voltage (I-V) plots of the as-deposited (filled circles), 500 8C (solid squares), 600 8C (solid diamonds), 700 8C (open triangles), and 800 8C (cross) annealed

Au/Pd contacts on a CVC; b as-loaded p-type GaN surfaces. The contact spacing was 10 lm.

Fig. 10.13 RMS roughness (nm) values for Pd/Au contacts on as-loaded (open circle) and CVC-treated surfaces (solid diamond) annealed at 500, 600, 700, and 800 8C for 2 min each in N2 ambient. RMS roughness values from a bare piece of p-GaN (solid circle) subjected to the same annealing schedule are included as a control.

10.5 Experimental Studies of Ohmic Contacts to p-Type GaN

tributed to contamination removal via the CVC process. These findings, in addition to those of Kim et al. [27], suggest that the as-deposited and annealed electrical and structural contact properties of Pd-based metallizations are a strong function of the surface-preparation method. King et al. [81] suggested that Pt would be an ideal candidate for ohmic contacts due to the fact that it is a high work function metal capable of extracting large quantities of H [80] which is incorporated during MOCVD growth of p-GaN and subsequently bonds with the Mg acceptors. Note that Ni and Pd have similar extraction capabilities. The authors [81] have investigated Pt and Pt/Au contacts on p-GaN (p*5–6 ´ 1016 cm–3) surfaces previously treated with NH4OH : DI solution. Following a postmetallization anneal at 750 8C for 10 min the qc values for these contacts were reported to be in the ranges of (3.4 ´ 10–2 X cm2–3.6 ´ 10–2 X cm2) and (5.7 ´ 10– 3 X cm2–1.6 ´ 10–2 X cm2), respectively. Jang et al. [37] reportedly achieved qc values as low as 2.0 ´ 10–5 X cm2 by depositing Pt contacts on a p-GaN (p = 1.8 ´ 1017 cm–3) surface previously treated in sequential BOE and (NH4)2Sx baths. The mechanism by which ohmic contacts are achieved using Pt-based schemes appears to be limited by the fact that no reactions occur in the Pt-GaN system up to 800 8C [101]. Therefore, Pt-gallide formation and the subsequent creation of Ga vacancies in the near-surface region, which would reduce qc, is limited to temperatures > 800 8C, wherein other portions of the device may be damaged. In this case ex situ and/or in situ surface pretreatments would provide the most promising process routes to achieving Pt-based ohmic contacts. Other studies [24, 81, 99, 103–108] have investigated multilevel metallizations in an attempt to overcome the limitations of bilayer metallization schemes. In several studies [103–106] a multilevel metallization was chosen such that the favorable Pt characteristics may be exploited in conjunction with another metal included in the metallization that forms interfacial reaction products with p-GaN. Jang et al. [103–105] investigated Ni/Pt/Au contact structures deposited on p-GaN surfaces previously treated using BHF solution. A minimum qc value of 2.1 ´ 10–2 X cm2 was achieved after annealing at 500 8C for 30 s in Ar2. Depth-profiling AES showed that Pt diffuses through the Ni to the p-GaN causing the Pt and Ni layers to intermix. Glancing-angle X-ray diffraction reveals the formation of Ga3Pt5 and Ga4Ni3 at the interface in addition to a Pt-Ni solid solution. This suggests that Ni disperses the surface contamination and subsequently dissociates p-GaN during the high-temperature postmetallization anneal, which is consistent with previous studies, to form new Ga-Pt and Ga-Ni phases. It is important to note that the depth-profiling AES suggests that Pt may act as a diffusion barrier to N. Therefore, the simultaneous formation of new gallide phases and the suppression of N diffusion and/or N vacancy formation lead to a reduction in the qc value. It may be assumed that gallide formation results in the creation of a significant number of Ga vacancies in the near-surface region. It is also possible that the new high work function Pt-Ni phase is in intimate contact with the underlying p-GaN. The contact structures, experimental conditions, and corresponding qc values from the studies above are shown in Tab. 10.3. The effects of in situ and/or ex situ surface pretreatment, contact metals, and postmetallization annealing conditions on the minimum qc values achieved have been briefly addressed.

519

2 ´ 1017 a) 2.9 ´ 1017 a) 3 ´ 1017 a)

3 ´ 1017 a) 3.6 ´ 1017 c) (4–6) ´ 1017 c) (4–6) ´ 1017 c) 4–6 ´ 1017 c)

Ni/Au Ni/Au Ni/Au

Ni/Au Ni/Au Ni/Au Ni/Au Ni/Au

NR NR NR NR NR

NR NR NR

NH3-CVC NR

1.8 ´ 1017 d) 1 ´ 1015 a) 1 ´ 1017 c) 1.1 ´ 1017 b) 1.41 ´ 1017 a)

Pt Ni/Au

NR

HCl : H2O (1 : 1) warm HCl : HNO3 (3 : 1) HCl : H2O (1 : 1) HCl : HNO3 acetone, HF, isopropanol HCl : H2O (1 : 1) BOE BHF BHF HCl : H2O (1 : 1)

5–6 ´ 1016 a)

Pt

Ni/Au Ni/Au

3 ´ 1017 a)

Pd

Thermal treatment

NR NR NR NR NR NR NR NR

500 8C-air 4 ´ 10–5 600 8C-N2 3.6 ´ 10–4 450 8C-Ar2/H2 0.1 450 8C-N2 500 8C-N2 500 8C-N2/O2 500 8C-N2 400 8C-N2

1.7 ´ 10–2 2.5 ´ 10–3 (2–3) ´ 10–3 7 ´ 10–3 3.31 ´ 10–2

[ NR 3±2 9.84 ´ 10–4

450 8C-N2 600 8C-N2/O2

NR NR

NR

NR

NR

as-deposited 500 8C-N2

0.2

20

[ [ NR NR [

[ [ NR

[ [

NR NR

NR

NR

[

[ [ [ [ NR

[ [ [

[ [

NR NR

NR

NR

NR

Specific contact Surface and/or interface analysis resistivity Electronic Chemistry Structure/ (X cm2) states morphology

3.4 ´ 10–2 3.6 ´ 10–2 2.0 ´ 10–5 3.4 ´ 10–1

750 8C

UHV annealing NR 600 8C, 10 min NR 450 8C-Ar2H2

NR NR

36% HCl, 96% H2SO4 : 30% H2O2 acetone, HF, isopropanol NH4OH : DI

1.5 ´ 1017 a)

Au

In situ treatment

BOE, (NH4)2Sx NR

Ex situ treatment

Ionized charge (cm–3)

Contact

23 36 84 84 21

86 25 38

71 33

37 24

81

38

67

Ref.

Tab. 10.3 Reported ohmic contact schemes for p-type GaN. Specific contact resistivity values are reported for room temperature. Ionized charge is reported prior to surface pretreatment

520

10 Ohmic Contacts to GaN

BOE NR

3 ´ 1016 b) (5–6) ´ 1016 b)

9.4 ´ 1014 a) 4.1 ´ 1017 a)

Pd/Au Pd/Au

Ni/Pt/Au Ni/Pd/Au

NR = not reported, CVC = chemical vapor clean a) carrier conc. b) NA-ND c) Mg concentration

NR

bonding (HCl : HNO3) (3 : 1) HCl : H2O (1 : 1) NH4OH : DI

4.4.2 ´ 1016 a)

Pd/Au

NR NR

NH3-CVC NR

In situ treatment

Ionized charge Ex situ treatment (cm–3)

Contact

Tab. 10.3 (cont.)

NR 5.7 ´ 10–3 1.6 ´ 10–2 2.1 ´ 10–2 1 ´ 10–4

700 8C-N2 750 8C 500 8C-Ar2 550 8C-O2

1.99 ´ 10–4

NR NR

NR NR

NR

[ NR

[ NR

[

[ NR

[ NR

[

Specific contact Surface and/or interface analysis resistivity Electronic Chemistry Structure/ (X cm2) states morphology

as-deposited

Thermal treatment

103 107

89 81

27

Ref.

10.5 Experimental Studies of Ohmic Contacts to p-Type GaN 521

522

10 Ohmic Contacts to GaN

10.6

Conclusions

A brief review of the theoretical and experimental approaches to fabricating ohmic contacts on GaN has been given. The Schottky-Mott, Bardeen, and metal-induced gap state models of the formation of the Schottky barrier at a metal-semiconductor contact interface and their relative importance to ohmic contact behavior on GaN has been addressed. The underlying principles regarding the development of stable, Ti-based ohmic contacts to n-type GaN for optoelectronic applications has been subsequently addressed. Although the specific contact resistivity for these contacts has been reported to be as low as 8.9 ´ 10–8 X cm2, the mechanism through which ohmic contacts are achieved is a strong function of surface-preparation methods, the constituent metals included in the contact structure and the corresponding atomic ratios, and postmetallization annealing ambients. A process route wherein ohmic contacts with consistent chemical, electrical, and structural properties is yet to be developed. Ohmic contacts to p-GaN with qc values consistently reported below 1 ´ 10–4 X cm2 continue to present a challenge. Ni/Au contacts continue to receive considerable attention and have resulted in some of the lowest qc values to date. An in situ and/or ex situ surface pretreatment that removes native surface contamination and/or favorably modifies the surface electronic properties is beneficial for ohmic contact formation. However, the mechanism through which ohmic behavior is improved continues to be debated. Postmetallization annealing of Ni/Au contact structures in various annealing ambients has been successful in further reduction of the qc value. However, like the n-type studies, the optimal temperature, time, and annealing ambient is still unclear. Furthermore, a clear picture of the resulting interfacial reaction products and the manner in which those products result in a lower qc value has yet to emerge. Pt, Pd, and multilayer metallization schemes used in conjunction with an ex situ surface pretreatment and/or high-temperature postmetallization anneal have been explored in an attempt to further reduce the qc values for ohmic contacts to p-GaN.

10.7

Directions for Future Research

Although knowledge of both the Schottky barrier height and the mechanism through which it is formed is critical to ohmic contact formation, the manner in which it is overcome and/or eliminated is equally important. X-ray and ultraviolet photoelectron spectroscopies are excellent techniques for examining the electrical and chemical properties of the interface formed between thin metal overlayers and prepared semiconductor surfaces. Wu et al. [64] have conducted a thorough investigation of the interface formed between a series of high and low work function metals (Mg, Al, Ti, Au, and Pt) and clean and ordered (1 ´ 1) n- and p-type GaN surfaces. X-ray and ultraviolet photoelectron spectroscopy were used to simultaneously determine the Schottky barrier for as-deposited and annealed inter-

10.8 Acknowledgements

faces as well as identify the formation of interfacial reaction products. In light of the fact that Ni- and Pd-based contact structures are excellent candidates for ohmic contacts to p-GaN, a photoelectron spectroscopy-based study of thin Ni and/ or Pd metal overlayers deposited on clean and ordered p-GaN surfaces and annealed in situ would be of significant interest. As Wu et al. [64] have shown, this approach both identifies interfacial reaction products and provides a quantitative measure of the subsequent effects on the Schottky barrier height and/or electronic states at the metal/semiconductor interface. Measurements of this type explicitly address the mechanism through which the ohmic contact is formed and provides a standard against which other studies of ohmic contact formation may be compared. In addition to the effects of surface preparation that have been outlined above, it has also been suggested that one of the primary reasons for the large range of results in the literature is variation in material quality from one research group to the next. In light of this difficulty, a comprehensive study of the effects of dislocation density, RMS roughness, substrate polarity (i.e., Ga versus N termination), Mg concentration, and/or carrier concentration on specific contact resistivity would provide invaluable information regarding the degree to which the material properties influence the chemical, electrical, and structural properties of the contact. A reduction in dislocation density via epitaxial growth of GaN substrates using a lateral overgrowth technique would allow a comparison of the electrical properties between contact structures on materials having both a high and a low density of dislocations. Dislocations have been previously shown to be electrically active, however, a study that explicitly addresses the effects of dislocations at the metal/GaN interface has not been conducted.

10.8

Acknowledgments

This work was supported by the Multidisciplinary University Research Program via the Office of Naval Research under contracts N00014-98-1-0384 (Colin Wood, monitor) and N00014-98-1-0654 (John Zolper, monitor). The authors also acknowledge Cree, Inc. for the SiC substrates. Robert F. Davis was partially supported by the Kobe Steel, Ltd. Professorship. The authors would also like to thank Dr. Victor Bermudez for many helpful discussions.

523

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10 Ohmic Contacts to GaN

10.9

References 1 2

3 4

5

6 7

8

9

10

11

12 13

14

15

S. Strite and H. Morkoc¸, J. Vac. Sci. Technol. B 10, 1237 (1992). S. Nakamura, M. Senoh, N. Iwasa, and S. Nagahama, Jpn. J. Appl. Phys. Part 2 34, L797 (1995). S. Yoshida and J. Suzuki, Jpn. J. Appl. Phys. Part 2 38, L851 (1999). B. S. Shelton, D. J. H. Lambert, J. J. Huang, M. M. Wong, U. Chowdhury, T. G. Zhu, H. K. Kwon, Z. Liliental-Weber, M. Benarama, M. Feng, and R. S. Dupuis, IEEE Trans. Electron Devices 48, 490 (2001). L. Zhang, L. F. Lester, A. G. Baca, R. J. Shul, P. C. Chang, C. G. Willison, U. K. Mishra, S. P. DenBaars, and J. C. Zolper, IEEE Trans. Electron Devices 47, 507 (2000). N. Stath, V. Harle, and J. Wagner, Mater. Sci. Eng. B 80, 224 (2001). E. H. Rhoderick and R. H. Williams, Metal-Semiconductor Contacts, Vol. 19, 2nd edn. (Oxford Science Publications, Oxford, 1988). Z. Fan, S. N. Mohammad, W. Kim, O. Aktas, A. E. Botchkarev, and H. Morkoc¸, Appl. Phys. Lett. 68, 1672 (1996). D. F. Wang, F. Shiwei, C. Lu, A. Motayed, M. Jah, K. A. Jones, and L. Salamanca-Riba, J. Appl. Phys. 89, 6214 (2001). S. Ruvimov, Z. Liliental-Weber, J. Washburn, K. J. Duxstad, E. E. Haller, Z.-F. Fan, S. N. Mohammad, W. Kim, A. E. Botchkarev, and H. Morkoc¸, Appl. Phys. Lett. 69, 1556 (1996). J. K. Sheu, Y. K. Sheu, G. C. Chi, M. J. Jou, C. C. Liu, C. M. Chang, W. C. Hung, J. S. Bow, and Y. C. Yu, J. Vac. Sci. Technol. B 18, 729 (2000). Y. J. Lin and C. T. Lee, Appl. Phys. Lett. 77, 3986 (2000). L. L. Smith, R. F. Davis, R.-J. Liu, M. J. Kim, and R. W. Carpenter, J. Mater. Res. 14, 1032 (1999). B. P. Luther, S. E. Mohney, and T. N. Jackson, Semicond. Sci. Technol. 13, 1322 (1998). P. Ruterana, G. Nouet, T. H. Kehagias, P. H. Komninou, T. H. Karakostas,

16

17

18

19

20

21

22

23

24

25

26

27

28 29

30

M. A. Di Forte Poisson, F. Huet, and H. Morkoc¸, Phys. Stat. Sol. (a) 176, 767 (1999). N. A. Papanicolaou, M. V. Rao, J. Mittereder, and W. T. Anderson, J. Vac. Sci. Technol. B 19, 261 (2001). B. P. Luther, S. E. Mohney, T. N. Jackson, M. A. Kahn, Q. Chen, and J. W. Yang, Appl. Phys. Lett. 70, 57 (1997). C. M. Pelto, Y. A. Chang, Y. Chen, and R. S. Williams, Solid-State Electron. 45, 1597 (2001). J. S. Kwak, S. E. Mohney, J.Y. Lin, and R. S. Kern, Semicond. Sci. Technol. 15, 756 (2000). A. K. Fung, J. E. Borton, M. I. Nathan, J. M. Van Hove, R. Hickman II, P. P. Chow, and A. M. Wowchak, J. Electron. Mater. 28, 572 (1999). J. M. DeLucca, H. S. Venugopalan, S. E. Mohney, and R. F. Karlicek Jr, Appl. Phys. Lett. 73, 3402 (1998). T. W. Kang, C. S. Chi, S. H. Park, and T.W. Kim, Jpn. J. Appl. Phys. 39, 1062 (2000). J. K. Sheu, Y. K. Su, G. C. Chi, P. L. Koh, M. J. Jou, C. M. Chang, C. C. Liu, and W. C. Hung, Appl. Phys. Lett. 74, 2340 (1999). Taek Kim, M. C. Yoo, and Taeil Kim, Mater. Res. Soc. Symp. Proc. 449, 1061 (1997). J. K. Kim, J. L. Lee, J. W. Lee, Y. J. Park, and T. Kim, J. Vac. Sci. Technol. B 17, 2675 (1999). J. K. Kim, J. H. Je, J.-L. Lee, Y. J. Park, and B.-T. Lee, J. Electrochem. Soc. 147, 4645 (2000). D.-W. Kim, J. C. Bae, W. J. Kim, H. K. Baik, J.-M. Myoung, and S.-M. Lee, J. Electron. Mater. 30, 183 (2001). J. K. Kim, J.-L. Lee, J. W. Lee, Y. J. Park, and T. Kim, Electron. Lett. 35 (1998). J. K. Kim, J. H. Je, J. W. Lee, Y. J. Park, T. Kim, I.-O. Jung, B.-T. Lee, and J.-L. Lee, J. Electron. Mater. 30, L8 (2000). J. K. Kim, K. J. Kim, B. Kim, J. N. Kim, J. S. Kwak, Y. J. Park, and J.-L. Lee, J. Electron. Mater. 30, 129 (2001).

10.9 References 31

32

33

34

35

36 37 38

39

40

41

42

43

44

45

46

J. K. Kim, J.-L. Lee, J. W. Lee, H. E. Shin, Y. J. Park, and T. Kim, Appl. Phys. Lett. 73, 2953 (1998). J. K. Kim, C. C. Kim, T. S. Cho, J. H. Je, J. S. Kwak, Y. J. Park, and J.-L. Lee, J. Electron. Mater. 30, 170 (2001). M.-R. Park, W.A. Anderson, and S.-J. Park, MRS Internet J. Nitride Semicond. Res. 5S1, W11.77 (2000). J.-L. Lee, J. K. Kim, J. W. Lee, Y. J. Park, and T. Kim, Solid-State Electron. 43, 435 (1999). T. Mori, T. Kozawa, T. Ohwaki, Y. Taga, S. Nagai, S. Yamasaki, S. Asami, N. Shibata, and M. Koike, Appl. Phys. Lett. 69, 3537 (1996). J.-S. Jang, S.-J. Park, and T.-Y. Seong, J. Appl. Phys. 88, 5490 (2000). J.-S. Jang, S.-J. Park, and T.-Y. Seong, J. Vac. Sci. Technol. B 17, 2667 (1999). R. Wenzel, G. G. Fischer, and R. Schmid-Fetzer, Mater. Sci. Semicond. Process 4, 357 (2001). I. P. Smorchkova, E. Haus, B. Heying, P. Kozodoy, P. Fini, J. P. Ibbetson, S. Keller, S. P. DenBaars, J. S. Speck, and U.K. Mishra, Appl. Phys. Lett. 76, 718 (2000). H. Amano, M. Kito, K. Hiramatsu, and I. Akasaki, Jpn. J. Appl. Phys. 28, L2112 (1989). P. Kozody, S. Keller, S. P. DenBaars, and U. K. Mishra, J. Cryst. Growth 195, 265 (1998). T. Usagawa, M. Kobayashi, T. Mishima, P. D. Rabinzohn, A. Ihara, M. Kawata, T. Yamada, E. Tokumitsu, M. Konagai, and K. Takahashi, J. Appl. Phys. 69, 8227 (1991). S. W. King, J. P. Barnak, M. D. Bremser, K. M. Tracy, C. Ronning, R. F. Davis, and R. J. Nemanich, J. Appl. Phys. 84, 5248 (1998). H. Ishikawa, S. Kobayashi, Y. Koide, S. Yamasaki, S. Nagai, J. Umezaki, M. Koide, and M. Murakami, J. Appl. Phys. 81, 1315 (1997). J. T. Trexler, S. J. Pearton, P. H. Holloway, M. G. Mier, K. R. Evans, and R. F. Karlicek, Mater. Res. Soc. Symp. Proc. 449, 1091 (1997). E. D. Marshall and M. Murakami, in Contacts to Semiconductors, Fundamen-

47 48 49 50

51

52 53 54

55

56

57

58 59

60 61

62

tals and Technology. L. J. Brillson, (ed.) (Noyes Publications, Park Ridge, NJ, 1993). J. Bardeen, Phys. Rev. 71, 717 (1947). A. M. Cowley and S. M. Sze, J. Appl. Phys. 36, 3212 (1965). V. Heine, Phys. Rev. A 138, 1689 (1965). W. E. Spicer, I. Lindau, P. Skeath, and C. Y. Su, J. Vac. Sci. Technol. 17, 1019 (1980). W. E. Spicer, I. Lindau, P. Skeath, C. Y. Su, and P. W. Chye, Phys. Rev. Lett. 44, 420 (1980). V. M. Bermudez, J. Appl. Phys. 86, 1170 (1999). N. Braslau, J. Vac. Sci. Technol. 19, 803 (1981). D. K. Schröder, Semiconductor Material and Device Characterization (John Wiley and Sons Inc., New York, 1990). W. Shockley, in A. Goetzberger and R. M. Scarlett, “Research and Investigation of Inverse Epitaxial UHF Power Transistors,” Rep. No. AFAL-TDR-64-2-7, Air Force Avionics Lab, Wright Patterson Air Force Base, OH, Sept. 1964. G. K. Reeves, “Specific Contact Resistance Using a Circular Transmission Line Model,” Solid-State Electron. 23, 487–490, May 1980; A. J. Willis and A. P. Botha, Thin Solid Films 146, 15 (1987). S. S. Cohen and G. Sh. Gildenblat, VLSI Electronics, 13, Metal-Semiconductor Contacts and Devices (Academic Press, Orlando, FL, 1986) 115; M. Ahmad and B. M. Arora, Solid-State Electron. 35, 1441 (1992). T. U. Kampen and W. Monch, Appl. Surf. Sci. 117/118, 388 (1997). M. Eyckeler, W. Monch, T. U. Kampen, R. Dimitrov, O. Ambacher, and M. Stutzman, J. Vac. Sci. Technol. B 16, 2224 (1998). W. Monch, J. Vac. Sci. Technol. B 17, 1867 (1999). J. Dumont, R. Caudano, R. Sproken, E. Monroy, E. Munoz, B. Beaumont, and P. Gibart, Mater. Res. Soc. Symp. Proc. 595, W11.79.1 (2000). V. M. Bermudez, J. Appl. Phys. 80, 1190 (1996).

525

526

10 Ohmic Contacts to GaN 63

64 65

66

67

68

69 70

71

72

73

74

75

76

77

78 79

80

V. M. Bermudez, D. D. Koleske, and A. E. Wickenden, Appl. Surf. Sci. 126, 69 (1998). C. I. Wu and A. Kahn, J. Vac. Sci. Technol. B 16, 2218 (1998). C. I. Wu, A. Kahn, A. E. Wickenden, D. Koleske, and R. L. Henry, J. Appl. Phys. 89, 425 (2001). Y. Koide, H. Ishikawa, S. Kobayashi, S. Yamasaki, S. Nagai, J. Umezaki, M. Koike, and M. Murakami, Appl. Surf. Sci. 117/118, 373 (1997). I. Waki, H. Fujioka, K. Ono, M. Oshima, H. Miki, and A. Fukizawa, Jpn. J. Appl. Phys. 39, 4451 (2000). J. Sun, K. A. Rickert, J. M. Redwing, A. B. Ellis, F. J. Himpsel, and T. F. Kuech, Appl. Phys. Lett. 76, 415 (2000). C. I. Wu and A. Kahn, J. Appl. Phys. 86, 3209 (1999). P. J. Hartlieb, A. Roskowski, R. F. Davis, W. Platow, and R. J. Nemanich, J. Appl. Phys. 91, 732 (2002). P. J. Hartlieb, A. Roskowski, R. F. Davis, and R. J. Nemanich, J. Appl. Phys. 91, 9151 (2002). J.-L. Lee, M. Weber, J. K. Kim, J. W. Lee, Y. J. Park, T. Kim, and K. Lynn, Appl. Phys. Lett. 74, 2289 (1999). J. K. Kim, J.-L. Lee, J. W. Lee, Y. J. Park, and T. Kim, J. Vac. Sci. Technol. B 17, 497 (1999). M.-H. Kim, S.-N. Lee, C. Huh, S.-Y. Park, J.-Y. Han, J.-M. Seo, and S.-J. Park, Phys. Rev. B 61, 10966 (2000). Q. Z. Liu, S. S. Lau, N. R. Perkins, and T. F. Kuech, Appl. Phys. Lett. 69, 1722 (1996). J. Neugebauer and C. G. Van de Walle, Mater. Res. Soc. Symp. Proc. 395, 645 (1996). R. Wenzel, G. G. Fischer, and R. Schmid-Fetzer, Mater. Sci. Semicond. Process 4, 367 (2001). A. Lahav, M. Eizenberg, and Y. Komem, J. Appl. Phys. 60, 991 (1986). T. Sands, V. G. Keramidas, A. J. Yu, K.-M. Yu, R. Gronsky, and J. Washburn, J. Mater. Res. 2, 262 (1987). J. D. Fast, Interaction of Metals and Gases Chap. 1, (MacMillan, New York, 1971).

81

82

83 84

85

86

87 88

89

90

91

92 93

94

95

96

D. J. King, L. Zhang, J. C. Ramer, S. D. Hersee, and L. F. Lester, Mater. Res. Soc. Symp. Proc. 468, 421 (1997). D. Qiao, L. S. Yu, S. S. Lau, J. Y. Lin, H. X. Jiang, and T. E. Haynes, J. Appl. Phys. 88, 4196 (2000). T. Maeda, Y. Koide, and M. Murakami, Appl. Phys. Lett. 75, 4145 (1999). Y. Koide, T. Maeda, T. Kawakami, S. Fujita, T. Uemura, N. Shibata, and M. Murakami, J. Electron. Mater. 28, 341 (1999). J.-K. Ho, C.-S. Jong, C. C. Chiu, C.-N. Huang, K.-K. Shih, L.-C. Chen, F.-R. Chen, and J.-J. Kai, J. Appl. Phys. 86, 4491 (1999). L.-C. Chen, J.-K. Ho, F.-R. Chen, J.-J. Kai, L. Chang, C.-S. Jong, C. C. Chiu, C.-N. Huang, and K.-K. Shih, Phys. Stat. Sol. (a) 176, 773 (1999). T. Kim, J. Khim, S. Chae, T. Kim, Mater. Res. Soc. Symp. Proc. 468, 427 (1997). J. K. Sheu, Y. K. Su, G. C. Chi, W. C. Chen, C. Y. Chen, C. N. Huang, J. M. Hong, Y. C. Yu, C.W. Wang, and E. K. Lin, J. Appl. Phys. 83, 3172 (1998). P. J. Hartlieb, A. Roskowski, R. F. Davis, B. J. Rodriguez, and R. J. Nemanich, Mater. Res. Soc. Symp. Proc. Fall 2001, in press. C. C. Kim, J. K. Kim, J.-L. Lee, J. H. Je, M.-S. Yi, D. Y. Noh, Y. Hwu, and P. Ruterana, MRS Internet J. Nitride Semicond. Res. 6, 4 (2001). C. C. Kim, J. K. Kim, J.-L. Lee, J. H. Je, M.-S. Yi, D. Y. Noh, Y. Hwu, and P. Ruterana, Appl. Phys. Lett. 78, 3773 (2001). H. Kim, D.-J. Kim, S.-J. Park, and H. Hwang, J. Appl. Phys. 89, 1506 (2001). J.-K. Ho, C.-S. Jong, C. C. Chiu, C.-N. Huang, C.-Y. Chen, and K.-K. Shih, Appl. Phys. Lett. 74, 1275 (1999). Z. Liliental-Weber, E. R. Weber, and N. Newman, in Contacts to Semiconductors, Fundamentals and Technology, Chap. 6, L. J. Brillson (ed.) (Noyes Publications, Park Ridge, NJ, 1993). H. S. Venugopalan, S. E. Mohney, J. M. DeLucca, B. P. Luther, and G. E. Bulman, J. Vac. Sci. Technol. A 16, 607 (1998). L.-C. Chen, F. R. Chen, J.-J. Kai, L. Chang, J.-K. Ho, C.-S. Jong, C. C. Chiu,

10.9 References

97

98

99

100

101

C.-N. Huang, C.-Y. Chen, and K.-K. Shih, J. Appl. Phys. 86, 3826 (1999). J. C. Jan, K. Asokan, J. W. Chiou, W. F. Pong, P. K. Tseng, M.-H. Tsai, Y. K. Chang, Y. Y. Chen, J. F. Lee, J. S. Wu, H.-J. Lin, C. T. Chen, L. C. Chen, F. R. Chen, and J.-K. Ho, Appl. Phys. Lett. 78, 2718 (2001). L.-C. Chen, J.-K. Ho, C.-S. Jong, C. C. Chiu, K.-K. Shih, F.-R. Chen, J.-J. Kai, and Li Chang, Appl. Phys. Lett. 76, 3703 (2000). J. T. Trexler, S. J. Miller, P. H. Holloway, and M. A. Kahn, Mater. Res. Soc. Symp. Proc. 395, 819 (1996). B. A. Hull, S. E. Mohney, H. S. Venugopalan, and J. C. Ramer, Appl. Phys. Lett. 76, 2271 (2000). K. J. Duxstad, E. E. Haller, K. M. Yu, M.T. Hirsch, W. R. Imler, D. A. Steigerwald, F. A. Ponce, and L. T. Romano, Mater. Res. Soc. Symp. Proc. 449, 1049 (1997).

102 C. C. Kim, W. H. Kim, J. H. Je, D. W. Kim,

103

104

105 106

107

108

H. K. Baik, and S. M. Lee, Electrochem. Solid-State Lett. 3, 335 (2000). J. S. Jang, K. H. Park, H. K. Jang, H. G. Kim, and S. J. Park, J. Vac. Sci. Technol. B 16, 3105 (1998). J. S. Jang, H. G. Kim, K. H. Park, C. S. Um, I. K. Han, S. H. Kim, H. K. Jang, and S. J. Park, Mater. Res. Soc. Symp. Proc. 482, 1053 (1998). J. S. Jang, S. J. Park, and T. Y. Seong, J. Electrochem. Soc. 146, 3425 (1999). J. S. Jang, I. S. Chang, H. K. Kim, T. Y. Seong, S. Lee, and S. J. Park, Appl. Phys. Lett. 74, 70 (1999). C. F. Chu, C. C. Yu, Y. K. Wang, J. Y. Tsai, F. I. Lai, and S. C. Wang, Appl. Phys. Lett. 77, 3423 (2000). L. Zhou, W. Lanford, A. T. Ping, I. Adesida, J. W. Yang, and A. Khan, Appl. Phys. Lett. 76, 3451 (2000).

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11

Electroluminescent Diodes and Laser Diodes Hiroshi Amano

Abstract

An historical overview of the development of the nitride-based devices including light emitting diodes and laser diodes after the first demonstration of the bluegreen light emitting diode grown by HVPE is given in this chapter.

11.1

Introduction

Today, when we walk around town, we can see beautiful bright billboards projecting news and commercial images. When we are driving, traffic signals show bright and uniform red, yellow, and green lights. Cellular phones show the full color images in the hand. Group III nitride-based light emitting diodes (LEDs) play a major role in all these luminescent displays. Today, nitride-based LEDs are very common and widely used. Who could foresee these flourishing developments in the 1970s and even 1980s? The capacity of next-generation optical storage disks will reach 30 GB per disk, which is twice as large as that of a digital versatile disk. In these systems, light sources are also composed of group III nitride-based violet laser diodes (LDs). Who could predict the realization of violet LDs using nitrides in the 1980s? All these GaN-based devices are fabricated on sapphire or SiC substrates; the lattice mismatch exceeds 16% and 2.5%, respectively. In the semiconductor field, there had been a belief that the lattice mismatch between the epitaxial layer and

530

11 Electroluminescent Diodes and Laser Diodes

the substrate should be less than 1% in order to achieve commercially feasible high-performance devices. Is this belief inapplicable for group III nitride devices? The answer is actually no. The development of growth technology and fabrication processes of group III nitrides and its devices has led to this incredible breakthrough. In this chapter, first, the history of the development of group III nitrides for application to light emitters is briefly reviewed. Then, the latest topics concerning nitride-based electroluminescent diodes and LDs are reviewed.

11.2

Historical Overview

The first nitride-based LED was demonstrated by Pankove et al. in 1971 [1]. Metal (m) and a homojunction of Zn-doped semi-insulating GaN (i) and unintentionally donor-doped highly conductive n-type GaN (n) composing the m-i-n structure were used. The demonstration of optical-pump lasing in the UV region at cryogenic temperatures by Dingle et al. [2] further raised the interest of nitride researchers. However, because of the poor reproducibility of the growth of GaN on sapphire substrates due to the large lattice mismatch between them, and the difficulty in controlling the thickness and conductivity, particularly when fabricating ptype GaN by hydride vapor phase epitaxy (HVPE), the majority of researchers discarded this material [3]. A new method for thin film growth technology was derived. Manasevit et al. [4] demonstrated the growth of GaN by metalorganic vapor phase epitaxy (MOVPE) in 1971. They used triethylgallium and ammonia as source gases, and obtained highly c-axis-oriented films on sapphire (0001) and on 6H-SiC (0001) substrates. After this success, it took 13 years to fabricate an m-i-n-type nitride LED by MOVPE [5]. At that time, the performance of the MOVPE-grown LED was limited and could never exceed the performance of LEDs fabricated by the previous method. Poor crystalline quality hindered the device functions. Great success in the growth of GaN crystal on sapphire was achieved in 1986 [6]. Use of a low-temperature (LT)-deposited buffer layer enabled the growth of high-quality GaN films with excellent reproducibility. Currently, this LT-buffer technique is one of the most popular de facto standard methods for the growth of GaN on sapphire substrates by MOVPE. Today, nominally undoped GaN grown in a highly pure atmosphere shows residual donor concentrations lower than 1014 cm–3. Conductivity control of n-type GaN from the undoped level to 1019 cm–3 can be achieved by doping Si or Ge as the donor impurity [7, 8]. However, a significant obstacle to conductivity control remained. GaN doped with an acceptor impurity, such as Zn or Mg, showed high resistivity similar to that of samples obtained by HVPE. Elucidation of the effect of low-energy electron beam irradiation (LEEBI) treatment on the Zn-doped GaN removed this obstacle. The blue luminescence intensity of Zn-doped GaN was enhanced by LEEBI

11.2 Historical Overview

treatment [9]. Then, the LEEBI treatment was applied to Mg-doped GaN [10]. The reason for choosing Mg as the acceptor impurity was that it was expected to have a lower activation energy than Zn [11]. This assumption was later verified experimentally [12]. Not only was the luminescence property changed but also the electrical conductivity, and p-type GaN could be fabricated. A GaN-based LED having a p-n junction was also fabricated for the first time, from which not only blue luminescence but also UV emission was observed. This technique was soon followed by and replaced with thermal annealing, by which the mass-production technology for the p-type GaN was established. The mechanism of Mg acceptor activation by hydrogen evacuation was confirmed both theoretically and experimentally [13, 14]. The establishment of the high-yield crystal growth technology using an LT buffer layer, conductivity control using Mg acceptors in addition to the special treatment for hydrogen evacuation from GaN, and conductivity control of n-type GaN by Si doping were thought to comprise a well-built framework that would lead to the fabrication of high luminescence efficiency LEDs. However, at that time, the luminescence efficiency of GaN was still low. In addition, the band gap of GaN is in the UV region. In order to achieve blue LEDs, control of the band gap was essential. Attempts were made to grow GaInN by MOVPE [15, 16]. Yoshimoto et al. [16] observed blue luminescence from GaInN with an InN molar fraction of up to 0.23. The first commercially available nitride-based blue LEDs utilized a Zn-related luminescence center in GaInN with a low InN molar fraction [17]. Codoping of Zn and a donor such as Si into the GaInN active layer was found to increase the blue luminescence intensity. However, the saturation of emission intensity and the broad spectrum of the Zn-related emission led researchers to choose quantum well(s) in order to use band-to-band transitions for blue light emission. The structure of GaInN on GaN was studied in detail. X-ray reciprocal space mapping showed that thin GaInN tends to be grown coherently on the underlying GaN [18]. The word “coherent growth” means that the inplane lattice constant of the upper layer is fixed at that of the underlying layer. The lattice constant of free-standing GaInN is larger than that of GaN. Therefore, in the case of coherent growth, the GaInN lattice is strained under strong compressive stress. Due to the strong piezoelectricity of nitrides, a large built-in potential develops in compressively strained GaInN, by which electrons and holes are separated in the quantum well; therefore, the transition probability is decreased [19]. Fig. 11.1 a and b show schematically the coherent growth of GaInN on GaN and the electron and hole wave functions in a single quantum well. As shown in Fig. 11.1 c, the use of very thin GaInN wells in a quantum-well structure solved the piezoelectricity problem in nitrides, thereby enabling a LED in which band-to-band transition is used, and subsequently leading to the realization of high-efficiency blue and green LEDs [20, 21]. The extremely high threading dislocation density in the cross-sectional transmission electron microscopic (TEM) image of GaInN-based blue LEDs presented by Lester et al. [22] astonished nitride researchers. The image showed threading

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a)

b)

c)

Fig. 11.1 a Coherent growth of GaInN on GaN; b piezoelectric field in the GaInN quantum well and the corresponding electron and hole separation for thick well and thin well; c photoluminescence efficiency at 77 K of GaInN/GaN quantum well as a function of GaInN quantum-well thickness.

11.2 Historical Overview

dislocation density on the order of 109 cm–2 or more in high-efficiency GaInNbased blue LEDs, which is at least three orders of magnitude higher compared to high-efficiency AlGaInP-based red LEDs. Much effort has been exerted by nitride researchers worldwide to clarify the mechanism underlying this discrepancy, that is, the high efficiency of LEDs in spite of the high density of threading dislocations. The tendency of In to segregate at the atomic-step edge or at the dislocation area, the decomposition of GaInN during the growth of the upper p-layer at high temperature, and the strong piezoelectricity of nitrides complicate the recombination mechanism [23, 24]. Several groups claimed that the formation of an InNrich region in GaInN by the segregation of InN creates a natural quantum dot or quantum disk structure, thereby screening nonradiative recombination at or around the threading dislocations [25, 26]. Another group proposed that the In atom itself acts as a strong hole-capture center, thereby screening the nonradiative recombination [27]. In any case, by using thin GaInN as an active layer, the efficiency of blue or green LED becomes less sensitive to the density of threading dislocations. Violet LDs have also been fabricated on sapphire substrates by applying an LT buffer layer, conductivity control for n-type and p-type, and GaInN-based quantum-well structures [28, 29]. After the first pulsed operation of lasing by electrical pumping in 1996, continuous wave operation at room temperature was also successfully achieved by Nakamura et al. in 1996 [30]. In the early period of the development of the nitride-based violet LDs, device lifetime was very short. High threading dislocation density was expected to be the cause of the device degradation. Several attempts were made to reduce the density of threading dislocations. Usui et al. and Zheleva et al. grew locally low dislocation density GaN on sapphire or SiC substrates by the epitaxial lateral overgrowth or lateral epitaxial overgrowth technique using a partially patterned substrate; this technique was initially proposed for the growth of Si on insulator or the growth of GaAs on Si [31–33]. Very thick GaN was grown on sapphire or GaAs by HVPE by the lateral growth method, by which a quasi-free-standing GaN substrate was realized [34–37]. Sakai et al. and Weber et al. clarified the mechanism of the reduction of threading dislocations that bend at the inclined facet of the surface. Similar methods have been proposed, such as pendeo-epitaxy and patterned substrate or cantilever epitaxy, all of which are based on the laterally seeded epitaxy by which the number of not only the threading dislocations, but also impurity-related defects can be reduced [38–43]. Optical properties, particularly the nonradiative property of the threading dislocations were studied in detail by spatially resolved cathodoluminescence. There are three major types of threading dislocations in a wurtzite system, namely, screw dislocations, edge dislocations and mixed dislocations. The nonradiative property of each type of dislocation for GaN was studied by several groups [44– 46]. They found optically dead zones around the ends of the dislocations in both GaN and GaInN. Fig. 11.2 summarizes the relationship between effective luminescent area and the dislocation density as a function of the size of the optically

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Fig. 11.2 Effective luminescent area and the dislocation density as a function of the size of the dark spot shown in the Fig. 11.9.

dead area in GaN or GaInN [47]. A large dead area corresponds to the results of screw or mixed dislocations, while a small dead area corresponds to edge dislocations. From the results in the figure, it is anticipated that the reason why the efficiency of the GaInN-based blue or green LEDs is insensitive to the density of threading dislocations is that the optically dead area is very small in this material system, which is related to the very short diffusion length of the minority carriers, therefore, the effective luminescent area is insensitive to the dislocation density, at least in the region of 109 cm–2. Improvement of the performance of nitride LEDs will lead to their application in lighting. The gateway to the use of LEDs as illumination devices was opened by combining blue LED and phosphors such as YAG or organics [48–50]. Excitation of three color phosphors by UV LED is also a candidate for realizing a white LED [51]. Today, LED lighting and optical storage using violet LDs are some of the hottest topics related to practical applications. In the next section, details of LED lighting, UV LEDs, and violet LDs are discussed.

11.3

White LEDs

White LEDs are one of the hottest topics in the nitride field. There are several methods of achieving white LEDs: (1) combination of red, green, and blue LEDs, (2) combination of red, green, and blue phosphors with a violet or UV LED, and (3) combination of a blue LED with yellow phosphors [48, 49, 51, 52]. Fig. 11.3 schematically shows how to obtain white light by each method. Fig. 11.4 shows the CIE graph in which the methods of realizing white light are shown. Each of the three methods has both advantages and disadvantages. Color rendering is

11.3 White LEDs

Fig. 11.3 Three methods to achieve white LEDs. Method 1: combination of red, green, and blue LEDs. Method 2: combination of red, green, and blue phosphors with violet or UV-LEDs. Method 3: combination of blue LED with yellow phosphor.

Fig. 11.4 Commission Internationale de l’Eclairage (CIE) chromatograph and each method shown in Fig. 11.3 of how to make white light. White light can be obtained by adding three primary colors (methods 1 and 2) or by adding blue and yellow (method 3).

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Light Emitting Diodes

Fig. 11.5 Evolution of lighting as a function of calendar year. Courtesy of Mike Krames, LumiLEDs (as of 2000).

good by methods (1) and (2), while the efficiency is the best with (1). The disadvantage of method (1) is that the driving circuit becomes complicated and the size of each pixel becomes at least three times larger compared to the other two methods. As for method (2), the total efficiency never exceeds the principal limit of the rate of each photon energy, i.e., “Stokes shift”. Method (3) is simple and fabrication is easy, so it can be used in applications that do not require good color rendering. Nowadays, the luminous efficiency of the LEDs is becoming closer and closer to that of the fluorescent light bulb. Fig. 11.5 summarizes the luminous efficiency of state-of-the-art red, green, blue, and white LEDs as a function of calendar year. In the near future, high-efficiency and high-color-rendering illumination will be realized by the LED, in which nitrides are expected to play major roles.

11.4

UV LEDs

The success of the nitride LEDs in the visible region pushes nitrides forward to the UV region. The efficiency of nitride LEDs becomes more and more sensitive to the nonradiative recombination center at or around the threading dislocations with shortening of the emission wavelength or decrease of the In content in the well. Fig. 11.6 shows the PL efficiency of 352 nm UV MQW and 410 nm violet MQW as a function of the dislocation density [53]. As shown in the figure, violet MQWs are not very sensitive to the density of dislocations, while UV LEDs are very sensitive to it. Fig. 11.7 summarizes the wall-plug efficiency or external quan-

11.4 UV LEDs Fig. 11.6 Photoluminescence efficiency at room temperature of GaInN/GaN quantum wells, which is 410 nm emission, and AlGaN/GaN quantum wells, which is 352 nm emission.

Fig. 11.7 State-of-the-art high-efficiency nitride-based LEDs as a function of EL peak wavelength [53–60, 71].

tum efficiency or the wall-plug efficiency of state-of-the-art nitride-based LEDs as a function of emission wavelength [54–60, 71]. Several attempts have been made to improve the efficiency of UV LEDs. One approach is to utilize In-containing alloys, that is, an AlGaInN quaternary alloy, in the well layer [55, 56, 59]. Another approach is to reduce the number of threading dislocations, by which the number of nonradiative recombination centers is also expected to be reduced. The quasibulk GaN substrate grown by HVPE, which, of course shows a good lattice match with GaN, was found to be promising for the fabrication of high-power UV LEDs

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with In-free AlGaN wells, although there is a self-absorption problem [57]. In order to fabricate efficient UV LEDs, thick AlGa(In)N with a low threading dislocation density is indispensable. As a substrate, sapphire has advantages over SiC or even GaN substrates because it is transparent in the UV region, but it has a much larger lattice mismatch with GaN. Compared to GaN, it is difficult to grow high-quality, thick AlGa(In)N. Although the crystalline quality of AlGaN on sapphire is improved by using an LT buffer layer, it progressively worsens with increasing AlN molar fraction [61]. The crystalline quality is significantly improved when an AlGaN layer is grown on a high-quality GaN layer, but a crack network originating from the tensile stress induced by the lattice mismatch between AlGaN and GaN is generated at a high density if the thickness of AlGaN exceeds a critical value [62]. One of the solutions to the fracture problem in the AlGaN-on-GaN heterostructure is to insert another LT AlN layer between the underlying GaN layer and the upper AlGaN layer, called an “LT interlayer” [63]. The major effects of inserting the LT interlayer are the reduction of tensile stress during growth and the reduction of the number of threading dislocations with screw components. It is important to emphasize that the crystalline quality of this AlGaN is superior to that grown on sapphire covered with an LT buffer layer, as confirmed by TEM observation. The effect of the additional LT interlayer was confirmed by several groups [64–66]. This LT-interlayer process was also used in the fabrication of a distributed Bragg reflector mirror based on an AlGaN/GaN multilayered structure. The disadvantage of the LT-interlayer technique is that it increases the density of edge dislocations, which also act as nonradiative recombination centers. Therefore, the fabrication of highly luminescent AlGaN is difficult. The epitaxial lateral overgrowth technique in which a dielectric mask such as SiOx or SiNx is used, is very effective for growing low-dislocation-density GaN on sapphire, SiC or Si, but it cannot be used in the growth of AlGaN, particularly with a high AlN molar fraction, due to the deposition of polycrystalline islands on the mask. Another method of growing low dislocation density AlGaN is to use grooved GaN. Fig. 11.8 schematically shows the structure for utilizing grooved GaN.

Fig. 11.8 Schematic view of the GaN trench structure in order to achieve low dislocation density AlGaN.

11.4 UV LEDs

Again, as shown in Fig. 11.9 a and b, it should be emphasized that the LT interlayer is essential for solving the fracture problem. Fig. 11.9 c shows the cross-sectional TEM image of the AlGaN grown on grooved GaN with low-temperature-deposited AlN interlayer. The cathodoluminescence image at cryogenic temperature shown in Fig. 11.10 shows that the grooved area is much brighter than that of the terrace area, indicating that dislocations act as the nonradiative recombination center. The efficiency of the AlGaN/GaN MQW with low dislocation density is

a SEM image and the schematic structure of Al0.19Ga0.81N on grooved GaN with low temperature-deposited AlN interlayer; b SEM image and the schematic structure of Al0.19Ga0.81N on grooved GaN without low temperature deposited AlN interlayer; c cross-sectional TEM image of the sample shown in Fig. 11.9 a. Fig. 11.9

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Fig. 11.10 Cathodoluminescence image at cryogenic temperature of

grooved GaN with low-temperature deposited AlN interlayer. Bright and dark correspond to the grooved and terrace area, respectively. The dark spot in the grooved area is the terminal of the dislocation.

comparable to that of the GaN/GaInN MQW. The effect of the reduction of threading dislocations was also confirmed by fabricating UV LEDs. Clear contrast of the EL emission between the terrace and grooved regions can be observed, suggesting that the reduction of threading dislocations is important for fabricating highly efficient UV LEDs. These growth processes are rather complex because etching and regrowth are unavoidable. In addition, in this process, the underlying GaN layer is necessary because it acts as the absorption layer for UV light. Another process is proposed for the growth of AlGaN: the use of a grooved substrate [67–70]. In this process, grooves are initially formed on the surface of a sapphire, SiC or Si substrate. Then, AlGaN is grown utilizing an LT buffer layer. The groove should be sufficiently deep so that the laterally grown AlGaN from the terrace covers the grooved region before the top of the AlGaN grown from the bottom of the groove reaches the laterally grown AlGaN. This process has several advantages over other processes. For example, it does not require etching or regrowth of GaN, and thus the problem of self-absorption can be avoided. It is also possible to reduce the thermal stress caused by the difference in the thermal expansion coefficients between AlGaN and the substrate. Recently, Yamada et al. [71] pointed out another important aspect of the performance of the UV LED, that is, light extraction efficiency. They fabricated a UV LED with much higher efficiency at a peak wavelength of 365 nm using a GaN active layer on a sapphire substrate. In order to alleviate the self-absorption problem, they removed the underlying thick GaN layer. In addition, they used highly reflecting electrodes that greatly improved the light-extraction efficiency. This result clearly showed that self-absorption in the underlying layer and in the p-contact layer, including the electrode and/or the substrate, is also significant in the UV region.

11.5 Violet LDs

11.5

Violet LDs

The initial stages of GaN-based violet LDs are grown on a thick n-type GaN contact layer. In order to avoid fracture caused by the lattice mismatch between AlGaN and GaN, the AlGaN cladding layer has been limited in thickness. Growth of a thick AlGaN cladding layer, e.g., 1-lm thick, quite often results in the generation of a crack network. The use of a relatively thin AlGaN cladding layer in the current GaN-based LDs resulted in poor optical confinement, and hence, a far-field pattern accompanied by the multiple spots of higher-order-mode operation caused by the penetration of the lasing light into an n-GaN contact layer has been observed [72]. By optical confinement calculations along the vertical direction, it is found that this type of light leakage can be suppressed by replacing an n-GaN contact with an n-AlGaN contact layer [73]. Using this new contact layer is also promising for realizing a crackfree LD. A single-robe far-field pattern along the vertical direction was achieved in the LD with the thick and crack-free n-AlGaN as a cladding layer [73]. Control of the transverse mode in the horizontal direction is also important. Up to now, the ridge waveguide structure has been widely adopted in GaN-based violet LDs. An important issue to control the transverse mode in the horizontal direction in the case of the ridge waveguide structure is discussed. An effective refractive index method was used for transverse-mode analysis [74]. We assume that the refractive index of the wurtzite GaN is isotropic, which does not seriously affect the preciseness of the transverse-mode analysis [75]. The eigen equation for the TE polarized mode is, d2 E…y† ‡ k20 ‰n…y†2 dy2

n2eff1 ŠE…y† ˆ 0

…1†

where, k0 is the wave number of electric field in vacuum, n(y) is the refractive index of materials, neff1 is the eigenvalue of the effective refractive index, and E(y) is the electrical field in the y-direction. According to the procedure of the effective refractive index method, effective refractive indices derived from Eq. (1) for both the inside and the outside of the stripe regions are used as refractive indices for transverse-mode calculation. Thus, neff1 for each region is substituted into n(x) in the equation below. d2 E…x† ‡ k20 ‰n…x†2 dx 2

n2eff2 ŠE…x† ˆ 0

…2†

Then, the electrical distribution in the x-direction, E(x), is obtained. Fig. 11.11 schematically shows the structure for violet LDs. Fig. 11.12 a and b show the difference between effective refractive indices of the inside and the outside of the ridge-stripe regions (Fig. 11.12 a) and confinement factors for the fundamental mode and 1st-order mode and the modal discrimination factor for a 1.5-lm wide ridge-wa-

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Fig. 11.11 Schematic structure of the ridge geometry of the nitride-based violet LD.

veguide structure (Fig. 11.12 b), respectively, as a function of the remaining p-AlGaN thickness after etching, which is denoted as “d” in the figure. The mode discrimination factor is the difference between confinement factors for the fundamental mode and the 1st-order mode, which represents the stability of the fundamental transverse mode. In order to achieve better optical confinement, neff should be as large as possible. In the case of the ridge-waveguide structure, the effective refractive index neff increases with the increase of “d”. At the same time, however, the difference between the refractive indices of the inside and the outside of the ridge-stripe regions decreases. In order to achieve index guiding, d should be less than 0.15 lm. From these calculations, it was found that very precise control of d is necessary to achieve both good optical confinement and stable transverse-mode operation. Several structures have been proposed to circumvent this problem [76, 77].

11.6

Summary

In this chapter, an historical overview of the GaN-based blue, green, and white LEDs on a sapphire substrate and recent topics was given. The accumulation of a large quantity of outstanding work, particularly in the area of MOVPE growth, has led to the fabrication of high-performance LEDs, many of which could not be anticipated in the 1980s. One of the major targets for nitride LEDs is their use in lighting. A vast lighting market exists. Nitride LEDs can play a major role and hence, they can contribute to environmental conservation because of their superior device lifetime. Of course, high efficiency is the premise in realizing them. Further progress in these areas will definitely open up new areas in optoelectronics and continue to have an impact on the compound semiconductor field.

11.6 Summary

Fig. 11.12 a Difference between effective refractive indices of the inside and

the outside of the ridge-stripe regions; b confinement factors for the fundamental mode and 1st-order mode and the modal discrimination factor for a 1.5-lm wide ridge-waveguide structure.

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11.7

Acknowledgments

The author is grateful to Professors Isamu Akasaki and Satoshi Kamiyama for much fruitful discussion. He is also grateful to Professors B. Monemar, Linköping University, Fernando Ponce, Arizona State University and David Cherns, University of Bristol and Drs. T. Takeuchi, C. Wetzel, S. Yamaguchi, and T. Detchprohm for fruitful discussions and assistance with the experiments. The author is also greatly indebted to Mr. Motoaki Iwaya and Shugo Nitta who made major contributions to this work.

11.8

References 1 2

3 4

5 6

7 8 9

10

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12

J. Pankove, E. Miller, D. Richman, and J. Berkeyheiser, J. Lumin. 4, 63 (1971). R. Dingle, K. Shaklee R. Z. Leheny, and R. Zetterstrom, Appl. Phys. Lett. 19, 5 (1971). I. Akasaki, Mater. Res. Soc. Symp. Proc. 510, 145 (1998). H. Manasevit, F. Erdman, and W. Simpson, J. Electrochem. Soc. 118, 1864 (1971). T. Kawabata, T. Matsuda, and S. Koike, J. Appl. Phys. 56, 2367 (1984). H. Amano, N. Sawaki, I. Akasaki, and Y. Toyoda, Appl. Phys. Lett. 48, 353 (1986). H. Amano and I. Akasaki, Mater. Res. Soc. Ext. Abst. EA-21, 165 (1990). S. Nakamura, T. Mukai, and M. Senoh, Jpn. J. Appl. Phys. 31, 2883 (1992). H. Amano, T. Kozawa, K. Hiramatsu, N. Sawaki, I. Akasaki, Y. Ishii, and K. Ikeda, J. Lumin. 40, 121 (1988). H. Amano, M. Kito, K. Hiramatsu, N. Sawaki, and I. Akasaki, Jpn. J. Appl. Phys. 28, L2112 (1989). J. Philips, “Bands and Bonds in Semiconductors” (translated in Japanese) Yoshioka-Shoten, p. 286. J. Orton and C. Foxon, “A8.5 Acceptors in GaN and related compounds”, in EMIS Datareview No. 23, Ed. by J. Edgar, S. Strite, I. Akasaki, H. Amano, and C. Wetzel (INSPEC, IEE, London, 1999) p. 300.

13

14

15

16

17 18

19

20

21

22

23

24

S. Nakamura, N. Iwasa, M. Senoh, and T. Mukai, Jpn. J. Appl. Phys. 31, 1258 (1992). J. A. Van Vechten, J. D. Zook, R. D. Horning, and B. Goldenberg, Jpn. J. Appl. Phys. 31, 3662 (1992). T. Nagatomo, T. Kuboyama, H. Minamino, and O. Omoto, Jpn. J. Appl. Phys. 28, L1334 (1989). M. Yoshimoto, T. Matsuoka, T. Sasaki, and A. Katsui, Appl. Phys. Lett. 59, 2251 (1991). S. Nakamura, T. Mukai, and M. Senoh, Appl. Phys. Lett. 64, 1687 (1994). T. Takeuchi, H. Takeuchi, S. Sota, H. Sakai, H. Amano, and I. Akasaki, Jpn. J. Appl. Phys. 36, L177 (1997). F. Bernadini, V. Fiolentini, and D. Vanderbilt, Phys. Rev. B 56, R10024 (1997). H. Amano and I. Akasaki, Ext. Abs. Solid State Device and Mater. Conf. 683 (1995). S. Nakamura, M. Senoh, N. Iwasa, and S. Nagahama, Jpn. J. Appl. Phys. 34, L797 (1995). S. D. Lester, F. A. Ponce, M. G. Craford, and D. A. Steigerwald, Appl. Phys. Lett. 66, 1249 (1995). Y. Chen, T. Takeuchi, H. Amano, I. Akasaki, N. Yamada, Y. Kaneko, and S. Y. Wang, Appl. Phys. Lett. 72, 710 (1998). T. Takeuchi, C. Wetzel, S. Yamaguchi, H. Sakai, H. Amano, I. Akasaki, Y. Kaneko, S. Nakagawa, Y. Yamaoka, and N.

11.8 References

25

26

27

28

29

30

31 32

33

34

35

36

37

38 39

Yamada, Appl. Phys. Lett. 73, 1691 (1998). S. Chichibu, T. Azuhata, T. Sota, and S. Nakamura, Appl. Phys. Lett. 69, 4188 (1996). Y. Narukawa, Y. Kawakami, M. Funato, Sz. Fujita, Sg. Fujita, and S. Nakamura, Appl. Phys. Lett. 70, 981 (1997). L. Bellaiche, T. Mattila, L. W. Wang, S. H. Wei, and A. Zunger, Appl. Phys. Lett. 74, 1842 (1999). S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, and Y. Sugimoto, Jpn. J. Appl. Phys. 35, L74 (1996). I. Akasaki, S. Sota, H. Sakai, T. Tanaka, M. Koike, and H. Amano, Electron. Lett. 32, 1105 (1996). S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, and H. Kiyoku, Appl. Phys. Lett. 69, 4056 (1996). Y. Ujiie and T. Nishinaga, Jpn. J. Appl. Phys. 28, L337 (1989). A. Usui, H. Sunakawa, A. Sakai, and A. Yamaguchi, Jpn. J. Appl. Phys. 36, L899 (1997). T. Zheleva, O. Nam, M. Bremser, and R. Davis, Appl. Phys. Lett. 71, 2472 (1997). K. Naniwae, S. Itoh, H. Amano, K. Itoh, K. Hiramatsu, and I. Akasaki, J. Cryst. Growth 99, 381 (1990). R. J. Molnar, R. Aggarwal, Z. L. Liau, E. R. Brown, I. Melngailis, W. Goetz, L. T. Romano, and N. M. Johnson, Mater. Res. Soc. Symp. Proc. 395, 1889 (1996). Y. Kumagai, H. Murakami, A. Koukitu, K. Takemoto, and H. Seki, Jpn. J. Appl. Phys. 39, L703 (2000). K. Motoki, T. Okahisa, N. Matsumoto, M. Matsushima, H. Kimura, H. Kasai, K. Takemoto, K. Uematsu, T. Hirano, and M. Nakayama, Jpn. J. Appl. Phys. 40, L140 (2001). A. Sakai, H. Sunakawa, and A. Usui, Appl. Phys. Lett. 71, 2259 (1997). As a text book, for example, “Introduction to Dislocations”, D. Hull and D.J. Bacon, 3rd edn, International Series on Materials Science and Technology, 37, 89 (1984).

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42

43 44

45

46 47

48 49 50 51

52

53

54 55

56

T. Gehrke, K. J. Linthicum, D. B. Thomson, P. Rajagopal, A. D. Batchelor, and R. F. Davis, MRS Internet J. Nitride Semicond. Res. 4S1, G3.2 (1999). T. Detchprohm, M. Yano, R. Nakamura, S. Sano, S. Mochiduki, T. Nakamura, H. Amano, and I. Akasaki, Mater. Res. Soc. Symp. Proc. 657, G5.7 (2001). C. I. H. Ashby, C. C. Willan, J. Han, N. A. Missert, P. P. Provencio, D. M. Follstaedt, G. M. Peake, and L. Griego, Proc. Electrochem. Soc. 18, 132 (2000). D. Cherns, private communication. T. Sugahara, H. Sato, M. Hao, Y. Naoi, S. Kurai, S. Tottori, K. Yamashita, K. Nishino, L. T. Romano, and S. Sakai, Jpn. J. Appl. Phys. 37, L398 (1998). T. Miyajima, T. Hino, S. Tomiya, K. Yanashima, H. Nakajima, T. Araki, Y. Nanishi, A. Satake, Y. Masumoto, and K. Akimoto, Phys. Stat. Sol. (b) 228, 395 (2001). D. Cherns, S. Henley, and F. A. Ponce, Appl. Phys. Lett. 78, 2691 (2001). H. Amano, S. Takanami, M. Iwaya, S. Kamiyama, and I. Akasaki, Proc. PLMCN-2 (2002). S. Nakamura, Proc. SPIE Int. Soc. Opt. Eng. 3002, 26 (1997). P. Schlotter, R. Schmidt, and J. Schneider, J. Appl. Phys. 64, 417 (1997). F. Hide, P. Kozodoy, and P. DenBaars, Appl. Phys. Lett. 70, 2664 (1997). K. Tadatomo, H. Okagawa, Y. Ohuchi, T. Tsunekawa, Y. Imada, M. Kato, and T. Taguchi, Jpn. J. Appl. Phys. 40, L583 (2001). M. Hashimoto, I. Akasaki, and N. Sawaki, Japan Display ’83, Proc. 3rd Int. Display Res. Conf. (1983). M. Iwaya, S. Terao, T. Sano, S. Takanami, T. Ukai, R. Nakamura, S. Kamiyama, H. Amano, and I. Akasaki, Phys. Stat. Sol. (a) 188, 117 (2001). T. Mukai and S. Nakamura, Jpn. J. Appl. Phys. 38, 5735 (1999). K. Tadatomo, H. Okagawa, Y. Ohuchi, T. Tsunekawa, Y. Imada, M. Kato, and T. Taguchi, Jpn. J. Appl. Phys. 40, L583 (2001). J. Han, M. Crawford, R. Shul, and S. Hearne, Mater. Res. Soc. Symp. Proc. 537, 7.7.1 (1991).

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11 Electroluminescent Diodes and Laser Diodes 57

58 59

60

61

62

63

64

65

66

67

M. Khan, V. Adivarahan, J. P. Zhang, C. Chen, E. Kuokstis, A. Chitnis, M. Shatalov, J. W. Yang, and G. Simin, Jpn. J. Appl. Phys. 40, L1308 (2001). T. Nishida and N. Kobayashi, Phys. Stat. Sol. (a) 188, 113 (2001). S. Nagahama, N. Iwasa, M. Senoh, T. Matsushita, Y. Sugimoto, H. Kiyoku, T. Kozaki, M. Sano, H. Matsumura, H. Umemoto, K. Chocho, T. Yanamoto, and T. Mukai, Phys. Stat. Sol. (a) 188, 1 (2001). H. Hirayama, A. Kinoshita, A. Hirata, and Y. Aoyagi, Phys. Stat. Sol. (a) 188, 83 (2001). Y. Koide, N. Itoh, K. Itoh, N. Sawaki, and I. Akasaki, Jpn. J. Appl. Phys. 27, 1156 (1988). K. Itoh, T. Kawamoto, H. Amano, K. Hiramatsu, and I. Akasaki, Jpn. J. Appl. Phys. 30, 1924 (1991). H. Amano, M. Iwaya, T. Kashima, M. Katsuragawa, I. Akasaki, J. Han, S. Hearne, J. A. Floro, E. Chason, and J. Figiel, Jpn. J. Appl. Phys. 37, L1540 (1998). C. C. Yang, M. C. Wu, C. A. Chang, and G. C. Chi, Mater. Sci. Eng. B 68, 22 (1999). D. D. Koleske, M. E. Twig, A. E. Wickenden, R. L. Henry, R .J. Gorman, J. A. Freitas, Jr, and M. Fatemi, Appl. Phys. Lett. 75, 3141 (1999). K. E. Waldrip, J. Han, J. Figiel, H. Zhou, E. Makarona, and A.V. Nurmikko, Appl. Phys. Lett. 78, 3205 (2001). M. Yano, T. Detchprohm, R. Nakamura, S. Sano, S. Mochizuki, T. Naka-

68

69

70

71 72

73

74

75

76

77

mura, H. Amano, and I. Akasaki, IPAP Conf. Ser. 1, 292 (2000). C. I. H. Ashby, C. C. Mitchell, J. Han, N. A. Missert, P. P. Provencio, D. M. Follstaedt, G. M. Peake, and L. Griego, Appl. Phys. Lett. 77, 3233 (2000). T. M. Katona, M. D. Craven, P. T. Fini, J. M. Speck, and S. P. DenBaars, Appl. Phys. Lett. 79, 2907 (2001). T. Detchprohm, S. Sano, S. Mochizuki, S. Kamiyama, H. Amano, and I. Akasaki, Phys. Stat. Sol. (a) 188, 799 (2001). Nikkei Electronics 10. 21, 28 (2002). D. Hofstetter, D. P. Bour, R. L. Thornton, and N. M. Johnson, Appl. Phys. Lett. 70, 1650 (1997). T. Takeuchi, T. Detchprohm, M. Iwaya, N. Hayashi, K. Isomura, K. Kimura, M. Yamaguchi, H. Amano, I. Akasaki, Yw. Kaneko, R. Shioda, S. Watanabe, T. Hidaka, Y. Yamaoka, Ys. Kaneko, and N. Yamada, Appl. Phys. Lett. 75, 2960 (1999). T. Sato, M. Iwaya, K. Isomura, T. Ukai, S. Kamiyama, H. Amano, and I. Akasaki, IEICE Trans. Electron. E Ser. C 2000 83, 573 (2000). G. Yu, H. Ishikawa, M. Umeno, T. Egawa, J. Watanabe, T. Jimbo, and T. Soga, Appl. Phys. Lett. 72, 2202 (1998). T. Asano, M. Takeya, T. Tojyo, S. Ikeda, T. Mizuno, S. Ansai, S. Goto, S. Kijima, T. Hino, and S. Uchida, Mater. Res. Soc. Symp. Proc. 693, 259 (2002). M. Kuramoto, A. Kimura, C. Sasaoka, T. Arakida, M. Nido, and M. Mizuta, Jpn. J. Appl. Phys. 40, L925 (2001).

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GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors Hadis Morkoç and Lianghong Liu

Abstract

Because of their large band gap, large high-field electron velocity, large breakdown field, large thermal conductivity, and robustness, GaN and its heterostructures with InGaN and AlGaN have recently attracted a good deal of attention for highpower/high-temperature electronics applications, and for use in optoelectronic devices operative in the UV and visible wavelengths. Specifically, the heterostructures based on GaN have paved the way to AlGaN/GaN MODFETs with CW power levels of about 6 W at 10 GHz in devices with 1-mm gate periphery that are comparable to power densities extrapolated from smaller devices. When four of these devices were power combined in a single-stage amplifier, a CW output power of 22.9 W with a power-added efficiency of 37% was obtained at 9 GHz. On the noise figure front, a minimum noise figure for a 1-mm device of 0.85 dB with an associated gain of 11 dB at 10 GHz was obtained. The expected electron mobility in GaN has recently been upgraded from a maximum of about 900 cm2 V–1 s–1 to perhaps as high as 2000 cm2 V–1 s–1, which bodes very well for electronic device applications. While the experimental device effort is progressing well, basic issues such as polarization-induced charge has gained prominence, as it is inextricable from charge induced/controlled by the gate. Last but not least, the GaN-based material system, though far from being perfected, has already demonstrated remarkable performance in optical emitters and optical detectors.

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12.1

Introduction

Semiconductor nitrides such as aluminum nitride (AlN), gallium nitride (GaN), and indium nitride (InN) are very promising materials for their potential use in optoelectronic devices (both emitters and detectors), and high-power/temperature electronic devices as have been treated in length and reviewed recently [1–7]. These materials and their ternary and quaternary alloys cover an energy band gap range of 1.9 to 6.2 eV, suitable for band-to-band light generation with colors ranging from red (potentially) to ultraviolet (UV) wavelengths. Specifically, nitrides are suitable for such applications as surface acoustic wave devices [8], UV detectors [9, 10], Bragg reflectors [11], waveguides, UV and visible light emitting diodes (LEDs) [12–14], and laser diodes (LDs) [15] for digital data read-write applications. During the last several decades, lasers and LEDs have expanded remarkably both in terms of the range of emission wavelengths available and brightness. The nitride semiconductor-based LEDs have proven to be reliable in such applications as displays, lighting, indicator lights, advertisement, and traffic signs/signals. Additional possible applications include use in agriculture as light sources for accelerated photosynthesis, and in health care for diagnosis and treatment. Lasers, as coherent sources, are crucial for high-density optical read and write technologies because the diffraction-limited optical storage density increases approximately quadratically in the ideal case as the probe laser wavelength is reduced. Nitride-based coherent UV sources are attracting a good deal of attention for optical storage devices. Optical storage would enable the storage and retrieval of inordinate number of images and vast quantities of text with untold efficiency. Other equally attractive applications envisioned include printing and surgery. When used as UV sensors in jet engines, automobiles, and furnaces (boilers), the devices would allow optimal fuel efficiency and control of effluents for a cleaner environment. Moreover, UV sensors that operate in the solar-blind region (260 to 290 nm) would have high detectivity because the ozone layer absorbs solar radiation at those wavelengths, thus virtually eliminating the radiation noise. Consequently, these detectors are expected to play a pivotal role in threat recognition aimed against aircraft and other vehicles [9, 10, 16]. GaN photodiodes [17] exhibited zero-bias responsivities of about 0.21 A W–1 at 356 nm that decreased by more than three orders of magnitude for wavelengths longer than 390 nm. The noise equivalent power (NEP) at a reverse bias of 10 V is (f >100 Hz) 6.6 ´ 10–15 W Hz–1/2, which is extremely small [18]. Detector speed while affected in terms of uniformity by the sheet resistance of the p-layer, which suffers from the notoriously low doping levels, is in the picosecond range [19]. Finally, the GaN-based detectors with AlN mole fractions approaching the solar-blind region of the spectrum have been fabricated into arrays for imaging. Detector arrays with pixel sizes of 32 ´ 32 have been fabricated and tested already [20]. GaN’s large band gap, large dielectric breakdown field, fortuitously good electron transport properties [21–23] (an electron mobility possibly in excess of 2000 cm2 V–1 s–1 and a peak velocity approaching 3 ´ 107 cm s–1 at room tempera-

12.1 Introduction

ture), and good thermal conductivity are trademarks of high-power/temperature electronic devices [24]. Sheppard et al. [25] have reported that 0.45-lm gate, highpower modulation-doped FETs (MODFETs) on SiC substrates exhibited a power density of 6.8 W mm–1 in a 125-lm wide device and a total power of 4 W (with a power density of 2 W mm–1) at 10 GHz. Other groups have also reported on the superior performance of GaN-based MODFETs on SiC and sapphire substrates with respect to competing materials, particularly at X band and higher frequencies [26–29]. What is astounding is that researchers at HRL Laboratories have recently demonstrated GaN/AlGaN MODFETs prepared by MBE on SiC substrates that exhibited a total power level of 6.3 W at 10 GHz from a 1-mm wide device. What is more astounding is that the power level is not really thermally limited as the power density extrapolated from a 0.1-mm device is 6.5 W. When four of these devices are power combined in a single-stage amplifier, an output power of 22.9 W with a power added efficiency of 37% was obtained at 9 GHz [30]. Equally impressive is the noise figure of 0.85 dB at 10 GHz with an associated gain of 11 dB. The drain breakdown voltages in these quarter-micrometer gate devices are about 60 V, which are in part responsible for such a record performance [31]. Applications of high-power GaN-based MODFETs include amplifiers operative at high power levels, high temperatures and in unfriendly environments such as radar, missiles, and satellites, as well as in low-cost compact amplifiers for wireless base stations. Many of these applications are currently met by pseudomorphic modulation-doped FETs [32]. Though in its infancy, efforts are underway to exploit nitrides for bipolar transistors. However, the materials quality needs to be improved more before performance expected from GaN can be obtained. Difficulties include the notoriously low p-type doping and low diffusion length in epitaxial layers. Nitride semiconductors have been deposited by vapor phase epitaxy (i.e., both hydride VPE [33] [HVPE], which has been developed for thick GaN layers and organometallic VPE [34] [OMVPE], which has been developed for heterostructures), and in a vacuum by a slew of variants of molecular beam epitaxy (MBE) [16]. All the high-performance light emitters, which require high-quality InGaN, have been produced by OMVPE. On the other hand, MBE has been very successful in producing structures that do not require InGaN for optical emitters. Some examples are FETs and detectors. With its innate refined control of growth parameters, in situ monitoring capability, and uniformity, MBE is well suited for depositing heterostructures and gaining insight to deposition/incorporation mechanisms. MBE’s control over growth parameters is such that any structure can be grown in any sequence. The structures based on conventional compound semiconductors such as IR lasers for CD players, surface-emitting vertical cavity lasers, and high-performance pseudomorphic MODFETs have all been produced very successfully, most of them commercially, by MBE. Nitride growth, however, requires much higher temperatures than those used in producing conventional group III–V semiconductors for which the MBE systems were designed. In addition, it has proved difficult to provide active N species at sufficiently high rates for nitride growth. Despite these mechanical/engineering limitations and its relatively late entry, with appro-

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priate modifications, MBE has already played a key role on a number of fronts, such as high-performance GaN-based MODFETs and fast solar-blind detectors. Interestingly, highest mobility 2 DEG systems were grown with MBE on templates prepared by HVPE, MOCVD and bulk GaN. Moreover, MBE-grown films on such templates produce very clean luminescence with only the excitonic transitions and their excited states observable. In this chapter, electron transport in bulk and two-dimensional systems based on nitrides, polarization issues, MODFET simulations, technology, and performance are discussed. A succinct discussion of nitride-based HBTs closes the chapter.

12.2

Electron Transport Properties in GaN and GaN/AlGaN Heterostructures

Electron mobility is a key parameter in the operation of n-channel FETs in that it affects the access resistances as well as the rate with which the carrier velocity increases with field. Consequently, we will treat the low-field mobility in GaN and its dependence on various scattering events first. This will be followed by treating the two-dimensional electron gas mobility in modulation-doped field effect transistors of direct relevance to technology important. Ultimately, electron mobility is limited by the interaction of electrons with phonons, and in particular with optical phonons. This holds for bulk mobility as well as that in AlGaN/GaN modulation-doped field effect transistors. The room-temperature electron mobility values in bulk GaN grown with HVPE to a thickness of 60 lm was reported for GaN as 950 cm2 V–1 s–1 [35]. Free-standing GaN templates grown by HVPE exhibited room temperature electron mobilities approaching 1400 cm2 V–1 s–1 [36]. Recent HVPE layers exhibit much higher mobilities on the surface of the layers, which approach that of free-standing templates. That reported for metal organic chemical vapor deposition (MOCVD) grown layers were also in excess of 900 cm2 V–1 s–1 [37], though the temperature dependence of mobility in this particular sample was unique. Early MBE layers exhibited mobilities as high as 580 cm2 V–1 s–1 on SiC substrates, which at that time were not as commonly used as in recent times [38]. Typically, however, the MBEgrown films produce much lower mobility values of 100–300 cm2 V–1 s–1 [39]. The lower mobilities have been attributed to both high dislocation densities [39–41] and elevated levels of point defects [42, 43]. Dislocations are considered by some to be an important scattering mechanism in films having dislocation densities above 1 ´ 108 cm–2 [39, 40]. One should keep in mind that these are preliminary attributes and more detailed experiments coupled with detailed analyses are needed to confirm the proposed models. Depending on the particulars of the growth and substrate preparation, GaN films grown by MBE typically have dislocation densities in the range of 5 ´ 109– 5 ´ 1010 cm–2 [39]. With refined procedures, however, dislocation densities in the 8 ´ 108–2 ´ 109 cm–2 can be obtained when grown directly on sapphire substrates

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures

with AlN or GaN buffer layers. Reduction of dislocation density, and other scattering centers that are inherently related to dislocations, is really the key to achieving high-mobility GaN is at the heart of buffer layer and or early stages of growth. Based on the premise that the [002] X-ray diffraction is affected by screw dislocations and the [104] peak by edge dislocations and the fact that RF-nitrogen-grown MBE layers produce excellent [002] peaks (in the 40–120 arcsec range) while the [104] peaks are wider and weaker (in the 180 to 300 arcsec) one can conclude that the majority of the dislocations in MBE layers are of propagating-edge type. The strength of MBE, i.e., 2D growth, does not bode well for dislocation reduction as the edge dislocations propagate along the c-axis going right through the sample, though the detailed picture is somewhat dependent on the particulars of the growth such as pitted or pit-free growth, which depends on the group V/III ratio. Some sort of 3D growth at the early stages of growth, as in the case of growth from vapor, followed by a smoothing layer would help reduce dislocations. The other option is to use HVPE or MOCVD buffer layers for MBE growth. This approach led to record or near-record bulk (1150 cm2 V–1 s–1 at RT, even higher of late) [44] and 2 DEG (53,500 cm2 V–1 s–1 at 4.2 K) mobilities [45]. It is clear that the buffer layers grown by the vapor phase epitaxy method help eliminate the main problem associated with MBE, that is the poor quality of the buffer layer. The other long-standing obstacle for MBE, difficulties associated with sapphire and SiC substrate preparation, has been eliminated. In the case of sapphire, a high-temperature anneal in an O2 environment produces atomically smooth and damage-free surface [46]. In the case of SiC, some form of H2 etching at elevated temperatures removes the surface damage caused by polishing [47] as in the case of sapphire. Controlling the Ga/N ratio and substrate temperature causes the dislocation density across the homoepitaxial interface to remain constant [48, 49]. While the above two studies are related to RF MBE, ammonia MBE has also produced GaN with very high electron mobilities (as high as 70,000 cm2 V–1 s–1 at 4 K) when grown on bulk GaN wafers, which in turn were grown under highpressure/temperature conditions [50]. Electron mobility is one of the most important parameters of the material with great impact on devices. The temperature dependence of mobility and the carrier concentration can be used to extract fundamental information regarding scattering mechanisms [51, 52]. As compared to the other III–V semiconductors, such as GaAs, GaN possesses many unique material and physical properties [1]. However, the lack of high-quality material, until very recently, prevented detailed investigations of carrier transport. The earlier transport investigations had to cope with poor crystal quality and low carrier mobility, which were well below predictions [53–56]. We should point out that unintentionally doped GaN exhibits n-type conduction with a typical electron concentration of *1017 cm–3, with heavy compensation. Typical compensation ratios observed for MOCVD- and MBE-grown films are about 0.3, though a lower ratio of *0.24 was reported for HVPE-grown crystals [57–59]. Compensation reduces the electron mobility in GaN for a given electron concentration. Another point that should be kept in mind is that GaN layers are

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often grown on foreign substrates with very different properties. The degenerate layer at the interface (caused by extended defects and impurities), spontaneous polarization at heterointerfaces, and piezoelectric effects should all be considered. Experiments show that, even for thick GaN grown by HVPE, the degenerate interfacial layer has an important contribution to the Hall conductivity, especially at low temperatures where freeze-out occurs for the donors in bulk, leading to domination by the interfacial layer [35, 60–62]. In these cases, the measured data must be corrected to extract meaningful numbers [57]. The typical extended defect density of GaN grown by various techniques is *109 cm–2 [63]. In many cases, the dislocation and defect scattering may also limit the carrier mobility, especially at low temperatures [64, 65]. Finally, many material and physical parameters of GaN were not available for some of the previous simulations where those parameters were treated as adjustable parameters. Needless to say, reliable parameters are required in the calculation of the electron mobility and in the accurate interpretation of experimental results. 12.2.1

Bulk Mobility in GaN

To treat bulk mobility, we made use of free-standing high-quality GaN templates grown by HVPE at Samsung where the questionable interface layer has been chemically removed. A quantitative comparison with theoretical calculations demonstrates that the one-layer and one-donor conductance model is sufficient to account for the measured data in the entire temperature range without considering any dislocation scattering and any adjustable parameter other than the acceptor concentration [66]. The sample shows a low impurity concentration, a low compensation ratio, negligible dislocation scattering, and high electron mobilities derived from the Hall measurements show the high-quality transport properties associated with the sample. A thick, *300-lm, GaN film was first deposited by HVPE on the c-plane of sapphire. It was then thermally decomposed at the film/substrate interface and lifted off by scanning a laser beam with a photon energy larger than that corresponding to the GaN band gap. Both sides of the free-standing GaN crystal were mechanically polished, and the Ga-face was dry etched to yield a smooth surface. Wet chemical etching was then applied to the N-face to remove some 30 lm of material, the region containing the high-conductance degenerate layer. The final thickness of the GaN template is about 200 lm. The sample has also been characterized by Xray diffraction, atomic force microscopy, and photoluminescence [67]. The Raman spectra were measured for this sample to derive the Debye temperature and the optical dielectric constant as literature values of these parameters vary depending on sample quality. The phonon energies measured in this sample are: A1(LO) = 737.0 cm–1; A1(TO) = 532.5 cm–1; E1(LO) = 745.0 cm–1; E1(TO) = 558.5 cm–1 with an accuracy of ± 0.5 cm–1. These phonon energies are very close to those measured by Azuhata et al. [68] for a thick GaN film grown on sapphire. The optical phonon modes were measured in a variety of scattering configurations

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures

Fig. 12.1 a A1(LO) phonon spectrum of the sample investigated. The scattering configuration is shown in the upper right corner; b A1(TO) phonon spectrum of the sample in-

vestigated. The E phonon spectra are also shown. The scattering configuration is shown in the upper left corner.

as indicated. As usual, X = (100), Y = (010) and Z = (001). Here Z was taken to be parallel to the growth direction. Shown in Fig. 12.1 a are the A1(LO) and A1(TO) phonon spectra where the half-width of the phonon modes is only 8 cm–1. E1(TO) and E2 phonon modes also appear in Fig. 12.1 b. Variable temperature Hall effect measurements were performed in the dark in the temperature range of 26.5 to 273 K using the van der Pauw geometry. Ohmic contacts were formed on the Ga-face with Ti/Al/Ti/Au metallization followed by rapid thermal annealing at 900 8C for 30 s [69]. Good ohmic contacts were verified over the measured temperature range inside the cryostat. Extreme care was taken for the accuracy of the experimental conditions such as the magnetic field, electrical current, and the sample temperature. The measured Hall mobility and carrier concentration are shown in Figs. 12.2 and 12.3, respectively, as a function of temperature. A mobility of 1425 cm2 V–1 s–1 was observed near room temperature (273 K) with the peak mobility being 7386 cm2 V–1 s–1 at 48 K. The temperature dependence of both the Hall mobility and electron concentration (lack of saturation) point to the absence of a degenerate interfacial layer after etching. Therefore, only the single-layer model with a single donor was successfully applied to the analysis of the data. The temperature dependence of the electron mobility was calculated by solving the Boltzmann transport equation (BTE) iteratively [51]. The following scattering processes were included: acoustic deformation potential scattering, piezoelectric scattering, polar optical phonon scattering, and ionized impurity scattering. Only one donor and one acceptor were assumed. The dislocation scattering was not considered because the dislocation density in our sample (< 106 cm–2) [67] is much less than that where dislocation scattering affects the transport properties (108 cm–2) [64, 65]. Likewise, neutral-impurity scattering was not included since it is insignificant. The material parameters used in the calculations are listed in Table 12.1.

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors Fig. 12.2 The measured Hall mobility data (solid squares) from the GaN template grown by HVPE as a function of temperature. The solid line is the calculated result using Na = 2.4 ´ 1015 cm–3, representing the best fit to the measured results. The upper and lower dotted lines are the calculated results using Na = 1.4 ´ 1015 and 3.4 ´ 1015 cm–3.

Fig. 12.3 The measured Hall densities nH (solid squares) as a function of reciprocal temperature from the GaN template grown by HVPE. The open circles represent the carrier density corrected by the Hall factor, n = nHrH. The solid line is the fit to the theoretical expression of charge balance with hole and neutral acceptor densities neglected.

Tab. 12.1 Material parameters of GaN used in the calculations

Parameter

Symbol (units)

Value

High-frequency dielectric constant Low-frequency dielectric constant Polar phonon Debye temperature Mass density Sound velocity Piezoelectric coefficient Acoustic deformation potential Effective mass

e? e0 hLO (K) q (kg m–3) vs (m s–1) P Eds (eV) m* (kg)

5.43 10.4 1060 6.10 ´ 103 6.59 ´ 103 0.118 8.54 0.22 m0

The high-frequency dielectric constant for this sample was calculated using the Lyddane-Sachs-Teller relation using the phonon frequencies of A modes, which should represent a benchmark value due to the high quality of the sample. Importantly, instead of allowing the acoustic deformation potential to be an adjustable fitting parameter, the recent unscreened acoustic deformation potential (Eds = 8.54 eV) was used. This value is deduced from recent 2 DEG-system mobilities at low temperatures where the acoustic phonon scattering is important [70]. If

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures

screening is included, a deformation potential of 12 eV describes experimental 2 DEG mobilities better [71]. However, this is not necessarily applicable here, in part because the sample under investigation has a very low electron concentration, and in part due to freeze-out at low temperatures. Therefore, the deformation potential without screening was used in our simulations as a fixed parameter. The other parameters were kept the same as those reported previously [1, 51] and shown in Table 12.1. The theoretical calculation was fitted to the measured data in concert with the temperature dependence of the electron concentration and charge neutrality. The donor and acceptor concentrations are used as the fitting parameters. The solid line in Fig. 12.2 represents the best fit to the measured data. The dotted lines give the estimated upper and lower bounds for the acceptor concentration. As shown, quantitative agreement with the measured mobility in the entire temperature range is obtained to within about 30%. The acceptor concentration obtained from the fitting is 2.4 ´ 1015 cm–3. The carrier concentration as a function of temperature is also calculated using the charge neutrality condition with hole and neutral acceptor density being neglected. The solid line shown in Fig. 12.3 represents the fit to the measured electron concentration corrected by the Hall factor. The impurity concentrations and the activation energy used in the fitting are ND = 1.76 ´ 1016 cm–3, NA = 2.40 ´ 1015 cm–3, and ED = 25.2 meV. The agreement between the ND and NA values derived from the mobility and the carrier concentration data demonstrates the self-consistency of the results with the assumed model. The actual value and the temperature dependence of the Hall factor are implicit in calculations and are shown in Fig. 12.4, where a degeneracy factor of 2 was assumed. Considering the screening effect, the donor binding energy ED0 can be calculated from ED0 = ED + aND1/3 = 30.7 meV, where the screening factor a = 2.1 ´ 10–5 meV cm. This result is close to the measured value from infrared absorption (29.0 meV) [72]. We note that the donor binding energy obtained here is higher than the 27.5 meV value derived for the HVPE sample with a higher donor concentration of

Fig. 12.4 Temperature dependence of the calculated Hall factor, rH.

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1.25 ´ 1017 cm–3 reported in Ref. [35]. The discrepancy may be introduced from the two-layer conductance in the latter case. As shown earlier [35, 60–62], the interface conductance mainly affects the low-temperature data. Since the donor activation energy can only be accurately determined from the low-temperature region in which ionized-impurity scattering is dominant, any high-conductivity interface contribution would make it difficult to deduce an accurate donor binding energy. The measured impurity concentrations ND and NA as well as the compensation ratio (NA/ND) of 0.14 are among the lowest values reported for bulk GaN grown by any technique. The peak mobility of 7386 cm2 V–1 s–1 and the value near room temperature are also among the highest for bulk GaN. The quantitative agreement between the calculations and the measured data demonstrates that the single-layer and single-donor model amply describes the conduction process. The results also show that dislocation scattering is not important for the sample under investigation in the entire measured temperature range, demonstrating the high crystal quality. 12.2.2

Polarization Effects, Mobility and Electron Concentration in 2 DEG Systems

As mentioned in the introduction, AlGaN/GaN heterostructures have been the subject of many recent investigations because of their potential for use in hightemperature, high-power devices [3, 24, 73, 74], due to the large band discontinuities and polarization-induced screening charge. While polarization effects cause a redistribution of weakly bound and free charges, they cannot directly produce free electrons to form a 2 DEG [75–77]. In the GaN-based system, issues dealing with heterointerfaces must include a discussion of polarization. Polarization induces field, which in turn affects the interface charge through screening in that mobile carriers move to where the fixed polarization charge with opposite polarity is. Since nitrides are large band gap materials that tend to be n-type with very low hole concentrations, mobile carriers are most likely donated by intentional donors or donor-like defects. The AlGaN barrier [78] and the AlGaN surface [79] have been suggested as the source of electrons. Positive surface charge has also been suggested to account for the experimental observations in the form of dependence of the 2 DEG density on the thickness and/or alloy composition of the AlGaN barrier [80, 81]. Typically, the AlGaN barrier is grown on a relatively thick GaN layer to form the basis for the 2 DEG system in a Ga-polarity sample. The inherent lattice mismatch causes a biaxial tensile strain, and the thermal mismatch causes a biaxial compressive strain in the growth plane. The resultant strain induces a macroscopic electric field in the polar material. In addition, due to the particular crystalline structure of the wurtzite lattice, a spontaneous polarization field is also found in both AlGaN and GaN even in the absence of strain. In heterostructures where the growth takes place along the (0001) direction, both the spontaneous and induced polarizations are directed opposite to the growth direction. The effect of polarization field on the position of the band edges has been calculated by several groups [75, 82–

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures

85]. Polarization-induced fields in Ga-polarity samples, just as any negative gatevoltage-induced field in FETs, increase the conduction band edge in the AlGaN barrier with distance from the interface. In the presence of free, weakly bound, and surface charge, the internal polarization field is screened by a redistribution of these charges. The surface states may be in the form of donor-like states, which donate their electrons to the lowest unoccupied energy states at the AlGaN/ GaN interface. The holy grail of GaN/AlGaN heterostructures is the debate on the origin of the carriers, which end up at the interface. The observed dependence of the 2 DEG density on the thickness and composition of the AlGaN barrier has been linked to surface donor states, the binding energy of which is roughly equal to the Schottky barrier height in n-type GaN [79]. Though this may point to the same surface states being responsible for a possible and weak Fermi level pinning, it is not noticeable on the surface of GaN. In addition, pinning of the surface Fermi level in n-type GaN requires electrons to be transferred from bulk donors to surface acceptor states, whereas an excess of surface donors is required to form a 2 DEG in an AlGaN/GaN heterostructure. This inconsistency can be resolved, however, by assuming that the surface defects are amphoteric (i.e., they can act as either acceptors or donors depending on the circumstances) [86]. The polarization fields present in nitride heterostructures are strong enough to shift the Fermi energy at the surface of the AlGaN barrier below the charge transition level of the surface defects for Ga-face growth. This causes the surface defects on the barrier to transform from being acceptor-like to donor-like surface defects, which can provide the electrons for the 2 DEG at the AlGaN/GaN interface [86]. Hsu and Walukiewicz [70] elaborated on the surface donor-like defect that is likely to form at the growth temperature and its manifestation as a source of carriers confined at the underlying interface between the AlGaN top layer and GaN below it. The model calculations appeared to be somewhat insensitive to parameters such as donor formation energy and surface Fermi level. One sensitive parameter is the strength of the polarization field, which will be discussed below. Spontaneous polarization has only recently been fully understood. As pointed out earlier [87], nitrides lack inversion symmetry and exhibit piezoelectric effects when strained along the [0001] direction. Piezoelectric coefficients in nitrides are almost an order of magnitude larger than in many of the traditional group III–V semiconductors [88]. In addition, wurtzite GaN has a unique axis, thus allowing spontaneous polarization (P0), whose values are given in Table 12.2, to be present even in the absence of any strain. This can manifest itself as polarization charge at heterointerfaces. The magnitude of the polarization charge, converted to number of electrons, can be in mid-1013 cm–2 level for AlN/GaN heterointerfaces, which is huge by any standards. For comparison, the interface charge in the GaAs/AlGaAs system used for MODFETs is less than 10% of this figure. An excellent review of the polarization effects can be found in Ref. [89]. Let us compare the relative importance of spontaneous polarization to piezoelectric polarization. For a biaxially strained layer, the effective piezoelectric polarization is given by

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors Tab. 12.2 Piezoelectric constants and spontaneous polarization charge in nitride semiconductors

e33 a) (C m–2 b)) e31 a) (C m–2) P0 (C m–2) (e31–(C31/C33 c)) e33)

AlN

GaN

InN

1.46 –0.60 –0.081 –0.86

0.73 –0.49 –0.029 –0.68

0.97 –0.57 –0.032 –0.90

a) e31 and e33 are piezoelectric constants. b) C m–2 is coulombs per square meter. c) C31 and C33 are elastic constants.

Pz;piezo ˆ ‰e31

…C31 =C33 †e33 Še? ;

…1†

where e? ˆ exx ‡ eyy is the inplane strain and C31 and C33 are elastic constants. For AlxGa1–xN coherently strained on a relaxed GaN substrate, the strain e? is expected to be proportional to x and given by e? = 2 (aGaN–aAlGaN)/aAlGaN, which is 0.051 x and is tensile. The piezoelectric polarization is then Ppiezo = –0.044 x, i.e., pointing in the [0001] direction. The corresponding difference in spontaneous polarization between AlxGa1–xN and GaN is also expected to be proportional to x, the AlN mole fraction, and is given by DPspon = –0.052 x. Consequently, the two are in the same direction for this particular orientation, and are comparable in magnitude. The total polarization for AlN/GaN interface, which is defined in this case as the sum of the piezoelectric polarization and the differential polarization charge is –0.096 x. Note that these are all in C m–2 and that 1 C m–2 = 0.624 ´ 1015 electrons cm–2. Thus, for x of the order of 0.1, we are dealing with total polarization charge of the order of mid-1012 cm–2. For a coherently strained InxGa1–xN layer on relaxed GaN, the difference in spontaneous polarization is much smaller, DPspon = – 0.003 x. Furthermore, the InxGa1–xN layer on GaN would be under compressive strain e? = –0.203 x, and Ppiezo = +0.183 x. Here the piezoelectric polarization dominates and is opposite in direction to the spontaneous polarization charge, but even larger in absolute magnitude. In the case of a coherently strained AlxIn1–xN layer on a relaxed GaN layer, the situation is unique in that for x = 0 we revert to the InN on GaN case, and for x = 1 we revert to the AlN on GaN case. Numerical figures can be generated for the total polarization charge following the expressions outlined above by using a linear extrapolation of the strain and differential spontaneous polarization. The total polarization at the interface is the sum of the piezoelectric and differential spontaneous polarization, Ptotal = DPspon + Ppiezo. Taking the normal modulation-doped structures, where the GaN buffer layer is assumed completely relaxed and the AlGaN barrier layer is assumed coherently strained, one arrives at the plot shown in Fig. 12.5 for the total polarization charge at the interface. Additionally, data for InGaN and AlInN on GaN are shown. For tensile-strained AlxGa1–xN or AlxIn1–xN (for large x values) on the GaN layer is under tensile strain and the piezoelectric and the spontaneous polari-

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures

zation are negative and point in the same direction, thus they add up. The spontaneous and piezoelectric polarizations oppose one another for compressively strained InxGa1–xN or AlxIn1–xN (for small x values) layers. To calculate the differential spontaneous and piezoelectric polarization associated with alloys, one can employ a linear interpolation for the spontaneous polarization, piezoelectric and elastic constants from the binary compounds [90]. As discussed above, the piezoelectric polarization in coherently strained AlxGa1–xN layers grown on GaN increases to –0.044 C m–2 for x = 1. For InGaN layers, the piezoelectric polarization increases up to +0.183 C m–2 for x = 1. The ternary Al0.82In0.18N can be grown lattice matched to GaN and the piezoelectric polarization vanishes. For lower Al concentrations, i.e., x < 0.82, the piezoelectric polarization increases due to increasing biaxial compressive strain. For higher Al concentrations, i.e., x > 0.82, the layer is under tensile strain and the piezoelectric polarization becomes negative (Fig. 12.5). Opposing strain and spontaneous polarization charge in AlxIn1–xN cancel one another for a mole fraction of about x = 0.7 with the underlying assumption that the AlxIn1–xN is coherently strained and the GaN layer on which it is grown is completely relaxed [91]. The discussion of more accurate effective mass calculations can be found in the MODFET modeling section.

Fig. 12.5 Piezoelectric, spontaneous, and total polarization charge of coherently strained AlGaN, InGaN, and AlInN alloys grown on completely unstrained Ga-polarity GaN buffer layers versus the alloy composition. The polarization values were determined by linear extrapolation of the physical properties from the binary compounds. The figure is similar to that reported by Ambacher et al. [91], but the parameters used are consistent with our previous publications.

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Some further words of caution about the above estimates are needed. If the AlGaN layers are not pseudomorphic but partially relaxed (by misfit dislocations, for example), then the piezoelectric effect would be reduced but the spontaneous polarization would still be present. If the interfaces are not atomically sharp but exhibit a certain degree of interdiffusion, the differences in spontaneous polarization would be reduced as well. Finally, if domains with inverted polarity exist, the overall polarization effects may be washed out. Also, note that in an inverted structure with nitrogen (N) polarity towards the surface, it may be possible to create a two-dimensional hole-gas (2DHG) at the AlGaN/GaN interface, provided that free holes are available. However, if an n-type GaN layer is placed on top, a 2 DEG may form on top of the AlGaN layer. Let us now consider a hypothetical case in which no free carriers exist. In this case, the polarization charge causes a linear band bending in AlxGa1–xN with no change in the band of the underlying GaN, as shown in Fig. 12.6. Let us also assume that there are surface states below this within the band gap as shown. As the AlGaN thickness is increased, the band bending would be such that the surface states would become ionized. The released electrons in the process would end up at the interface, which tends to screen the polarization charge. If the surface state concentration were not sufficiently high, the surface Fermi level comes very close to the valence band. This implies that holes should be present within the AlGaN layer near the surface. This positive charge needs to be balanced by a negative charge at the interface, the source of which could be surface states. In reality, the semiconductor system contains defects and free carriers that would make the picture somewhat more complicated. For one thing, the Fermi level may not be able to come as close to the valence band as that shown in the figure. The surface defect supposition has recently been forwarded with experimental backing [92]. With Ga polarity, the conduction band edge of AlxGa1–xN will slope up towards the surface of the AlxGa1–xN layer. The band diagram shown would hold in this hypothetical case only if the AlxGa1–xN layer thickness is such that the Fermi level at the surface is still a few kTs away from the valence band edge. If the AlxGa1–xN thickness were made larger, the Fermi level near the surface would be very close to the valence band, causing a positive hole-charge at the surface, as shown in Fig. 12.6. A negative image charge would then form at the heterointerface, tending to screen the polarization charge. This charge is different from the polarization charge in that it is mobile and can partake in current flow in addition to altering the band diagram. In short, the polarization charge is a fixed charge. However, it would induce mobile charges to screen it if they are present. The recent device literature is confusing as some authors imply that polarization charge alone is capable of doping a semiconductor. Misleading nomenclature with no physical basis such as “piezodoping” has already been coined. To make the point in another way, polarization charge causes band bending, and any free carriers, if present in the system, would tend to screen the polarization charge. The screening charge represents the mobile carriers whose source could be native defects, impurity dopants (intentional or unintentional), and surface states.

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures

Fig. 12.6 Schematic representation of very simple-minded band structure of an AlGaN/ GaN structure with varying AlGaN thickness, as one goes from a to c, which demonstrates

how the surface charge could participate in the screening of the polarization-induced charge or the field. Patterned after Ref. [79].

Returning to modulation-doped structures with AlxGa1–xN barriers, the sign of the polarization is such as to produce a potential energy for electrons sloping down from the Ga-face towards the N-face. Thus, for a structure in which the Ga-face is turned towards the surface, the potential will slope down from the AlxGa1–xN surface towards the AlGaN/GaN interface and helps to drive carriers towards the 2 DEG forming at this interface. For example, if there is an ohmic metal contact on the AlxGa1–xN surface, electrons will flow towards the 2 DEG below that layer. The most favorable situation for enhancing sheet carrier concentration would occur for an InGaN quantum well on top of relaxed n-GaN and below an AlGaN barrier, with the whole structure having cation polarity towards the surface. In that case, the field will slope down towards the InGaN/AlGaN interface in the quantum well and will help localize the carriers in the 2 DEG. Note that the piezoelectric polarizations estimated here are based on the theoretical values for a perfectly insulating material. The free carriers that are present in each layer screen the field. For example, if free carriers are provided from metal contacts and they flow towards the 2 DEG, this process sets up a screening field, which counters the polarization-induced field. Under equilibrium conditions, if they are reached, the net field is determined by the condition that the chemical potential for electrons (the Fermi level) must be constant throughout the structure. This depends on the doping and band bending in the substrate and, possibly, in each of the layers. At the very least, one may expect these fields to be reduced by a factor corresponding to the macroscopic dielectric constant, i.e., a factor of order 10 but possibly larger if the conductivity of the layers increase by the free carriers in the system. Consequently, a more realistic expectation for the effect on sheet carrier concentration is on the order of 1011–1012 electrons cm–2. The difference between these and traditional device structures without polarization effects is that for uniform dopant concentrations, one obtains parabolically varying potentials with distance, whereas here the linear terms come from polarization on top of the parabolic terms. These linear terms lead to variations of the

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Fig. 12.7 Artistic view of twisted and tilted columnar growth in GaN along with Gaand N-polarity regions.

potential over a shorter distance scale determined by the thickness of the layers, whereas the parabolic terms correspond to the space-charge regions. Thus the linear terms may help to localize carriers if the polarity of the structure is chosen properly. The immediate impact of this polarization is that the field generated by this process must be considered together with that induced by the applied voltage and charge redistribution. Moreover, as alluded to earlier, free carriers can also be drawn from any shallow and weakly bound impurities and metal in contact with the semiconductor. In any case, the free carriers would tend to screen the piezoelectric-induced polarization field. An additional complicating factor in nitrides in relation to polarization is that the semiconductor tends to twist and tilt in a columnar mode, in an effort to minimize strain as shown in Fig. 12.7. Multiple polarity has been confirmed in epitaxial GaN layers on sapphire substrates by convergent beam electron diffraction [93–95]. These columns do not necessarily have the same cation/anion ordering polarity as shown in Fig. 12.7. In addition, stacking faults would also lead to mixed polarity samples. In the presence of strain, Ga-polarity domains and N-polarity domains would have opposite polarization, causing increased scattering. Figure 12.8 is a schematic representation of an ideal inversion domain boundary formed in growth along the [0001] direction. On the left of the boundary, the growth initiates with N, and on the right it begins with Ga. On the left side, the bond along the [0001] direction is from Ga to N; this is called Ga polarity. On the right side, the [0001] bonds are from N to Ga; this is called N polarity. In N polarity and under tensile strain, the PE field generated points toward the surface, whereas that for the Ga-polarity region points in from the surface. When the strain is compressive, the direction of the field changes. Yet an additional complicating factor is the asymmetry in the apparent (measured) barrier discontinuities between GaN and its binary and ternaries caused by polarization [96–98] which we have not really discussed here.

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures Fig. 12.8 Domains in GaN, with N polarity (nitrogen surface layer) on the right and Ga polarity (with Ga on surface) on the left side under compressive residual strain. The arrows show the direction of the piezoelectric field in each of the domains. The dotted line indicates the schematic representation of an ideal inversion-domain boundary formed along the c-axis.

To reiterate, the spontaneous polarization arises simply because of the ionicity of the bonds and the low symmetry in wurtzite. In fact, Bernardini et al. [99] showed that the field that occurs in quantum wells is determined by the difference in spontaneous polarization between the two bulks and the PE contribution. The field (i.e., the slope of the potential) is quite independent of the offset (i.e., the dipole discontinuity that occurs at the interface between the two materials). In considering a normal MODFET (N-MODFET) structure where the larger band gap AlGaN donor layer is deposited on top of a GaN channel layer (see Fig. 12.9) both the spontaneous polarization and piezoelectric polarization must

Fig. 12.9 GaN-based normal modulation-doped structures with Ga polarity and GaN- and InGaN-active layers. If the sign of strain were to change, from tensile to compressive, then the direction of the piezoelectric polarization would change. In that case, the spontaneous and piezoelectric polarization charges would oppose one another, and the larger one would determine whether hole or electron accumulation is favored at the interface.

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be accounted for. For an NMODFET structure with Ga polarity, the potential will slope down from the surface of the AlGaN layer towards the AlGaN/GaN interface and will help to drive free electrons towards the interface forming a 2 DEG as shown in Fig. 12.9. For example, if there is an ohmic metal contact on the AlGaN surface, electrons will flow towards the 2 DEG below the AlGaN layer from contacts. Since the nitride semiconductors in question have large band gaps, thermal generation rates are minuscule and the role played by thermally generated carriers can be ignored. A case of importance in GaN-based semiconductors is the polarity of the epitaxial layer, i.e., whether the Ga or the N plane forms the surface. It is therefore essential that the N-face case also be considered. The case of an AlGaN (tensilestrained)/GaN (relaxed) heterostructure with nitrogen polarity for an n-type GaN and for a p-type GaN buffer layer is shown in Fig. 12.10, as in the cases depicted in Fig. 12.9 where the piezoelectric polarization and spontaneous polarization charges support one another. Unlike the Ga-polarity case, the polarization charge is such that the screening charge will be made of holes, if they are present in the film. If holes constitute the minority charge in the film, then the thermal process is the means by which they would be created. However, this process in a wide band gap semiconductor such as GaN is very slow and the equilibrium condition may not be attained. If the strain in AlGaN were compressive, the direction of the piezoelectric polarization vector would change causing the piezoelectric polarization to counter the spontaneous polarization. This would actually represent the

Fig. 12.10 AlGaN/GaN-based normal modulation-doped structures

with N polarity for two cases, one for n-type and the other for ptype buffer layer. If the sign of strain were to change, from tensile to compressive, then the direction of the piezoelectric polarization would change. In that case the spontaneous and piezoelectric polarizations would oppose one another, and the larger one would determine whether hole or electron accumulation is favored at the interface.

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures

case when the epitaxial films are relaxed at the growth temperature and upon cooling to room temperature, the film would be under compressive strain if on sapphire substrates. This is due to the expansion coefficient of sapphire being larger than that of GaN. In such a case, the larger of the two would dominate and determine whether hole or electron accumulation would be favored. If, on the other hand, the film is grown on a SiC substrate, the strain due to thermal expansion would be tensile. This would lead to the case where the piezoelectric polarization and spontaneous polarization would support one another. Inverted modulation-doped structures can also be used to interrogate the picture in effect and perhaps take advantage of the unique features presented. In such a case, the AlGaN layer precedes the GaN top layer where the charge accumulation would occur. The interface between the AlGaN layer and the bottom GaN layer, which is referred to as the buffer layer would be graded to avoid a normal interface. Figure 12.11 shows, schematically, an AlGaN/GaN-based inverted modulationdoped structures with Ga, and N-polarities. As can be seen, in the case of Ga po-

Fig. 12.11 AlGaN/GaN-based inverted modulation-doped structures

with Ga, and N polarity. As can be seen, in the case of Ga-polarity and tensile strain in AlGaN, both the piezoelectric and spontaneous polarization vectors support each other leading to hole accumulation at the interface if holes are present in the system. The other source, thermal generation rate is very small and the semiconductor structure cannot be expected to reach equilibrium by this means at room temperature in a reasonable period of time. On the other hand, with N polarity and tensile strain in AlGaN, the structure favors electron accumulation at the interface. If the sign of strain were to change, from tensile to compressive, then the direction of the piezoelectric polarization would change. In that case the spontaneous polarization and piezoelectric polarization would oppose one another, and the larger one would determine whether hole or electron accumulation is favored at the interface.

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larity and tensile strain in AlGaN, both the piezoelectric and spontaneous polarization vectors support each other leading to a hole accumulation at the interface if holes are present in the system. Since the thermal generation rate is very small, the semiconductor structure cannot be expected to reach equilibrium by this means at room temperature in a reasonable period of time. On the other hand, with N polarity and tensile strain in AlGaN, the structure favors electron accumulation at the interface. If the sign of strain were to change, from tensile to compressive, then the direction of the piezoelectric polarization would change. In that case the spontaneous and piezoelectric polarization charges would oppose one another, and the larger one would determine whether hole or electron accumulation is favored at the interface. Ambacher et al. [91] employing Hall effect and capacitance-voltage profiling measurements, measured the sheet carrier concentration and its profile in modulation-doped structures at room temperature, the results of which are shown in Fig. 12.12. As seen in the figure, the sheet carrier concentrations are consistently larger than those expected from piezoelectric polarization alone. Since the GaN buffer contribution was verified to be negligible, an additional source, namely spontaneous polarization, was invoked to explain the observations. The contribution from an unintentionally doped barrier layer also was found to be negligible as the measured 2 DEG concentration with increasing barrier thickness up to 650 Å (x = 0.25) did not appear to affect the results. The highest measured sheet carrier concentrations for 0.2 < x < 0.45 are in good agreement with the calculated values of total polarization charge taking spontaneous polarization and the measured strain relaxation of AlGaN into account. The maximum sheet carrier concentration for undoped AlGaN/GaN (and also for InGaN/GaN) heterostructures is limited to about 2 ´ 1013 cm–2 due to strain relaxation of the top alloy layer. The calculated and measured sheet carrier concentrations of undoped MODFET structures with alloy compositions x < 0.2 are not in good agreement. The measured sheet carrier concentrations are up to 5 ´ 1012 cm–2 smaller than the predicted ones. In addition, the large scattering of the measured sheet carrier concentrations for heterostructures with similar barrier thicknesses and alloy compositions is unexpected and much larger than the error in experiments. For a more accurate calculation of the polarization charge in Ga-polarity modulation-doped structure, see the section on MODFET modeling. The physics literature appears to be fairly clear in that the polarization charge is a bound charge and that any free carriers act only to screen it. However, the device reports on GaN FETs have gone so far as to suggest that the piezoelectric effect in and of itself is sufficient to provide the free carriers needed for devices. Polarization effects, particularly spontaneous polarization, have immense impact on measured band discontinuities. For example, the dependence of measured band discontinuities on the order in which the larger and the smaller band gap semiconductors are grown, is one that can be attributed to polarization effects [97, 98]. To reiterate, as a result of polarization, the static potential at the GaN/AlN interface is different from that at the AlN/GaN interface that gives rise to interface charge larger than the charge densities used in devices. A substantial level of ef-

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures Fig. 12.12 Comparison of calculated

and measured electron sheet carrier concentrations in Ga-face AlGaN/GaN heterostructures. The dashed lines are calculated results for pseudomorphic structures. The solid lines are indicative of the calculated results, which take the measured partial strain relaxation into account (for more details, see Refs. [90, 91]).

fort has been expended toward determining band discontinuities, but the field is in desperate need of more indepth investigations in improved structures. The observed asymmetry in AlN/GaN and GaN/AlN interfaces caused by spontaneous polarization is within the experimental errors of Martin et al. [96–98]. Inversion domains (see Fig. 12.7) combined with any strain in semiconductor nitrides lead to flipping PE fields (see Fig. 12.8) with adverse effects on our ability to characterize the films, let alone exploit this phenomenon for devices. Such a flipping field would also cause increased scattering of carrier as they traverse in the c-plane. Simply put, identical device structures with different polarity layers would have widely differing performance underscoring the importance that these issues will have to be investigated and reconciled. The polarity mixing causes the PE-induced electric field to flip from one domain to the next, causing a variation in the sheet carrier concentration along the channel of an FET-like device. The same polarity mixing would have deleterious effects in the base of an HBT as well and depending on the polarity the induced field would either aid or impede minority carrier transit. 12.2.3

Partial Strain Relaxation

We, heretofore, dealt only with a coherently strained AlGaN top layer and a relaxed GaN buffer layer in the case of normal modulation-doped structures and relaxed AlGaN and coherently strained GaN top layer in the case of inverted modulation-doped structures. This is, of course, an assumption whose validity has not been confirmed. In reality, a most likely scenario is that a partial relaxation would take place coupled with a residual thermal strain. Ambacher et al. [91] treated this

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issue of partial relaxation. As pointed out by Ambacher et al., calculations of the critical thickness of InGaN and AlGaN grown on GaN show that for a typical AlGaN barrier thickness of about 20 nm, strain relaxation should occur for alloy compositions above x = 0.2. At the outset, we should mention that the critical thickness, the thickness above which the film begins to relax, is difficult to determine because of the large density of dislocations in this material system. Nevertheless, proceeding as if it can be done does, indeed, give an estimate, which is very useful. In order to determine the alloy composition and relaxation of the barrier, the lattice constants a(x) and c(x) were measured by high-resolution X-ray diffraction (HRXRD) [90]. For barrier thicknesses of about 25 nm, macroscopic strain relaxation was observed for alloy compositions of xc = 0.20 and 0.38 for InGaN and AlGaN, respectively. In both cases the degree of relaxation increased nearly linearly with increasing alloy composition for x > xc. Naturally, for a barrier with a fixed alloy composition, the piezoelectric polarization and the sheet charge induced by that polarization decrease linearly with increasing level of relaxation, r. The polarization-induced charge at the interface for a Ga-face AlGaN/GaN heterostructure versus Al concentration is shown for different degrees of strain relaxation in Fig. 12.13. The maximum sheet charge caused by piezoelectric polarization of a strained 30-nm thick barrier was calculated using the measured degree of relaxation. As can be seen, for a barrier with x = 0.4, the total sheet charge induced by spontaneous and piezoelectric polarization decreases if AlGaN becomes partially or completely relaxed. Hsu and Walukiewicz [70] incorporated issues related to polarization into a normal modulation-doped structure, calculating the dependence of parameters such

Fig. 12.13 Piezoelectric polarization-

induced sheet charge at the interface of a Ga-face AlGaN/GaN heterostructure for different degrees of relaxation of the barrier layer (dashed lines). The solid line was calculated taking into account the measured degree of relaxation for AlGaN top layers with thicknesses of 25 ± 5 nm. The figures have been modified to be consistent with the piezoelectric and polarization-charge figures used in our previous publications.

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures

Fig. 12.14 a 2DEG densities as functions of

AlGaN barrier Al composition; b 2DEG densi-

ties as a function of thickness of a Al0.27Ga0.73N barrier. After Ref. [70].

as the sheet carrier concentration on structural parameters. While this issue will be treated in detail in the FET section, we will discuss the treatment by Hsu and Walukiewicz since it relates the sheet concentration to structural parameters and discusses the electron mobility. Figure 12.14 a shows the dependence of the 2 DEG density as a function of Al content of an AlxGa1–xN barrier with a thickness of 31 nm. Values of A = 7.9 ´ 104 V cm–1 and B = 1.15 ´ 107 V cm–1 in P(x) = A + Bx describing the dependence of polarization on AlN mole fraction led to good quantitative agreement with experiments. In principle, the parameter A is related to the uncompensated, spontaneous polarization field in GaN. Its relatively small value indicates either that this spontaneous polarization is very small, or that it is well compensated by charges from unintentional dopants within the AlGaN layer. Figure 12.14 b shows the dependence of the 2 DEG density on the thickness of an Al0.27Ga0.73N barrier. Figure 12.15 shows the calculated dependence of the 2 DEG density on the barrier thickness for several alloy compositions at 4 K, formed by surface donors in an unintentionally doped structure. For very thin barriers (< 30 Å for a barrier with x = 25% and < 160 Å for x = 5%), the defect level is below the Fermi energy and so the surface defects are neutral. In this case, only the electrons from any dopant in the barrier are transferred to the GaN well and if one assumes a donor concentration of 5 ´ 1016 cm–3, the density remains below 1011 cm–2. Once the barrier thickness increases to the point of bringing the defect level above the Fermi energy, electrons are transferred from these surface donors and the 2 DEG density increases rapidly. At very low alloy compositions (5%), the 2 DEG density rises continuously at an approximately constant rate throughout the entire range of barrier widths. The reason for this is that as the barrier width increases, the donor charge transition state energy also increases, due to the polarization field. This leads to an increase

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors Fig. 12.15 Calculated 2DEG densities in AlGaN/GaN heterostructures as a function of barrier width for three different Al compositions. After Ref. [70].

in the energy gain from transferring electrons from the donors to GaN. Consequently, the donor formation energy decreases and the surface defect concentration increases. For larger barrier alloy compositions, the 2 DEG density increases very rapidly at first, followed by a leveling for barrier thicknesses greater than 250 Å. The initial increase is due to the effect of the polarization field on the donor level in that larger Al fractions in the barrier result in larger polarization fields and a more rapid increase in defect concentration. As the 2 DEG density approaches 1013 cm–2, the opposing field due to the transfer of electrons becomes comparable in magnitude to the polarization field. This field acts to reduce the rate at which the defect formation energy is lowered. For a barrier of sufficient thickness, this charge-transfer field could completely cancel the polarization field and thereafter, the 2 DEG density would be independent of barrier thickness assuming that the AlGaN barrier remains coherently strained and is not relaxed. 12.2.4

Low-field Transport in 2 DEG Systems

Calculations of the electron mobility at the AlGaN/GaN interface have been performed [70] using methods that have been described previously [78]. The scattering mechanisms considered were acoustic phonons, Coulomb scattering from both the donor-like defects on the AlGaN barrier surface and unintentional dopants in the GaN, and alloy-disorder scattering. In addition, interface-roughness scattering was also included. Figure 12.16 shows calculated 2 DEG mobilities at low temperature as a function of barrier width for several heterostructures with different Al compositions. Calculations show three distinct regions [70]. For very small barrier widths, the mobility is quite low and increases slowly with increasing barrier width. Comparing these curves with those in Fig. 12.15, one can see that the 2 DEG density is

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures Fig. 12.16 Low-temperature 2 DEG

mobilities as a function of barrier thickness for four different AlGaN/ GaN heterostructures with different Al barrier compositions. After Ref. [70].

very small in this region, and is due to unintentional dopants in the bulk of the AlGaN barrier. Consequently, Coulomb scattering by charged impurities in the GaN well and the AlGaN barrier keeps the mobility low. In the region with a sudden increase of the mobility, the vast majority of the 2 DEG electrons originate from donors at the surface of the AlGaN barrier. In this region, the high electron density reduces the efficacy of Coulomb scattering, which results in much higher mobilities. Moreover, most of the Coulomb scattering centers are at the surface of the AlGaN barrier, away from the carriers at the AlGaN/GaN interface. Finally, when the 2 DEG density becomes high enough the alloy disorder scattering, which varies with the square of the electron concentration, is the dominant scattering mechanism and the mobility decreases with increasing 2 DEG density. Maximum mobilities are generally achieved for barrier thicknesses between 50 Å (x = 0.25) and 200 Å (x = 0.05). Figure 12.16 indicates that maximum mobilities are obtained for 2 DEG densities in the range of about 3.5 ´ 1012 cm–2 (x = 0.25) to 5 ´ 1011 cm–2 (x = 0.05). Figure 12.17 shows the overall and individual mobilities as a function of barrier thickness for a 2 DEG at the interface of a Al0.07Ga0.93N/GaN heterostructure. This is the Al alloy fraction that would produce the highest possible low-temperature mobilities for the indicated unintentional doping levels [70]. The component mobility curves illustrate the dominant scattering mechanisms in each of the three different regions mentioned above. At a barrier thickness of 110 Å, the surface-defect ionization energy is pushed above the Fermi energy and there is a rapid increase in both the mobility and the 2 DEG concentration. For barriers that are thicker than 150 Å, alloy disorder becomes the dominant scattering mechanism. A maximum electron mobility of somewhat above 105 cm2 V–1 s–1 is predicted for a barrier width of about 150 Å and a corresponding 2 DEG density of 1.8 ´ 1012 cm–2. These calculations indicate that for a standard, undoped AlGaN/GaN heterostructure, the maximum low-temperature mobility is only slightly larger than 105 cm2 V–1 s–1. The principal reasons for the lower values here as compared to those obtained in GaAs/AlGaAs

571

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors Fig. 12.17 2 DEG mobility as a func-

tion of AlGaN barrier thickness for a Al0.07Ga0.93N/GaN heterostructure. After Ref. [70].

heterostructures are stronger alloy-disorder scattering (resulting from the much higher 2 DEG density and larger conduction band offsets found in AlGaN/GaN heterostructures) and, to a smaller extent, relatively high levels of residual impurities in the nitride layers. The calculated mobilities agree with the experimental values well for barrier Al compositions less than about 15%, as shown in Fig. 12.18 [70]. However, for higher Al fractions, the measured mobilities are a nearly constant factor of 2 to 2.5 lower. There are two possible reasons. First, as can be seen in Fig. 12.14 a, the electron density exceeds 6 ´ 1012 cm–2 for x > 0.14. This corresponds roughly to the electron density at which the higher sub-bands in the GaN quantum well begins to be occupied, which causes increased scattering. Secondly, the lattice mismatch at the interface increases with increasing x, leading possibly to increased roughness and thereby reduced electron mobility at the interface. In the end, technological issues may come to be the culprit, as was the case in the early development of the GaAs/AlGaAs heterointerface. The effect of interface-roughness scattering on the total mobility has been estimated using 15 Å as the parameter for the characteristic lateral extent of the islands of roughness and adjusting the height of the islands in order to obtain the best fit with experimental data [70]. A constant island height of 0.9 Å produced the fit shown in Fig. 12.18 a (for a constant barrier thickness and variable barrier composition), and Fig. 12.18 b (for a constant barrier composition and variable barrier thickness) [70]. The points represent experimental data and correspond to the samples in Fig. 12.14 a. The solid line is the calculated mobility neglecting interface-roughness scattering. The dashed line is the calculated mobility including interface-roughness scattering. One possible interpretation of the data is a sudden degradation of a near perfect interface for heterostructures with a barrier of greater than 15% Al. The above arguments indicate that the highest electron mobilities are expected from heterostructures with 2 DEG densities in the range of a few times 1012 cm–2.

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures

Fig. 12.18 a 2 DEG mobilities as a function of

Al composition of the barrier. The points represent experimental data and correspond to the samples in Fig. 12.14 a. The solid line is the calculated mobility neglecting interfaceroughness scattering. The dashed line is the calculated mobility including interface-roughness scattering; b 2 DEG mobilities as a func-

tion of thickness of a Al0.27Ga0.73N barrier along with the experimental data points correspond to the samples in Fig. 12.14 b. The solid line is the calculated mobility neglecting interface-roughness scattering. The dashed line is the calculated mobility including interface-roughness scattering. After Ref. [70].

Since the polarization-induced charge transfer increases with increasing width and Al composition of the barrier, the highest mobilities are limited to heterostructures with relatively thin barriers with low Al content for undoped structures. A maximum electron mobility of about 105 cm2 V–1 s–1 at 4 K can be expected from heterostructures with a 15-nm thick Al0.07Ga0.93N barrier [70]. Figure 12.19 compares the temperature-dependent mobility, both calculated and measured for an Al0.09Ga0.91N/GaN heterostructure [70]. The points represent the experimental data. The calculations were performed for a constant 2 DEG density of 2.3 ´ 1012 cm–2. The low-temperature mobility is dominated by alloy disorder scattering with only small contributions from ionized centers and acoustic phonon scattering. Above 10 K, however, scattering by acoustic phonons becomes important and it is responsible for a weak but still clearly discernible temperature dependence of the mobility. The acoustic-phonon component of the mobility varies roughly as 4.02 ´ 106(1/T) cm2 V–1 s–1 and is about an order of magnitude larger in AlGaN/GaN heterostructures than in AlGaAs/GaAs systems. The calculations reviewed above indicate that scattering by ionized impurities is important only for heterostructures in which the 2 DEG density is 1012 cm–2 or smaller. Consequently, if one wishes to increase the electron mobility one should reduce the effect of alloy disorder and interface-roughness scattering along with improved AlGaN technology. The penetration depth of the 2 DEG into an Al0.09Ga0.91N barrier of height DEc = 0.2 eV is zp = 0.9 nm leading to the assertion that the alloy scattering is the dominant mechanism [70]. One could envision a

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors Fig. 12.19 2DEG mobilities as a function of temperature in an Al0.09Ga0.91N/GaN heterostructure with a 16-nm thick barrier. After Ref. [70].

composite barrier design consisting of a very thin layer of AlN, grown at the interface, followed by a thicker Al0.07Ga0.93N layer. Because the penetration depth of electrons into AlN is only 3 Å and the electron wave function decays exponentially, a layer of AlN of only a few angstroms thickness would sufficiently confine the electrons in the binary compounds and nearly eliminate alloy scattering. The thin AlN film at the interface should not significantly affect the charge transfer, which is determined mostly by the composition and thickness of the much thicker remaining part of the barrier. Thus, for a barrier composed of 5 Å of AlN followed by 120 Å of Al0.07Ga0.93N, one could expect to obtain a 2 DEG with a density between 2 and 3 ´ 1012 cm–2, but with negligible alloy disorder scattering. 12.2.5

High-Field Transport

FETs by their nature rely on transport under high electric fields. As such, highfield effects are an integral part of any short channel FET, realizing that low field effects too are important in that they determine many of the parasitic resistances with detrimental effects on device performance. Consequently, the high-field properties of any semiconductor contemplated for use in FETs must be scrutinized in terms of its high field transport and semiconductor nitrides are no exception. High-field transport in nitride semiconductors has recently been reviewed [100]. However, a short treatment of results is deemed necessary for inclusion in this chapter for completeness. While the bulk of the experimental studies and, to some extent, calculations have focused on GaN, the transport properties from the point of electron mobility and velocity of InN are much more conducive for FETs. Holding InN back is, among other factors, its poor quality and high unintentional electron concentration. As has been the case for the GaAs system, it is very likely that some composition, or a range of compositions, of InGaN will be used for

12.2 Electron Transport Properties in GaN and GaN/AlGaN Heterostructures Fig. 12.20 Calculated electron drift

velocity versus applied electric field for GaN, Al0.2Ga0.8N, Al0.5Ga0.5N, Al0.8Ga0.2N, and AlN. For this calculation, the random alloy potential was set equal to conduction band offsets. Lattice temperature is 300 K, and electron concentration is equal to 1017 cm–3. After Ref. [100].

FET channels while taking full advantage of GaN and AlGaN in the rest of the structure. Consequently, transport properties, inclusive of low and high field, of nitride semiconductors InN, GaN, AlN, and their alloys will be briefly reported following Ref. [100]. The steady-state electron drift velocity versus electric field has been calculated for the nitride binaries and ternaries at different temperatures and various doping concentrations [100]. The results for 300 K and an electron concentration of 1017 cm–3 will be shown here. Figure 12.20 shows the calculated electron steadystate drift velocity versus applied electric field, for GaN, Al0.2Ga0.8N, Al0.5Ga0.5N, Al0.8Ga0.2N, and AlN. This set of calculations is made assuming the maximum alloy scattering rate. The alloy scattering was observed to be the dominant scattering mechanism when the random alloy potential was set equal to the conduction band offset between GaN and AlN. A significantly lower drift velocity is observed when alloy scattering is present, which is simply a result of the higher total scattering rate. Moreover, in the presence of alloy scattering the peak velocity occurs at a higher applied field compared to the case when alloy scattering is neglected.

Fig. 12.21 Calculated electron drift

velocity versus applied electric field for GaN, In0.2Ga0.8N, In0.5Ga0.5N, In0.8Ga0.2N, and InN. For this calculation, the random alloy potential was set equal to conduction band offsets. Lattice temperature is 300 K, and electron concentration is equal to 1017 cm–3. After Ref. [100].

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors

This is also due to the fact that in the presence of alloy scattering, the total scattering rate is higher; thus a higher field is required to heat the carriers prior to the onset of intervalley transfer. Figure 12.21 shows the calculated electron drift velocity versus applied electric field for GaN, In0.2Ga0.8N, In0.5Ga0.5N, In0.8Ga0.2N, and InN. The random alloy potential is set equal to the conduction band offsets. It should be mentioned that for InxGa1–xN compounds the random alloy scattering potential calculated from Phillips’ theory of electronegativity differs in values on the same order as the conduction band offsets.

12.3

Modulation-Doped Field Effect Transistors (MODFETs)

With its reduced impurity scattering and unique gate capacitance-voltage characteristics, the MODFET has become the dominant high-frequency device. Among the MODFET’s most attractive attributes are close proximity of the mobile charge to the gate electrode and high drain efficiency. As in the case of emitters, the GaN-based MODFETs have quickly demonstrated record power levels at high frequencies with very respectable noise performance and large drain breakdown voltages. In MODFETs, the carriers that form the channel in the smaller band gap material are donated by the larger band gap material, and ohmic contacts or both. Since the mobile carriers and their parent donors are spatially separated, shortrange ion scattering is nearly eliminated, which leads to mobilities that are characteristic of nearly pure semiconductors. A Schottky barrier is then used to modulate the mobile charge that in turn causes a change in the drain current. Because of this heterolayer construction, the gate can be placed very close to the conducting channel, resulting in large transconductances [101]. Figure 12.22 presents a

Fig. 12.22 a Schematic representation of an

AlGaN/GaN modulation-doped field effect transistor (MODFET); b schematic band structure of an AlGaN/GaN modulation-

doped heterostructure in which the free carriers are provided to the GaN layer by the dopant impurities placed in the larger band gap AlGaN barrier layer.

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

schematic representation of a GaN/AlGaN MODFET heterostructure in which the carriers are provided by the donors in the wider band gap AlGaN. In a MODFET device under bias, the carriers can also be provided by the source contact. 12.3.1

MODFET Model

The Schrödinger equation and Poisson equation can be used self-consistently in order to study the channel formation and current flow mechanisms in GaN-based MODFET [101, 102]. Several approaches have been used to define the system Hamiltonian used in the Schrödinger equation, namely effective masses [103], k. p expansion [104] and tight-binding expansion [105, 106]. The use of sophisticated models, such as k. p or tight-binding, is justified, perhaps even made necessary, by the complex wurtzite band structure, particularly for determining the valence band states. Thus, calculations of optical processes involving band-to-band transitions must consider the details of the band structure beyond the simple effective mass approximation (EMA) [107, 108]. However, even when only the conduction band processes are of interest, EMA is still a very accurate means of determining the properties of interest. In fact, nitride-based semiconductors in the wurtzite structure possesses a conduction band with a minimum, which can be described reasonably well within such an approximation. Within the effective mass theory Schrödinger equation takes the form [101, 103, 109]   h2 d 1 d u ‡ eV…z†u ˆ Eu ; 2 dz m…z† dz

…2†

where m (z) is the (position-dependent) effective mass, V the electrostatic potential, u the electron wave function and E the energy level. Nonparabolicity may induce deviations from the simple parabolic band model, however this will not substantially change the results that we will present. In the nitride semiconductors with wurtzite structure, spontaneous and piezoelectric polarization effects are present [110], which necessitates that the Poisson equation be solved for the displacement field, D (z) d d D…z† ˆ dz dz

 e…z†

d V…z† ‡ P…z† dz

 ˆ e p…z†

n…z† ‡ ND‡


NA ;

…3†

where e is the dielectric constant, P the total polarization, n (p) the electron (holes) charge concentration and N+D (N–A) the ionized donor (acceptor) density. In the self-consistent procedure, potential V is obtained using Eq. (3) from an initial guess of the mobile charge concentration, and then inserted into the Schrödinger’s equation, Eq. (2) which is solved to get the energy levels and wave functions of the systems. The new electron charge density is obtained by applying Fermi statistics as follows:

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors

n2D …z† ˆ

h EF Ei i m…z†kB T X jui …z†j2 ln 1 ‡ e kB T ; 2 pg i

…4†

where EF is the Fermi level, Ei the energy of the i-th quantized level, T the temperature and kB the Boltzmann constant. The calculated density is then inserted into the Poisson equation (Eq. (3)) and the iteration repeated until convergence is achieved. Convergence of the self-consistent algorithm can be improved by adopting a special relaxation mechanism. Here we have used a first-order expansion of the model reported in Ref. [111]. In the following, we consider two MODFET structures, namely a single heterojunction AlGaN/GaN normal modulation-doped FET (NMODFET) where the AlGaN donor layer is grown on top of the GaN channel layer, and an “inverted” GaN/AlGaN/GaN MODFET (IMODFET) where the channel layer is grown on top of the AlGaN donor layer. The NMODFET structure consists (from the gate to the substrate) in a 150-Å n-doped (n = 1018 cm–3) AlGaN, 50-Å unintentionally doped AlGaN layer and a thick GaN buffer. The IMODFET consists (from the gate to the substrate) in a 300-Å unintentionally doped GaN layer, 50-Å unintentionally doped AlGaN, 150 Å n-doped (n = 1018 cm–3) AlGaN, 300-Å unintentionally doped AlGaN layer, and a thick GaN layer. We consider a residual doping of 1017 cm–3 in both GaN and AlGaN layers. We use a Schottky barrier (uB) of 1.1 eV for the metal/GaN interface and a uB = 1.2 eV for the metal/AlGaN interface. Calculations have been performed for AlxGa1–xN with Al content of x = 0.1, 0.2, 0.3, 0.4. Both [0001] and [0001] growth directions are considered. In the simulations, we have used an effective mass of 0.19 for electrons and 1.8 for holes in both GaN and AlGaN layers. The band gaps and band discontinuities of the AlGaN layers used are given in Table 12.3. As discussed previously, the presence of polarization is quite important in the nitride-based N-MODFET. The conduction band edge profile for the NMODFET grown in the [0001] direction is depicted in Fig. 12.23 for the cases (1) with both spontaneous and piezoelectric polarization fields, (2) without considering the polarization fields, (3) with only the piezoelectric polarization fields. The difference in piezoelectric and spontaneous polarization between AlGaN and GaN layer manifest itself as a fixed 2D-charge density at the interface between the two materials. For the [0001] growth direction considered in figure the difference in polarization

Tab. 12.3 Band gap and conduction band discontinuities with respect to GaN of the AlxGa1–xN

layer x (Al)

EG (eV)

DEC (eV)

0.1 0.2 0.3 0.4

3.62 3.85 4.09 4.35

0.17 0.33 0.51 0.69

12.3 Modulation-Doped Field Effect Transistors (MODFETs) Fig. 12.23 Calculated conduction

band edge for the NMODFET structure grown in the [0001] direction for VG = 0 with and without polarization fields.

between the two materials induces a positive charge (r = +1.12 ´ 1013 cm–2) at the Al0.2Ga0.8N/GaN interface. Electrons are attracted by this positive charge, tending to accumulate at the interface and thus forming a conductive channel. Moreover, the high electric field due to the interface charge, favors the buildup of a large channel density and of a strong channel confinement. Within the AlGaN layer, the strong electric field compensates the space charge contribution coming from the ionized donors. Consequently, it prevents the appearance of the parasitic channel that would otherwise form in the doped AlGaN layer [104, 112]. The comparison reported in Fig. 12.23 between the three cases with different contribution of the polarization fields shows the importance of considering both spontaneous and piezoelectric polarizations in GaN-based device modeling. In fact, when neglecting the spontaneous polarization, as was done recently [113–116], the channel electron density is underestimated [104]. Clearly the sign of the polarization charge is crucial. For the same NMODFET structure grown in the [0001] direction, the resulting polarization charge would be negative (with the same magnitude) and electrons would be repelled from the channel as shown in Fig. 12.24. The distribution of the free electron charge in the channel is shown in Fig. 12.25 for several values of the Al concentration of the AlGaN layer. Increasing the Al content induces a larger polarization charge at the GaN/AlGaN interface and consequently a higher channel electron concentration.

Fig. 12.24 Calculated conduction band

edge for the NMODFET structure grown in the [0001] direction for VG = 0.

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors Fig. 12.25 Electron density distribution

in the channel of the [0001]-grown NMODFET for VG = 0 for several Al contents of the AlxGa1–xN layer.

The calculations we have shown so far are obtained by considering only the polarization charge at the AlGaN/GaN interface. In reality, however, polarization charges that form at the metal/AlGaN interface and at the end of the GaN buffer region should be accounted for. The metal/AlGaN charge is completely screened by the charges induced on the metal surface and can therefore be neglected. On the other hand, the charges at the end of the buffer region may induce a large deviation with respect to the situation depicted above. Oberhuber et al. [104] have considered a –r/2 charge at the interface between the GaN buffer layer and the nucleation layer. The exact amount of such charge depends, however, on the morphology of the heterojunction and may differ from the theoretical value r = DP/e. The situation is less critical if the bottom interface is far from the main AlGaN/ GaN heterojunction. In this case, the polarization charge that arises can be completely screened by the residual doping of the GaN substrate. On the contrary, if such an interface is close to the AlGaN/GaN heterojunction, the polarization charge can completely deplete the channel. In our simulations we have considered a thick GaN substrate. Thus, the effect of the polarization charge at the end of the GaN substrate is completely screened. The band edge profile and electron densities for the IMODFET grown in the [0001] direction are shown in Figs. 12.26 and 12.27, respectively. A comparison of the conduction band edges with and without polarization charges is also plotted. As for the N-MODFET, the presence of the fixed and positive polarization charge at the GaN/AlGaN interface induces the formation of a channel not present in the absence of the polarization charge. For the IMODFET a –r polarization charge is also present at the end of AlGaN region (i.e., at the AlGaN/GaN interface). Similar to the [0001]-grown N-MODFET, a larger Al content of the AlGaN layer induces a larger polarization charge at the GaN/AlGaN interface and consequently an increase of electron concentration in the channel. Naturally, for the [0001] orientation the interface charge forms below the AlGaN layer which is not what is desired for an I-MODFET. What is desired is the formation of the electron sheet layer on top of the AlGaN layer, which is possible when the [0001] orientation is employed. The structure in its present shape, i.e., the [0001] polarity, would show FET performance provided that the AlGaN layer is completely depleted but with small transconductance. If the AlGaN is not depleted, then the device would func-

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

tion as a MESFET dominated by transport in the AlGaN layer unless the gate potential is large enough to deplete the AlGaN layer. To eliminate the formation of an interface electron charge at the bottom of the AlGaN layer, the bottom heterointerface should be graded substantially. In that case, the [0001] polarity would cause the band diagram to accumulate holes at the top interface if they are present. That top interface would accumulate electrons in the [0001] polarity. The channel charge density is therefore controlled by two factors: (1) the gate bias as in traditional NMODFET device, (2) the Al content of the AlGaN layer, which tailors the polarization field. Charge control in nitride-based devices can be achieved by adjusting two independent parameters and thus offers a wide degree of flexibility with respect to traditional devices. This can be seen from the sheet charge concentration in the channel as obtained by integrating the electron density distribution along the z-direction. Considering the explicit dependence of the sheet charge density on the gate voltage VG, we have: Z ns …VG † ˆ

n…VG ; z†dz :

Fig. 12.26 Conduction band edge

for the IMODFET structure grown in the [0001] direction for VG = 0 with and without polarization fields.

Fig. 12.27 Electron density distri-

bution in the channel of the [0001]-grown IMODFET for VG = 0 for several Al contents of the AlxxN layer.

…5†

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors Fig. 12.28 Channel electron density

as a function VG (for several AlN mole fractions) for the NMODFET grown along the [0001] direction.

Fig. 12.29 Channel electron density

as a function VG (for several AlN mole fractions) for the IMODFET grown along the [0001] direction.

Figures 12.28 and 12.29 show the sheet electron density in the channel as a function of gate bias for several Al contents in the AlGaN layer for both [0001]-grown NMODFET and [0001]-grown I-MODFET, respectively. Naturally, the channel electron density increases for larger Al contents of the AlGaN layer. We note also that the density is higher for the NMODFET with respect to the IMODFET because of the particulars relating to the band bending on the top interface of the I-MODFET. As mentioned earlier, the IMODFET structure is intended to be used with [0001] orientation for investigative purposes only as the body of work in the AlGaAs/GaAs system showed the NMODFET to be the desired device structure. Finally, the equilibrium static charge in undoped MODFET structures and current-voltage characteristics of the same have been calculated, in a similar fashion to that reported above. The simulated structure is a normal MODFET with Ga-polarity layers wherein the AlGaN barrier is situated on top of the GaN channel layer [102]. Figure 12.30 a and b display the conduction band edge and electron density profile, respectively, for a normal MODFET with the AlxGa1–xN barrier thickness of 20 nm and Al content x = 0.1, 0.2, 0.3, and no doping neither AlxGa1–xN nor GaN. Compared to the intentionally or unintentionally doped cases (shown in Figs. 12.23 and 12.25), the conduction band well at the heterointerface becomes a little shallower and the electron density reduces slightly. Figure 12.31 a and b display the conduction band profile and electron density distribution, respectively, for a

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

Fig. 12.30 a Conduction band edge; b elec-

tron density profile for the NMODFET with a AlxGa1–xN barrier thickness of 20 nm and Al

Fig. 12.31 a Conduction band edge; b elec-

tron density profile for a NMODFET with a AlxGa1–xN barrier thickness of 30 nm and Al

content x = 0.1, 0.2, 0.3, and no doping neither AlxGa1–xN nor GaN, VG = 0.

content x = 0.1, 0.2, 0.3, and no doping neither AlxGa1–xN nor GaN, VG = 0.

NMODFET with AlxGa1–xN barrier thickness of 30 nm and the same set of Al mole fractions as above, and no doping neither AlxGa1–xN nor GaN. A thicker AlxGa1–xN layer induces a larger electron density at the heterointerface because of larger band bending in AlGaN and its implications to the charges in the bulk and on the surface of the same, as depicted in Fig. 12.14 b.

12.3.1.1 Drain Current Model in MODFETs

We have implemented a quasi-2D [117–119] model for the calculation of the current-voltage characteristics of the nitride MODFETs. This model makes use of the exact value of the sheet charge density in a MODFET device channel, obtained from the self-consistent Schrödinger-Poisson solution presented above. We assume a FET model shown in Fig. 12.32 where the x-axis is along the channel and the z-axis is along the growth direction. The model also considers the presence of a drain (RD) and source (RS) resistance. When a drain bias (VD) is ap-

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors Fig. 12.32 Schematic representation of

the quasi-2 D FET model used.

plied, the potential along the channel may be considered as varying gradually from the source bias (VS) to VD. In this situation, it is still possible to calculate the sheet charge density ns at every section grid, provided that one considers the V(x) potential (on the top surface) for each point of the channel. Since for n-channel devices, VD is positive and VS is zero, V(x) contributes to the channel depletion and the sheet charge density ns for the generic x section of the FET will therefore be ns …x† ˆ ns …VG

V…x†† :

…6†

By neglecting diffusion contributions, the source-to-drain current IDS is given by: IDS ˆ

qWv…x†ns …x† ;

…7†

where W is the gate width and v(x) the electron mean velocity, supposed independent of the transverse coordinate. The dependence of the drift velocity on the longitudinal electric field is empirically given by v…x† ˆ

l0 F…x† F…x† 1‡ ; FC

…8†

where F(x) is the electric field ( = –dV(x)/dx), l0 is the low-field mobility and Fc = vsat/l0 is the electric field at saturation. Parasitic components are included explicitly through the drain and source resistances (RD, RS) VSe ˆ VS ‡ IDS RS VDe ˆ VD

IDS RD ;

…9†

where VDe and VSe represent the effective bias boundaries of the gate region on the drain and source sides, respectively. For a certain value of IDS, we can calculate VD by solving Eq. (7). The explicit equation for the current is

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

IDS ˆ qW

l0 F…x† n…VG F…x† 1‡ FC

V…x†† :

…10†

The numerical solution is based on the discretization of this expression into N sections, each with amplitude h, so that Nh = L, where L is the gate length. Given the (i–1)-th section potential, the i-th potential Vi = Vi–1 + Fi h where Fi is the i-th section electric field. We have, then, the N relations: IDS ˆ qW

l0 F i n…VG Fi 1‡ FC

Vi

1

Fi h† :

…11†

Since the (i–1)-th section potential is known from the previous step, this is a nonlinear equation in the unknown Fi. Solving iteratively for all the N sections, one obtains the value of the drain voltage VD consistent with the assumed current. Repeating this procedure for a suitable range of values of IDS, one obtains the set of corresponding values of VDS and thus the MODFET I-V characteristics, which are elaborated on below.

12.3.1.2 I-V Characteristics

In this section we discuss the simulated I-V characteristic of the normal and inverted MODFET, obtained for a gate length of L = 0.3 lm. We have chosen a drain and source contact resistivity of about 1 X mm which is consistent with experimentally measured values on these types of devices [120]. We use a saturation velocity of 2.5 ´ 107 cm s–1 [22], while for the low-field mobility we choose a value of l0 = 1100 cm2 V–1 s–1, slightly higher than the GaN bulk value, according to the experimental and theoretical results for similar devices [22, 104, 121, 122]. In Fig. 12.33, we show the IDS versus VDS for the [0001] polarity MODFET for several gate (VGS) voltages. The results are presented for both x = 0.2 (Fig. 12.33 a) and x = 0.4 (Fig. 12.32 b), Al concentration of the top layer. For x = 0.2, the MODFET reaches pinch-off for a bias voltage of VGS = –4.4 V while for x = 0.4 the pinchoff is reached at VGS = –9.5 V. On the other hand, the saturation drain current for x = 0.2 is IDS = 2.4 A/mm at VGS = 0 and it increases up to 5.76 A mm–1 for an Al content of x = 0.4. Thus, the current flowing in the devices depends strongly on the Al content of the top layer. This is essentially due to the increasing of the channel electron density induced by the increase of the polarization charge going from an Al content of 0.2 up to 0.4. This peculiarity of the MODFET should be considered in the design of these devices since fluctuation of the alloy composition of the top layer may induce large variation with respect to nominal electrical values of the device. It should also be pointed out that the gate leakage would determine the extent of gate voltage that can be applied to the gate. For a gate bias of 9.5 V and AlGaN layer thickness of 20 nm, the vertical field under the gate near the source can reach 4.75 MV cm–1. This means that MODFETs utilizing

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Fig. 12.33 a IDS versus VDS for the [0001] po-

larity normal MODFET for several gate (VGS) voltages and for x = 0.2; b IDS versus VDS for

Fig. 12.34 a IDS versus VDS for the [0001] polarity IMODFET for several gate (VGS) voltages and for x = 0.2; b IDS versus VDS for the

the [0001] polarity normal MODFET for several gate (VGS) voltages and for x = 0.4.

[0001] polarity IMODFET for several gate (VGS) voltages and for x = 0.4.

large mole fractions of Al may require thin AlGaN layers or recessed gates to keep the gate voltage smaller. A similar situation is obtained for the IMODFET with the GaN/AlGaN/GaN structure grown in the [0001] direction, meaning with N polarity. The calculated IDS versus VDS characteristics are reported in Fig. 12.34 a and b for x = 0.2 and x = 0.4 Al composition of the AlGaN layer, respectively. Also, in this case, the pinch-off bias depends critically on the Al composition and varies from –3.9 V for x = 0.2 up to –9 V for x = 0.4. Saturation currents are lower for the IMODFET at x = 0.2 with respect to the equivalent NMODFET structure. Such a difference, however, is negligible for the case with x = 0.4. 12.3.2

Experimental Considerations

GaN-based FETs are intended primarily for power application at high frequencies. Consequently, traditional small-signal considerations have to be augmented by large-signal specific issues. The main parameter facing a power device is the max-

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

imum power level that can be obtained and the associated gain. In many applications the noise figure of the device must also be considered. In simple terms, if the device has large drain breakdown voltage, high gain at high frequencies, and high drain efficiency, the stage is set for a desirable device. Even in a well-designed device in a semiconductor with all the accolades, the thermal wall is a very formidable one. Thus, it is imperative that the effect of temperature on device performance is accounted for accurately. As in small signal modeling, the first step in power modeling is to establish the basic device geometrical factors that are needed to calculate the current-voltage characteristics. Once these are known, the output characteristics superimposed with the load line can be used to estimate the power level that can be obtained from the device, provided that it is not limited by the input drive as shown in Fig. 12.35. In class-A operation, the maximum power that can be expected from the drain circuit of a device is given by Pmax ˆ

Idson …Vb Vknee † ; 8

…12†

where Idson is the maximum drain current (this is the drain current with a small positive voltage on the gate electrode), Vb is the drain breakdown voltage, and Vknee is the knee voltage, as shown in Fig. 12.35. The allowable positive gate voltage (&1 V) will depend on the channel doping and the work function of the gate metal. The positive gate voltage is limited by the onset of forward Schottky-diode current. The DC load line shown in Fig. 12.35 would be used in a class-A RF amplifier with the maximum drain voltage Vd = Vb/2. The slope of the load line is 1/RL where RL is the value of the load resistance at the output of the FET. What can be gleaned from Eq. (12) is that Vb and Idson must be made as large as possible. The utility of wide band gap semiconductors such as GaN at this juncture is that the drain breakdown voltage is larger than that in conventional group III–V semiconductors. In general, the drain can be swung to voltages up to within 80%

Fig. 12.35 Schematic representation of I-V characteristics with a

load line for a Class-A operation.

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of the drain breakdown for a 20% margin of safety. It should be pointed out that the maximum drain current in nitride semiconductor-based MODFETs is in the same ballpark as that of more conventional semiconductors. This implies that increased power-handling capability is a direct result of large breakdown voltages and thermal conductivity and the fact that higher junction temperatures can be tolerated. The ability to increase drain bias increases the load resistance and makes it easier to impedance match, particularly in devices with large gate widths. In power devices, power dissipation within the device increases the junction temperature and alters the output characteristics. On the one hand, higher junction temperatures with respect to the case temperature would enhance the heat dissipation to the power of four of the temperature differential, but along with it comes reduced current and increased series resistances, which in turn increase the heat dissipation. Moreover, the thermal conductivity of the semiconductor decreases with increased temperature, exacerbating the situation. Consequently, the effect of junction temperature on the output characteristics must be taken into consideration. Temperature-dependent material parameters, if known, can be used to calculate the output characteristics with respect to temperature. However, a more pragmatic approach, particularly when the aforementioned parameters and or models required are not available, can be taken in which one measures the output characteristics of the device under consideration as a function of temperature. The junction temperature is critically dependent on the substrate thermal conductivity that is available for various substrates including GaN [1]. The functional dependence of thermal conductivity on temperature is v…T† ˆ v…T0 †…T=T0 †

r

;

…13†

where the coefficient r is 0.559, 0.443, 0.524, and 0.544 for Si, GaAs, SiC, and sapphire, respectively [123]. Thermal conductivities of sapphire, SiC, GaAs, and Si as a function of temperature are shown in Fig. 12.36. In the figure, v (T0) has also been appropriately reduced to account for the doping of the substrate material.

Fig. 12.36 Thermal conductivity ver-

sus temperature for SiC and sapphire. After Ref. [123].

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

12.3.3

Schottky Barriers for Gates

Any semiconductor device requires metal contacts and MODFETs are no exception. These devices require ohmic source and drain contacts as well as a rectifying Schottky barrier for controlling the charge in the channel. Schottky barrier-related processes for GaN-based devices are nascent, but rapid progress is being made. Until recently it has been difficult to fabricate good quality single-crystal films on which a Schottky metal could be deposited, and upon which the properties of Schottky barriers could be studied. However, considerable progress has been made with Pt-GaN Schottky barriers [124, 125], which have been successfully implemented in GaN-based MODFETs [24, 126, 127]. Recent successes in growing good quality single-crystal group III–V GaN layers prompted the studies of fundamental electrical property of metal-semiconductor barriers on GaN. In order to determine the properties of only the metal-semiconductor junction, one must be able to model the semiconductor. Semiconductors with large defect concentrations are notorious for exhibiting parasitic processes in current-voltage and capacitance-voltage characteristics that cloud the picture. Consequently, good epitaxial layers as well as good metal/semiconductor interfaces are imperative. During the evolutionary period, while the sample quality is acceptable, the temperature and frequency dependence of the capacitance-voltage characteristics and temperature-dependent current-voltage characteristics are measured and analyzed for determining the effective metal-semiconductor barrier height. To get a large Schottky barrier height for rectifying metal contacts on GaN, which is imperative for low leakage, metals with large work functions such as Au and Pt [124] have been explored. Hacke et al. [128] have studied Schottky barriers made of Au on unintentionally doped n-GaN grown by HVPE. The forward current ideality factor was nidl*1.03 and the reverse bias leakage current was < 10–10 A at a reverse bias of –10 V. While the current-voltage measurement indicated the barrier height to be 0.844 eV, the capacitance measurements led to a value of 0.94 eV. However, the reported barrier height for Au/n-GaN ranges from 0.80 to 1.1 eV in various studies. One possible cause is different surface treatment. Maffeis et al. [129] investigated the influence of premetallization surface preparation on the structural, chemical, and electrical of Au-nGaN interfaces. The Schottky barrier with very low ideality factor (1.10) and high barriers (1.25 eV) was fabricated with UHV annealing at 600 8C for 10 min [129]. Suzue et al. [124] and Mohammad et al. [125] have studied the Pt Schottky barriers on unintentionally doped n-GaN. Temperature-dependent current-voltage and capacitance-voltage characteristics in the range of –195 8C to 42 8C were studied to gain insight into the current conduction mechanism. Any excess current observed is traditionally attributed to defects (generation-recombination centers) and surface leakage current. The ensuing current is called the Shockley-Read-Hall (SRH) recombination current resulting from the midgap states. If one neglects this excess current, a barrier height of about 0.8 eV is deduced as opposed to about 1 eV deduced from the C-V measurements. Because of the effect of excess current on

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a

b Fig. 12.37 a Variation of the inverse square

capacitance, C–2 with the applied bias V for various signal frequencies, x, in Pt-GaN Schottky barriers. Curves 2 and 3 lie in be-

tween curves 1 and 4, respectively; b temperature dependence of C–2 versus the applied bias V in Pt-GaN Schottky barriers.

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

the slope of the I-V curve, C-V measurements in this particular case may represent the metal barrier height. An examination of the C-V plots, however, indicated that, under reverse bias condition, the capacitance depended insignificantly on the sample temperature and the signal frequency as shown in Fig. 12.37 a and b. This leads one to conclude that the density of traps has been lowered. The curves corresponding to all temperatures were largely linear, which yielded barrier heights ranging between 0.95 and 1.05 eV. Reduced capacitance with decreasing temperature is consistent with relatively deep donors. Binari et al. [130] determined Ti Schottky barrier heights to be 0.58 and 0.59 eV from the current-voltage and capacitance measurements, respectively. The ideality factor nidl is approximately 1.28. The diode series resistance (Rs) is 100 X. The measurement of barrier height to p-GaN is very difficult due to the lack of high-quality p-type epilayer and low resistance ohmic contact. The high I-V ideality factor prevents reliable barrier height data from being obtained from the I-V curves. In addition, these barriers obtained from I-V measurements are usually inconsistent with the ones from C-V measurements. Hartlieb et al. [131] fabricated a Pd/p-GaN Schottky barrier on chemical-vapor-cleaned p-type GaN surface. The final barrier height was 1.3 ± 0.1 eV. The difference between the predicted value (0.9 eV) and observed one arises from the interface dipole term, which is a result of the complicated interaction between extrinsic and intrinsic surface states as well as the contribution from metal-induced gap states. The work of Cao et al. [132] revealed that the removal of interfacial oxides causes the reductions in barrier height. It may partly explain the considerable amount of scatter for contact properties reported in literature. On the other hand, the crystal quality and polarity of GaN also have a direct impact on the electronic properties of Schottky contact. The Ni/Au Schottky contacts formed on different epilayers grown by MOCVD have barrier height/ideality factor of 0.80 eV/1.17 for sapphire substrate, and 0.92 eV/1.13 for SiC substrate [133]. Karrer et al. [134] compared the Pt Schottky contacts on Ga- and N-face GaN. Different barrier heights, 1.1 eV for Gaface and 0.9 eV for N-face, were determined by I-V measurements. C-V measurements confirmed the greater barrier heights for Ga-face material. The ternary AlxGa1–xN is an essential component of nitride-based MODFETs, which makes the investigation of metal-AlxGa1–xN contacts imperative. Khan et al. [135] reported the fabrication of a Cr/Au Schottky barrier on n-AlGaN. Moreover, Khan et al. [136] studied the Schottky barrier characteristics of the Au-AlxGa1–xN system. A typical current-voltage characteristic of an Al0.14Ga0.86N Schottky diode had an ideality factor of 1.56 under reverse bias and a threshold voltage of about 0.9 V at 0.1 A. The reverse bias leakage current was recorded to be marginally low (10–10 A) for a reverse bias of –10 V. By using the current-voltage method, the barrier height and the electron affinity were determined to be 0.94 eV and 4.16 eV, respectively. From the C–2 versus V plot, the same barrier height and the electron affinity were deduced to be 1.3 ±0.05 eV and 3.8 eV, respectively. As the AlGaN quality increases, more indepth investigations must be undertaken to get an accurate picture of intrinsic parameters. In short, the current conduction mechanism in metal-semiconductor structures is strongly affected by surface and bulk states. De-

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viations from an ideal ideality factor, such as is the case here, indicates such states. The situation gets more complicated with AlGaN and gets worse as the AlN mole fraction is increased. Likewise, capacitance-voltage measurements also are affected by states that are charged, either at the interface or in the bulk. As is the case in many facets of research and development, insights into the metal-nitride contacts will be gained in an evolutionary manner together with the developments in nitride layers. 12.3.4

Contacts to GaN

Ohmic contacts in power devices are extremely important because they affect their efficiency as well as heat dissipation. Initial inferior results helped fuel concerns that GaN-based electronic devices may not perform well. Early specific contact resistivities on n-type GaN using Al and Au metallizations [137] were in the range of 10–4 and 10–3 X cm2. Major improvements were realized by using Ti/Au [138] and Ti/Al [139] in that specific contact resistivities in the high 10–6 X cm2 were obtained with the latter. Carrying the Ti/Al contact work one step further, Wu et al. [140] confirmed that, except at very high annealing temperatures, the ohmic contact suggested by Lin et al. [139] functions very effectively. At very high temperatures, Al in the metal contact melts and tends to ball up, resulting in rough surfaces and increased ohmic contact resistances as pointed out already by Lin et al. [139]. In an attempt to circumvent this difficulty, Wu et al. [140] designed a separate layer-metallization method where a realignment and deposition of a second thin Ti layer, and a 2000-Å Au overlayer were carried out. Specific contact resistivities were in the range of 3.0 ´ 10–6 X cm2 to 5.5 ´ 10–6 X cm2, depending on the doping concentration in the semiconductor. In an attempt to obtain improved ohmic contacts, Fan et al. [141] have designed a multilayer ohmic contact method. By using a composite metal layer of Ti/Al/Ni/ Au (150 Å/2200 Å/400 Å/500 Å), they obtained very low contact resistivities. Specifically, for n-GaN with doping levels between 2 ´ 1017 cm–3 and 4 ´ 1017 cm–3, they obtained specific contact resistivities in the range of qs = 1.19 ´ 10–7 X cm2 to 8.9 ´ 10–8 X cm2, respectively. The resistance RT between the two contacts was measured at 300 K using a four-point probe arrangement. The contact resistivity qs was derived from a plot of RT versus gap length. The method of least squares was used to fit a straight line to the experimental data. These straight lines, and the actual experimental results for both alloyed and nonalloyed contacts are shown in Fig. 12.38. Calculation of the contact resistivity was based on the assumption that the semiconductor sheet resistance underneath the contacts remains unchanged, which is not true for nonalloyed contacts. As for the current conduction mechanism in these ohmic contacts, the large metal-semiconductor barriers diminish the possibility of thermionic emission-governed ohmic contacts to GaN. The alternative mechanism is some form of tunneling that may take place if the GaN is so heavily doped as to cause a very thin depletion region. Tunneling is possible if, due to annealing (for example, at 900 8C for 30 s), Al and Ti

12.3 Modulation-Doped Field Effect Transistors (MODFETs) Fig. 12.38 Least-squares linear

regression of the total resistance between the two adjacent ohmic contact pads in multiple-layer Ti/Al/Ni/Au ohmic contacts on GaN.

along with Ni undergo substantial interaction with each other and GaN. Investigations showed that Ti receives N from GaN, forming a metallic layer, while the lack of N on GaN provides the desired benefit of increased electron concentration through N vacancy formation [142]. Aluminum passivates the surface and also possibly reacts with Ti to form TiAl. In contrast to n-GaN, stable ohmic contacts with low resistivity to p-GaN are much more difficult to achieve due to the large work function of p-GaN, residual hydrogen passivation effect, and relatively low hole concentration. Ni-, Au-, Pd-, and Pt-based metal schemes with high work functions (> 5.0 eV) have been widely investigated and relatively low resistivity of the order of 10–4 to 10–6 X cm2 can be realized now. Improved Ni/Au ohmic contacts to moderately doped p-GaN (NA = 1017–18 cm–3) have been demonstrated by annealing in O2/N2 and resistivity as low as 4.0 ´ 10–6 X cm2 was achieved [143–145]. Two mechanisms were proposed for the resistivity reduction, i.e., NiO as a p-type semiconductor forms a thin Schottky barrier with p-GaN by Ho et al. [144, 145], or the presence of oxygen during annealing helps to remove the residual hydrogen which bonded with Mg or N atoms in the p-GaN epilayer by Koide et al. [146]. The oxidized Ni/Pd/Au [147] and oxidized Ru/Ni [148] ohmic contacts on p-GaN (NA = 3–4 ´ 1017 cm–3) also exhibited low resistivity of 1.0 ´ 10–4 X cm2 and 4.5 ´ 10–5 X cm2 respectively. Both Hull et al. [149] and Qiao et al. [150] found that the presence of oxygen in the annealing could reduce the resistivity of p-GaN, which supports the argument of Koide et al. [146]. The surface treatment of GaN prior to the metal deposition has a strong effect on the final performance of the contacts. Kim et al. [151, 152] reported that boiling aqua regia is effective in reducing oxygen and carbon. The treatment causes the shift of the surface Fermi level of p-GaN and subsequently the reduction of band bending below the contact. The surface Fermi level on the KOH-treated surface lies about *1.0 eV closer to the valence band than that of HCl-treated p-GaN surface [153]. It was also found that the surface treatment by (NH4)2S solution helps to remove the interfacial oxide and shift the Fermi level to an energy level

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near the valence band [154]. The reduction of barrier height at the abrupt and unreacted interface results in the decrease of the contact resistivity. In addition, Ti itself is also effective in reducing the surface contaminations when incorporated into ohmic contacts on n-GaN [155]. Zhou et al. [156] fabricated a Ti/Pt/Au ohmic contact after annealing in a N2 ambient at 800 8C for 2 min, which has a resistance of only 4.2 ´ 10–5 X cm2 on moderately doped p-GaN (NA = 3.0 ´ 1017 cm–3). Other approaches such as employing AlGaN/GaN superlattices [157, 158] and InGaN-capping layers [159] have also been examined to improve the contacts. These structures reduce the effective ionization energy of Mg and also utilize piezoelectric and polarization effects to increase the hole density. The low resistance obtained is of the order of 10–4 X cm2. However, the final resistivity of ohmic contact to p-GaN has high sensitivity to the conditions of all steps during the contact formation and the performance of contacts may rely on the deliberate controlling of these conditions [158]. 12.3.5

Experimental Performance of GaN MODFETs

Initial GaN MODFETs utilized the background donors in the AlGaN layer, the density of which is not controllable, to say the least, and any other free and weakly bound electrons drawn to the interface. Congruent with the early stages of development and the defect-laden nature of the early GaN and AlxGa1–xN layers, the MODFETs exhibited very low transconductances (of the order of 20 mS mm–1), and large on-resistances. In addition, they also exhibited a low-resistance state, which was relatively high to begin with, and a high-resistance state before and after the application of a high drain voltage (20 V). As in the case of GaAs/AlGaAs MODFETs, hot-electron trapping in the larger band gap material at the drain side of the gate is primarily responsible for the current collapse. The negative electron charge accumulated because of this trapping causes a significant depletion of the channel layer, more probably a pinch-off, leading to a drastic reduction of the channel conductance and the decrease of the drain current. This continues to be effective until the drain-source bias is substantially increased, leading to a space-charge injection and giving rise to an increased drain-source current. With improvements in the materials quality available, the transconductance, current capacity, and drain breakdown voltage are all increased to the point that GaN-based MODFETs are now strong contenders in the arena of high-power devices/amplifiers, particularly at X band and higher frequencies. As is the case for the FET device structure, improved and high resistivity buffer layers have once again played a pivotal role. For chronological purposes, a brief review of the latest class of MODFETs with high transconductances and current levels is given later in this chapter. The first breakthrough in the N-MODFETs based on GaN came in the 1994– 1995 time period in the author’s laboratory [126]. These devices with a gate length of 3 lm and gate width of 40 lm exhibited transconductances of about 120 mS mm–1 with low on-resistances as they had doped AlGaN donor layers and

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

Fig. 12.39 a Output I-V characteristics of the

first GaN MODFET, which exhibited respectable performance. The 3-lm gate device had a gate length of 3 lm, low-resistance ohmic contacts and low-leakage Schottky barriers;

b output I-V characteristics of a GaN MODFET on sapphire with a 2-lm gate, which exhibits negative output conductance due to thermal effects associated with the relatively low thermal conductivity of sapphire.

low-resistance ohmic contacts. The I-V characteristics of an early NMODFET device are shown in Fig. 12.39. Shortly thereafter, devices with a gate length of 2 lm, gate width of 40 lm, and the drain-source separation of 4 lm exhibited drain currents of approximately 500 mA mm–1 and extrinsic transconductances of approximately gem = 185 mS mm–1, which are shown in Fig. 12.39 b. The drain breakdown voltage for a 1-lm gate-drain spacing was approximately 100 V, the exact value depending on the layer design and quality of the layered structure. Soon thereafter, other laboratories achieved similar results in similar structures. What is unique with AlGaN/GaN MODFETs as compared to their GaAs counterparts is the polarization charge discussed earlier. As indicated before, the terminology of polarization, particularly the piezoelectric component has been used rather liberally. Even terms such as “piezoelectric doping” have been coined, and very high sheet carrier concentrations observed have been ascribed to piezoelectric polarization only. We have to recognize that ultimately, regardless of the source of the carriers, the strength of the electric field that can be accommodated by the semiconductor under the gate without excessive leakage sets an upper limit on the number of carriers at the interface. Use of multi-2 DEG structures is one obvious method to increase the current capability of MODFETs, and they have been employed. In those cases, the GaN layer is straddled by two doped AlGaN layers that donate electrons to the channel, thus increasing the number of electrons available for current conduction. By Hall effect measurement, the mobility and sheet carrier densities in the 2 DEG were about 304 cm2 V–1 s–1 and 3.7 ´ 1013 cm–2, respectively, at room temperature. The sheet carrier concentration may have been affected by the piezoelectric effect. A number of double heterochannel MODFETs (DHCMODFETs) with gate lengths of 1.5 to 1.75 lm and a gate width of 40 lm have been reported [160].

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The maximum drain saturation current IDS corresponding to a drain-source voltage VDS = 7 V, and gate source voltage VGS = 3.5 V in a DHCMODFET is about 1100 mA mm–1, which is important because in high-power devices the input is momentarily forward biased. The DHCMODFET has a room-temperature extrinsic transconductance of gm = 270 mS mm–1. The value of the total resistance RT extracted from the linear region of the I-V curves is 4 X mm–1. Near pinch-off, the drain breakdown voltage is about 80 V, indicating excellent power potential of the device. These measurements were made in a nitrogen-pressurized container to avoid possible oxidation of the contacts and probes. The maximum drain-source current and extrinsic transconductance of the DHCMODFET are 500 mA mm–1 and 120 mS mm–1, respectively. These devices maintain reasonable output characteristics at temperatures as high as 500 8C with maximum drain current and extrinsic transconductance values of 380 mA mm–1 and 70 mS mm–1, respectively. Cooling to room temperature restored the characteristics, which demonstrates the robustness of this material system and of the metallization employed. It should be noted, however, that high-power operation requires large drain breakdown voltages with the added benefit of having large output resistances, which ameliorates impedance matching. The heat dissipation is a major problem, however, in GaN MODFETs on sapphire substrates as the thermal conductivity of this substrate is about 0.3 W cm–1 K–1 (may even be somewhat lower). To make matters worse, the thermal conductivity decreases rapidly as the temperature increases. Consequently, devices show a decreasing drain current (negative differential output conductance) as the drain bias is increased, and, needless to say, the power performance is degraded. To overcome this, one must either remove the sapphire substrate followed by mounting the structure on a substrate with better thermal conductivity, employ flip chip mounting, or grow the structure on a substrate with better thermal conductivity. Among the substrates with better thermal conductivity are Si and in particular SiC. Layers on Si, however, are not of as high a quality as one would like, which leaves SiC substrates, which are expensive and suffer from inferior surface characteristics (or smoothness) due to the hardness of SiC. Early attempts in the author’s laboratory to grow GaN layers on SiC met with difficulty due to the surface damage roughness, though occasionally very high mobility could be obtained [161]. Two approaches can be employed to remove the surface damage. One is the mechanical/chemical polish, which is very slow, and the other is etching in H and Cl environment at very high temperatures such as 1300 8C. GaN layers grown on Htreated SiC at high temperature exhibited much lower defect concentration as compared to SiC treated with wet chemical, and wet and dry chemical treatments [162]. The H-cleaning process has been adopted as a standard procedure for MBE growth of GaN on SiC [163] with a cleaning temperature of about 1700 8C. The author. in collaboration with the group of E. Janzen at Linköping University was able to H-etch Leyl SiC followed by MODFET growth. These devices did not exhibit the negative differential resistance characteristic of the sapphire substrates. However, SiC substrates prepared by the sublimation method did not appear to

12.3 Modulation-Doped Field Effect Transistors (MODFETs) Fig. 12.40 Output characteristics of

a 3-lm gate AlGaN/GaN MODFET grown on Leyl SiC substrate that is void of the output negative conductance. However, the Leyl substrates are highly conductive and not well suited for FETs due to RF shorting/ loading. Nevertheless, experiments of this kind serve to prove the point that the negative output conductance observed in devices on sapphire are most likely of thermal origin.

survive this high-temperature H-etching process. Researchers have exploited the in situ H-etching process [164] and HCl-etching process [165]. Reports detailing these processes and their effects have appeared in the open literature already. The I–V characteristics of the particular device prepared in 1996 on SiC substrates are shown in Fig. 12.40. These results were reported in meetings dealing with the development of high power devices and the case was made for SiC substrates as intrinsically being better for GaN power MODFET applications. Several groups participating in those meetings expended a good deal of effort on SiC substrates with initially comparable high-power performance to that on sapphire. Other groups later propelled GaN MODFETs on SiC substrate to their pinnacle with outstanding performance, as will be discussed below. It should be pointed out that the pitch of gates for a power FET on a substrate with very good thermal conductivity can be made smaller than on a substrate with inferior thermal conductivity. Consequently, the chip size can be made much smaller, in addition to other advantages. MODFETs have progressed to a point where microwave performance has been established for a variety of devices with gate lengths as wide as 2 lm and as narrow as about 0.2 lm. To appreciate the rapid development of the device, its evolution will be succinctly discussed. A typical MODFET structure with 2-lm gate length has been tested for small-signal S-parameters performed at bias conditions used for the power measurements (i.e., 15 V, –2.5 V, and 20 mA for the drain voltage, gate voltage, and drain current, respectively). The unity current gain cutoff frequency (fT) and maximum frequency of oscillation (fmax) were 6 GHz and 11 GHz, respectively, at both 15 and 30 V bias. Values of fT and fmax in excess of 50 GHz and 100 GHz have been reported for short gate length devices (about 0.2 lm), respectively. As touched upon earlier, devices on sapphire substrates suffer from the low thermal conductivity of sapphire substrates and exhibit negative differential resistance in the output characteristics. Remedies include better heat sinking by flip-chip mounting and the use of high-resistivity 4H or 6H-SiC substrates, which provide good thermal conductivity but are costly. GaN MODFET devices that have been prepared in the author’s laboratory on conducting 6H-SiC substrates exhibited output characteristics that lacked the neg-

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ative resistance (i.e., they exhibited good heat sinking). There have subsequently been a few reports of MODFET power devices on high-resistivity SiC [25, 28, 29] and p-type SiC [27] substrates with phenomenal improvement in power-handling capability, notwithstanding the rapid progress on sapphire substrates. On sapphire, recent 0.7-lm gate-length Al0.5Ga0.5N/GaN MODFETs exhibited a current density of 1 A mm–1, three-terminal breakdown voltages up to 200 V, and CW power densities of 2.84 and 2.57 W mm–1 at 8 and 10 GHz, respectively, representing a marked performance improvement for GaN-based FETs. Increasingly outstanding power levels are being achieved with near-half-micrometer or smaller gate lengths. To follow the evolution of the developments, a few examples are cited here. With 0.7-lm gate length devices on SiC substrates, where the gate-source spacing and gate–drain spacing were 0.5 and 0.8 lm, respectively, a total output power of 2.3 W in a device with a 1.28-mm gate periphery has been obtained [28]. The power gain at the 2.3 W output power point was 3.6 dB with a poweradded efficiency (PAE) of 13.3% for a drain bias of 33 V. The current and power gain cutoff frequencies were 15 and 42 GHz, respectively. The contact resistance, though not the best, was between 2.6 and 3.5 X mm–1. The maximum normalized transconductance was 270 mS mm–1 and the drain current was 293 mA mm–1. Steady improvement in power performance has led to very recent results at HRL laboratories with record-breaking performance [30]. The output I-V characteristics of a 250-nm gate length AlGaN/GaN MODFET device of HRL on SiC is shown in Fig. 12.41. Typical DC characteristics include 600 mA mm–1 current performance and > 60 V drain breakdown voltage. The small signal current and power gains as a function of frequency of another device are shown in Fig. 12.42. The current gain cutoff and maximum power gain cutoff frequencies measured were about 48 and 100 GHz, respectively, for –5.5 V and 12.5 V gate and drain bias voltages, respectively. The minimum noise figure and the associated gain of the device whose I-V characteristic was mentioned above are shown in Fig. 12.43. A minimum noise figure of 0.85 dB at 10 GHz with an associated gain of 11 dB is simply remarkable.

Fig. 12.41 The output I-V characteristics of a 0.25-lm gate AlGaN MODFET on sapphire fabricated at HRL laboratories. Note the negative differential output conductance due to the poor thermal conductivity of sapphire substrate. Courtesy of N. X. Nguyen and C. Nguyen.

12.3 Modulation-Doped Field Effect Transistors (MODFETs) Fig. 12.42 Small-signal current

and power gains as a function of frequency of a 0.25-lm gate AlGaN MODFET on sapphire fabricated at HRL laboratories. Courtesy of N. X. Nguyen and C. Nguyen.

Fig. 12.43 The minimum noise fig-

ure and the associated gain of a 0.25-lm gate AlGaN MODFET on sapphire fabricated at HRL laboratories. Courtesy of N. X. Nguyen and C. Nguyen.

At HRL laboratories, 6.3 W of CW output power was obtained at 10 GHz from a 1 mm-wide transistor device. More importantly, the power density remained nearly constant as the device size was scaled upward from a 0.1 mm width, where the device exhibits 6.5 W mm–1, to 1.0 mm. These record-setting transistors were epitaxially grown AlGaN/GaN heterostructures on semi-insulating SiC substrates by MBE. HRL has developed a growth process using molecular beam epitaxy (MBE) that has virtually eliminated material defects common to other reported GaN devices, thereby enabling the scaling. MBE growth also produces device characteristics with less than 5% standard deviation over the 2-inch diameter SiC substrate, a six-fold improvement over previously reported results. As will be discussed in the amplifiers section, the researchers at HRL laboratories have expanded their work to amplifiers with several cells and showed very good power scalability up to 2 mm of total gate periphery [30]. Using 250-nm gate devices, a CW output power of 22.9 W with an associated power-added efficiency

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors

of 37% was measured for an amplifier at 9 GHz with four 1-mm gate periphery devices. Furthermore, the same authors [30] also showed a CW power density of 4 W mm–1 at 20 GHz that is the state-of-the-art figure for any three-terminal solidstate device at this frequency. In contrast to the earlier devices whose DC characteristics were mentioned before, the newer devices had a maximum drain current density exceeding 1.4 A mm–1, and the peak transconductance of the devices biased at Vds of 15 V was 250 mS mm–1. The reverse-bias gate-to-source breakdown voltage of the devices measured at 1 mA mm–1 of gate leakage current typically exceeded 80 V. Small-signal RF performance of MODFETs as characterized in the 0.5 to 40.5 GHz range, and the cutoff frequencies estimated as will be discussed below. The best results are shown in Table 12.4 for various gate lengths of 200-lm wide devices. Continuous wave power measurement of 0.1-mm, 1-mm, and 2-mm devices was performed at 10 GHz using a load-pull system [30]. The gate length of the particular device subjected to this particular test was 25 nm. Maximum output power levels of 0.65 W, 6.3 W, and 10.5 W were measured for devices with 0.1-

Tab. 12.4 The current gain cutoff and maximum oscillation frequencies versus gate length. After

Ref. [30] Gate length (nm)

Current gain cutoff (fT : GHz)

Maximum oscillation (fmax : GHz)

250 150 50

55 80 110

100 120 >140

Fig. 12.44 Large-signal characteristics of 2-mm wide device at

10 GHz. The maximum CW output power of this device was 10.5 W. After Ref. [30].

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

Fig. 12.45 Large-signal characteristics of 0.15 lm ´ 200 lm GaN

MODFET at 20 GHz. The maximum CW power density of this device was 4 W mm–1. After Ref. [30].

mm, 1-mm, and 2-mm total gate periphery, respectively, and scale nearly linearly. Shown in Fig. 12.44 is the output power versus the input power of a 2-mm device. Measurements at higher frequencies were also made to determine the device response in terms of its power performance. Using a series of 150 nm ´ 200 lm gate devices, a CW output power density of 4 W mm–1 at 20 GHz was obtained [30]. The results of load-pull measurements at 20 GHz are shown in Fig. 12.45. These are the highest reported data for a three-terminal solid-state device at this frequency. 12.3.6

Power Amplifiers

Power-combining single-stage X band power amplifiers have been reported using four 1-mm gate periphery devices mentioned above [30]. The model used for circuit design was extracted from DC and RF device characteristics [30]. Parameters needed for modeling were deduced from the small signal S-parameters in the form of a standard equivalent circuit. Commercial parameter-extraction tools that are available can be used for this purpose. The optimum load impedance for a maximum power-combining efficiency was determined by loadpull measurements with the design goals of matching into 50-X ports, having a peak power gain of 8 dB at 9 GHz, and 3 GHz bandwidth. Input and output matching networks were built using discrete capacitors and sapphire microstrip elements. Transistors were wire bonded to matching networks. The fixture was mounted onto a water-cooled heat sink for heat dissipation [30]. The power performance of the amplifier at 9 GHz is shown in Fig. 12.46. A CW output power of 22.9 W with an associated

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors Fig. 12.46 Power performance

of a single-stage GaN MODFET power amplifier utilizing four discrete 1-mm device cells. Source pads were interconnected by an abridge technique to reduce the source resistance as well as the source inductance. The peak output power of the amplifier is 22.9 W. After Ref. [30].

Fig. 12.47 Simulated and experimental RF power density data for Si, GaAs, SiC, and GaN FETs. After Ref. [123].

power-added efficiency of 37% was measured for an amplifier at 9 GHz with four 1-mm gate periphery devices. In power devices, the thermal limitation can never be eliminated completely, as is also the case in nitride devices, particularly when fabricated on sapphire substrates with a thermal conductivity of only approximately 0.3 W. Inclusion of thermal limitations leads to results shown in Fig. 12.47 for devices that compete in the highpower device arena [24, 123]. Since new device developments do, in general, compete with existing and alternative technologies, a brief account of competing technologies for the power arena is given below. The Si metal semiconductor FET (MESFET) analytical curve, modeled for its simplicity, is slightly above the SiC analytical curve and indicates a maximum power density of 0.35 W mm–1 at VdS = 7 V, which is slightly lower than 0.39 W mm–1. Since Si RF MESFETs are unavailable, commercial Si RF metal-oxide semiconductor FET (MOSFET) results were used for comparison instead. At low voltages, the Si MOSFET data parallel the analytical curve suggesting

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

the validity of the functional dependence of power density on drain voltage. Also shown are two higher power density data points 0.4 W mm–1, VdS = 28 V and 0.87 W mm–1, VdS = 48 V. These higher power densities were obtained with specially designed RF power MOSFETs that incorporate a lightly doped drain and field plates that significantly increase the breakdown voltage. The GaAs analytical curve shows the highest power density of all the devices at the lowest voltages primarily because of the higher electron mobility of GaAs. However, the low breakdown field limits the GaAs MESFET’s drain voltage to about 8 V and power density to 0.63 W mm–1 including thermal effects. Typical commercially available GaAs MESFET power densities are below 1 W mm–1. However, high-performance GaAs FETs with more complex device cross sections have achieved power densities as high as 1.4 W mm–1 at 18 V. At 100 V, the SiC MESFET has calculated maximum power densities of 7.96 W mm–1 with thermal effects and 9.7 W mm–1 without thermal effects. The highest demonstrated CW power density 3.3 W mm–1 (Vds = 50 V) for a SiC MESFET [166] is also shown for comparison. Additional SiC data again illustrate the functional dependence of power density on drain voltage. The GaN analytical results are highly dependent on the thermal conductivity of the substrate. With a sapphire substrate, the device is severely thermally limited to 2.24 W mm–1 at 30 V with a resulting channel temperature of over 400 8C. With a SiC substrate, however, the analysis predicts that a GaN MODFET could achieve 14.5 W mm–1 at 100 V with a channel temperature of about 300 8C. We should caution that while the power density figure can be used during the evolution process, eventually the total power figure must prevail. Normalized power-density measurements, though frequently reported (a trap the present author also fell into), are often misleading because smaller gate widths naturally lead to larger power densities. This experimental datum point is actually slightly higher than the simulated result, possibly because of the very small size of the experimental device (100 lm width). The GaN results of analytical models are highly dependent on the thermal conductivity of the substrate. With a sapphire substrate, the device is severely thermally limited to 2.24 W mm–1 at 30 V with a resulting channel temperature over 400 8C. However with a SiC substrate [123], the analysis predicts that a GaN MODFET could achieve 14.5 W mm–1 at 100 V while keeping the channel temperature at about 300 8C. The key to further improvements lies within our ability to control the polarity of the films, to prepare inversion-domain-free material, and to reduce defects. If the past few years are any indication, substantial progress is in the wings. 12.3.7

Anomalies in GaN/AlGaN MODFETs

Field effect transistors, in general, and modulation-doped field effect transistors, in particular, exhibit anomalies in their output I-V characteristics. Among the causes of these anomalies are channel carriers being trapped in the wide band gap material and bulk, meaning the buffer layers. In addition, surface states, if

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors

Fig. 12.48 Schematic representation of an AlGaN/GaN MOD-

FET indicating how the surface charge and charge injection into traps in the buffer layer and defects in AlGaN could serve in depleting conducting channel carriers. For simplicity, all the 2DEG is assumed to be due to donors placed in the AlGaN. In addition, the regions from which carrier injection takes place are limited to the spacing between the gate and drain electrodes, the exact location is chosen arbitrarily.

present and not passivated, could act to reduce the sheet conducting charge, particularly between the gate and the drain region of the FETs [167]. This is depicted schematically in Fig. 12.48. Some AlGaAs/GaAs MODFETs, which are the predecessor of the current AlGaN/GaN MODFET, exhibit behavior similar to what was then termed “current collapse” [168]. This behavior was attributed to carrier injection from the channel to the AlGaAs at reasonably high fields where they are trapped at low temperatures. With below gap light excitation, increasing temperature, and exchange of the source and drain terminals, the effect could be eliminated. The GaAs buffer layer for the AlGaAs/GaAs-based device is of high quality so that its trapping effect was not dominant. The surface states in the AlGaAs/ GaAs device were not deemed to have a profound effect on the current-voltage characteristics. However, it is always a prudent approach to passivate the surface states, as was done in the AlGaAs/GaAs device, as they greatly affect the device operation with time. In the AlGaAs/GaAs variety, the trapping effect in the AlGaAs barrier was attributed to DX levels, which are caused by lattice-distorting defects, which causes massive change in the band gap of the semiconductor at the local level, and their behavior could be described by a lattice-coordination diagram. Since this effect reduced with lowering AlAs mole fraction, AlGaAs/InGaAs pseudomorphic modulation-doped FETs were developed [169], which are the dominant compound semiconductor FETs in industry at the moment, to mitigate the effect of DX centers. In the AlGaN/GaN system, the surface states and or defects play a much more important role due to polarization fields as the layers are on polar surfaces. Anomalous characteristics, such as the so-called current collapse, kinks in the I-V characteristics, and long-term instability, have haunted the device from the time of early development. Preliminary investigations of these phenomena were undertaken some years earlier [170]. Now that these devices are strong contenders in the market place for systems applications, these phenomena are getting a good deal of attention. One of the anomalous behaviors is the drain current lag that prevents attainment of RF power congruent with the DC output characteristics of

12.3 Modulation-Doped Field Effect Transistors (MODFETs) Fig. 12.49 Schematic representa-

tion of RF current lag superimposed on top of DC drain I-V characteristics with a load line.

the device. For a maximum drain voltage of 50 V (drain bias of 25 V) and maximum drain current of 1 A, one should normally get 6.25 W and 12.5 W in class A and class B operations assuming an ideal case with zero saturation voltage, and no thermal limitation. However, the observed values in the laboratory are, in general, substantially smaller. This is due to current lag that is basically a failure on the part of drain current to keep up with the gate bias voltage in response to a high-frequency large-signal gate modulation [171], attributed to surface states. The drain current lag is schematically shown in Fig. 12.49 where the load line and quiescent operating conditions for class A operation are shown. Also shown are the extremes of DC current as governed by the load line. Current lag is meant to indicate that the RF current (shaded) fails to follow the gate bias and thus the drain current at high frequencies is lower than that measured under DC conditions. The RF current can be determined by the use of the so-called load-pull tuning. It can also be measured under active loading conditions with the use of a high-speed sampling scope for measuring the output RF voltage, in response to an RF input drive, wherein the voltage measured can be converted to current, knowing the load value. Traps are usually attributed to the current collapse. The loss of channel carriers as a result of being trapped at defects produces a large transverse electric field, which leads to the current collapse. The assumption is supported by the fact that the light incident on the collapsed device photoionizes the trapped carriers and causes a restoration of the drain current [172, 173]. The sudden removal of the current reduction at large VDS (> 25 V) observed by Dietrich et al. [174] can also be explained by the field-enhanced carrier emission from traps. However, these traps are still not clearly located in GaN MODFET. It was assumed that these traps are located in the high-resistivity GaN buffer layer [175]. The authors utilized the photoionization spectroscopy technique to examine the traps responsible for current collapse located in the GaN buffer layer grown by MOCVD. The areal trap concentration and trap photoionization cross section for two deep traps were determined. It was revealed that the deepest trap is a carbonrelated defect, while the midgap trap may be associated with grain boundaries or

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors

dislocations. It was also proposed that the traps reside in the heterojunction interface, in the AlxGa1–xN barrier layer, and/or at the metal/semiconductor interface according to the gate-drain conductance and capacitance measurements [176]. The trap density of approximately 1012 cm–2 eV–1 and time constant of the order of 1 ls were determined, but the location could not be determined unambiguously. The work of Schaadt and Yu [177] indicates that electrons are trapped at or near the AlxGa1–xN surface according to the dC/dV data. The emission times for these traps can be as long as several hundred ms. Recently, lattice distortions linked to the minimization of the polarization field have been proposed as a likely cause of current lag, in this particular case current collapse [178]. Through an investigation of time decay of current in response to a pulsed voltage applied between the terminals of adjacent ohmic contacts, in the form of a gated transmission line measurement (GTLM) pattern, the authors argue that the time dependence of the current is caused by transient variations of the gate-source and gate-drain resistances, while the channel resistance under the gate remains unaffected. According to these results of the GTLM measurements, the source and drain series resistances are responsible for the current collapse. An increase in the source series resistance should lead to a decrease of current. The same should also cause an increase in the knee voltage, the drain voltage at which the drain current reaches quasisaturation. One plausible explanation for the increase in series resistance during the current transient is the change in strain under and around the gate metal. Increased gate bias from its initial value toward a more negative value causes the electric field in the AlGaN barrier layer to increase, which in magnitude is comparable to the built-in piezoelectric field, several MV cm–1. If the GaN layer underneath the AlGaN layer is not strained, one then surmises that the AlGaN barrier layer undergoes an inplane tensile strain to match its lattice constant to the underlying GaN layer. If so, the change in the electric field with gate bias would not affect strain in the GaN channel. On the other hand, the surface region of the GaN layer may be somewhat strained. Thus, an increase in the electric field due to increasing gate bias, which is comparable to the piezoelectric field, could increase the tensile strain in the AlGaN layer under the gate. This would expand the AlGaN barrier layer laterally. Processes responding to the piezoelectric-induced field, transients of which are slow, could be associated with traps and cause the observed current collapse and lag. In the AlGaN layer under the gate, the gate metal provides a source of electrons in response to the induced piezoelectric charge. Therefore, this region is not expected to contribute to the current collapse [178]. The current lag can be measured as a function of frequency in the RF regime with an appropriate load line. Since the drain current does not follow the input stimulus due to surface traps, the term “lag” has been coined to describe the phenomenon. The surface must be appropriately passivated to avoid this degradation. The effective methods so far have been the use of low-temperature AlN [179] or Si3N4 [180] postgrowth and fabrication passivation layers. Better pinch-off characteristics, lower gate leakage current, reduction of current collapse, and increase of output power have been observed with surface passivation using Si3N4 [181–184]. The alternative

12.3 Modulation-Doped Field Effect Transistors (MODFETs) Fig. 12.50 Output drain current-

voltage characteristics for an AlGaN/GaN MODFET with a 250-Å AlGaN layer and a width of 50 lm. The dotted lines are for VDS < 10 V and the solid lines are for VDS up to 20 V. After Ref. [167].

dielectrics MgO and Sc2O3 also have been studied and may have advantages over Si3N4 since hydrogen with high concentration in typical PECVD Si3N4 layers may deteriorate the long-term reliability [185]. However, whether surface state contributes significantly to current collapse remains unclear. If passivation alone is sufficient to eliminate the current lag, the issue of lattice distortion becomes an interesting one in that it raises the question whether the surface states are involved and if so whether passivation layers alter the strain picture also. The drain characteristics for a GaN MODFET with a 250-Å Si-doped AlGaN layer that exhibit the aforementioned anomalies are shown in Fig. 12.50, where two sets of characteristics are included for the same device. The characteristics indicated by the dashed lines are the result when the maximum VDS is limited to 10 V. On the other hand, the solid lines are for those measured when the maximum VDS is 20 V. By comparing these characteristics, a reduction in drain current for VDS < 8 V is noted. This reduction in current after the application of a high drain voltage is referred to as current collapse. This effect is similar to that reported for GaN MESFETs and is attributed to hot-electron injection and trapping in the GaN buffer layer [186, 187]. As mentioned above, at high drain voltages, electrons are injected into the GaN buffer layer, where they are trapped. This trapped charge depletes the 2 DEG from beneath the active channel and results in a reduction in drain current for subsequent VDS traces. The trapped charge can be released through illumination or thermal emission. The gradual reduction in current for VDS > 10 V (seen in Fig. 12.50) is attributed to self-heating due in part to the sapphire substrate with low thermal conductivity. The effect of SiN passivation on the drain characteristics is shown in Fig. 12.51 for the same device before and after passivation. The drain current went up as a result of the increase in nsh. It can be seen that the reduction in current associated with the current-collapse phenomenon is unaffected. This is consistent with the proposed mechanism for current collapse, i.e., hot electron injection and trapping in the buffer layer without surface involvement.

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors Fig. 12.51 Measured drain char-

acteristics of the device of Fig. 12.50 before and after SiN.

12.3.8

Low-Frequency and High-Frequency Noise Performance

The low-frequency and high-frequency noise characteristics of GaN MODFETs are very important for the microwave applications of these devices. Investigation of the origin of noise is important for understanding the physical processes taking place in the device. Although, GaN MODFETs with excellent microwave performance have been fabricated for high-power and high-temperature applications, there is still little investigation on the noise properties.

12.3.8.1 Low-Frequency Noise

Low frequency noise can be upconverted to high frequencies, limiting the performance of these transistors even in the microwave range. Low-noise electronics for communications necessitates some level of knowledge with respect to the origin of the processes responsible for low-frequency noise in GaN MODFETs. The lowfrequency noise of GaN MODFETs usually exhibits flicker characteristics in the form of 1/f c-dependence with c being close to 1. The dimensionless Hooge parameter, a, is commonly used, as shown as below, where f is frequency, N is the number of carriers, and SI/I2 is the relative spectral density of noise. aˆ

SI c f N: I2

…14†

The first reported Hooge parameter, a, for the GaN MODFET had an approximate value of 10–2 [188]. Later, transistors with low values of a&10–4–10–5 were reported [189–191], where the a parameter is comparable to those for commercial GaAs FETs. These values are much smaller than those in some GaN films, such as a&150 in p-type GaN [192] and a&5–7 in n-type GaN [193], although a recent

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

n-type thick sample with improved structural perfection has a&5 ´ 10–2 [194]. Two mechanisms have been proposed to explain this suppression for GaN MODFET’s low-frequency noise [195]. Levinshtein et al. [190, 196] presumed that a high degree of degeneracy in a GaN MODFET results in the reduction of noise level, where the noise is caused by the occupancy fluctuations of the localized states with an energy-dependent capture cross section. Garrido et al. [189] and Weimann et al. [197] thought that the mobility fluctuation in the channel, as the noise source, is due to the dislocations. The very effective screening of the dislocation by the 2D gas in the MODFET suppresses the noise level. It was demonstrated that the dependence of the Hooge parameter, a, related to dislocations on the number of carrier (ns from 5 ´ 1012 to 1 ´ 1013) in the channel follows a power-law dependence where the exponent is –1 for all samples. Rumyantsev et al. [198] reported that a increases as the carrier concentration increases at highly doped channels (about 6 ´ 1013), although the relationship between a and the carrier concentration obeys the same power law as above for lowly doped channels. The minimum of the Hooge parameter corresponds to nearly the same carrier concentration where the maximum mobility is achieved. The increase of the Hooge parameter at higher concentrations may result from the electron spillover from the 2D channel to a parallel low-mobility conducting channel [198]. On the other hand, the noise contribution of contacts may still be very important. It was found that the total noise power density could be reduced by one order of magnitude (at VGs = 0 V) by improving contact technology [189]. It should also be mentioned that FET channels relying on polarization-induced mobile charge may lead to a reduced Hooge parameter, as the doped cousins would suffer from doping fluctuations. It was observed that the noise level in GaN films is dependent on the structural perfection, or the imperfection as the case may be [192, 194], which is also true for noise performance in GaN MODFETs. The noise level for MODFETs grown on sapphire substrates is one order of magnitude larger than those on SiC substrates [199, 200]. Figure 12.52 displays the typical frequency dependencies of the relative spectral noise density of the drain current fluctuations SI/I2D for the transistors grown on sapphire and SiC substrates [199]. In Fig. 12.52, the noise spectrum for sample Sp2 has a plateau at low frequencies, which is a characteristic feature of the generation-recombination (g–r) noise. Only at very low noise levels (Hooge parameter on the order of 10–4) does the contribution of generation-recombination noise become significant. It was found that g–r noise for devices grown on sapphire has an activation energy DE&0.42 eV [200]. On the contrary, the temperature sensitivity for the noise level of devices grown on SiC is very weak, which is essential for high-temperature applications. Balandin et al. [201] reported DE*0.85 eV for transistors grown on sapphire and DE*0.20–0.36 eV for those grown on SiC. The trap densities for undoped and doped device are 1.1 ´ 1016 cm–3 and 7.1 ´ 1017 cm–3, respectively [202]. Rumyantsev et al. [203] reported a large activation energy DE*0.8–1.0 eV for GaN MODFET and MOS-MODFET (MODFET with SiO2 whose role is prematurely likened to the gate dielectric in Si MOSFETS) grown on insulating 4H-SiC. The analysis in-

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors

Fig. 12.52 Typical frequency dependence of the relative spectral noise

density of drain current fluctuations SI/I2D for devices fabricated in wafers grown on sapphire substrates (Sp1 to Sp3) and from the wafers grown on SiC substrate (SC1), 300 K. The inset shows the Hooge parameter, a, for the samples from different wafers. Wafers Sp1 to Sp3 were grown on sapphire substrates; wafers SC1 to SC3 were grown on SiC substrates. After Ref. [199].

dicates that the traps responsible for the observed g–r noise could originate in the AlGaN barrier layer, which has an estimated trap density of about 5 ´ 1016 cm–3. Gate-voltage dependence of the relative drain current noise spectral density can be utilized to distinguish different noise sources. Baladin [204] reported that the noise spectral density in a GaN MODFET is inversely proportional to the effective gate voltage in a wide range of biases, which means that the measured noise comes from the channel of the device. It was also found that the slope c of the 1/f c noise density spectrum is in the 1.0–1.3 range for all devices and decreases with decreasing (i.e., more negative) gate bias [205]. The linear dependence of the exponent c on the gate bias can be explained by the fact that the band bending due to bias increase will change the number of effective traps and, thus, the time constants contributing to the 1/f' noise. These experimental data support the carrier-density fluctuation model for low-frequency noise rather than mobility fluctuation model. In most studies, the experimental results revealed that the 1/f noise is dominated by the channel noise rather than that originated at contacts or on the surface of the structures [189, 204, 206]. In addition, the noise spectra displayed drastically different behavior in terms of its dependence on the gate voltage in the range of low (VGt £ VG £ 0) and high biases (VG < VGt), where VGt is the threshold voltage [207]. Further investigations are required to distinguish the spatial redistribution of effective noise sources in the transistor channel. Rumyantsev et al. [206] studied the effect of gate leakage current on noise properties for two types of device, i.e., regular MODFET and MOS (metal oxide semi-

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

conductor)-MODFET. It was found that the effect depends on the level of noise in the device. At relatively high level of 1/f noise (a = 10–3), the gate leakage current does not contribute to the output noise. In contrast, for a low level of 1/f noise (a = 10–5–10–4) it has a profound effect. The gate leakage is related to the material quality of the AlGaN and GaN epilayers in different types of MODFETs [206]. As discussed before in this chapter, the strain due to the lattice mismatch between GaN and AlxGa1–xN induces an electric field and significantly changes the carrier distribution near the interface resulting from its highly piezoelectric nature. Balandin et al. [201, 208] designed two GaN/AlxGa1–xN transistors grown on SiC substrates. The same sheet density in the 2D channel is obtained by different doping and Al content, i.e., one has external doping and low Al content, while the other has high Al content without external doping. The results indicate that the noise of the undoped channel is much smaller (up to two orders of magnitude) than that of the doped channel device. This increase was attributed to additional defects generated due to doping addition, which was suggested as leading to increased g–r and flicker noise. When the dust settles, this may be related to doping fluctuations as moderate doping levels, which is certainly the case here, lowers defects, contrary to the aforementioned assertion.

12.3.8.2 High-Frequency Noise

Preliminary investigations of the high-frequency noise performance have shown that GaN MODFETs have respectable microwave noise properties that are nearly comparable to those of AlGaAs/GaAs MODFETs. Table 12.5 displays recent studies of the microwave noise performance for GaN MODFETs. These encouraging results serve to motivate further investigations. Figure 12.53 shows the dependence of the minimum noise figure and associated power gain on (a) frequency, (b) temperature, and (c) drain current [209]. Lu et al. [213] also studied the effect of surface passivation on a high-frequency GaN MODFET with 0.25-lm gate length. Although the gate leakage current was smaller after passivation, the noise measurements after passivation showed that the devices exhibited about 0.2–0.25 dB increase in Fmin. This was mainly due to the 1–1.5 dB decrease of associated power gain attributed to the increase Cgs and

Tab. 12.5 High-frequency noise characterization of GaN MODFETs

Reference

Gate length (lm)

Drain bias (V)

Gate bias (V)

f, (GHz)

Fmin (dB)

Associated gain (dB)

Nguyen et al. [210] Ping et al. [209] Deng et al. [211] Lu et al. [212]

0.15 0.25 2 0.12

6 10 10 10

&–3 –4 –1.5 –4.8

10 5/10 2 8

0.60 0.77/1.06 0.58 0.53

13.5 14.12 14.13 12.1

611

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors Fig. 12.53 Dependence of the minimum

noise figure (Fmin) and associated power gain for a 0.25-lm gate device on a frequency; b temperature (at 10 GHz, for drain and gate biases of 10 and –4 V, respectively); c drain current (at 10 GHz, for a drain bias of 10 V). After Ref. [209].

Cgd. It was concluded that the effect on microwave noise performance is a combination of effects of lower gate leakage current and higher surface dielectric constant. Noise performance of linear two-ports can be described in terms of four parameters – the minimum noise figure, equivalent noise resistance, optimum source resistance, and optimum source reactance. Each of these noise parameters can be expressed in terms of intrinsic device parameters and extrinsic parasitics. Assuming that the spectral noise densities can be expressed as the summation of the sources due to velocity fluctuation and introducing a noise fourpole with an

12.3 Modulation-Doped Field Effect Transistors (MODFETs)

equivalent noise conductance Gn, an equivalent noise resistance Rn, and a complex correlation impedance Zc, one can get Fmin shown as Eq. (15). The detailed MODFET noise modeling can be found in [214]. Fmin ˆ 1 ‡ 2 Gn

  ! Rn 1=2 2 ; Rc ‡ Rc ‡ Gn

…15†

where Rc is the real parts of Zc. The noise and gain performance of the MODFET depend critically upon the device parameters (gate length, carrier mobility, barrier thickness). To date there has been little published work to optimize the GaN transistor geometry for low-noise operation. However, the Fukui equation, shown as Eq. (16), provides a useful semiempirical expression for estimating Fmin at room temperature.   0:5 KF F  gmo …Rg ‡ Rs † Fmin ˆ 10 log 1 ‡ dB ; Ft

…16†

where gmo is the intrinsic transconductance (mS), Rg the gate resistance function of the device geometry (X), Rs the source resistance function of the device geometry (X), and KF the empirical fitting factor. Delegebeaudeauf et al. [215] developed a relationship of KF as a function of the optimum bias current Iopt:  0:5 Iopt KF ˆ 2 Ec Lgmo

…17†

with the cutoff frequency estimated as Ft ˆ vsat =2 pL ; the Fmin can be expressed as (

Fmin

 0:5 ) 4 pFL Iopt …Rg ‡ Rs † dB : ˆ 10 log 1 ‡ vsat Ec L

…18†

The work by Oxley [216] indicates that the above model predictions for minimum noise figure agree well with experimental data up to about 26 GHz. However, the discrepancy between predictions and experiment increases with increasing frequency since the Fukui model does not take into account the gate-to-drain capacitances and the higher-order frequency terms. It was estimated that a very low noise figure of 0.4 dB at 12 GHz might be feasible from a GaN MODFET with an improved Ft, which is dependent on material quality.

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12.4

Heterojunction Bipolar Transistors

Heterojunction bipolar transistors, based on the traditional compound semiconductors and the SiGe/Si system, have progressed to the point where their speed and power performance are very attractive for many applications requiring high performance. Compared to FETs, higher linearity and larger power densities per unit wafer area can be obtained in bipolar transistors. In addition, being a vertical device, larger breakdown voltages can be obtained, allowing larger load resistances to be used that are easier to impedance match. Unlike field effect transistors, their closest competitors, bipolar devices rely on minority carrier transport and, as such, their critical dimension is the vertical one, which is determined by deposition as opposed to lithography. In the silicon world, because of their large current handling capability, bipolar transistors (BJTs) are even used in unison with field effect devices, CMOS, to drive large capacitive loads for even faster performance (BiCMOS). As alluded to earlier, the basic operation of a bipolar transistor involves minority carrier injection in the forward-biased emitter-base junction, minority carrier transfer through the base, and the collection of these same carriers in the reverse-biased collector junction. Increasing the minority carrier injection efficiency while maintaining a high base doping is a basic requirement for transistors designed for high-frequency and highspeed applications. These design criteria are difficult to achieve using a homojunction emitter, but they may be realized through the use of a heterostructure. Two semiconductors having different band gaps and a close lattice match form such a heterostructure. A heterojunction in this structure results from an abrupt change in chemical composition during the epitaxial growth process. The heterojunction bipolar transistor (HBT) was first proposed by Shockley [217] followed by reports [218, 219] pointing out potential advantages over conventional homojunction devices (BJTs). Because the semiconductor material with the wider band gap is used as the emitter, this transistor was initially called the wide band gap emitter transistor. The structure consists of a lightly doped n–-GaN collector, a p+-GaN (or a graded AlGaN for field-aided transport across the base), and an n–-AlGaN emitter layer

Fig. 12.54 Schematic diagram of an AlGaN/GaN heterojunction

bipolar transistor (HBT) with or without a compositionally graded base.

12.4 Heterojunction Bipolar Transistors Fig. 12.55 Schematic band

diagram of an npn HBT under normal bias conditions (forward biased emitter-base junction and reverse-biased collector-base junction). The arrows indicate the carrier motion.

capped with a n+-GaN contact layer. A schematic diagram of what a fabricated device would look like is shown in Fig. 12.54. Shown in Fig. 12.55 is the schematic band diagram of an npn HBT under normal bias conditions (forward-biased emitter-base junction and reverse-biased collector-base junction). The arrows indicate the carrier motion. While the forward-injected electrons do not really experience any barrier, the reverse injected holes from the base experience a large barrier. Consequently, the emitter injection efficiency is high. A good-quality base coupled with a very small thickness increases the base transport factor. In cases where the diffusion length is small and/or the surface recombination is severe, grading Al mole fraction in an AlGaN base down toward the collector causes an electric field in the base, helping the electron motion in an effort to increase the base transport factor and thus the overall current gain. Although the HBT concept was proposed some 50 years ago, only in the last fifteen years have HBTs recorded dramatic advances. These advances were, to a large extent, fueled by improved crystal growth methods, such as molecular beam epitaxy (MBE), metal-organic chemical vapor deposition (MOCVD) and ultrahigh-vacuum chemical vapor deposition (UHVCVD). These technologies provided atomic level precision in layer thickness and doping concentrations with unprecedented control, ensuring improvements in material quality. Physicists and engineers were thus able to explore new device structures, and to verify nonequilibrium transport mechanisms such as ballistic transport in heterostructures. The current gain hEE of an HBT is sensitive to the material quality, and as the quality improves the HBT current gain increases. The highest current gain cutoff frequencies reported for various conventional compound semiconductors are in the range of about 50–200 GHz [220]. GaAs/AlGaAs layers grown by MBE and MOCVD can be commercially obtained for HBT fabrication. Today’s AlGaAs/GaAs digital, analog, and microwave IC chips with more than 104 devices are produced in three-inch production lines. The high-speed performance of bipolar transistors is represented by the currentgain, cutoff frequency fT, and the maximum oscillation frequency fmax. High-end commercial Si BJTs with polysilicon emitters exhibit fT of 20–30 GHz and fmax of 15–25 GHz. For Si/SiGe/Si bipolar transistors, the reported fT is 116 GHz [221] or somewhat larger, and the reported fmax is 120 GHz [222] or somewhat larger.

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12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors

GaN-based electronic devices such as high-power and heat-tolerant heterojunction bipolar transistors (HBTs) can be important components of integrated systems designed for high-frequency and high-speed applications, for example, in satellites and all-electric aircraft. As mentioned earlier, GaN HBTs could lend themselves to high-power operation with larger operating voltages and better linearity than those that can be attained by FETs. The basic operation of HBTs, involving minority carrier injection in the forward-biased emitter-base junction, minority carrier transfer through the base, and the minority carrier collection in the reverse-biased collector junction, also lead to high-speed performance, which is imperative. This high-speed performance is represented by the current-gain, cutoff frequency fT, and the maximum oscillation frequency fmax [219]. The latter parameter is critically dependent on base resistance, which is a problem for GaN, which is known to suffer from low hole concentration in p-type layers, about 1018 cm–3. In addition, the deep nature of the most commonly and successfully used dopant, Mg, causes temperature-dependent ionization. This leads to a temperature-dependent base resistance, which may actually drop with increasing temperature even though the hole mobility would decrease somewhat. The first heterojunction bipolar transistor utilizing nitride semiconductors was a hybrid in that both GaN and SiC technologies were used. A GaN/SiC HBT with high current gain has been reported by Pankove et al. [223]. The energy band gap of GaN and SiC are 3.4 eV and 2.9 eV, respectively. Both GaN and SiC have high thermal conductivities, the latter being 1.3 W cm–1 K–1 for GaN (higher in GaN with higher quality, as about 2.3 W cm–1 K–1) and for SiC 4.0 W cm–1 K–1 (lower for high-resistivity SiC). Both materials are reasonably closely lattice matched (in the greater scheme of things). In the HBT by Pankove et al., the n-GaN emitter, 0.57 lm thick, had an unintentional doping level 1 ´ 1018 cm–3 (grown by MBE), and the 6-H p-SiC base, 0.2 lm thick, had a doping level 9 ´ 1018 cm–3. The SiC substrate with n-type doping of 1.8 ´ 1018 cm–3 formed the collector. The GaN layer was etched in a CCl2F2 plasma in unwanted regions during device fabrication. High doping concentrations in the base as well as in the collector led to negligible early voltage and very small breakdown voltage. The common collector configuration used to get at the current gain in the light of a leaky collector junction relied on differential current gain, which was very high. Using appropriate parameters, one can calculate an emitter injection efficiency of 0.999999. Moreover, using a mobility of 110 cm2 V–1s–1 and a lifetime of 5 ls, the diffusion length and the base transport factor were calculated to be 37.7 lm, and 0.999987 (both for SiC), respectively [223]. The calculated parameters lead to a current gain of 80,409, which is very close to experimental observations. Base transit time sB, together with emitter transit time, and the transit time at the junction, provides the total transit time in an HBT. The transit time has been widely investigated for well-known and well-established bipolar transistors, including Si homojunction bipolar transistors [224, 225], heterojunction SiGe HBTs [226, 227] and AlGaAs/GaAs HBTs [228]. These studies suggested that, for the sake of lower base resistance, the base doping concentration of an HBT must be increased. However, such an increase accompanies a very minimal increase in the

12.5 Conclusions

built-in potential and a decrease in the carrier mobility in the base. The increased built-in potential lowers the base transit time sB. On the other hand, the decreased mobility increases the base transit time sB. Nonuniform doping and the compositional grading of the base also influence the base transit time sB. Numerical simulations in order to determine the room-temperature dependence of the base transit time on various parameters, such as base doping and base compositional grading of Npn GaN/InxGa1–xN HBTs were undertaken some years ago [229]. Additional simulations using a compact simulator of the DC and cutoff frequency performance of GaN/AlGaN have also been performed [230, 231]. As in any calculation, the results depend on the parameters used. In HBTs based on GaN, the major problem is one of a good estimate for the base diffusion length, which critically depends on the layer quality. Other issues include collector breakdown voltage, heterojunction band discontinuities and surface states on the extended regions of the base (beyond the emitter region). Generally speaking, the minority carrier hole diffusion length in GaN would be smaller than conventional compound semiconductors. In very high-quality GaN templates, this diffusion length of holes in n-type material was measured to be about 1 lm on the nitrogen face, which represents the early stages of growth on sapphire and is more defective, and 4 lm on the Ga-face which is some 200 lm away from the initial substrate epitaxial layer interface. Likewise, the minority carrier lifetime ranged from 50 ns near the N-face to 800 ns near the Ga-face [232]. These numbers are really sensationally outstanding, which call for extreme caution, as additional measurements must be made to gain confidence in the results. Most of the conclusions of Refs. [230, 231] are complementary and predictable. Basically, the current gain is limited by carrier transport across the base, the cutoff frequency is limited by the base transit time, which can be enhanced by using a graded junction, and graded base would reduce the transit time. Use of pnp HBTs, to circumvent the high base resistance plaguing the npn device, runs into the hole-transport limitations across the n-type base. As expected, the authors of Ref. [230] also argue that the polarization effects are unlikely to adversely affect the performance of HBTs, current gains in the range of 200–2000 may be possible at room temperature, and the cutoff frequency appears to be around 30 GHz. Despite the odds, experimentalists have been charging ahead. First reports indicated current gains of about 3 [233, 234], and 6 with an early voltage of about 400 V [235].

12.5

Conclusions

Modulation-doped field effect transistors (MODFETs) based on the GaN material system have been discussed. Unlike the GaAs-based MODFETs on (100) surfaces, polarization-induced charge in the GaN-based devices on the polar (0001) surfaces is quite large. Consequently, even undoped structures contain sheet electron concentrations in the 1013 cm–2 region. An indepth discussion of polarization effects

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for normal and inverted MODFETs has been presented. Donor-like surface defects most likely provide the charge. Experimental data and theoretical results have been provided on the particulars of the interface charge in relation to parameters such as the AlGaN mole fraction and thickness. In addition, calculation results for electron distribution and current-voltage characteristics of MODFETs have been presented. On the experimental side of MODFET performance, CW power levels of about 22.9 W at 9 GHz have been reported in devices with four 1-mm gate periphery devices in a single-stage power-combining scheme with an associated power-added efficiency of 37%. A minimum noise figure of 0.85 dB with an associated gain of 11 dB at 10 GHz has been obtained. A discussion of the current collapse of lag occurring in GaN-based MODFETs has been presented. In closing, GaN-based MODFETs have made great strides and are continuing to do so despite the less than ideal materials properties. Anomalies in the current-voltage characteristics at low and high frequencies observed in these devices are attributed to traps in the structure, surface states, and slow trapping processes associated with the field-induced lateral extension of the strain near the gate. It may be only a matter of time for inclusion of these devices in systems. Finally, a short discussion of heterojunction bipolar transistors, the state of which is really in its infancy, has been provided.

12.6

Acknowledgments

This work was supported by the Air Force Office of Scientific Research, the Office of Naval Research, and the National Science Foundation and monitored by G. L. Witt and D. Johnstone (AFOSR) C. E. Wood, Y. S. Park and M. Yoder (ONR), and Verne Hess and U. Varshney (NSF). The author appreciates fruitful discussions with and the assistance of Profs. Aldo Di Carlo, Paolo Lugli, W. Lambrecht, M. S. Shur, F. Bernardini, R. Cingolani, D. Rode, C. Kurdak, and D. Huang, and Drs. Fabio Sacconi, C. Nguyen, X. Nguyen, W. Walukiewicz, J. Albrecht, and O. Ambacher. Many of these individuals also provided many of their reprints, and preprints. The MODFET model inclusive of polarization charge was developed by Prof. A. Di Carlo and his colleagues at the University of Rome. Finally, the authors would like to thank their colleagues and associates for their contributions throughout the evolution of much of the work reported here. Prof. M. Z. Iqbal and a VCU student, J. Spradlin, read the manuscript very carefully.

12.7 References

12.7

References 1 2 3 4

5 6 7 8

9 10

11 12 13 14

15

16 17

H. Morkoç, Nitride Semiconductors and Devices (Springer, Heidelberg, 1999). S. N. Mohammad andH. Morkoç, Prog. Quantum. Electron. 20, 361 (1996). S. N. Mohammad, A. Salvador, and H. Morkoç, Proc. IEEE 83, 1306 (1995). H. Morkoç, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, and M. Burns, J. Appl. Phys. Rev. 76, 1363 (1994). S. T. Strite and H. Morkoç, J. Vac. Sci. Technol. B 10, 1237 (1992). O. Ambacher, J. Phys. D: Appl. Phys. 31, 2653 (1998). S. J. Pearton, J. C. Zolper, R. J. Shul, and F. Ren, J. Appl. Phys. 86, 1 (1999). M. T. Duffy, C. C. Wang, G. D. O’Clock, S. H. McFarlane III and P.J. Zanzucchi, J. Electron. Mater. 2, 359 (1973). M. Razeghi and A. Rogalski, J. Appl. Phys. 79, 7433 (1996). G. Y. Xu, A. Salvador, W. Kim, Z. Fan, C. Lu, H. Tang, H. Morkoç, G. Smith, M. Estes, B. Goldenberg, W. Yang, and S. Krishnankutty, Appl. Phys. Lett. 71, 2154 (1997). I. J. Fritz and T. J. Drummond, Electron. Lett. 31, 68 (1995). S. Nakamura, T. Mukai, and M. Senoh, Appl. Phys. Lett. 64, 1687 (1994). For a review see: H. Morkoç and S. N. Mohammad, Sci. Mag. 267, 51–55 (1995). For a review see: H. Morkoç and S. N. Mohammad, Light Emitting Diodes, in Wiley Encyclopedia of Electrical Engineering and Electronics Engineering, J. Webster (ed.) (John Wiley and Sons, New York 1999). S. Nakamura, M. Senoh, N. Nagahama, N. Iwara, T. Yamada, T. Matsushita, H. Kiyoku, Y. Sugimoto, T. Kozaki, H. Umemoto, M. Sano, and K. Chocho, Jpn. J. Appl. Phys. 38, L1578 (1997). H. Morkoç, IEEE J. Selec. Top. Quantum Electron. 4, 537–549 (1998). J. D. Brown, Zhonghai Yu, J. Matthews, S. Harney, J. Boney, J. F. Schetzina, J. D. Benson, K. W. Dang, C. Terrill, Thomas Nohava, Wei Yang, and Subash Krishnankutty, MRS Internet Journal, http://nsr.mij.mrs.org/4/9/

18 19 20

21 22 23

24

25

26

27

28

29

30

31 32

H. Temkin, Texas Tech University, private communication. J. C. Campbell, University of Texas at Austin, Private communication. J. Schetzina et al. in Proceedings of the International Conference on Silicon Carbide and Related Materials, October 10– 15, 1999, Research Triangle Park, NC, USA. B. K. Ridley, J. Appl. Phys. 84, 4020 (1998). U. V. Bhapkar and M. S. Shur, J. Appl. Phys. 82, 1649 (1997). J. Kolnik, I. H. Oguzman, K. F. Brennan, R. Wang, P. P. Ruden, and Y. Wang, J. Appl. Phys. 78, 1033 (1995). H. Morkoç, Beyond SiC! III-V Nitride Based Heterostructures and Devices, in SiC Materials and Devices, Y. S. Park (ed.), Willardson and Beer Series, Willardson and Weber (eds.) 52, Chap. 8, pp. 307–394 (Academic Press, 1998). S. T. Sheppard, K. Doverspike, W. L. Pribble, S. T. Allen, J. W. Palmour, L. T. Kehias, and T. A. Jenkins, IEEE Electron. Dev. Lett. 20, 161 (1999). Y.-F. Wu, B. P. Keller, P. Fini, S. Keller, T. J. Jenkins, L. T. Kehias, S. P. DenBaars, and U. K. Mishra, IEEE Electron. Dev. Lett. 19, 50 (1998). A. T. Ping, Q. Chen, J. W. Yang, M. A. Khan, and I. Adesida, IEEE Electron. Dev. Lett. 19, 54 (1998). G. J. Sullivan, M. Y. Chen, J. A. Higgins, J. W. Yang, Q. Chen, R. L. Pierson, and B. T. McDermott, IEEE Electron. Dev. Lett. 19, 198 (1998). S. Binari, J. M. Redwing, G. Kelner, and W. Kruppa, Electron. Lett. 33, 242 (1997). M. Micovic, A. Kurdoghlian, P. Janke, P. Hashimoto, D. W. S. Wong, J. S. Moon, L. McCray, and C. Nguyen, IEEE Trans. Electron. Dev. 48, 591 (2001). N. Nguyen and C. Nguyen (HRL Laboratories), private communication. T. Henderson, M. I. Aksun, C. K. Peng, H. Morkoç, P. C. Chao, P. M. Smith, K. H. G. Duh and L. F. Lester, IEEE Electron. Dev. Lett. 7, 649 (1986).

619

620

12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors 33

34

35

36

37 38

39

40 41

42

43

44

45

46

47

R. J. Molnar, W. Goetz, L. T. Romano, and N. M. Johnson, J. Cryst. Growth 178, 147 (1997). S. Yamaguchi, M. Kariya, S. Nitta, T. Takeuchi, C. Wetzel, H. Amano, and I. Akasaki, J. Appl. Phys. 85, 7682 (1999). D. C. Look, D. C. Reynolds, J. W. Hemsky, J. R. Sizelove, R. L. Jones, and R. J. Molnar, Phys. Rev. Lett. 79, 2273 (1997). D. Huang, F. Yun, P. Visconti, M. A. Reshchikov, D. Wang, H. Morkoç, D. L. Rode, L. A. Farina, Ç. Kurdak, K. T. Tsen, S. S. Park, and K. Y. Lee, Solid-State Electron. 45, 711 (2001). S. Nakamura, T. Mukai, and M. Senoh, J. Appl. Phys. 71, 5543 (1992). M. E. Lin, B. Sverdlov, G. L. Zhou, and H. Morkoç, Appl. Phys. Lett. 62, 3479 (1993). H. M. Ng, D. Doppalapudi, T. D. Moustakas, N. G. Weimann, and L. F. Eastman, Appl. Phys. Lett. 73, 821 (1998). D. C. Look and J. R. Sizelove, Phys. Rev. Lett. 82, 1237 (1999). N. G. Weimann, L. F. Eastman, D. Doppalapudi, H. M. Ng, and T. D. Moustakas, J. Appl. Phys. 83, 3656 (1998). Z. Q. Fang, D. C. Look, W. Kim, Z. Fan, A. Botchkarev, and H. Morkoç, Appl. Phys. Lett. 72, 2277 (1998). K. Wook, A. E. Botohkarev, H. Morkoç, Z. Q. Fang, D. C. Look, and D. J. Smith, J. Appl. Phys. 84, 6680 (1998). B. Heying, I. Smorchkova, C. Poblenz, C. Elsass, P. Fini, S. DenBaars, U. Mishra, and J. S. Speck, Appl. Phys. Lett. 77, 2885 (2000). M. J. Manfra, L. N. Pfeiffer, K. W. West, H. L. Stormer, K. W. Baldwin, J. W. P. Hsu, D. V. Lang, and R. J. Molnar, Appl. Phys. Lett. 77, 2888 (2000). J. Cui, A. Sun, M. Reshichkov, F. Yun, A. Baski, and H. Morkoç, MRS Internet Journal – The URL for the front page is http://nsr.mij.mrs.org/5/7/. J. A. Powell, D. J. Larkin, and A. J. Trunek, Use of Gaseous Etching for the Characterization of Structural Defects in Silicon Carbide Single Crystals, Silicon Carbide, III-Nitrides, and Related Materials, G. Pensl, H. Morkoç, B. Monemar, and E. Janzen (eds.) 264–268, 421–424 (Trans. Tech. Publications, 1998).

48

49

50 51 52 53

54 55

56 57 58 59

60

61

62 63

64

65 66

E. J. Tarsa, B. Heying, X. H. Wu, P. Fini, S. P. DenBaars, and J. S. Speck, J. Appl. Phys. 82, 5472 (1997). B. Heying, R. Averbeck, L. F. Chen, E. Haus, H. Riechert, and J. S. Speck, J. Appl. Phys. 88, 1855 (2000). N. Grandjean, CHREA-CNRS, Valbonne, France private communication. D. L. Rode, Semicond. Semimet. 10, 1– 90 (1975). K. Seeger, Semiconductor Physics, 2nd edn. (Springer, Berlin, 1982). V. W. L. Chin, T. L. Tansley, and T. Osotchan, J. Appl. Phys. 75, 7365 (1994). D. L. Rode and D. K. Gaskill, Appl. Phys. Lett. 66, 1972 (1995). S. C. Jain, M. Willander, J. Narayan, and R. Van Overstraeten, J. Appl. Phys. 87, 963 (2000). B. K. Ridley, B. E. Foutz, and L. F. Eastman, Phys. Rev. B 61, 1682 (2000). S. Dhar and S. Ghosh, J. Appl. Phys. 86, 2668 (1999). V. W. L. Chin, T. L. Tansley, and T. Osotchan, J. Appl. Phys. 75, 7365 (1994). D. C. Look, D. C. Reynolds, J. W. Hemsky, J. R. Sizelove, R. L. Jones, and R. J. Molnar, Phys. Rev. Lett. 79, 2273 (1997). M. G. Cheong, K. S. Kim, C. S. Oh, N. W. Namgung, G. M. Yang, C. H. Hong, K. Y. Lim, E. K. Suh, K. S. Nahm, H. J. Lee, D. H. Lim, and A. Yoshikawa, Appl. Phys. Lett. 77, 2557 (2000). W. Götz, L. T. Romano, J. Walker, N. M. Johnson, and R. J. Molnar, Appl. Phys. Lett. 72, 1214 (1998). R. P. Joshi, Appl. Phys. Lett. 64, 223 (1994). P. Visconti, K. M. Jones, M. A. Reshchikov, R. Cingolani, H. Morkoç, and R. J. Molnar, Appl. Phys. Lett. 77, 3532 (2000). H. M. Ng, D. Doppalapudi, T. D. Moustakas, N. G. Weimann, and L. F. Eastman, Appl. Phys. Lett. 73, 821 (1998). Q. S. Zhu and N. Sawaki, Appl. Phys. Lett. 76, 1594 (2000). D. Huang, F. Yun, P. Visconti, M. A. Reshchikov, D. Wang, H. Morkoç, D. L. Rode, L. A. Farina, Ç. Kurdak, K. T. Tsen, S. S. Park, and K. Y. Lee, Solid-State Electron. 45, 711 (2001).

12.7 References 67

68

69

70 71 72

73

74

75

76 77 78 79

80

81

82 83

P. Visconti, K. M. Jones, M. A. Reshchikov, F. Yun, R. Cingolani, H. Morkoç, S. S. Park, and K. Y. Lee, Appl. Phys. Lett. 77, 3743 (2000). T. Azuhata, T. Sota, K. Suzuki, and S. Nakamura, J. Phys.: Condens. Matter. 7, L129 (1995). M. E. Lin, Z. Ma, F. Y. Huang, Z. F. Fan, L. H. Allen, and H. Morkoç, Appl. Phys. Lett. 64, 1003 (1994). L. Hsu and W. Walukiewicz, J. Appl. Phys. 89, 1783 (2001). W. Walukiewicz, private communication. Y. J. Wang, R. Kaplan, H. K. Ng, K. Doverspike, D. K. Gaskill, T. Ikedo, I. Akasaki, and H. Amano, J. Appl. Phys. 79, 8007 (1996). Özgür Aktas, W. Kim, Z. Fan, S. N. Mohammad, A. Botchkarev, A. Salvador, B. Sverdlov, and H. Morkoç, Electron. Lett. 31, 1389–1390 (1995). S. C. Binari, J. M. Redwing, G. Kelner, and W. Kruppa, Electron. Lett. 33, 242 (1997). H. Morkoç, A. Di Carlo, and R. Cingolani, Solid-State Electron. 46, 157–202 (2002); Hadis Morkoç, Aldo Di Carlo, and R. Cingolani, GaN-Based Modulation Doped FETs in Low-dimensional Nitride Semiconductors, B. Gil (ed.), (Oxford University Press, Oxford, UK) in press. H. Morkoç, R. Cingolani, and B. Gil, Solid-State Electron. 43,1909 (1999). L. Hsu and W Walukiewicz, Phys. Rev. B 56, 1520 (1997). L. Hsu and W. Walukiewicz, Appl. Phys. Lett. 73, 339 (1998). I. P. Smorchkova, C. R. Elsass, J. P. Ibbetson, R. Vetury, B. Heying, P. Fini, E. Haus, S. P. DenBaars, J. S. Speck, and U. K. Mishra, J. Appl. Phys. 86, 4520 (1999). M. S. Shur, A. D. Bykhovsky, and R. Gaska, Solid-State Electron. 44, 205 (2000). P. M. Asbeck, E. T. Yu, S. S. Lau, W. Sun, X. Dang, and C. Shi, Solid-State Electron. 44, 211 (2000). L. Hsu and W. Walukiewicz, Appl. Phys. Lett. 73, 339 (1998). M. S. Shur, A. D. Bykhovsky, and R. Gaska, Solid-State Electron. 44, 205 (2000).

84 85

86 87

88

89 90

91

92

93 94

95

96

97

R. Oberhuber, G. Zandler, and P. Vogl, Appl. Phys. Lett. 73, 818 (1998). N. Maeda, T. Nishida, N. Kobayashi, and M. Tomizawa, Appl. Phys. Lett. 73, 1856 (1998). W. Walukiewicz, Appl. Phys. Lett. 54, 2094 (1989). A. D. Bykhovski, V. V. Kaminski, M. S. Shur, Q. C. Chen, and M. A. Khan, Appl. Phys. Lett. 68, 818 (1996). F. Bernardini, V. Fiorentini, and D. Vanderbilt, Phys. Rev. B 56, R10024 (1997). For a review see R. Resta, Rev. Mod. Phys. 66, 899 (1994), and references therein. O. Ambacher, J. Smart, J. R. Shealy, N. G. Weimann, K. Chu, M. Murphy, W. J. Schaff, L. F. Eastman, R. Dimitrov, L. Wittmer, M. Stutzmann, W. Rieger, and J. Hilsenbeck, J. Appl. Phys. 85, 3222 (1999). O. Ambacher, B. Foutz, J. Smart, J. R. Shealy, N. G. Weimann, K. Chu, M. Murphy, A. J. Sierakowski, W. J. Schaff, L. F. Eastman, R. Dimitrov, A. Mitchell, and M. Stutzmann, J. Appl. Phys. 87, 334 (2000). I. P. Smotchkova, C. R. Elsass, J. P. Ibbetson, R. Vetury, B. Heying, P. Fini, E. Haus, S. P. DenBaars, J. S. Speck, and U. K. Mishra, J. Appl. Phys. 86, 4520 (1999). B. Daudin, J. L. Rouviere, and M. Arley, Appl. Phys. Lett. 69, 2480 (1996). P. Vermaut, P. Ruterana, G. Nouet, A. Salvador, and H. Morkoç, Philos. Mag. A 75, 239 (1997). V. Potin, P. Ruterana, G. Nouet, A. Salvador and H. Morkoç, in Proc. of Gallium Nitride and Related Materials II Symposium, C. R. Abernathy, H. Amano, and J. C. Zolper (eds.) 468, 323–328 (Materials Research Society, Pittsburgh, PA, USA, 1997). G. A. Martin, S. Strite, A. Botchkarev, A. Agarwal, A. Rockett, H. Morkoç, W. R. L. Lambrecht, and B. Segall, Appl. Phys. Lett. 65, 610 (1994). G. A. Martin, Ph. D. Thesis, Semiconductor electronic band alignment at heterojunctions of wurtzite AlN, GaN and InN, Department of Physics, University of Illinois (1996).

621

622

12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors 98 G. A. Martin, A. Botchkarev, A. Agar-

99 100

101

102

103

104 105

106

107

108

109

110

wal, A. Rockett, and H. Morkoç, Appl. Phys. Lett. 68, 2541 (1996). F. Bernardini and V. Fiorentini, Phys. Rev. B 57, 1 (1998). M. Farahmand, C. Garetto, E. Bellotti, K. F. Brennan, M. Goano, E. Ghillino, G. Ghione, J. D. Albrecht, and P. P. Ruden, IEEE Trans. Electron Devices 48, 535 (2001) and references therein. H. Morkoç, H. Ünlü, and G. Ji, Fundamentals and Technology of MODFETs, Vols. I and II (Wiley and Sons, Chichester, West Sussex, UK, 1991). F. Sacconi, A. Di Carlo, P. Lugli, and H. Morkoç, IEEE Trans. Electron Devices 48, 450 (2001). G. Bastard, in Wave Mechanics Applied to Semiconductor Heterostructures (Edition de Physique, Paris, France, 1987). R. Oberhuber, G. Zandler, and P. Vogl, Appl. Phys. Lett. 73, 818 (1998). A. Di Carlo, S. Pescetelli, M. Paciotti, P. Lugli, and M. Graf, Solid State Commun. 98, 803 (1996). A. Di Carlo, Phys. Stat. Sol. 217, 703 (2000); F. Della Sala, A. Di Carlo, P. Lugli, F. Bernardini, V. Fiorentini, R. Scholz, and J. M. Jancu, Appl. Phys. Lett. 74, 2002 (1999); A. Di Carlo, F. Della Sala, P. Lugli, V. Fiorentini, and F. Bernardini, Appl. Phys. Lett. 76, 3950 (2000). R. Cingolani, A. Botchkarev, H. Tang, H. Morkoç, G. Coli, M. Lomascolo, A. Di Carlo, F. Della Sala, and P. Lugli, Phys. Rev. B 61, 2711 (2000). A. Bonfiglio, M. Lomascolo, G. Traetta, R. Cingolani, A. Di Carlo, F. Della Sala, P. Lugli, A. Botchkarev, and H. Morkoç, J. Appl. Phys. 87, 2289 (2000). P. Lugli, M. Paciotti, E. Calleja, E. Munoz, J. J. Sanchez-Rojas, F. Dessenne, R. Fauquembergue, J. L. Thobel, and G. Zandler, in Pseudomorphic HEMTs: Technology and Applications, R. L. Ross, S. Swensson and P. Lugli (eds.) (Kluwer Press, Dordrecht, 1996), pp. 141–163. V. Fiorentini, F. Bernardini, F. Della Sala, A. Di Carlo, and P. Lugli, Phys. Rev. B 60, 8849 (1999).

111 A. Trellakis, A. T. Halick, A. Pacelli,

112

113

114

115

116

117 118 119 120 121

122

123

124

125

126

127

and U. Ravaioli, J. Appl. Phys. 81, 7880 (1997). K. Lee, M. S. Shur, T. J. Drummond and H. Morkoç, IEEE Trans. Electron. Devices 31, 29 (1984). E. T. Yu, G. J. Sullivan, P. M. Asbeck, C. D. Wang, D. Qiao, and S. S. Lau, Appl. Phys. Lett. 71, 2794 (1997). P. Ramvall, Y. Aoyagi, A. Kuramata, P. Hacke, and K. Horino, Appl. Phys. Lett. 74, 3866 (1999). R. Gaska, J. W. Yang, A. Osinsky, A. D. Bykhovski, and M. S. Shur, Appl. Phys. Lett. 71, 3673 (1997). R. Gaska, J. W. Yang, A. Osinsky, A. D. Bykhovski, M. S. Shur, V. V. Kaminski, and S. M. Soloviov, Appl. Phys. Lett. 72, 64 (1998). B. Carnez, A. Cappy, et al., J. Appl. Phys. 51, 784 (1980). P. A. Sandborn et al., IEEE Trans. Electron Devices 34, 985 (1987). C. M. Snowden et al., IEEE Trans. Electron Devices 36, 1564 (1989). H. Morkoç, Naval Res. Rev. 51, 28 (1999). M. J. Murphy, B. E. Foutz, K. Chu, et al., MRS Internet J. Nitride Semicond. Res. 4S1, G8.4 (1999). Y. F. Yu, B. P. Keller, S. Keller, D. Kapolnek, P. Kozodoy, S. P. DenBaars, and U. K. Mishra, Appl. Phys. Lett. 69, 1438 (1996). C. Weitzel, L. Pond, K. Moore, and M. Bhatnagar, Mater. Sci. Forum 264–268, 907–912 (1998). K. Suzue, S. N. Mohammad, Z. F. Fan, W. Kim, Ö. Aktas, A. E. Botchkarev, and H. Morkoç, J. Appl. Phys. 80, 4467 (1996). S. N. Mohammad, Zhifang Fan, A. E. Botchkarev, W. Kim, Ö. Aktas, A. Salvador, and H. Morkoç, Electron. Lett. 32, 598 (1996). Ö. Aktas, W. Kim, Z. Fan, S. N. Mohammad, A. Botchkarev, A. Salvador, B. Sverdlov, and H. Morkoç, Electron. Lett. 31, 1389 (1995). Ö. Aktas, Z. Fan, A. Botchkarev, M. Roth, T. Jenkins, L. T. Kehias, and H. Morkoç, IEEE Electron. Device Lett. 18, 293 (1997).

12.7 References 128 P. Hacke, T. Detchprohm, K. Hiramat-

129

130

131

132

133

134 135

136

137 138

139

140

141

142

143

144

su, and N. Sawaki, Appl. Phys. Lett. 63, 2676 (1993). T. G. G. Maffeis, M. C. Simmonds, S. A. Clark, F. Peiro, P. Haines, and P. J. Parbrook, J. Appl. Phys. 92, 3179 (2002). S. C. Binari, H. B. Dietrich, G. Kelner, L. B. Roland, K. Doverspike, and D. K. Gaskill, Electron. Lett. 30, 909 (1994). P. J. Hartlieb, A. Roskowski, R. F. Davis, W. Platow, and R. J. Nemanich, J. Appl. Phys. 91, 732 (2002). X. A. Cao, S. J. Pearton, G. Dang, A. P. Zhang, F. Ren, and J. M. Van Hove, Appl. Phys. Lett. 75, 4130 (1999). B. J. Zhang, T. Egawa, G. Y. Zhao, H. Ishikawa, M. Umeno, and T. Jimbo, Appl. Phys. Lett. 79, 2567 (2001). U. Karrer, O. Ambacher, and M. Stutzmann, Appl. Phys. Lett. 77, 2012 (2000). M. A. Khan, J. M. Van Hove, J. N. Kuznia, and D. T. Olson, Appl. Phys. Lett. 58, 2408–2410 (1991). M. R. H. Khan, H. Nakayama, T. Detchprohm, K. Hiramatsu, and N. Sawaki, Solid-State Electron. 41, 259–266 (1997). J. S. Foresi and T. D. Moustakas, Appl. Phys. Lett. 62, 2859 (1993). M. A. Khan, J. N. Kuznia, A. R. Bhattarai, and D. T. Olson, Appl. Phys. Lett. 62, 1786 (1993). M. E. Lin, Ma, F. Y. Huang, Z. Fan, L. Allen, and H. Morkoç, Appl. Phys. Lett. 64, 1003 (1994). Y. Wu, W. Jiang, B. Keller, S. Keller, D. Kapolnek, S. DenBaars, and U. Mishra, Proc. Solid-State Electron. 41, 75–78 (1997). Z. Fan, S. N. Mohammad, W. Kim, Ö. Aktas, A. E. Botchkarev, and H. Morkoç, Appl. Phys. Lett. 68, 1672–1674 (1996). S. Ruvimov, Z. Liliental-Weber, J. Washburn, K. J. Duxstad, E. E. Haller, S. N. Mohammad, Z. Fan, and H. Morkoç, Appl. Phys. Lett. 69, 1556 (1996). J. K. Ho, C. S. Jong, C. C. Chiu, C.-N. Huang, and K. K. Shih, Appl. Phys. Lett. 74, 1275 (1999). J. K. Ho, C. S. Jong, C. C. Chiu, C.-N. Huang, K. K. Shih, L. C. Chen, F. R. Chen, and J. J. Kai, J. Appl. Phys. 86, 4491 (1999).

145 L. C. Chen, J. K. Ho, C. S. Jong, C. C.

146

147

148 149

150

151 152

153

154

155

156

157

158

159

160

161

Chiu, K. K. Shih, F. R. Chen, J. J. Kai, and L. Chang, Appl. Phys. Lett. 76, 3703 (2000). Y. Koide, T. Maeda, T. Kawakami, S. Fujita, T. Uemura, N. Shibata, and M. Murakami, J. Electron. Mater. 28, 341 (1999). C. F. Chu, C. C. Yu, Y. K. Wang, J. Y. Tsai, F. I. Lai, and S. C. Wang, Appl. Phys. Lett. 77, 3423 (2000). H. W. Jang, W. Urbanek, M. C. Yoo, and J. L. Lee, Appl. Phys. Lett. 80, 2937 (2002). B. A. Hull, S. E. Mohney, H. S. Venugopalan, and J. C. Ramer, Appl. Phys. Lett. 76, 2271 (2000). D. Qiao, L. S. Yu, S. S. Lau, J. Y. Lin, H. X. Jiang, and T. E. Haynes, J. Appl. Phys. 88, 4196 (2000). J. K. Kim, H. W. Jang, C. Jeon, and J. L. Lee, Curr. Appl. Phys. 1, 385 (2001). J. K. Kim, K. J. Kim, B. Kim, J. N. Kim, J. S. Kwak, Y. J. Park, and J. L. Lee, J. Electron. Mater. 30, 129 (2001). J. Sun, K. A. Rickert, J. M. Redwing, A. B. Ellis, F. J. Himpsel, and T. F. Kuech, Appl. Phys. Lett. 76, 415 (2000). J. K. Kim, J. L. Lee, J. W. Lee, Y. J. Park, and T. Kim, J. Vac. Sci. Technol. B 17, 497 (1999). B. P. Luther, J. M. DeLuca, S. E. Mohney, and R. F. Karlicek Jr., Appl. Phys. Lett. 71, 3859 (1997). L. Zhou, W. Landford, A. T. Ping, I. Adesida, J. W. Yang, and A. Khan, Appl. Phys. Lett. 76, 3451 (2000). Y. L. Li, E. F. Schubert, J. W. Graff, A. Osinsky, and W. F. Schaff, Appl. Phys. Lett. 76, 2728 (2000). A. P. Zhang, B. Luo, J. W. Johnson, F. Ren, J. Han, and S. J. Pearton, Appl. Phys. Lett. 79, 3636 (2001). T. Gessmann, Y. L. Li, E. L. Waldron, J. W. Graff, E. F. Schubert, and J. K. Sheu, Appl. Phys. Lett. 80, 986 (2002). Zhifang Fan, Changzhi, Lu, A. Botchkarev, H. Tang, A. Salvador, Ö. Aktas, W. Kim, and H. Morkoç, Electron. Lett. 33, 814 (1997). M. E. Lin, S. Strite, A. Agarwal, A. Salvador, G. L. Zhou, N. Teraguchi, A. Rockett and H. Morkoç, Appl. Phys. Lett. 62, 702 (1993).

623

624

12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors 162 P. Ruterana, P. Vermaut, G. Nouet, A.

163

164

165

166

167

168

169

170 171 172

173

174

Salvador, and H. Morkoç, MRS Internet J. Nitride Semicond. Res. 2, 42 (1997)). C. D. Lee, V. Ramachandran, A. Sagar, R. M. Feenstra, D. W. Greve, W. L. Sarney, L. Salamanca-Riba, D. C. Look, Bai Song Bai, W. J. Choyke, and R. P. Devaty, IEEE. J. Electron. Mater. 30, 162 (2001). J. A. Powell, D. J. Larkin, and A. J. Trunek, in Silicon Carbide, III-Nitrides, and Related Materials, G. Pensl, H. Morkoç, B. Monemar and E. Janzen (eds.) 264– 268, 421–424 (Trans. Tech. Publications, 1998). J. A. Powell, D. J. Larkin, P. G. Neudeck, J. W. Yang and P. Pirouz, Silicon Carbide and Related Materials, M. G. Spencer, R. P. Devaty, J. A. Edmond et al. (eds.) pp 161–164, IOP Publishing, Bristol, 1994. K. E. Moore, C. E. Weitzel, K. J. Nordquist, L. L. Pond III, J. W. Palmour, S. Allen, and C. H. Carter Jr, IEEE Electron. Device Lett. 18, 69 (1997). S. C. Binari, K. Ikossi-Anastasiou, J. A. Roussos, W. Kruppa, D. Park, H. B. Dietrich, D. D. Koleske, A. E. Wickenden, and R. L. Henry, IEEE Trans. Electron. Dev. 48, 465 (2001). R. Fischer, T. J. Drummond, J. Klem, W. Kopp, T. Henderson, D. Perrachione and H. Morkoç, IEEE Trans. Electron. Dev. 31, 1028 (1984). W. T. Masselink, A. Ketterson, J. Klem, W. Kopp and H. Morkoç, Electron. Lett. 21, 937 (1985). W. Kruppa, S. C. Binari, and K. Doverspike, Electron. Lett. 31, 1951 (1995). C. Nguyen, N. X. Nguyen, and D. E. Grider, Electron. Lett. 35, 1380 (1999). P. B. Klein, J. A. Freitas Jr, S. C. Binari, and A. E. Wickenden, Appl. Phys. Lett. 75, 4016 (1999). P. B. Klein, S. C. Binari, J. A. Freitas Jr, and A. E. Wickenden, J. Appl. Phys. 88, 2843 (2000). R. Dietrich, A. Wieszt, A. Vescan, H. Leier, J. M. Redwing, K. S. Boutros, K. Kornitzer, R. Freitag, T. Ebner, and K. Thonke, MRS Internet J. Nitride Semicond. Res. 5, 2 (2000).

175 P. B. Klein, S. C. Binari, K. Ikossi, A. E.

176

177 178

179

180

181

182

183

184

185

186

187

188

189

Wichenden, D. D. Koleske, and R. L. Henry, Appl. Phys. Lett. 79, 3527 (2001). E. J. Miller, X. Z. Fang, H. H. Wieder, P. M. Asbeck, E. T. Yu, G. J. Sullivan, and J. W. Redwing, J. Appl. Phys. 87, 8070 (2000). D. M. Schaadt and E. T. Yu, Mater. Res. Soc. Symp. Proc. 680, E5.1.1 (2001). G. Simin, A. Koudymov, A. Tarakji, X. Hu, J. Yang, M. Asif Khan, M. S. Shur, and R. Gaska, Appl. Phys. Lett. 79, 2651 (2001). W. J. Schaff, Jeonghyun Hwang, and B. Green, “The effect of a MBE grown AlN surface layer on the DC and RF characteristics of GaN Heterojunction Field Effect Transistors” in preparation. R. Vetury, N. Q. Zhang, S. Keller, and U. K. Mishra, IEEE Trans. Electron. Dev. 48, 560 (2001). X. Hu, A. Koudymov, G. Simin, J. Yang, M. Asif Khan, A. Tarakji, M. S. Shur, and R. Kaska, Appl. Phys. Lett. 79, 2832 (2001). B. M. Green, K. K. Chu, E. M. Chumbes, J. A. Smart, J. R. Shealy, and L. F. Eastman, IEEE Electron. Dev. Lett. 21, 268 (2000). A. V. Vertiatchikh, L. F. Eastman, W. J. Schaff, and T. Prunty, Electron. Lett. 38, 387 (2002). W. Lu, V. Kumar, R. Schwindt, E. Piner, and I. Adesida, Solid-State Electron. 46, 1441 (2002). B. Luo, J. W. Johnson, B. P. Gila, A. Onstine, C. R. Abernathy, F. Ren, S. J. Pearton, A. G. Baca, A. M. Dabiran, A. M. Wowchack, and P. P. Chow, SolidState Electron. 46, 467 (2002). S. C. Binari, W. Kruppa, H. B. Dietrich, G. Kelner, A. E. Wickenden, and J. A. Freitas, Jr, Solid-State Electron. 41, 1549 (1997). P. B. Klein, J. A. Freitas Jr, S. C. Binari, and A. E. Wickenden, Appl. Phys. Lett. 75, 4016 (1999). M. E. Levinshtein, F. Pascal, S. Contreras, W. Knap, S. L. Rumyantsev, R. Gaska, J. W. Wang, and M. S. Shur, Appl. Phys. Lett. 72, 3053 (1998). J. A. Garrido, B. E. Foutz, J. A. Smart, J. R. Shealy, M. J. Murphy, W. J. Schaff, L. F. Eastman, and E. Muñoz, Appl. Phys. Lett. 76, 3442 (2000).

12.7 References 190 M. E. Levinshtein, S. L. Rumyantsev, R.

191

192 193

194

195

196

197

198

199

200

201

202 203

204 205

Gasja, J. W. Yang, and M. S. Shur, Appl. Phys. Lett. 73, 1089 (1998). A. Balandin, S. Cai, R. Li, K. L. Wang, V. Ramgopal Rao, and C. R. Viswanathan, IEEE Electron. Dev. Lett. 19, 475 (1998). A. K. Rice and K. J. Malloy, J. Appl. Phys. 87, 7892 (2000). N. V. Dyakonova, M. E. Levinshtein, S. Contreras, W. Knap, B. Beaumont, and P. Gibart, Semicond. 32, 257 (1998). M. E. Levinshtein, S. L. Rumyantsev, D. C. Look, R. J. Molnar, M. Asif Khan, G. Simin, V. Adivarahan, and M. S. Shur, J. Appl. Phys. 86, 5075 (1999). M. E. Levinshtein, S. L. Rumyantsev, M. S. Shur, R. Gaska, and M. A. Khan, IEEE Proc. Circuits Devices Syst. 149, 32 (2002). A. P. Dmitriev, E. Borovitskaya, M. E. Levinshtein, S. L. Rumyantsev, and M. S. Shur, J. Appl. Phys. 90, 301 (2001). N. G. Weimann, L. F. Eastman, D. Doppalapudi, H. M. Ng, and T. D. Moustakas, J. Appl. Phys. 83, 3656 (1998). S. L. Rumyantsev, N. Pala, M. S. Shur, R. Gaska, M. E. Levinshtein, P. A. Ivanov, M. Asif Khan, G. Simin, X. Hu, and J. Yang, Semicond. Sci. Technol. 17, 476 (2002). S. Rumyantsev, M. E. Levinshtein, R. Gaska, M. S. Shur, A. Khan, J. W. Wang, G. Simin, A. Ping, and T. Adesida, Phys. Stat. Sol. (a) 176, 201 (1999). S. Rumyantsev, M. E. Levinshtein, R. Gaska, M. S. Shur, J. W. Yang, and M. A. Khan, J. Appl. Phys. 87, 1849 (2000). A. Balandin, K. L. Wang, S. Cai, R. Li, C. R. Viswanathan, E. N. Wang, and M. Wojtowicz, J. Electron. Mater. 29, 297 (2000). A. Balandin, Mater. Res. Soc. Symp. Proc. 680, E5.3.1 (2001). S. L. Rumyantsev, N. Pala, M. S. Shur, E. Borovitskaya, A. P. Dmitriev, M. E. Levinshtein, R. Gaska, M. A. Khan, J. Yang, X. Hu, and G. Simin, IEEE Trans. Electron. Dev. 48, 530 (2001). A. Balandin, Electron. Lett. 36, 912 (2000). A. Balandin, S. V. Morozov, S. Cai, R. Li, K. L. Wang, G. Wijeratne, and C. R.

206

207

208

209

210

211

212

213

214

215

216 217 218 219 220

Viswanathan, IEEE Trans. Microw. Theory Tech. 47, 1413 (1999). S. L. Rumyantsev, N. Pala, M. S. Shur, R. Gaska, M. E. Levinshtein, M. Asif Khan, G. Simin, X. Hu, and J. Yang, J. Appl. Phys. 88, 6726 (2000). S. A. Vitusevich, S. V. Danylyuk, N. Klein, M. V. Petrychuk, V. N. Sokolov, V. A. Kochelap, A. E. Belyaev, V. Tilak, J. Smart, A. Vertiatchikh, and L. F. Eastman, Appl. Phys. Lett. 80, 2126 (2002). A. Balandin, S. Morozov, G. Wijeratne, S. J. Cai, R. Li, J. Li, K. L. Wang, C. R. Viswanathan, and Yu. Dubrovskii, Appl. Phys. Lett. 75, 2064 (1999). A. T. Ping, E. Piner, J. Redwing, M. Asif Khan, and I. Adesida, Electron. Lett. 36, 175 (2000). N. X. Nguyen, M. Micovic, W.-S. Wong, P. Hashimoto, P. Janke, D. Harvey, and C. Nguyen, Electron. Lett. 36, 469 (2000). J. Deng, T. Werner, M. S. Shur, R. Gaska, A. Khan, G. Simin, and J. W. Wang, Low frequency and microwave noise characteristics of GaN and GaAs-based HFETs, International Conference on Compound Semiconductor Manufacturing Technology, 2001. W. Lu, J. Yang, M. Asif Khan, and I. Adesida, IEEE Trans. Electron. Dev. 48, 581 (2001). W. Lu, V. Kumar, R. Schwindt, E. Piner, and I. Adesida, Solid-State Electron. 46, 1441 (2002). H. Morkoç, H. Ünlü, and G. Ji, Fundamentals and Technology of MODFETs, (Wiley and Sons, Chichester, West Sussex, UK, 1991). D. Delagebeaudeuf, J. Chevrier, M. Laviron, and P. Delescluse, IEEE Electron. Dev. Lett. 6, 444 (1985). C. H. Oxley, Solid-State Electron. 45, 677 (2001). W. Shockley, US Patent No. 2 569 347, issued 1951. H. Kroemer, Proc. IRE 45, 1535 (1957). H. Kroemer, Proc. IEEE 70, 13 (1982). G. B. Gao, S. N. Mohammad, G. M. Martin, and H. Morkoç, in International Journal of High Speed Electronics and Systems, in Compound Semiconductor Electronics: The Age of Maturity M.S.

625

626

12 GaN-Based Modulation-Doped FETs and Heterojunction Bipolar Transistors

221

222

223

224 225

226

Shur (ed.) (World Scientific Publishing Company, ISBN 981-02-2325, 1996), pp. 85–174. E. F. Crabbé, B. S. Meyerson, J. M. C. Stork, and D. Harame, IEEE IEDM 93 Tech. Dig., p. 83, 1993; and A. Schüppen, A. Gruhle, U. Erben, H. Kibbel, and U. König, Electron. Lett. 30, 1187 (1994). A. Schüppen, A. Gruhle, U. Erben, H. Kibbel, and U. König, IEEE IEDM 94 Tech. Dig., pp. 377–380, 1994. J. I. Pankove, S. S. Chang, H. C. Lee, R. J. Molnar, T. D. Moustakas, and B. Van Zeghbroeck, IEDM Tech. Dig. pp. 389–392 1994. K. Suzuki, IEEE Trans. Electron. Dev. ED-38, 2128 (1991). D. Rosenfeld and S. A. Alterovitz, IEEE Trans. Electron. Dev. 41, 848 (1994); D. Rosenfeld and S. A. Alterovitz, Solid-State Electron. 37, 119 (1994); J. B. Kuo and T. C. Lu, Solid-State Electron. 36, 917 (1993); T. C. Lu and J. B. Kuo, IEEE Trans. Electron Devices 40, 766 (1993). S. S. Winterton, C. J. Peters, and N. G. Tarr, Solid-State Electron. 36, 1161 (1993).

227 G. B. Gao and H. Morkoç, Electron.

Lett. 27, 1408 (1991). 228 C. M. Mazier and M. S. Lundstrom,

229 230 231

232 233 234 235

IEEE Electron. Device Lett. 8, 90 (1987). See also D. Ritter, R. A. Hamm, A. Feygenson, and P. R. Smith, Appl. Phys. Lett. 64, 2988 (1994). S. N. Mohammad and H. Morkoç, J. Appl. Phys. 78, 4200 (1995). D. L. Pulfrey and S. Fathpour, IEEE Trans. Electron. Devices 48, 597 (2001). C. Monier, F. Ren, J. Han, P.-C. Chang, R. J. Shul, K.-P. Lee, A. G. Bacca, and S. Pearton, IEEE Trans. Electron. Devices 48, 597 (2001). L. Chernyak, Y. J. Park, and H. Morkoç, unpublished results. F. Ren et al., MRS Internet J. Nitride Semicond. Res. 3, 41 (1998). L. S. McCharty et al., IEEE Trans. Electron Device Lett. 20, 277 (1999). L. S. McCharty, I. S. Smorchkova, H. Xing, P. Kozodoy, P. Fini, J. Limb, D. L. Pulfrey, J. S. Speck, M. J. W. Rodwell, S. P. DenBaars, and U. K. Mishra, IEEE Trans. Electron Devices 48, 543 (2001).

627

13

GaN-Based UV Photodetectors Franck Omnes and Eva Monroy

Abstract

Visible-blind ultraviolet (UV) photodetectors are critical components in a number of applications, including UV astronomy, solar UV monitoring, engine control, flame sensors, detection of missile plumes, and secure space-to-space communications. Despite the widespread commercial use of Si and SiC photodiodes for such applications, wide band gap compounds appear to be nowadays the most suitable choice for the fabrication of semiconductor photodetectors in the UV spectral range. AlxGa1–xN alloys present the advantage of a direct band gap, which can be tailored from 365 nm to 200 nm by changing the aluminum mole fraction. These materials are also remarkably tolerant to aggressive environments, due to their thermal and chemical stability and radiation hardness. This chapter intends to focus on the performances and potentialities of a variety of state-of-the-art AlxGa1–xN-based UV photodetectors.

13.1

Introduction

Ultraviolet light (UV) was first mentioned in 1801 by J. W. Ritter, who remarked for the first time that some chemical reactions were influenced by an invisible light whose wavelength was smaller than the violet. Ultraviolet light has a wide spectral range, that starts from the visible (400 nm, 3.1 eV) and reaches at the other end the X-ray spectral low-energy frontier (10 nm, 124 eV). Thus, the overall energetic spectral width of UV light typically covers 80 times that of the visible region. It can be divided into 4 spectral regions:

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· · · ·

UV A, for wavelengths between 400 and 320 nm (from 3.1 to 3.87 eV), UV B, for wavelengths between 320 and 280 nm (from 3.87 to 4.43 eV), UV C, for wavelengths between 280 and 200 nm (from 4.43 to 6.20 eV), Far UV, for wavelengths between 200 and 10 nm (from 6.2 to 124 eV).

Given its specific light absorption properties, the Earth atmosphere does not allow the free propagation of a light whose wavelength is lower than 200 nm: the farUV spectrum located in the 200–10 nm therefore needs a high level of vacuum to propagate, and for that reason is very commonly called “vacuum UV” (VUV). The main applications of UV detectors are as follows: · biological and chemical sensors (ozone detection, determination of pollution levels in air, biological agents detection, etc.), · flame sensors (fire alarm systems, missile-plume detection, combustion engine control), · spatial optical communications (intra- and intersatellite-secured communications), · emitters calibration and UV imaging, including solar UV measurements and astronomical studies, · etc. The photodetector design for such applications is generally calibrated to display at the same time a high responsivity, a good linearity of the photocurrent as a function of the incident optical power, a wide band gap (in the case of semiconductors), a low level of noise and a high level of spectral selectivity. The priority given to these different factors strongly depends on the type of application. A low value of the response time can also be of a high interest in applications where a realtime fast signal treatment is necessary, such as UV imaging. As the Sun is the most important natural source of terrestrial UV light, most of the applications of UV detectors are naturally driven to solar UV measurements. UV photodetectors therefore require in general visible and infrared blindness in order to confer on them a sufficient level of UV selectivity. UV detectors therefore mainly work as high pass filters, and they are classified as “visible-blind” detectors when their cutoff wavelengths are in the 400 nm to 280 nm range, and “solarblind” detectors when cutoff wavelengths are shorter than 280 nm. In the latter case, solar-blind detectors are blind to the whole solar UV light spectrum coming to the ground on Earth, as ordinarily the UV C band is totally absorbed in the upper layers of the atmosphere. Visible-blind detectors are widely used in flamedetection applications, and they are also potentially of a high interest to space applications such as secured optical telecommunications between satellites, using UV wavelengths lower than 280 nm that cannot be seen nor detected on Earth. The UV light in space represents 9% of the overall light power emitted by the Sun. The ozone stratospheric layer totally absorbs the UV C spectral band. It is widely admitted that the UV radiations with wavelengths lower than 280 nm never reach the surface of the Earth. The only UV radiation coming to the ground is therefore composed of the attenuated UV A and UV B bands, that are both re-

13.1 Introduction

sponsible for most of the biological effects of sunlight. The biological effects of UV light are at a maximum for the UV B, whose photon energy is the highest thus holding more ionization power. They notably directly contribute a lot to the generation of erythema or skin cancers. However, it has been recently demonstrated that the UV A light, although commonly considered as much less dangerous to the health, is able to penetrate deep below the skin surface where it creates cellular damage because of its high level of ionization power. Mostly, the UV A light may damage the genetic material of the cells, and therefore is able to generate cancers in a way similar to the UV B radiation, especially when the skin is exposed to the Sun light for long periods of time or in the case of frequent exposures. On the other hand, the solar UV skin illumination actively participates in the D vitamin synthesis process in the body, so a reasonable amount of solar exposure is totally beneficial to every human being, preventing bone-fragilizing problems. The ionizing power of UV light can also be used in a more general way to activate a number of light-sensitive organic and inorganic chemical reactions. Another specific interest of the UV light remains in its bactericidal action, which makes UV illumination suitable for a number of applications to biological cleaning. Finally, let us recall that the stratospheric ozone layer is naturally regenerated in the upper layers of the Earth’s atmosphere by the way of the UV-assisted transformation of oxygen into ozone. The fast depletion of the stratospheric ozone layer that is notably due to human activity, and the resulting growing exposure of the ground to dangerous spectral components of the solar UV light raise an increasing need of UV detection systems for solar UV detection and dosimetry. Therefore, visible-blind UV detectors are nowadays integrated in a growing number of UV A and UV B monitoring systems devoted to ground solar dosimetry for environmental studies as well as applications to biology, medical sciences or research in cosmetics (solar creams or other products that modify the human skin sensitivity to solar illumination, etc.). Portable solar dosimeters are also commercially available for the selective UV B dosimetry. The spectral response of such transducers fit very closely the spectral sensitivity curve of the human skin to erythema (more detail will be given later in this chapter). A wide variety of UV photodetectors fitted to such applications is available today. Photomultiplier tubes have been used for a long time for the purpose of UV detection, and they are still widespread in laboratories. However, they often result in bulky, expensive and fragile detection systems, although their high level of UV sensitivity can hardly surpass the other kinds of UV photodetectors that can be used in this spectral window. The growing need for miniaturized and reliable UVdetection systems for portable or shipped applications has driven the development of semiconductor-based UV photodetectors, where the active devices are mainly photoconductors, Schottky junction photodiodes, p-i-n photodiodes, or metal-semiconductor-metal photodiodes. Small band gap semiconductors were first considered to perform UV detection, such as silicon and some III–V compounds (GaP, GaAsP, etc.) whose band gap is typically located in the infrared (Si) or in the visible red (GaAsP). Exceptionally,

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the chosen band gaps reach the yellow in the special case of GaP, which is their upper limit. The most important drawback of silicon and other small band gap semiconductors, in general, is they cannot be directly exposed to the incident radiation. First, the direct exposure of such transducers to the daylight obviously results in a response that is affected by the visible and the infrared spectral components. This unfortunately makes it impossible to selectively extract the information related to the UV-incident light with a bare detector. Furthermore, the quantum efficiency of a semiconductor-based photodetector (that is, the electron-hole pair creation rate per absorbed photon) is maximum for photon energies higher than the band gap, but located close to the gap energy in a quite narrow spectral interval. When the photon energies are much larger than the band gap (this is very common in the case of UV light), part of the light energy is lost in the form of heat in the semiconductor lattice where phonons modes are excited. This results in lowering the quantum efficiency in the short wavelength part of the light spectrum. The use of small band gap semiconductors for UV detection has therefore increased the development of selectively absorbent filters (high pass filters). Sometimes, a phosphor-based filter is used, that absorbs the UV light and reemits towards the detector a light whose spectral features correspond to photon energies that are close to the band gap of the semiconductor [1]. However, this results in any case in rather complicated and expensive systems, that are also sometimes strongly affected by the ageing of the filters that is subject to significantly change and alter their ultimate performances. A new generation of semiconductor-based UV photodetectors has recently emerged, that involve wide band gap semiconductors such as silicon carbide (SiC), diamond, and gallium nitride (GaN) or AlGaN alloys. Silicon carbide, whose band gap is 2.86 eV at room temperature (T = 300 K) (6HSiC), has brought the detectors significantly closer to the useful spectral range. Commercial applications such as SiC-based “solar-blind” flame detectors working in the UV C range are already available. However, let us mention that the insertion of high pass optical filters is still necessary in such applications in order to tune the photodetecting system to the appropriate spectral range. The development of monocrystalline GaN and AlxGa1–xN (x = 0–1) epitaxial layers has recently opened the way to naturally visible-blind UV photodetectors with a high level of performances and reliability. The direct band gap of AlxGa1–xN is an increasing function of the Al mole fraction x, and lies in the 3.42 eV (k = 362 nm) (x = 0) – 6.2 eV (k = 200 nm) range. This spectral range notably includes the UV B and UV C cutoffs, which respectively correspond to 3.87 eV (or k = 320 nm) and 4.43 eV (or k = 280 nm). Therefore, it becomes possible to fabricate filter-free UV photodetectors, and this considerably simplifies the UV photodetection systems. It notably opens the door to shrinking the overall system size and to increasing their reliability. Furthermore, the high chemical stability of GaN and AlxGa1–xN compounds (comparable to that of SiC) qualifies these materials for the fabrication of photodetectors that are naturally harsh-environment resistant. They notably can quite easily stand like SiC-based devices high operating temperatures and, in the case of photovoltaic detectors, high values of the reverse bias voltage can be applied. As AlxGa1–xN

13.2 UV to Visible Contrast

alloys are direct band gap semiconductors at all values of the Al composition, the optoelectronic properties of these materials are better than those of SiC whose indirect band gap is not so favorable to the phenomena that are related to the electronhole pair photogeneration. For all these reasons, as we will demonstrate in this chapter, III-nitrides are a very good technical solution for UV photodetection, which is at the same time flexible, reliable and very well suited to the whole range of applications to visible-blind and solar-blind photodetection. It notably enables the fabrication of low-cost, efficient and reliable UV photodetectors for all these applications. In this chapter, we will first briefly focus on the Si- and SiC-based UV photodetectors’ main features. We will then consider in detail several kinds of III-nitridebased UV photodetectors: photoconductors, Schottky photodiodes, metal-semiconductor-metal (MSM) photodiodes, and p-i-n photodiodes. The most relevant advances in the fields of nitride-based avalanche photodiodes and phototransistors will finally be reviewed.

13.2

UV to Visible Contrast

A white light source (Xe lamp) with a strong UV emission coupled to a monochromator is used for the spectral response measurement of UV photodetectors. The photocurrent of the device is measured as a function of the wavelength, which is normalized with respect to the optical power P(k) of the lamp determined with a precisely calibrated pyrometer. In order to increase the sensitivity of the measurement and notably eliminate the DC-parasitic light coming from the environment. However, it is important to maintain the modulation frequency of the signal with respect to the bandwidth of the photodetector. If not the case, the signal can be distorted by the measurement system. The spectral response of the photodetector is mainly light absorption dependent. In direct band gap semiconductors, a sharp edge of the spectral response can be observed close to the band gap of the semiconductor, which takes very low values at wavelengths longer than the gap wavelength value. In the case of UV photodetectors, the UV to visible contrast is defined as the Rimax (k = kG)/ Ri (k = 400 nm) ratio, where Rimax is the maximal value of the responsivity at the gap wavelength kG and Ri (k = 400 nm) is the responsivity value at the limit of the visible spectrum. The UV to visible contrast may be mostly limited by the two following factors: · The presence of electrically and optically active deep levels in the gap of the semiconductor. These deep levels notably come from the extended or point defects of the semiconductor material crystalline structure, but can also originate from the presence of deep impurities, or from levels related to surface imperfections. · In the case of front-side-illuminated Schottky-based photodetectors equipped with a semitransparent contact, the photoemission of carriers by the metal.

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13.3

Si and SiC UV Photodetectors

The most common commercial technical solutions for UV photodetection are mainly Si- or SiC-based. Some applications that are a little less common use compound semiconductors like GaAs, GaP, and GaAsP. Mainly, Schottky barrier photodiodes are fabricated with these materials. This special range of devices notably fits very well for VUV-detection applications, for which they offer a remarkable operating stability. The recent emergence of diamond-based UV photodetector technologies enable the realization of short cutoff wavelength photoconductors (kc = 225 nm) associated with a high UV/visible contrast that covers 6 orders of magnitude [2, 3]. Such devices are of great interest and fit very well to UV photodetector applications and high-energy particle detection, mainly due to the high level of radiation hardness of diamond. However, the development of this special range of photodetectors is hindered by the technical difficulty to get high-quality monocrystalline epitaxial films. The final material is in the best cases a polycrystal whose adjacent grains are significantly misoriented. This results in a large density of electrically and optically active defects that notably significantly hinders the operation of the photoconductors in terms of responsivity and UV/visible contrast. However, let us outline that diamond-based UV photodetectors are now commercially available, which is the clear indicator of a growing interest for these devices for UV photodetection and its applications [4]. 13.3.1

Silicon-Based UV Photodiodes

The use of “UV-enhanced” p-n junction silicon-based photodiodes is the most common and the cheapest commercial solution for UV photodetection. It drives to low-cost detectors that are convenient to most of the applications for UV detection in a very wide spectral range, which lies from the near UV to the VUV, and even reaches the energetic spectral threshold of the soft X-ray light. However, the general shape of their spectral response is not uniform and notably reaches the infrared region, as the gap of silicon is 1.1 eV at room temperature (300 K). In order to make their performances fit with the requirements of UV detection, it is therefore necessary to put in front of the detector an absorbent filter, in order to select the spectral range corresponding to the targeted application. This often increases the cost of the final detection system, as the filters are often technologically complex, which significantly increases their cost. Silicon-based UV photodiodes split into two major families, which are the p-n junction photodiodes and metal-oxide-semiconductor photodiodes, respectively [1, 5]. The first family of Si UV photodetectors includes shallow p-n junction photodiodes, where the p-n junction is typically located at a 0.2 lm depth, coated with a thin SiO2 surface layer. This insulating oxide surface layer plays the double role of surface passivation layer and antireflection coating. Junction depth is a very important parameter, as light absorption is increasingly superficial when the photon

13.3 Si and SiC UV Photodetectors

energy becomes high. In the case of p-n junction photodiodes, it is necessary for optimizing their performances and maximizing the photocurrent that the greatest number of carriers photogenerated by UV reach the junction zone without recombining. For the same reason, the control of the surface recombination phenomena is a key point in the case of Si-based UV photodetection. This can be achieved by bringing a special care to wafer surface preparation, which is of special importance when far-UV need to be detected: in such a case, the fine control and the optimization of the Si/SiO2 interface properties, which results in lowering the surface trap density by naturally producing on the silicon surface an electric field that limits, and in favorable cases cancels, the carrier-recombination phenomena at the interface. The highest performances have been obtained by Korde et al. [6, 7] on p-n junction Si-based UV photodiodes of the non-p-type. These authors have diffused phosphorus (P) into a dislocation-free Si(p) substrate. A 60 nm-thick SiO2 layer has been grown on top of the wafer. Given its thickness, it absorbs all radiation of a wavelength less than 120 nm, which unfortunately makes this kind of photodiodes useless in applications to high-energy UV, and notably VUV detection. This photodiode has a 100% internal quantum efficiency in the 350–600 nm spectral window. It is interesting to note that for wavelengths shorter than 350 nm, the internal quantum efficiency is larger than unity, due to secondary impact ionization phenomena. As a high kinetic energy is communicated to the photogenerated electron-hole pairs, it is possible to create by impact on the chemical bonds additional electron-hole pairs. On the other hand, when the wavelength is larger than 600 nm, the quantum efficiency becomes less than 1, due to the deep absorption of the light far from the p-n junction, which thus generates electron-hole pairs that cannot diffuse to the junction as their diffusion lengths are too short. Therefore, they recombine in the volume of the semiconductor and they do not contribute to the photocurrent. Let us briefly focus at this step on the Si-based p-n junction photodiodes that are designed to detect the VUV up to an energy of 124 eV. Although the basic design of the p-n junction itself remains almost identical, the surface oxide layer is much thinner than in the more conventional case that we previously described. In such photodiodes, the typical surface oxide layer thickness is 4.5 nm, which is 10 or 20 times smaller than in other kinds of UV photodiodes. This presents a double advantage: first, this layer is transparent to all short-wavelength radiations, and also, the oxide volume is strongly reduced with respect to the conventional technical solutions, thus markedly reducing the possibility for UV light and humidity to generate recombining traps in the oxide material (which ordinarily explains most of the ageing of Si-based UV photodiodes). Therefore, it greatly improves the performance stability of the device when exposed to very high energy photon illumination. The electron-hole pair photogeneration gives rise to carriers with a large kinetic energy, that multiply by the way of secondary impact ionization phenomena. In the high photon energy range, the internal quantum efficiency g of the VUV Si photodiodes typically follows a linear variation as a function of the photon energy E, which can be written as: g = E/3.63 eV [5]. In order to

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better describe the corresponding orders of magnitude, let us mention that the typical value of the internal quantum efficiency of a VUV Si photodiode is typically of 30 for a photon energy of 124 eV. These photodiodes are in a general way coupled to a bandpass filter that selects the 10–50 nm spectral range. This filter is composed of thin metallic layers (Al/C, Al/C/Sc, Ti, Sn, Ag, etc.) [5]. Si-based charge inversion-type photodiodes [1, 5] appear to be quite similar to the metal-oxide-semiconductor structures that are designed for field effect transistor applications: the significant effects for photodetection are closely related to the presence of the electric field at the Si/SiO2 interface. An intense electric field is established close to the surface, which precisely corresponds to the region where the high photon energy light is absorbed. Therefore, this configuration is favorable for maximizing the internal quantum efficiency of the photodiode, which is further enhanced even more by the near total absence of any dead-zone recombining surface layer like the one that traditionally featured in the early generations of Si UV junction photodiodes. Charge-inversion UV photodiodes have a high internal quantum efficiency in the 250–500 nm spectral range, and have a 120-nm cutoff wavelength that mainly relates to the high-energy light absorption by the surface oxide layer. However, it can be outlined that the operating features of this kind of photodiode degrades with time under UV illumination, as the UV light tends to degrade the properties of the oxide layer. Furthermore, charge-inversion UV photodiodes have a smaller linearity range than p-n junction photodiodes, which can be explained by the effect of a high electrical resistance related to the bidimensional charge layer at the SiO2/Si interface. 13.3.2

SiC-Based UV Photodetectors

The best performances of SiC-based UV photodetectors are obtained for 6H SiCbased p-n junction photodiodes [5]. The optimized n-on-p structure is made of a 0.2–0.3-lm thick SiC(n+) layer grown on top of a SiC(p) substrate. The doping levels are, respectively, about 5 ´ 1018 cm–3 for the SiC(n+) layer, and 5–8 ´ 1017 cm–3 for the p-type SiC substrate. The structure is terminated by a SiO2 passivation layer grown on the surface. A nickel ohmic contact is realized on the n+ side of the device. Typical responsivity values lie in the 150–175 mA W–1 range at a 270nm wavelength, which corresponds to a 70 to 85% internal quantum efficiency. At k = 200 nm, the responsivity is 50 mA W–1 for the same device. The spectral response displays a peak responsivity with a typical wavelength lying in the 268 nm to 299 nm range. These devices display a low dark current of 10–11 A at –1 V reverse bias at T = 473 K (or 200 8C) [8]. 6H SiC-based Schottky photodiodes working in the 200–400 nm spectral range are also available [5]. The best performances are obtained for SiC(p)-based Schottky devices, as the Schottky barrier height is twice the SiC(n) value on SiC(p). Furthermore, the diffusion length is much larger for electrons than for holes. Very low leakage currents are obtained on Schottky junctions realized on SiC(p). Leakage current values lower than 1 pA are commonly measured for reverse-bias

13.4 III-Nitride-Based UV Photodetectors

voltage values of –10 V. However, Anikin et al. [9] report the realization of a highquality Schottky junction on SiC(n). The gold Schottky contact gives, in this case, a Schottky barrier height that lies in the 1.4 to 1.63 eV range. The operating features of these devices display a very low leakage current, that is of the order of 100 pA for a reverse bias voltage of –100 to –170 V, together with a high responsivity of 150 mA W–1 at a wavelength of 215 nm [5].

13.4

III-Nitride-Based UV Photodetectors

III-nitrides currently represent one of the most interesting and flexible technical solutions for UV photodetection when considered in the midst of all other semiconductor families available for such application. The first characterization studies of polycrystalline gallium nitride (GaN) are more than 30 years old. The development of the epitaxial techniques of this material has been hindered for several decades because of the inadequacy of the available growth technologies, and also because of the absence of a lattice-matched substrate. This has made it impossible to develop material suitable for applications. Sapphire substrates are today used widely for the epitaxial growth of thin III-nitride layers and their corresponding applications to electronic and optoelectronic devices, despite a large lattice mismatch of about 16% with GaN, together with a large difference between their two thermal expansion coefficients. The metalorganic vapor phase epitaxy growth method, as well as the plasma-induced or gas-source molecular beam epitaxy, which was more recently introduced, already enable the growth of device-quality GaN and related compounds layers that are suitable for a number of applications, such as short-wavelength LEDs emitting from the green to the blue light, and even reach the UV spectrum, blue lasers, field effect transistors and UV photodetectors. 13.4.1

Photoconductors 13.4.1.1 Spectral Response

AlGaN-based photoconductors consist of a 1-lm thick AlGaN(Si) epitaxial layer, where two ohmic contacts are deposited. A DC bias is applied to the photoconductor, and the device is mounted in series with a small-value resistance. The induced photocurrent is simply deduced from the voltage drop in the load resistance when the photoconductor is illuminated. GaN- and AlGaN-based photoconductors display a highly optical power-dependent responsivity that is proportional to P–c, 0.5 < c < 0.95 over more than 5 decades (Fig. 13.1) [10, 11]. This behavior is independent of the excitation wavelength, as is shown in the inset of Fig. 13.1. The value of k is sample dependent, and is in a general way a decreasing function of the electrical resistivity of the layer. It has also been observed that the value of c decreases with temperature (Fig. 13.1).

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Fig. 13.1 Gain variation of GaN photoconductors as a function of the incident light power, for different values of the device temperature.

Fig. 13.2 plots the spectral response of AlGaN-based photoconductors for different values of the aluminum mole fraction. The experimental data take into account a correction with respect to the power spectrum of the incident light. The close to band gap spectral response peaks are attributed to excitonic light absorption phenomena. An expected shift of this peak towards the short wavelengths is observed when the Al mole fraction is increased.

Fig. 13.2 Spectral response of AlGaN photoconductors for different values of the Al mole fraction and different Si-doping levels.

13.4 III-Nitride-Based UV Photodetectors

The UV/visible contrast in these devices is much lower than that expected from the absorption coefficient of the material. Thus, the mechanism involved in the photoconductive responsivity cannot be only semiconductor optical absorption. This fact, together with the sublinear dependence of photocurrent on optical power, tends to support the photoconductive mechanism described by Garrido et al. [12]. This model assumes that the current responsivity, Ri, consists of two terms, one due to the photogenerated free carriers, Dn, and the other due to the light-induced modulation of the effective conduction cross section, DS. Ri ˆ

DI qVB le ˆ …SDn ‡ nDS† ; LPopt Popt

…1†

where q is the electron charge, le is the electron mobility, L is the distance between contacts, S is the conductive section, VB is the bias voltage and n is the free carrier concentration. The conduction cross section does not correspond to the geometrical section of the devices, due to the presence of depletion regions around lattice discontinuities (threading dislocations, grain boundaries, and interfaces), similar to those shown in the diagram of Fig. 13.3. Charged regions around threading dislocations have recently been observed in GaN films by Hansen et al. [13] using scanning capacitance microscopy. Light ab-

Fig. 13.3 Energy bands diagram in a photoconductor section perpendicular to the electrical current (from Ref. [12]).

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sorption induces a shrinking of these depletion regions, modulating the conduction section (see Fig. 13.3). Substituting in (1) the value of Dn [5]: Dn ˆ ggs

Popt ; hc=k

…2†

where g is the quantum efficiency, g is the photoconductive gain, s is the excess of free carrier lifetime and hc/k is the photon energy, we obtain: Ri ˆ

  DI qVB le ggsS n ˆ DS : ‡ L Popt hc=k Popt

…3†

The spectral dependence of the first term of this equation is given by g(k) ´ k. Since the quantum efficiency is a direct function of the absorbance, a good visible rejection would be expectable if this term was dominant. However, the dependence of photoconductive responsivity on optical power deduced from Fig. 13.4 suggests that the dominant mechanism in these detectors corresponds to the second term of Eq. (3), that is, to the modulation of the effective conduction cross section. This mechanism also explains the high response below the band gap: the levels responsible for visible absorption can be due either to defects homogeneously distributed in the semiconductor, such as dopants or vacancies, or to defects localized in lattice discontinuities (dislocations, grain boundaries and interfaces). If charged, defects originate a depletion region around them, reducing the

Fig. 13.4 Normalized photocurrent decay of Al0.23Ga0.77N photoconductors for different values of the doping level, after a short He-Cd laser pulse illumination.

13.4 III-Nitride-Based UV Photodetectors

effective conduction section of the device (see Fig. 13.3). Total light absorption by those defects may be negligible, so that they hardly affect the absorption coefficient and hence the photovoltaic detection. However, their effect on photoconductive responsivity is huge, since the charge concentrated in these discontinuities changes and thus modulates the effective conduction cross section.

Time Response All the samples showed persistent photoconductivity (PPC) effects. As shown in Fig. 13.4, the detectors show extremely slow and nonexponential transient responses. Those could be responsible for the frequency-dependent responsivity observed by several groups [14–17]. Different explanations have been given for PPC in GaN. Si or Mg have been proposed as the origin of PPC in doped samples [18, 19], and oxygen contamination has also been suggested [20]. PPC has also been attributed to intrinsic material defects, such as Ga vacancies [21, 22] or the defect responsible for the yellow photoluminescence emission [23, 24]. Kung et al. [15] and Binet et al. [25] explain the nonexponential shape of the photocurrent decays with a model that assumes the presence of a trap level in the band gap, that is ionized by the incident radiation. When the light is removed, ionized traps behave as recombination centers, whose efficiency decreases with time, as they recapture electrons. This model fits precisely the first few milliseconds of the photocurrent decays and their dependence with the optical power [25], but it fails to explain the long nonexponential tails observed by most of the groups working with AlGaN photoconductors so far. The slow photocurrent decays can be explained by the recombination of electrons in the deep levels located at extended defects or dislocations [10, 12]. The band bending around these defects provokes a spatial separation for electrons and holes, that can be responsible of the PPC. When the light is switched off, electrons tend to recombine, but they have to cross the potential barrier that separates them from their recombination centers. The height of this barrier depends on the charge in the defect, so that it changes with time as recombination is taking place. In this process, the space charge region (SCR) slowly recovers its width in the dark, and thus the resistance of the device also evolves slowly, and nonexponentially towards its value in the dark. This model can be applied either if the dominating defect is in dislocations, in the AlGaN/air or AlGaN/substrate interfaces. However, it is difficult to discriminate among these regions, and their relative importance might depend on the crystalline quality of the material. The contribution to responsivity and PPC of the AlGaN-substrate interface has been proven by Seifert et al. [26], who observed an increase of the photocurrent and the persistence when illuminating the samples through the substrate (polished sapphire). However, when the device is front-side illuminated with radiation above the band gap, the light does not reach the substrate, so that the PPC in this case should be due to dislocations or the AlGaN/air interface. 13.4.1.2

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Theoretical and experimental studies have been performed to determine what kind of metastable defects could be considered as responsible for the PPC origin in GaN and AlGaN. In summary, although a number of defects of different kinds can theoretically explain the bistable behavior in GaN, it seems that they cannot justify the persistent effects in GaN and AlGaN samples, independently of the nature of doping (Si, Ge, or Mg) and of the epitaxial growth technique used to elaborate the materials (MOVPE or MBE). A contribution from these defects cannot be eliminated, but the model based on the modulation of the transverse conductive section is able to explain the results obtained on a large number of very different samples. Furthermore, the modellization made by Garrido et al. explains with a high level of accuracy the photocurrent behavior of these devices as a function of time.

Effect of a Frequency Modulation of the Incident Optical Signal In order to improve the absolute value of the above band gap responsivity, it is necessary that the second term of Eq. (3) becomes less important than the first term. Taking into account that the conduction section modulation is a very slow phenomenon, one can reasonably expect that the use of a lockin detection system can eliminate all the frequency lower than the optical chopper frequency. Another specific advantage of this lockin detection system is that the photocurrent is independent of the DC phenomena [21]. The responsivity variation as a function of the chopping frequency is displayed in Fig. 13.5 [10]. 13.4.1.3

Fig. 13.5 Responsivity of a GaN photoconductor as a function of the optical incident power at different values of the chopping frequency, using a lockin detection system. The experimental data are compared with the responsivity of a Schottky barrier photodiode.

13.4 III-Nitride-Based UV Photodetectors

Fig. 13.6 Normalized spectral response of a GaN photoconductor, measured at different values of the chopping frequency of the optical incident signal. Experimental data are compared with the spectral response of a GaN Schottky barrier photodiode that was fabricated from the same GaN(Si) sample.

The responsivity becomes flatter when increasing the frequency from 7 Hz to 700 Hz, as the defect-related space charge regions involved in the DC photocurrent mechanism do not have enough time to react. For the same reason, the responsivity decreases with frequency as also observed by other groups [15, 21]. The effect of the frequency on the photoconductive spectral response is depicted in Fig. 13.6 [10]. When the mechanism responsible for the PPC is reduced by increasing the chopping frequency, the cutoff becomes sharper and the spectrum below the band gap tends to the photovoltaic response. However, the Schottky visible rejection remains much better even for f = 700 Hz. In conclusion, their responsivity mechanism makes photoconductors unsuitable for applications requiring speed or a certain spectral contrast, unless lockin detection is used. In this configuration, however, these devices lose all their advantages, since their responsivity is considerably reduced and the detection system becomes more complex and expensive. 13.4.2

AlGaN-Based Schottky Barrier Photodiodes Electrical Properties Planar and vertical structures are commonly used in the fabrication of Schottky barrier photodiodes. Both kinds of structures give similar operating theoretical features. The vertical structure is the most interesting for the realization of fast devices having a high responsivity value. However, current limitations of the III13.4.2.1

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13 GaN-Based UV Photodetectors

Fig. 13.7 Typical I-V variation of AlxGa1–xN Schottky barrier photodiodes

on sapphire.

nitride device-fabrication technology (e.g., related to the RIE etching damage caused by the mesa etching) result in a device performance degradation, which affects the bandwidth and noise level. Fig. 13.7 shows typical current-voltage (I-V) characteristics of AlxGa1–xN Schottky photodiodes. In GaN devices, the ideality factor is about 1.2, with a series resistance in the range of 20–50 X, and leakage resistances higher than 1 GX. The leakage current increases with aluminum content, and the ideality factor is also higher, reaching values of about 4. Thus, reliable information on the Schottky barrier height cannot be obtained from the I-V curve on AlGaN materials, due to the high values of ideality factors. A linear variation of 1/C2 as a function of the reverse bias voltage is observed on Schottky photodiodes fabricated with Ni- and Au-semitransparent Schottky contacts. Barrier heights of 0.86 eV and 1.2 eV can be deduced for Ni and Au, respectively. The barrier height of the gold contacts precisely fits the results that are given by the Schottky-Mott theory, but the corresponding value for the Ni contact is lower than the value that can be deduced from the same theory. These experimental data are in agreement with the results obtained by Guo et al. [27], who explain the lower value of the Schottky barrier of the Ni contact by the way of the presence of a Ga4Ni3 at the metal/semiconductor interface.

Responsivity In contrast with photoconductive detectors, Schottky barrier devices show a photocurrent dependence that behaves linearly with incident power in the range measured (10 mW m–2 to 2 kW m–2) (inset of Fig. 13.8). Fig. 13.8 also plots the spectral responsivity of AlxGa1–xN Schottky diodes with different Al contents (x = 0, 13.4.2.2

13.4 III-Nitride-Based UV Photodetectors

Fig. 13.8 Normalized room-temperature spectral response of AlGaN-based Schottky barrier photodiodes for different values of the Al mole fraction. Inset: photocurrent variation as a function of the incident light power.

0.19, 0.26, and 0.35). A UV/visible contrast of more than three decades is obtained. The cutoff wavelength shifts from 362 nm to 293 nm. Responsivity is flat for wavelengths shorter than the band gap. A slight decrease of the absolute responsivity has been observed with increasing Al content: absolute values of responsivities deduced from Fig. 13.8 are 54, 45, 30, and 10 mA W–1 above the band gap, for x = 0, 0.19, 0.26, and 0.35, respectively. The sharpness of the cutoff in Schottky barrier photodetectors indicates that the only limitation in the UV/visible contrast is given by absorption of deep defects, in contrast with the results obtained in photoconductors.

Time Response The photodetector time response is limited by the RC constant of the device, where C is the sum of the diode internal capacitance and the load capacitance, and R is the sum of the load resistance and the series resistance of the device. Therefore, the photocurrent decay time constant (time for the photocurrent to fall from maximum to 1/e) depends linearly on the load resistance as shown in Fig. 13.9. Minimum time constants of 69 ns have been recorded in diodes with a diameter } = 1 mm, reaching 15 ns for } = 240 lm [28]. 13.4.2.3

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Fig. 13.9 Photocurrent decay time variation as a function of the load resistance, measured on AlGaN-based Schottky barrier photodiodes of different sizes.

Noise and Detectivity 1/f noise is dominant at low and medium frequencies in GaN and AlGaN Schottky photodiodes [28–31], although shot noise might become dominant at high frequencies [31]. Thus, the noise power spectral density, Sn, was found to satisfy the relationship 13.4.2.4

Sn ˆ s0

Ida ; fc

…4†

where Id is the dark current, f is the frequency, and s0, c, and a are dimensionless fitting parameters. Values of c*1 and a*2 have been found. 1/f noise is typically related to the presence of traps near the semiconductor surface [32]. The noise equivalent power, NEP, of these devices is obtained as NEP ˆ

s hi2shot i ‡ hi21=f i Ri

;

…5†

where ishot is the shot noise current, i1/f is the 1/f noise current and Ri is the device responsivity. The value of hishoti can be estimated by hishoti = 2 q Id BW, where BW is the photodiode bandwidth, whereas hi1/fi is obtained integrating Sn(f) over the bandwidth. A NEP normalized to the square root of the bandwidth of 8 pW Hz–1/2 and 41 pW Hz–1/2 has been obtained respectively in GaN/Au and Al0.22Ga0.78N/Au Schottky photodiodes, at –2 V bias [28]. Detectivities of 6.1 ´ 109 W–1 Hz1/2 cm and 1.2 ´ 109 W–1 Hz1/2 cm have been reported, respectively, in GaN/Au and Al0.22Ga0.78N/Au Schottky photodiodes, at –2 V bias [28].

13.4 III-Nitride-Based UV Photodetectors

Epitaxial Lateral Overgrown (ELOG) GaN-Based Schottky Barrier Photodiodes In spite of these promising characteristics, the heteroepitaxial growth of GaN results in a high dislocation density (*108 cm–2), and this limits the UV/visible contrast in GaN photodetectors. The recent development of epitaxial lateral overgrown (ELOG) GaN [33, 34] has reduced the dislocation density by at least two orders of magnitude. Semitransparent Au Schottky-barrier photodiodes have been fabricated on twostep ELOG GaN layers [35], displaying a responsivity of 130 mA W–1. An improvement of one order of magnitude in the UV/visible contrast has been observed, in comparison with devices on standard GaN on sapphire, as shown in Fig. 13.10. The dark current, whose value is smaller than 1 nA cm–2 at –1 V bias voltage, is significantly lower than standard GaN/sapphire Schottky barrier photodiodes. The time response of the device is RC limited, and the reduced residual doping level in these epitaxial layers induces bandwidth values that are higher than 30 MHz, 12 MHz, and 8 MHz for devices of 200 lm, 400 lm, and 600 lm diameter, respectively. A detectivity of 5 ´ 1011 W–1 Hz1/2 cm has been determined for ELOG GaN photodiodes with a diameter of 400 lm, at –3.4 V bias voltage. 13.4.2.5

Application of AlGaN Photodetectors to the Simulation of the Biological Effects of UV Light The UV radiation can produce a number of biological effects [36–39]: 13.4.2.6

· Pigmentation: maximum at k = 360–440 nm. · Solar erythema: maximum of sensitivity at k < 297 nm.

Fig. 13.10 Normalized responsivity of ELOG GaN-based Schottky photo-

diodes, compared with the responsivity of similar GaN/sapphire devices. Inset: variation of the photocurrent with incident light power.

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Fig. 13.11 Normalized spectral response of an AlGaN Schottky

photodiode, compared to the erythema standard action curve (CIE).

· · · · ·

D2 and D3 vitamin synthesis: k = 249–315 nm. Yield is maximum at 290 nm. Damage to plants: k < 317 nm. Bactericidal action: k = 210–310 nm. Yield is maximum at 254 nm. Carcinogenic effect: UVB and UVC. Maximum at 310 nm. ADN damage: k < 320 nm. The effect increases rapidly when the wavelength decreases.

Simple, accurate, reliable, and low-cost instruments are therefore necessary to evaluate the biological effects of the UV radiation. Wide spectral range UV detectors have also been developed to monitor the UV A and UV B erythema action [36]. Commercial UV dosimeters include small band gap photodiodes (Si, GaAs, GaP), together with a series of filters that are placed in the optical path of the incident light. Muñoz et al. [40, 41] have demonstrated that the use of a special mole fraction of Al and suitable growth conditions for AlGaN Schottky photodiodes makes it possible to precisely fit the UV A and UV B erythema action curve (Fig. 13.11). The spectral response of these devices thus provides direct information on the UV light biological effects. In this application, the absorption tails of state-of-theart AlGaN-based detectors make it possible to correctly weight the UV A and UV B spectra, to accurately fit the erythema reference functions.

13.4.3

Metal-Semiconductor-Metal (MSM) Photodiodes

Typical metal-semiconductor-metal (MSM) AlGaN-based photodiodes use two interdigitated Ni/Au Schottky contacts deposited on a micrometer-thick AlxGa1–xN

13.4 III-Nitride-Based UV Photodetectors

nonintentionally doped epitaxial layer, with 2, 4, and 7 lm finger widths and spacings. The optical area of the devices is 250 ´ 250 lm2. The detectors are electrically biased, and are connected in series to a transimpedance amplifier. Spectral response studies are done with a 150-W Xe lamp coupled to a monochromator. The optical measurement system is calibrated using a pyroelectric detector. The responsivity and its dependency with the incident light power can be easily determined using an excitation with nonfocused gas lasers (He-Cd, k = 325 nm; Ar, k = 458 nm, 488 nm). The time response of the detectors is measured using the fourth frequency of a Nd-YAG laser (266 nm), with 10-ns Gaussian pulses. Noise characterization was performed using a SR530 lockin amplifier, the background noise power density of the system lying in the 10–26 A2 Hz–1 range.

Electrical Properties The MSM detectors show a very low dark current density that is indicative of high-quality Schottky barriers and low defect density material. As shown in Fig. 13.12, the experimental current density of small devices fits quite well the thermionic emission model for MSM structures, including the Schottky barrier lowering due to image-force effects [42]. Considering the ideal GaN Richardson constant (A = 26 A cm–2 K–2), a barrier height qU0 = 1.04 eV and a doping concentration ND = 6 ´ 1016 cm–3 are obtained. In contrast, large-area devices show a contribution from tunneling (Fig. 13.12) [43]. 13.4.3.1

Fig. 13.12 Current-voltage characteristics of MSM photodiodes with different optical area, Aopt. Dotted lines correspond to fits assuming thermionic emission transport and tunnel transport.

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Spectral Response Fig. 13.13 shows the spectral response of AlGaN MSM photodiodes at different bias. The responsivity is relatively flat over the band gap, with a sharp cutoff wavelength that shifts to shorter wavelengths with increasing Al content (Fig. 13.13) [44]. A visible rejection of four to five orders of magnitude is obtained at 5 V, and the same behavior is observed for higher bias. However, the UV/visible contrast decreases by one decade when the bias is reduced from 5 V to 1 V, and remains at *103 for lower bias [45]. The photocurrent scales approximately linearly with the optical power for wavelengths both above and below the band gap. This behavior is independent of bias. The variation of the responsivity with bias has been analyzed for diodes with different sizes, and excitation over the band gap (Fig. 13.14) [45]. For VB < 2 V, the responsivity scales sub-linearly with bias (R!V0.7 B ), which fits the theoretical behavior expected for an MSM photodiode in the absence of gain calculated from a one-dimensional model (dashed line in Fig. 13.14). An abrupt increase of the responsivity is observed between 2 V and 5 V, indicative of a biasactivated gain mechanism, which saturates for higher bias. This behavior is independent of the finger width and the gap spacing, as also shown in Fig. 13.14. The gain mechanism at high bias is also wavelength dependent. For wavelengths longer than the band gap, the device follows the trend expected for a MSM photodiode in absence of gain. The deviation from this behavior appears only for wavelengths shorter than 370 nm, so that the enhancement of the visible rejection with bias and the gain are due to the same mechanism. 13.4.3.2

Fig. 13.13 Spectral response of AlGaN MSM photodiodes, mea-

sured under different bias. Triangles were obtained with the 458 nm and 488 nm lines of an Ar+ laser.

13.4 III-Nitride-Based UV Photodetectors

Fig. 13.14 Responsivity dependence on bias for GaN MSM

photodiodes, measured for excitation above the band gap (325 nm).

Time Response Gain in photodetectors is usually related to slow phenomena. Thus, the time response of these devices has also been analyzed. The photocurrent decays are exponential, with time constants corresponding to the RC product of the measuring system, independent of bias. The variation of photocurrent response time with load resistance presents no trace of saturation for low resistances [44]. From these measurements, we can only conclude that the minimum response time of our devices is quite far below 10 ns. The maximum bandwidth of the MSM photodiodes could be limited either by the RC product or by the carrier transit time of the detector, both are estimated to be in the picosecond range. Given the device geometry and material properties (doping concentration, barrier height), the reach-through voltage of these MSM structures should be > 200 V, even for the devices with a pitch of 2 lm. Thus, most of the applied voltage drops in the reverse-biased contact (cathode), and the photocurrent is produced by absorption in the cathode space-charge region, with a small negative contribution by the anode. The higher responsivity observed in devices with a shorter gap spacing is not due to a more intense electric field, but to a higher number of fingers in the illuminated region. Therefore, responsivity saturation at high bias is not due to a full depletion of the device, but to gain saturation. The gain mechanism observed is only active at a bias higher than 2 V, and for excitation above the band gap. This mechanism is responsible for the superlinear increase of the responsivity with bias [44, 46], and for the enhancement of the UV/visible contrast that is observed in AlGaN-based MSM photodiodes. Gain in interdigitated MSM photodiodes has been attributed to different mechanisms [47–49]. The most often suggested process consists of electron tunneling enhanced by hole accumulation at the cathode. This accumulation may be due to 13.4.3.3

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traps located either in the semiconductor surface, in the bulk material, or in a thin insulating layer between the metal and the semiconductor. Trapping at surface states or dislocations produces persistent photoconductivity effects and a sublinear behavior with optical power, degrading the spectral response of the device. Both the linearity and the fast response of MSM photodiodes prove the absence of this gain mechanism, which is dominant in GaN and AlGaN photoconductors [10]. The presence of deep hole traps in bulk n.i.d. GaN is responsible for the photoresponse at excitation wavelengths longer than the band gap, but the fact that gain is not observed for k > 370 nm rules out trapping at these levels as the origin of this gain. The increase in hole density in the vicinity of the cathode can also be explained by the difference in transit speeds between electrons and holes [47]. However, this phenomenon cannot explain a gain that is only active for wavelengths above the band gap. Finally, we can speculate about an avalanche process in the valence band as being responsible for the gain. At high bias, holes generated in the valence band near the cathode move towards the contact driven by the intense electric field, and might have enough energy to induce new transitions by impact ionization. However, recent calculations of the multiplication coefficients in GaN [50] suggest that higher voltages (> 20 V) are required to achieve impact ionization in this material. In conclusion, further research is necessary to clarify the origin of the gain in AlGaN MSM photodiodes.

Noise The noise performance of the MSM devices was measured up to 28 V. At this bias, the spectral noise power of the GaN detectors remains always below the background noise level of the system, which implies a normalized noise equivalent power (NEP) lower than 2 pW Hz–1/2 in devices with finger width and gap spacing of 2 lm. At 28 V bias, a NEP*24 pW Hz–1/2 was measured in Al0.25Ga0.75N photodiodes [43]. 13.4.3.4

13.4.4

p-n and p-i-n Photodiodes

The performances of the first GaN p-n junction photodiodes were mainly limited because of the high electrical resistivity of the p-type layer due to the difficulties to obtain a good p-type doping level, together with the high resistivity of the corresponding ohmic contact [51, 52]. Fast p-n junction GaN photodiodes can now be obtained, with a time response as short as 105 ns [53] and a very low noise level (NEP*61 fW Hz–1/2 at a reverse-bias voltage of –3 V) [54]. The performances of these devices have even been improved by inserting a nonintentionally doped semiconductor region (p-i-n photodiodes) [55–58] and by the use of AlGaN/GaN heterostructures [59–61]. Al0.20Ga0.80N/GaN heterostructure photodiodes arrays have also been reported, with 32 ´ 32 [62] and 128 ´ 128 pixels [63], with a high level of performances in terms of responsivity and detectivity. AlxGa1–xN p-i-n photo-

13.4 III-Nitride-Based UV Photodetectors

diodes with large Al mole fractions (up to 76% [64]) have also been described. However, the optimization of such devices remains difficult because of the p-type doping level, that remains low and hardly reaches the 1017 cm–3 range, and because of the high resistivity of the corresponding ohmic contact. This has a double consequence: first, the time response of the AlxGa1–xN p-i-n photodetector cannot be reduced down to a sufficiently low value for the high series resistance related to the poor conducting properties of the ohmic contact. On the other hand, the noise level is high in the device due to the poor quality of the ohmic contact, which results in much lower detectivity values than in GaN p-n and p-i-n photodiodes.

Spectral Response A linearity is observed over more than 5 decades for the photocurrent in AlxGa1–xN p-n and p-i-n junction photodiodes as a function of the incident light power [53, 65, 66]. Typical responsivity values of homojunction p-n and p-i-n junction photodiodes lie in the 100–150 mA W–1 range, and this corresponds to 30 to 44% values of the external quantum efficiency. These results can be significantly improved when an AlxGa1–xN layer (of n- or p-type) is used in the illuminated area, in order that photons with a wavelength of 365 nm are directly absorbed at the junction level: it is thus possible to avoid the carrier losses by diffusion. A high responsivity of 200 mA W–1 has been measured at k = 365 nm for a back-side-illuminated sapphire-Al0.28Ga0.72N(n)-GaN(i)-GaN(p) [61]. A decrease in the responsivity has been observed in homojunction AlxGa1–xN photodiodes when the Al mole fraction increases in the ternary alloy, which is most likely due to a decrease in the photocarrier diffusion length [65]. A maximum responsivity of 57 mA W–1 has been reported at k = 287 nm, which corresponds to a 25% quantum efficiency [67]. An increase of the responsivity is observed in all cases as a function of the bias voltage [54, 57, 59, 61, 65, 66]. This result confirms that the responsivity is limited by the carrier diffusion length. When the reverse bias voltage increases, the space charge region width increases accordingly, so that the carriers issued from the photoionization process far from the junction are collected. Fig. 13.15 displays the typical spectral response of p-i-n AlxGa1–xN photodiodes obtained for different aluminum mole fractions. A relatively flat spectral response above band gap can be observed, with a cutoff spectral edge shifting towards the short wavelengths when the Al content increases. A UV/visible contrast larger than 4 orders of magnitude is measured in all these devices. An Ar+ laser has been used for the evaluation of the response in the visible, at a wavelength of 514 nm (Fig. 13.15). The short diffusion length of the carriers may affect the above band gap spectral response of AlxGa1–xN-based p-i-n photodiodes [29, 53, 54, 59]. The absorption increases as the wavelength decreases, so that more superficial light-absorption phenomena occur. This means that the electron-hole pairs are generated before the junction region in the upper layers, and thus must diffuse up to the junction to be able to contribute to the charge collection. Therefore, a small diffusion length induces a decrease of the responsivity at shorter wave13.4.4.1

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13 GaN-Based UV Photodetectors

Fig. 13.15 Spectral response of AlxGa1–xN-based p-i-n photodiodes (x = 0,

0.05, and 0.15).

lengths. This effect is even more enhanced when thick surface layers are used [65]. The nitride-based p-i-n detectors features display a sharp cutoff edge towards large wavelengths, whose energetic position is directly linked to the energy gap of the semiconductor material that is used for the active layer. However, an additional cutoff wavelength located in the short wavelength side is also required for some applications, that defines a spectral window for the UV detection. In their theoretical study, Pulfrey and Nener [68] have investigated the possibility to use AlxGa1–xN/GaN p-i-n heterostructures as bandpass UV detectors, with a high-energy cutoff wavelength precisely corresponding to the energy gap of AlxGa1–xN. In such a case, the AlxGa1–xN layer must be thick enough to be able not only to enhance the responsivity peak, but also to act as an integrated highpass filter. Devices that include a 1-lm thick Al0.10Ga0.90N layer [60] or a 1.5-lm thick Al0.28Ga0.72N [61] have demonstrated the possibility to achieve a rejection factor over more than 2 decades in the short-wavelength region.

Time Response The time response of GaN p-n and p-i-n photodiodes is, in general, limited by the RC product. They also present an exponential decay of the photocurrent [53, 54]. Minimum time responses of 27 ns have been measured on devices with a 200 ´ 200 lm2 optical area, for a zero bias voltage [54]. The time response lowers to 11 ns for a bias voltage of –6 V, which can be explained by the reduction of the junction capacitance. Faster time responses (12 ns at zero bias voltage) are ob13.4.4.2

13.4 III-Nitride-Based UV Photodetectors

tained in AlGaN/GaN heterojunction photodiodes with a 250-lm diameter [59]. However, a nonexponential photocurrent decay is often observed in these devices, with characteristic decay times that are larger than predicted by the simple limitation by the RC product [52, 55, 56, 65]. A correlation between this behavior and the capacitance variation with respect to frequency has been developed [65]. The capacitance has a given value at a specific frequency that increases with temperature. In all cases, it has been demonstrated that the time response decreases when a reverse bias voltage is applied, in agreement with the observed phenomena in the operation of capacitance-limited devices [52–54, 56, 58]. This behavior is indicative of the presence of a defect level in the semiconductor that cannot react to the excitation beyond a given frequency. An estimate of the activation energy of this defect, measured by admittance spectroscopy [69], is about 99 meV [65]. When taking into account both this weak activation energy and the high value of the defect concentration (*1018 cm–3) as determined by capacitance-voltage measurements at low frequency, it is possible to conclude that this defect is most likely represented by a substitutional magnesium atom. However, this 99-meV value is small in comparison with the thermal activation energy of Mg that can be determined by temperature-dependent Hall effect measurements, which is 150 meV in this case [70]. A similar capacitive behavior has been observed by Zohta et al. [71] in blue and green electroluminescent diodes. Extremely fast GaN p-i-n photodiodes have been reported by Carrano et al. [58, 72], with time responses lower than 1 ns at a –5 V bias voltage. This result has been obtained by increasing the thickness of the “i” layer up to 1 mm, which induces extremely low capacitance values in the device. Hence, the RC product is no longer the limiting factor in the time response, which is only limited by the transit time of the carriers. The only drawback of this special kind of device is related to its low responsivity value, which is 30 mA W–1 at a –5 V bias voltage. Such devices can operate at high bias voltages, and for this reason they are ideal for ultrafast signal detection.

Noise The spectral noise density under illumination and under reverse-bias conditions is flat in the high-frequency range, and fits the Sn = 2 · q · Iph relationship given by the shot noise theory. A normalized noise power as low as 6.6 fW Hz–1/2 has been obtained for p-n junction photodiodes at –3 V reverse bias [54, 73]. As these devices display a 200 ´ 200 lm optical area, their normalized detectivity is high and reaches 3 ´ 1012 W–1 Hz1/2 cm. 13.4.4.3

p-i-n Photodiodes on ELOG GaN Al0.33Ga0.77N-based p-i-n photodiodes fabricated on ELOG GaN have been reported [67]. The corresponding devices have been elaborated using a standard ELOG technology, using a SiO2 mask with stripes of 35 lm width and windows openings of 5 lm. The diode mesas (10 ´ 100 lm2) have been realized on the 13.4.4.4

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13 GaN-Based UV Photodetectors

materials regions corresponding to the wings of the lateral growth patterns (out of the coalescence region, and out of the opening of the SiO2 mask). Supplemental devices of a 30 ´ 100 lm2 active area have also been fabricated for comparison. These particular devices overlap the coalescence region that is located at the junction of the wings of lateral growth. Finally, devices of a similar shape with square mesas of 300 ´ 300 lm2 area have been fabricated on plain GaN on sapphire. Leakage current densities as low as 10 nA cm–2 have been measured on the smallest devices located on the wings of lateral growth. This leakage current density is one order of magnitude lower than that measured on the devices that include the coalescence boundaries, and is more than 6 orders of magnitude lower than in the case of devices fabricated from plain GaN on sapphire. This low value of the leakage current can be correlated to the thorough reduction of the dislocation density, as these defects induce a reinforcement of the tunnel-assisted carrier transport phenomena [74]. Furthermore, the spectral response display a sharper cutoff edge in the case of the devices made on the ELOG wings, and this is valid when the coalescence region is covered as well as when it is not. All these results are consistent with the corresponding observations made on Schottky photodiodes fabricated from ELOG [35].

GaN-Based Avalanche Photodiodes Avalanche photodiodes offer the combined advantages of a fast operation, a high degree of sensitivity, and of a high optical gain. They are reverse-biased p-n junctions, where the bias applied is close to the breakdown voltage [75]. The photogenerated carriers cross the structure at their saturation velocity because of the intense electric field applied, and are able to produce secondary electron-hole pairs by the means of ionizing collisions with the lattice. These new electrons and holes drift in opposite directions, and some of them are able to further generate supplemental carriers. This carrier generation process is known as the impact-ionization process, and is responsible for the carrier multiplication, and thus generates gain. The calculations for the determination of the ionization parameters of electrons and holes in GaN indicate that the electric field values necessary to allow the multiplying effect are very large [76, 77]. Moreover, negative effects are expected on the noise performances of GaN-based avalanche photodiodes, as one can predict that the ionization coefficients of electrons and holes are of comparable values. Finally, the high defect density in the GaN material makes it difficult to achieve a homogeneous carrier multiplication over the whole optical area of the device. GaN-based p-n junctions have been biased at their breakdown limit (42–43 V), and an optical gain has been observed [78]. However, the breakdown is not homogeneous because of a large density of defects, as is demonstrated by the presence of glowing spots corresponding to the blue light emission. An homogeneous carrier avalanche multiplication has been recently reported in GaN-based p-i-n photodiodes [79, 80], with a time response lying in the 100–500 ns range, and limited by the RC product [80]. 13.4.4.5

13.4 III-Nitride-Based UV Photodetectors

Ruden [81] has proposed for the fabrication of avalanche photodiodes a hybrid structure with a III-nitride/Si heterostructure that should be able to combine the visible-blind properties of AlGaN with the favorable impact ionization of Si. The light would be absorbed in the wide band gap material region (direct band gap), and the multiplying effect would take place in the Si region. Thus, this device could be operating at a bias voltage of only 10 V. 13.4.5

Phototransistors

A phototransistor is a photodetector whose internal gain is larger than unity. GaNbased bipolar and field effect transistors have been reported [61, 82].

Bipolar Phototransistors In a bipolar phototransistor, the reverse-biased base-collector junction works as a p-n junction photodiode, and its photocurrent is amplified by the transistor effect. In the most common configuration, the base contact is not connected (floatingbase operating mode). Yang et al. [61] report the fabrication of a GaN(n)/GaN(p)/GaN(i)/ Al0.20Ga0.80N(n) heterojunction phototransistor. Electrical contacts have been deposited on collector and emitter, and the base has been left floating. The UV light penetrates into the device through the substrate (sapphire), crosses the Al0.20Ga0.80N(n) layer, and is absorbed in the GaN(i) layer. The photogenerated electron-hole pairs are separated by the electric field in the i-region, and the electrons and holes drift towards the base and the collector, respectively. The accumulation of holes in the floating base increases the injection of electrons coming from the emitter, that results in a current gain. A gain larger than 105 has been demonstrated. It has been demonstrated that GaN-based phototransistors display a sublinear behavior of the photocurrent as a function of the incident light power, but also show persistent photoconductivity (PPC) in a similar way to that in photoconductors. In a normal regime, the holes should recombine in the base with the electrons coming from the emitter. However, the holes are trapped on the defects, which reduces their recombination rate and provoke persistent charge effects. Yang et al. [61] have demonstrated that the recombination is enhanced when a bias is applied to the detector, so that holes are forced to pass into the emitter. A bias voltage pulse thus acts as an electrical “reset”. To avoid the persistent effects, the phototransistor is submitted to a voltage “reset” pulse before each measurement (voltages of 7 to 10 V are used for this purpose), and the photocurrent is measured at a bias voltage of 3 to 4 V. In such operating conditions, the responsivity is still decreasing as a function of the optical power, and the gain is strongly dependent on the frequency, so that the gain-bandwidth product remains at a constant value. The spectral response of the device at 10 Hz input optical signal mod13.4.5.1

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ulation frequency displays an excellent UV/visible contrast over 8 orders of magnitude [61].

Field Effect Phototransistors AlGaN(n)/GaN(n)/GaN(i) heterostructure field effect transistors have also been used in the photodetection mode [82], with an illumination through the substrate (sapphire). The photogenerated holes are driven to the channel, where they are rapidly drifted to the drain by the intense electric field. These devices display high responsivity values that reach 3000 A W–1, with a sharp cutoff edge and a time response of the order of 200 ls. 13.4.5.2

13.5

Conclusions

The development of “visible-blind” UV photodetectors is nowadays widely motivated by the large number of possible applications to fields such as UV astronomy, ozone-layer monitoring, engine control, missile-plume detection, flame detection, secured space-to-space communications, etc. With these targets in view, photoconductors, Schottky photodiodes, metal-semiconductor-metal photodiodes, p-n and p-i-n photodiodes and phototransistors based on AlxGa1–xN materials have been developed in the recent period complementarily to the older and widely commercialized UV photodiodes technologies based on Si and on SiC. It is important to outline that all these nitride-based detectors offer an increased technological flexibility, notably because of the wide band gaps that are accessible with the AlxGa1–xN materials that allow the realization of detection systems that do not need any intermediate spectral optical filters, with performances that are at least as reliable as the other technologies available. The AlxGa1–xN photoconductors display a high internal gain at room temperature (*100 for Popt = 1 W m–2). However, this gain is associated with a sublinear behavior as a function of the incident light power, a weak UV/visible contrast and strong and undesirable persistent photoconductivity effects. These drawbacks make them useless in most applications. The use of a modulation of the incident optical signal together with a lockin detection considerably increases the linearity and the UV/visible contrast. However, the photoconductors lose most of their advantages in this configuration, mostly because the responsivity of the devices is strongly reduced and because the detection system becomes much more complex and therefore more expensive. The Schottky photodiodes present a uniform and flat response when they are excited above the gap, independently of the incident light power and the temperature. They also have a sharp cutoff edge, with an UV/visible contrast of more than 103. Their time response is RC limited, with a minimal time response of typically 1 ns. It is therefore clearly proven that these devices are very well suited to environmental studies and to the fabrication of UV photodiode arrays.

13.7 References

Metal-semiconductor-metal (MSM) photodiodes with very low leakage currents have been fabricated. These devices display a linear variation of the photocurrent as a function of the incident light power, and have a typical UV/visible contrast of 104. Given their large bandwidth and their low noise level, these devices can represent an excellent choice when there is the need to cover detection needs in the visible-blind optical communications. Moreover, a possibility could be to put on the same chip AlxGa1–xN MSM photodiodes with III-nitride-based field effect transistors with the purpose of monolithically fabricating integrated optical receivers. P-n and p-i-n photodiodes have a very good linearity with the optical power, and display a UV/visible contrast of 104. However, their response time is ordinarily limited by the presence of trap levels related to the magnesium, which can also be responsible for some degradation of their spectral response. The minimal cutoff wavelength is mostly limited by the difficulty to achieve a high p-type doping level in AlxGa1–xN alloys with a high Al mole fraction. Therefore, it is still necessary to improve the p-type doping of these materials in order to increase the performances of the devices as well as their reliability. Phototransistors offer the combination of a very high gain and a record UV/visible contrast of 108. These devices are therefore promising for applications where a high spectral resolution is needed, despite their narrow bandwidth that makes them unable to operate at high frequencies. In summary, the current results globally confirm that the AlxGa1–xN alloys represent the best choice in the field of semiconductors fitted to UV photodetection. However, the performance of these devices is still hindered by the large defect density in the heteroepitaxial layers. Hence, significant improvements are expected from the progresses in the epitaxial crystal growth techniques and III-nitride technologies, such as the epitaxial lateral overgrowth technique.

13.6

Acknowledgments

The strong and continuous support of Pierre Gibart, Elias Muñoz, Bernard Beaumont, and Fernando Calle is gratefully acknowledged.

13.7

References Y. A. Goldberg, Semicond. Sci. Technol. 14, R41 (1999). 2 R. D. McKeag, S. S. M. Chan, and R. B. Jackman, Appl. Phys. Lett. 67, 2117 (1995). 3 M. D. Whitfield, S. S. M. Chan, and R. B. Jackman, Appl. Phys. Lett. 68, 290 (1996). 1

A. Mainwood, Semicond. Sci. Technol. 15, R55 (2000). 5 M. Razeghi and A. Rogalski, J. Appl. Phys. 79, 7433 (1996). 6 R. Korde and J. Geist, Appl. Opt. 26, 5284 (1987). 7 L. R. Canfield, J. Kerner, and R. Korde, Appl. Opt. 28, 3940 (1989). 4

657

658

13 GaN-Based UV Photodetectors 8 9

10

11

12

13

14

15

16

17

18

19

20

21 22

J. A. Edmond, H. S. Kong, and C. H. Carter Jr, Phys. B 185, 453 (1993). M. M. Anikin, A. N. Andreev, S. N. Pyatko, N. S. Savkina, A. M. Strelchuk, A. L. Syrkin, and V. E. Chelnikov, Sens. Actuators A 33, 91 (1992). E. Monroy, F. Calle, E. Muñoz, F. Omnes, B. Beaumont, and P. Gibart, J. Electron. Mater. 28, 238 (1999). E. Muñoz, E. Monroy, J. A. Garrido, I. Izpura, F. J. Sanchez, M. A. SanchezGarcia, E. Calleja, B. Beaumont, and P. Gibart, Appl. Phys. Lett. 71, 870 (1997). J. A. Garrido, E. Monroy, I. Izpura, and E. Muñoz, Semicond. Sci. Technol. 13, 563 (1998). P. J. Hansen, Y. E. Strausser, A. N. Erickson, E. J. Tarsa, P. Kozodoy, E. G. Brazel, J. P. Ibbettson, U. Mishra, V. Narayamurti, S. P. Den Baars, and J. S. Speck, Appl. Phys. Lett. 72, 2247 (1998). D. Walker, X. Zhan, A. Saxler, P. Kung, J. Xu, and M. Razeghi, Appl. Phys. Lett. 70, 949 (1997). P. Kung, X. Zhang, D. Walker, A. Saxler, J. Piotrowsky, A. Rogalski, and M. Razeghi, Appl. Phys. Lett. 67, 3792 (1995). L. B. Flannery, I. Harrison, D. E. Lacklison, R. I. Dykeman, T. S. Chen, and C. T. Foxon, Mater. Sci. Eng. B 50, 307 (1997). B. Shen, K. Yang, L. Zhan, Z. Chen, Y. Zhou, P. Chen, R. Zhan, Z. Huang, H. Zhou, and Y. Zheng, Jpn. J. Appl. Phys. 38, 767 (1999). J. Z. Li, J. Y. Lin, H. X. Jiang, A. Salvador, A. Botchkarev, and H. Morkoç, Appl. Phys. Lett. 69, 1474 (1996). C. Johnson, J. Y. Lin, H. X. Jaing, M. A. Khan, and C. J. Sun, Appl. Phys. Lett. 68, 1808 (1996). A. Y. Polyakov, N. B. Smirnov, A. V. Govorkov, M. G. Milovidskii, J. M. Redwing, M. Shin, M. Skowronski, D. W. Greve, and R.G. Wilson, Solid-State Electron. 42, 627 (1998). C. H. Qiu and J. I. Pankove, Appl. Phys. Lett. 70, 1983 (1997). G. Beardie, W. S. Rabinovich, A. E. Wickenden, D. D. Koleske, S. C. Bi-

23 24

25

26

27

28

29

30

31

32 33

34

35

36 37 38 39

nari, and J. A. Freitas Jr, Appl. Phys. Lett. 71, 1092 (1997). H. M. Chen, Y. F. Chen, M. C. Lee, and M. S. Feng, J. Appl. Phys. 82, 899 (1997). C. V. Reddy, K. Balakrishnan, H. Okumura, and S. Yoshida, Appl. Phys. Lett. 73, 244 (1998). F. Binet, J. Y. Duboz, E. Rosencher, F. Scholz, and V. Härle, Appl. Phys. Lett. 69, 1202 (1996). O. P. Seifert, O. Kirfel, M. Munzel, M. T. Hirsch, J. Parisi, M. Kelly, O. Ambacher, and M. Stutzman, MRS Internet J. Nitride Semicond. Res. 4S1, G5.5 (1999). J. D. Guo, F. M. Pan, M. S. Feng, R. G. Guo, P. F. Chou, and C. Y. Chang, J. Appl. Phys. 80, 1623 (1996). E. Monroy, F. Calle, E. Muñoz, F. Omnes, P. Gibart, and J. A. Muñoz, Appl. Phys. Lett. 73, 2146 (1998). Q. Chen, J. W. Yang, A. Osinsky, S. Gangopadhyay, B. Lim, M. Z. Anwar, M. A. Khan, D. Kuksenkov, and H. Temkin, Appl. Phys. Lett. 70, 2277 (1997). A. Osinsky, S. Gangopadhyay, B. Lim, M. Z. Anwar, M. A. Khan, D. Kuksenkov, and H. Temkin, Appl. Phys. Lett. 72, 742 (1998). A. Osinsky, S. Gangopadhyay, B. Lim, M. Z. Anwar, M. A. Khan, D. Kuksenkov, H. Temkin, I. K. Shmagin, Y. C. Chang, J. F. Muth, and R. M. Kolbas, Appl. Phys. Lett. 72, 551 (1998). A. Van der Ziel, Proc. IEEE 58, 8 (1970). A. Usui, H. Sunakawa, A. Sakai, and A. Yamaguchi, Jpn. J. Appl. Phys. 36, L899 (1997). O. H. Nam, M. D. Bremser, T. Zheleva, and R. F. Davis, Appl. Phys. Lett. 71, 2638 (1997). E. Monroy, F. Calle, E. Muñoz, B. Beaumont, F. Omnes, and P. Gibart, Electron. Lett. 35, 1488 (1999). A. F. McKinley and B. L. Diffey, CIE J. 6, 17 (1987). F. R. De Gruji and J. C. Van der Leun, Health Phys. 67, 314 (1994). R. B. Setlow, Proc. Natl. Acad. Sci. USA 71, 3363 (1974). L. W. Jones and B. Kok, Plant Physiol. 41, 1037 (1966).

13.7 References 40

41

42 43 44 45

46

47 48 49 50

51

52 53

54

55

56

57

E. Muñoz, E. Monroy, F. Calle, M. A. Sanchez, E. Calleja, F. Omnes, P. Gibart, F. Jaque, and I. Aguirre de Carcer, Proc. SPIE 3629, 200 (1999). E. Muñoz, E. Monroy, F. Calle, F. Omnes, and P. Gibart, J. Geophys. Res. 105, 4865 (2000). S. M. Sze, Physics of Semiconductor Devices, 2nd edn (Wiley and Sons, 1981). E. Monroy, F. Calle, E. Muñoz, and F. Omnes, Electron. Lett. 35, 240 (1999). E. Monroy, F. Calle, E. Muñoz, and F. Omnes, Appl. Phys. Lett. 74, 3401 (1999). E. Monroy, F. Calle, E. Muñoz, and F. Omnes, Phys. Stat. Sol. (a) 176, 157 (1999). D. Walker, E. Monroy, P. Kung, J. Wu, M. Hamilton, F. J. Sanchez, J. Diaz, and M. Razeghi, Appl. Phys. Lett. 74, 762 (1999). S. F. Soares, Jpn. J. Appl. Phys. 31, 210 (1992). M. Klingenstein and J. Khul, SolidState Electron. 37, 333 (1994). J. Burm and L. F. Eastman, IEEE Photon. Technol. Lett. 8, 113 (1996). I. H. Oguzman, E. Bellotti, K. F. Brennan, J. Kolnik, R. Wang, and P. P. Ruden, J. Appl. Phys. 81, 7827 (1999). X. Zhang, P. Kung, D. Walker, J. Piotrowski, A. Rogalski, A. Saxler, and M. Razeghi, Appl. Phys. Lett. 67, 2028 (1995). Q. Chen, M. A. Khan, C. J. Sun, and J. W. Yang, Electron. Lett. 31, (1995). E. Monroy, E. Muñoz, F.J. Sanchez, F. Calle, E. Calleja, B. Beaumont, P. Gibart, J. A. Muñoz, and F. Cusso, Semicond. Sci. Technol. 13, 1024 (1998). A. Osinsky, S. Gangopadhyay, R. Gaska, B. Williams, M. A. Khan, D. Kuksenkov, and H. Temkin, Appl. Phys. Lett. 71, 2334 (1997). J. M. Van Hove, R. Hickman, J. J. Klaassen, P. P. Chow, and P. P. Ruden, Appl. Phys. Lett. 70, 2282 (1997). D. Walker, A. Saxler, P. Kung, X. Zhang, M. Hamilton, J. Diaz, and M. Razeghi, Appl. Phys. Lett. 72, 3303 (1998). J. C. Carrano, T. Li, P. A. Grudowski, C. J. Eiting, D. Lambert, J. D. Schaub,

58

59

60

61

62

63

64

65

66

67

68 69

70

R. D. Dupuis, and J. C. Campbell, Electron. Lett. 34, 692 (1998). J. C. Carrano, T. Li, D. L. Brown, P. A. Grudowski, C. J. Eiting, R. D. Dupuis, and J. C. Campbell, Electron. Lett. 34, 1779 (1998). G. Y. Xu, A. Salvador, W. Kim, Z. Fan, C. Lu, H. Tang, H. Morkoç, G. Smith, M. Estes, B. Goldenberg, W. Yang, and S. Krishnankutty, Appl. Phys. Lett. 71, 2154 (1997). S. Krishnankutty, W. Yang, T. Nohava, and P. P. Ruden, MRS Internet J. Nitride Semicond. Res. 3, art. 7 (1998). W. Yang, T. Nohava, S. Krishnankutty, R. Torreano, S. McPherson, and H. Marsh, Appl. Phys. Lett. 73, 1086 (1998). J. D. Brown, Z. Yu, J. Matthews, S. Harney, J. Boney, J. F. Schetzina, J.D. Benson, K. D. W. Dang, C. Terril, T. Nohava, W. Yang, and S. Krishnankutty, MRS Internet J. Nitride Semicond. Res. 4, art. 9 (1999). J. D. Brown, J. Boney, J. Matthews, P. Srinivasan, J. F. Schetzina, T. Nohava, W. Yang, and S. Krishnankutty, MRS Internet J. Nitride Semicond. Res. 5, art. 6 (2000). P. Sandvik, D. Walker, P. Kung, K. Mi, F. Shahedipour, V. Kumar, X. Zhang, J. Diaz, C. Jelen, and M. Razeghi, Proc. SPIE 3948, 265 (2000). E. Monroy, M. Hamilton, D. Walker, P. Kung, F. J. Sanchez, and M. Razeghi, Appl. Phys. Lett. 74, 1171 (1999). D. Walker, P. Kung, P. Sandvik, J. Wu, M. Hamilton, I. H. Lee, J. Diaz, and M. Razeghi, Proc. SPIE 3629, 193 (1999). G. Parish, S. Keller, P. Kozodoy, J. P. Ibbetson, H. Marchand, P. T. Fini, S. B. Fleischer, S. P. DenBaars, U. K. Mishra, and E. J. Tarsa, Appl. Phys. Lett. 75, 247 (1999). D. L. Pulfrey and B. D. Nener, SolidState Electron. 42, 1731 (1998). P. Blood and J. W. Orton, Electrical Characterization of Semiconductors: Majority Carriers and Electron States, Techniques of Physics, Vol. 14 (Academic Press, London, 1992). I. Akasaki, H. Amano, M. Kito, and K. Hiramatsu, J. Lumin. 48/49, 666 (1991).

659

660

13 GaN-Based UV Photodetectors 71

72

73

74

75

76

77

Y. Zohta, H. Kuroda, R. Nii, and S. Nakamura, J. Cryst. Growth 189/190, 816 (1998). J. C. Carrano, T. Li, C. J. Eiting, R. D. Dupuis, and J. C. Campbell, J. Electron. Mater. 28, 325 (1999). D. W. Kuksenkov, H. Temkin, A. Osinsky, R. Gaska, and M. A. Khan, J. Appl. Phys. 83, 2142 (1998). L. S. Yu, Q. Z. Liu, Q. J. Xing, D. J. Qiao, S. S. Lau, and J. D. Redwing, J. Appl. Phys. 84, 2099 (1998). P. Bhattacharya, Semiconductor Optoelectronic Devices, (Prentice Hall, New Jersey, 1994). J. Kolnik, I. H. Oguzman, K. F. Brennan, R. Wang, P. P. Ruden, and Y. Wang, J. Appl. Phys. 78, 1033 (1995). I. H. Oguzman, E. Bellotti, K. F. Brennan, J. Kolnik, R. Wang, and P. P. Ruden, J. Appl. Phys. 81, 7827 (1997).

78 79

80

81 82

A. Osinsky, M. S. Shur, R. Gaska, and Q. Chen, Electron. Lett. 34, 691 (1998). J. C. Carrano, D. J. H. Lambert, C. J. Eiting, C. J. Collins, T. Li, S. Wang, B. Yang, A. L. Beck, R. D. Dupuis, and J. C. Campbell, Appl. Phys. Lett. 76, 924 (2000). K. A. McIntosh, R. J. Molnar, L. J. Mahoney, K. M. Molvar, N. Efremow Jr, and S. Verghese, Appl. Phys. Lett. 76, 3938 (2000). P. P. Ruden, Proc. SPIE 3629, 174 (1999). M. A. Khan, M. S. Shur, Q. Chen, J. N. Kuznia, and C. J. Sun, Electron. Lett. 31, 398 (1998).

661

Subject Index a absorption and reflection spectra 281, 286 activation energy 211, 220, 224 admolecules 208, 221 adsorption 207, 210, 212 AFM 135, 137, 143 AlGaN 169, 174, 180, 538, 541, 550, 578, 594, 638, 646, 651 AlN 383, 411, 421, 538, 539, 540 anneal 500, 509, 512 asymmetric boundaries 409 atomic force microscopy 53, 62, 84, 95 atomic structure 402, 410, 416, 426 Au 499, 509, 520 avalanche photodiode 654

b band bending 497, 510 band structure 304 Bardeen model 494 basal stacking faults 149, 158, 391, 399, 412 bicrystallography 386 blue emission 40 blue LED 531, 535 buffer layer 530, 531, 540 bulk gallium nitride 5, 20

c cathodoluminescence 68, 84 CBED 156 cellular growth 17, 18 chemical vapor clean 509, 510 CIE 534, 535, circuit mapping 326–333, 337 ff., 358 ff., 406 constitutional supercooling 17, 18 contact 492, 505, 520 crystal growth 3, 8, 14 crystallography 370

CSL 387, 404, 409 cubic GaN 148 f. current collapse 604

d dechloruration 230 deep sates 89 defect characterization 324 ff. defect interactions 357 ff. 2DEG 556, 569 desorption 207, 210, 211 dichromatic complex 388 diffusion 215, 216, 220 diffusion barrier 314 dislocations 331, 337 ff., 354 ff., 360, 473, 482, 531, 534, 539 – bending 63, 82 – core 402, 409 – loops 62, 64 dissociation 10 dissociative adsorption 9 dissolution kinetics 8 doping 146 drain current model 583

e ECR plasma source 244, 248 effective luminescent area 533, 534 electron affinity 493, 511 electronic applications 3 electronic structure 289 emission spectrum 38, 39 enthalpy 199 entropy 200 epitaxy 46, 440, 451, 491 equilibrium constant 199, 204, 214 excitonic transition 234 experimental conditions 226, 229, 233 experimental performance 594

662

Subject Index extended defects 24, 25, 51, 379 external quantum efficiency 536, 537

f Fermi level 494, 511 finite elements modeling 470 f. first-principles calculations 299 formation mechanisms 411, 419, 432

g GaCl3 210, 219 GaCl2-HCl 229, 231 GaInN 531, 534 gallium-based nitrides 439, 463 GaN 45, 107, 197, 326, 379, 433, 529, 550, 578, 636, 655 – substrate 4, 19, 20 – -on-sapphire 137, 149, 156 geometrical phase 460, 463 grain boundaries 404 green LED 534, 535 growth 216, 227, 230 – kinetics 131, 140, 163, 244 – pressure 265, 267 – rate 219, 225, 230 – temperature 245, 259, 267 – thermodynamics 5

h H2 210, 217 Halide Vapor Phase Epitaxy (HVPE) 66, 91, 194, 195, 196, 529, 537 Hall measurements 251, 264, 270 HBTs 182 heterojunction bipolar transistors 614 heterostructures 140, 163, 174, 440 hexagonal GaN 120, 131, 148 f. HFETs 180 high field transport 574 high frequency noise 611 High Nitrogen Pressure Solution Growth (HNPSG) 3, 4, 13 high pressure 3, 5, 6 high pressure growth 3, 4, 13 High-Resolution Transmission Electron Microscopy (HRTEM) 62, 73, 82, 130, 150, 328, 337, 357, 361, 402, 441 homoepitaxy 40

i IDB Holt 425, 427 IDBV 425, 428 image processing 441 indium compounds 476 InGaAs 454, 471

InGaN 163, 165, 169, 477 intentional seeding 13, 17, 22 interactions 430 interface 493, 496 interface junction lines 352, 355, 363 interfacial structure 322, 345–349, 353, 355, 361, 366 interlayer 538, 539 intersubband transitions 174 inversion domain 381, 398, 423 inversion domain boundaries 150, 158, 163, 349 ionization potential 493, 507 I-V characteristics 585

k kinetics 207, 213, 225, 299, 313, 316

l laser diodes 38, 45, 47, 54 lateral epitaxial overgrowth 45 lattice distortion 473 lattice specific heat 279 LEDs 169, 171, 529, 534, 542 LEEBI 530, 531 light emitting diodes 26, 35, 36 local strain 462, 466 low field transport 570 low frequency noise 608 low-angle boundary 463, 474

m mass transfer 215, 220, 224 mechanism 210, 227, 230 mechanochemical polishing 19 Metal Organic Vapor Phase Epitaxy (MOVPE) 26, 27, 35, 48, 59, 80, 265, 530, 542 metal-induced gap states 494, 498 metalorganic MBE 257 metal-semiconductor-metal photodiode 646, 649 Mg-doping 16, 22 Mg-doping 531 misfit dislocations 154, 322, 345, 401 mobility 550, 552 mode-discrimination factor 541, 542, 543 modulation-doped FETs 549, 576, 594 molecular beam epitaxy (MBE) 32, 33, 34, 107, 140, 182 morphological instability 17 morphology 495, 517 MQW structure 31, 36, 37

Subject Index

n

r

nanopipes 403 native contamination 493, 508 native defects 52 Ni 511, 520 nitridation 242, 249, 259 III-nitrides 107, 163, 181, 635 nitride semiconductors 321 nitrogen plasma 109, 111, 118 nitrogen solubility 7, 8, 19 noise reduction 447, 450 nonlinear elasticity 472 nonpolar surfaces 299 nucleation 11, 16, 20, 220, 224, 232 nucleation layer 48

Raman and Infrared spectra 275, 277 reaction 128, 210, 230 reactor design 248, 266 reflectivity 233 residual donors 94 RHEED 121

o ohmic 492 ohmic contact 592 optical band-gap 281, 285 optical emission spectroscopy 112, 115 optical output 39, 40 optoelectronic devices 169, 170, 174 optoelectronics 4, 26, 40

p parasitic deposition 227, 231, 234 partial pressure 205, 215, 219 partition function 202, 214, 221 Pd 515, 520 pendeoepitaxy 77 phonon dispersion relations 278 phosphor 534, 535 photoconductor 635, 638, 641 photoluminescence 22, 29, 30, 52, 88, 97, 281, 284 phototransistor 655 f. piezoelectric polarization 568 p-i-n photodiode 650, 652 f. pinning 494 plasma-assisted MBE 244 point defects 21, 22, 23 polar surfaces 303–311 polarity 120, 149, 156, 556, 562 power amplifiers 601 prismatic stacking faults 415, 422 Pt 515, 520 p-T phase diagram 6

q quantum dots 451, 453, 470 quantum well 469, 476

s sapphire 382, 393, 420 – nitridation 149 f., 162 – substrate 529, 538 Schottky barrier 493, 589 – photodiode 641, 644, 646 Schottky-Mott model 493 seeded growth 18, 19, 22 segregation 440, 469 selective etching 25 semiconductors 440, 492 SiC 383, 389, 419 SiC substrate 529, 540 single-crystalline InN layers 242 solution growth 3, 8, 14 specific contact resistivity 496, 505, 520 spontaneous polarization 557 stacking-faults 322, 341, 349, 355, 369 step flow 28 steps 392, 420 STM 124 strain relaxation 567 stress 73, 90, 472, 474 stress relaxation 453, 471 sublimation 74 substitutional impurities 16, 22 substrate preparation 127, 148 f. supersaturation 18, 19, 20, 207, 217, 230 surface coverage 211, 216, 219 surface diffusion 314, 315 surface energy 298 surface morphology 248, 259, 267 surface passivation 606 surface reconstruction 120 surface state 494, 510 surface structure 120 surface treatment 497, 505, 520 symmetric boundaries 406

t TEM 130, 156, 176 f. tetragonal distortion 468 thermal stability 5 thermodynamic equilibrium 296 thermodynamical study 198, 206, 236 thin-foil effect 467, 469

663

664

Subject Index threading dislocations 51, 58, 77, 80, 135, 147, 158, 379, 401, 411 Ti 497, 505 tilt 64 TLM 496 topological analysis 321 transistors 179 transmission electron microscopy 468 transverse mode 541, 542 tunneling 495 twins, double-positioning 322, 361 two dimensional electron gas 33 two-dimensional nucleation 11

u UV detectors 171 UV LED 534, 537, 540 UV photodetector 629

v V/III ratio 246, 260 violet LED 541

w wall-plug efficiency 536 white LED 535, 541 wide bandgap semiconductors 108 work function 493, 507

x X-ray diffraction 251, 264

y YAG 534 yellow luminescence 93