Oxygen in Silicon, Volume 42 (Semiconductors and Semimetals)

Oxygen in Silicon SEMICONDUCTORS A N D SEMIMETALS Volume 42

a Semiconductors and Semimetals A Treatise

Edited by R . K . Willardson

Eicke R. Weber CONSULTING PHYSICIST DEPARTMENT OF MATERIALS SCIENCE SPOKANE, WASHINGTONAND MINERAL ENGINEERING OF CALIFORNIA AT UNIVERSITY Albert C. Beer BERKELEY CONSULTING PHYSICIST COLUMBUS. OHIO

Oxygen in Silicon SEMICONDUCTORS AND SEMIMETALS

Volume 42 Volume Editor

FUMIO SHIMURA SHILLIOKA INS717UTE OF S C l t N ( I A N I ) I F CHNOLOCY SHLILIOKA JAPAN

W ACADEMIC P R E S S , I N C . Hrrrc o u r i Bruce B; Compurri , Puh/r\Irc,r \

Boston

London

Sun Dicgo N P M 'Y o t h Sydney T d q o Torotito

This book is printed on acid-free paper @ COPYRIGHT 0 1994 BY ACADEMIC PRESS,INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY A N Y MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR A N Y INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION I N WRITING FROM THE PUBLISHER.

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LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Semiconductors and semimeta1s.-Vol.

1-New

York: Academic Press, 1966-

v.: ill.; 24 cm. Irregular. Each vol. has also a distinctive title. Edited by R. K. Willardson, Albert C. Beer, and Eicke R. Weber ISSN 0080-8784 = Semiconductors and semimetals

I . Semiconductors-Collected works. 2. Semimetals-Collected works. I. Willardson, Robert K. 11. Beer, Albert C. 111. Weber, Eicke R. QC6 l0.9.S48 621.3815'2-dc I9 85-6423 19 AACR2 MARC-S Library of Congress ISBN 0-12-752142-9 (v. 42)

[8709]

International Standard Book Number: 0-12-752142-9

Printed in the United States of America 94959697 9 8 7 6 5 4 3 2 1

Contents ...

LISTOF CONTRIBUTORS , PREFACE ,

Xlll

xv

Chapter 1 Introduction to Oxygen in Silicon F . Sh irn i i r ~

Chapter 2

The Incorporation of Oxygen into Silicon Crystals

W . Lit1 I . Introduction . 11. Silicon Crystal Growth I . Float Zone Silicon Growth 2. Crochralski Silicon Growth 111. Characteristics of Czochralski Silicon Growth , I. Dopant Distribution 2. “Unintended Dopants” 3. Effective Segregation Coefficient . 4 . Convection Flows in Crochralski Melt . 5 . Macroscopic Radial Impurity Uniformity , 6. Microscopic Inhomogeneity in Czochralski Silicon . I V . Oxygen Incorporation and Segregation in Czochralski Silicon Growth I . Incorporation Mechanism , 2 . Oxygen Segregation and Microscopic Inhomogeneity . V . Controlled Oxygen Silicon Growth . I . Normal Crochralski Growth , . 2. Magnetic Field Applied Crochralski Growth (MCZ) . , 3. Continuous Czochralski Silicon Growth . . V l . Summary . References .

Chapter 3

9 10 10

12 15 IS 16 19

20 21 22 24 24 34 37 31 42 46 50 50

Characterization Techniques for Oxygen in Silicon

T. J . Shqffrirr and D . K. Schrodrr 1. Introduction . 11. Physical Techniques . . I . lnfrared Spectroscopy

53 55 55 V

vi

CONTENTS

2. Transmission Electron Microscopy 3. X-Ray Diffraction and Topography 4. Secondary Ion Mass Spectrometry . Ill. Chemical Techniques . 1. Defect Etches . 2. Inert Gas Fusion . . 3. Activation Analysis Techniques . IV. Electrical Techniques . 1. Deep Level Transient Spectroscopy 2. Recombination Lifetime . 3. Generation Lifetime . V. Summary . References .

.

.

58 62 66 69 69 12

t

.

74 77 78 79 81 85 86

Chapter 4 Oxygen Concentration Measurement

W . M . Bullis I. Introduction

.

11. Infrared Absorption Measurements Under Ideal Conditions

.

Ill. Infrared Spectrometers . . I . Dispersive Infrared Spectrometers . 2. Fourier-Transform-Infrared Spectrometers . IV. Analysis of Oxygen Spectra . I . Baseline . 2. Analysis Method: Peak Height or Integrated Area? . . 3. Multiple Reflection and Interference Fringes . 4. Spectrum Collection Method: Air Reference or Difference? 5 . Reference Specimen Characteristics . 6. Back-Surface Condition . 7. Free-Carrier Absorption . 8. Interference from Absorption Peaks Due to Precipitates . 9. Specimen Temperature . . . . V. Absolute Determinations and Calibration Factors . . I . Calibration Factors for Room Temperature Measurements 2. Routine Absolute Measurements in Heavily Doped Silicon VI. Standards and Reference Materials . I . Standard Test Methods 2. Certified Reference Materials . VII. Summary . Acknowledgments . References .

95 99 102 102

107 I I3 113 I 15 118 121 121 122 128 134

135 136 136 142 144 144 14.5 147

147 148

Chapter 5 Intrinsic Point Defects in Silicon S . M . Hu 1. Introduction . 11. Swirl Defect Manifestation of Intrinsic Point Defects

153 156

vii

CONIENTS

111. Thermal Defects in Silicon . I V . Self-Diffusion . . I . Point Defects and Self-l)ilfusion 2 . Self-Diffusion from Isotope Experiments . 3 . Self-Diffusion from Kinetics of Extended Defects . V . Coexistence of Vacancies and Self-lnterstitials in Silicon . V I . Interstitial Configuration and Charge-Enhanced Migration , I . Geometrical Configurations and Migration Pathways of the Self-Interstitial . 2. Charge-Enhanced and Athernial Migration of the Self-Interstitial VII. Formation and Migration Parameters of Point Defects . , I . Studies of Point Defects from Irradiations . 2 . Vacancy Formation Energy from Positron-Lifetime Measurements 3 . Point Defect Concentrations rrom Thermal Expansion Measurements 4. Estimation of Self-lnterstitial Concentration from Oxygen Precipitation . 5 . Diffusivity of the Self-lnter,titial from Membrane Experiments . 6. Defect Parameters from Model-Fitting Au and Pt Diffusion . VIII. Defect Energetics and Pathways from Theoretical Calculations . 1X. Summary . Reference5 ,

i59 160

160 161 162 164 166 166 170 172 172 175 175 176 177

178 179 184 185

Chapter 6 Some Atomic Configurations of Oxygen

B . Pqjot I . Introduction

.

11. Spectroscopy of Localized Mode5 in Semiconductors 1. Localized Modes and Resonant Modes .

Ill.

IV.

V.

V1.

VII.

2. lntensities . 3 . Stress-Induced Effects Interstitial Oxygen . I . Static Properties . . 2. Dynamic Properties 3 . Perturbation by Foreign Atoms . Quasi-Substitutional Oxygen . 1 . Spectroscopies o f the Oxygen-Vacancy Defect 2. Thermal Stability . . 3 . Other 0-Related Irradiation Defects . Comparison with Other Light Element Impurities 1. Carbon . 2 . Nitrogen . 3 . Hydrogen . . Oxygen in Other Semiconductors I . Germanium . . 2 . Gallium Arsenide . . Summary . Acknowledgments . References .

191 194 194 196

.

1%

. .

. .

.

. .

. . .

. . .

200 200 210 21 I 217 217 220 222 224 224 226 228 233 233 236 243 244 245

viii

CONTENTS

Chapter 7 Electrical Properties of Oxygen in Silicon J . Michel and L . C . Kimerling I. Introduction

. . . . . .

.

11. Thermal Donors . 1. Donor Introduction

.

2. Spectroscopy . 3. Heat Treatment at 350-500°C . 4. Atomic and Electronic Structure . 5 . Current Understanding and Unresolved Issues 111. New Donors . References .

.

.

. . .

251 251 252 254 266 211 280 282 284

Chapter 8 Diffusion of Oxygen in Silicon

R . C . Newman and R . Jones I. Introduction

.

11. Direct Measurements of Normal Oxygen Diffusion

.

. 1 . Single Oxygen Diffusion Jumps . . . 2. Profiles 3. Summary . . 111. Indirect Measurements of Normal Oxygen Diffusion I . Do,,Determined from Oxygen Precipitation at High Temperatures 2. Oxygen Aggregation at Intermediate Temperatures . 3. Oxygen Aggregation at Low Temperatures . 1V. Enhanced Oxygen Diffusion Not Involving Hydrogen . I . Effects Due to the Injection of Vacancies and I-Atoms by 2 MeV Electron Irradiation . . 2. The Effects of Excess /-Atoms 3. Rapid Diffusion of Di-Oxygen Defects . 4. Effects Due to Carbon . . 5. Effects Due to Metallic Contamination . 6. Summary . V. Silicon Containing Hydrogen Impurities . 1. Silicon Heated in Hydrogen Gas . 2. Silicon Heated in RF Plasma . 3. An Outline Model and Summary . VI. Theoretical Modeling of Oxygen Diffusion . 1 . Theoretical Methods . 2. Theory of the Diffusion Constant . 3. Interstitial Oxygen . 4. Diffusion of 0, Catalyzed by Hydrogen . . 5. The Oxygen Dimer . 6. Other Oxygen Aggregates . . V11. Constraints on Models of Thermal Donor Centers V111. Summary . Acknowledgments . . . References . . .

. . . . . . .

. . . . . . . . . .

. .

.

. .

.

. . . .

290 292 293 296 298 298 299 303 305 308 309 312 314 316 317 317 318 319 323 324 326 327 331 332 335 339 341 342 345 341 347

ix

CON1 ENTS

Chapter 9 Mechanisms of Oxygen Precipitation: Some Quantitative Aspects

T . Y . Tan und W . J .

7'ciyIor

I . Introduction . 11. Volume Shortage Associated with Oxygen Precipitation 111. Precipitate Nucleation I . The Homogeneous Nucleation Model , 2. The Strain Relief Models IV. Precipitate Growth . I. The 0, Diffusion-Limited Precipitate Growth Behavior 2. The Dominant Strain Relief Mechanism: I-Emission . V . The Effect of Carbon V1. Defect Generation . 1. Si Self-Interstitial Gener-ation , 2 . Prismatic Dislocation Loop Punching . V I I . Summary: The Free Energy and Flux Balance Treatment of Precipitation Problem References .

.

. .

353 357 358 359 362 367 367 37 I 374 379 379 379

the Oxygen 386 387

Chapter I0 Simulation of Oxygen Precipitation

M . Schrrms I. Introduction . 11. Model Types . I . Nucleation Models 2. Deterministic Growth Models , 3. Combined Nucleation and Growth Models . 4. Monte Carlo Models , 5. Models Based on Rate 01' Fokker-Planck Equations 111. Models and Experimental Rewlfs . I . General Kemarks . 2. One-, Two-. and Three-Step Thermal Cycles . 3. Multistep Thermal Cycle\ 1V. Computer-Aided Design of Oxygen Precipitation , . I . Substitutional Annealinga 2. Influence of Process Variations . V . On the Interactions of Oxygen with Other Defects . 1. Current Models . 2. Generalized Precipitation i-:quations . V I . Summary . References .

Chapter I 1

39 I 393 393 396 400 402 404 413 413 416 424 47-8 42X 43 I 435 435 441

443 444

Oxygen Effect on Mechanical Properties

K . Sutnino and I . Yonrnupi I Introduction 11 Plastic Deformation and DisloLatlon\

in

Silicon Crystals

450 45 I

X

CONTENTS

111. Influence of Dispersed Oxygen Atoms on the Mobility of Dislocations

in Silicon . . . 1. Methodological Problems in the Measurement of Dislocation Velocities . 2. Velocity of Dislocations in High-Purity Silicon . 3 , Velocity of Dislocations in Silicon Containing Oxygen Impurities 4. Morphology of Dislocations in Motion . 5. Interpretation of the Oxygen Effect on Dislocation Velocity . IV. Immobilization of Dislocations by Oxygen . . . 1. Release Stress of Dislocations Immobilized by Oxygen Impurities 2. State of Oxygen Segregated on Dislocations . . . V . Effect of Oxygen on Dislocation Generation . I , Generation of Dislocations . 2. Oxygen Effect on Dislocation Generation . . V1. Mechanical Properties of Silicon as Influenced by Oxygen Impurities . 1 . Mechanical Properties of High-Purity Silicon Crystals 2. Oxygen Effect on Mechanical Properties of Dislocation-Free Crystals . 3 . Oxygen Effect on Mechanical Properties of Dislocated Crystals 4 . Theoretical Derivation of Yield Characteristics . . 5. Wafer Strengthening by Oxygen Impurities . VII. Influence of Oxygen Precipitation on Mechanical Strength 1. General Features in the Softening of Silicon Related to Precipitation of Oxygen . . 2. Yield Strength of CZ-Si with Oxygen Precipitation . . 3. Mechanism of Precipitation Softening V111. Effects of Nitrogen and Carbon Impurities on Mechanical Properties of Silicon . 1. Nitrogen Effect . 2. Carbon Effect . . . 1X. Summary . References .

454 454 455 451 460 46 1 463 463 461 469 469 472 474 414 476 471 48 I 488 490 490 493 496 499 499 504 504 5 10

Chapter I2 Grown-in and Process-Induced Effects W . Bergholz 1. Introduction . . . 11. Oxygen Precipitation During High-Temperature Processes . . I . Overview: Morphology and Phases of Oxygen Precipitates 2. Factors That Determine the Type of Oxygen Precipitate . 3. Oxygen Precipitation in Different Temperature Regimes . 4 . Multiple-Step Temperature Annealings . 5. Other Factors That Affect Oxygen Precipitation . . 6. Oxygen-Related Defects and Process-Induced Defects Ill. Grown-in Defects: Precipitation and Intrinsic Defect Aggregation During Crystal Growth . 1. Oxygen Precipitation During Crystal Growth . . . 2 . Intrinsic Defects . 3. Grown-in Defects and Gate Oxide Quality .

513 515 515 522 526 540 544 547 55 I 55 1 552 564

xi

C‘ONTFNTS

4. Speculations on the Origin-Formation Mechanisms of Grown-in . Defects I V . Summary . References .

570 57 I 572

Chapter 13 Intrinsic/lnternal Gettering

F. Shimura 1. lntroduction . 11. Surface and Interior Microdefect\

.

I . Surface Microdefects

2. Interior Microdefects 3. Summary of Process-Induced Microdefects

.

517 579 580 583 590 593 593 596 596 599 599 599 606 610 610 611 612

.

614

.

615

. .

619 621 622 623 62.5 625 628 630 633 634 63.5 636 640 647 651

.

. .

I l l . Gettering . I . General Remarks . 2. Elimination of a Contamination Source . 3. Intrinsicilnternal Gettering IV. Oxygen Behavior in Silicon I . Oxygen Effect o n Silicon Wafer Properties . 2. Oxygen Precipitation and Redissolution , . 3 . Oxygen Out-Diffusion and Denuded Zone Formation V. Internal Gettering Process and Mechanism . , I . Thermal Cycle . 2. Gettering Mechanism 3. Gettering Sinks . VI. Summary . References .

. .

. .

. . .

Chapter 14 Oxygen Effect on Electronic Device Performance

H . T sity N I. Introduction . I I . Device Characteristics and (‘ry5tal Defects . . I , Device Structure vs. Cryrtalline Defects . . 2. Failure Modes in LSI Devices . Ill. Defect Generation . . I . Oxygen Precipitate Related Modes . 2. Residual Stress of SiOz Film . , 3. Oxygen Related Defects hy Ion Implantation . 4. Oxide Film Degradation 5 . Lattice Defect Generation h i e t o Heavy Metal Contamination . I V . Improvement of Device Yield I . Intrinsic Gettering Application to VLSl . . 2 . Homogenization of Precipitated Oxygen . . 3. Intrinsic Gettering Application of Epitaxial Wafers to VLSl . 4. Getterability for Heavy Metal Impurities .

. . . . . .

.

xii

CONTENTS

5 . Control of Mechanical Strength 6. Advanced Intrinsic Gettering V. Summary . Acknowledgments . References .

INDEX

.

CONTENTS OF PREVIOUS VOLUMES.

.

. .

t

.

. . . . .

652 660 663 663 664 665 680

List of Contributors Numbers in parenthe5es indicate the page\ on which the authors' contribution5 hegin

W. BERGHOLZ ( 5 13). Siemens A G , WernerM*erkstr.2 , 8400 Regensburg, Germuny. W . M . BULL.IS ( 9 3 , Mutrriuls d; Metrologv, 1477 Enderby Way, Sirnny 1~ I P , CUliforn iu 94087. S . M. H u , (153) IBM East Fishkill Fucdity, 1580 Route 52, HopeM'ell Jct., N r w York 12533. R . JONES (290). Depurtrnent of P1iy.sic.s. University of Exeter, Stocker Roud, E.\-etc.r EX4 4 Q L . U K . L . C . KIMERLING (25 l ) , Deprrrttnent of Materiuls Science and Engineering. Mussuchusettt.s lnstitutr o f Technology, Rootn 13-5094, Carnhridge, Mussuchusi.tts 02139. W . LIN(9),AT&T Bell Luhorutories, 555 Union Blvd., Allentm-n, Pennsyltwiiu 18103. J . MICHEL(25I ) , Departtnrnt o f Muterials Science und Engitwering, Massachusetts Institutcl (?f Technology. Room 13-5094, Cambridge, Mirssuchrrsetts 02139. R . C . NEWMAN (290). Intet-tli.sc~iplinaryResearch Center, University of London, Prince Consort Roud. London S W7 2BZ, U K . B . PAJOT(1911, Groupr dri Physique des Solides, UnivrrsitP Paris 7 et Paris 6 , Tour 23, 2 p1uc.e J i r s s i e u . F-75251 Paris Cedex 05, Frunce. M. SCHREMS (391 ), Integrutc,d Circuir Advanced Process Engineering Depurtment, Toshiba Corporulion, Kornukai. Toshibu-rho, Saiwwiku, Kal-lwsaki 210, Japan. D. K . SCHRODER ( 5 3 ) . Centcr jiir Solid Stute Electronics Research, Arizonu Stute University, Ti.rnpe. Arizona 85287. T . J . SHAFFNER ( 5 3 ) , Texas Instriimrnts, Incorporated, Marerials Science Lahorutor.y, P.O. Box 6559.16, Dullus, Texas 75265. I;. SHIMURA (577),Department (fMaterials Science, Shizuoku Institute o f Science and Technology, 2200-2 T o y o . s a ~ wFukuroi, ~ Shizuoku 437, Japan. xiii

xiv

LIST OF CONTRIBUTORS

K. SUMINO (450), Institute for Materials Research, Tohoku University, Katahira, Sendai 980, Japan. T. Y . TAN(353), Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27706. W. J . TAYLOR (353),Motorola APRDL, Mail Stop K-10,3501 Ed Bluestein R d . , Austin, Texas 78721. H. TSUYA(619), Research and Development Group, NEC Corporation, Shimokuzawa, Sagamihara 229, Japan. I . YONENAGA (450), Institute for Materials Research, Tohoku University, Katahira, Sendai 980, Japan.

Preface Silicon, which has been and will be the dominant material in the semiconductor industry, will carry us into the ultra-large-scale integration (ULSI) era. The silicon semiconductor industry now requires the minimum concentration of harmful defects and impurities in silicon crystals in order to improve the device manufacturing yield and operation performance. These requirements are becoming increasingly stringent as the technology changes from LSI t o U L S I . At present almost all the silicon wafers used for microelectronic circuit fabrication are prepared by the Czochralski (CZ) method or its modification; these silicon wafers contain oxygen on the order of atoms/ cm'. N o matter how much oxygen is incorporated in silicon wafers. the resulting impurity critically affects the properties and yield of electronic devices because of the effect o n the mechanical and electrical properties of the wafers as well as on the lattice defects incorporated. Recently it has been recognized that t h e surface microroughness of polished silicon wafers. which can greatly affect t h e device performance, may also be related to the impurity and related microdefects. Under the circumstances, for the last three decades both academia and industry have devoted a great deal of attention to the investigation of the behavior of oxygen in silicon. The investigation was particularly extensive during the decade when the beneficial effect of oxygen on device performance was discovered. Even greater attention should be devoted to this subject as the technology of microelectronic circuits approaches ULSI and beyond. It is therefore extremely important to understand the behavior of oxygen in silicon from both the scientific and the engineering points of view and to control not only the oxygen concentration but also its agglomeration phenomenon. Accordingly, this volume reviews the latest understanding of the behavior and roles of oxygen in silicon from both the experimental and theoretical points of view. The fourteen chapters, written by recognized authorities representing industrial and academic institutions, cover thoroughly the phenomena related to oxygen in silicon from crystal growth to device fabrication processes. Some indispensable diagnostic techniques for oxygen are covered as well. Because the chapters may be read independently, the editor retained some overlapping among the chapters. xv

xvi

PREFACE

Moreover, all the related discussions among the chapters may not necessarily agree with each other. The editor intended to leave such argument to show that oxygen in silicon is still a highly debated subject. The authors of the individual chapters were encouraged to describe the fundamentals in order to make the volume as useful as possible both to graduate students and to scientists from other disciplines as well as to active participants in the exciting arena of silicon-based microelectronics research. The editor’s experience in working on semiconductor technology at an electronic device manufacturer, at an electronic materials manufacturer, and at a university should ensure that this volume is one in which both the fundamental and practical matters of this interdisciplinary area will be discussed. Finally, I trust that this volume will prove to be an important and timely contribution to the semiconductor and microelectronics literature. Fumio Shimura

SEMICONDUCTORS A N U SEMIMETALS. VOL. 42

CHAPTER 1

Introduction to Oxygen in Silicon F . Shimura DEPARTMENT OF MATERIALS SCIENCE SHIZUOKA INSTITUTE OF SCIENCE A N D TECHNOLOGY, SHIZUOKA. JAPAN

The growth of single crystals of silicon from high-purity polysilicon is a critical beginning step for the fabrication of electronic devices based on silicon. Although various techniques have been utilized to convert polysilicon into single crystals of silicon, two techniques have dominated the production of silicon single crystals because they meet the requirements of the microelectronic device technology. One is a zone-melting method commonly called the ,flour-zone (FZ) method (Keck and Golay, 1953; Keck et al., 1954),and the other is a pulling method generally called the Czochrulski (CZ) mc4iod although it should be called more properly the Ted-Little method (Teal and Little, 1950). It is estimated that about 80% of the single crystal silicon used for device manufacturing is produced by the pulling method (Zulehner and Huber, 19821, i.e., CZ silicon, and that is a reason we have a great interest in the crystals. In the Teal and Little method, which modified the technique to determine the crystallization velocity of metals developed by Czochralski (Czochralski, 1918). a single crystal is grown by pulling from the melt contained in a quartz or vitreous silica (SO,) crucible. The surface of crucible that contacts the silicon melt is gradually dissolved (Chaney and Varker, 1976) as a result of the reaction SiO,

+ Si+

2SiO.

(1)

This reaction enriches the silicon melt with oxygen. Most of oxygen atoms evaporate from the melt surface as volatile silicon monoxide ( S O ) , but some of them incorporate into a silicon crystal through the crystal-melt interface (Kaiser and Keck, 1957). These oxygen atoms can greatly affect the electrical, chemical, mechanical, and physical properties of a silicon crystal. In 1954 the presence of oxygen in silicon single crystals was first demonstrated with a phenomenon showing the large resistivity change induced by heat treatment (Fuller et al.. 1954), although the phenomenon was not correlated to oxygen in silicon at that time. Fuller et al. found 1 Copyright @ 1994 hy Academic P r e s . Inc.

All rights of reproduction In any form reserved ISBN &I?-752142-9

2

F. SHIMURA

that the resistivity of CZ silicon crystals changed greatly when the crystals were heat treated at 430-450°C. By heating the crystals to temperatures above about 500°C the change was reversed. This finding surely provided the momentum; since then oxygen in silicon has been one of the most important subjects in the field of silicon materials science and engineering. Two years later, by means of infrared absorption spectroscopy, Kaiser, Keek, and Lange first confirmed that CZ silicon single crystals contain oxygen as an impurity in concentrations on the order of magnitude higher than the usual doping impurities (Kaiser, Keck, and Lange, 1956). At the same time, the oxygen concentration was correlated to the intensity of the infrared absorption band at 9 pm or 1106 cm-' (Hrostowski and Kaiser, 1957; Kaiser et al., 1956; Kaiser and Keck, 1957), and shortly Hrostowski and Kaiser obtained the solubility of oxygen in silicon (Hrostowski and Kaiser, 1959). On the basis of the infrared absorption analysis, it has been established that oxygen atoms incorporated into silicon dominantly occupy interstitial sites in the silicon lattice with average positions midway between two neighboring silicon atoms along the four equivalent (1 1 1) bond directions (Kaiser et al., 1956).Two neighboring silicon atoms give up their covalent bond and engage with an interstitial oxygen atom instead, forming an isosceles triangle with Si, 0, Si at the corners. With Si-0 distances of 1.6 A and assuming the Si-Si distance to be essentially unchanged (2.34 the bond angle Si-0-Si is approximately 100". Because of the crystal symmetry, the nonlinear Si-0-Si bridge has six equivalent positions. Transition between those six positions occur frequently because the transition does not involve the breaking of chemical bond; that is, it requires a small activation energy (Corbett and Watkins, 1961). Soon after, the work by Fuller et al. (1954) on the resistivity change induced by heat treatment and Kaiser et al. (1956) on the verification of impurity oxygen in CZ silicon single crystals, it was confirmed that oxygen as an impurity incorporated into CZ silicon in an electrically neutral form can be caused to provide donors, called thermal donors, in the low-temperature range (400-500°C) and the states can be annihilated by a subsequent at higher temperatures (>650"C) (Fuller and Logan, 1957; Kaiser, 1957; Kaiser, Frisch, and Reiss, 1958). Recent investigation has shown, however, more complicated behavior of oxygen-related carriers, which greatly depends on the heat-treatment temperature (Capper, et al., 1977). Eventually, another type of oxygen donor, called new donor (Kanamori and Kanamori, 1979), can be formed in CZ silicon subjected to heat treatment in the temperature range between 600 and 1000°C. For convenience, the oxygen donors formed around 450°C are occasionally referred to as old donors. The new donors can be annihilated by heat

A),

1.

INTRODU("rI0N T O OXYGEN IN SILICON

3

treatment at a high temperature, e.g., >IIO0"C (Cazcarra and Zunino, 1980). Thus a standard heat treatment in the temperature range between 650 and 800°C for the annihilation of old donors can cause the generation of new donors. In order to avoid the generation of new donors during old donor annihilation, therefore, rapid thermal processing (RTP) at 650°C for a short time, on the order of seconds, has been suggested as an effective alternative donor-annihilation step (Wilson, Paulson, and Gregory, 1985). Since the concentration of oxygen incorporated into CZ silicon crystals exceeds the solid solubility in the practical temperature range, the supersaturated oxygen can precipitate during subsequent heat treatment. Patel and Chaudhuri (1962) showed that the yield point of a "dislocation-free" CZ silicon crystal is lowered by almost a factor of 5 after heat treatment at 1000°C for 76 hrs. The degradation in mechanical strength of silicon has been attributed to dislocations generated by the precipitation of supersaturated oxygen (Kondo, 1981 ; Patel, 1977; Patel and Chaudhuri, 1962; Sumino, 1981; Yasutake, Umeno, and Kawabe, 1980). This yield behavior in semiconductors has been shown to be governed by the dynamical behavior of dislocations (Patel and Chaudhuri, 1962) as first pointed out for LiF by Johnston and Gilman (Johnston and Gilman, 1959). It has been recognized that the oxygen precipitation can cause warpage of silicon wafers during thermal processing (Leroy and Plougonven. 1980; Shimizu, Watanabe, and Kakui, 1985). With regard to the characterization of lattice defects generated by oxygen precipitation in CZ silicon, there have been a large variety of observations by means of transmission electron microscopy (TEM) for the materials heat treated under various conditions (Bender, 1984; Bourret, Thibault-Desseaux, and Seidman, 1984; Gaworzewski et al., 1984; Maher, Staudinger, and Patel, 1976; Matsushita, 1982; Ponce, Yamashita, and Hahn, 1983; Shimura, Tsuya, and Kawamura, 1980a). The first and most thorough characterization was made by Maher et al. in 1976, and then followed by Shimura et al. in 1980. In brief, the defects produced by oxygen precipitation in CZ silicon are ( I ) SiO, precipitates ( X = 21, (2) extrinsic-type perfect dislocations associated with the precipitates, and (3) extrinsic-type stacking faults associated with the precipitates. That is, it may define that impurity oxygen atoms, SiO, precipitates, and dislocations or stacking faults are the first-, second-, and third-order defects in CZ silicon. The second- and third-order defects can degrade the mechanical strength of CZ silicon wafers. Because of the detrimental effect of oxygen, in terms of the electrical and mechanical properties. on silicon wafers, oxygen had been recognized as a harmful impurity in silicon for many years. Therefore, on the

4

F. SHIMURA

basis of the CZ method several new crystal growth techniques that minimize the incorporation of oxygen into silicon crystals were investigated (Hoshi, et al., 1980; Suzuki, et al., 1981; Watanabe, et al., 1981). One of them is the magnetic-field-applied CZ (MCZ) method, which utilizes the effect of magnetic field applied to the silicon melt on melt flow damping. Although at this moment the MCZ method has been used to grow silicon crystals with a wide variety of oxygen concentrations, from low to high, that cannot be obtained by the conventional CZ method (Ohwa, et al., 1986; Suzuki, et al., 1986; Takasu, et al., 1990), the technique was first applied by Hoshi, et al. (1980) to grow CZ silicon crystals that contain impurity oxygen of low concentration. The second epoch-making year might be 1976 when Rozgonyi, Deysher, and Pearce first reported that interior defects produced by oxygen precipitation can be effective to suppress epitaxial stacking faults or the origin in CZ silicon wafers. This phenomenon showing a beneficial effect of impurity oxygen in CZ silicon was first reported as in situ gettering (Rozgonyi, et al., 1976). In 1977, Tan, Gardner, and Tice further clarified this phenomenon and termed it intrinsic gettering, so as to distinguish it from extrinsic gettering, which had been commonly used in the silicon device industry. Since then, the intrinsic gettering or internal gettering (IG) technique has been extensively investigated and applied to the fabrication of microelectronic devices using CZ silicon wafers. Because the IG effectiveness depends on the type and density of interior defects, which in turn depend on the initial oxygen concentration of the silicon wafer, annealing temperature, and time, a great deal of attention has been devoted to the investigation on the behavior of oxygen in CZ silicon both in the silicon academia and industry. Although the growth process and the related phenomena of oxygen precipitates have been extensively investigated (Patel, 1981; Lin, 1990), the nucleation process has not been completely understood yet. Homogeneous nucleation is nucleation from a homogeneous phase, as it is called, in which nucleation occurs randomly; while, catalyzing nucleation, where discontinuities such as lattice defects and second-phase particles in the matrix supply the nucleation sites, is called heterogeneous nucleation. Heterogeneous nucleation requires far less energy than homogeneous nucleation and is by far the more commonly observed in any system. Based mainly on the analyses of experimental results, it has been proposed by different investigators that the nucleation for oxygen precipitation in silicon would be a homogeneous process (Freeland, et al., 1977; Osaka, Inoue, and Wada, 1980), a heterogeneous process (Ravi, 1974; Shimura, Tsuya, and Kawamura, 1980b), or a combination of homogeneous and heterogeneous processes (Batavin, 1970). The major difficulties in this

I.

INTRODLICTION TO OXYGEN I N SILICON

5

argument may partly lie in the definition of homogeneous and heferogen ~ w i i s(Hu. 19861, although the physical difference between them is very clear, and in uncertainty on whether the process experimentally observed is the nucleution or g r o w f h process of oxygen precipitates. Putting the definition aside, it has been widely accepted that oxygen precipitation depends greatly not only on the initial oxygen concentration, i.e.. the oxygen supersaturation ratio, but also on various heterogeneous fucfors (Shimura and Tsuya, 1982). For example, subsidiary impurities such as carbon (Kishino, Matsushita, and Kanamori, 1979: Kung, Forbes, and Peng. 1983; Oehelein, et al.. 1981; Shimura. 1986; Usami, Matsushita. and Ogino, 1984) and nitrogen (Chiou, et al., 1984; Shimura and Hockett, 1986). In particular. a significant enhancement effect of oxygen precipitation due to the presence of carbon atoms has been widely observed since Kishino et al. first reported the phenomenon in 1979. In addition. the effect of thermal history on oxygen precipitation has been strikingly shown for silicon samples obtained from various positions of a CZ silicon ingot grown by the continuous-feeding CZ method (Shimura, 1991). Moreover, in addition to the beneficial effect of oxygen in silicon in terms of the 1G capability. it has been recognized that CZ silicon containing more oxygen as an impurity is less vulnerable than oxygen-lean FZ silicon to thermal stress in the device fabrication processes (Leroy and Plougonven, 1980; Hu, 1977). High-temperature processing of silicon wafers during electronic device manufacturing often produces sufficient thermal stresses to generate slip dislocations and warpage (Leroy and Plougonven, 1980: Takasu, et al.. 1981). These effects bring about yield loss due to leaky junctions, dielectric defects, and reduced carrier lifetime, as well as reduced photolithographic yield because of the degradation of wafer flatness. Deformation experiments have systematically shown that FZ silicon is more easily deformed than CZ silicon before preheating, while after preheating CZ silicon becomes more susceptible to plastic deformation (Kondo, 1981). A very drastic difference in the mechanical strength has been observed between F% and CZ silicons when they contain dislocations; that is, CZ silicon is much stronger than FZ silicon against thermal stresses (Sumino, et al., 1980). The difference in mechanical strength is attributed to the difference in the concentration of oxygen and associated defects (Kondo. 1981; Sumino, et al.. 1980; Patel and Chaudhuri. 1962; Yonenaga, Sumino, and Hoshi. 1984). This difference in mechanical stability against thermal stress is the dominant reason why CZ silicon crystals have been used almost exclusively for the fabrication of 1Cs whose level of integration requires a large number of thermal process steps. Howevet, it should be noted that as mentioned previously oxygen, if it

6

F. SHIMURA

precipitates too much, in CZ silicon can degrade the mechanical strength of the wafer. In summary, no matter how much oxygen is incorporated in silicon wafers used for the fabrication of electronic devices, the impurity critically affects the properties and yield of the devices because of the following three factors: (1) internal defects produced by oxygen precipitation benefit the gettering effect (IG),(2) mechanical strength of silicon wafers greatly depends on the oxygen concentration and state, i.e., dissolved oxygen atoms or SiO, precipitates, and (3) oxygen donors are formed at a specific temperature. Consequently, it is very important to understand the behavior of oxygen from the electrical, chemical, and structural points of view, and to control not only the concentration but also the precipitation in silicon. All these issues will be discussed and reviewed in detail from the experimental and theoretical points of view in the following chapters of this volume. Finally, we would like to emphasize that oxygen in silicon is still, and will be further, one of the hottest subjects in the field of silicon-based materials science and technology.

REFERENCES Batavin, V . V. (1970). Sov. Phys. Crystuogr. 25, 100. Bender, H. (1984). Phys. Stat. Sol. ( a ) 86, 245. Bourret, A.. Thibault-Desseaux, J., and Seidman, D. N. (1984). J. Appl. Phys. 55, 825. Capper, P., Jones, A. W., Wallhouse, E. J., and Wilkes, J. G. (1977). J. Appl. Phys. 48, I 646. Cazcarra, V. and Zunino, P. (1980). J . Appl. Phys. 51, 4206. Chaney, R. E.. and Varker, C. J . (1976). J. Crystal Growth 33, 188. Chiou. H. D., Moody, J., Sandfort, R., and Shimura, F. (1984). In VLSI Science and Technologyll984, K. E. Bean and G. A. Rozgonyi, (eds.), p. 59. The Electrochemical Society, Princeton, N.J. Corbett, J . W., and Watkins, G . D. (1961). J. Phys. Chem. Solids 20, 319. Czochralski, J. (1918). 2. Phys. Chern. 92, 219. Freeland, P. E., Jackson, K. A., Lowe, C. W., and Patel, J. R. (1977). Appl. Phys. Lett. 30, 31. Fuller, C. S., Ditzenberger, J. A,, Hannay, N. B., and Buehler, E. (1954). Phys. Rev. 96, 833. Fuller, C . S . , and Logan, R. A. (1957). J. Appl. Phys. 28, 1427. Gaworzewski, P., Hild, E., Kirschit, F. G . , and Vecsern YCs, L. (1984). PhyA. Stat. Sol. ( I ) 85, 133. Hoshi, K.. Suzuki, T., Okubo, Y., and Isawa, N. (1980). Ext. Abstr., 157th Electrochem. SOC. M e e t . , p. 811. Hrostowski, H. J., and Kaiser, K. H. (1957). Phys. Rev. 107, 966. Hrostowski. H. J., and Kaiser, K. H. (1959). J. Phys. Chern. Solids 9 , 214. H u , S. M. (1977). Appl. Phys. Lett. 31, 53.

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INTRO1)UCTION TO OXYGEN IN SILICON

7

Hu. S . M. (1986). In Oxvgen. Carbon, Hvdrogen, und Nitrogen in Ctyvsfalline Silicon. J . C. Mikkelsen. J r . . S. J. Pearton. J . W. Corbett, and S. J . Pennycook (eds.). p. 249. Materials Research Society, Pittsburgh. Johnston. W. G.. and Gilman, J . I 1959). J. Appl. Phys. 30, 129. Kaiser. W. (1957). Phys. Ret.. 105. 1751. Kaiser. W.. Frisch. H. L.. and Reizs. H. (1958). Phys. Rev. 112, 1546. Kaiser. W.. and Keck. P. H. (1957). J . A p p l . Pliys. 28, 882. Kaiser. W.. Keck, P. H.. and Lange. C. F. (1956). Phys. Re\,. 101, 1264 Kanamori. .4.. and Kanamori. M (19791. J. Appl. Phys. SO, 8095. Keck, P. H.. and Golay. M. J . E. (1953). Phys. R e v . 89, 1297. Keck, P. H., Van Horn, W.. Soled. J . . and MacDonald. A . (1954). Rev. Sci. lnstrirni. 25,

331. Kishino. S.,Matsushita. Y . . and Kanamori. M. (1979). Appl. Phys. Left. 35, 213. Kondo. Y . (1981). I n Semiconductor Silicon 198/. H . R. Huff, R. J. Kriegler. and Y . Takeishi (eds.). p. 220. The Electrochemical Society, Pennington. N . J . Kung. C. Y.. Forbes, L.. and Peng. J . 11. (1983). Muter. R e s . Bull. 18, 1437. Leroy. B.. and Plougonven, C. (1980). J . Elecfrochem. Soc. 127, 961. Lin. W . (19%). I n Semiconductor S i l i w n 1990. H. R. Huff. K. G. Barraclough. and J. Chikawa (eds.), p. 569. The Electrochemical Society. Princeton, N.J. Maher. D. M . . Staudinger. A,. and Patel. J . R. (1976). J. Appl. Phvs. 47, 3813. Matsushita. Y. (1982).J . Crv.stal C;robt.tli 56, 516. Oehrlein. G. S.. Challou. D. J . . Jaworowski. A . E.. and Corbett. J . W. (19811. PIi!.\. Lert. 86, 117. Ohwa. M.. Higuchi. T.. Toji. E.. Watanabe. M.. Homma. K.. and Takasu. S. (1986). In Semic.onductor Silic.un l Y N 6 . H . R. Huff. T . Abe, and B . Kolbesen (eds.1. p. 117. The Electrochemical Society. Pennington. N .J. O u k a . J . , Inoue. N . , and Wada, K (1980). A p p l . Phys. L e f t . 36, 288. Patel. J . R. (1977). I n Semicondrcc~rorSilicwn lY77. H. R. Huff and E. Sirtl (eds.). p . 521. The Electrochemical Society. Princeton. N . J . Patel. J . R. (1981). I n .Srmic.ondrcc./or Silic-on l Y X / . H. R. Huff, R . J . Kriegler. and Y . Takeishi (eds.). p. 189. The Electrochemical Society. Pennington. N . J . Patel. J . R.. and Chaudhuri. A . R. (1962). J . A p p l . Phys. 33, 2223. Ponce. F. A,. Yamashita. T.. and Hahn, S. (1983). Appl. Phg.s. Lett. 43, 1051. Ravi. K. V . (1974). J . Electroc.hrrn. .So( . 121, 1090. Rozgonyi. G . A,. Deysher. R . P.. and Pearce. C . W. (1976). J . Elec,rroc.hem. So(. 123, 1910. Shimizu. H., Watanabe, 'T., and Kakui, Y . (1985). Jopun. J . Appl. Phy.5. 24, 815. Shimura. F. (1986). J . Appl. Phy.t. 5Y. 3 3 1 . Shimura. F. (19911. Solid Sirrtr Plienomentr IY-20, I . Shimura. F.. and Hockett. R. S. (1986). A p p l . Plivs. Left.48, 224. Shimura. F.. and Tsuya. H. (1982).J E/rcrroc.lirm. S ~ K 129. . 1062. Shimura. F.. Tsuya. H . , and Kawamura. T . (19XOa). J . Appl. PhyA. 51, 269. Shimura. F.. Tsuya. H . . and Kawumura. T. (I980b). Appl. Phys. Lefr. 37, 483. Sumino. K. (1981). In .Srmic.ondicc/ o r .Silic.on I Y R I . H . R. Huff, R. J . Kriegler. and Y. Takeishi (eds.). p. 208. The Electrochemical Society. Pennington. N.J. Sumino. K . . Harada. H.. and Yonenaga. I . (1980). Japtrn. J . Appl. Pliys. 19, L49. Suzuki. T.. Isawa, N . . Okubo. Y.. and Hoshi. K . (1981). I n Semiconductor Silicijn I W l , H . R. Huff. R. J . Kriegler. and Y. Takeishi (eds.), p. 90.The Electrochemical Society. Pennington. N.J.

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Suzuki, T., Isawa, N., Hoshi, K . , Kato, Y., and Okubo, Y . (1986). In Semiconductor Silicon 1986, H. R. Huff, T . Abe, and B. Kolbesen (eds.), p. 142. The Electrochemical Society, Pennington, N.J. Takasu, S . , Otsuka, H., Yoshihiro, N., and Oku, T. (1981). Japan. J . Appl. Phys., s ~ p p l . 20, 25. Takasu, S., Takahashi, S., Ohwa, M., Suzuki, O., and Higuchi, T. (1990). In Semiconductor Silicon 1990, H. R. Huff, K. G . Barraclough, and J. Chikawa (eds.), p. 45. The Electrochemical Society, Princeton, N.J. Tan. T. Y.. Gardner, E. E., and Tice, W. K. (1977). Appl. Phys. Lett. 30, 175. Teal, G. K., and Little, J. B. (1950). Phys. Rev. 78, 647. Usami, T., Matsushita, Y., and Ogino, M. (1984). J . Crystal Growth 70, 319. Watanabe, M., Usami, T., Muraoka, H., Matsuo, S . , Imanishi, Y., and Nagashima, H. (1981). In Semiconductor Silicon 1981, H. R. Huff, R . J. Kriegler, and Y. Takeishi (eds.), p . 126. The Electrochemical Society. Pennington, N.J. Wilson, S. R . , Paulson, M. W., and Gregory, R. B. (1985). Solid Stare Techno/. (June), 185. Yasutake, K., Umeno, M., and Kawabe, H. (1980). Appl. Phys. Lett. 37, 789. Yonenaga, I., Sumino, K., Hoshi, K . (1984). J . Appl. Phys. 56, 2346. Zulehner, W., and Huber, D. (1982). In Crystals 8: Silicon, Chemical Etching, J. Grabmaier (ed.), p. I . Springer-Verlag, Berlin.

SEMICONDIIC'IORS AND SLMIMETALS. VOL 42

CHAPTER 2

The Incorporation of Oxygen into Silicon Crystals Wen Lin ATBT BE1 I I ABORATORlkS ALLENTOWN. PENNSYLVAP,IA

1. 11.

INTRODlJCTlON

. .

9

GROWTH . . . . . . . . . . . . .

10 10 12 15

. . .

SILICON CRYSTAL

,

.

. .

.

. . . .

. .

.

.

. . . . . . . . , . . . . . . . . . . 111. CHARACTERISTICS OF CZOCHRALSKI SILICON GROWTH . . . 1 . Dopunt Distribution , , . . . . . . . . . . , . 2. "Unintended Dopunts ' ' . . . . . . . . . . . . . 3 . Eflectii.e Segrrgtrtion CoyfJicirn/ . , . . . . . , . 4. Convection F1iw.s in Czochrtrlski Melt . . . . . . . 5 . Moc,roscopic Rudiul Itnpitrity Uniformity . . . . . . 1 . F/out Zone S i l k o n Growth 2. Czochrulski Silicon GroMSth

. . .

6 . Mic.rosc.opic lnliotnogmeity in Czochralski Silicon . .

Iv.

VI.

16

19 20 21 22

OXYGFN lNCORPoRATION AND SEGREGATION IN CZOCHRALSKI SILICON

v.

IS

GROWTH . . . .

.

,

,

.

,

. .

.

.

.

,

1 . Incorporution Meclitrnism . . . . . . , . . . . 2 . Orvgen Segregrrfion trnd Microscopic Inhomogeneity

. ,

GROWTH. . . . . . . . 1 . Normu/ Czochrtr/.ski G r o ~ ~ t .h . . . . . . . . . . 2. Magnetic Field Applit,d C:ochralski Growth ( M C Z ) . 3 . Continuous C;oc hrtrl.\& Silicon Growrh . . . . . , SUMMARY . . , . . . . . . . . , . . . . . . Rejiwnces . . . . . . . , . . . , . . . . , ,

COYTROLLED OXYGkN SI1,ICON

24 24 34 37 37 42 46 50 50

I. Introduction Interstitial oxygen is perhaps the most important consideration in silicon crystals for VLSI/ULSI fabrication. The relevance of oxygen to integrated circuit fabrication is due primarily to oxygen's ability to form oxide precipitates and to generate lattice defects in a controlled manner for impurity gettering during device processing. In addition. the presence of interstitial oxygen in silicon gives an added strengthening effect to the silicon lattice, which can prevent plastic deformation and slip during wafer thermal processing. A wide range of oxygen concentrations, from 10 ppma to over 10 ppma (ASTM. 1980) in Czochralski (CZ) silicon. have been applied in IC device processing. depending on the nature of thermal 9 Copyright \C I994 hv Academic Pre\s. Inc All nghh of reproduction m any form rererved ISBN 0-I?-75?14?-9

10

WEN LIN

processing and sensitivity of the device to gettering or defect generation. In general, for device processing technologies in which gettering by precipitates is essential, high or medium oxygen concentrations are needed. When the device performance is more sensitive to lattice defects, the oxygen related defect formation is intentionally avoided by using CZ silicon that has little or no precipitation capability. In either case, an understanding of the process thermal sequence and matching oxygen level in CZ silicon is essential. The use of silicon materials with uncontrolled oxygen concentrations can result in adverse effects. To comply with the needs of integrated circuit fabrication, controlled oxygen incorporation during silicon growth is necessary. The goal has been to grow silicon at a desired oxygen concentration level with substantial axial and radial uniformity. The purpose of this chapter is to discuss how oxygen is incorporated during silicon growth and technologies for the control of concentration and uniformity. We first review the single crystal preparation by float zone and Czochralski growth methods. This is followed by a discussion of the characteristics of Czochralski silicon growth, in particular, our understanding of the oxygen incorporation mechanisms, both macro- and microscopic. Finally, the controlled oxygen incorporation is discussed in normal CZ, and their modified versions, CZ growth under applied magnetic field and continuous CZ growth. 11. Silicon Crystal Growth 1. FLOAT ZONESILICON GROWTH

The float zone (FZ) method is based on the zone-melting principle and was invented by Theuerer (1962). Figure 1 shows a schematic of the FZ process. A polysilicon rod is mounted vertically inside a growth chamber under vacuum or in an inert atmosphere. A needle-eye coil provides radio frequency power to the rod causing it to melt and maintain a narrow, stable molten zone. The levitation effect of the radio frequency field helps to support a large molten zone. As the molten zone is moved along the polysilicon rod, the molten silicon solidifies into a single crystal and, simultaneously, the material is purified. To begin the growth, in the bottom-seed FZ, the seed crystal is brought up from below to make contact with the drop of melt formed at the tip of the poly rod. A necking process is carried out to establish a dislocation-free feature before the “neck” is allowed to increase in diameter to form a taper and reach the desired diameter for steady-state body growth. During the growth, the shape of the molten zone and crystal diameter are monitored by infrared sensors,

2.

THF INCORPORATION OF OXYGEN INTO SILICON CRYSTALS

11

N=k-r Single Crystal

Seed __

FIG. I . Schematic of a floa~Lone silicon growth arrangement

and they are adjusted by the rf power input to the coil and travel speed. Details of FZ technology are discussed by Keller and Muhlbauer (1981). Current FZ technology can produce high-quality FZ silicon up to 150 mm in diameter in production quantities. FZ crystals are doped by adding the doping gas phosphine (PH,) or diborane (B,H,) to the inert gas for n- and p-type, respectively. Polysilicon rods for FZ growth may also be doped in the gas phase and dopant redistribution by zone melting. Since the doping is by gas phase interaction with the molten silicon, axial dopant uniformity is achieved. However, due to the very nature of FZ growth configuration, the small "hot zone" lacks thermal symmetry. As a result, temperature fluctuations, remelting phenomenon and dopant segregation cause FZ silicon to display more microscopic dopant inhomogeneity or dopant striations than that observed in the CZ silicon. Severe dopant microinhomogeneity can be improved in n-type FZ via NTD (neutron transmutation doping) (Meese, 1979). In NTD, a high-purity (undoped) FZ crystal is subjected to thermal neutron bombardment, causing some of silicon isotope '"Si (-3.1%' of Si) to form unstable isotope "Si, which decays to form stable phosphorus isotope 3'P, such that '"Si(n, y )

- "Si

j'P

+

p

(7.6 hr)

Since neutron bombardment (hoth thermal and fast neutrons) induces radiation damages, the irradiated crystal must be annealed at about 700°C for defect annihilation and to restore resistivity due to the phosphorus doping. In the FZ silicon with NTD. the dopant striations are greatly reduced. However, the NTD method is feasible only for high-resistivity,

12

WEN LIN

phosphorus-doped FZ. Low-resistivity doping of FZ by NTD would require excessively long irradiation (more lattice damages) and is not feasible. The NTD process for the p-type doping is not available. Unlike CZ growth, the silicon molten zone in the FZ growth is not in contact with any substances except ambient gas, which may contain doping gas. Therefore, the F Z silicon can easily achieve much higher purity and higher resistivity (FZ silicon’s resistivity ranges from few tens to a few thousands ohm-cm) than the CZ silicon (generally, <50 ohm-cm). A large volume of F Z silicon is used in the fabrication of semiconductor power devices and infrared sensors. However, its application in the microelectronic IC fabrications is rather limited. The main reason is FZ’s low interstitial oxygen content. The oxygen content of FZ crystal is in the range of 10l6 atoms/cm3, which is two orders of magnitude below that of CZ silicon and far below the solid solubility limit at 1C’s thermal processing temperatures. Consequently, FZ silicon lacks the ability of oxygen precipitation and associated internal gettering potential. Furthermore, the “residual level” of oxygen in FZ also results in lower mechanical strength than the CZ in terms of its ability to withstand thermal stress and suppress slips, wafer bow and warp during high-temperature processing (Leroy and Plougonven, 1980; Takasu et al., 1981). The presence of “sufficient” interstitial oxygen in CZ silicon appears to have strain hardening effect in the silicon lattice and serves as obstacles for dislocation initiation and propagation. Numerous studies (Patel and Chaudhuri, 1962; Yonenaga, Sumino, and Hoshi, 1984) have shown that the difference in mechanical strength can be attributed to the difference in the oxygen content and associated defects. These are the main reasons that CZ silicon is used almost exclusively for IC processing. In order to overcome FZ’s shortcomings, oxygen (Sumino et al., 1980) and nitrogen (Abe et al., 1981) doping during FZ growth have been reported. It was shown that doping concentrations of 1-1.5 x lOI7 atoms/cm3 for oxygen or 1.5 x lOI5 atoms/cm3 for nitrogen can significantly increase FZ’s strength. Nitrogen-doped FZ proves useful in microelectronics device fabrication where an oxygen-free effect is desirable (Jastrzebski et al., 1987). Chapter 1 1 of this book will discuss the oxygen effect on mechanical properties in detail. 2 . CZOCHRALSKI SILICON GROWTH

Czochralski pulling method (CZ) is named after J. Czochralski (1918). However, the pull-from-melt method widely employed today was developed by Teal and Little (1950). Small-diameter CZ silicon crystals were first used in the early 1960s for IC fabrication. The development of the

?. T H E

INCORWRArlON OF OXYGEN INTO SILICON CRYSTALS

13

dislocation-free growth technique and automatic diameter control in the late 1960s led to a rapid growth in silicon crystal diameter and charge size i n the last two decades. Today, 200 mm silicon crystals, weighing over 80 kg are not uncommon, and 300 mm diameter silicon growth is already under development. In the ULSI era, the emphases on the CZ silicon crystals for ICs are in the uniformity of dopant and oxygen incorporation and microdefect control. Much research and development effort is devoted to these aspects in order to satisfy the stringent requirements of IC processing for deep submicron devices. A CZ silicon growth process is controlled by many variables. It involves aspects of heat transfers and phase transitions. Modern CZ silicon growth equipment transforms the “art” of crystal growth into engineering. Although most of the steps in the growth process can be monitored and controlled by a computer or microprocessor, many critical steps still require the judgement and attention of an experienced operator. Therefore, significant differences exist in the properties of the crystals grown from different grower designs and growth processes. Figure 2 shows a schematic of a typical modern CZ grower for large diameter silicon growth. Major components include the so-called hot

Cable Reel Rotation System

IrnageSensing Device Seed Holder Gate Valve View Port Silica Crucible

Graphite Susceptor , Hot

Thermal Shield

Zone

Electrode

t FIG 2 Schematic of a typical (‘lochridski silicon growing rystern (after Abe. 1985)

14

WEN LIN

zone, crystal pull and rotation, crucible lift and rotation and diameter and temperature sensing devices. The puller is operated under a reduced pressure inert ambient. CZ silicon growth consists of three major parts: (1) seeding and necking, (2) body growth and (3) tang growth and termination. The necking process is one of the critical steps in dislocation-free CZ growth, the body growth cannot be initiated without a successful necking process. The necessity of the procedure and principle of the necking follow, and they are common to the FZ growth discussed in the previous section. A CZ growth process begins with the melting of polysilicon nuggets and doping element or alloy contained in a silica crucible. Temperature adjustments and stabilization follow the melt-down such that the melt surface temperature is slightly supercooled. A crystal seed (-12 mm in diameter) attached to the end of the steel cable is dipped into the melt. If the crystal-melt contact forms a smooth meniscus, the “necking” process based on Dash’s (1958) technique may begin. The reason for necking is as follows: The growth of a dislocation-free silicon has to be “extended” from a dislocation-free silicon lattice. Although the seed crystals used in CZ are usually dislocation free, upon contact with the melt, dislocations are generated due to thermal shock. These dislocations must be eliminated before the full-diameter crystal growth can begin. Necking is a procedure to out-grow dislocations. During necking, the seed crystal is gradually decreased in diameter by increasing pull speed and temperature adjustment. The goal is to reach a steady state neck growth condition with a neck diameter of 3-4 mm and a pull rate of 4-6 mm/min. The dislocation-free crystal is usually achieved after a few centimeters of growth. Two phenomena may occur during the necking. When the seed diameter is large in the early stage of necking, the thermal stress causes dislocation movements by glide, cross slip and climb mechanisms, where temperature is above the “plastic” temperature (>9OO0C). In the growth of ( 1 11) and (100) crystals, the growth axes are oblique or perpendicular to { 1 1 I} slip planes. The dislocations can glide out of the crystal surface at some time. For ( 1 10) growth, because ( I 10) is contained in a { I 1 1) plane, the seed has to be oriented a few degrees off the pulling axis toward the direction perpendicular to the ( I 11) plane, to facilitate dislocation eliminations. When the neck is 3-4 mm in diameter under high-speed pulling, the stress is relatively small, causing slow or no movement of the prevailing dislocations. When dislocation movement is slower than the advancing solid-liquid interface, the dislocation-free feature is obtained. Typically, the dislocation-free status is accompanied by the

2.

THE I N C O R P O R A T I O N O F O X Y G E N INTO SILICON C R Y S T A L S

15

growth of strong ridges (( 100) crystals) or “flats” (( I 1 1) crystals) on crystal’s symmetry positions. which are actually due to prominent { 1 I I } facet growth at these positions (Lin and Hill, 1983a). Once dislocation-free growth is achieved through the necking. the diameter may be expanded by “shoulder” growth until it reaches the desired diameter. The body growth is under automatic diameter control (ADC). in which the pull rate is slaved by optically monitored crystal diameter variations. The ADC is also assisted by minor temperature adjustments slaved by the long-term pull rate changes. The crystal growth process is terminated by a gradual decrease from full diameter to zero in a low pull speed in order to minimize thermal stress by the diameter change and associated slip generations. After the heater power is off, the crystal usually stays in the grower for a period of time for cooling before it is removed from the grower. The total dwell time and temperatures that crystal experienced in the grower constitute the so-called thermal history of the silicon crystal. The thermal history of CZ silicon determines the state of nuclei for oxygen precipitation and is an important consideration. as is oxygen concentration, in oxygen precipitation kinetics. The heart of a CZ puller is the hot zone. The design of heater and heat shields, for example, will determine radial and vertical thermal gradient in the melt. These thermal characteristics are intimately related to the growth characteristics, such as interface shape and related thermal stress generation (Lin and Benson. 1987). Although this concept is fundamental to large-diameter silicon growth. little is known about the correlation between crystal growth system hot-zone design factors and growth characteristics. Empirically, for a given growing system an optimum growth condition is usually obtained by modifying hot-zone components or by varying the growth parameters by trial and error. Hot-zone thermal characteristics affect many aspects of silicon crystal properties including oxygen incorporation behavior and the thermal history of the grown crystal. Since hot-zone design varies from one grower to another. the crystals grown from different growers are expected to differ in these properties. Thermal convection and forced convection conditions are also important controlling factors for CZ crystal properties and will be discussed in the following section. 111. Characteristics of Czochralski Silicon Growth

I . DOPANT DISTRIBUTION

In the growth of silicon crystah from large melts using automatic diameter control mechanisms involving pull rate or temperature changes

16

W E N LIN

slavea to optical diameter measurements, the axial dopant distributions follow the normal freezing behavior (Pfann, 1965), that C,(X) = Co k (1

-

x)’-~,

(1)

where C,, k and x are crystal dopant concentration, dopant segregation coefficient and fraction of melt solidified, respectively. C, is the initial dopant concentration of the melt. Complete mixing takes place in the melt by vigorous thermal convection, and the segregation coefficient of the dopant assumes equilibrium value k , in most instances. In the reduced pressure growth of heavily doped silicon involving dopants with high vapor pressure, such as antimony, the k value can deviate significantly from the equilibrium value (k assumes a value greater than k,). Due to dopant segregation, there is a spread in dopant concentration along a CZ crystal. The degree of the spread depends on the k value of the dopant. The smaller is the k value, the larger the spread in concentration. The segregation effect of the dopants often limits the “yield” of the CZ silicon crystals. Nonstandard CZ methods, such as double crucible method (Benson, Lin and Martin, 1981; Lin and Hill, 1983a) and continuous growth method (Fiegl, 1983) have been used to eliminate the effect due to segregation, see Fig. 3. The axial microscopic uniformity is controlled by the microscopic growth rate. Thermal convection, thermal asymmetry and pull-rate fluctuations are sources of microscopic growth fluctuations. The nature of the microinhomogeneity of impurity in CZ crystals will be discussed following the discussion of melt convection flows and effective segregation coefficient. 2. “UNINTENDED DOPANTS” Impurities in the crucible material or the vapor above the melt can first be incorporated into the melt and then, the silicon during crystal growth. Oxygen and carbon are the major impurities incorporated into CZ silicon. Their concentrations in CZ crystals are on the order of 10l8 atoms/cm’ and 10l6atoms/cm3for oxygen and carbon, respectively. The silica crucible is an infinite source for oxygen. Molten silicon dissolves the silica and absorbs oxygen. Unlike normal dopants, oxygen in the silicon melt is a dynamic system and oxygen distribution is not homogeneous in the melt. The oxygen concentration incorporated into the crystal is a result of complex interaction between functions such as crucible dissolution rate and nature of the fluid flow (which determines how the oxygen-rich melt is transported). Therefore, the axial oxygen profile of a silicon crys-

2.

THE INCORPORATION OF OXYGEN INTO SILICON CRYSTALS

17

CAPILLARY

INNER CRUCIBLE

MELT

OUTER CRUCIBLE

L A.-.....-!-* Meltdown Inner Crucible

Chamber

(b) FIG. 3 . ( a ) Schematic representation of a double crucible growth arrangement (after Benson et al. 1981: the paper was originally presented at the spring 1981 meeting of the Electrochemical Society. Minneapolis). (h) C.'ontinuous liquid-feed Czochralski growth furnace (after Lorenrini, Iwata and Lorenz 1977).

18

WEN LIN

tal is not the result of normal freezing behavior and concentration profile can vary widely depending on the grower thermal characteristics and growth parameters used. The source of the carbon is the graphite material making up the hot zone of the grower. The silicon monoxide evaporated from the melt surface interacts with hot graphite components and is reduced to carbon monoxide before re-entering the melt following SiO

+ 2C

-

Sic

+ CO.

The introduction of CO into the melt is a continuous process. The incorporation from vapor phase and residual carbon content in the starting polysilicon (<0.2 ppma) result in a normal freezing-type carbon concentration profile in CZ silicon (carbon has a small segregation coefficient, k , = 0.07). Carbon in silicon has not been shown to affect device characteristics. Carbon concentrations of up to 4 ppma did not directly change DRAM performance or yield (Craven et al., 1986). However, carbon in silicon has been observed to enhance oxygen precipitation. To utilize this property for oxygen precipitation enhancement, one needs to grow silicon with controlled carbon incorporation, both in concentration level and uniformity. Such silicon growth process has not been reported. For VLSI/ULSI applications, it is a common practice to keep carbon at minimum levels (<0.5 ppma). Besides carbon and oxygen, metal atoms can enter the growing crystal. Metallic elements, especially transition metals, are among the most undesirable contaminants in silicon material for device processing due to its role as charge carrier killers. They are also fast diffusers in silicon at elevated temperatures. Fortunately, due to the small values of their segregation coefficients no significant metal can be grown into silicon crystals when the melt is contaminated with metal. However, transition metals transported in the vapor phase can condense and diffuse through silicon crystal surface at high temperatures and quickly into the bulk. The diffusion of metal contaminants is most “effective” at the grown crystal surface above the melt. The metal contaminants can be evaporated from an overheated metal or alloy surface of grower components. An example is the stainless steel shaft or cable for crystal pull and rotation, which is usually not water cooled. Overheating of these parts occurs when they are too close to the hot zone. The use of an extended seed chuck (seed holding device attached to the bottom of the steel shaft or cable, made of ceramic materials or graphite) would minimize the overheating of the steel shaft or cable.

2.

THE INCORPORATION OF O X Y G E N INTO SILICON CRYSTALS

3. EFFECTIVE SEGREGATION

19

('OEFFICIENT

The degree of incorporation of an impurity at the freezing front is controlled by its segregation coefficient. When the solidification rate is low, o r the impurity concentration is dilute, the segregation coefficient assumes a value very close or identical to the equilibrium value. In CZ silicon growth with finite or higher growth rate, the dopant ( k , < I ) incorporation behavior was found to result in a k value that is deviated from the equilibrium value: for example. the k was observed to increase with increasing growth rates (Kodera. 1963). This behavior is due to finite diffusivity of the dopant that cannot equalize the concentration change at the solidification front quickly. Because the concentration of impurities is higher at the solidification front. a larger number of impurity atoms is incorporated into the crystal than would be expected from the concentration in the bulk melt outside the diffusion-controlled layer. This recults in a higher degree of impurity incorporation and an effective segregation coefficient krffthat is larger than the equilibrium value, k,). Burton, Prim and Schlicter (BPS) (1953) extended the plain rotating disc treatment (Cochran, 1934) for the diffusion boundary layer for crystal growth and showed that the degree of incorporation or the effective segregation coefficient of an impurity is related to diffusion boundary layer thickness. 5 . and growth rate,fas

where D and k,, are the diffusion coefficient and equilibrium segregation coefficient of the impurity, respectively. The thickness of the diffusion boundary layer depends on the diffusivity of the impurity, kinematic viscosity u of the melt and crystal rotation rate w as

From this expression, it is seen that the instantaneous incorporation rate is microscopic growth-rate controlled when other parameters are held constant. The growth rate fluctuations are the source of microscopic inhomogeneity in the crystal. On the other hand, at any given interface. the uniformity of the boundary layer thickness across the interface controls radial uniformity. The CZ crystal's radial and microscopic impurity uniformity will be discussed later in terms of t h e BPS equation.

20

WEN LIN

(b)

(a)

(4

FIG.4. Convection patterns in a Czochralski melt due to (a) thermal convection, (b)crystal rotation and ( c ) crucible rotation.

4. CONVECTION FLOWS IN CZOCHRALSKI MELT The major convective fluid flows in the CZ melt that affect the growth are thermal convection flows due to the existence of a nonvertical temperature gradient and forced convection induced by crystal and crucible rotation as shown in Fig. 4 (other convection flows are those caused by crystal pulling and surface tension). The basic thermal convection flow generated in a melt can be symmetrical or asymmetrical, with the hot melt rising along the crucible wall and descending at the crucible center as is shown in Fig. 4a. The basic flow pattern is determined by the crucible geometry, aspect ratio (height over diameter of the melt), and thermal boundary conditions. The driving force is given by the dimensionless Grashof number NGr:

N,,

=

ga AT R3 Iv2,

(5)

where g is the acceleration due to gravity, a is the melt thermal expansion coefficient, A T is the temperature difference over the crucible diameter R and v is the kinematic viscosity of the melt. From this expression it is clear that, as the grower is scaled up in charge size (so is the crucible diameter), a stronger thermal convection is generated due to the direct contribution of the third power of R and increasing in temperature gradient in the melt. Melt turbulence associated with strong thermal convection cause temperature fluctuations in the melt and contribute to microinhomogeneity in dopant and oxygen incorporation. It is a common practice in CZ growth to use crystal rotation to override the deleterious effects of thermal convection discussed previously. The effects of crystal rotation are twofold. Similar to a rotation disc, the crystal rotation forms a uniform hydrodynamic boundary layer across the interface. Burton et al. (1953) extended the plain rotating disc treatment for the diffusion boundary layer for crystal growth, Eq. (3). Second,

2.

T H E INCORPORATION OF O X Y G E N INTO SILICON CRYSTALS

21

the rotating crystal draws a uniform flow from the central region of the melt, perpendicular to the interface over the radius and spins it outward radially near the surface, Fig. 4b. As a result, the convection flow by the crystal rotation counters and reduces the thermal convection flow and the convection flow induced by the crucible rotation (which has the same general flow pattern as thermal convection, see Fig. 4c). The magnitude of the flow induced by the crystal rotation is characterized by dimensionless Reynolds number N R e : N,, = w r ' l v , (6) where w is the crystal rotation rate and r is the crystal radius. While forced convection, i.e., the crystal rotation, has the effect of overriding harmful thermal convection, the net effect depends on the relative magnitude of the two components. The relative effect of the two components may be expressed by a ratio, Na, INGr.If NK, > N,,, the crystal rotation will effectively isolate the segregation process at the growth interface from the thermal convection in the melt (Carruthers, Witt and Reusser, 1977). Therefore, small melt and high crystal rotation would suppress the effect of thermal convection. S . MACROSC~PIC RADIALIMPIJRITYUNIFORMITY

I n the silicon growth from a homogeneous melt, the radial uniformity is controlled by the uniformity of boundary layer thickness across the interface. In Eq. (31, if the growth rate is assumed to be uniform across the interface, then the radial uniformity of the impurity is determined by the variation in boundary layer thickness. It may be shown (Carruthers, 1967), in the case of dopant in silicon, that the rate of change in k,,. with respect to the variation in diffuse boundary layer thickness is very sensitive in the range of layer thickness encountered in the silicon CZ growth. The effect is greater for n-type than for the p-type dopant in silicon. The relevance of the melt convection condition to the radial impurity incorporation is the following. In the absence of thermal convection, the result of the crystal rotation would be a uniform diffusion boundary layer over the crystal radius at the interface. Hence, if the crystal rotation is the only source of convection, no radial segregation will result from the fluid flow effect and impurity incorporation is uniform across the crystal radius. In a real crystal growth, however, the thermal convection flows form a general pattern in the crucible as rising streamlines along the crucible walls that fall in the center following a gradually curved path. See Fig. 4a. This path results in a stagnation point near the center of the crystal interface. Therefore, when thermal convection is strong compared to forced convection, the

22

WEN LIN

diffusion boundary layer thickness at the outer region of the interface may be reduced by the thermal convection velocity while the effect is small in the region near the center of the interface. Thus thermal convection flow causes a radial variation in boundary layer thickness. If the segregation coefficient of the dopant involved, k,, is smaller than unity, one finds a significant radial variation in impurity incorporation; it is high in the center and low in the outer region of the crystal. The farther the k value deviates from the unity, the greater are the radial variations. For the same principle, fast crucible rotation can cause variation in the boundary layer thickness and radial gradient in incorporation. As discussed earlier, harmful thermal convection effects can be suppressed by increased crystal rotation and by small melt growth. Lin and coworkers (Benson et al., 1981; Lin and Hill, 1983b) have demonstrated such effects by using a double crucible arrangement. See Fig. 3a. The use of a smaller diameter and low aspect ratio (i.e., ratio of melt height to crucible diameter) inner crucible reduced the effect of thermal convection. The improvements on radial dopant uniformity and random dopant concentration fluctuations, characteristic of the thermal convection, were observed for As, P, Sb and oxygen for which the segregation coefficients deviated significantly from unity. 6. MICROSCOPIC INHOMOGENEITY I N CZOCHRALSKI SILICON

In general, the microscopic inhomogeneity of impurity in C Z silicon crystals is a result of growth-rate fluctuations and impurity segregation during crystal growth. The growth-rate fluctuations cause variations in the impurity incorporation levels. The lattice strain associated with local impurity concentration variations gives rise to the so-called striation, as may be revealed by chemical etching or X-ray topography. Severe microscopic dopant inhomogeneity corresponds to a large variation in carrier concentration and is not desirable in silicon materials used for device fabrication, especially when such variation is comparable to the device feature size. This is an important consideration in VLSI fabrication. Large oxygen striations can result in preferential precipitation, often observed as concentric ring patterns in etched wafers following heat treatments. In CZ silicon growth there are several sources of microscopic growth rate variations, and discussion of these follows. a. Noncentrosymmetric Thermal Distribution in the Silicon Melt

In large-melt silicon growth, finite thermal asymmetry exists about the center of the melt. During crystal growth, as the crystal is rotated about the growth axis, the interface experiences slightly different temperatures

2.

THF LNCORPORAlION OF OXYGEN INTO SILICON CRYSTALS

\

GROWTH RATE

,

\

23

,-.

I M P U R I T Y I NCORPOR ATlON

FIG.5 . Schematic illustration of growth-rate fluctuation and its relationship with micro\topic impurity fluctuations in CZ crystal. Here,f'and w are growth rate and crystal rotation rate, respectively (after Lin and Stovala. 1985. Reproduced with permission of the Electrochemical Society. Inc.).

at different positions in the melt. Therefore. the growth rate of a given crystal element parallel to the crystal axis fluctuates periodically, as illustrated schematically in Fig. 5 . I n general, the fluctuation is most pronounced in the crystal elements furthest from the crystal center. The periodicity of the fluctuation is determined by the average growth rate, .f; and crystal rotation rate w , as/'iw. The variations in the impurity incorporation level that correspond to the growth-rate variations are commonly referred to as rotutiontrl stricrtions. When the equilibrium segregation coefficient (A,)) of the element involved is less than unity, the fluctuation in impurity incorporation level is in phase with the growth rate fluctuation. If k , > I , the fluctuations will be out of phase (see Fig. 5). The relationship may be realized readily by examining the Eq. ( 3 ) . h. Thermal Con~iPc.tion-Ri.ltrtrdli~rntprrtituri~ Flirctuations

Growth rate fluctuations caused by thermal convection related temperature variations are mostly random in nature, and etched striations are

24

WEN LIN

characteristically aperiodic. When thermal convection is significant, the microstriations bear the signature of high-frequency fluctuations on the order of tens of hertz. c. Automatic Diameter Control-Induced Perturbation Growth-rate fluctuation can be further perturbed by the automatic diameter control mechanism commonly employed in silicon crystal growth. The crystal pull-rate is slaved by optically monitored crystal diameter variations in order to maintain a preset diameter. The pull-rate adjustments are both “instantaneous” (a few seconds) and “long term” (minutes). The long-term pull-rate adjustment determines the average growth rate. The instantaneous pull-rate adjustment imposes modifications on the microscopic growth-rate fluctuations resulting from thermal asymmetry and thermal convection. The net effect is to smear the periodic nature of the impurity fluctuation resulting from the melt thermal asymmetry. IV. Oxygen Incorporation and Segregation in Czochralski Silicon Growth 1. INCORPORATION MECHANISM

Unlike most intended dopants in silicon CZ crystal growth, which show “normal freezing” behavior under normal growth conditions, oxygen is an unintended dopant that enters the silicon melt continuously by dissolving the silica crucible. The incorporation behavior of oxygen into silicon is the result of complex interplay among crucible dissolution, surface evaporation, thermal convection and forced convection, as shown in the Fig. 6. In a side-heated CZ hot zone, the dissolution of the silica crucible is the highest at the side wall of the crucible. The silicon melt dissolves SiO, and absorbs its oxygen. The oxygen-rich silicon melt would rise along the crucible wall, following the thermal convection flow pattern to near the melt surface, and then to the melt center, where it is drawn toward the crystal for incorporation by the forced convection induced by the crystal rotation. When the oxygen-rich melt is near the surface, a great portion of the oxygen is evaporated through the free surface. The oxygen concentration incorporated into the growing crystal, therefore, is proportional to the oxygen concentration in the melt adjacent to the growing crystal. During steady-state growth, there exists a dynamic equilibrium of oxygen between the four controlling factors in the system. Due to the difference in thermal characteristics of different hot-zone designs, the oxygen incorporation behavior varies from one grower design to another. The major oxygen-controlling factors are discussed in the following.

2.

T H E INCORPORATION OF OXYGEN INTO SILICON CRYSTALS

-

LCRUCIBLE SILICA ~3

25

HEATER'

C R U C I E OISSOLUTION

0 FORCED CONVECTION

THERMAL CONVECTION

! SURFACE EVAPORATION

FIG.6. Schematic of a silicon Cmchralski growth system showing relationship among oxygen-controlling factors (after Benson et al. 1981; the paper was originally presented at the spring 1981 meeting of the Electrochemical Society, Minneapolis).

LI.

Efiect of Surface Evapotnrion cind Crucible Dissolution

In the absence of thermal and forced convection (a hypothetical case), the melt oxygen concentration is proportional to the ratio of melt-crucible contact area to the available free surface area. In such a case the transport of oxygen would depend entirely on diffusion. This ratio constantly decreases as the aspect ratio is reduced during the growth. The variation of this ratio is the basic characteristic of the axial oxygen profile of CZ silicon, in which the concentration is observed to gradually decrease from the seed end toward the tang end. See, for example, Fig. 12. However, the dependence of concentration on this geometric ratio is influenced by the crucible dissolution rate and ambient pressure. The dissolution rate of the silica is material density and temperature dependent. Therefore, using a crucible with a n inner wall made of "porous silica," for example, would enhance the dissolution rate. Increasing the meltcrucible contact area by using corrugated inner surface will obviously serve similar purpose. Mathematical modeling of the observed oxygen incorporation behavior based on dissolution and evaporation, as carried out by Carlberg, King and Wit1 (1982), is merely a first-order approximation. In actual silicon growth. oxygen incorporation and uniformity are greatly affected by thermal convection and forced convection. N o modeling effort thus far accurately takes these factors into account.

26

WEN LIN

r

24

150

200

pc c

23 c

a

n

CRYSTAL DIAMETER (mm)

150100

22

250

c

275

c

c

Q

z 21

;

20

LL

‘z W g

t

19

18

0 0

z l7

W

2 X 0

16

15

0

I

I

I

01

02

03

I

1

I

1

0 4 05 06 07 CRYSTAL CROSS SECTION AREA CRUCIBLE CROSS SECTION AREA

I

08

I 09

FIG.7. Oxygen concentration measured as a function of the fraction of melt surface being covered by the growing crystal during crown growth. The crystal crown accounts for less than 10% of the initial charge.

A study of oxygen evaporation from the melt surface was made using “shoulder” growth of a 300 mm diameter crystal from a 350 mm diameter crucible. In this experiment, the effect of the free melt surface evaporation on the oxygen level during crystal crown growth was examined. Figure 7 plots oxygen concentration variation in the grown silicon as the melt surface is covered by the growing “shoulder.” The relationship between oxygen concentration and available surface is not linear. When the crystal shoulder diameter is small (<125 mm), the oxygen evaporation (and therefore the oxygen concentration of the growing crystal) is very sensitive to the diameter change. When the majority of the surface is covered with the crystal, the evaporation seems to remain nearly constant. By extrapolating the curve in Fig. 7, the oxygen concentration corresponding to a very small and to a maximum size of crystal (when the melt is fully covered) may be obtained. The maximum oxygen evaporation accounts for about 30% of the available dissolved oxygen. This value is much lower than generally conceived, that over 90% of the dissolved oxygen from crucible is evaporated from the melt surface (Hoshikawa et al., 1981). Further discussion of the oxygen incorporation behavior on the 300 mm diameter crystal growth will be made in a later section. Lin and Hill (1983a) studied the effect of ambient pressure on the oxygen distribution in the melt and grown crystal via crystal growth experiments.

2.

27

THE INCORPORAIION OF OXYGEN INTO SILICON CRYSTALS

Based on the experimental evidence, physical models of oxygen distributions in large silicon melts were proposed and are shown schematically in Fig. 8. I t is shown that thermal convection is the main oxygen transport mechanism when the melt aspect ratio is high in a large melt growth. The oxygen-rich flow conforms with the suggested thermal convection pattern shown in Fig. 4a. Experimental results also showed that, under atmospheric pressure, the oxygen distribution is not uniform near the melt center. where a stagnant region of low oxygen concentration exists. The nature of this nonuniformity is displayed in crystals' radial oxygen profiles near the seed end, Fig. 9a. However, as the crystal growth progresses. the forced convection due to crystal rotation modulates the oxySiO SIO

t (a)

t (b)

ATMOSPHERIC

REDUCED

PRESSURE

PRESSURE

Fib 8 Schematic repre\entation\ ot oxygen distributions in silicon melt at high nnd low melt level configurations The dot\ m d line5 represent oxygen concentration (a) At reduced pressure ( b ) At atmmpheric preswre (Attei 1 x 1 and Hill. 1983a )

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WEN LIN

2o

30 40

m

r 0

NEAR SEED

NEAR SEED

25

50

20

30

t0

RADIAL DISTANCE Imm)

25 50 RADlAL DISTANCE (rnm)

FIG.9. Radial profiles of 9 Frn 1R transmission at various stages of growth: g = fraction solidified. (a) At atmospheric pressure. (b) At reduced pressure (18 torr). Oxygen concentration is computed in accordance with ASTM F121-80 (ASTM 1980). (After Lin and Hill. 1983a.)

gen distribution and results in local mixing, and the gross nonuniformity near the stagnant region is largely diminished. On the other hand, under the reduced pressure, Fig. 9b, the oxygen distribution in the melt is more uniform near the surface of the melt. The grown crystal possesses better radial oxygen uniformity. When thermal convection is not significant, as in the case of a low aspect ratio configuration, the melt oxygen is both diffusion rate and crucible dissolution rate dependent. The melt tends to be uniform in oxygen. Both enhanced forced convection and ambient pressure have little effect on the oxygen uniformity. b. Effect of Crystal and Crucible Rotation

For a given system, i.e., fixed starting melt geometry and hot-zone thermal distribution, etc., the parameters that can significantly alter the oxygen incorporation are crucible and crystal rotations and growth-rate

2.

29

THE INCORPORAllON OF OXYGEN I N T O SILICON CRYSTALS

variations. The effect of crystal-crucible rotation on the fluid flow patterns were studied in the past by simulation using a fluid of viscosity similar to that of silicon melt at room temperature. Figure 10 shows the fluid flow patterns due to various combination of crystal and crucible rotations. In the real crystal growth, however, the flow patterns can be significantly altered by the presence of thermal convection. The results of the simulation provide very useful information on the effect of rotational parameters. Kakimoto et al. (1988, 1989) observed thermal and forced convection flows of silicon melt directly during Czochralski growth using X-ray radiography with solid tracers, for various crystal and crucible

SMALL

SMALL

LARGE

SMALL

c-

t

4

c

SMALL

[T!,V-r"l LARGE

CRUCIBLE DOM I N AT ING

MEDIUM

SMALL

COUNTERROTATION

CRYSTAL DOM I N AT IN G

1

1

t

-

LARGE

SMALL

LARGE

SMALL

FIG 10 The variation of Czochralshi How patterns with relative rotation directions and magnitudes of crystal and crucible (after Carruthers and Nassau, 1968).

30

WEN LIN

0.0

0.1 0.2

0.4 0.5 0.6 0.7 FRACTION SOLIDIFIED

0.3

0.0

0.9

1.0

FIG.11. Axial oxygen profile of silicon grown with crystal rotation of 30 rpm and crucible rotation of 2 rpm (in iso-rotation). The dashed line represents profiles due to normal growth.

rotation speeds. The effect of nonaxial symmetrical temperature distributions on the thermal convection flows was clearly observed. The suppression of thermal convection by crystal rotation-induced forced convection was also evidenced. One way to gain information on the flow properties of a growing system is to analyze grown crystals following parametric growing experiments. One finds that forced convection is effective in controlled oxygen incorporation. As discussed previously, crystal rotation rate determines the magnitude of the upward melt flow. This flow can serve as oxygen transport from crucible bottom to the growing interface. The net effect on the overall flow pattern and oxygen incorporation depends on its magnitude and rotational direction relative to the crucible rotation. Figure 11 shows an “uncommon” oxygen profile of silicon grown under high crystal rotation (30 rpm) with crucible in iso-rotation mode (2 rpm). At about 30% of melt solidified, the oxygen incorporation underwent a mode change and sharply increases to a very high concentration level (-25 ppma). This behavior indicates that as the melt aspect ratio is reduced during the crystal growth, at some transition point, the strong forced convection

2.

THt I N C O R P O R A l I O N O F O X Y G E N INTO SILICON CRYSTALS

31

takes over as the dominant transport mechanism that draws oxygen-rich melt from the crucible bottom to the growing interface. Crucible rotation develops radial pressure gradients that enhance the thermal convection flow arising from nonvertical temperature gradient as shown in Fig. 4c. Therefore. fast crucible rotation helps the transport of oxygen from near the crucihle wall to the growing crystal and enhances incorporation. Figure 12 shows the effect of crucible rotation on the incorporation level. Fast melt flow also results in a thinner melt-crucible boundary diffusion layer. a condition that will enhance crucible dissolution. Figure 13 shows several axial oxygen concentration profiles of silicon grown with several combinations of crystal and crucible rotation rates, under both counter- and iso-rotation conditions in the same grower and a reduced pressure. These results show that the forced convection induced by crystal-crucible rotations has very significant effects on the melt flow pattern. even in the presence of thermal convection. The bulk

CRYSTAL ROTATION

20 RPM

I 0.2

1

I

0.6 FRACTION SOLIDIFIED 0.4

I 0.8

1.o

Fib. 12. Oxygen profiles at variow crucible rotation rates. with crystal rotation rate held at 28 rpm (after Moody, 1986; the paper was originally presented at the spring 1986 meeting of the Electrochemical Society).

32

WEN LIN

11

0

0.1

0.2

0.3 0.4 0.5 0.6 FRACTION SOLIDIFIED

0.7

0.8

FIG. 13. Axial oxygen profiles of silicon crystals grown with several combinations of crystal and crucible rotation rates.

of the incorporation behavior is consistent with, and can be interpreted from, the simulated flow patterns, Fig. 10. c. Incorporation in p

+ and n + Silicon Crystal Growth

In recent years, the use of n / n + and pip+ epitaxial structures in VLSI/ULSI has significantly increased, due to the structure’s potential in reducing latch-up susceptibility in CMOS and alpha particle-induced soft error in memory devices. In such applications, both n- and p-type silicon are normally degenerately doped to concentrations in the range of atoms/cm3. There is no distinguishable difference in the oxygen precipitation kinetics between n- and p-types in the lightly doped region (typically, 101S/cm3).However, as the dopant is increased to the degenerately doped region of interest (0.005-0.02 ohm-cm), the behavior becomes drastically different depending on the conductivity type (Tsuya et al., 1983). In this resistivity range, oxygen precipitation is retarded in Sb-doped silicon while the kinetics are at their peak for p-type, borondoped silicon. Due to these properties, the p + substrates provide good internal gettering while Sb-doped n + leads to poor microdefect formation and intrinsic gettering during silicon processing. The possible sources of differences in precipitation kinetics in p + and n + were investigated.

2.

THE 1NCORPORATlON O F OXYGEN lNTO SILICON CRYSTALS

33

Oxygen diffusion mechanism was found not to be affected by the presence of heavy Sb or light boron (Oates and Lin, 1988a). The nucleation mechanisms for oxygen precipitates have been thought to be different in p + and n + . Experimentally, the oxygen incorporation in n + and p + have been found to be different from the lightly doped silicon (Oates and Lin, 1988b). Figure 14 shows the axial oxygen distribution in 100 mm diameter p + (0.005-0.01 ohm-cm) and n + (0.02-0.08 ohm-cm) crystals as measured by SIMS, compared to the distribution band of p - (8-20 ohm-cm) grown with the same conditions. It is seen that on the average, the p + crystals exhibit about 25% higher incorporation rate than n + crystals (with p + contents higher than p - , while n + are lower). Other studies (Walitzki et al., 1986; Nozaki et al.. 1986) also show the dependency of oxygen incorporation on doping level, but to different degrees. In considering the oxygen incorporation mechanism, one would not be surprised to find that the dependency obtained would vary somewhat depending on the melt size, melt aspect ratio. etc. used in the crystal growth experiments. Several possible mechanisms behind the dependency of oxygen incorpo-

30

-zk

100 mm SILICON GROWTH 18 kg CHARGE

25

a

0

20

t a b-

5

0

15

z

0 0

z

g X

10

0 P- IR 5

0

1

0

0

P+ SIMS

X

N + SlMS

I

I

0.2

I

0.4

1

I 0.6

I

I

0.8

I

1.0

FRACTION SOLIDIFIED

FIG. 14. A comparison of oxygen incorporation levels of lightly doped p and heavily doped p and n ( p + and n + ) silicon crystals grown under identical conditions (after Oates and

Lh.

1988a).

34

WEN LIN

ration on the dopant concentration have been suggested (Itoh et al., 1984; Shimura et al., 1985; Barraclough and Series, 1986). Some data indicate that the reduced oxygen incorporation into heavily Sb-doped silicon is due to Sb203evaporation from the melt, thus reducing oxygen concentration in the melt (Itoh et al. 1984). Others explain the lower oxygen incorporation observed in heavily Sb-doped silicon as due to accelerated SiO evaporation from the melt caused by simultaneous evaporation of elemental antimony (Barraclough and Series, 1986). In the case of p + crystal growth, the enhanced oxygen incorporation is speculated as due to enhanced crucible dissolution by heavily boron-doped silicon melt. It is pointed out here that the difference in oxygen incorporation level cannot account for the difference observed in precipitation kinetics in p + and n + . The difference in the nucleation mechanism probably plays a significant role. 2. OXYGEN SEGREGATION AND MICROSCOPIC INHOMOGENEITY

Segregation of oxygen is an important characteristic in Czochralski silicon crystal growth since it relates to oxygen nonuniformity and consequently, the nonuniform precipitation characteristics. Generally, the degree of impurity segregation during solidification of a dilute solution may be described by an equilibrium segregation coefficient, k , = CJC,, where C, and C, are impurity concentrations in the solid and adjacent liquid, respectively. Finite segregation exists when the k , has a value that deviates from unity; the greater is the deviation, the greater the segregation. The equilibrium segregation coefficient of oxygen in silicon has been of interest for some time. A range of k , values have been reported by various authors (for example, Trumbore, 1960; Yatsurugi et al., 1973; Lin and Hill, 1983b; Harada et al., 1985), ranging from greater to less than unity and including unity. In large silicon melt growth, the crystal’s axial dopant distributions were found to follow normal freezing behavior with its effective segregation coefficients approaching equilibrium value (Carruthers et al., 1977). Unlike most dopant elements, the crystal’s axial oxygen distribution does not follow normal freezing since the oxygen in the silicon melt is a dynamic system, as discussed previously. Therefore, oxygen segregation effects are not reflected in the crystal’s axial oxygen distribution. As shown in Fig. 13, the axial profile can vary significantly depending on the growth parameters used. These profiles are not the result of oxygen segregation. One can freely fit a normal freezing-type power function to such an oxygen profile and obtain an “effective” coefficient. But the

2.

THF. INCORPORA1 I O N O F OXYGEN lNTO SILICON CRYSTALS

35

coefficient so obtained cannot be related to the equilibrium segregation coefficient of oxygen, which is a physical constant associated with the Si-0 binary phase relationship. Segregation plays a rather important role in macro- and microscopic incorporation of oxygen and its uniformity in grown silicon. In the solidification process, far from the equilibrium situation, the impurity incorporation is basically governed not only by the equilibrium segregation coefficient, but also by thc instantaneous growth rate, as described by Eq. ( 3 ) . In terms of the relationship. if k , were unity for oxygen. there would be no change in oxygen incorporation rate in response to imposed growth rate change. and there would be no oxygen striations in silicon crystals. However, just as for the case of dopants in silicon, macro- as well as microscopic oxygen variations have always been observed in CZ silicon, and they result in significant segregation (that is, nonunity equilibrium segregation coefficient) and growth-rate fluctuations. Experimentally, the oxygen incorporation level was observed to change with growth rate under controlled experiments (Lin and Hill, 1983a). that is, oxygen does segregate during solidification. From such experiments, an equilibrium segregation coefficient of -0.3 was deduced. Similarly, Lin and Stavola (1985) studied the origin of microscopic oxygen inhomogeneity and its effect on oxygen precipitation using largespacing oxygen striations prepared by a manually controlled crystal growth (that is, the forced pull-rate change of the automatic diameter control mechanism is absent). The periodic nature of the profile shown in Fig. IS is a result of growth rate fluctuations (due to noncentral symmetrical temperature distribution in the melt) and oxygen segregation. The experiment shows that oxygen does segregate significantly, which corresponds to a nonunity segregation coefficient. The phase analysis showed that X , < I for oxygen and that oxygen behaves similarly to arsenic in silicon. Therefore, oxygen segregation produces inhomogeneity when there is a perturbation in growth rate. Heat treatment experiments of silicon containing microfluctuations in oxygen concentration show that the precipitation is not uniform; rather the precipitation is enhanced in the highoxygen region of fluctuations. Fig. 16. Such behavior can impede the formation of the denuded zone where the high-oxygen regions meet the wafer surface, resulting in n o denuded zone at these locations. The phenomenon corresponds to the “oxygen rings” often observed on a heattreated wafer surface following preferential chemical etch. In general, a segregation coefficient less than unity implies an eutectic phase diagram. The melting temperature of silicon containing oxygen is

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‘ 18 OE

I 40

I

I

I

20

0

d (mm)

FIG.15. The 9 pm infrared absorption scans along the growth direction of a crystal grown at a crystal rotation rate of 2 rpm and a constant pull rate of 9 cm/hr. Insert shows scan positions with respect to the experimental crystal. Horizontal lines on the crystal represent scratch markers. (After Lin and Stovala, 1985. Reproduced with permission of the Electrochemical Society, Inc.)

lower than pure silicon. On the other hand, if k , > 1 , the solidus would terminate with a peritectic reaction. The k , = 1 would indicate a situation where liquidus and solidus merge, a condition not consistent with the phase rule. Based on k , = 0.3, Mikkelsen (1985) presented a schematic phase diagram for Si-0 with the Si-SiO, eutectic. More recently, Jackson (1988) calculated the solidus, liquidus, the eutectic point and temperature of the Si-0 phase diagram at the Si end, using k , = 0.3, as is shown in Fig. 17. Ekhalt and Carlberg (1989), in their study of oxygen solubility, also proposed a phase diagram in which the slope of the liquidus near the Si is consistent with k , < 1.

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THE IN(~ORPOKAII0N OF OXYGEN INTO SILICON CRYSTALS

37

FIG 16 Micrograph of etched d i c o n showing enhanced oxygen precipitation in the high-oxygen region of fluctuation\ \hewn in Fig I5

V. Controlled Oxygen Silicon Growth 1 . NORMAL

C Z O C H R A L s K l GROW[-H

For ease of discussion, oxygen concentrations in silicon crystals for integrated circuit applications may be conveniently classified into high, medium and low concentration ranges. If we designate 14-17 ppma as the medium range, the concentrations above and below this range are referred to as high and low concentrations, respectively.

1415.0

0

I

0

W

a

2 l-

a

a W n

I, I-

I I

1.8r10'8 ATOM / cc

1414.9 0

10

2

2x10-2

ATOMIC PERCENT OXYGEN

F I G 17 Si-0 phdw diagram cdlculdted by Jackson (1988) using ku hith permisvon of the Anienca Society tor Metdls)

=

0 3 (reproduced

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21

t

-0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0

0.9

FRACTION SOLIDIFIED

FIG.18. Axial oxygen profile of a silicon crystal showing the effect of crucible rotation rate on oxygen incorporation level.

From previous discussions, it is seen that forced convection is an effective tool for controlling oxygen incorporation. In order to achieve a desired oxygen level with axial uniformity in a silicon crystal, the following may be carried out. Experimentally, for a given growing system, one can establish oxygen incorporation profiles as a function of crystal and crucible rotation rates via parametric studies such as shown in Fig. 12. Using selected rotational parameters at different stages of crystal growth, one can develop and tailor the growth processes to grow crystals of desired oxygen concentration with substantial axial and radial uniformity. Figure 18 shows an example of using variable crucible rotation rates to change the oxygen incorporation levels during the growth, while the crystal rotation rate is maintained constant. It shows that crucible ramping to a higher rotation rate effectively raises the oxygen level and changes the oxygen concentration profile. We also found that the incorporation level can be further enhanced when alternate ramping-up and -down of crucible rotation at medium and high rates are employed, as shown in the Fig. 18. Presumably, the action causes a local “disturbance” and thinning of the boundary layer between the crucible and the melt, thus increasing crucible dissolution. The example in Fig. 18 demonstrates the usefulness

2.

39

1HE INCORPORATION OF OXYGEN INTO SILICON CRYSTALS

of forced convection in enhancement or retardation of oxygen incorporation. With the proper use of forced convection, including the use of alternate ramping-up and -down of the crucible rotations, more uniform axial incorporation for high and medium range of oxygen can be achieved. Concentration profiles a and h of Fig. 19 are oxygen profiles as a result of using variable crucible rotations for high and medium concentration levels. In the growing systems in which the forced convection alone cannot achieve the level or uniformity desired, additional sources of oxygen may be added by increasing the melt-crucible contact surface. Methods such as sand blasting the crucible surface (Patrick et al., 1977) and addition of an extra quartz rod or ring placed at a strategic location (Secco. 1985) have been used. Figure 20 shows a crucible design with its bottom surface fabricated in corrugated configuration. It is shown that the additional contact sources uniformly increases the incorporation level, curve h of Fig. 21, as compared with curve c , grown with a normal crucible. Curve

0

I 0.1

1 0.2

1

0.3

1 I I 0.5 0.6 0.7 FRACTION SOLIDIFIED I 0.4

I 0.8

I 0.9

1.0

FIG. 19. Uniform axial oxygen profiles of silicon crystals using variable crucible rotation rates during growth (curves (1 and h ) . as compared with that due to normal growth (curve c ) .

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FIG.20. Schematic of the cross-sectional view of the crucible design with corrugated crucible bottom.

0

0.1

0.2

0.3

0.4 0.5 0.6 0.7 FRACTION SOLIDIFIED

0.8

0.9

1.0

FIG.21. Axial oxygen profiles showing enhanced incorporation by ( a ) extra quartz adhered to crucible bottom and ( b ) corrugated crucible bottom. Curve (c) is due to normal growth and curve (6) is due to the use of forced convection conditions for low-oxygen incorporations.

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THE INCORPORATION OF OXYGEN INTO SILICON CRYSTALS

41

shows an oxygen profile resulted from silicon growth with extra quartz material adhered to the crucible bottom surface for an added oxygen source under normal growth conditions. It is pointed out that profiles a , b and c are from the use of a fixed set of crystal and crucible rotations. When variable forced convection parameters are applied, the concentration profiles may be tailored to improve axial uniformity as is shown in Fig. 19. Curve u of Fig. 19 is the result of using variable crucible rotation on crystal growth with added quartz material adhered to the crucible bottom. While thermal convection, crucible and crystal rotations all have effects on the oxygen incorporation level, these parameters also have great impacts on the radial oxygen gradient. The relevance of these parameters to radial impurity uniformity has been discussed in Section 111.5 of this chapter. In order to achieve radial oxygen uniformity, the melt flows causing the radial nonuniformity in the diffusion boundary layer thickness have to be suppressed. For example, when using a high crucible rotation rate to enhance oxygen incorporation, the radial oxygen uniformity is degraded unless a high crystal rotation in the opposite direction is used. As discussed earlier. the crucible rotation creates a fluid flow in the same general direction as the thermal convection, Fig. 4c. Such flow will cause the diffusion boundary layer to be thinner at the edge than at the center of the interface. Consequently, more oxygen is incorporated at the center than at the edge of the crystal. Increased crystal rotation suppresses the effect of crucible rotation and thermal convection flows and results in a thinner diffusion boundary layer. Thickness variations in the thinner boundary layer would cause less radial gradient in oxygen incorporated. Fast crystal rotations also result in more mixing in the melt adjacent to the growing interface and tend t o improve the melt concentration uniformity. It should be mentioned that there exists a drastic decrease in oxygen concentration in the CZ crystal’s radial oxygen profiles near the crystal’s periphery region. This is due to oxygen out-diffusion during crystal growth following solidification. In the large melt growth, the controllability for low-level oxygen incorporation is more limited than that for the medium and high incorporation levels due to the domination of thermal convection function as the transport of oxygen-rich melt. This is more so for the growth of the crystal portion near the seed end. Curve d in Fig. 21 represents a typical range of concentration profiles in the low oxygen range ( 1 1-14 ppma) that may be obtained with the experimental hot zone used. In this range, further uniformity of the profile can be obtained by increasing the incorporation level of the lower concentration portion of the profile using crucible ramping. However, suppressing the seed-end oxygen incorporation by forced

(1

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convection is usually not an efficient process. It often results in degradation in the oxygen radial gradient and other disadvantages in growth conditions and crystal properties. From the preceeding discussion, one realizes that in normal CZ growth, the small or low-aspect ratio melt configurations would facilitate the incorporation of low-level oxygen due to reduction of thermal convection. Such a growth environment may be obtained by growing silicon from a small or shallow inner crucible of a double-crucible type setup. Axial uniformity as well as concentration control using a double-crucible setup has been demonstrated (Lin and Pearce, 1980). Although such apparatus is more involved than a normal CZ growth, as the CZ charge size continues to increase, the concept of small and shallow melt growth of double crucible is certainly extended to continuous CZ growth, to be discussed later in this section. For silicon materials requiring low oxygen and low microdefect density, the most effective method is the growth under applied magnetic field. For very low-level oxygen incorporation (a few ppma), crucibles made of nonoxygen-containing materials, such as Si,N,, have been used for silicon crystal growth (Watanabe et al., 1981; Watanabe, 1984). In this case, the source of oxygen is from the silica beads added in the silicon melt. The oxygen incorporation would be controlled by the ratio of surface area of the SiO, beads to the free-melt surface. In general, the oxygen incorporation in normal batch CZ silicon growth from a large melt can be controlled to within 2 1.5 ppma of the normal concentration range of interest. 2. MAGNETIC FIELDAPPLIED CZOCHRALSKI GROWTH (MCZ)

From the previous discussion, it is clear that thermal convection in a large silicon melt plays a major role in determining many aspects of the crystal quality of CZ silicon. In particular, oxygen concentration as well as dopant and oxygen uniformity are of concern. The ability of a magnetic field to suppress the thermal convection in electrically conducting fluids was demonstrated in the 1960s in crystal growth experiments (Utech and Flemings, 1966). In 1970, a transverse magnetic field was applied for the same purpose in a CZ growth of indium antimonide (Witt, Herman and Gatos, 1970). The application of a magnetic field across an electrically conductive melt increases the effective kinematic viscosity of the melt (Chandrasekhar, 1952) and thus suppresses the thermal convection and related temperature fluctuations in the melt. Hoshi et al. (1980) first reported on CZ silicon crystal growth under an applied horizontal magnetic field. Aside from a reduction or elimination of impurity striations, MCZ displayed potential for growing low-oxygen,

2.

THF INCORPORA~IION OF OXYGtN INTO SlLlCON CRYSTALS

43

low-microdefect and higher resistivity CZ silicon for applications in power devices and imaging devices such as CCD. Since 1980, various types of magnetic field configurations (Takasu et al.. 1990). in terms of field directions (VMCZ for vertical or HMCZ for horizontal) and the magnet types used (normal conductive or superconductive). have been developed and crystal growth studies have been carried out. In general, both VMCZ and HMCZ growth have been shown to reduce temperature-fluctuation related growth-rate fluctuations, resulting in reduced impurity striations. However, the magnetic field effects on impurity incorporation behavior vary widely depending upon the field direction with respect to the growth axis, and field strength. For example, increased field strength enhances oxygen concentration under a vertical field (Braggins and Thomas, 1986b). whereas oxygen incorporation is retarded under an increased horizontal magnetic field (Hoshi et al., 1985). Therefore. a horizontal magnetic field facilitates the incorporation of low (<:S x 10’’ atomsicm’) to medium (5-10 x 10” atomsicmj) oxygen concentrations, whereas a vertical field facilitates the growth of silicon with medium to high (>IO’’ atomsicm’) oxygen concentrations. In fact. extremely high oxygen concentrations, near or above the solubility limit, can be incorporated under certain growth conditions with vertical magnetic fields (Ohwa et al., 19x6; Braggins and Thomas, 1986b). Forced convection induced by crystal and crucible rotations can also perturb oxygen incorporation under a magnetic field. Several large diameter ( 100125 mrn) MCZ crystal growth experiments from large melts (20-30 kg) have provided information on the difference in oxygen incorporation behavior between HMCZ and VMCZ. For example. Ohwa et al. (1986) made a comparison of oxygen incorporation behavior between VMCZ and HMCZ using the same puller, as is shown in Fig. 22. In HMCZ mode, a low level of oxygen concentration (-4 ppma) is incorporated in a horizontal magnetic field of 0.25 Tesla (2500 G ) with good axial uniformity. The crystal rotation shows no effect on the incorporation level under this condition. However, another study (Hoshi et al.. 1985) showed that, under HMCZ, an increase in crucible rotation would increase the oxygen incorporation level. As is in the normal CZ high crucible rotation would often result in some degradation in radial uniformity. In such an instance, the use of a higher crystal rotation rate would help to reduce the oxygen radial gradient. Figure 22 also shows that, in VMCZ mode, higher oxygen concentration may be incorporated using a magnetic field strength one-third of that for HMCZ. Unlike HMCZ, the oxygen incorporation level in VMCZ is a strong function of crystal rotation and the incorporation switches to a much higher level through a sharp transition during the crystal growth. Both the incorporation level and the transition

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t

.y

; x

0

HMCZ

0.25 Tesla 30 kg 0 25 rpm rn 15 rpm

t 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

FRACTION SOLIDIFIED

FIG.22. Oxygen profiles of silicon crystals grown under horizontal and vertical applied magnetic fields under the conditions indicated (after Ohwa et al. 1986. Reproduced with permission of the Electrochemical Society, Inc.).

point are clearly a function of crystal rotation, indicating that under VMCZ mode the crystal rotation induced forced convection acts as a major transport mechanism. Figure 23 shows models proposed by Hoshi, Isawa and Suzuki (1986) for the magnetic damping of the melt flow for VMCZ and HMCZ. In view of the model for VMCZ, the melt flow from outer to center of the melt (which flows perpendicular to the vertical magnetic flux) is retarded. Under this condition, the forced convection induced by the crystal rotation is an effective transport for the oxygen-rich melt from the crucible bottom to the growing crystal. As the melt aspect ratio is reduced during the crystal growth, at some transition point, the forced convection would take over as the dominant transport mechanism and the incorporation level is sharply increased. The occurrence of this “transition” seems to depend on the crystal rotation used; the higher is the crystal rotation, the

2.

1 H E I N C O R P O R A I ION OF O X Y G E N INTO SILICON CRYSTALS

45

Sooner this transition will occur during the growth. It is interesting to note that the observed "transition" in incorporation level for the VMCZ growth is similar to that discussed earlier for normal CZ growth under high crystal rotation (30 rpm) with crucible in iso-rotation mode ( 2 rpm) (see Fig. 1 1 ) . In both cases. the behavior is attributed to strong crystalrotation induced convection. In the case of HMCZ, the model of Hoshi et al. shows that the horizontal magnetic flux damps the vertical melt flow near the wall due to thermal convection and crucible rotation, resulting in retarded oxygen transport and, therefore, a low level of oxygen incorporation. The forced convection induced by the crystal and crucible rotations are more effective in the horizontal direction, parallel to the magnetic flux. Thus, the increased crucihle rotation would help crucible dissolution and transport of the oxygen-rich melt follow flow path delineated in the model. The results by Ohwa et al. discussed previously and other largediameter. large-melt VMCZ growth indicate that oxygen incorporation (and other growth characteristics) in VMCZ is affected by many variables and is not easily controlled. Furthermore, impurity segregations were observed to depend on the vertical field strength (Series et al., 1985; Braggins and Thomas. 1986a). The segregation coefficient of the impurity (such as carbon, oxygen. phosphorus or gallium) tends to increase (toward unity) as the magnetic field increases. However, the radial uniformity of these impurities is significantly degraded in a vertical field (Braggings and Thomas, 1986b). For example, the radial oxygen gradient in a silicon crystal of 100 mm diameter can reach 30-50% when grown in a high vertical field. These properties are not desirable. The change in segregation and severe degradation of the radial gradient found for growth

-

---+

MAGNETIC FLUX FORCED CONVECTION BY us FORCED CONVECTION BY oc OXYGENFLOW

4

VMCZ

HMCZ

FIG 2 3 The effect of vertical and horimntal mdgnetic field on damping melt Row in Crochral\ki crucible (after Hoshi et dl 1986)

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in VMCZ have not been reported for HMCZ growth. From considerations of growth control ability and crystal properties, HMCZ is the preferred approach for MCZ growth. The HMCZ method can grow large diameter silicon with oxygen levels ranging from a few ppma to over 20 ppma with axial concentration uniformity. 3. CONTINUOUS CZOCHRALSKI SILICON GROWTH

The idea of the continuous CZ growth came about due to the fact that as the silicon diameter continues to increase, the maximum grown crystal length of the batch CZ process is limited by the charge size. The initial motivation of the approach of the continuous growth was for the increased crystal length and thus improved throughput and operation cost of the CZ grower. A continuous CZ growth based on a two-container system was first demonstrated by Fiegl (1983). In addition to increased crystal length, many other desirable crystal properties were also demonstrated. In particular, the arrangement affords the use of a small and shallow melt CZ setup in the growing container. In many ways, a twocontainer arrangement with crystal pulling from constant melt volume is the same as a double-crucible operation. Figure 24 is a generalized two-container system reconfigured from a constant-volume doublecrucible, where V , and V , are melt volume in outer and inner crucibles, respectively, in a straight double-crucible setup. The reconfigured arrangement facilitates the addition of polysilicon and dopant. Only the outer crucible (the feeder) needs to be lifted or adjusted for the melt level control for constant volume or melt level in the growing crucible.

t FIG.24. Schematic showing a generalized two-container arrangement for crystal growth from a constant volume melt by continuous feed.

2.

THE INCORPORA1 ION OF OXYGEN INTO SILICON CRYSTALS

0

47

INCREASED V2

f w Z I

DECREASED Vp 0

V-VOLUME SOLlDlFlEO

FIG.3. Axial oxygen. dopant and impurity concentration distributions along the cryjtal grown from the arrangement shown in Fig. 24. The oxygen concentration level can he adjusted by changing the melt volume.

The system offers the same advantages as the double crucible in axial uniformity in dopant and oxygen and the small melt effect. Figure 25 shows the uniform axial oxygen profile due to “constant volume” growth. The uniform axial dopanl profile at concentration C,, is obtained when initial doping of the growing crucible i s C,,/k and feeding crucible is maintained at C,,. The incorporation behavior of the impurities in the feed material is similar to one-pass zone leveling (Pfann, 1965) with the “z.one width” being equivalent t o the melt volume in the growing crucible, C;. In the continuous growth mode, V , is the total melt volume

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15

-

DIAMETER PULL SPEED P-TYPE

14 -

100mm 100 mm/hr

<1W>

-

0

20

40 60 80 CRYSTAL LENGTH (cm)

100

120

FIG.26. Uniform axial oxygen distributions from “constant volume” continuous-feed silicon growth. The oxygen level is shown to depend on the melt size (after Fiegl 1983).

passing from the feeding (outer) crucible to the growing crucible before V , is consumed and reduced. The oxygen concentration level is determined by the volume and aspect ratio of the melt in the growing crucible (see Fig. 26). While the continuous “feed-and-pull” system with two containers appears straightforward, many engineering challenges remain to be solved or improved for the method to be practical. Among the problems to be solved are liquid melt transfer and establishment of thermal stability and radial thermal symmetry in the melt while receiving the melt from an external source. In recent years, with the availability of high-purity, small-diameter silicon beads from the fluidized bed process, “feed-andpull” may be carried out in a double-crucible arrangement like those shown in Figs. 27a and 27b. If the total melt volume is kept constant, the partition separating the two melt concentrations becomes unnecessary. The resulting “one melt” growth retains the advantages of doublecrucible arrangements, Fig. 27c. In this arrangement, the oxygen concentration level is controlled, as in the two-container case, by the melt volume and aspect ratio. However, the application of forced convection for additional oxygen incorporation control is more restricted than for standard batch processes. Furthermore, in this design, the single crucible contains a physical barrier to prevent unmelted silicon particles from

2.

THE INCORPORA1 ION O F OXYGEN INTO SILICON CRYSTALS

49

FIG.27. Crystal growth from double-crucible arrangements with (a) constant melt level or ( h ) constant inner crucible melt volume. maintained by continuous-feed ( c ) crystal growth from a slngle container equipped with ii circular silica baffle. Melt level is kept constant by continuous feed. The melt concentration I S maintained at Co/k.

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reaching the growing crystal and a baffle that reduces thermal convection. One may also view the continuous feed mechanism as playing the role of the outer crucible which supplies silicon with dopant concentration C,, (the intended concentration in the crystal). The small-diameter polysilicon beads certainly add a new dimension to the development of continuous “feed-and-pull’’ silicon growth. The continuous-mode growth also provides flexibility where melt volume and aspect ratio of the growing crucible can be adjusted for oxygen incorporation level. This is especially important for the low oxygen incorporation, which can not be easily attained in the standard CZ growth with melt size of 80 kg or larger. VI. Summary

We have reviewed the current understanding of the oxygen incorporation mechanisms and technologies for control of oxygen level and uniformity in CZ silicon growth. We first reviewed FZ and CZ growth methods and pointed out the importance of oxygen in CZ silicon for microelectronic device processing. The general characteristics of C Z silicon growth pertaining to oxygen incorporation and thermal history were discussed. The understanding of the oxygen incorporation mechanisms and their interactions have facilitated the development of CZ growth processes for more uniform oxygen distribution at desired incorporation levels. As the crystal diameter and grower charge size are scaled up, due to the dominance of the severe thermal convection of the large melt, the controllability for low-level oxygen incorporation is more limited. For low-oxygen, low-microdefect density CZ silicon, the most effective method is the growth under an applied magnetic field. Extensive studies in large-melt MCZ growth in the last decade have shown that HMCZ is the preferred choice over the VMCZ, from the considerations of both control ability and crystal properties. Crystal growth from small melt and constant melt volume provided by double crucible arrangement yields improved axial and radial oxygen uniformity. The double-crucible methodology can be extended to a generalized two-container, continuous “feed-and-pull” growth system with the benefits of the double crucible in addition to increased crystal length. The availability of recently developed polysilicon beads simplifies the development of a crystal growth process using continuous “feed and pull.”

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H . R. Huff. R. J . Kriegler. and Y . 'lakeishi (eds.).p. 54. Electrochem. So c ., Princeton. N.J. ASTM. ( 1980). Standards F-121. ASTM. Philadelphia. Barl-aclough, K . G . . and Ward. P. J . (19x3). E l c ~trocheni. So(.. Meet. E x t . Ah.$rr. l67rh. 414. Barraclough. K. G . . and Series. R . W. 119x6). I n Reduced Tc7mp Proc..fiir V L S I . R. Reif ( e d . ) .p. 457. Electrochem. Soc.. Pennington. N . J . Bensun. K . E., Lin. W.. and Martin. E . 1'. (1981). I n Semiconductor Silicon IYXI. H . R. Huff. R . J. Kregler. and Y . Takeishi (eds.1. p. 33. Electrochem. Soc.. Princeton. N . J . Braggins. T. T , . and Thomas. R. N . I I986a). Electrochem. Soc. Merr. E x t . Ahsrr. 169,

p. 351. Braggins. T. T.. and Thomas. R . N . I IYXhb). Elrc trochem. Soc.. Mrr.1. Exr. Ahsrr. 169, p. 354. Burton, J . A . . Prim, R . C . . and Slichtei-, W. P (1953). J . Chrni. Phys. 21, 1987. ('arlberg. T.. King. T. B.. and Witt. A . F. (19x2). 1.Elec,trochern. Sot.. 129, 189. Carruthers. J . R . (1967). J . Elrc,rroc-/it,ni.S o c . 114. 959. Carruthers. J . K . . and N a s s a u . K. (196X). J . Appl. Phys. 39, 5205. Carruthers. J . R.. Witt, A . F.. and Keu\sei-. R . E . (1977). I n Semiconduc.tor Silicon 1977. H . K. Huff and E. Sirtl (eds.). p. 61. Electrochem. Soc.. Princeton. N . J . ('handrasekhar. S . I 1951). Philos. M(i,q. 4 3 7 ) . 501. Cochran. W. G. (1934).!'roc.. C o m h d g r Phil. Sot,. 30, 365. Craven. R . A . . Baily. W. E.. Moody, J. W . . Falster. R. J., and Shive. L. W . (1986). Mrrr. He.\. Sot.. Svnip. Pro<..59, 359. Czochralski. J . (1918). Merallr. Z . P h n . (-hem 92, 219. Dash. W . C . (1958). J . Appl. Plixs. 29. 736. khalt. U.. and Carlberg. T. (1989). J . tlc,c.frr)c.hrm.SOC. 136, 5 5 1 . iegl. 6 .(1983). Solid S r c r r r 7 e C / i n ( J / .(August). 121. Haradn. H.. Itoh, T.. Ozawa, N.. ; m i Ahe. T. (1985). In V L S / .Sc.renc.eond 7rC'hJl<JhJ,~?; I98.7, M. W. Bullies and S. Brovdo (eds.),p. 526. Electrochem. Soc.. Pennington. N . J . Hoshi. K . . Suruki. T . , Okubo. Y . . and l s a w a . N . (1980). Elrc.troc~lic~m. So(..Mrci. E.rr. Ahstr.. 157, p. 811. Hoshi. K.. Isawa. N . . Suruki. I'.. and Okubo. Y. (1985).J . Elu.rroc./ir,m. Soc. 132. hO3. Hoshi. K . . Ihawa. N . , and Suzuki, 1'. (19x6). UL..I'/ (August) 5 1 . Hoshikawa. K . . Hirata. H..Nakanishi. ti . and Ikuta. K . (1981 ) . I n Sc,,?ii(,ondrrc,t~r Silccon IYNI. H . R. Huff and E. Sirtl (eds.).p. 101. Electrochem. Soc.. Princeton. N . J . Hurle. D. 1'. J . , and Series. R. W. I 1980. J . Crv.rt. Grorcrh 73, I . Itoh. Y.. N o m k i . T.. Masui. T.. and Abe. T (19x4). Proc. J l s r . Appl. Phys. Con/:. Kawasaki. Japan. p. 609. Jackson. K. A . (198x1. Bull. ~ f A l / o vI'lru.tc. Dicrgrcrnts 9(5). 548. JastrLebski. L.. Cullen, G . W.. Soydm. R , Harbeke. G . . Lagowski. J . . Vecrumba, S..and Herrv. W. N . (19x7). J . Elcv.rc-iu Iiczm S C K . 134. 466. . r o ~ . /88, / i 356. Kakimoto, K.. Eguchi. M.. Watanabe. t1.. and Hibiya, T. (19x8). J . C t ~ s tG Kakimoto. K.. Eguchi. M.. Watanahe. H.. and Hibiya. 1'.119x9).J . Ciysr. Groii.rh 89, 412. Keller. K.. and Muhlbauer. A . (19x1 1 Fhwtitig Lotic. S i l i ~ ~ Marcel n. Dekker. N e w York. Kodera. H.(1963).J p f i . J . A p p l . !'/I\.\. 2, ?I?. Kondo. Y. (1981). I n Srniic.ondrccrr,r- Silccon I Y X I . H . R. Huff. R . J . Kriegler. and Y Takeishi ( e d s . ) .p. 220. Electrochem S o c . . Princeton. N.J. Sot,. 127, 961. 1.eroy. H . . and Plougonven. C. (l9XO) 1.Clrc~rr~tc.hem. t i n . W.. (1990). i n "Semiconductoi Silicon 1990" (H.K . Huff. K . G . Barraclough and J-I Chikawa. eds.). p. 569. Electrochem. Soc.. Pennington. New Jersey. Lin. W . . and Benwn. K . E. (1987) Anttrctrl K c i , . of'Mtitrriul.\ . S ( . i ~ n c . r17, 273.

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Lin, W., and Hill, D. W. (1983a). Silicon Processing, ASTM STP 804, p. 24. Lin, W., and Hill, D. W. (1983b). J. Appl. Phys. 54, 1082. Lin, W., and Pearce, C. W. (1980). J. Appl. Phys. 51, 5540. Lin, W., and Stovala, M. (1985). J . Electrochem. SOC. 132, 1412. Lorenzini, R. E., Iwata, A., and Lorenz, K. (1977). U. S. patent 4,036,595. Meese, J. M. (ed.). (1979). Neutron Transmutation Doping in Semiconductors. Plenum Press, New York. Mikkelsen, J. C., Jr. (1985). Mat. Res. SOC.Symp. Proc. 36, 205. Moody, J. W. (1986). In Semiconductor Silicon 1986, H. R. Huff, T. Abe, and B. Kolbesen (eds.), p. 100. Electrochem. SOC.,Pennington, New Jersey. Nozaki, T., Itoh, Y., Masui, T., and Abe, T. (1986). J . Appl. Phys. 59, 2562. Oates, A. S . , and Lin, W. (1988a). J. Cryst. Growth 89, 117. Oates, A. S., and Lin, W. (1988b). Appl. Phys. Lett. 53, 2660. Ohwa, M., Higuchi, T., Toji, E., Watanabe, M.,Homma, K., and Takaku, S. (1986). In Semiconductor Silicon 1986, H. R . Huff, T. Abe and B. Kolbesen (eds.), p. 117. Electrochem. S O C . , Pennington, N.J. Patel, J. R., and Chaudhuri, A. R. (1962). J . Appl. Phys. 33, 2223. Patrick, W. J., Scilla, S. J., and Westdorp, W. A. (1977). U.S. patent 4,010,064. Pfann, W. G. (1952). Trans. A m . Inst. Min. Metull. Eng. 194, 747. Pfann, W. G. (1965). Zone Melting. John Wiley & Son, New York. Schmidt, P. F., and Pearce, C. W. (1981). J . Electrochem. SOC. 128, 630. Secco d’Aragona, F. (1985). U.S. patent 4,545,849. Series, R. W . , Barraclough, K. G., Hurle, D. T . J., Kemp, D. S. and Rae, G. J. (1985). Electrochem. Soc. Meet. Ext. Abstr. 167, p. 396. Shimura, F., Dyson, W., Moody, J. W. and Hockett, R. S. (1985). In VLSI Science und Technology 1985, M. W. Bullies and S. Broydo (eds.), p. 507. Electrochem. SOC., Pennington, N.J. Sumino, K., Yonenaga, I., and Yusa, A . (1980). Jpn. J . Appl. Phys. 19, L763. Takasu, S., Otsuka, H., Yoshihiro, N., and Oku, T. (1981). Jpn. J. Appl. Phys., Suppl. 20(1), 25. Takasu, S., Takahasi, S., Ohwa, M., Suzuki, O., and Higuchi, T. (1990). In Semiconductor Silicon 1990, H. R. Huff, K. G. Barraclough and J.-I. Chikawa (eds.), p. 45. Electrochem. SOC.,Pennington, N.J. Teal, G . K., and Little, J. B. (1950). Phys. Rev. 78, 647. Theuerer, H. C. (1962). U.S. patent 3,060,123. Trumbore, F. A. (1960). Bell Sys. Tech. J . 39, 205. Tsuya, H., Kondo, Y., and Kanamori, M. (1983). Jpn. J. Appl. Phys. 42, 525. Utech, H. P., and Flemings, M. C. (1966). J. Appl. Phys. 37, 2021. Walitzki, H . , Roth, H. J., Refflw, J., Pahlke, S., and Blatte, M. (1986). In Semiconductor Silicon 1986, H. R. Huff, T. Abe and B. Kolbesen (eds.). p. 86. Electrochem. SOC., Pennington, N.J. Watanabe, M. (1984). ASTM Symp on Semiconductor Processing, Abstract, San Jose. Watanabe, M., Usami, T., Muraoka, H., Matsuo, S., Imanishi, Y., and Nagashima, H . (1981). In Semiconductor Silicon 1981, H . R. Huff, R. J. Kriegler and T. Takeishi (eds.), p. 126. Electrochem. SOC.,Pennington, N.J. Witt, A. F., Herman, C. J., and Gatos, H. C. (1970). J . Muter. Sci. 5, 822. Yamashita, K., Kobayashi, S., Toshihiko, A,, Kawata, Y., and Shiraiwa, T. (1989).ASTM STP 990. ASTM, Philadelphia. Yatsurugi, T., Akiyama, N., Endo, Y., and Nozaki, T. (1973). J. Electrochem. S O C . , 120, 915. Yonenaga. I.. Sumino, K., and Hoshi, K. (1984). J. Appl. Phys. 56, 2346.

S 1 : M I C O N l ~ I ~ ( ' I O K SA N D SEMIMETALS. V O L 42

CHAPTER 3

Characterization Techniques for Oxygen in Silicon T. J . Shnffner T E Y A ~INSTRUMFNTS. I N C O R P O R A I ri) DAL I AS. TEX4S

D.K . Schroder ARl7.0NA STATE UNIVERSITY TEMPE. ARIZONA

I. 11.

INTRODUCTION . . . . . . . . . PHYSICAL. TECHNIQLII \ . . . . . . I . Infrared Spec tro.\c'opr , . . . 2. 7ruristnission Elcc~tronMic,ro.\c,opy 3. X-RU?;Diffrac.tiori cind Topogruphv 4. Sec,ondaM I o n M t r . i \ Spec.trometry ,

111.

IV.

V.

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

. . . . . .

51 5s 55

I . l)qfec,t Etches . . . . : . . . . . . . . . . . . 2 . I n e r t G i s Fusiori . . , . , . . . . . . . . . . .

58 62 66 69 69 12

3 . Actir~ationAna/!.si.\ 7 . e hniytrc.c ~ . . . . . . . . . . .

74

EI.EC.TRICAI. TECHNIOCIES . . . . . .

17

1 . Deep LtPivl Trati.\ic,nt Sprc,/rosc-oppy . . . . . . . . . 2 . Recombination I.(ti,tirnr . . . . . . . . . . . . . . 3 . C k n era t ion Lifvt in7 o . . . . . .

78 79

SUMMARY . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . .

85 86

CHEMICAL TECHN1Ql't.S

.

.

.

.

.

.

. . . . . . . . .

81

I. Introduction The earliest measurements of oxygen in semiconductor silicon date back to the 1950s. The motivation at that time was to understand its role as an n-type dopant in Czochralski silicon and determine optimum thermal treatments for p-n junction formation (Fuller et al.. 1954). Others were interested in the adverse effects of lithium-oxygen complexes on performance of silicon-based alpha particle detectors (Baker, 1970). Pioneers in the application of inert gas fusion and infrared spectroscopy (Kaiser and Keck, 1957; Hrostowski and Kaiser, 1957) began to establish the quantitative framework within which the beneficial properties of oxygen precipitation would later be discovered. The progression to 4- and 16-kilobit random access MOS memory prod53 Copyright C 1994 by Academic Pre\,. Inc. All right\ of reproduction in any form reserved. ISBN &1?-75214?-9

54

T . J . SHAFFNER AND D. K. SCHRODER

TABLE I MATERIALS CHARACTERIZATION TECHNIQUES FOR OXYGEN I N SILICON Concentration Physical Techniques

t Infrared spectroscopy (FTIR)

Uniformity

t X-ray topography (XRT)

Secondary ion mass spectrometry (SIMS) Bragg spacing comparator Chemical Techniques

Inert gas fusion analysis (IGFA)

Microstructure TTransmission electron microscopy (TEM) Small-angle neutron scattering (SANS) X-ray rocking curves (XRC)

t Defect

etch and optical microscopy (OM)

Charged particle activation (CPA) Gamma photon activation (GPA) Electrical Techniques

Deep-level transient spectroscopy (DLTS)

Photoconductive decay (PCD) Surface photovoltage (SPV)

t Core techniques applied during early development.

ucts during the subsequent 20 years provided an important manufacturing yield incentive that focused characterization efforts on refresh loss failures. It was the combined application of infrared spectroscopy, X-ray topography, and transmission electron microscopy that began to uncover the complex physics and chemistry of oxygen precipitation (Rozgonyi, Deysher, and Pearce, 1976; Patrick, Hearn, and Westdorp, 1979; Freeland, 1980; Huff et al., 1983; Vohse, 1985; Rivaud, Anagnostopoulos, and Erikson, 1988; Simpson et al., 1989). These core techniques fulfilled three essential requirements to measure concentration, uniformity, and microstructure. The requirements have since become driving forces behind the selection and development of many other techniques that are available today. While it is possible to provide an overview of only a limited number here, the reader is referred to other general (Shimura, 1989; Richter, 1985) and specialized (Stingeder et al., 1989; Simpson et al., 1989; Schomann and Graff, 1989; Pajot, 1977) reviews of the topic. In the following sections, we survey the techniques outlined in Table I, with emphasis on strengths and weaknesses of each for the oxygen application. The objective is to provide general perspective without tech-

3.

CHARACTERIZATION 1 CCHNIQUES FOR OXYGEN IN SIl ICON

55

nical details, since these are available in the cited literature and other chapters of the present volume. 11. Physical lechniques

Physical techniques are t h o w that rely on incident probes of photons, electrons, or ions and are distinguished here from those that couple with wet chemical separations or electrical measurements. They encompass the traditional core tools previously mentioned and others that are summarized in Table I .

I . INFRARED SPECTROSCOPY Infrared vibrational spectroscopy reveals the presence of dispersed oxygen in Czochralski silicon crystals as well as silica precipitates produced under controlled high-temperature annealing. It has evolved as the most popular technique. owing in part to capability for nondestructive analysis within a 30-minute time frame. sensitivity at room temperature near the ppma level, and the ready availability of moderately priced instruments through more than 40 vendors (Lubkin, 1992). Its dominance in silicon metrology is highlighted in this volume by the comprehensive treatment that follows in Chapter 4. (i.

Origin of' Sigtiu1

Oxygen dissolves in silicon near the melting point (1412°C) at concentrations near I0lx atomsicm' by forming two strong Si-0 bonds with nearest neighbor Si atoms. I n t h i b configuration, it is considered interstitial and denoted by 0,.Symmetric and asymmetric stretching modes of the Si,O molecule underly the popular I107 c m - ' band, as well as others. The examples selected in Table 11 highlight that the atomic physics is

Position Band

Origin

(Lm ' 1

(pm)

Comments

0, 0,

Symmetric stretching Asymmetric stretching A\ymnietr-ic stretching Oxygen precipitate Asymmetric + tunneling Asymmetric + phonon

514 I059 I107 I226

19.45

Temperature dependent Isotope effect on I107 band Most widely used band Attributed to platelets Weak relative to 0, Si-phonon coupling

0,

O,, 0,

0,

1227 1720

9.44

9.03 8.16 8.15 5.81

56

T . .I.SHAFFNER AND D. K. SCHRODER

1300

I

I

1200

1100

1000

Wavenumber (cm-')

FIG. 1. Sequential infrared spectra of Czochralski silicon with increasing anneal exposure. The 1226 cm-' peak grows at the expense of 1107 cm-' (adapted from Sun et al., 1988).

complicated, evoking effects of temperature, isotope, coupling to the Si lattice, Si-Si potential barrier tunneling, and other factors (Chen and Schroder, 1987). Growth of a precipitate band (0,)at 1226 cm-' can be observed following a recipe of thermal anneals, as illustrated in Fig. 1. It has been attributed to the formation of oxide platelets (Kung, 1989; Wada, Inoue, and Kohra, 1980; Hu, 1980); and Sun, Lagowski and Gatos (1988) report a linear calibration with loss of interstitial oxygen, based on consideration of overlapping features. Their work demonstrates that, although overlaps are troublesome in the 950- 1250 cm- range, quantification is possible with experimental care.

'

b. Meusurement Issues

The transmittance (T,) for a normal incidence infrared probe on a double-side polished silicon slab of thickness d is expressed by an equation of the form T -

( 1 - R)2exp ( - ad) 1 - R2exp(-2ad)'

3.

CHARACl ERIZATION I K H N I Q U E S FOR OXYGEN IN SILICON

57

where R is the internal surface reflectivity and (Y an absorption coefficient. Effects of absorption by free carriers and lattice vibrations are considered negligibly small for float zone silicon, which is oxygen free for practical purposes (<200 ppba for Baker, 1970). and provides an ideal empirical baseline reference. The backside of wafers used in manufacturing is rarely smooth. It is in fact deliberately mechanically abraded, implanted, or covered with polysilicon to function as a gettering sink for fast diffusing impurities. Different algorithms that model R for backside roughness give concentration numbers that differ by several parts per million, and it is questionable if much improvement is possible. Shirai ( 1991) recently applied an off-normal polarized infrared configuration to reduce internal multiple reflections. He employed light with p-polarization ( E vector in a surface normal plane) incident at the Brewster angle and observed no interference fringes characteristic of reflections. In fact, measurements demonstrate that backside roughness works to advantage in the technique. which is designated as PPBIR @-polarized Brewster angle incidence infrared spectroscopy). Oxygen quantification is performed by measuring (Y in the 1107 c m - ' band at room temperature. Infrared transmission ( T , ) through a float zone slab of the same thickness combined in ratio with Eq. ( 1 ) yields

This is a form of the Lambert-Beer law, that relates transmitted intensity to concentration of an absorbing species. In this application it ignores reflections. which are frequently approximated by a semi-empirical algorithm (Engelbrecht, 1990: Schoniann and Graff, 1989; Iizuka et al., 1985). The simplicity of ( 2 ) facilitates determination of a(,, which is then converted to ppma or atomsicm' through a constant of calibration. Calibration factors at room temperature have been published by many authors, starting with Kaiser and Keck in 1957. Recent worldwide round robins were organized by ASTM (American Society for Testing and Materials), JElDA (Japan Electronic lndustry Development Association). DIN (Deutsches Institut fur Norniung), and other organizations to reach general acceptance of a universal factor (Murray et al., 1992; Baghdadi et al.. 1989; Inoue, Wada and Osaka, 1987; Iizuka et al., 1985; Yuezhen and Qimin, 1985). These have helped reduce the confusion. but the factor adopted in a given application remains largely a matter of individual preference. A comprehensive discussion of this topic follows in Chapter 4 of this volume. Routine oxygen measurements are desirable over a wide range of re-

58

T. 1. SHAFFNER AND D. K . SCHRODER

sistivity, but infrared spectroscopy is useful only for lightly doped silicon with resistivities greater than 0.1 R-cm for n-type, and 1.0 R-cm for p-type silicon. Beyond these limits, absorption associated with free carriers results in a drastic increase in a0,even to the extreme of preventing the analysis. Intensity loss in the 1107 cm-' band is accompanied by curvature in the baseline used for background correction, and weaker features in the remaining vibrational modes. Oates and Lin (1988) developed refined algorithms for peak measurement to address the problem and report resistivity limits reduced by an order of magnitude (0.015 R-cm for n-type and 0.05 R-cm for p-type). Chen and Corelli (1972) propose the difficulty can be overcome by trapping majority carriers on deep defect centers produced by fast neutron irradiation. Complete carrier removal is possible for doses near 10'' neutrons/cm2 (Pajot, 1977). Barraclough (1990) used 15 MeV electron irradiation to generate defect centers in lOI9 cm-3 boron doped silicon. c . Instrumentation

Fourier transform infrared spectrometers based on the interferometer design for increasing light acceptance aperture became widespread during the past decade. The improvement commands a significant advantage for sensitivity enhancement, but it is interesting that uniformity between users of conventional grating spectrometers may be somewhat better (Schomann and Graff, 1989). Initial success with the infrared application motivated acceptance of the Fourier transform approach for other techniques, including photoluminescence, Raman spectroscopy, nuclear magnetic resonance, and atomic absorption. Small-spot infrared instruments are commercially available as the result of evolutionary improvements in lens design, stage control, and computer processing. These press the spatial resolution diffraction limit near I k m , and are finding applications to microsegregation issues, involving Czochralski growth striations, influence of carbon, and precipitate distribution (Yao and Witt, 1987; Fusegawa and Yamagishi, 1992). Using a band at 1230 cm-' thought related to oxygen platelets, Borghesi, Geddo, and Pivac (1991a) concluded that precipitates form into clusters of up to 100 krn across during annealing, even within surface epitaxial films (Borghesi et al., 1991b). 2. TRANSMISSION ELECTRON MICROSCOPY It is difficult to unravel the origin and function of atomistic defects without a means of directly imaging their physical structure and environment. Transmission electron microscopy fulfilled this need for oxygen in

3.

C H A K A ( T E R I Z A 7 I O N I f C H N I O U E S FOR OXYGEN IN SILICON

59

FIG,. 2. Transmission electron rnrcrogriiph of metal cluster entrapment at a stacking fault complex in silicon. X-ray analysis confirmed the nodules are copper.

silicon almost two decades ago and became established as an indispensable tool for describing the complicated role of precipitation. It was images like Fig. 2 that provided the first direct evidence of metal cluster entrapment at dislocation sites and fostered the concept of impurity entrapment.

In transmission electron microscopy (TEM), a coherent beam of electrons passes through the sample. which is typically a thin, 3 mm diameter disk carefully prepared from bulk silicon. The magnified electron image projected from the back side onto a fluorescent screen attains high spatial resolution, to the extreme of I .4 A in the modern phase contrast configuration. These instruments have evolved from improvements in design and fabrication of the electron objective lens, which previously was limited by spherical aberrations. Commercial TEMs operate at voltages between 100 and 300 k V , although 400 and even 1000 k V instruments are available. The high-voltage instruments offer increased penetration of accelerated electrons, and this

60

T. J. SHAFFNER AND D. K. SCHRODER

relaxes demand on the tedious and delicate procedures required for sample thinning. At 1,000 kV, an 8 pm suspended film of silicon can be imaged, while at 100 kV, the useful thickness is limited to less than 0.5 pm. For phase contrast, or lattice imaging, this diminishes to a meager 15 nm (Buseck, Cowley, and Eyring, 1988; Vanhellemont et al., 1985; Vohse, 1985). Recipes for preparing silicon sections are in the literature (Rivaud et al., 1988; Thompson-Russell and Edington, 1977; Sheng and Chang, 1976), but most microscopists prefer to develop their own, based on comprehensive personal experience. A typical methodology for silicon makes use of mechanical polish and lapping, chemical thinning in HF/HNO, solutions, and controlled etching with a gentle beam of argon ions. Analytical microscopes are equipped with accessories for X-ray microanalysis, electron energy loss spectroscopy (EELS), electron diffraction, and a variety of specimen holders for heating, cooling, and straining experiments. By far, high-resolution images are the most frequently used of these for oxygen studies. lmproved transparency of the protective window on energy dispersive detectors has extended sensitivity to the soft X-ray of oxygen (0.531 keV), but the fluorescence yield remains inherently low. This limits practical measurement to concentrations in the atomic-percent regime. The sensitivity of energy loss spectroscopy is similar. These accessories can be used to confirm the presence of oxygen in precipitates, but remains insensitive to dispersions at the ppma level. h. Precipitate Morphology

Transmission electron micrographs were the first to reveal existence of thin amorphous oxygen platelets that grow within a {loo} habit plane. These typically evolve along two perpendicular (1 10) directions following thermal anneals above 600°C. A host of investigations has uncovered other shapes, the most prominent being rodlike 80 A diameter needles along the (110) direction and the amorphous octahedral prism (Kung, 1989; Simpson et al., 1989; Steeds et al., 1989; Hahn et al., 1988; Tsai, Stephens, and Meyer, 1987; Tiller, Hahn, and Ponce, 1986; Vohse, 1985; Shimura, 1981; Wu and Washburn, 1977). Examples of these are shown in Fig. 3 . Details correlating precipitate morphology with anneal history, doping level, carbon content, and stress in the lattice are left to other chapters of this book, and Vanhellemont, Bender, and Claeys (1987) also provide a thorough summary. Vacancies and interstitial Si atoms cannot be directly observed by electron microscopy but are fundamental to formation of

3.

C H A R A C l ERIZATION 1FC'HNIQUES FOR OXYGEN IN SILICON

61

b'r6. 3 . Tr~lnsmissionelectron micrographs of(a) rod, ( b ) platelet, and ( c ) prism morphologieb. The respective dimensions ai-e YO0 nm (length). 500 nm (diagonal). and 140 nm 1 diagonal ).

dislocation networks, prismatic loops, and stacking faults. Polyhedral precipitates can grow at the expense of platelets within the 650-850°C temperature range. Rivaud et al. (1988) detected a depletion zone where precipitates within a 1.6 k m diameter sphere dissolved and reformed into an octahedral prism. From the micrograph, they were able to estimate an oxygen diffusion coefficient (1.3 x lo-'? cm2/sec). (,.

Iristrrrmetitntion

With the modern high-resolution electron microscope (HREM). it is possible to form a diffraction image of individual silicon lattice planes that provides an ideal internal calibration for dimensional measurement. The capability also permits assessment of crystallinity in small atom clusters, but this is of limited value for oxygen precipitates that are predominantly amorphous. Nevertheless. continuous improvement in resolution will facilitate routine imaging in general, and possibly permit direct identification of point defects in the distant future. The high-brightness advantage of the field emission electron source for microprobe X-ray and energy loss analysis was realized during initial trials on the TEM during the mid-1970s. Today, high-vacuum gun chambers ( 10- ") Torr) effectively eliminate contamination at the emission tip, which was responsible for an instability problem in earlier instruments. Microscope products including TEM, SEM, and the Auger microprobe are just now becoming available with the accessory once again. it is not

62

T. J . SHAFFNER AND D. K . SCHRODER

TABLE 111

DIFFRACTION TECHNIQUES APPLIED TO OXYGEN IN SILICON Technique

Information Provided

X-ray rocking curves' Berg-Barrett topography2 Section topography' Scanning Lang Topography4 Double crystal topography5 Triple crystal topography6 Anomalous transmission' Bragg spacing cornparato9 Diffuse X-ray scattering9 y-ray diffraction'O Small-angle neutron scattering"

Gauge of crystal perfection Wafer surface defect image Wafer cross section defect image Wafer volume defect image; wafer warpage High-strain resolution surface image High-resolution rocking curves and images Gauge of crystal perfection Oxygen effect on lattice parameter Precipitate size and number density Precipitate size and number density Precipitate size, orientation, density

'Imai et al., 1987, 1988; Patrick et al., 1979 'Tanner, 1988 'Partanen et al., 1992; Holland et al., 1991; Simpson et al., 1989; Kishino et al., 1978 'Shimizu et al., 1985; Huff et al., 1983 'Entin and Smirnova, 1989; Imai et al., 1988 'Kawado et al., 1991; Zaumseil et al., 1987 'Freeland, 1980; Patel, 1973 'Shaffner et al., 1986 ylida et al., 1988; Hahn et al., 1988 "'Magerl et al., 1990; Schneider et al., 1989; Kinder et al., 1988 "Messoloras et al., 1989; Bergholz et al., 1989

unusual to achieve a probe diameter of 5 A or less with a lo4 brightness increase over the hot filament source. The ultimate limitation will relate to specimen damage caused by excessive current density in the probe (10' A/cm2).

3. X-RAYDIFFRACTION A N D TOFQCRAPHY X-ray techniques offer a rich variety of capabilities that provide information ranging from oxygen precipitate morphology and density to wafer warpage and silicon crystal perfection. Many of these were resurrected from the metallurgical field and applied for the first time to the study of oxygen in silicon about a decade ago. Of those listed in Table 111, X-ray rocking curves and the topographies are the most popular. u.

Origin of Contrast

As single crystals of high perfection, silicon wafers are well suited for X-ray diffraction measurements. Interstitial and precipitated oxygen can

3.

CHARACTERIZATION 1 t ( HNIQUES FOR OXYGEN I N S I I ICON

63

be treated in diffraction physics as perturbations to an otherwise nearly perfect material. Diffracted intensities are attributed to a combination of kinematical and dynamical effects. The kinematical theory accounts for Bragg reflections from small and nearly aligned mosaic blocks that approximate the perfect silicon lattice, or the ideally imperfect crystal. Waves scattered by each block are treated independent from one another and from the lattice. The angular separation of the blocks, or rnostric spread, can be estimated from X-ray rocking curves that track diffracted intensity as the crystal is slowly rotated through a select Bragg reflection. The full-width-half-maximum typically increases by a factor of two or more in Czochralski silicon relative to float zone silicon (Entin and Smirnova, 1989). The dynamical theory includes wave interactions that take place within a perfect crystal. within which multiple diffraction occurs. This leads to coherent interference between perfectly parallel wavefronts, and the prirnury r.wtirrction effect that directly reduces measured intensity. Interactions can also result in a standing wave pattern, which produces nodes in intensity coincident with atoms in the crystal. In this case, there is a large decrease in photoelectric absorption and a corresponding increase in transmitted X-ray intensity (the rirzornalous trunsrnission effect). Lack of coherence with atomic sites results in surface reflection interference fringes (Pendrlliisung fringes). Anomalous transmission is a fragile phenomenon that is easily destroyed by imperfections in the lattice and, as such, is sensitive to oxygen during early stages of precipitate formation. Patel (1973) used this fact to determine that float-zone silicon contains interstitial oxygen below the detection limits of infrared spectroscopy. Freeland (1980) and Partanen, Tuomi, and Katayama (1992) later concluded the method is not as applicable to small oxygen precipitates. The interplay among all of these effects in silicon crystals is complex and is largely why it is difficult to achieve absolute quantification. There are also other contrast mechanisms involving angular divergence, geometric focusing. diffuse scattering (Patel, 1975), and the Debye-Waller factor (lida et al.. 1988). Generally. all respond to stress and thereby to lattice distortions forced by oxygen precipitation, punched-out dislocations, and other crystal defects. h. The Topogrciphies

X-ray topography is essentially a radiography technique that uses only the intensity from a select Bragg reflection. The single diffracted beam is separated from others by a configuration of slits, collimators, or mechani-

64

T. J . SHAFFNER AND D. K . SCHRODER

cal moving parts. In Berg-Barrett topography, for example, the film cassette is placed parallel to the wafer surface, which is fully flooded at grazing incidence by a vertical slit of Mo,, X-rays. Other configurations are suited for transmission images. Section topography is popular because of simplicity in experimental setup and image interpretation. One simply allows the slit of X-rays penetrating through the wafer to fall on a shielded beam stop and observes forward-diffracted intensity at an off-angle commensurate with the Bragg reflection of choice. Diffracted intensity from each volume element in the cross section maps point-by-point onto the film. The method is particularly useful for imaging the oxygen denuded zone (Simpson et al., 1989; Tanner, 1988) and assessing the size and density of precipitates as a function of heat treatment and oxidation (Partanen et al., 1992; Freeland, 1980; Kishino et al., 1978). Lang topography adds mechanical scanning motion that sweeps the film and wafer together across two slits that collimate the incident and diffracted X-ray beams. It detects lattice strains that accompany oxygen precipitates and early on (Huff et al., 1983; Shimura, 1989) provided images that assisted Czochralski silicon growth engineers in improving radial and between-wafer uniformity as illustrated in Fig. 4. It also senses processing defects and is ideally suited for quantifying bow in the wafer. In one such study, Shimizu, Watanabe, and Kakui (1985) describe a relationship between warpage and the logarithm of oxygen defect density, observing a pronounced increase (>20 Fm) above 109/cm3. While the Lang camera remains useful in such applications, the superior strain sensitivity of double and triple crystal configurations is attracting more recent attention. The advantage demonstrated in Fig. 4 originates from the low divergence of X-rays presented to the sample by a high-quality reference crystal. To emphasize this point, we consider the expression from Bonse (1962) relating diffracted intensity contrast (AZ/fi at a Bragg angle 8 to oxygen-induced lattice distortions:

AIll

Ad

-tan0 d

+ Aci + A p .

(3)

The specimen descriptives are A d l d (relative change in lattice spacing) and the component of local lattice rotation, A a . It is evident that any offset ( A p ) caused by divergence in the incident probe must be small relative to these for a successful measurement to take place. for Both A d l d and A a assume a range of values between k 0.5 X oxygen in as-grown wafers (Imai et al., 1988; Shaffner, Matyi, and Lui, 1986). This is beyond values associated with Lang topography ( w4), but within reach of the double crystal methods (lo-% Imai et al. (1987 and

3.

CHARACTERIZATION I E C H N I Q U E S FOR OXYGEN IN SILICON

65

FIG.4. (a) Scanning Lang X-ray topograph of bulk oxygen precipitation where superirefresh performance of patterned DRAM circuits occurs (Huff et al., 1983). (b) Double crystal topogrdph of strain related defects in a 7 km epi-film on { 100) silicon.

1988) were able to decouple Adld and ACX in a study relating oxygen concentration to Czochralski growth striations. c. Twnds

There are nearly ten vendor? of commercial double crystal cameras. compared with only one in the early 1980s. It was during this period that X-ray topography and rocking curve techniques reached maturity

66

T . J . SHAFFNER A N D D. K . SCHRODER

for semiconductor applications. Today, efforts with oxygen in silicon focus on rocking curve deconvolution (Tanner, 1988; Zaumseil et al., 1987; Liu et al., 1987), synchrotron applications (Schneider et al., 1989), and contrast modeling (Holland et al., 1991). These advances continue to evolve with improvements in high-collimation X-ray sources and broad beam capability for topography applications. Kawado et al. (1991) report achieving 0.01 arcsec (5 x rad) divergence with a triple crystal synchrotron based camera. Short wavelength X-ray sources underpin the emerging science of y-ray diffraction, offering advantages of reduced absorption and small angle scattering kinetics. For X = 0.04 A, Bragg angles are near 2", and rocking curves become sensitive to localized tilt in the atomic planes (ha),more so than to changes in lattice parameter ( A d d ) . Wavelengths on this order can be provided by radioactive sources like '9ZIr (0.039 and ' 9 8 A ~ (0.030 A), or a synchrotron X-ray ring. The angular divergence in y-ray cameras is relatively large (Ap = 3"). so they are better suited for the quantitative analysis of scattering centers than high-resolution strain imaging. Applications to precipitates in silicon provide a statistical measure of their size, number density, and morphology. An analogy with grazing incidence X-ray and small-angle neutron scattering (SANS) exists, and it.is not uncommon to find these complementary methods applied in the same laboratory (Magerl, Schneider, and Zulehner, 1990; Messoloras et al., 1989; Kinder, Messoloras, and Stewart, 1988).

A)

4. SECONDARY ION MASSSPECTROMETRY Secondary ion mass spectrometry (SIMS) is capable of detecting all elements in the periodic table, including oxygen. It does so by collecting ionized fragments that are etched from the outer 100-200 A of the surface by a rastering probe of Csf ions. In the resulting m/e (mass-to-charge) spectrum, one identifies peaks that originate from molecules and single atoms of various charge states. SIMS detects both interstitial and precipitated oxygen, unlike infrared methods, which are limited predominantly to the interstitial species. Additional infrared problems with weak signals from heavily doped material and an inability to provide depth profiles provided incentive for specialists to develop their technique for the oxygen application. The extent of this success is illustrated in Fig. 5 , where the surface denuded zone in Czochralski silicon was measured and compared with oxygen diffusion calculations by Shimura, Higuchi, and Hockett (1988). Other examples

3.

CHARACTERIZAI ION

I r c H N I Q U E S FOR OXYGEN

I N SILICON

-Calculated _ _ _ SlMS _-.

67

I

4 2 4

6

8

10

Deplh (him)

FIG.5 . SlMS profiles of oxygen i n C'rochralski silicon after heat treatment at 750°C' for 64 hour\ compared to the calculalrd diffu\ion profile (reprinted with permission after Shiinura et a l . . 1988).

of quantification (Goldstein. Chu, and Bleiler, 1993: Borghesi et al.. 1990; Oates and Lin. 1988). diffusion measurements (Pagani. 1990: Shimurd et al.. 1988; Rath et al., 19841, and dopant influence on oxygen (Bleiler et al.. 1090: Walitzki et al., 1086) are in the literature. The challenge in SIMS is background signal, which is present as residual gas in the analysis chamber in the form of HzO, CO, 02,NO, and hydrocarbon molecules. Detection limits for oxygen are controlled by the balance established between [he constant absorption rate from the gas and the rate of sample erosion during sputtering. A number of moderately successful approaches are available to minimize the background, but a standard methodology has yet to be defined and interlaboratory comparisons carried out. n. Deuling with the Bac~kgrorrrztl

The base pressure of vacuum stations used in mass spectrometry is typically below lo-' Torr, but all increase to this level or higher during dynamic operation, when the C's' probe is turned on. This is also the regime of most vacuum contaminants containing oxygen, whose partial pressures range from 0.3 x 10 ' Torr for CO, to 0.7 x lo-' Torr for water vapor. Such species are incorporated as a component ( I J of the measured oxygen intensity ( I ) when they adsorb onto the surface of the specimen.

68

T. J . SHAFFNER AND D. K. SCHRODER

The effect is minimized by a liquid nitrogen cryoshield and mild baking of the specimen in situ. Meuris, Vandervorst and Borghs (1989) propose the expression

z = I, + I,

+Id

+ Ioxy,

(4)

which also includes memory effects (ZJ, redeposition from the exposed crater wall (fd), and the desired bulk oxygen concentrations (Ioxy). Specialists have found that Zoxy increases with high incident ion density, while the background components in (4) generally do not. These remain constant because the efficiency of oxygen attachment to the surface is controlled predominantly by the sticking coefficient. Ishitani et al. (1988) demonstrated the effect on a float zone silicon reference by observing invariance of I 6 0 - signal with a change in raster size. This raster effect is becoming common practice for improving oxygen measurements. Gara et al. (1990) and others noticed that the intensities of I6O- from Czochralski and float zone silicon are equal at low energy (0-85 eV), but differ by a factor of two or more within the 85-165 eV energy distribution tail. The phenomenon is not well understood, although it is believed the low-energy regime encompasses surface activation barriers, gas ionization, binding energy effects, and in some cases the formation of oxygen precipitates. The operator simply biases the sample (voltage offset technique) to suppress these for improved detectability . b. Perspective

Initially, SIMS techniques were not taken seriously for oxygen quantification because of the residual gas limitation. However some now claim the problem is resolved and quote reproducibility figures over a six month period below +.4% (Stingeder et al., 1989). It is perhaps more telling that others still rely on reference silicon that is carefully calibrated by infrared spectroscopy. Makovsky and Goldstein (1988) report better than 2% relative standard deviation based on 4 standard wafers in a 12 sample load. This includes differences that exist between instruments, operators, and calibration technique. Oxygen quantification by mass spectrometry is following a development path analogous to infrared spectroscopy during the 1980s. Already established as mature characterization tools, both encountered unfamiliar limitations in the oxygen application, Details of the infrared analysis have since been worked out, and interlaboratory comparisons initiated to establish a common denominator of measurement. It is likely that SIMS methodology will follow suit, providing the driving force from heavily doped silicon remains intact.

3.

CHARACTEKIZAl ION 1 t.CHNIQUE.7 FOR OXYGEN I N SILICON

69

Profiles entirely free from interference can be measured in a straightforward manner in special experiments with the lSO isotope. Test samples prepared by ion implantation provide an independent avenue for measuring the detection limit, which Wilson. Novak, and Norberg (1988) report as 8 x 10'' atoms/cm3.This indicates the best performance achieved by conventional SlMS today (in the low ppma) remains orders of magnitude behind that possible in a contamination free environment. 111. Chemical Techniques

Techniques based on acid etches, gas extraction, and phase separations are available for the characteriration of oxygen in silicon. As outlined in Table 1, these are suited more f c concentration ~ and uniformity measurement than for determination o f microstructure. In many cases, a physical sensor (optical microscope, infrared spectrometer, or particle detector) functions as the detection element.

I . D ~ F E CETCHES T Wet chemical etches extend the utility of optical microscopy by providing selective surface relief of stacking faults, dislocations. and point defects in the form of an etch pit or mound. These may originate from anomalies at the atomic scale and grow during etching into surface features detectable by the naked eye. In this sense, a pit or mound provides magnification as well as a faceted structure that is easily seen at low magnification (100-500 x ) in a phase contrast microscope. High information content and simplicity of use promoted early acceptance of defect etching as a core technique for the oxygen application. With a little skill. a micrograph like that in Fig. 6 can be prepared at low cost and in less than 15 minutes. The image reveals number density of bulk precipitates. depth of the denuded zone, and impurity aggregates at the epitaxial and polysilicon film inteiftaces. The etch composition is expressed by a weight percent ratio of the components or by simple volumetric proportions. This can be confusing if concentrations or molarity of the solutions are not specified. To avoid misunderstanding, it is advisible to research the original references of an etch before attempting to implement the process. u.

B u ~ i cChtJtnistty

Silicon can be chemically etched in aqueous solutions containing an oxidizing agent like nitric acid and an anion such as F- that is capable of forming water soluble complexes. Isotropic etches that were used orig-

70

T. J . SHAFFNER AND D. K . SCHRODER

FIG.6. Phase contrast optical micrograph of a wafer in cross section prepared with a 5-minute Wright-Jenkins etch. The total thickness is 385 km.

inally to clean and chemically polish wafers are based mostly on an HF-HNO, mixture (Schwartz and Robbin, 1959). Silicon is first oxidized by nitric acid, and then the oxide is dissolved by HF. The reaction often referenced is by Turner (1960):

18HF + 4HN0,

+ 3Si + 3H,SiF, + 4 N 0 + 8 H,O.

(5)

Frequently, acetic acid (CH,COOH) is added to reduce surface tension, which in most cases provides a smoother etch. The planar formula is one example (8%: 75%: 17%, H F : HNO, : CH,OOH) that works equally well (-5 Fmlmin) in all crystallographic directions, as the name indicates. The rate changes significantly with proportions of the mixture (0.2 km/min for 1 :9 :3). A Dash etch uses the same chemicals but is orientation dependent and suited for point defect delineation. It etches p - or n-type silicon in the (1 11) direction about twice as fast (46 &min) as in the (100). The rate jumps to 2.5 km/min for doping levels above 5 x lOI8/cm3. Generally, chromium radicals enhance anisotropy and sensitivity to doping. A Sirtl etch (1 : 1, H F : 5M-CrO,) reveals defects on (111)oriented surfaces, and a Secco etch (2 : I , HF :0. 15M-K,Cr,07) works best for { 100). Ultrasonic agitation eliminates gas bubble formation and reduces etch time from hours to 20-40 minutes. A Schimmel etch ( 2 : 1 : I .5, H F : 1M-CrO, :H,O) works well on heavily doped (100) silicon. The addition of Cu(NO,), sharpens defect delineation, and is thought to affect localized oxidation at the site. Wright Jenkins (1977) considers

3.

CHAKACTEKIZATION TFCHNIQUES FOR OXYGEN IN SII ICON

71

Cr,Oy as the principal oxidizing agent, while relative proportions of HNO, and CrO, control reproducible etch facets. Acetic acid promotes a smooth background surface finish. Chromic acid-based solutions have been used for silicon defect delineation for nearly 30 years, but recent studies indicating their carcinogenic nature have prompted strict legislation governing waste treatment and disposal. MEMC Electronic Materials ( M E M C etch) revisited the acetic acid formulas for a solution t o this problem and propose a (36 :35 : 18 : 21, HF: HNO,: CH,OOH : H 2 0 )mixture that mimics the properties of Wright and Sirtl etches (Chandler, 1990). Etching is sometimes carried out in an electrochemical cell configuration, but the approach is less convenient and not as frequently applied. When an ohmic wire contact is made to the silicon wafer, it becomes the anode in a suitable electrolyte. such as H F in water. This produces a smooth and specular surface. and anisotropic behavior sometimes results from exposure to light (Uhlir, 195s). Waggener and Dalton (1972) demonstrated precise control of the etch rate is possible with KOH. h. Sirminary

Table LV lists properties of a number of common etches. Although selection from these is a matter of judgment, the Wright Jenkins and Secco etches are quoted often in recent literature for oxygen precipitate studies (cf., Simpson et al.. 1989; Walitzki et al., 1986). These are supplemented by cleaving techniques for bulk analysis and dry oxidation anneals to promote stacking fault growth. Scanning electron microscopy provides higher imaging resolution when required (Kung, 1989). Our understanding of etch behavior remains incomplete, but general patterns can be predicted. We know that orientation dependence. for example, relates to atomic lattice packing density and bonds available in the crystallographic planes of silicon. Interstitial oxygen and dopants introduce strain into these configurations. Etch facets are determined by the inclination of dislocations to the surface. Such phenomena are discussed in the references of Table 1V and in recent similar tabular summaries (Runyan and Bean, 1990). Focused investigations of these are not likely to continue in the immediate future. because a skilled operator can already achieve reproducible results without it. Toward this end, standard procedures are defined in the industry (ASTM Standard F26, 198th; ASTM Standard F47, 1988b),and it is common practice to confirm precipilate number counts with electron microscopy.

72

T. J . SHAFFNER AND D. K. SCHRODER

TABLE IV CHEMICAL DEFECTETCHES FOR SILICON AT 25°C Chemistry H F HNO, CH,OOH

Name Planar' Planar B1

Composition H F : HNO,: CH,OOH 8%:75%: 17% H F ;HNO, :CH,OOH

Etch Rate 5 pmimin

0.2 pm/min

1 :40: I 5

sopori2 Dash).l MEMC4 H F CrO,

SirtP Schimmelb Modified Schimme16 Yang7

HF: HNO,:CH,COOH 36: 2 : 20 H F : HNO,:CH,OOH 1:3: 10 H F : HNO, : CH,OOH 36: 25 : I8

20 pmimin

HF: CrO, 1 : I(5M) H F ;CrO, 2: I(1M) HF: CrO,: H,O 2: I(1M): 1.5 HF: CrO, 1 : I(l.5M)

4pmlmin

1300 Aimin {loo) 46 Aimin { 1 1 I} I pmimin

2 p/rnin

I pimin 1.5 pmimin

Comments Uniform in all directions Slightly faster for { 100) Uniform in all directions Etches p ' , n + at 2.5 pm/min Alternate to CrO, hazard Delineates ( 1 1 I) Needs agitation Delineates { 100) 0.6-15 Ckm n , p Delineates (1001 in heavy doped Delineates { I 1 I} (100) and (110)

HF Cr207

Secco8

HF: K,Cr,07 2: l(O.15M)

1.5 pmimin

Delineates {IOO} Needs agitation

HF HNO, CH,OOH CrO, Cu(NO,)?

Wright Jenkins9

H F : HNO,: CrO, : H 2 0 :CH,OOH : Cu(NOJZ ' 3H20 2:1:1(5M):2:2:2 gm

I pmimin

Delineates (100) and{Ill)for .02-20 Rcm Needs agitation

KOH

KOH'

KOH : H 2 0 1:2

8.000 Aimin { 110) 13 Aimin { 1 1 I}

High anisotropy Used at 80°C

'Bean, 1978 'Sopon, 1984 3Dash, 1956 4Chandler, 1990 5Sirtl and Adler, 1961 6Schimmel, 1979 'Yang, 1984 'Secco d'Aragona, 1972 'Wright Jenkins, 1977

2. INERTGASFUSION Inert gas fusion analysis (IGFA) is an established technique in the metallurgical field for measuring oxygen, nitrogen, and hydrogen content in solid samples. Early application of the method to semiconductor silicon dates back to Kaiser and Keck (1957), who used it to calibrate the first infrared spectra of interstitial oxygen. Today, it is the accepted way to prepare reference standards at 10" atoms/cm3 levels and higher.

3.

CHARACTERIZATION TECHNIQUES FOR OXYGEN IN SILICON

73

Fusion analysis of silicon is performed at molten temperatures with a metal flux (typically Fe, Ni, or Sn) in a graphite crucible. C O molecules form, as oxygen escapes and combines with carbon from the graphite. The gas is collected within a vacuum environment (Vacuum Fusion Analysis, see Graff et al., 1973) or transported by an inert carrier gas like helium U t w r Gus Fusion Aiiulysis, see Fricioni and Essig, 1986) to an infrared detector or chromatograph column. Gas fusion is less complicated and often preferred in a high throughput situation. u . The Silicon Applicution

A cylindrical crucible with capacity for a multi-gram charge of silicon reaches temperatures in excess of 2,200"C under resistive or inductive heating. It acts as a carbon resistor in the impulse fusion configuration and can draw up to 1,300 A initially. Induction fusion treats the crucible as an inductor centered in the load portion of a high frequency coil (0.4 MHz, 4 kW). Both resistive (Walitzki et al.. 1986) and inductive (Shaw, Bredeweg. and Rossetto, 1991) furnaces are used in the oxygen application. Helium is the common carrier gas. It is used initially to flush atmospheric oxygen from the fusion environment as well as impurities that escape from the crucible during degassing. Oxygen can be detected in the stream as CO or as carbon dioxide (CO?),depending on system design. In the latter, C O is converted by exposure to highly oxidized copper that is heated to 350-400°C. I z 0 5 has also been used (Rath et al., 1984). Excess oxygen molecules in the catalyst attach to form CO?. By the same mechanism, any hydrogen in the stream reacts to produce moisture, which must be removed with a drying agent. Absorption of CO and COz takes place in selective regions of the infrared spectrum, which are normally monitored by a temperature sensing element equipped with the appropriate bandpass filter. The arrangement is crude relative to modern Fourier transform infrared spectrometers. but is cost effective. Phase sensitive electronics based on pulsed beam schemes are occasionally used to press for ultimate sensitivity, which Stingeder et al. (1989) quote as I x 1Olh atoms/cm3for oxygen. h. Sitrfuce Oxides

Inert gas fusion breaks the physical and chemical bonds between oxygen atoms and the silicon host. Modern instruments permit this to be carried out with a recipe of programmed thermal stages, not unlike the lower temperature analogs of thermogravimetric analysis (TGA) and thermal desorption spectroscopy (TDS). In effect, this is a crude spectros-

74

T. J . SHAFFNER AND D. K . SCHRODER

- 5

C

.-0 4-

- 4

:

5-.Y

- 3 .t C

- 2

0

20

40 60 a0 Analysis Time in Seconds

100

:

1 120

FIG.7. Oxygen evolution in inert gas fusion analysis of silicon oxidized for 30 min at 900°C (reprinted with permission after Shaw et al., 1991).

copy that allows a particular phase of oxide to complete its decomposition before another phase begins. Shaw et al. (1991) found that surface contaminants can be identified by maintaining silicon slightly below the melting point for 60 seconds before increasing power. The procedure reproduced in Fig. 7 discriminates between adsorbate films, surface oxide, and the oxygen signal from bulk silicon. The authors demonstrate that the middle peak varies systematically with surface exposure at 900°C to pure oxygen, while the others do not. They conclude from energy arguments that reactive surface oxides are made up of volatile SiO, in addition to an unidentified but more stable phase that contributes a small error to the bulk measurement. This expanded capability will be difficult to do without, once it is routinely available. It offers a built-in monitor for flagging contamination problems that could introduce errors of 10% or more into the bulk oxygen measurement.

3. ACTIVATION ANALYSIS TECHNIQUES Activation techniques require an accelerator facility and cannot be considered routinely available or low in cost. However, they are well suited as a source of reliable reference materials for most of the techniques covered in this chapter. The unique strengths that make this possible are a complete decoupling of the measurement from the chemical environment and an inherent capability for quantification. Radioactivation requires only pure element standards or compounds of stable stoichiometry. In activation analysis, the sample is exposed to photons or particles of sufficient energy that a reaction takes place within the I6O nucleus. This

3.

CHARACTERIZATION TI-( H N l Q U t S FOR OXYGEN IN SILICON

15

I ABLE, V

A< T I C A T I O N Rr ACTIONS WITH OXY(3FN I h I E C T E D

0 Te c h n ique

Reaction

t Mo\t used for oxygen

in

(MeV)

Half-Life (min)

BY

POSITRON ANNIHILATION

Sensitivity (atornsicrn')

Interference

silicon

is accompanied by emission o f a proton or neutron and the formation of (p') emitter. The diametric 51 1 keV y-rays characteristic of positron-electron annihilation are then counted with a NaI(T1) or Ge(Li) solid state detector. At least eight nuclear reactions with oxygen are known, based on probeh of y-rays. protons, tritium. 'He. and (Y particles (Hoste and Vandecasteele, 1989). From those given in Table V, two are applied consistently for oxygen in silicon. The y source defines gamma photon activation analysis (GPAA), and ionized 'He is the basis for most charged particle activation analysis (CPAA).

a metastable positron

(i .

Gu t y i m (i P hot o t i A c t irw t ic v i

The threshold, or Q resonance. of the "0(y, n)I5O reaction is 15.7 MeV. so photon energy in excess of this must be provided before the experiment is possible. A E R E Harwell generate high-energy bremsstrahlung radiation from a tungsten target for this purpose. using 35 MeV electrons from a Linac accelerator (Barraclough et at., 1986: Barraclough. 1990). The y-rays penetrate uniformly throughout the silicon, which i s typically 3-6 mm on a side ( 2 5 0 mg). The technique is well suited for calibration of infrared absorption. because the analysis volume is similar. The sample is sandwiched between reference slabs of stoichiometric Li,B,O,. For maximum specificity and sensitivity, "0 must be chemically sepa-

76

T. 1. SHAFFNER AND D. K . SCHRODER

rated from the matrix to avoid interferences caused by other elements. The presence of 19Ffor example, also contributes an 150daughter (Table V). The "C(y, n)"C reaction produces "C, which, like 150,is a positron emitter. Separation can be carried out before irradiation by distillation (Nozaki, Yatsurugi, and Endo, 1976) to avoid the duplicate daughter problem or after irradiation (radiochemical separation) to ensure that positrons from "C are eliminated. Postactivation procedures alone suffice when I9F in bulk silicon is below sensitivity of the technique. The I5O produced from fluorine at the surface can be removed with an HF-HN03 etch, which itself is benign and contributes nothing to the activity. Radiochemical separation is based on the graphite fusion technique described previously in Section 111.2. However, the I5O half-life of 122 sec places a time limit on the procedure. It is desirable to complete this phase of measurement as quickly as possible, knowing that degradation in counting statistics is an exponential process. Fusion is usually stopped in about 3 minutes and evolving gaseous activity measured for an additional 10 minutes or more (Nozaki et al., 1971). Barraclough et al. (1986) report a total 6 minute separation that resulted in 0.5 ppm by weight sensitivity to oxygen. In this regard, the longer half-life associated with charged particle activation ( I 10 min) provides an important advantage. b. Charged Particle Activation A 3 MV Van de Graaff accelerator is adequate for charged particle activation, which can be performed for oxygen in about an hour (Bakraji et al., 1991; Nozaki et al., 1976). In this energy range, the reaction has a high cross section and is more selective. A cyclotron is used to produce high-energy particles, which penetrate deeper into the silicon (up to 200 pm for 3He, Iizuka et al., 1985). He is a common projectile that offers flexibility for light elements in addition to oxygen, including C, N, F, and Be (Ricci and Hahn, 1968). Apha particle (4He)reactions for I6O require energy in excess of 20 MeV, so the low Q 3He is often preferred. Samples are typically irradiated for 15-45 min, depending on the ion current (500 nA-2 PA). As with GPAA, they are cleaned by mechanical polish or acid etch following activation. However, it is necessary to remove 1.5 pm or more of silicon when He ions are used, because they can introduce artifacts from channeling and recoil implantation of '*F. The p' counting proceeds as before, following radiochemical separation or in some cases, separation by half-life. The latter assumes all interfering species decay by positrons with a half-life measurably different

3.

CHARACTERIZATION TFCHNIQUES FOR O X Y G E N IN SILICON

77

from that of "F ( 1 10 min). The technique works well with "C (20,s min half-life). which can simply be left to decay before counting is started. Stoichiometric standards (quartz or sapphire) are used for calibration, and detectability of a few ppb is possible (Yatsurugi et al., 1973).

IV. Electrical Techniques Interstitial oxygen in silicon is not electrically active. Oxygen does not introduce deep energy levels into the energy gap nor does it change the sample resistivity. Hence electrical measurements are not able to determine oxygen densities. When oxygen forms thermal donors, the donor density can be measured electrically as a change in resistivity. When oxygen precipitates as SiO,, these precipitates become recombination centers that can be detected by electrical techniques. Electrical characterization techniques can, therefore, be used only when oxygen does not exist as isolated interstitial impurities. Many integrated circuit wafers are processed causing oxygen to diffuse out of the sample near the surfaces and to precipitate in the bulk. This results in denuded zones formed at the top and bottom surfaces of the wafer and heavily precipitated interiors (see Fig. 6 ). A key electrical property of a wafer containing denuded zones (DZ), and precipitated bulk is the difference in recombination and generation center densities in these two regions. This leads to very different recombination and generation lifetimes as both of these lifetimes are inversely proportional to the recombination center density. There are few structural defects and few metallic impurities in the DZ, whereas the precipitated bulk contains high densities of both. No other electrical property varies as much between the two regions as the lifetime. For example, the resistivity is essentially constant since the doping density does not change. There may be a small change in mobility since the substrate contains more scattering centers. However, this change is sufficiently small that it does not lend itself readily to a measurement of the DZ width. There is, of course, a very significant change in structural defect density. This property is exploited for DZ thickness measurement by crosssectional chemical etching, X-ray section topography, or transmission electron microscopy, but the DZ width is most sensitively detected by electrical measurements such as lifetime or diffusion length measurements or by deep-level transient spectroscopy. In this chapter we limit the electrical characterization of denuded zones to techniques that measure the recombination center density, the recombination lifetime, the generation lifetime, or the minority carrier diffusion length.

78

T. J . SHAFFNER AND D. K. SCHRODER

1 . DEEP-LEVEL TRANSIENT SPECTROSCOPY Deep-level transient spectroscopy (DLTS) measurements are made on samples containing a means of creating a reverse-biased space charge region such as Schottky diodes or pn junctions. DLTS is very useful in detecting small concentrations of impurities and defects exceeding the sensitivity of chemical analysis techniques such as SIMS and Auger spectroscopy. DLTS systems with detection limits as low as loiocm-3 have been constructed. DLTS was first introduced in 1974 and has evolved into a routine characterization technique for semiconductor materials and devices (Lang, 1974; Miller, Lang, and Kimerling, 1977). Many variations on the original capacitance transient method and on the data analysis have been developed. These variations were adopted to make the measurement technique appropriate for specific material types and device structures. DLTS application to oxygen in silicon has been sparse. It has been used to monitor oxygen precipitates (Hwang and Schroder, 1986) and new thermal donors (Hoelzlein, Pensl, and Schulz, 1984). It has been speculated that the recombination properties are due to interface states at the SilSiO, interface, where SiO, represents the oxide precipitate (Hwang and Schroder, 1986). It is possible to determine the spatial density distribution of defects into the sample by varying the pulse amplitude during DLTS measurements. An energy level in the band gap of a semiconductor can be characterized by exploiting its emission behavior as a function of temperature. The activation energy of a deep level is the energy between the energy level and its respective band. Deep levels are also called traps. What determines the type of a trap (electron trap or hole trap) is its proximity to either the conduction or valence band. A level above midgap tends to be an electron trap because the transition probability of electron capture from the conduction band is greater than that of hole capture from the valence band. Conversely, a trap below midgap is usually a hole trap. Once captured, the electrons will remain in the traps until enough thermal energy is acquired to enable them to be emitted to the conduction band. The rate (en) at which electrons occupying a deep level at energy E , are emitted to the conduction band is an exponential function of temperature. Therefore, at a particular temperature, filled traps (electron traps in this case) will empty with a characteristic time constant 7, = I / e n .This time constant can be measured experimentally by measuring the time response of a Schottky barrier or a pn junction after a pulse that fills the deep level with carriers. The measurable parameter can be either

3

C HARAC7 ERIZATION I t C HNlOUFS FOR OXYGEN IN S l I ICON

79

capacitance, charge, o r current. In standard DLTS, the capacitance transient is most commonly monitored.

It is often desirable to know the spatial distribution of traps in a semiconductor device. Such information can be obtained by measuring the amplitude of the capacitance transients at various reverse bias voltages and pulse amplitudes. Several methods for obtaining such profiles (Lefevre and Schulz, 1977) are available and usually require corrections to the raw data for effects of nonabrupt depletion region edges, electric field dependent emission rates. and incomplete filling of traps in the modulated region (Stievenard and Vuillaunie, 1986). 2. RECOMBINATION LIFETIME

We classify lifetimes into two broad categories: recombination lifetimes and generation lifetimes. The recombination lifetime, T,, obtains when there are excess carriers in the semiconductor and recombination dominates over generation. The generation lifetime, T ~ is, measured when thermal generation dominates over recombination and other generation mechanisms, such as optical or avalanche generation. Occasionally, the recombination lifetime is further divided into low injection level and high injection level lifetimes. We make no such distinction here, since the main purpose of this chapter is not a detailed discussion of lifetimes, but rather the application of lifetime characterization to DZ width measurements. A more detailed discussion of lifetimes can be found elsewhere (Schroder. 1990a, 1990b). The recombination lifetime consists of three components. each due to a distinct recornbination mechanism. These three mechanisms are multiphonon or Shockley-Read-Hall (SRH) recombination, radiative recombination, and Auger recombination. SRH recombination proceeds through deep-level impurities, and the energy released is dissipated in the form of phonons. During radiative recombination the energy is given off as photons. Mobile carriers receive the energy during Auger recombination. Each of these mechanisms is associated with a lifetime. The resulting net lifetime is given by

SRH lifetime dominates for moderately doped silicon. The radiative lifetime is of little importance in silicon, and Auger lifetime is important only at high injection levels or for highly doped regions.

80

T. J . SHAFFNER AND D. K . SCHRODER

The SRH recombination lifetime is (Shockley and Read, 1952; Hall, 1952; Schroder, 1990b)

which simplifies to

T,(SRH) = T,,

(8)

under low-level injection conditions for the electron minority carrier lifetime in p-type substrates. A similar expression can be derived for the minority hole lifetime in n-type substrates. Recombination lifetime is an effective measure of the DZ width. The lifetime can be measured directly or indirectly as the minority carrier diffusion length L,. The two are related by L, = (D,,T,)"*. Techniques that determine T , or L, sample a depth approximately equal to the minority carrier diffusion length. Since the DZ is generally much narrower than L,, clearly both the DZ and the precipitated bulk are sampled. This complicates the interpretation of the experimental data. The lifetime is most conveniently measured by the photoconductive decay (PCD) method and the diffusion length by the surface photovoltage (SPV) method (Schroder, 1990b). Diffusion length measurements yield an effective diffusion length for samples consisting of regions with differing diffusion lengths. Consider the structure of Fig. 8. It consists of a denuded zone of width WD, with diffusion length L,, , a precipitated region with diffusion length Lnz,and a back surface with surface recombination velocity s2.The effective diffusion length is given by (Schroder, 1984)

+ w I+ L W D l L W , , - I

FIG.8 . Schematic of an MOS capacitor formed on a sample containing a denuded zone and precipitated bulk. W is the space-charge region width.

3.

where a

=

('HARACI ERIZATION TFCHNIQUES FOR OXYGEN IN SILICON

81

[(WDz - W)/LrTll and y is given by =

L,,, [s2L,,/D,i+ tanh(P)I L,,, I 1 + (.~J,,~ID,)tanh(P)l'

(10)

where p = W,,ILn2. For the case of a precipitated sample, with typically L,,z << L,, and WL,r> ZL,,?,y can be written as y L,,/Ln2. Furthermore, for (WDz W ) < 0.2Lr,,we find I-

L,,,,ff-(wD, (1.

w + L , i 2 N l + L,,,/L,,)=(W,,,

-

w + LnJ.

(11)

Lift.tinze Profilirig

There are many recombination lifetime measurement techniques (Schroder. 1990b): most do not lend themselves to lifetime profiling. One method that does lend itself to profiling is the free-carrier absorption method (Waldemeyer, 1988). In this method, a pulsed excitation laser beam generates e-h pairs. The time dependence of these electron-hole pairs is measured by a probe beam. The photon energy of the probe beam is less than the semiconductor band gap and the sample is relatively transparent to the probe beam. Absorption of the probe beam is due to free-carrier absorption with the free carriers provided by the excitation beam. Hence, the probe beam monitors the time-dependent excess carrier density. One particular implementation is shown in Fig. 9(a) (Grivickas et al.. 1992). The diameters of the excitation and the probe beams are 4.5 mm and 20-50 p,m, respectively. The lifetime through the sample thickness is determined by scanning the probe beam in the y-direction. For one sample, containing a denuded zone and precipitated bulk, the lifetime profile of Fig. 9(b) was obtained. The DZ lifetime is higher than in the precipitated bulk, and the DZ width can be determined from such a lifetime profile. The lifetime decrease at the surface is likely caused by surface recombination. The advantage of this method is the ability to determine 7, spatially by probe beam scanning. The main disadvantage for denuded zone width determination is the cross-sectional sample preparation and the rather large probe beam diameter of 20 to 50 p,m. This can presumably be decreased.

3 . GENERATION LIFETIME Recombination processes have generation counterparts. The inverse of SRH recombination is thermal generation of electron-hole pairs or

82

T. I . SHAFFNER AND D. K . SCHRODER

HeNe Probe Beam - 3.39 pm DenudedZones

4 Excitation Beam - YAG

0.8

Detector

,

SRH generation. Optical absorption is the inverse of radiative recombination and avalanche or impact ionization is the counterpart to Auger recombination. For a device kept in the dark with sufficiently low applied voltage for impact ionization to be negligible, only SRH generation need be considered. It is important during generation lifetime measurements to be certain that generation be due to thermal electron-hole pair generation only. All other generation mechnisms should be eliminated during the measurement. This means that the applied voltages should not be excessive and the sample must be kept in absolute darkness, especially for the very long lifetime material appropriate for today’s high purity materials and processing. This may require special precautions for the probe station. For example, it may be necessary to eliminate the clear plastic hoses sometimes used to supply dry nitrogen to the probe station. Such hoses may act as light pipes. Under reverse bias conditions, where generation lifetime measurements are made, the generation lifetime is defined as (Schroder, 1982)

3.

CHARACTERIZATION I I C HNlOUES FOR OXYGEN IN SILICON

83

The generation lifetime is the time required to generate an electron-hole pair. It depends inversely on the recombination center or defect density and on the electron and hole capture cross sections, just as the recombination lifetime does. In addition, it depends on the energy level E,. Because of this dependence, the generation lifetime is generally much higher than the recombination lifetime in a given device. Due to the dependence of T~ on N , , the generation lifetime is as good a monitor of defects as the recombination lifetime, and T~ measurements are much easier to make. The lifetime discussions of the previous section must be modified when the sample consists of regions with very different lifetimes. Consider the sample geometry of Fig. 8. A metal-oxide semiconductor capacitor (MOS-C) is formed on the sample. The pulsed gate voltage creates a space-charge region of width W . W decreases as a function of time due to thermal ehp generation and is detected by measuring the capacitance (Schroder. 1990b). As long as W is contained within the D Z . it is obvious that we are dealing with a 4imple MOS-C with uniform or reasonably uniform 7,. However. when W punches into the precipitated bulk, the lifetime will change. All discussions of generation lifetime determination from pulsed MOS-Cs also obtain for determination of T~ from diode leakage current measurements (Grove, 1967). a . Lifk.timc Pro$ling

The depth variation of the lifetime is very nonuniform for devices containing denuded zones and precipitated interiors. There are other examples with nonuniform lifetimes. Misfit dislocations can be deliberately introduced during epitaxial layer growth by incorporating a small fraction of germanium into the silicon (Kadzimski et al.. 1988). It is difficult to probe lifetime variations into the wafer with recombination lifetime measurements, since the sampled depth is approximately equal to the diffiision length. However. pulsed MOS-C measurements lend themselves very well to such measurements because the space-charge region width is under the operator's control, and can be easily varied by varying the gate voltage applied to an MOS capacitor. Kerber used pulsed MOS capacitors to determine the spatial variation of the leakage current into the sample (Kerber, 1992). The MOS-C is pulsed into deep depletion. but only the inifid portion of the C-t decay curve is monitored for increasingly higher gate voltage pulses. The approach has two advantages: ( i ) the measurement time is reduced compared to a C-f decay in which the entire decay curve is measured; ( i i ) since only the initial portion of the <'-f decay curve is measured and the MOS-C never enters total inversion, the applied gate voltage is mainly

84

T. J . SHAFFNER AND D. K . SCHRODER

dropped across the semiconductor, preventing oxide breakdown. This is especially important for thin oxide devices that cannot withstand high voltages. Fowler-Nordheim tunneling begins at electric fields of 6 MV/ cm (6 V for 100 oxide) giving erroneous C-t responses, as tunnel currents remove minority carriers from the inversion layer. The reverse leakage current I,,, is determined as a function of scr width W and the depth-dependent generation lifetime is given by

A

These considerations show that the generation lifetime lends itself to a determination of the DZ width because it samples the generation properties in a well-defined volume given by the product of the MOS-C area and the scr width. Profiling through the DZ assumes that the scr can be made as wide as the DZ by varying the gate voltage. This is not possible if the DZ is so wide that the scr cannot be extended throughout the DZ due to oxide or semiconductor breakdown. A complication in T~ measurements is the contribution from the quasineutral region below the scr. The quasi-neutral region current is generally assumed to be negligible compared to the scr current in reverse-biased Si devices at room temperature. That approximation becomes questionable in devices containing a denuded zone and a precipitated bulk because the minority carrier diffusion length is very low. The scr leakage current of a reverse-biased junction or MOS-C in deep depletion and the quasi-neutral region current are given by

The ratio of these two currents I,,,/Zg,, is plotted in Fig. 10. The scr current that is usually assumed to be dominant becomes less dominant as T~ increases or L, decreases. This is exactly what happens in the DZ and in the precipitated bulk. As temperature increases, the quasi-neutral region current becomes dominant especially for DZ regions with high T ~ This has important implications for semiconductor devices fabricated on wafers with denuded zones and precipitated bulk because the measured generation lifetime is an effective value that may be significantly influenced by the generation-recombination properties of the precipitated bulk. Paz and Schneider (1985) compared chemical etching, X-ray section topography, TEM, and pulsed MOS-C measurements to determine the DZ width. They found the DZ, when determined by the pulsed MOS-C,

.

3.

CHARACTERIZATION T I - C H N I Q U t S FOR OXYGEN IN SILICON

10-5

I 0-3

10 4

10-2

85

10-1

L, (cm)

FIG. 10. The ratio I,,,/l,,, for silicon at N, = 10” crn-‘.

T

300 K . W = 2 km. D, = 30 crn!/sec. and

to be considerably narrower than when measured by chemical etching or section topography. For example, the DZ width, as defined by a T~ reduction to 50% of its maximum value, was 5 p m in one case. Section topography gave 40-60 p m for the same sample. This indicates that one must interpret visual data such as section topographs or chemical etch micrographs very carefully. Defects too small to be detected by these techniques may nevertheless be sufficiently electrically active to degrade device performance. Only electrical techniques are able to detect such low densities of defects. V. Summary

In this review, we have described over 16 characterization techniques for measuring oxygen in silicon. Table VI illustrates how each has its own strengths and weaknesses for the description of concentration. uniformity, and microstructure. Initially, we selected four core techniques as those most heavily used and essential during the development of the technology. Today, nearly all I6 qualify for this definition. The literature includes new methods applicable to oxygen measurement that can be only briefly mentioned here. Among these, optical tomography (Fillard et al., 1992; Katayama, 1990) and positron annihilation (Sharma et al., 1992; Rohatgi, Schaffer. and DeWald, 1988; Dannefaer and Kerr. 1986) improve on contactless evaluation and our understanding of vacancy clusters, respectively. Kittler and Seifert (1985) discuss electron beam induced current ( EBIC), which permits diffusion length measurement and direct observation of gettering efficiency. Castaldini et al.

86

T. J . SHAFFNER AND D. K . SCHRODER

TABLE VI

SUMMARY OF CHARACTERIZATION TECHNIQUES FOR OXYGEN IN SILICON

Concentrution: Fourier transform infrared Secondary ion mass spectrometry Inert gas fusion analysis Charged particle activation analysis Gamma photon activation analysis Deep-level transient spectroscopy Bragg spacing comparator Uniformify: Defect etches Lang X-ray topography Double crystal topography Triple crystal topography Surface photovoltage Pulsed MOS capacitor Microstructure: Transmission electron microscopy X-ray rocking curves Small-angle neutron scattering

Common Acronym

Sample Damage

Best X-Y Resolution

FTlR SIMS IGFA CPAA GPAA DLTS

No Yes Yes Yes Yes Yes No

5

Lang DCT

Yes No

No

SPV

No Yes Yes

TEM XRC SANS

Yes No Yes

w

5 wm 5 mm 5 mm

6 mm 1 mm I cm 1

w

>I0 >10 >I0 I I

pm pm pm

Sensitivity (atomsicm’)

I x 10’6 5 x 1017 I x 1016 s x 1014 5 x 10” 1 x 10’0 I x 10’6

Ad/d Adld 10.’ Adid

mm mm

15

60 60 120

120 60

45 30 60 240 240

60 60

A

1.4 8 mm I cm

Time (min)

Adld

300 240 120

(1987) compare this with the light excited counterpart (LBIC). Michel, Meilwes, and Spaeth (1989) acquire electron spin resonance spectra (ENDOR) in a study of oxygen thermal donor centers. The new techniques, as well as all of those covered in this chapter, were revitalized from a variety of other established disciplines and improved for the oxygen application. We anticipate this will continue and that further advances in silicon gettering technology will depend on the development and application of characterization tools. REFERENCES ASTM Standard F26. (1988a). “Standard Test Method for Detection of Oxidation Induced Defects in Polished Silicon Wafers.” 1988 Annual Book ofASTM Standards. Am. SOC. Test. Mat., Philadelphia. ASTM Standard F47. (1988b). “Standard Test Method for Crystallographic Perfection of Silicon by Preferential Etch Techniques.” 1988 Annual Book ofASTM Standards. Am. SOC.Test. Mat., Philadelphia. Baghdadi. A., Bullis, W. M., Croarkin, M. C., Li, Y., Scace, R. I., Series, R. W., Stallhofer, P., and Watanabe, M. (1989). “Interlaboratory Determination of the Calibration Factor for the Measurement of the Interstitial Oxygen Content of Silicon by Infrared Absorption.” J . Electrochem. SOC. 136(7).2015.

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CHAKACTtRIZATION l I ( HNIQLIES FOR OXYGEN IN SIL.ICON

87

Baker. J . A. ( 1970). “Determination of Parts pel- Billion of Oxygen in Silicon.” Solid-State Elcc.fronic,.s 13, 1431, Bakraji. E. H . , Blondiaux. G. B., L)ucouret. 6 . .and Debrun, J. L. (1991). “Study o f the Lattice Location of Oxygen in Semiconductors by Combining Channeling and Charged Particle Activation.” Nucl. / n \ / t u ) n . M e ~ hB56-57, . 896. Barraclough. K . G . (1990). “Oxygen i n C‘zochralski Silicon for ULSL.” J . Crysf. GroK,rh 99, 654. Barraclough. K . G . . Series, R. W.. Hislop. J . S . . and Wood, D. A. (1986). “Calibration of Infrared Absorption by Gamma Activation Analysis for Studies of Oxygen in Silicon.” J . E/ecrrnclirm. Soc. 133(1). 1x7. Bean. K. E . (1978). “Anisotropic Etching of Silicon.” IEEE Trans. Electr. D e v . ED-23 lo), 11x5.

Bergholz, W . , Binns, M. J . . Booker. G R . , Hutchison, J . C., Kinder, S. H . . Messoloras, S.. Newman. R. C . . Stewart. K. J . . and Wilkes, J. G . (1989). “ A Study of Oxygen Precipitation in Silicon Using High-Resolution Transmission Electron Microscopy, Small-Angle Neutron Scattering and Infrared Absorption.“ Phil. Magazine B 59(5), 499.

Bleiler. R. J . , Chu. P. K . , Novak. S. W . . and Wilson. R. G. (1990). “Study of Possible Matrix Effects in the Quantitative Determination of Oxygen in Heavily-Doped Czochralski Silicon Crystals.” In 7 l h I n / . Con,/: Secondary /on Mass Specfromelr~ISIMS VII), A. Benninghoven, C . A. Evans. K . 11. McKeegan, H . A. Storms, and H . W . Werner (eds.). p. S07. John Wiley & Sons, New York. Bonse, U . (1962). Wrec.1 Obsertaricm of Impc~rfcctionsin Crystals, p. 431. John Wiley & Sons. New York. Borghesi. A . , Geddo. M . . Guizzetti. G . . and Geranzani. P. (1990). “Interstitial Oxygen Determination in Heavily Doped Silicon.” J . Appl. Phvs. 68(4), 1655. Borghesi. A.. Geddo. M.. and Pivac. B . ( I 9 9 l a ) . “Infrared Study of Oxygen Precipitates in Czochrdlski Grown Silicon J Appl. Phyr. 69(10). 7251. Borghe\i. A.. Geddo. M.. Pivac, B. Stella. A.. and Lupano. P. (1991b). “Direct Evidence of Oxygen Precipitates in Epitaxial Silicon Obtained by Micro-Fourier Transform Infrared Spectroscopy.” A p p l . PI7 Buseck. P . . Cowley, J.. and igh Resolution 7runsmission Electron Mic.ro.\c,opy. p. 500. Oxford University Press. New York. Ca\taldini. A.. Cavallini, A.. Poggi. A . . and Su\i. E. (1987). “On the Electrical Activity of Stacking Faults and Oxygen Microprecipitates.“ Gettering and Dqfrcr Enginrering in Srvnicmdrrcior T r ~ c h n o l o g v .ti. Richter (ed.), p. 248. GADEST ‘87, Acad. Sci.. Germany. Chandler. T. C. ( 1990). “MEMC Etch-A Chromium Trioxide-Free Etchant for Delineating Dislocations and Slip in Silicoii ’ ’ J . Elec./roc.liern. Soc. 137(3). 944. Chen. C . S . . and Corelli, J . C. ( 1972). “Infrared Spectroscopy of Divacancy-Associated Radiation-Induced Absorption Band4 in Silicon.” Phys. Rev. 544). 150SB. Chen. C. S.. and Schroder. 0. K . 119x7). “Vibrational Modes and Infrared Absorption of Interstitial Oxygen in Silicon.” App/ Pl7v.s. A 42, 257. Dannefaer. S.. and Kerr. D . 11986) “Oxygen in Silicon: A Positron Annihilation Investigation.“ J . A p p l . Pltys. 60(4). 1313 Dach. W. C. (19.56). “Copper Precipitation on Dislocations in Silicon.” J . A p p l . Phys. 27(10). 1193. Engelbrecht. J . A . (1990). ”A Technique for Obtaining the Infrared Reflectivity of Back Side-Damaged Silicon Sample\. J . Elec.troc hem. Soc. 137( I). 300. ”

”

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Hwang. J . M., and Schroder, D. K . (1986). "Recombination Properties of OxygenPrecipitated Silicon." J . Al~pl.Phys. 59, 2476. Hwang. J. M.. Schroder. 0 . K., and Goodman. A. M. (1986). "Recombination Lifetime in Electron D e v . L e f t . EDL-7, 172. Oxygen-Precipitated Silicon. I lida. S . . Sugiyama, H., Sugita. Y . . and Kawata. H. (1988). "Measurement and Analysis of the Static Debye-Waller Factor of Cz-Silicon with Small Oxygen Precipitates." J a p . J . Appl. Phys. 27(6), 1081. lizuka, T . . Takasu, S . , Tajima. M . , Arai. T.. Nozaki, T.. Inoue, N.. and Watanabe. M. (1985). "Determination of Conversion Factor for Infrared Measurement of Oxygen in Silicon." J . Electrochem. So(,. 132(7), 1707. Imai. M . , Noda. H.. Shibata, M.. and Yatsurugi. Y . (1987). "X-Ray Topography ofGrowth Striations in Czochralski-Grown Si Wafers.'' Appl. Phvs. Lett. 50(7), 395. Imai. M.. Shiraishi. Y., Shibata. M . . Noda. H . . and Yatsurugi. Y. (1988). "Quantitative Measuring Method of Growth Striations in Czochralski-Grown Silicon Crystal." J . Electrochem. Soc. 135(7). 177Y. Inoue. N.. Wada. K.. and Osaka, J . (1987). "Oxygen in Silicon." In Defects andProprrrie.s Nf'Semic-ofiduc,tors: Defeci Enpiticering. J . Chikawa. K. Sumino, and K . Wada (eds.). p. 197. KTK Sci. Pub.. Tokyo. Ishitani. A.. Okuno. K.. Karen. A . . Karen, S . . and Soeda. F. (1988). "Improvement of Oxygen Detection Limit in Silicon by Use of the Secondary Ion Energy Distribution and Background Subtraction." In Materrtrls und Process Characterization f o r I.'LSI. 19x8 (ICMPC '88). X . F. Zong. Y. Y. Wang. and J . Chen (eds.). p. 124. World Scientific. Singapore. Kaiser. W.. and Keck, P. H. (1957). "Oxygen Content of Silicon Single Crystals.'' J . Appl. Phys. 28(8), 882. Katayama, K. ( IYYO). "Characterilation of Oxygen Precipitates in CZ-Silicon Crystals by Light-Scattering Tomography." Jup. J . Appl. Phvs. 29(2), L198. Kawado. S . . Kojima, S . . Maekawa. I . . and Ishikawa, T. (1991). "Influence of Crystal Imperfection on High-Resolution Diffraction Profiles of Silicon Single Crystals Measured by Highly Collimated X-Ray Beams." Appl. Phys. Lett. 58(20), 2246. Kerber. M. ( 1992). "A Comprehensive Method Combining Deep-Depletion Profiling and Capacitance Transients to Evaluate Energy and Depth Distribution of MOS Bulk Defects." IEEE Trans. Electron l h , . ED-39, 706. Kinder. S . H.. Messoloras. S . . and Stewart. K. J . (1988). "A y-Ray and Small-Angle Neutron Scattering Study of Oxygen Precipitation in Silicon Single Crystals." Phrl M a g . Lett. 58(4), 183. Kishino. S . . Isomae, S . . Tamura. M.. and Maki, M . (1978). "Growth Behavior of Oxidation Stacking Faults and Microdefects in Silicon During High-Temperature Annealing." J . Appl. Phys. 49(6), 3255. Kittler. M.. and Seifert, W. (19851, "Investigation of Gettering-Related Phenomena using EBIC: Diffusion Length Measurements-Vertical Distribution ( I ) Defect StudiesGettering Efficiency (2):' Gct/errng und Defect Engineering in /he Semkondirctor Indtrstry. H. Richter (ed.), p. 269. GADEST '85. Acad. Sci., Germany. Kung. C. Y. (1989). "Effect of Thermal History on Oxygen Precipitates in Czochralski Silicon Annealed at 1050°C." J . A p p l . P l i y s . 65(12), 4654. Lang. D. V . (1974). "Deep-Level Transient Spectroscopy: A New Method to ChardcteriLe Traps in Semiconductors." J . i l p ~ ~Phvs. l 45, 3023. Lefevre. H.. and Schulz, M. (1977). "Double Correlation Technique (DDLTS) for the Analysis of Deep Level Profiles in Semiconductors." Appl. Phvs. 12, 45.

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Liu, H. Y., Chang, P. H., Liu, J., and Mao, B. Y. (1987). “Dopant Redistribution of Boron Implanted Silicon During Rapid Thermal Annealing.” Mat. Res. Soc. 92, 15. Lubkin, G. B. (1992). “Ninth Annual Buyers’ Guide.” Physics Today 45(8), BG-211. Magerl, A., Schneider, J. R., and Zulehner, W. (1990). “A Neutron Backscattering Study of Lattice Deformation in Silicon Due to SiO, Precipitation.” J. Appl. Phys. 67(1), 533. Makovsky. J., and Goldstein, M. (1988). “Progress in the ‘Load Line Calibration’ Methodology for Quantitative determinations of [O] in Silicon by SIMS.” Materials and ProcesS Characterization for V L S I , 1988 (ICMPC ’88), X. F. Zong, Y. Y. Wang, and J . Chen (eds.), p. 21. World Scientific, Singapore. Messoloras, S., Stewart, R. J., Schneider, J. R., and Zulehner, W. (1989). “Anisotropic Small-Angle Neutron Scattering from Oxide Precipitates in Silicon Single Crystals.” Semicond. Sci. Technol. 4, 340. Meuris, M.. Vandervorst, W., and Borghs, G. (1989). “Improved Quantification and Detection Limits for Oxygen Analysis in AI,Ga, _,As/GaAs Multilayers with Secondary Ion Mass Spectroscopy.” J. Vuc. Sci. Technol. 7(3), 1663. Michel, J., Meilwes, N., and Spaeth, J. M. (1989). “ENDOR Investigations on Heat Treatment Centers in Oxygen Rich Si.” Mat. Sci. Forum 38-41, 607. Miller, G. L.. and Lang, D. V., and Kimerling, L. C. (1977). “Capacitance Transient Spectroscopy.” Annual Review ofMaferials Science, R. A. Huggins, R. H. Bube, and R. W. Roberts (eds.), Ch. 7. Annual Reviews, Palo Alto, Calif. Murray, R., Graff, K., Pajot, B., Strijckmans, K., Vandendriessche, S., Griepink. B.. and Marchandise, H. (1992). “lnterlaboratory Determination of Oxygen in Silicon for Certified Reference Materials.” J. Electrochem. SOC. 139(12). 3582. Nozaki, T., Makide, Y., Yatsurugi, Y., Akiyama, N., and Endo, Y. (1971). “A New RadioTracer Technique for the Evaporation Study of Light Elements from Molten Silicon.” Int. J. Appl. Rad. Isotopes 22, 607. Nozaki, T., Yatsurugi, Y., and Endo, Y. (1976). “Charged-Particle Activation Analysis: Studies on Carbon, Nitrogen and Oxygen Mainly in Semiconductor Silicon.” J. Radioanal.yrica1 Chem. 32, 43. Oates, A. S . , and Lin, W. (1988). “Infrared Measurements of Interstitial Oxygen in Heavily Doped Silicon.” J. Cryst. Growth 89, 117. Pagani, M. (1990). “Secondary lon Mass Spectroscopy Determination of Oxygen Diffusion Coefficient in Heavily Sb Doped Si.” J. Appl. Phys. 68(7), 3726. Pajot, B. (1977). “Characterization of Oxygen in Silicon by Infrared Absorption.” A n a h i s 3 7 ) . 32. Partanen, J.. Tuomi, T., and Katayama, K. (1992). “Comparison of Defect Images and Density Between Synchrotron Section Topography and Infrared Light Scattering Microscopy in Heat-Treated Czochralski Silicon Crystals.” J. Electrochem. Soc. 139(2). 599. Patel, J . R. (1973). “X-Ray Anomalous Transmission and Topography of Oxygen Precipitation in Silicon.” J . Appl. Phys. 44(9), 3903. Patel, J . R. (1975). “X-Ray Diffuse Scattering from Silicon Containing Oxygen Clusters.” J. Appl. Cryst. 8, 186. Patrick, W.. Hearn, E., and Westdorp, W. (1979). “Oxygen Precipitation in Silicon.” J. Appl. Phys. 50(1 I), 7156. Paz, O., and Schneider, C. P. (1985). “Determination of the Denuded Zone in CzochralskiGrown Silicon Wafers Through MOS Lifetime Profiling.” IEEE Trans. Electron Dev. ED-32, 2830. Radzimski, Z., Honeycutt, J., and Rozgonyi, G. A. (1988). “Minority-Carrier Lifetime

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C H A R A C T t R I Z A l ION 1 FCHNIQUES FOR OXYGEN I N SILICON

91

Analysib of Silicon Epitaxy and Hulk Crystals with Nonuniformly Distributed Defects." lEEE 7nin.s. Elec,fron Dev ED-35, 8 0 . Rath. H . J . . Stallhofer. P.. Huber. I).. and Schmitt. B. F. (1984). "DeterminationofOxygen in Silicon by Photon Activation Analysis for Calibration of the Infrared Absorption." J . Electrochem. Soc-. 131(8). I Y N . Ricci, E . . and Hahn. R. L. (1968). "Rapid Calculation of Sensitivities. Interferences. and Optimum Bombarding Energies in 'He Activation Analysis." Atiu/vticu/ Chemistry @ ( I ) . 54. Richter. H. ( 1985). "Gettering in the Silicon Device Techology-An Overview." Grttc~ring und I)c~fec.r Enginuering i n / h c Scniiconductor Indusrrv. H. Richter (ed.), p. 1. G A D E S T '85. Acad. Sci.. Germany. Rivaud. L.. Anagnostopoulos. C. N.. and Erikson. G. R . (1988). "A Transmission Electron Microscopy (TEM) Study of Oxygen Precipitation Induced by Internal Gettering in Low and High Oxygen Wafer\." J . E/ecrroc.hern. Soc. 135(2). 437. Rohatgi. A.. Schaffer. J . P.. and DeWald. A. B. (1988). "Defect Characterization in Semiconductors by Positron Annihilation Spectroscopy." Diugnostic Techniques ,for Semic.ondirc.tor Muterid& und Ile~~ic.t,.s XX-20, T. J . Shaffner and D. K. Schroder (eds.). The Electrochemical Society. Pennington. NJ. p. 168. RoLgonyi. G . A , , Deysher. R. P.. and Pearce. C W. (1976). "The Identification, Annihilation. and Suppression of Nucleation Sites Responsible for Silicon Epitaxial Stacking Faults." J . Elec-rrochern. So(.. 123( 12). 1910. Runyan. W. R.. and Bean. K. t . ( 1990). Semiwnducror Integruied Circuir Processing Technology. p. 242. Addison-Wehlev. Reading, Mass. Schimmel. D. C;. (1979). "Defect Etch for (100) Silicon Evaluation." 1.Elecrrochern. Soc. 126(3),479. Schneider, J . R.. Nagasawa. H . . Berman. L . E.. Hastings. J . B.. Siddons. D. P., and Zulehner. W . (1989). "Test of Annealed Czochralski Grown Silicon Crystals as X-Ray Diffraction Elements with 145 KeV Synchrotron Radiation." N u ( . / . lnstrum. Mrrh. A276, 636. Schomann. I;..and Graff. K. (1989). "C'orrection Factors for the Determination of Oxygen in Silicon by IR Spectrometry." J . Elec,troc/iem. Soc. 136(7). 2025. Schroder. D. K . (1982). "The Concept o f Generation and Recombination Lifetime5 in Semiconductors." IEEE Truns. E/cc.tron Drv.ED-29, 1336. Schroder. D. K. ( 1984). "Effective 1,iletimes in High Quality Silicon Devices." Solid-Stute Electroti. 27, 247. Schroder. D. K . (1990a). "Carrier Lifetimes in Silicon." In Handbook of Semiconductor Silic,on Tec,hno/ogv.W . C. O'Mara and R . B. Herring (eds.). p. 550. Noyes Publ.. Park Ridge. NJ. Semic,o~idirc.rorMaf rri ul and Device Charwterizution. Ch. 8. Schroder. D. K . ~,19Wb)b). John Wiley & Sons. New York. Schwartz. B., and Kobbin. H . (1959). "Chemical Etching of Silicon. Part I , The System H F . HNO,. H:O and HC2HI0,." J . Elec.rroc.hem. Soc. 106(6), 505. Secco d'Aragona. F. (1973). "Dislocation Etch f o r (100) Planes in Silicon." J . Elrc-rrochem. .So(,. 119(7). 948. Shaffner. T . J.. Matyi, R. J . . and L i u . H. Y . (1986). "X-Kay Diagnostic Techniques for VHSIC Silicon." p. 60. NAV ELXX Contract Document N00039-83-C-0722. Naval Research Laboratory, Washington, D.C. Sharma. S . C.. Hyer. R. C.. Horhabri. N . , Pas, M. F.. and Kim. S. (1992). "Depth and Radial Protiles of Defects in C'zochralski-grown Silicon." Appl. f h . y s . Letr. 6l( 16). 1939.

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Shaw, R. W., Bredeweg, R., and Rossetto, P. (1991). “Gas Fusion Analysis of Oxygen in Silicon: Separation of Components.” J . Electrochem. Soc. 138(2), 582. Sheng, T., and Chang, C. (1976). “Transmission Electron Microscopy of Cross Sections of Large Scale Integrated Circuits.” ZEEE Trans. Electr. Dev. ED-23(6), 531. Shirnizu, H. , Watanabe, T., and Kakui, Y.(1985). “Warpage of Czochralski-Grown Silicon Wafers as Affected by Oxygen Precipitation.” Jup. J . Appl. Phys. 24, 815. Shimura, F. (1981). “Octahedral Precipitates in High Temperature Annealed CzochralskiGrown Silicon.” J . Cryst. Growth 54, 588. Shimura, F. ( 1989). Semiconductor Silicon Crystal Technology. Chapter 6. Academic Press, New York. Shimura. F.. Higuchi, T., and Hockett, R. S. (1988). “Outdiffusion of Oxygen and Carbon in Czochralski Silicon.” Appl. Phys. Lett. 53(1), 69. Shirai, H. ( 1991). “Determination of Oxygen Concentration in Single-Side Polished Czochralski-Grown Silicon Wafers by p-Polarized Brewster Angle Incidence Infrared Spectroscopy.” J . Electrochem. Soc. 138(6), 1784. Shockley, W.. and Read, W. T . (1952). “Statistics of the Recombinations of Holes and Electrons.” Phys. Rev. 87, 835. Simpson, M. B . , Halfpenny, P. J . , Emmott, M. A,, Brown, J., Steeds, J . W.. Johnson, F., and Brinklow, A. (1989). “Oxygen Precipitation in Silicon during CMOS Processing: An FTlR Microspectroscopic, X-Ray Topographic and TEM Study of Spatial Variation in Defect Formation.” Semicond. Sci. Techno/. 4, 701. Sirtl, E., and Adler, A. (1961). “Chromsaure-Fluasaure als Spezifisches System zur Atzgrubenentwicklung auf Silizium.” Z . FluJsaure. 52, 529. Sopori, B. L. (1984). “A New Defect Etch for Polycrystalline Silicon.” J . Electrochem. Soc. 131(3), 667. Steeds, J . W., Johnson, F., Simpson, M. B . , and Augustus, P. D. (1989). “Characterization of Macroscopic Defects in Silicon after Processing for CMOS and Bipolar Circuits.” Mar. Sci. Eng. 84, 373. Stievenard. D., and Vuillaume, D. (1986). “Profiling of Defects Using Deep Level Transient Spectroscopy.” J . Appl. Phys. 60,973. Stingeder, G.. Gara, S. , Pahlke, S., Schwenk, H., Guerrero, E., and Grasserbauer, M. (1989). “Quantitative Determination of Oxygen in Silicon by Combination of FTIRSpectroscopy, Inert Gas Fusion Analysis and Secondary Ion Mass Spectroscopy.” Fresenius Z . Anal. Chem. 333, 576. Sun, Q., Lagowski, J., and Gatos, H. C. (1988). “Microscopic Analysis of the Behavior of Interstitial and Precipitated Oxygen During Intrinsic Gettering in Si.” In Defects in Elecfronic Materials, M. Stavola, S . J. Pearton, and G . Davies (eds.), 104, p. 205. Mat. Res. SOC.,Pittsburgh, PA. Tanner, B. K. (1988). “X-Ray Topography and Precision Diffractometry of Semiconducting Materials.” In Diugnostic Techniques f o r Semiconductor Materials and Devices 88-20, T. J . Shaffner and D. K . Schroder (eds.), p. 133. The Electrochemical Society, Pennington, NJ. Thompson-Russell, K. C., and Edington, J. W. (1977). Electron Microscope Specimen Prepurution Techniques in Materials Science. Macmillan Publishing, New York. Tiller, W. A., Hahn, S., and Ponce, F. A. (1986). “Thermodynamic and Kinetic Considerations of the Equilibrium Shape for Thermally Induced Microdefects in Czochralski Silicon.” J . Appl. Phys. 59(9), 3255. Tsai, H. L., Stephens, A. E., and Meyer, F. 0. (1987). “Oxygen Precipitation in Heavily Boron-Doped Silicon Crystals.” Appl. Phys. Left. 51(1 I ) , 849.

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93

Turner. D. R. (1960). "On the Mechirnim o f Chemically Etching Germanium and Silicon." J . Elcc,/roc.ht-ni.Soc. 107( 10). 810. Uhlir, A. (1955). "Electrolytic Shaping of Gel-manium and Silicon." Bell Syst. Tech. J.. 35, 333. Vanhellemont. J.. Claeys. C.. Van1,anduyt. J . . and Amelinckx. S . (1985). "A Quantitative HVEM Technique for the Determination of Film Stresses and Critical Glide Forces in Silicon Substrates." In G t ~ r t e r t r trnd r ~ ~ 1 k f e c . fEngineering in the Setnic.onducror Indusf r y , H. Richter (ed.). p. 255. GADEST ' 8 5 . Acad. Sci., Germany. Vanhellemont. J.. Bender. H . . and Claeys. c'. (1987). "HVEM as a Diagnostic Tool for VLSl Processing." In Grrteririr: utrd 1)c:fi~c.tEnginerring in Semiconducror 7ec.hnologv. H. Richter (ed.). p. 130. GADEST '87. Acad. Sci.. Germany. VOhse, H. (1985). ".4s Grown and Process-Induced Defects in Silicon Characterized by TEM." In C;rrrt,ring trnd D ~ f r cI Enqinrr~ringin the St>miconducror Indusrry. H. Richter (ed.1, p . 2 3 . GAUEST '85, Acad. Sci.. Germany. Wada. K . . Inoue. N.. and Kohra. K . ( I Y X O ) . "Diffusion-Limited Growth of Oxide Precipitate\ in Czochralcki Silicon." J . C'rvsr. GroM.th 49, 749. Waggener. H . A.. and Dalton. J . V . (1972). "Control of Silicon Etch Rates in Hot Alkaline Solutions by Externally Applied Potentials." Elecrrochem. .So(.. Ahslr.. no. 273. Waldcmeyer. J . ( 1988). "A Cont,ictle\\ Method for Determination of Carrier Liferime. Surface Recombination Velocity. and Diffusion Constant in Semiconductors." J . A p p l . Phv-. 63, 1977. WalitLki, H . . Rath. H. J.. Reffle. J . Pahlke. S . . and Blatte, M. (1986). "Control o f 0 x y g e n and Precipitation Behaviour of Heavily Doped Silicon Substrate Materials." In Sernic.orrduc.rorSi/ic.on 1986. 86-4. H . R Huff and T . Abe (eds.), p. 86. The Electrochemical Society. Pennington, NJ Wilmn. R. G . , Novak. S. W.. and Norherg. J. C . (1988). "Improved SIMS Backgrounds and Detection Sensitivities for- Implants via the Use of Rarer Isotopes. Including 'H, 1'C3 1". lXOo.3"Si. 34s. and 'dFe," 61h Inr. C'onj: S t w v i d u ~Ion Muss Specrromrtry (SIMS V I ) . A. Benninghoven. A . M. Huher. and H. W. Werner (eds.). p. 339. John Wiley & Sons. New York. Wright Jenkins, M. (1977). "A New Prelerential Etch for Defects in Silicon Crystals." J . E/ec.rroc.hc.rn. So(.. 124(5). 757 Wu. W . K.. and Washburn. J . (19771. "On the Shrinkage of Rod-Shaped Defects in Boronlon-Implanted Silicon." J . A ~ [ J Plrvc. /. 48( 10). 3742. Yang. K. H. (1984). "An Etch for I>elineation of Defects in Silicon." J . Electrochem. So(.. 13115). 1140.

Yao. K. H.. and Wilt, A. F. (1987). "Scanning Fourier Transform Infrared Spectroscopy of Carbon and Oxygen Micro\egregation in Silicon." J . C'rvsr. Growrh 80, 453. Yatsurugi. Y.. Akiyama, N., Endo. Y . . and N o u k i . T. (1973). "Concentration. Solubility, and Equilibrium Distribution Coefficient of Nitrogen and Oxygen in Semiconductor Silicon." J . Elrc!rochern. SO( 120(7).975. Yuezhen, L., and Qimin, W . (1985). "Keview o f the Accurate Determination of Oxygen in Silicon." In R e t ~ i e ~ofv Progrt,.q.\ in Quunrilutitv iVondesrrucrive Evuluution. p. 957. Plenum Pres\. New York. Zaumseil, P., Winter, U.. Servidori. M . . and Cembali. F. (1987). "Determination of Defect and Strain Distribution in Ion Implanted and Annealed Silicon by X-Ray Triple Crystal Diffractometry." In G I t r e r i n g r ~ t i d1)qfec.r Engineering in Semiconducror Tec,hno/og.v, H . Richter (ed.). p. 195. GADEST '87. Acad. Sci., Germany. ,

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S E M I C O N I I I I ( ' I O K S A N D SEMIMETALS. VOL. 42

CHAPTER 4

Oxygen Concentration Measurement W . M . Bullis MATERIALS & METROLOGY 5CrNNYVALP. CALIFORNIA

1. 11.

INTRODUCTION . . . . . . . . . . . . . . . . . . INFRARED ABSORPTION Mt ~ S I I R E M F N T SUNDERI D ~ A I . CONDITIONS . . . . . . . . . . . . . . . . . . . . 111. I N F R A R E D S P E C T R O M t l t R S . . . . . . . . . . . . . I . 1)i.spersii~eIqfrurc,tl .Spr,c-trometrr.s . . . . . . . . . 2. Fourier- Trun.\,fo,-iti-lnfr(irc,d S p c ~ t r o r n e t e r s . . . . . . Iv. A N A IYSlS OF O X Y C l tw SPEC TKA . . . . . . . . . . . . . I . Busc~linr~ . . . . . . . . . . . . . . . . . 2. Anuly.sis M e t h o d . Pcul / f r i g h t o r Intrgrutcd Areti! . . 3 . Multiple Refiec.ti~intint/ Interf>,rrnce Fringes . . . . . 4. SpcJc,trirmCollec l i o n Method: A i r Rqf'erence or LXflerence? . . . . . . . . . . . . . . . . . . 5. Rc
v.

VI.

VII.

A B S O L I I T E ~ ~ E T E R M I h A r l O NAb N D C A I . I B R A T I O N F A C T O R S

1 . Ccilibrution ~ t i c ~ l r /~i )rr r R o o m Temperuture Matr.si~rc~inent.s . . . . . . . . . . . . . . 2 Routine Ahsolrite Metrsiirerrrents in Herivily D o p e d Silicon . . . . . . . . . . . . . . . . . . . STANDARDS A N D REI+WL-N( F MATFHIALS. . . . . . I . Stuiidurd Test Mc,th,d.\ . . . . . . . . . . . 2. Certified Re.fcreirc.t~Mtrteriul.~ . . . . . . . . S U M M A R.Y . . . . . . . . . . . . . . . . . Achnon.led,~tnent.s . . . . . . . . . . . . . Rqfirences . . . . . . . . . . . . . . . .

US

99 I02 I02 I07 I13 I13 II S I I8

I21 111

,

122 118 I34 I35 I36

. . .

13h

. . . . .

I42 I44 I44

,

.

. . . . . . . . . . . . . .

I45 I47 I47 I48

1. Introduction

There are two reasons for wanting to know the oxygen content of a silicon specimen. From a research point of view, one wants to relate the oxygen concentration to physical phenomena such as precipitation, solubility. diffusion, and interaction with other defects in the crystal. Such information leads to an understanding of the effect of oxygen on

95 Copyright 10 1994 by Academic Prrs,. Inc All nghts of reproduction in any form ie\crved ISBN O - I 2 ~ 7 % 2 1 4 2 - Y

96

W . M. BULLIS

the electrical, mechanical, and optical properties of silicon. For this application, it is important to have an accurate measure of the oxygen content in order to permit theoretical modeling of the phenomena and their dependence on oxygen content. The study of oxygen in silicon has led to many advances in the understanding of the physics of the solid state. Most silicon devices and circuits are produced on wafers cut from Czochralski crystals that have a relatively high concentration of oxygen. Because oxygen has a great deal of influence on various properties of silicon that are of practical importance for its application to the fabrication of integrated circuits, sensors, and other semiconductor devices, it is necessary to control the amount of oxygen in these wafers. Although accurate knowledge of the oxygen content is desirable, it is by no means essential for the control of manufacturing processes, if the characteristics of a material with a particular, but not necessarily accurately known, oxygen content can be adequately correlated with device properties and yields. For this application, the most important properties for the method of determination are that it be precise, nondestructive, and rapid. Although there are many methods for characterizing oxygen in silicon, as enumerated in the previous chapter, most routine determinations of oxygen content, especially those in production environments, are carried out by infrared absorption spectroscopy, which meets these three requirements. In the intermediate infrared region of the spectrum, between 2000 and 500 cm-' (wavelength range between 5 and 20 pm), there are three mechanisms for absorption of radiation: lattice absorption, impurity absorption, and free-carrier absorption. Pure silicon is generally transparent in this region but there are a number of lattice absorption bands that arise from multiple phonon transitions. The room temperature absorption spectrum of pure silicon is shown in Figure 1; additional details and phonon transition assignments may be found in the papers by Johnson (1 959) and Pajot (1977). It should be noted that only about half of the incident radiation is transmitted through the specimen because of the high reflectivity at the surface due to the high index of refraction of silicon; the reflectivity of silicon is almost exactly 0.300 in the infrared spectral range of interest, so that only 70% of the radiative intensity enters the silicon. Since two surfaces are involved in a transmission measurement, the reflective loss occurs twice. However, multiple reflections within the silicon specimen may cause the actual transmittance to exceed 50%. Impurities such as oxygen, carbon, and nitrogen also have absorption bands in this spectral range. These bands arise from the absorption of energy in the silicon-impurity bonds. The principal band due to interstitial oxygen, which occurs at 1107 cm-I, was first observed by Kaiser, Keck,

4.

97

OXYGEN CON( ENTRATION MEASUREMENT

F-----------

'

Vb', ivi:r-iiiiiil

" "

1 w

' '

"

I

"

'

" "

' '

" "

'

"

' '

I"

" "

'

(rm-')

FIG. I. Absorption spectrum of carbon-free, high-resistivity, double-side polished silicon slices with (dashed lines) and without (solid lines) oxygen impurity. The major silicon lattice peaks are identified by the upward pointing open triangles. The 515 and 1107 c m - ' lines associated with oxygen are identified by downward pointing open triangles. The broad peak at about 1225 c m - ' and the shoulder on the low-wavenumber side of the oxygen peak are probably due to oxide precipitates in the sample.

and Lange (1956), who concluded correctly that it was due to absorption by the asymmetric stretching vibration of the Si-0-Si bond. They also pointed out that this band could be used as a quantitative measure of the oxygen content of a silicon specimen. This is the band that is most widely used for measurement of oxygen concentration. As shown in Figure 1, it overlaps the relatively strong lattice band centered at 1 1 18 cm- which must be taken into account when making the determination. Another, much smaller, oxygen-related band occurs at 515 c m - ' . The band appears to be due to the symmetric stretching mode (Stavola, 1984). This band has also been suggested as a candidate for quantitative determinations of oxygen content, especially in heat treated specimens (Series, 1982). Shimura, Ohnishi, and Tsuya (1981) suggest that the ratio of the absorption in the 515 cm-' band to that in the 1107 cm-' band changes with oxygen precipitation, so that it would not be suitable for use in the presence of precipitation. On the other hand, Gaworzewski et al. (1984) assert that the ratio is unaffected by precipitation. Further, they conclude

'

98

w. M. BULLIS

that since the 515 cm-’ peak is unaffected by any band associated with silicon-oxygen precipitates, it is well suited for determination of oxygen concentration in the presence of precipitates. Krishnan, Stout, and Watanabe (1989) report an extremely weak band at 560 cm-’. The assignment of this band is uncertain; its absorption is ~ 0 . that 1 of the 515 cm-‘ band. In addition, there are two very small oxygen-related peaks located at 1013 and 1227 cm-’ on either side of the principal band centered at 1107 cm-’ (Pajot and von Bardeleben, 1984) and another very small band at 1720 cm-’ (Lappo and Tkachev, 1970). The 1013 cm-’ band is an overtone of the 515 cm-’ band (Pajot et al., 1985; Pajot and Cales, 1986) and the 1227 cm-’ band is a combination band (Bosomworth et al., 1970). The 1720 cm-’ band has been attributed to a combination of the asymmetric Si-0-Si bond stretching vibration and the strong two-phonon silicon transition. A narrow band at 607 cm-’, often seen in silicon spectra, is due to substantial carbon; it is on the side of the strongest of the silicon lattice bands, the two-phonon peak at 610 cm-‘. Absorption by free carriers in the silicon must also be taken into account for p-type specimens with resistivity less than about 4.5 Kl * cm ( p = 3 x 10I5 atoms/cm3) and for n-type specimens with resistivity less than 0.5 R . cm ( n = 1 x 1OI6 atoms/cm3) (Koster and Bittersberger, 1992). As the resistivity is further decreased, the free-carrier absorption eventually limits the transmission to the extent that other methods must be utilized for the determination of oxygen content. In applying the method, it is also necessary to consider scattering from the specimen surfaces and scattering from or absorption by oxide precipitates that may be present in heat-treated specimens. Before considering these points in detail, we first review in the next section the general procedures for making and analyzing infrared absorption measurements on an ideal high-resistivity sample specimen with wellpolished plane-parallel surfaces using an ideal, oxygen-free reference specimen of exactly the same thickness. Section 111 describes the types of instrumentation available for making infrared absorption measurements in the appropriate spectral range together with their strengths and limitations. The methods for analyzing the infrared spectrum under realistic conditions are discussed in Section IV. This section considers the various corrections that may be necessary as a result of specimen properties, including the presence of oxide precipitates. Absolute chemical methods that are required to establish a “calibration factor” (or “conversion coefficient”) to convert the infrared absorption to oxygen concentration are described briefly in Section V along with the various experiments designed to obtain calibration factors. This section also considers the use

4

OXkCIFN

(

O N ( I NTRATION MEASURFMENT

99

of chemical methods to determine oxygen content of very heavily doped specimens that cannot be measured by infrared absorption. Standardized measurement methods and the certified reference materials that are available for the measurement are discussed in Section V1. The chapter concludes with a brief summary. 11. Infrared Absorption Measurements Under Ideal Conditions

The basis for determination of the concentration of oxygen in silicon is Beer's Law, which states that the absorption due to an impurity is proportional to its concentration. Thus it is necessary to determine the absorption that can be attributed to the oxygen impurity. There are several methods for making this determination: the single-beam difference method. the double-beam difference method, and the air-reference method (Pajot. 1977; ASTM. 1987). The first two are relative measurements; the last provides a measure of absolute transmittance. In the single-heam d(fli)retice method. the transmittance of two specimens is measured sequentially in the same beam. These spectra may be ratioed to obtain the relative transmittance of one against the other. They may also be converted to absorbance spectra. in which case the relative spectrum is the difference between the two absorbances. This method requires that the instrument be stable during the time required to measure one specimen, exchange specimens, and measure t h e second specimen. In the double-heurn dflerence mothod, the beam is split so that a portion passes through each of two samples simultaneously. The beams are then recombined in such a way that the signal detected is proportional to the ratio of the transmitted intensities. In some cases the output signal may be converted to a differential absorbance spectrum. In the uir-reference method, only one specimen is measured, and the transmittance is determined directly. This method may be conducted on single-beam instruments. in which case the transmittance of the specimen is ratioed against the transmittance measured with no sample in the beam (also known as a bmckgrorrnd spectrum), or it may be made with double-beam instruments with one open beam. As noted earlier, for silicon specimens with polished front and back surfaces ("double-side" polished; no surface scattering) and no oxide precipitates (no internal scattering or oxygen-related absorption other than that from the interstitial oxygen), the total absorption, a, consists of three components, all of which are functions of the wavelength (or wavenumber) of the incident radiation: cx = (x"x

+ a"h + a+,

(1)

100

W. M. BULLIS

where a,,, aph,and afCare the absorption coefficients due to the oxygen impurity, the silicon lattice, and free carriers, respectively. In addition, the radiation from the source, the transmission through the spectrometer, and the responsivity of the detector vary with the wavelength of the radiation. Although the latter variations are accounted for by the background spectrum or open beam of the air-reference method, the absorption due to the silicon lattice and free carriers remains along with the absorption due to oxygen. Therefore the determination ideally is made by either the single-beam or the double-beam difference method with the use of a sample specimen, which contains oxygen, and a reference specimen, which is identical to the sample specimen except that it contains no oxygen. If the I107 cm-’ band is employed, the transmittance of both specimens is determined over the spectral range between 900 and 1300 cm-’ with a spectral resolution of 4 to 5 cm-I. In converting the transmittance to absorbance it is necessary to take into account the multiple reflections within the specimens; failure to do this results in errors of 10% or more for highresistivity, double-side polished specimens that are 2 mm or less in thickness and have absorption coefficients due to oxygen of less than 4 cm-’ (Thurber, 1970). The transmittance, Ti(v),of a double-side polished specimen is related to the absorption coefficient at each wavenumber, v , as follows (ASTM, 1987, Appendix XI):

where i may be s or r , for the sample or reference specimen, respectively; R is the reflectance of silicon (which can be taken as 0.300 in this spectral range); ai(v)is the absorption coefficient of the specimen, in cm-I, as a function of wavenumber; and diis the specimen thickness, in cm. The absorption coefficient can be expressed in terms of the transmittance as follows: 1 cui(v)= --In

-(I

-

R)’

4

+ V(1 - R)4 + 4R2[Tj(v)I2 2 R2 Ti( v)

3

(3 1

where the symbols are the same as those for Eq. (2). The difference absorption spectrum, Aa(u) is obtained as follows (see Fig. 2):

A~(v= )

OL,(V)

- a,(v).

(4)

The absorption coefficient due to oxygen, sox, is obtained by first establishing the wavenumber, 5, at which the absorption is a maximum, and

4.

101

O X Y G F N C O N ( ENTKATION M E A S U R E M E N T A

L'

4.8

7

-

7

7

-0.2 Wavenumber (cm-')

FIG. 2 . Difference absorption spectrum of a high-resistivity. double-side polished silicon slice and an oxygen-free reference 41ce o f the same thickness in the region o f the 1107 c m - oxygen band. The dashed curve\ \how the sample and reference absorbance 5pectra. The values u,,(L) and n,(b) (see t e x t ) are indicated.

'

then sub5tracting the value of ba\eline absorption, value. cy,,(ij) at this wavenumber u,,\ = cx[,(ij)

- cyJi4.

cyb(ij),

from the peak (5)

The interstitial oxygen concentration. [O,], is then determined as the product of a,,,and a calibration factor. u , established through the use of independent chemical determination\:

As will be discussed in Section V I . the preferred value of calibration factor is the International Oxygen Coefficient, uloc.88 ( = 6.28 ppmai cm-I), which was established in 1988 through a comprehensive international dual round robin experiment (Baghdadi et al., 1989). For the case in which the ratio of the transmittances of the sample and reference specimens is obtained directly, the absorption due to oxygen, cy,,\, is obtained as follows (Ciraff, 1983) if it assumed that both specimens have the same thickness:

102

W.

aox=

M. BULLIS

-d IIn (A

+ w),

(7)

where A = Tb(1 - B2)/2Tr,,,B = ( l / R ) exp(a d ) , Tb is the baseline ph. transmittance at the wavenumber of the band minimum (G), T,,, is the relative transmittance at G, R is the reflectance of silicon (= 0.300), and d ( = d, = d,) is the specimen thickness. Thus, in this case it is necessary to have separate knowledge of @tph at f . This can be obtained from an absolute (air-reference) measurement of the lattice absorption spectrum in a high-resistivity oxygen-free specimen. Values reported in the literature range from 0.82 (k0.05) cm-l (Pajot, 1977)to 0.885 cm-l (Schomann and Graff, 1989). The most widely used room temperature value for aph at i, is 0.85 cm-'. However Baghdadi et al. (1989) point out that the determination of aoxis quite insensitive to the exact value of a p h ; a 10% change in a p h results in only a 0.25% change in sox. There are many issues which complicate this deceptively simple picture presented for the ideal case. Some of these relate to the measuring spectrometer, others relate to the sample characteristics, and some result from interactions between the two. The following sections deal with these complications. 111. Infrared Spectrometers

Both dispersive and Fourier-transform infrared spectrometers are in wide use for determining oxygen in silicon. If properly adjusted and used. each is suitable for the purpose. However, each has its advantages and limitations. 1. DISPERSIVE INFRARED SPECTROMETERS In dispersive spectrometers, radiation from the source is focused on the specimen, and the transmitted light is passed through a monochromator to provide spectral dispersion. The transmittance is determined as a function of wavenumber by a radiation sensitive detector. The spectral resolution is controlled by a slit of varying width that permits only a portion of the radiation from the monochromator to pass to the detector. Most dispersive spectrometers are constructed as double-beam instruments in which the radiation is ( I ) split into two paths, one of which contains the sample specimen and the other a reference specimen; (2) chopped so that the signals from the two paths have opposite phases; and (3) then recombined and passed through the monochromator. In this way, the signal detected is proportional to the ratio of the transmitted intensities. The following discussion is limited to double-beam instru-

4.

OXYGEN CONC t N T K A T l O N MEASUREMENT

103

ments. The optical paths of two such instruments are shown in Figures 3 and 4. Historically, double-beam dispersive spectrometers with prism dispersion were the first type of spectrometer to be used for determining oxygen in silicon. These instruments employed the double-beam difference method. Early instruments of this type were analog instruments, and their computational abilities were limited; hence, the reference specimen needed to have the same suiface preparation, conductivity type, resistivity, and thickness as the sample specimen. In addition, the absorption spectra obtained by these instruments were generally not corrected for multiple reflections. Modern dispersive spectrometers use a grating monochromator, which generally results in improved wavenumber resolution. In most cases, electronic beam balancing is employed to improve the repeatability of the measurements. Many such spectrometers are controlled by computers that capture the data in digital form and permit its subsequent manipulation. With a computer-controlled instrument. it is readily possible to correct the ratioed spectrum for multiple-reflection effects. Instrumental issues associated with dispersive spectrometers include establishment of the 100% and 0% lines, mid-scale linearity of the optical system and detector, wavenuniber accuracy, and temperature effects. Also, when the instrument is of the double-beam type, in which both the sample and reference specimens are measured together, a correction must be made for any differences in thickness between the sample and reference specimens. a . 100% Line

On double-beam spectrometer5. the 100% line is determined by recording a transmittance spectrum with both beams empty. For a properly adjusted instrument, the variation around the 100% line, which is indicative of the noise of the instrument, should not exceed 0.5% over the range from 900 to 1300 c m - ' . h. 0% Line The 0% line is determined by recording a transmittance spectrum with the sample beam blocked at the sample position. Any radiation that reaches the detector under these conditions has not passed through the sample specimen; hence such radiation would not be affected by the absorption of a sample. Deviations over the range from 900 to 1300 c m - ' should not exceed 0.2%.

c 0 P

I REFERENCE SPECIMEN

SAMPLE SPECIMEN TM

BSSP: C: D: EM: ES:

Baffle and Secondary Source Positton Chopper (Mirror) Dectector Ellipsoidal Mirror Entrance Slit

FM: GT: MPA: OF: PAS: PB:

Flat Mirror Grating Table Mirror Palr Assembly Optical Filters Polarizer Accessory Positton Pupil Baffle

PM: S: SBS: TM: XS:

Parabolic Mirror Source Sample Beam Shutter Toroidal Mirror Exit Slit

FIG.3. Optical system of a Perkin-Elmer Model 580 dispersive 1R spectrometer.

4. OXYGEN ('ON( E N r R A T l O N MEASUREMENT

105

106 c.

W . M. BULLIS

Mid-Scale Linearity

The mid-scale linearity can be verified by examining the transmittance of a high-resistivity, double-side polished silicon specimen (with or without oxygen) in the neighborhood of 2000 cm-'. In this spectral region, silicon is transparent, and there are no lattice bands. Consequently, the transmittance of a double-side polished specimen is governed only by the reflectivity ( R = 0.300) and is given by

T(2000 cm-')

=

( I - R)' 1 -R2

=

0.538.

Deviations from this value by a significant amount (I I%) indicate that the spectrometer has linearity or other instrumental problems. d . Wavenurnber Accuracy

Wavenumber accuracy can be checked by measuring the transmittance of a polystyrene film that has sharp absorption bands at several wavenumbers in the range of interest. Wavenumber accuracy is particularly important in connection with determination of specimen temperature as described in the next subsection. e . Temperature Effects

Because all of the source radiation is focused directly on them in dispersive spectrometers, the specimens may be heated significantly above ambient temperature. Schomann and Graff (1989) have examined the effects of this temperature variation in considerable detail. They found that C, the wavenumber of the transmittance minimum (or absorption maximum) in cm-', varies linearly with temperature over the range between 250 and 320 K. Their work was extended by Murray et al. (1992), who report the following relation between the temperature, 8, in K , and C: - +) e = (1131.912 0.084 ' In high-resistivity specimens, Murray et al. (1992) also found lattice absorption at 1107 cm- is linear with temperature:

'

aph= 0.925

+ 3.8 x

10-3(8,,a,

-

310)cm-',

where em,, is the measured specimen temperature as found from Eq. (9). This value of aphis used in Eq. (7) to determine the value of aOx at the measurement temperature, aox(Omeas). Then, to find the oxygen concentra-

4.

107

OXYGF N ( O N ( f NTRATION MEASUREMENT

tion, aOxis corrected to the reference temperature, the calibration factor employed,

€Jref,

appropriate to

and multiplied by the calibration factor.

f : Thickness Dijferenc.e.s Betrc.tJrnS a m p l e and Reference Specimens

Although the thickness of the reference specimen is expected to be nearly the same as that of the sample specimen, there are usually small differences between them. If the sample and reference transmittance spectra are obtained and transformed to absorption spectra independently. the thickness difference can be easily accommodated by using the appropriate value of thickness for each specimen in Eq. (3). If only the ratio of the transmittance spectra is available, Schomann and G a f f (1989) have shown that, if the product of the thickness difference and the lattice absorption at 1107 cm is small compared with unity, the absorption due to oxygen can be corrected for the thickness difference as follows:

’

aoycorr

(xtl\l

I

-

aph(d\

~

dr)I,

(13)

where ci,, is the absorption coefficient calculated from Eq. ( 7 )with d = tf,, and d, and d, are the thicknesses of the sample and reference specimens, respectively.

3. FOURIER-TRANSFORM-INFRARED SPECTROMETERS Fourier-transform-infrared (FT-IR) spectrometers have significant advantages in speed and signal-to-noise ratio over dispersive spectrometers. The advent of microcomputers has made feasible the complex calculations required for these instruments. In FT-IR spectrometers. the radiation is passed through an interferometer with a moving mirror whose position is accurately known as a function of time and then through the specimen to the detector. The signal on the detector is an interferogram, which is Fourier transformed to yield an emission spectrum. The transmittance of a specimen is determined by ratioing its emission spectrum to the background emission spectrum of the open beam. Most FT-IR spectrometers are single-beam instruments so the sample and reference transmittances are determined i n sequence. In many instruments, the reference transmittance spectrum can be stored in memory and so only

108

W.

M. BULLIS

INTERFEROMETER

FIG.5 . Optical system of a Nicolet Model ECO-IS FT-IR spectrometer.

the sample spectrum is measured. Because the spectra are obtained independently, multiple-reflection and thickness corrections may be made readily. This type of instrument is in widespread use for the measurement of oxygen content in silicon (Krishnan et al., 1989). The optical system of a typical FT-IR spectrometer is shown in Figure 5 . General issues associated with Fourier-transform spectrometry, including zero filling, undersampling, and phase corrections are beyond the scope of this chapter. For a discussion of these issues, the reader is

4.

OXYGEN C ON( t NTRA TION MEASUREMENT

109

referred to the literature on the subject (see, for example, Vidrine, 1980; Krishnan and Ferraro, 1982). Instrumental issues associated with measurement of absorption in silicon by FT-IR spectrometers include effects of apodization, resolution (including interference fringes), emissivity from the specimen, and ADC errors. As for dispersive spectrometers, it is necessary to establish the 100% and 0%.lines, mid-scale linearity of the optical system and detector, and wavenumber accuracy of FT-IR spectrometers. The temperature excursions of the specimen are not as great as in dispersive spectrometers so the issue of temperature effects is less important. This is because only a portion of the radiation from the source impinges on the specimen and also because the measurement time is usually much shorter. a . 100% Line

In single-beam FT-IR spectrometers, the spectra are collected sequentially. This implies a need for stability at least over the time during which related spectra are collected. Stability as well as instrument noise level can be checked by ratioing two open-beam (background) emission spectra taken at times separated by an interval sufficient to collect the desired number of sample or reference specimen spectra. The average level of this open-beam transmittance should be within 0.5% of 100%. and the fluctuation about this level should not exceed 0.5%.

6. 0% Line In FT-IR spectrometers it is not possible to obtain a spectrum with the beam blocked. Therefore the 0% line between 900 and 1300 c m - ' is checked by collecting a spectrum with a polished sapphire substrate in the beam. Sapphire does not transmit at wavenumbers less than 1800 cm- I , and so a n y signal observed in this region is due to stray or scattered light in the instrument. As with dispersive spectrometers, deviations should not exceed 0.2% between 900 and 1300 cm-I. c. Mid-Scule Linearity Mid-scale linearity in FT-IR spectrometers should be checked by measuring the transmittance of a high-resistivity , double-side polished silicon specimen in the neighborhood of 2000 c m - ' as suggested in Section 11I.l.c. Deviations from 53.8%' by 1% or more in this spectral range indicate that the spectrometer has linearity or other instrumental problems. Because of the large cone angle of the beam in typical FT-IR spectrometers, changes in aperture size or angle of incidence may change the signal

110

W . M. BULLIS

level reaching the detector, resulting in errors that may appear to relate to beam geometry, but that may instead be due to system nonlinearities ( Baghdadi, 1984). d . Wavenumber Accuracy

Wavenumber accuracy should be verified with a polystyrene film specimen as suggested in Section 1II.l.d. e. Temperature Effects Even though temperature effects are not usually significant, the procedures for determination of the specimen temperature (Section 111.1.e) can also be applied t o FT-IR spectrometers. If the reference temperature at which the calibration factor has been established differs significantly from the ambient temperature, a correction for this temperature difference is necessary to obtain the correct oxygen concentration.

f. Apodization Because the interferogram in FT-IR spectrometers is truncated as a result of the finite distance traveled by the moving mirror, artifacts may be introduced into the spectrum by the transformation. The amplitudes of these artifacts are reduced if the interferogram is multiplied by a function, called an apodization function, prior to making the transformation. This function reduces the magnitude of the interferogram away from the main burst. Baghdadi (1984) has studied the effect of cosine, HappGenzel, and triangular apodization on the observed peak height of the 1107 cm- oxygen absorption band. He found that application of such a function resulted in a reduction of the observed peak height as compared with a “boxcar” function, which involves no reduction of the interferogram but cuts it off at finite points on either side of the main burst. The effect increased as resolution was reduced; triangular apodization resulted in the greatest reduction of peak height, as shown in Figure 6.

’

g . Resolution

Because of their greater sensitivity, FT-IR spectrometers are often operated at higher resolution than dispersive spectrometers. Hence, to compare results obtained from one of these instruments with results obtained on another, the effect of the instrument resolution on the observed peak height must be taken into account. The 1107 cm-’ oxygen band is quite broad (FWHM of about 32 cm-’ at room temperature) so this effect is not expected to be large. For example, there is only a 0.2% decrease

4.

OXYCIEN

(

ONCt N l K A I I O N MEASUREMENT

ht:.;~

111

it1 JI-I 0,'J~vetiiirnbrr 51

FIG. 6 . The effect of various apodiration functions on the relative magnitude of the oxygen peak height. The error bars. shown on the curve for triangular apodization. repreSen1 the largest standard deviation observed for the cosine, Happ-Gensel. or triangular apodization functions at the indicated resolution (after Baghdadi, 1984).

in peak height if the resolution is changed from 2 c m - ' to 5 c m - - ' . A somewhat larger reduction in peak height is expected when the resolution is degraded to 8 cm-I; however, the effect can be reduced somewhat by curve fitting the peak to find the maximum value. If the resolution, Au, is less than 1/(2nd)where n is the index of refraction ( n = 3.42 for silicon in the near to intermediate infrared region) and d is the specimen thickness, sinusoidal variations in amplitude, known as jringes, are observed in the transmittance spectrum of a specimen with two well-polished surfaces as a result of the interference of the multiply reflected beams. The most direct way to reduce the magnitude of these fringes is to reduce the measurement resolution. Since a sinusoidal signal appears as a narrow spike in the interferogram. it is also possible to reduce its magnitude by means of software manipulation of the interferogram (Hirschfeld and Mantz, 1976; Krishnan and Ferraro, 1982; Hyland, Ast. and Baghdadi, 1987) to eliminate the spike. A possible drawback to this procedure is that any other information contained in the same portion of the interferogram is also lost. Nevertheless, this technique is frequently used to eliminate the interference fringes.

112

W . M. BULLIS

Clark and Moffatt (1978) proposed a technique based on direct subtraction of a sinusoidal signal from the transmittance spectrum. This technique has the advantage of avoiding elimination of information that may be concealed under the spike in the interferogram. Unfortunately, it works well only for regions of low absorption, and therefore it is not of wide applicability to silicon studies. Incidence at the Brewster angle can also be employed (Krishnan, 1983; Shirai, 1991) to reduce multiple-reflection effects (and also the interference fringes), but this leads to other complications and so has not been widely used up to the present. The advantages of and problems introduced by the use of Brewster-angle incidence are considered further in Section IV. h . Emissivity

In FT-IR spectrometers with an axially symmetric light path, radiation emitted o r reflected from the specimen surface may be sensed by the detector. These instruments sometimes employ cooled MCT detectors that are sensitive to radiation at o r near room temperature. Murray et al. ( 1992) observed systematic differences between measurements made with dispersive and FT-IR spectrometers; the transmittance at 1107 cm-' recorded with the FT-IR spectrometers was up to 5% less than that recorded with dispersive instruments. They suggest that this difference can be explained by considering the emission from the specimen. Because emissivity is proportional to absorption, oxygen-containing Czochralski silicon specimens exhibit greater emission in the neighborhood of 1107 cm than oxygen-free reference specimens (Stierwalt and Potter, 1962). Murray et al. (1992) show that use of the source-on-source-off technique proposed by Birch and Nicol(l987) can reduce the error significantly. In this technique, the transmittance measurements are made first with the source on and then with the source off. The ratio of these measurements yields the true transmission spectrum. This procedure should be carried out for both the sample and reference specimens to obtain more nearly correct transmittance spectra, which can then be treated in the usual way. Murray et al. (1992) also note that the effect is considerably reduced in systems that employ room temperature detectors, such as the commonly encountered DTGS pyroelectric detector and is absent entirely in FT-IR spectrometers with roof-top mirrors, which utilize an asymmetrical geometry in which the beam is incident only on one side of the mirror and is reflected back by the reverse side. It should also be absent in modern FT-IR spectrometers designed for measurements on materials with a high index of refraction; in these instruments the beam strikes the ~

'

4.

OXYGEN C O N C t NTRATION MEASUREMENT

113

sample at an angle between 10 and 20" from the normal in order to permit both reflectance and transmittance measurements in the same instrument without having to physically move optical components.

i. ADC Errors The signals in FT-IR spectrometers are digitized by means of analogto-digital converters ( ADCs). Errors introduced by these essential components of the electronic system have been considered by Baghdadi and Gladden (1985). They showed that linearity errors in the ADC can change the shape and peak magnitude of the transformed transmittance or absorbance spectrum, leading to systematic errors that are instrument dependent. Differences in ADC characteristics can also result in changes of instrument performance upon changes of electronic components. IV. Analysis of Oxygen Spectra Many factors must be considered in connection with the analysis of the infrared spectrum to determine the absorption coefficient due to oxygen even with the assumption that the spectrometer has provided an accurate measure of the transmittance spectrum for the specimen. These are 0 0 0

0 0 0

0 0

Baseline Analysis method (peak height or integrated area) Multiple reflections and interference fringes Spectrum collection method (air-reference or difference) Reference specimen characteristics Back-surface condition Free-carrier absorption Interference from absorption peaks due to precipitates Specimen temperature

Although some of these points have been considered briefly in connection with the discussion of ideal specimens and instrumentation, the discussion in this section considers these issues in the context of actual test specimens. 1 . BASELINE

Ideally, the baseline transmittance at the wavenumber (5) of the oxygen band minimum in a ratioed spectrum [ T,(u)lT,.(u)]would be 100%. Similarly, in the ideal case, the baseline absorbance at 5 of a difference spectrum [ U , ~ ( V )- C K , ( V ) ] would be 0. However, because of small differences

114

W . M. BULLIS

in surface and other characteristics of the sample and reference specimens, the baseline absorbance or transmittance may differ from the ideal values. Further, particularly in direct-reading double-beam spectrometers, it is frequently customary to adjust the gain so that full transmittance in the sample beam corresponds to a reading of 80-90%. Consequently, it is customary t o determine the baseline graphically or analytically. For double-side polished sample and reference specimens of approximately the same thickness and similar resistivity and conductivity type, the baseline is expected to be straight, but it may have a slight slope; the question remains as to the wavelength range over which the baseline should be constructed. Recalling that small peaks at 1013 and 1227 cm-' due to the presence of oxygen flank the I107 cm-' oxygen band, it is clear that these regions must be excluded. However, some authorities recommend construction of the baseline over a much wider wavenumber region than others. For example, in ASTM Test Method F 1188 (ASTM, 1988a), the baseline for the ratioed transmittance spectrum is taken from the average transmittance in the range 900 to 1000 cm-' on one side to the average transmittance in the range 1200 to 1300 cm-' on the other. Not only does this baseline extend over a very wide wavenumber range, but its upper end range includes the 1227 cm-l peak. In ASTM Test Method I189 (ASTM, 1988b), the baseline is drawn between the maxima of the transmittance spectrum in the ranges between 1010 and 1060 cm-' and between 1200 and 1260 cm-' (as fit by a third-order polynomial). This range is smaller than that used in ASTM Test Method F 1188, but each end range includes a small oxygen-related peak. Nevertheless, the influence of these peaks on the point of maximum transmittance is expected to be rather small. On the other hand, the 1993 revision of the DIN oxygen standard (DIN, 1974) recommends construction of the baseline of the ratioed transmittance spectrum using the average transmittance in the range 1025 to 1040 c m - ' on the one side and the average transmittance in the range 1180 to 1195 cm-I on the other. The extremes of this much shorter baseline lie between the two small oxygen-related peaks. As will be seen in the next subsection, other authors suggest that the baseline be constructed over even shorter intervals. As described previously, the baseline is usually chosen as the straight line between the limits of the baseline range. However, if there is significant free-carrier absorption or if both sides of the specimens are not polished, the actual baseline of the spectrum may be curved and use of a linear baseline may lead to inaccurate determination of the interstitial oxygen concentration. The presence of absorption peaks due to oxide precipitates also may interfere with the establishment of a suitable base-

4.

OXYGFN

(

115

O N < I N T K A T I O N MEASUREMENT

line for the determination. These effects and the influence of the choice of baseline region on their impact will be discussed later in this section.

2 . ANALYSIS METHOD: PEAKH E t G t I T

OR

lNTEGRATED AREA?

I n Section 11, it was tacitly assumed that the oxygen content in silicon should be derived from the peak value of the transmittance or absorbance. This, in fact, is the procedure which has been embodied in several standard test methods (ASTM. 1988a, 1988b; DIN, 1974). However, use of the integrated area of the oxygen peak for this purpose offers several advantages. In this method, the impurity absorbance band is integrated from u I ( V ) where the absorption coefficient due to oxygen is -0 at both limits. One advantage is that the integrated area of the oxygen band is less dependent on the resolution of the spectronieter because the reduction in peak height due to reduced resolution is offset by an increase in the width of the impurity band (Pajot, 1977). However, this benefit is reduced when very short interval baselines are employed, such that the absorption coefticient due to oxygen is not = O at either or both of the limits of the baseline. Another advantage is that the optical specimen thickness can be derived directly from the measurements. (1.

I n t egrLi t e d-A ren Method

Series (1982) has considered the application of this technique to the measurement of oxygen and carbon in silicon in great detail. In his procedure, the transmittance spectra of both a sample specimen and an oxygenand carbon-free reference specimen are collected and transformed to a difference absorbance spectrum [ A A ( v ) = a,(u)d, - a,(v)d,] using Eqs. ( 3 ) and ( 5 ) if the spectra are obtained independently or Eq. (7) with T,, = I if the ratio of the transmittances of the sample and reference specimens is obtained directly." Linear baselines are fitted to the absorbance curve in the region of the 1107 cm-I oxygen band and in the region of the 610 c m - ' two-phonun band by averaging over the upper and lower baseline limit intervals given in Table I . The absorbance spectrum, *Series ( 1982) has developed approximate relationships for these equations in order to avoid overflow errors when using fixed point arithmetic. The approximation for Eq. ( 3 ) is a , ( v ) d , = -In[ T , ( u ) l - In[( I t K ) / (I

-

R)]

t

R'{ I

~

[ 7 . , ( u ) l 2 [I( + R ) / (I

-

R)]'}

m d the approximation equivalent to t
-. 1 he of

(1.

~

a , ( u ) d ,=

error introduced by

tije

~

I n [ I ( v ) ] t H'exp[ - 2 u , ( v ) d , ]

{[T(v)l'- I }

of thew approximations does not exceed 4% for all values

116

W.

M. BULLIS

TABLE I INTERVALSUSEDFOR THE INTEGRATED-AREA METHOD OF ANALYZING THE OXYGEN ABSORBANCE SPECTRUM (Series, 1982)

Interval

Contributions from

Lower Limit of Baseline (cm-')

Central Region (cm-')

Upper Limit of Baseline (cm-')

1 2 3

silicon-oxygen silicon-carbon silicon-carbon

1080-1090 580-595 580-595

1090-1120 610-630 595-610

I 120-1 130 630-640 630-640

corrected for the baseline, is then integrated over the three central areas listed in the table. Because interval 1 contains contributions from both silicon and oxygen and intervals 2 and 3 contain contributions from both carbon and silicon, the following equations are obtained:

where Abi(u) is the absorbance under the baseline in interval i, kph;is the integrated absorption due to phonons per unit thickness over interval i, koxl is the integrated absorption due to interstitial oxygen per unit thickness per unit oxygen content in interval 1, kcai is the integrated absorption due to carbon per unit thickness per unit carbon content in interval i, d, is the sample specimen thickness, Ad = d, - d,, and d, is the reference specimen thickness. The constants k are evaluated from the spectra of two standard doubleside polished specimens of known thickness. One of the standards (the reference standard) is free of measurable carbon and oxygen; the other standard (the oxygen-carbon standard) contains known amounts of substitutional carbon, [C,],, and interstitial oxygen, [O,]O. Two different spectra are determined: the first is the spectrum of the reference standard against air, and the second is the spectra of the oxygen-carbon standard against the reference standard. With data from these spectra, Eqs. (14), (15), and (16) can be solved for the six constants, k . The equations, with these values of the constants, are then used to compute the thickness, carbon content, and oxygen content of the sample specimen from the measurement of differential absorbance against the

4.

117

O X Y G F N CONC t N T R A l ION M E A S U R E M E N 1

TABLE 11

INTERVALS USEDFOR

THE INTEGRATEI)-AREA METHOD OF ANALYZING T H E OXYGEN ABSORBANCE SPECTRUM (Vidrine. 1980)

Interval

Contributions from

Lower Limit of Baseline (cm ’ )

Central Region (cm-’)

Upper Limit of Baseline (crn ’ )

I 2 3

silicon-oxygen silicon silicon-carbon

1030- I065

1090-1 125 6 12-626

1145-1 1x0

570- 588

570-588

602-607

632-650 632-650

reference standard. Thickness and carbon concentration are obtained by solving Eqs. (15) and (16). With the established value of thickness, Eq. (14) can be solved for the oxygen concentration. In addition to avoiding the necessity of determining the sample specimen thickness independently, this procedure has the further advantage that if the differential absorbance approximations are used, the errors introduced tend to cancel each other in the process of evaluating the oxygen and carbon concentrations. Series (1982) showed that Beer’s law applies for spectral resolutions of 5.5 cm - I o r better for the carbon determination and 7 cm-l or better for the oxygen determination using a double-beam dispersive spectrometer. He also demonstrated that the method is very insensitive to a thickness mismatch between sample and reference specimens. Vidrine (1980) also describes a similar, but not as detailed or comprehensive, integrated-area technique with slightly wider baseline intervals and tighter intervals for the carbon and silicon (two-phonon) bands, as listed in Table 11. This work was done with an FT-IR instrument operating with resolution as low as 0.6 c m - ’ with either boxcar or HappGenzel apodization. Absorbance was determined as the common (base 10) logarithm of the transmittance without taking multiple reflections into account. He emphasizes that this technique does not yield total integrated peak absorbance but rather t h e integrated peak absorbance above a specified baseline. h. Curi*e-FitMethod f o r Dotc’rminrition o j Peak Height

Although the discussion of Section 11 depends on knowledge of the transmittance at the band minimum (or peak absorbance at the band maximum), an explicit procedure for obtaining this value was not discussed. In early analog instruments, the spectrum was plotted and the extremum determined from the plot. With the advent of digital comput-

118

W . M. BULLIS

ers, it is more reliable to fit the spectrum near the extremum and compute the extreme value. Numerous procedures for fitting the oxygen peak have been reported. ASTM Test Method F 1189 (ASTM, 1988b) requires fitting a fourthorder polynomial to the air-reference transmittance spectrum of a sample specimen over the range from 1090 to 1123 cm-I using a least-squares fitting algorithm. The 1993 revision of the DIN oxygen standard (DIN, 1974) provides an alternative numerical method that involves quadratic interpolation using three neighboring T-u pairs around the minimum of the ratioed transmittance spectrum to find t and Tre,. Series (1982; see also Series and Livingston, 1986) has also developed a more general curve fitting routine. In its complete form, it can be employed to determine the effective specimen thickness and the carbon and oxygen concentrations. If the sample specimen thickness is determined independently, the oxygen band alone may be analyzed. The spectrum in the wavenumber range between 1080 and 1130 cm-' is expressed as follows: A ( v i ) = a, -I- a,u,

+ d,AAh(Ui)+ d,[Oi]AAx(vj)+ 8(vi).

(17)

where A ( v j )is the sample absorbance spectrum as measured by the airreference method, a, and a , are the linear baseline terms, d, is the (predetermined) sample specimen thickness, [Oil is the oxygen concentration in the sample specimen, AAh(ui)is the absorbance spectrum due to phonons per unit thickness, A&(ui)is the absorbance spectrum due to interstitial oxygen per unit thickness per unit oxygen content, and S(ui) is the contribution of both random and coherent noise to the measured absorbance spectrum. Measurements made on two standards as described previously in connection with the integrated-area method are used to establish the values for Abh(vj)and AAx(uj).Then a least-squares procedure is used to find the best fits to the baseline terms and the interstitial oxygen concentration. This technique takes account of the actual shape of the absorption band and does not force it to match a polynomial function. The interval over which the spectrum is fitted is somewhat arbitrary. The interval indicated here was chosen to avoid interference arising from precipitate bands and curved baselines as will be discussed later in this section. 3 . MULTIPLE REFLECTIONS AND INTERFERENCE FRINGES

Many authors (Thurber, 1970; Pajot, 1977; Graupner, 1983; and Stallhofer and Huber, 1983) have demonstrated the need for taking the effects of multiple reflections into account when converting the transmittance of a double-side polished silicon specimen into absorbance. Equations

4.

OXYGFN

(

O N ( 1 NlRATION MEASUREMENT

119

appropriate to both the single-beam difference method (Eq. (3)) and double-beam difference method ( E q . (7)) were discussed in Section I I . * If multiple reflections are ignored, the transmittance, T , of a specimen of thickness, d , is related to the absorption coefficient, a, by the simple formula 7

=

(1

-

K)?(>-""

(18)

where R is the reflectance (0.300).Thus, in the absence of free-carrier absorption, the absorption coefficient due to oxygen is given by

where 7re,is the ratio of the transmittance of the sample specimen. T,, t o the transmittance of the reference specimen, T,. The relationship of Eq. (19) was employed in early double-beam spectrometers and cited in the analysis of the results of measurements by the double-beam difference method in ASTM Test Method F 121 (ASTM, 1970b), first published in 1970. The errors encountered in neglecting multiple reflections when measuring double-side polished specimens vary depending on the thickness of the specimen. as shown in Figure 7 . In very thick specimens or in specimens with one or two rough surfaces, the effects of multiple reflection are reduced and can be neglected. Typical single-side polished silicon wafers provide an intermediate case in which neither of t h e limiting cases (inclusion or exclusion of multiplereflection effects) applies; this topic will be considered further in subsection 6 of this section. Also, it should be observed, in passing, that because of the large background absorbance due to the silicon two-phonon transition, the carbon peak at 607 cm can be analyzed without considering multiple reflections. As noted previously, interference fringes are observed in infrared absorption spectra measured with high resolution on thin, double-side polished silicon specimens. Since interference fringes are most often observed in spectra obtained with FT-IK spectrometers because of the higher resolution at which such spectrometers are operated, their origin and methods for reducing them were discussed briefly in Section III.2.g. Interference fringes do not appear, of course, under conditions where multiple reflections are not important. One method for eliminating the effect of multiple reflections is to illuminate the specimen with p -

'

*Approximations to these equation\ developed by Series (1982) are given in the previoub subection.

120

W. M. BULLIS

Wafer Thickness:

1

300 p m 400 prr 500 prr 600 Urn 700 /*.m 800 p m 1.0mm 1.2 mm

1.4mm 1.7 mm

2.0 mm

2.5 mm 4%

0.0 0.5

:

' 1 ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' I 'd

1.0

1.5 2.0

2.5

3.0

3.5

4.0 4.5 5.0

FIG.7. Percent difference between the absorption coefficient, c&, determined without including the effects of multiple reflection and the absorption coefficient, a,,, determined including multiple reflection effects, as a function of .Ax. For these calculations, free-carrier absorption was assumed to be negligible.

polarized* radiation incident at the Brewster angle (73.7' from the normal in silicon) (Krishnan, 1983). One potential problem with this technique is the relatively wide cone angle of the incident radiation in FT-IR spectrometers with focused beam, as most such instruments have. Thus not all the radiation may be incident at the Brewster angle. Recently Shirai (1991, 1992) has examined this method in detail. In one experiment he measured 620-km thick specimens with two parallel polished surfaces as well as specimens with one polished surface and one bright (acid) etched surface. For this case, he found that interference fringes are effectively suppressed in the measurements made at Brewsterangle incidence at a resolution of 1 cm-' while large fringes were observed in the measurements made with normal incidence at a resolution of 2 cm-I. Krishnan (1983) has suggested another method for eliminating the effects of multiple reflection. In this method, spectra are collected in the usual way, with unpolarized illumination at normal incidence. An effec* Shirai ( 1991) defines p-polarized radiation as the electromagnetic wave whose magnetic vector is perpendicular to the plane of incidence.

4.

O X Y G E N C ONC'ENTRATION MEASUREMENT

121

tive thickness of the specimen based on an unspecified silicon lattice absorption peak is employed in the analysis of the 1107 c m - ' oxygen absorption band. The oxygen concentration as determined by this method on several groups of adjacent wafers with different characteristics was found to be relatively independent of both specimen thickness and backsurface finish, both of which influence the multiple reflections. This approach is also appropriate for use in analyzing spectra taken with instruments that have nonnormal incidence; the effective thickness of the sample for such configurations cannot be readily determined in any other way. 4. SPECTRUM COLLECTION METHOD:AIR REFERENCE OR DIFFERENCE?

As noted previously, there are two methods for making infrared absorption measurements to determine the oxygen concentration in silicon. The air-reference method returns the total transmittance spectrum of silicon. Thus spectra obtained by this method include contributions from the silicon lattice and free carriers as well as from impurities. For the present the discussion is restricted to high-resistivity materials so that free-carrier absorption can be neglected. However, since there is a silicon lattice peak in the neighborhood of the 1107 cm-' oxygen peak, its absorbance at 1107 cm- I must be determined independently and substracted from the measured absorbance in order to obtain the absorbance due to oxygen. Although the absorption coefficient of this phonon band is generally accepted to be about 0.85 cm (Baghdadi et al., 1989), the value 0.5 c m - ' is used in ASTM Test Method F 1189 (ASTM, 1988b) to account for the fact that some of the silicon band falls below the baseline as constructed in that method. The uncertainty in the precise value of this absorption is a major drawback to the use of the air-reference method to determine oxygen concentration because any error in this value is reflected directly as an error in the oxygen absorption.

'

5 . REFERENCE SPECIMEN CHAKACTERISTICS

In the difference method it is necessary to choose an oxygen-free reference specimen with appropriate characteristics. Ideally, the reference specimen would be identical to the sample specimen in all respects except that it contains no oxygen. Customarily, a float-zoned slice is used as the reference specimen. Such slices may typically contain about 100 parts per billion atomic (ppba) of oxygen.* For example, the low oxygen reference *The uncertainty in determining this level of oxygen by an absolute method. such as charged-particle activation analysis. I\ typically about ? 25-30%'. This represents an uncertainty of less than 0.2% for a wafer with an oxygen concentration of about 20 ppma.

122

W . M. BULLIS

standard (CRM 368) issued by the Community Bureau of Reference (BCR) is reported to contain 121 ppba oxygen (Vandendriessche et al., 1990). This represents an error of about 0.6% for a silicon wafer with a mid-range oxygen content of about 20 parts per million atomic (ppma). Such an error, while not large, may be significant under certain circumstances in which case the oxygen concentration of the reference specimen should be udded to the measured oxygen concentration in order to obtain the correct oxygen concentration in the sample specimen. The 1993 revision of the DIN oxygen standard (DIN, 1974) requires that the reference have an oxygen concentration below 50 ppba or a known oxygen concentration less than 500 ppba, but no procedure for making the selection is given. ASTM Practices F 120 (ASTM, 1987) suggest that the reference specimen be selected as the one containing the lowest amount of oxygen from a group of slices taken from 5 to 10 different crystals thought to be oxygen free as determined by a series of comparison measurements. Li et al. (1986) proposed a method based on the use of low temperature (78 K) spectra for selection of the oxygen-free reference specimen. At 78 K, the oxygen band splits into two peaks while the silicon lattice band in the same region of the spectrum does not. Therefore, oxygen-free specimens can be selected as those that exhibit no observable band splitting at low temperature. Other important attributes of the reference specimen are thickness, surface condition, and carrier density. Differences in thickness are most significant in analysis of double-beam difference spectra. A correction applicable to the analysis of such spectra for the case of small differences (ap,, . A d << 1) due to Schomann and Graff (1989) was described in Section 111.1.f. Series (1982) has demonstrated that relatively large thickness differences between sample and reference specimens can be accommodated for both the integrated-area and curve-fitting methods he describes. 6. BACK-SURFACE CONDITION

Most wafers used for device and integrated circuit production are polished on one side and etched on the other. The roughness of the etched surface varies from quite smooth for bright acid-etched surfaces to very rough for caustic-etched surfaces. If the back surface is not flat and smooth, it scatters radiation out of the beam, thus reducing the measured transmittance of the specimen. This has a number of consequences. First, if the scattering is large enough the detected signal is reduced such that the measurement either cannot be made or is inaccurate because of low signal-to-noise ratio. Second, if the measurement can be made, the base-

4.

OXYGFN

(

O N ( f N 1 RAT ION MEASUREMENT

123

line is curved because the amount of scattering is a function of wavenumber; the curvature is generally such that use of a linear baseline over a relatively wide interval tends to overestimate the oxygen content. Third, in the presence of significant scattering from the back surface, neither inclusion nor exclusion of multiple-reflection effects in the analysis provides the correct answer; inclusion of multiple reflections (Eq. (7)) underestimates the true oxygen content while neglect of multiple reflections ( E q . (19)) overestimates it (Graff. 1983). Many authors have sought ways to determine the oxygen content in silicon wafers with a variety of back-surface conditions. Series (1982) showed that the use of a narrow range in the curve-fitting method as discussed in Section IV.2.b significantly reduced the influence of the curved baseline when measuring back damaged wafers. The integrdtedarea method, described in Section 1V.2.a, gave a result that was systematically 5% lower; this discrepancy was attributed to the neglect of multiple reflections in the conversion of transmittance to absorbance for the integrated-area analysis. Subsequently, an interlaboratory test in the United Kingdom showed that considerably better results for samples with transmittance greater than 5%. at I100 c m - ’ could be obtained with this method if a short baseline was used and multiple reflections were accounted for with the scattering treated as an additional internal absorption (Series and Griffiths, 1986). Results are summarized in Table 111. Abe et al. (1983) compared the results of measurements using the double-beam difference method (ASTM, 1970b) with those obtained using the integrated-area method described by Vidrine (1980). As expected. the double-beam difference method yielded higher values of oxygen content than the integrated-area method. However, both methods showed a dependence on both sample thickness and back-surface condition. As a result, these authors concluded that to permit comparisons to be made the infrared absorption measurement “must be made with the same instrumentation and specimen preparation.” The Brewster-angle method discussed earlier in connection with elimination of interference fringes (Krishnan. 1983) also provides a means for reducing the effects of back-surface scattering. Shirai (1991) reported a I : I correlation between oxygen as determined by the Brewster-angle method on single-side polished wafers with acid-etched back surfaces and that obtained on double-side polished wafers over the oxygen range from 7.S to 10 x 10” atoms/cm’; the standard deviation was found to be 0.054 x 10” atoms/cm3. A I : 1 correlation with a similar standard deviation (0.055 x 10’’ atoms/cm3) was also found in a comparison of measurements on single-side polished wafers by the Brewster-angle method and on double-side polished wafers by the conventional (normal-incidence)

TABLE I11

SUMMARY OF RESULTS OF UK EXPERIMENT ON SILICON WAFERS WITH DIFFERENT BACK-SURFACE FINISH (Series and Griffiths, 1986) ~~

~~

[O,]

=

Float Zone 0.00 2 0.00 ppma

%T@ Back-Surface Finish*

1100 cm-l

~

~

~~

~

~

~

~

High Oxygen Czochralski [O,] = 14.85 ? 0.23 ppma

%T Q 1100 cm-'

Deviation (ppma)

Low Oxygen Czochralski [O,] = 10.62 2 0.17 ppma %T @ 1100 cm-'

Deviation (PPma)

Chemical-mechanical polish

51

-0.05

0.06

50

0.00 t 0.11

44

Bright chemical polish Polysilicon film ( 1 pm) Deep KOH etch As sawn (both surfaces) Deep acid etch Shallow KOH etch

49 18 12 8 6 5

-0.05 2 0.08 0.00 2 0.09 -0.05 2 0.08 -0.10 2 0.12 0.12 2 0.16 0.17 2 0.20

42 18 12 6 13 6

-0.14 2 0.12 0.07 2 0.24 0.10 2 0.17 0.21 2 0.26 0.01 2 0.19 0.38 2 ,033

41 18 13 5 3 3

~

5

~

~

~

Deviation (ppma)

0.01 2 0.10 -0.27 2 -0.06 2 0.06 2 0.15 2 0.92 2 1.69 2

0.06 0.19 0.13 0.27 0.28 0.45

~~

Nore-%T is baseline transmittance at 1100 cm-I; the deviation is the difference between the average oxygen content determined by the eight participants in the round robin experiment and the oxygen content determined on 2-mm thick double-side polished specimens by the double-beam difference method taking multiple reflections into account. In this work, the new ASTM (ASTM, 1970b) or DIN (DIN, 1974) calibration factor (4.9 ppmalcm- ') was used. Although the float-zoned samples very possibly contained a small amount of oxygen, the oxygen level in these samples was assumed to be zero. *Unless otherwise noted, the front surface finish is a chemical-mechanical polish.

$

? W

F

t:

Wl

4.

DXYGtN

(

O N C t N T R A T I O N MEASUREMENT

125

analysis taking multiple reflections into account. In this work. the “JEIDA” calibration factor, 3.03 x loi7atoms/cm7. c m - ’ (Iizuka et al., 1983, 1985), was used. More recently Shirai (1992) reported on determinations of oxygen by the Brewster-angle method in acid-etched (both sides) and single-side polished, acid-etched wafers with baseline transmittance at 1107 c m - ’ in the range from 19 to 75%.* In each of these cases, the values obtained by the Brewster-angle method were within 2% of the value determined by the single-beam difference method on equivalent double-side polished wafers taking multiple reflections into account. Again the standard deviation of t h e differences was similar (0.056 x 10’’ atoms/cmi); in these measurements the slightly higher IOC-88 calibration factor, 3.14 x 10’’ atoms/cm’ . c m - ’ (Baghdadi et al., 1989), was used. This work also demonstrated that corrections could be made to accommodate sample and reference specimens of significantly different thickness. Krishnan (1983) also applied his effective-thickness method, which was discussed in Section IV.C, to the measurement of several groups of adjacent p-type. { 1 1 I ) wafers, approximately 520 pm thick, with different back-surface finishes. In one case. for six wafers, he obtained an average oxygen content of 16.94 ppma with a standard deviation of 0.13 ppma (calibration factor unspecified. h u t is probably new ASTM (ASTM, 1970b)). In a second case, for ten wafers, he obtained an average of 18.83 ppma with a standard deviation of 0.30 ppma. This insensitivity to back-surface finish was subsequently confirmed by independent measurements using a spectrometer which contained software based on this technique (Bullis and Coates, 1987). They examined bright-etched and singleside polished, caustic-etched wafers, about 0.5 mm thick, and bright-etched 2-mm thick slices and found that the oxygen measurements on both wafer types yielded a consistent wafer-slice relationship with unity slope, almost no offset, and a total range of k 0 . 6 ppma, using the old ASTM calibration factor (ASTM, 1970b). These variations are of the same order as local variations in oxygen concentration along the length of a silicon crystal (Schomann and Graff, 1989). Stallhofer and Huber (1983) investigated the effect of different backsurface conditions on the applicability of the multiple reflectance correction. They concluded that, for wafers with transmittance 252% at 1600 cm- the multiple reflection correction is valid and that for wafers with transmittance less than about 25% at 1600 c m - ’ (or <40%1 between 1400

’.

* Note thdt becdu5e reflection 1 5 wppressed dt Brewster-angle incidence. the transmiltdnLe through a double-hide polished specimen cdn approach 100% as compared with the 5 2 8‘ji maximum trdnsmittnnce obtdined dl normdl incidence

126

W . M. BULLIS

and 900 cm-I), multiple reflections are suppressed and the simple relationship of Eq. (19) applies. For wafers with intermediate transmittance values, they concluded that neither extreme is appropriate and empirically determined correction factors are required. Graff (1983) carried out a very detailed study of the effect of backsurface scattering on the determination of oxygen in silicon by infrared absorption. He demonstrated that the effects of back-surface scattering can be correctly accounted for in the multiple-reflection analysis by including an additional absorption term along with the absorption due to oxygen, phonons, and free carriers. A ratio-recording double-beam dispersive spectrometer was used, and oxygen concentration was computed using the DIN calibration factor (DIN,1974). This method requires independent knowledge of the absolute transmission of the wafer. Measurements were made on wafers with oxygen content about 6.25 x 10” atoms/cm3and transmission of 12.2 to 49.5% resulting from various backsurface treatments. Analyzed in the conventional fashion, with or without taking account of multiple reflections, the measured oxygen content increased by 18-19% over the range of transmission studied. There was a shift of about 17% between the results obtained with and without taking account of multiple reflections. When analyzed according to the proposed method, the deviation between oxygen content measured on samples with transmission ranging from 10 to 50% was reduced to about 3%. Schomann and Graff (1989) considered the application of this technique in detail for various types of spectrometers. The basic measurement involves collection of two spectra: (1) an air-reference spectrum of the sample specimen to establish the effective absorption, a + ,resulting from the combined effects of back-surface scattering and phonon absorption, and (2) a relative transmission spectrum to obtain the absorption due to oxygen. With a simple double-beam spectrometer without microprocesSOY, a + is obtained from the baseline transmittance, TL, at the wavenumber of the oxygen peak (6) by using Eq. (3) with T;(C) = TL to calculate the baseline absorbance and then adding 0.4 cm-’ in order to account for the remainder of the phonon absorption. The absorption coefficient due to oxygen is then calculated from a relative transmission spectrum obtained with a reference specimen of the same thickness, carrier density, and back-surface condition using Eq (7) with (Yph replaced by a’. The principal drawback to this method when used with a simple dual-beam spectrometer is that a large stock of reference wafers with different characteristics is required. Two methods are suggested for use with a microprocessor-assisted double-beam spectrometer without data station. The first is similar to that described in the previous paragraph except that an air-reference

4.

OXYCF N C ONC I N r R A T I O N M F A S U R E M E N

127

r

spectrum of a reference specimen that has back-surface scattering characteristics very nearly the same as those of the sample specimen is used to obtain T,(C). This spectrum is adjusted at both sides of the oxygen absorption band to match the air-reference sample spectrum to account for differences in thickness. The transmittance of the adjusted spectrum at t is used in Eq. (3) to find a ' ; the thickness used is that of the sample specimen, d,\, because of the adjustment. Then the transmittance at the peak of the air-reference sample spectrum, 7:\(C), is used to obtain a,, from Eq. (7) with the following substitutions: aph+ a s ; T,, -+ 7;(6); Tre,+= T\(ij);and d += d,. The second method employs a double-side polished reference specimen of the same thickness as the sample specimen. An absolute spectrum (in which the transmittance is adjusted to exactly 100% in the absence of specimens in the beams) of the ratio of the transmission of the sample specimen to that of the double-side polished reference specimen is obtained, and a baseline is constructed graphically. In this case, a ' is first obtained from Eq. (7) with the following substitutions: aOx a + ; 7h + 1 ; and TrCI += Th, the baseline transmittance of the ratioed spectrum at ij. The same equation is applied a second time to find a o x ;in this case. a + is substituted for a,,,,, but all other symbols retain their original meanings. The method is much less demanding in terms of the variety of reference specimens required if a sportromefrr with d a f u station (computerassisted spectrometer) is available. Either single-beam or double-beam instruments may be used; in either case. air-reference spectra of the sample specimen and any reference specimen are collected. The technique is similar to the first method described in the previous paragraph except that. in this case, the air-reference spectrum of any reference specimen can be fitted precisely to the air-reference spectrum of the sample specimen by rotation, shifting. and scaling. The baseline is constructed between 1188 c m - and 1032 cni ': it may be constructed automatically by averaging the transmittances of the I S cm-' wide regions around these two wavenumbers. This technique obviates the necessity for having a wide range of reference specimens with different characteristics. The mean measurement error (standard deviation of several measurements) reported by Schomann and Graff (1989) is about 2 2%. Schwenk (1987) also reported finding similar precision. This method is included in the 1993 revision of the DIN oxygen standard (DIN, 1974) as Method B. Shive and Schulte (1984) undertook a pragmatic approach based on the use of a collection of reference standards at 1 ppma (old ASTM) intervals to calibrate commercial FT-I K spectrometers. The oxygen range covered was 30 2 3 pprna (old ASTM). The wafers had a thickness of 381, 508.

-

'

128

W.

M. BULLIS

or 635 pm. Calibration values were found from measurements on doubleside polished quarter sections of the wafers using the single-beam difference method with correction for multiple reflections. They found that a bias of less than 1 ppma was obtained for double-side polished wafers and single-side polished wafers with mechanical back damage or causticetched back surfaces. However, unpredictable biases as much as k 3 ppma (old ASTM) were encountered when measuring single-side polished wafers with acid-etched back surfaces or with back-surface polysilicon films (enhanced gettered). They attributed this problem to the variable reflectivity of these back-surface treatments. Hild and Gaworzewski (1985) derived an expression for the ratio of the transmittance at the baseline of an air-reference spectrum of the sample specimen to the transmittance at the oxygen peak. To evaluate this expression, it is necessary to measure a reflectance spectrum in addition to the transmittance spectrum. Data were collected on 500-pm thick silicon wafers with various back-surface finishes yielding baseline transmittance in the range 20 to 50% and analyzed by (1) the simple ratio method neglecting multiple reflections, (2) this method, and (3) Graff’s method (Graff, 1983) as described in the previous paragraphs. As expected, the apparent oxygen concentrations determined by the simple ratio method increased with increasing baseline transmittance, while both this method and Graff’s method yielded essentially constant values within about ~f: 0.3 x lo” atoms/cm3 (DIN). Thus this method does not appear to provide sufficient improvement to warrant the determination of the reflectance spectrum for each specimen. More recently, Engelbrecht (1990) revisited this issue. He proposes that the reflectance be deduced from the baseline transmittance. His data show a linear relationship between the reflectance of wafers with back surfaces damaged by various grades of Emery paper and the baseline transmittance. However, different functions were obtained from measurements made on three different spectrometers. Further, it is not clear that these results can be generalized to other types of back surfaces, particularly in view of data from Hild and Gaworzewski (1985), which show different reflectance-transmittance curves for different (but unspecified) back-surface conditions, as well as the observations of Shive and Schulte ( 1984). Therefore, the proposed approach seems somewhat unreliable in the absence of further confirming data.

7. FREE-CARRIER ABSORPTION

In sufficient quantities, free electrons and holes in the silicon crystal absorb energy from incoming optical radiation. Spitzer and Fan (1957)

4.

OXYGEN CONCENTRATION MEASUREMENT

129

found that the absorption in n-type silicon increased with both free-carrier density (at a constant wavelength) and wavelength (at a constant density). They also found that the absorption in heavily doped samples did not vary significantly with temperature. Similar dependencies were found in p-silicon by Hara and Nishi (1966). Schumann et al. (1971) reviewed prior literature and added additional data on the dependence of absorption coefficient on free-carrier density. They found absorption in the near infrared in p-type silicon was greater than that in n-type silicon; they also observed that the semi-classical theoretical model for free-carrier absorption (Schumann and Phillips, 1967) did not fit the experimental data at longer wavelengths. Subsequently, Schroder, Thomas. and Swartz (1978) also reviewed the available absorption data and found the following very approximate expressions for the absorption coefficient due to free carriers:

I x 10-'0nlv2,

(20)

afcy= 2.7 x I 0 - ' 0 p l u 2 ,

(21)

afcn=

in n-type silicon and

in p-type silicon for wavenumbers between 2500 and 1000 cm-' and carrier densities from loi6to 10" atoms/cm3. In these equations, afCis the free-carrier absorption coefficient, n and p are the electron and hole densities, respectively, and u is the wavenumber. Weeks (1984) reported that free-carrier absorption at 1107 cm-l in ntype silicon with resistivity below O.S R . cm ( n = 1 x 1016 atoms/cm3) is large enough to affect the oxygen determination. He also notes that at resistivity 50.05 R . cm ( n 2 2 x 10'' cm-j) the reflectivity, R , is affected by the presence of the free carriers, as also noted by Pajot (1977). At very high free-carrier density, the reflectivity goes through a minimum at some wavenumber that is related to the plasma frequency of the crystal: in n-type silicon the reflectivity minimum occurs at 1107 cm-l for an electron density of about 3.6 x 10" atoms/cm3(resistivity = 2 mR . cm) (ASTM, 1992a). Weeks also showed that free-carrier absorption affects the oxygen determination in p-type silicon at resistivity below 1 R . cm. The reflectivity minimum occurs in p-type silicon at I107 cm-' for a hole atoms/cm7(resistivity = 4 mR . cm) (ASTM, density of about 2.7 x 1992a). Gladden and Baghdadi (1986) attribute the errors in oxygen determination introduced by free-carrier absorption to the curvature of the baseline. Accordingly, they obtain a "free-carrier baseline" by taking a difference absorption spectrum between a sample specimen (with free-carrier absorption) and a reference specimen (without free-carrier absorption), thus

130

W.

M. BULLIS

eliminating the phonon contribution to the absorption coefficient; in their experiments all specimens were double-side polished to avoid introducing complications from back-surface scattering. They fitted the free-carrier baseline so obtained to the following expression over the wave number range 1300 to 1000 cm-’, omitting the interval from 1200 to 1060 cm-’ to avoid the 1107 cm-’ oxygen band: Ina,(u)

=

InN

+ mlnu + b,

(22)

where afc(v) is the absorption due to free carriers, u is the wavenumber, N is the free-carrier density ( n or p), m is the slope, and b is the intercept; the reported values of m and b are listed in Table IV. When arC(v)was subtracted from the measured absorption, the baselines became straight and horizontal. In the previously discussed round robin experiment conducted by the U K (Series and Griffiths, 1986), measurements were also made using the short-baseline, integrated-area method developed by Series (1982) on several 500 pm thick boron-doped wafers with resistivity about 0.1 fl . cm and several 350 pm thick antimony-doped wafers with resistivity in the range 0.02-0.03 R . cm. Results are summarized in Table V. Reasonably consistent results were obtained for all specimens with transmittance at 1100 cm-’ 2 0.5%. Oates and Lin (1988) further studied the application of this method to low-resistivity wafers. They compared measurements on n-type wafers with resistivity from 0.015 to 0.022 R . cm andp-type wafers with resistivity from 0.008 to 0.054 1R . cm with secondary ion mass spectrometry (SIMS) measurements using “load line calibration” methodology (Goldstein and Makovsky, 1989; ASTM, 1992b). Because of the low transmittance of heavily doped specimens, the infrared spectrum can be quite noisy. To test for this possibility, Oates and Lin divided the 1120-1090 cm-’ oxygen band into three regions, each 10 cm-’ wide, and calculated an oxygen concentration from each of the regions. Degradation of the spectrum by noise in the measurement is indicated by significant differences between the oxygen values calculated from the three regions. The procedure, which is detailed in an appendix to the paper, is similar to that described in Section IV.2.a except that now three calibrations are required in the oxygen band. All heavily doped wafers tested were double-side polished to avoid additional complications from back-surface scattering. It was found that, if the wafer is thinned to about 200 pm, measurements could be made on n-type specimens with resistivity as low as 0.015 R . cm, and on p-type specimens with resistivity as low as 0.05 R . cm. In all cases, the infrared measurements yielded oxygen concentrations lower (by 0.2 to 3.4 ppma, DIN) than the SIMS measurements; this difference could not be assigned to the presence of

4. OXYGFN (

ON( INTRATION MEASUREMENI

131

132

W . M. BULLIS

TABLE V SUMMARY OF RESULTS OF U K EXPERIMENT ON LOW-RESISTIVITY WAFERS (Series and Griffiths, 1986) Surface Condition

%T at I I 0 0 cm-'

Average [O,], ppma (DIN)

Boron doped, 500 pm thick, 0.1 Cl . cm: 18.44 Chemically thinned 10 16.92 Bright chemical etch I 16.78 Bright chemical etch 4 14.54 Bright chemical etch 3 17.44 Bright chemical etch I 13.58 Bright chemical etch 0.6 Antimony doped, 350 pm thick, 0.02-0.03 R . cm: 9.64 Bright chemical etch I .5 9.06 Bright chemical etch 0.9 9.04 Bright chemical etch 0.5 11.18 Bright chemical etch 0. I

Sample Standard Deviation, ppma (DIN) 0.40 0.42 0.36 0.46 1.10 2.10

1.12 1.60 2.86 9.40

precipitated oxygen. In view of the claimed 2 10% standard deviation of SIMS measurements (Bleiler et al., 1986), the agreement was considered satisfactory. Hill (1990) extended the technique of Shive and Schulte (1984) to the case of single-side polished, n-type wafers with resistivity ranging from 0.02 to 0.05 R . cm and oxygen concentration ranging from about 25 to about 35 ppma.* Because the free-carrier absorption masks the 610 c m - ' silicon peak, the wafer thickness must be determined independently. Standards were prepared from wafers with resistivity about 0.03 R cm, thickness about 675 p,m, and surface finish the same as the wafers to be tested; the oxygen content of these standards was determined by SIMS using load line calibration methodology (Goldstein and Makovsky, 1989; ASTM, 1992b); the standard deviation of the measured oxygen concentration of a high-resistivity standard of known oxygen content was *0.7 ppma during the series of SIMS runs made for the experiment. The software used in the spectrometers employed in the experiment compares the area under the oxygen peak with the area under the oxygen peak of a standard specimen. The standard deviations for oxygen determinations on two heavily doped control wafers over 19 runs were ? 0.13 ppma for *Neither the back-surface finish nor the calibration factor used were specified, but from the data presented in the paper, these can be inferred to be acid etch and old ASTM, respectively.

4.

OXYGEN t O N ( I NrRATlON MEASUREMENT

133

the 0.045 0 . cm wafer and t 0.04 ppma for the 0.026 (1 . crn wafer. The average difference between infrared measurements by this method and SIMS measurements was 0.04 ppma with a standard deviation of 2 0.88 ppma. Measurements on two different instruments yielded an average difference of 0.19 ppma with a standard deviation of 20.51 ppma. Offsets up to 3 ppma were observed between these two instruments when doubleside polished calibration wafers were employed. indicating the importance of using calibration wafers with the same surface finish as the wafers to be measured. An extensive study of free-carrier absorption in both n- and p-type wafers with resistivity less than 5 i1 . cm was recently reported by Koster and Bittersberger ( 1992). They measured free-carrier absorption directly in boron- and phosphorus-doped float-zoned samples with dopant density from I x I O l 4 to 4 x 10’’ atoms/crn’ and various thicknesses from 0.4 to 2 mm. They found that the free-carrier absorption at 1107 c m - ’ could be represented by the following expressions:

in ti-type silicon (for carrier density up to 10’’ atoms/cm3, above which a small quadratic term must be added) and (YfL,’

=

1.43 x IO-lhp,

(24)

in p-type silicon. The free-carrier absorption in p-type silicon is found to be more than four times stronger than in n-type silicon for the same carrier density. These equations, which represent the best current information regarding free-carrier absorption in silicon, are plotted in Figure 8 together with those given by Schroder et al. (1988). The additional absorption due to free carriers affects the correction for multiple reflections because the latter depends on total absorbance. Koster and Bittersberger provide additional correction factors for this effect, which may be employed for determinations of oxygen concentration in n-type silicon with resistivity between 0.5 and 0.1 I I . cm or in p-type silicon with resistivity between 4.5 and 0 . 5 12 . cm. For specimens in these resistivity ranges, typical software routines in commercial infrared spectrometers can correct the baseline adequately; for lower resistivity specimens, reference specimens matched to the sample specimen in thickness and resistivity must be used. Another way to deal with the issue of free-carrier absorption is to trap the carriers on deep centers created by bombarding the specimen with high energy particles, as suggested by Pajot (1977), who used irradiation with fast neutrons to trap carriers excited from boron impurities when making oxygen determinations at low temperatures. Tsuya et al. ( 1985)

W.

1 o-? 10l4

I

loi5

M. BULLIS

I

loi6

Ll

loi7

u

1Ol8

Free Carrier Density (carriers/cm3)

FIG.8. Free-camer absorption coefficient of n- and p-type silicon at 1107 cm-'. The solid curves are from Koster and Bittersberger (1992) and the dashed curves are from Schroder et al. (1978).

showed that irradiation by a 7-MeV electron flux density of 5 x lo'* atoms/cm3 was sufficient to permit determinations of the oxygen absorption in 400 pm thick specimens containing 5 x 10l8antimony atoms/cm3 (pre-irradiation resistivity = 0.01 i2 . cm). In making the determination, it was necessary to account for the oxygen tied up in A-centers created in the irradiated sample. Similar results were also achieved using samples doped with the same amount of phosphorus.

8. INTERFERENCE FROM ABSORPTION PEAKS DUETO PRECIPITATES One of the reasons for measuring oxygen concentration in silicon is to establish the reduction in interstitial oxygen concentration following thermal cycles during which oxygen precipitation may occur. For this purpose, one determination is made before the thermal treatment and the second after it. The amount of oxygen that precipitates is found from the difference of the two oxygen readings (ASTM, 1989). However, wafers that contain precipitated oxygen also exhibit absorption bands characteristic of the various SiO, modifications which form (Tempelhoff, Spiegelberg, and Gleichmann, 1977). Detailed studies of the

4.

O X Y G E N ('ON('ENTKATI0N MEASUREMENT

135

infrared absorption spectra of oxide precipitates have been carried out by Tempelhoff et al. (1979). Hu (1980), and Gaworzewski et al. (1984). For the purposes of this chapter it is sufficient to observe that under certain conditions rather broad bands may appear. One of these bands is centered in the neighborhood of 1220 to 1230 c m - ' and the other is centered i n the range from 1030 to I I10 c m - ' depending on the temperature of the anneal cycle. These bands, which may appear individually or together, can interfere with the establishment of the baseline for the oxygen determination. They can also appear to contribute to the oxygen peak at I107 cm if too wide a baseline is chosen for the determination. The short-baseline curve-fit technique (see Section IV.2.b) has been shown to be successful in determining the oxygen concentration in precipitated wafers (Series, 1982: Series and Livingston, 1986). They also investigated the 515 c m - ' peak. which can be related to the oxygen content in 2-mm thick, double-side polished specimens. The intensity of this peak was compared with the oxygen as determined from the I107 c m band by both the peak-height and short-baseline, curve-fit methods. Measurements were made on 2-mm thick. double-side polished samples with oxygen in the range from 36 to 30 ppma (old ASTM) that were heat treated for varying times at temperatures from 650" to 1050°C to produce residual interstitial oxygen in the range from I to 20 ppma. The peakheight method yielded oxygen values that were too high by as much as 6 ppma; however, the short-baseline. curve-fit method yielded correct oxygen values for wafers heat treated at temperatures up to 1000°C. In the latter case, the precipitate bands can be approximated by straight lines that are incorporated into the linear baseline used in the analysis. A systematic offset (about 2 ppma) observed in the samples heat treated at 1050°C is attributed to changes in the shape of the I107 cm- oxygen band that arise from the pairing of the oxygen atoms as discussed by Shimura et al. (1981). These results suggest that the short-baseline, curvefit method is well suited to analysis of spectra in which the band of interest is superimposed on inteifering bands of unknown shape.

'

9. SPECIMEN TEMPERATURE Temperature effects for small excursions about room temperature were considered in detail in Section 1ll.l.e. As noted there, these effects are larger in dispersive spectrometers than in FT-IR spectrometers because of the larger temperature excursions in the former type of instrument. Oxygen determinations can also be made at cryogenic temperatures, although it is not necessary t o lower the temperature for measurements of oxygen in Czochralski silicon. If the sample is cooled to cryogenic

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W . M. BULLIS

temperatures the 1107 cm-' oxygen band intensifies and narrows. The band maximum shifts to higher wavenumbers and, below 140 K, splits into two distinct bands (Hrostowski and Kaiser, 1956). At 77 K, the more intense band is centered at 1128 cm-'; the relative peak intensity of this band at 77 K is 2.4 (Li, Shen, and Wang, 1983) to 2.6 (Graff et al., 1973) times the intensity of the 1107 cm-' band at room temperature. Measurement of this band enables detection of oxygen down to 20 ppba (DIN). For very sensitive measurements, particularly in float-zoned silicon, Pajot (1977) prefers temperatures below 10 K. Here the 1128 cm-' band has disappeared and the principal line, at 1136.4 cm-', is very sharp (full width at half maximum = 0.6 cm-') and accompanied by two weaker peaks at 1134.5 and 1132.7 cm-', which are due to the less abundant silicon isotopes of mass 29 and 30 (Pajot and Deltour, 1967). For this measurement, thick samples and high resolution are required. In addition, there may be interference from absorption due to electrically active impurities, as discussed in Section IV.7. All the early work was done with dispersive spectrometers; Krishnan and Hill (I98 1) found essentially the same dependencies using an FT-IR spectrometer. V. Absolute Determinations and Calibration Factors

Since infrared absorption is a relative measurement, absolute chemical methods are required to establish the calibration factor that relates the absorption to the impurity content. In addition, since infrared methods are not suitable for measuring oxygen in very low resistivity silicon (see Section IV.7), chemical methods must be used for such measurements. Most substrates for n/n+ and p / p epitaxial wafers for CMOS application cannot be easily measured by infrared absorption. This section briefly reviews chemical methods that have been used in developing the calibration factors for relating the infrared absorption coefficient to the interstitial oxygen concentration. Since chemical methods are sensitive to total, rather than interstitial, oxygen content, it is essential to ensure that all oxygen in the sample for which infrared and chemical measurements are to be compared is in the interstitial state. This can be accomplished by means of a very high-temperature heat treatment (e.g., I h at 1300°C in argon) followed by a rapid quench (> IS"C/min) to room temperature (Jastrzebski et al., 1982). +

1. CALIBRATION FACTORS FOR ROOM TEMPERATURE MEASUREMENTS

Many workers have reported the results of experiments to obtain the calibration factor for oxygen absorption at room temperature. These are

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OXYCitN

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summarized in Table V1. The table lists the number of data points used in developing the calibration factor, the error range specified for the infrared and chemical measurements, the sensitivity limit of the chemical method, the range in oxygen content of the samples used as determined by the chemical method (converted to ppma, if reported in atoms/cm’), and the reported calibration factor. Blank spaces indicate that no information was supplied in the paper. Calibration factors in parentheses were xaled from published graphs, and those in brackets were computed from published data tables. The temperature of the measurement was not indicated in most cases. Barraclough et al. (1986) indicate that their value was obtained at 30°C. Murray et al. ( 1992) conclude that both their value and IOC-88 (Baghdadi et al.. 1989) are referenced to 310 K (37°C). In view of the relatively small temperature coefficient of aOx( - 0.16%’/”C), the systematic error introduced by neglecting the temperature variation over the temperature range 295 t o 3 15 K (22 to 42°C) is on the same order of magnitude as observed multilaboratory measurement reproducibility (Murray et al., 1992). In the initial determinations of oxygen in silicon (Kaiser, Keck, and Lange, 1956; Kaiser and Keck, 1957) vucuum fusion analysis (VFA) was used as the basis of calibration* for the infrared measurements. In this method, the silicon sample is etched in concentrated H F to remove the surface oxide and then melted in a graphite crucible containing liquid iron at 1700°C. forming carbon monoxide, which is detected in a gas analyzer. The claimed accuracy of this technique is 5 2 x lo” oxygen atomsicm’. I n this technique, which was also used by Graff et al. (1973). care must be taken to avoid interference from oxygen in the surface oxide, since any such oxygen is also detected in the instrument. lnerr gus$uion analysis (IGFA) is a similar technique except that the vaporized sample is transported with an inert gas, usually helium. Baker (1970) used this method as the basis of calibration in his study. The results were widely scattered but the resulting calibration curve was accepted for many years (see Section V l ) . The group at the Shanghai Institute of Metallurgy (He et al., 1983; Li and Wang. 1985) extensively refined the IGFA technique, taking great care to prepare samples with smooth surfaces. replacing the iron with nickel-tin to improve the extraction of *‘There is some confusion over the actual value of the calibration factor found by Kaiser and Keck. The value found IS not quoted in the paper. The value given in the table ( 5 . 6 ) was scaled from the published plot of oxygen by VFA against the measured absorption coefficient at I107 c m I. Pajot (1977) quotes a value of 5.7, Baker (1970) quotes a value of 5.76. and the slope of the graph published in the early ASTM standard (ASTM. 1964) is 5.45.In this chapter, the Kaiser and Kecli calibration factor is taken as 5.6 unless otherwise noted.

F

TABLE V1

w

00

OF CALIBRATION FACTOR EXPERIMENTS SUMMARY

Source

Chemical Method(s) Used

No. of Data Points

Kaiser and Keck (1957) Iglitsyn, Kekelidze, and Lazaeva (1965) Aleksandrova et al. (1967) Rook and Schweikert (1969) Kim (1969. 1971) Baker (1970) Gross et al. (1972) Yatsurugi et al. (1973) Graff et al. (1973) Abe et al. (1983) He et al. (1983) H e et al. (1983) Iizuka et al. (1983, 1985) Rath et al. (1984) Chu, Hockett, and Wilson (1986) Barraclough et al. (1986) Regolini et al. (1986) Baghdadi et al. (1989) Murray et al. (1992)

VFA LD CPAA CPAA CPAA IGFA CPAA CPAA VFA CPAA IGFA CPAA CPAA PAA SIMS PAA CPAA CPAA, PAA CPAA, PAA

12 8 3 4 6 99 4 12 8 67 7 22 8

2 21 8 20 6

Stated Error (infrared)

Stated Error (chemical)

Sensitivity Limit, ppma (chemical)

5 4 ppma

10% 20% f 3 ppma
f5%

0.5% 2 2% 21.5% (5%

2 3 ppma 2

15%

t- 2% <15%

f 3% 2

1%

23.5%

0.01 3 0.02 0.01 8
0.6

Oxygen Content Range. ppma (chemical)

Calibration Factor. ppma/cm-

4-33 1-26 5-10 4.8-10.9 11-28 4-35 0.9-28 0.2-8 9-20 7-30 1-18 0.4-22 5-42 12-25 18-25 4-20 0.5-25 0-30 0-2 1

(5.6) [I21 [11.4] l6.21 V.41 9.63 t 2.29 l7.81 (5.9) 4.9 f 0.2 6.0 6.2 2 0.1 6.2 t 0.4 6.06 f 0.04 6.0 f 0.4 6.9 5 0.7 5.22 t 0.6 6.0 f 0.4 6.28 f 0.18 6.04 f 0.38

'

Notes-No information was provided in the published papers for entries left blank. Calibration factors in parentheses were determined by scaling a graph published in the cited paper. Calibration factors in brackets were calculated from tabular data published in the cited paper. In most cases, the number of data points is the number of determinations. However, for those studies that involved contributions from many laboratories (e.g., Iizuka et al., 1983, 1985; Baghdadi et al., 1989; and Murray et al., 1992) each data point represents the average of many determinations. For the SIMS measurement K h u , Hockett, and Wilson, 1986) the stated uncertainty in the ion implant dose calibration is 2 10%.

E

5 W

C r

5

4.

OXYGEN

(

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O N ( t NTKATION M E A S U R E M E N T

T A B L E V11 NUCLEAR REACTIONS FOR No.

1)ETI.Cl.ION

OF

O X Y G E N IN SII.ICON BY CPAA

Activating Particle

Reaction

I

proton ( p )

IHO( p . n ) IKF

2

alpha particle (4He)

"Olu. p n )

3

Helium-3 ('He) Tritium

IhO('He.p)'"F '"0 (.I. n ) '"t:

4

"F

+ "O('He.

n ) I8Ne$

'*F

the carbon monoxide, thoroughly outgassing the graphite crucible, and stabilizing the extraction temperature. In this way, they were able to obtain a background blank reading less than 0.1 kg, data that fell very close to the calibration curve, and a detection limit < I ppma. Iglitsyn, Kekelidze. and Lazaeva ( 1965) utilized the lithium dijfhsion (LD) method described by Pel1 (1960, 1961) as t h e basis of Calibration. They reported significantly higher oxygen concentrations than were obtained by infrared, but the infrared procedures are not defined and the precise calibration factor used is not given. If it is assumed that the procedures and calibration factor are those of Kaiser and Keck (19571, the calibration factor found by lglitsyn et al. is 11.4. Neubrand (1973) used the LD method in conjunction with the measurement of the LiO concentration by electron spin resonance to measure float-zoned specimens with oxygen concentration lower down to less than 2 ppba, which he found as the lower limit of detection for this method. Neubrand also compared the LD method with infrared measurements. In the one example reported, the latter gave a value about 20% higher than that obtained from the LD measurement if the Kaiser and Keck calibration factor is used. This result is opposite t o that found by lglitsyn et al. A number of workers have applied charged purtkle uc'tivation cinulysis (CPAA) to the determination of oxygen in silicon. Schweikert and Rook ( 1970) found three reactions to bc suitable for this determination. These reactions, listed in Table V11. use a primary (activating) particle to convert one of the oxygen isotopes into '*F. The 18F decays by positron emission to "0, with a time constant of I10 minutes and can be distinguished from some, but not all, other reaction products by observing the decay kinetics (Aleksandrova et al.. 1967). Aleksandrova et al. (1967) examined a few samples using helium-3 activation and found that the oxygen concentration measured by CPAA was twice that found from infrared absorption, but the infrared calibration

140

W. M. BULLIS

factor was not stated. Early work in the United States was carried out by Rook and Schweikert (1969), who carefully examined four samples using a-particle activation. They found slightly higher oxygen concentrations than were obtained using the Kaiser and Keck calibration. They also compared measurements by two or more of the suitable reactions and obtained equivalent results to within the stated error of the measurement. CPAA determinations were also carried out by Kim (1969, 1971) and Gross et al. (1972), both using helium-3 activation. In each case, oxygen concentrations significantly higher than those determined by infrared absorption (using the Kaiser and Keck calibration factor) were reported. Nozaki et al. (1974) have also made extensive studies of the CPAA technique for determination of oxygen and other light elements using helium-3 activation. They report a calibration factor slightly larger than that of Kaiser and Keck (1957), based on measurements of samples from 3-in. diameter crystals with very low oxygen concentrations (4ppma). On extrapolation to higher oxygen concentrations, this calibration curve fell below most of the data points; however, samples from quenched crystals fell on the curve (Yatsurugi et al., 1973). This result suggests that the cause of the discrepancy was that some of the oxygen in the unquenched crystals was in the form of SiO, precipitates. A subsequent comparison of infrared absorption measurements with helium-3 activation analysis was made by Abe et al. (1983) on larger diameter crystals that did not contain precipitates. This study showed that the same calibration curve applied to oxygen concentrations as high as 30 ppma. Nozaki’s CPAA measurements were also the basis of the first extensive interlaboratory test of oxygen measurements by infrared absorption, which was carried out in the early 1980s under the auspices of the Japan Electronic Industry Development Association (JEIDA) (Iizuka et al., 1983, 1985) with nearly similar results. He et al. (1983) also examined a number of samples by CPAA using alpha particle activation. They obtained results very close to their IGFA results. More recently, Regolini et al. (1986) found a similar value for the calibration factor using tritium as the activating agent for reaction 4 of Table VII. About the same time, two research groups used photon activarion analysis (PAA) coupled with radiochemical separation by inert gas fusion analysis as the chemical method for establishing the calibration factor. The photons (y-rays) are produced by bombarding a tungsten target with 30-32 MeV electrons, producing photons with energy >16 MeV that excite the reaction: I60(y, n ) 150.The I5O decays by positron emission with a half-life of 2.03 min. IGFA is required to separate the I5O from other positron emitters formed in the activation; this step was done after

4. OXYGFN

(

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O N ( EN TRATION MEASUREMENT

etching of the specimen surfaces to remove activated surface oxide. Rath et al. (1984) fused the sample in a graphite crucible with iron as the metallic band at 2000°C in a helium atmosphere. The oxygen was detected as CO,, which was generated from the CO formed by the reaction of oxygen with the graphite using Schutz reagent, 1205.They found a calibration factor that was somewhat larger than the one found by Barrdclough et al. (1986), who performed the 1GFA step using copper and graphite powders instead of iron and detected the oxygen as CO instead of COz.* Chu, Hockett, and Wilson (1986) derived a calibration factor based on measurements of silicon wafers implanted with oxygen and measured by secondary ion muss specfrometry (SIMS) using a Cs beam. Implant fluences of 5 x lo1 atoms/cm’ were used to ensure that the peak oxygen level (=2 x IO’O atoms/cm3) in the implanted region was much greater than the original oxygen concentration. Good consistency was obtained for the two samples studied by this technique. The first double round robin study was carried out in the mid-1980s under the auspices of a number of standards organizations worldwide (Bullis et al., 1986; Baghdadi et al., 1989; Baghdadi. Scace, and Walters, 1989). Samples were cut from 20 different 100-mm diameter Czochralski crystals grown by commercial silicon producers in the United States, Japan, and Germany. A float-zoned sample (assumed to be oxygen-free to the limit of detection) was also included with the sample sets for the infrared measurements. Absolute chemical measurements were performed at eight laboratories in the United States, Europe, and Japan using either CPAA, PAA. or IGFA. Infrared absorption measurements were made at 18 laboratories in the United States, Europe, Japan, and China. Details of the test methodologies used for each of the techniques are reported in Baghdadi et al. (1989b). The procedures used to obtain the absorption coefficients from the reported infrared spectra are detailed in Baghdadi et al. (1989a). The statistical analysis of these data, also described in detail in the same report. resulted in a value 6.28 ? 0.18 ppma/cm-’, which has been designated as IOC-88. This value is based on data from all the infrared laboratories and from the four absolute laboratories that provided the most consistent results. Data were also taken on sets used in the JElDA experiment (Iizuka et al., 1983, 1985), but these data were not used in deriving the calibration factor. This study drew two conclusions regarding measurement reproducibility. First. the +

*The calibration factor reported by Barraclough et al. 1986) was revised upward slightly following publication of the manuscript (Series. private communication): the value in Table V I I S the revised value.

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W . M. BULLIS

reproducibility of the infrared measurements was very much better than the reproducibility of the absolute measurements. Second, even under the best of conditions, differences on the order of 3% may occur between infrared measurements made in two different laboratories. At about the same time, the BCR conducted a detailed study to calibrate its reference standards (see Section VI). This study was made on samples from three 76-mm diameter crystals. The resulting value for the calibration factor was slightly smaller, but in “good” agreement with the IOC-88 value (Murray et al., 1992). There were some cross links between the measurements made in the BCR study and the study that led to the determination of the IOC-88 calibration factor, but these did not influence the outcome of either study. 2. ROUTINE ABSOLUTE MEASUREMENTS IN HEAVILY DOPEDSILICON Use of epitaxial layers on heavily doped substrates of the same conductivity type for high-density integrated circuits is growing. It has also been recognized that control of oxygen content of these substrates is important for device performance. Consequently, there is a need for a routine measurement technique that can be applied to samples so heavily doped that infrared absorption measurements can not be made. Two techniques have been utilized for this purpose: IGFA and SIMS. a. Inert Gas Fusion Analysis

Walitzki et al. (1986) reported on the use of IGFA procedures for routine analysis of heavily doped n + and p + epitaxial substrates. A modified LECO RO 316 oxygen analyzer was employed for the analysis. In this procedure, square cross-section samples weighing approximately 0.5 g are etched to remove surface impurities and native oxide. They are then introduced into a previously outgassed double-wall graphite crucible together with high-purity nickel as a metal flux and melted at 2200°C. The oxygen is detected as CO. The effects of measurement variations are reduced by taking the mean of five or more individual measurements at each measurement point. IGFA results are generally reported in Fg/g (or ppmw). Conversion from ppmw to ppma involves the ratio of the molecular weight of silicon, ZSi, to the molecular weight of oxygen, Z,, as follows: 1 ppmw = 1.754 ppma.

(25)

1 ppma = 0.570 ppmw.

(26)

Conversely,

4

OYYGFN ( O N C I h I K A I I O N MEASUKEMthT

143

Although IGFA is an absolute technique, Walitzki et al. routinely calibrate the results obtained against the oxygen as determined by infrared absorption using more lightly doped samples. They found that the oxygen concentration, in ppma, determined by infrared absorption (DIN calibration factor) is 0.435 times the oxygen concentration, in ppmw, determined by IGFA. Thus to convert the infrared absorption coefficient to oxygen concentration, as measured by IGFA, would require a calibration factor of 6.42 [ = 4.9/(0.435 x I .754)1 ppmaicm- I, which is only slightly higher than the present consensus value. h. Srcondat-y l o t i Mass Spri.rtornerry

SIMS has been used for some time to determine oxygen profiles in silicon (Rath et al., 1985). Bleiler et al. (1986) describe the extension of SIMS measurements to routine determination of the bulk oxygen content of heavily doped silicon substrates. A Cameca-IMS type ion microanalyzer with a 'j3Cs+primary ion source was used for the measurements. The primary ion beam is focused to a spot about 200 p m in diameter and rastered over a 250 pm x 250 p m area. A relatively high sputtering rate of about 250 A/s is employed. The secondary ion signal is obtained from the central area of the raster, about 85 pm in diameter. Prior to the measurement, the samples are baked in air for 30 min at 100°C to remove adsorbed water. The oxygen signal from the residual gas in the instrument needs to be reduced to as low a level as possible; this is checked by including an oxygen-free float-zoned sample in the load. Typically the background signal is equivalent to 1 ppma or less of oxygen. The intensity of the secondary ion beam due to ' Y o is converted to oxygen concentration using a factor based on the response to a high resistivity Cz sample with oxygen content determined by infrared absorption, which is included in each load. This calibration method, known as the loadfactor mrrhod, provides a load specific factor that reduces the effect of instrumental variations between loads. In the initial stages of the development of this method, up to nine test samples could be included in a load along with the float-zoned and Cz standards; such a load can be analyzed in a 4-hour period. More recently, Goldstein and Makovsky (1989) introduced the "load line calibration" methodology for SIMS measurements. This methodology utilizes two or more, high-resistivity, p-type silicon calibration standards with oxygen content established by infrared absorption measurements. A float-zoned reference is also measured to ensure that the instrumental background is reduced to the desired level, but this measurement is not used for establishment of the load line. The method can be extended to monitor load-to-load reproducibility by including an addi-

144

W . M. BULLIS

tional calibration standard with known oxygen content, which is tested as an “unknown.” For the run to be accepted, the measured oxygen content of this standard must agree with its known value to within a predetermined range. If the load line is calculated from three standards, a significant improvement in measurement reproducibility can be achieved; Makovsky, Goldstein, and Chu (1989) show that with this method load-toload measurement reproducibility is better than ? 2%. Bleiler et al. (1989) have shown that matrix effects that might result from the difference in doping level between the samples used for calibration and the heavily doped substrates do not affect the accuracy of the measurement. Throughput has also been increased with the use of a 16-specimen holder that can be analyzed in the same elapsed time as the earlier smaller load. VI. Standards and Reference Materials

I . STANDARD TESTMETHODS ASTM Committee F- 1 on Electronics developed the first standardized test method for oxygen content of silicon. This method, adopted in 1964 (ASTM, 1964), was an air-reference method, based on the work of Kaiser and Keck (1957). It required thick (1-3 mm) slices polished on both sides; analysis of the spectrum recognized the possibility of multiple reflections. Calibration was provided in the form of a graph that allowed for the fact that the lattice absorption at 1107 cm-’ must also be taken into account. Since no numerical factor was given in the method, there has been some inconsistency in interpretation of the calibration.* In 1970, ASTM changed the recommended method to a double-beam difference method, ignoring effects of multiple reflection (ASTM, 1970b). The calibration factor cited in this standard was 9.63 ppmalcrn-’. This factor, which was based on the work of Baker (1970), later came to be known as the old ASTM factor. The method, which was coupled to a general procedure for infrared absorption measurements in semiconductors (ASTM, 1970a), remained in place until 1988, but the calibration factor was changed to 4.9 ppma/cm-’ in 1980. This smaller factor, known as the new ASTM or DIN factor, was based on the work of Graff et al. (1973); it was chosen by ASTM in order to bring the ASTM method into correspondence with the test method adopted by DIN Committee NMP 221 (DIN, 1974), which had cited this value for the calibration factor since its initial approval. Following completion of the experimental work in the international round robin experiment (Baghdadi et al., 1989), ASTM Committee F-1 *See the first footnote in Section V. I .

4.

OXYtiEN

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145

undertook complete revision of the oxygen test methods. First. ASTM Practices F 120 (ASTM, 1987) were revised completely to explicitly include the use of FT-IR as well as dispersive spectrometers and to account for the effects of multiple reflections in double-side polished samples, which were still required to carry out the procedure. The following year, two additional test methods (ASTM, 1988a, 1988b) were adopted. The first of these, ASTM Test Method F 1188, embodied the procedures used in analyzing the international round robin experiment. The method requires 2-mm thick, double-side polished samples; it is based on the double-beam difference method but it does take account of multiple reflection effects. The spectrometer is not required to have computer control, but use of a computer significantly simplifies the procedure and analysis. The second, ASTM Test Method F 1189 (ASTM. 1988b3, requires the use of a computer-assisted spectrometer and can be used on double-side polished samples as thin as 0.3 mm. Computer programs for analysis of the data in accordance with this method have been made available by the National Institute of Standards and Technology (Gladden et al., 1988). About the same time, DIN Committee NMP 221 began a major revision of DIN 50 438, Part I (DIN, 1974) to include new work on thin, single-side polished wafers. A tentative revision was published in 1990; after further revisions and clarifications the fully approved revision was published in 1993. All these recent revisions cite the IOC-88 calibration factor, 6.28 ppma/cm- I , based on the results of the international round robin experiment, as does the Guo Biao standard adopted by the Peoples Republic of China. ASTM has also standardized the SlMS method for measuring oxygen in heavily doped substrates (ASTM. 1992b). This standard includes both the load factor and load line calibration procedures.

2 . CERTIFIED REFERENCE MATERIALS Several national laboratories have issued certified reference materials (CKMs) to assist in improving the reliability and reproducibility of measurements of oxygen in silicon. The first such CRMs were issued by JEIDA in 1985. When issued. these CRM sets were based on the calibration factor (6.06 ppma/cm- '1 found in the JEIDA interlaboratory test (lizuka et al., 1983, 1985). Each set consisted of four 2-mm thick. doubleside polished slices, 50 mm in diameter (Inoue et al., 1986). Nominal oxygen levels were 0 (float-zoned reference), 12, 16, and 20 ppma (JEIDA factor). Because absorption coefficients were provided on the certification, these may also be calibrated to the IOC-88 factor.

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In 1990, the BCR of the Commission of the European Communities issued CRMs for the oxygen measurement. These are supplied in two parts. CRM 368 is a low oxygen content float-zoned reference standard (Vandendriessche et al., 1990). This CRM is a 51-mm diameter, 2-mm thick, double-side polished slice with 69 19 ng/g (0.121 k 0.033 ppma) oxygen. CRM 369 consists of three 76-mm diameter, 2-mm thick, doubleside polished slices with nominal oxygen contents of 13.2, 18.7, and 24.1 ppma (IOC-88) (Vandendriessche et al., 1991). The relative transmittance for each sample was determined by the double-beam difference method by a single laboratory taken as the “pilot” laboratory. In addition, selected samples were measured in a four-laboratory round robin experiment to obtain the best achievable accuracy. In this experiment, only results from dispersive infrared spectrometers were used. The relationship between the interlaboratory and pilot laboratory results was used to calculate the certified value of relative transmittance at a reference temperature of 310 K. The stated uncertainty for the relative transmittance determination is 0.004 for all samples. Certified values of the oxygen mass fraction as determined by CPAA were obtained from measurements on representative samples. The stated uncertainties for the oxygen mass fraction are 0.5, 0.6, and 0.7 ng/g (0.88, 1.05, and 1.23 ppma) for the low, medium, and high oxygen samples, respectively. The US National Institute of Standards and Technology (NIST) is developing oxygen standard reference materials which were issued in the spring of 1994 under the designation SRM 2551 (Rennex, 1994). Each set consists of four double-side polished, 2-mm thick silicon samples, each 25 mm x 25 mm in area. Three of the samples were cut from the central region of 3-in. or 100-mm diameter Czochralski crystal sections with room temperature resistivity > 3 R cm; nominal oxygen concentrations were 17, 23, and 26 ppma (IOC-88). The reference specimen was cut from a float-zoned crystal with oxygen concentration less than that quoted for BCR CRM 368. Comparison measurements were made with test specimens evaluated in the international oxygen round robin experiment (Baghdadi et al., 1989) in order to establish the oxygen concentrations. In conducting the certification measurements, emphasis was placed on spectrometer reproducibility rather than on the uncertainty in the oxygen determination. The single-beam difference method was employed and the determinations were made from analysis of the peak heights of absorption spectra suitably corrected for multiple-reflection effects. The measurements were made on a Model MB-100 Bomen FT-IR spectrometer, a small instrument with very rigid construction, which is important for achievement of high precision. Resolution of 4 cm-’ and a 2-mm diameter

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DTGS room-temperature detector were used. The specimens were located 50 mm behind the focal point of the optical beam and the beam diameter at the sample position was 5 mm. A light cone was placed in front of the detector to eliminate errors due to spatial nonuniformities of the detector response. This nonuniformity was found to be the largest single source of measurement imprecision. N o effects that could be attributed to the emissivity problems noted in the BCR study (Murray et al.. 1992) were observed. The precision of the FT-IR measurements was found to be about 0.15% as compared with the 6% uncertainty in the absolute determinations. The same instrument and analysis procedures were applied to a BCR CRM 369 set; results obtained were within 1%' of the stated oxygen concentration. V11. Summary

Routine measurement of oxygen in silicon can be accomplished with state-of-the-art Fourier-transform or dispersive infrared spectrometers on silicon wafers that are not too heavily doped. However, there is still some disagreement as to values obtained from different instruments and on samples with different surface preparation. Despite the recent appearance of certified reference materials for this determination and the recent revisions of the DIN standard test procedure, some additional standardization effort remains to be completed, both for the infrared absorption and the routine chemical methods. Activity is now in progress in Japan, within the Silicon Wafer Committee of Semiconductor Equipment and Materials International (SEMI). to develop a standard test procedure for the Brewster angle method (Shirai, 1991, 1992). Further work is required on the ASTM standards to extend them to single-side polished wafers and to account for the nonnormal incidence angle of modern FT-IR spectrometers. Further development of the SIMS method is also required to provide procedures for assuring that the wafers used for calibration meet the desired uniformity characteristics. The existing standard test method for oxygen uniformity (ASTM, 1985) provides sampling plans that are too coarse for this application. In addition, development of a standard method for IGFA would be a useful addition to the standards literature. A(XNOWI.EIX;MENTS The author would like to acknouledge u5eful divxssions with many individuals on various aspects of oxygen measurements in vlicon over the years. including A. Baghdadi. B. Rennex. and K. I . Scace of NIST. M . Kulkarni of IBM. K . Krishman of BioRad. K. Graff

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of Telefunken Microelectronic, R. Boyle and J. Steele of Nicolet, M. Watanabe of Toshiba ULSI Laboratory, Y.Li of Shanghai Institute of Metallurgy, R. Series and K. Barraclough of RSRE. He would also like to thank K. Graff, B. Pajot of UniversitC Paris VII, and R. Murray of Imperial College for a preprint of their article on the BCR study and K. Nishikida of Perkin Elmer and R. Boyle for furnishing illustrations of infrared spectrometers.

REFERENCES Abe, T., Gotoh, S., Ozawa, N., and Masui, T. (1983). In Silicon Processing, ASTM STP 804, D. C. Gupta (ed.), pp. 469-476. ASTM, Philadelphia. Aleksandrova, G. I., Demidov, A. M., Kotel’nikov, G. A,, Pleshakova, G. P., Suhov, G. V . , Choporov, D. Y., and Shmanenkova, G. I. (1967). Atomnayu energiya 23, 106-109 [in Russian]. ASTM. (1964). “Tentative Method of Test F 45 for Oxygen Content of Silicon.” (Discontinued 1970.) ASTM. (1970a). “Standard Practices F 120 for Determination of the Concentration of Impurities in Single Crystal Semiconductor Materials by Infrared Absorption Spectroscopy.” (Revised completely in 1987; see ASTM, 1987.) ASTM. (1970b). “Standard Test Method F 121 for Interstitial Atomic Oxygen Content of Silicon by Infrared Absorption.” (Note-In 1980, the calibration factor between peak absorption at 1107 cm-’ and the interstitial oxygen content used in this method was changed from 9.63 ppmalcm-’ (old ASTM) to 4.9 pprnalcm-’ (new ASTM or DIN). Discontinued in 1990.) ASTM. (1985). “Standard Test Method F 951 for Determination of Radial Interstitial Oxygen Variation.” Annual Book of ASTM Standards, Vol. 10.05. Published annually by ASTM, Philadelphia. ASTM. (1987). “Standard Practices F 120 for Determination of the Concentration of Impurities in Single Crystal Semiconductor Materials by Infrared Absorption Spectroscopy.” Annual Book of ASTM Standards, Vol. 10.05. Published annually by ASTM, Philadelphia. (Note-These practices were revised completely in 1987; to distinguish between the two standards, a new citation is placed here. The background material on multiple reflections was inadvertently lost in the revision: it was returned to the standard in 1988 as Appendix XI.) ASTM. (1988a). “Standard Test Method F 1188 for Interstitial Atomic Oxygen Content of Silicon by Infrared Absorption.” Annual Book of ASTM Standards, Vol. 10.05. Published annually by ASTM, Philadelphia. ASTM. (1988b). “Standard Test Method F 1189 for Using Computer-Assisted Infrared Spectrophotometry to Measure the Interstitial Atomic Oxygen Content of Silicon Slices Polished on Both Sides.” Annual Book of ASTM Standards, Vol. 10.05. Published annually by ASTM, Philadelphia. ASTM. (1989). “Standard Test Methods F1239 for Oxygen Precipitation Characterization of Silicon Wafers by Measurement of Interstitial Oxygen Reduction.” Annual Book of ASTM Standards, Vol. 10.05. Published annually by ASTM, Philadelphia. ASTM. (1992a). “Standard Test Method F 398 for Majority Carrier Concentration in Semiconductors by Measurement of Wavenumber or Wavelength of the Plasma Resonance Minimum.” Annual Book of ASTM Standards, Vol. 10.05. Published annually by ASTM, Philadelphia. ASTM. (1992b). “Standard Test Method F 1366 for Measuring Oxygen Concentrations in

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CHAPTER 5

Intrinsic Point Defects in Silicon S.M .

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DEFECTMANIFESTATION O F INTRINSICPOINT DEFECTS 11. SWIRI. DEFECTSI N SII.I( ON . . . . . . . . . . . . . 111. THERMAL 1v.

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is that of acting as vehicles of atomic transport processes such as diffusion and certain activated processes such as the dynamics of solid deformation. They also serve as progenitors of extended crystalline defects such as point defect clusters, stacking faults and dislocations, which are harmful to semiconductor devices. Of particular interest to the reader of this book is their role in oxygen precipitation and vice versa. In 1977, it was accidentally discovered (Hu, 1977b) that oxygen precipitation is retarded when silicon specimens are annealed in oxidizing ambients. A subsequent detailed investigation confirmed this phenomenon (Hu, 1980a). It had by that time already been established (Hu, 1974) that thermal oxidation of silicon causes excess self-interstitials to be injected into the silicon substrate. Together with the well-known fact that the agglomeration of interstitial oxygen atoms into SiO, precipitates produces local strain, it was proposed (Hu, 1980a) that oxygen precipitation can be modeled by the reaction 2x0,

+ ySis GS

xSi0,

+ (y

-

x)Si,,

where the subscript I indicates an interstitial configuration. An excess of silicon self-interstitials causes this reaction to shift to the left, consequently retarding the precipitation. Various experimental observations have since confirmed the precipitation-retardation effect of oxidizing ambients (Schaake, Barber, and Pinizzotto, 1981; Craven, 1981; Oehrlein, Lindstroem, and Corbett, 1982; Tan and Kung, 1986). Conversely, oxygen precipitation may cause the generation of self-interstitials, as given in the forward direction of the reaction. This prediction has also been confirmed by observations of the growth of stacking faults (Hu, 1980b; Rogers et al., 1989; Rogers and Massoud, 1991a; Shimura, 1992) and the enhanced diffusion of phosphorus and the retarded diffusion of antimony (Kennel and Plummer, 1990) accompanying oxygen precipitation. In silicon heavily doped with antimony, the precipitation of oxygen has been found to be retarded (de Kock and van de Wijgert, 1981; Tsuya, Kondo, and Kanamori, 1983; Shimura et al., 1985). Various explanations have been proposed. One explanation (Wada and Inoue, 1986; Bains et al., 1990; Gupta et al., 1992) is that the oxygen thermal donor is the precursor of an embryonic precipitate (Ourmazd, Schroter, and Bourret, 1984), and that the rate of formation of thermal donor is reduced by a high electron concentration (cc n - * ) (Wada, 1984). Other explanations invoke the roles of point defects in precipitate nucleation (de Kock and van de Wijgert, 1981; Shimura et al., 1985). For example, it was suggested (Shimura et al., 1985) that the suppression of oxygen precipitation may be caused by the complexing of lattice vacancies with antimony atoms,

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thereby reducing the availability of vacancies required for precipitate nucleation. Diffusion in silicon has been extensively investigated since the mid 1950s. Until 1968, it had always been assumed, implicitly or explicitly, that the point defect that mediates diffusion in silicon is the vacancy. A “regular” interstitial is conceptually one that wanders through lattice interstices all by itself without displacing lattice or substitutional atoms. But diffusion by an interstitiu/(.y mechanism was already suggested by Seitz (1950). Seitz was discussing generic diffusion without reference to specific materials. Experimental diffusion data in metals tend to indicate a preponderance of the vacancy mechanism. Seeger and Chik (1968) argued that self-diffusion in silicon at high temperatures. as well as diffusion of group 111 and V dopants, most likely proceed via an interstitialcy mechanism rather than a vacancy mechanism. But no unequivocal experimental evidence was given in support of this speculation. Hu (1974) proposed that both vacancies and self-interstitials actually coexist as two basic intrinsic point defects in silicon of essentially equal importance and that diffusion of substitution impurities in silicon proceed via a dual vacancy-interstitialcy mechanism. The contribution of the interstitialcy mechanism as a fraction to the total diffusivity varies with dopant species. Hu arrived at this conclusion by bringing together the phenomena of enhanced diffusion and generation of stacking faults in the thermal oxidation of silicon, and analyzing their common features and causal relations such as the effects of surface orientation and oxidizing ambients. A second proposition was made at the same time that thermal oxidation generates excess silicon interstitials. This proposition is essential for the experimental observation of the oxidation enhanced diffusion (OED) and the formation of oxidation stacking faults (OSF). In a later section, we will discuss the facts and the reasoning leading to this conclusion. Since then, many phenomena have been discovered which have been explained very well by this model. Most of these phenomena are related to the discoveries of additional sources of generation of nonequilibrium point defects and their annihilation. Some sources generate excess vacancies, while others generate excess self-interstitials, affecting the diffusion of different dopants in different ways according to the dopants’ characteristic interstitialcy components. Knowledge about the relative contributions of the vacancy and the interstitialcy to the diffusion of a dopant becomes crucial for the prediction of diffusion profiles in presence of nonequilibrium point defects. Many of these phenomena have been discussed very thoroughly in a recent review by Fahey, Griffin. and Plummer (1989a). Two other fairly recent reviews (Frank et al., 1984; Hu, 1985) should also be of interest to the reader.

156

s. M. HU 11. Swirl Defect Manifestation of Intrinsic Point Defects

As a new part of a silicon crystal is freshly grown from a melt, it contains equilibrium concentrations of vacancies and self-interstitials, as well as their complexes. As that part of the crystal moves away from the melt and becomes colder, the majority of these grown-in point defects become excess over their new equilibrium concentrations at a lower temperature, and are subject to population reduction. In a crystal that is substantially dislocation free, the only avenues open to their depopulation are the vacancy-interstitial annihilation, and the agglomeration among like species themselves into extended defects. This is in contrast to the fate of excess point defects in thin silicon wafers, in which they can depopulate, beside via vacancy-interstitial annihilation in the bulk, by escaping to the wafer surface and thereby vanish. (We should note, however, that the occasional presence of nucleation centers, typically stress centers, may induce the excess point defects to agglomerate, even in thin wafers, into extended defects. A prime example is the formation of oxidation stacking faults.) These more macroscopic microdefects, as they are commonly called, can readily be examined visually by a number of techniques such as preferential etching, copper-decoration, and transmission electron miscroscopy (TEM). These microdefects are usually distributed throughout a crystal in a striated pattern, due to the nonuniformity in the temperature field in the crystal growth environment in which a crystal rotates during growth. As the solid-melt interface is usually concave, the distribution of these microdefects on a flat-cut surface of a wafer exhibits swirl pattern from preferential etching. For this reason, these microdefects are also referred to as swirl defects. Plaskett (1965) first reported the occurrence of what were thought to be clusters of vacancies in the inner region of a silicon crystal. The width of the cluster-free outer ring of a wafer cut from the crystal is about 1.5 mm, which was thought to be indicative of the vacancy diffusion length in the temperature transient during the growth. Abe, Samizo, and Maruyama (1966) first reported the distribution of shallow etch pits of microdefects in swirl patterns. Swirl defects were first studied in detail by de Kock (1973). He noted two kinds of such microdefects, which he termed type A and type B. These were conjectured to be clusters of point defects or clusters of complexes of impurities and point defects. A-defect is, relatively speaking, quite large and can be readily examined by TEM. Subsequently, FOll and Kolbesen (1975) identified the A defects as an interstitial type dislocation loops. From this observation, they proposed that the dominant intrinsic point defect in silicon is the self-interstitial. The A defects would form from the agglomeration of excess self-

5

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P O I N I DFFFCTS I N SILICON

157

interstitials that had been left after vacancy-interstitial annihilation. The B-defect could not be characterized by TEM; but such defects can be revealed in their spatial distribution by means of selective etching or metallic decoration. Hu (1977a) suggested an alternative model of swirl defect formation: The excess vacancies and self-interstitials do not annihilate completely, and significant fractions of the excess populations of both species agglomerate, separately and in parallel, into the A- and the B-defects. The larger A-clusters are agglomerates of self-interstitials in the form of dislocation loops ( interstitial-type disks), while the smaller B-clusters, as yet unidentified, are agglomerates of vacancies in the form of small globules. There is a simple reason for the preference of interstitial-type extended defects to take disk shape: it is the geometry of minimum strain energy for a mismatched inclusion in a matrix, as shown by Nabarro (1940). An interstitial type inclusion represents an insertion of extra matter into a matrix and consequently produces a normal compression against the host matrix. A spherical cavity, by contrast, produces no. or very little. strain in the host matrix. It is for this reason that it cannot be detected by TEM (aside from a small change in matter density). For vacancy clusters. the spherical cavity is therefore the geometry of minimum energy, in both the strain energy and the surface energy components, and is the preferred form. A plausible explanation for the separate agglomeration of excess vacancies and self-interstitials among like species is that there may exist an energy barrier to the vacancy-interstitial recombination. One can see the rationale of the existence of a recombination barrier if one recognizes that the equilibrium configurations of the vacancy and the interstitial involve relaxation of atomic structure surrounding each defect (Hu. 1977a). From a study of the enhancedretarded transients of antimony diffusion under thermal oxidation. a recombination energy barrier of = I .4 eV has been estimated (Antoniadis and Moskowitz, 1982). As an alternative, an entropy barrier for vacancyinterstitial recombination has been proposed (Gosele, Frank, and Seeger, 1982). The idea derives from the suggestion (Seeger and Chik, 1968),that, at high temperatures, the silicon self-interstitial is an extended structure of a disordered region; and so, too, may be the vacancy. An extended point defect is one of the explanations for the very large preexponential factor experimentally found for the silicon self-diffusion. It is argued (Gosele et al., 1982) that the vacancy-interstitial recombination event is preceded by the reordering of the structures of both point defects that results in a negative entropy of about - I I .5 k. The vacancy-interstitial recombination will take place, regardless of which or both barriers: but the rate of recombination may not be fast enough to prevent self-agglomeration of vacancies and self-interstitials in parallel. De Kock and van de Wijgert

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(1980) have endorsed such a model for the formation of the A- and the B-defects. An alternative model (Petroff and de Kock, 1976; Fall, Gosele, and Kolbeson, 1977; Roksnoer, 1984) is that the self-interstitial is the predominant point defect in silicon at high temperatures, and that Bdefects are interstitial agglomerates that would collapse into A-defects. Two more types of microdefects, the C-defect (de Kock, Stacy, and van de Wijgert, 1979) and the D-defect (Roksnoer and van den Boom, 1981) have later been reported. The C-defect seen only sometimes, is somewhat of a mystery. The D-defect, like the B-defect, is very small and in general invisible to TEM. Nonetheless, Roksnoer and van den Boom suggested that it results from agglomeration of vacancies, a view that has received support from many subsequent investigators. However, a contrary view has been expressed by the Ioffe group (Sorokin et al., 1991), who reported that strain contrast of microdefects can be obtained with high-resolution electron microscopy and that all microdefects, including the D-defect, are of an interstitial type. Their model of microdefect formation is as follows: In regions of vacancy excess, vacancies will create complexes with interstitial oxygen atoms (not self-interstitials) to form D-defects. In regions of interstitial supersaturation, self-interstitials, oxygen, and carbon atoms agglomerate to form B-defects that, with further addition of self-interstitials, become A-defects. At present, a definitive conclusion about these microdefects remains unavailable. Under the experimental conditions of Roksnoer (1984), who grew his crystals by the pedestal method (somewhat similar to the floating-zone method), D-defects will not form until the crystal growth rate exceeds 5.4 mm/min. In contrast, A- and B-defects may start to form at a crystal growth rate of S0.2 mm/min, but will not form when the growth rate exceeds 4.5-5.0 mm/min. The threshold growth rates for the appearance and disappearance of various types of microdefects depend strongly on the diameter of the crystals and the method of crystal growth. For example, it has been reported that (Yamagishi et al., 1992), in their Czochralski crystals, D-defects start to appear at a growth rate of 5 0 . 8 mm/min. It should be noted that there are many differences between float-zone and Czochralski silicon crystals aside from the higher oxygen content in the latter. The temperature distribution during the growth is also quite different. While it would seem that the threshold growth rate may be indicative of the diffusion-limited annihilation velocity of a particular point defect species at the melt-crystal interface, model analysis is predicated on the appropriateness of assumptions. Voronkov (1982) has given estimates for C , , D,, C,, and D, from just such an analysis. But Voronkov’s formulation of the swirl defect formation is an oversimplification, considering the crystal velocity from the interface and the concentration gradient as the

5.

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IWIN I Ut~FECTSI N SILICON

159

only factors driving a point defect flux. Among the more important factors ignored is the thermal diffusion in a rapidly varying temperature field along the crystal axis. Also, the effect of impurity atoms on the formation of swirl defects. as has been noted by many researchers, was also not taken into account in Voronkov’s formulation. At the present time, there is still no satisfactory model for the formation of the various types of swirl defects, but they are undoubtedly manifestation of intrinsic point defects. There have been relatively few investigations of swirl defects in Czochralski silicon crystals. Most results (de Kock et al., 1979; de Kock and van de Wijgert, 1980; Pimentel and BritoFilho, 1983; Harada, Abe, and Chikawa, 1986; Yamagishi et al., 1992) seem to indicate similar behaviors in the formation of microdefects in both kinds of crystals. Hence. at the present time, it is difficult to assess the role of oxygen in the formation of microdefects. 111. Thermal Defects in Silicon

The subject of “thermal defects” in silicon has a rather interesting and protracted history. Since the first observation reported by Gallagher (1955), various investigators have reported that, when a silicon substrate is heated at some high temperatures (generally, 5800°C) for some length of time and then quenched, a significant concentration of deep-level donors is introduced into the substrate. These deep-level centers have since been called thermul defects. Early speculations on the identity of these centers range from silicon self-interstitials (Bemski and Dias, 1964) to vacancy clusters (Elstner and Kamprath, 1967; Boltaks and Budarina, 1969). In the investigation of Boltaks and Budarina (19691,the concentration of the thermal point defects was derived from measurements of the change in specimen density and lattice constant after quenching. Both Elstner and Kamprath (1967) and Boltaks and Budarina ( 1969) reported the energy of formation of “vacancy” to be 2.5-2.8 eV. Quenching experiments for the investigation of native point defects in silicon have proven to be difficult and unreliable. Unlike in most metals, the concentrations of both the self-interstitial and the vacancy are very low. The change in the length of a specimen is related to the change in the volume of the specimen by A l / l = AVC’I(3V). For an increase of the vacancy the length of a silicon specimen increases concentration by 1 x 10“ cm by less than 0.7 x lW7. a change too small to be measured accurately. Furt hermore. silicon samples can be easily contaminated by fast diffusing impurities such as copper, nickel, and iron, which can diffuse through silica furnace tube at high temperatures. While the opinions of various investigators diverged, their experimental results exhibit a high degree of

’,

160

s. M. nu

agreement. The donor level observed in various investigations was in a narrow neighborhood around ( E , + 0.40) eV. Various investigations since 1977 (Gerson, Cheng, and Corbett, 1977; Lee, Kleinhenz, and Corbett, 1977; Weber and Riotte, 1978; Feichtinger, Waltl, and Gschwandtner, 1978; Rijks, Bloem, and Giling, 1979; Weber and Riotte, 1980; Graff and Pieper, 1981; Glinchuk and Litovichenko, 1981), however, have led to the general consensus that the “thermal defects” are after all not native defects or their clusters but are contaminants from the furnace, passing through silica tubes, and getting into the silicon substrates. It may be remarked that Collins and Carlson (1957) already expressed their suspicion that there could be a connection between the thermal defects observed by Gallagher and the iron donor in silicon that they studied, because of their many similarities. IV. Self-Diffusion 1 . POINT DEFECTS AND SELF-DIFFUSION

Random movements of vacancies or self-interstitialcies give rise to self-diffusion: (1) DSC, = 4”D”CV 4- 4,D,CI, where D,, D,, and D, are the self-, vacancy, and interstitialcy diffusivities, and Cs, C,, and C , are the lattice site, vacancy, and interstitialcy concentrations, respectively. The terms 4v and 4, are the vacancy and the interstitialcy correlation factors, respectively, applicable to the diffusion of labeled lattice atoms occurring only in self-diffusion experiments. All other processes such as the Kirkendall effect, the shrinkage of stacking faults, the dynamic deformation-recovery , etc., involve the selfdiffusion of “normal” unlabeled host atoms for which the correlation factors are inapplicable and should be dropped from Eq. (I). As indicated in Eq. ( l ) , the self-diffusivity is a combination of the concentrationdiffusivity products of the vacancy and the self-interstitialcy. A possible contribution of Pandey’s (1986) concerted-exchange mechanism has not been included in Eq. (1). At the present time there is no experimental data in support of this model. In most materials, usually one species, either the self-interstitial or more often the vacancy, is overwhelmingly dominating and is the only species that needs to be considered for all practical purposes. It is one of nature’s fortuities that, in silicon, the vacancy and the self-interstitial are equally important, at least in the temperature range of practical interest. Two important properties of a point defect species are its concentration and diffusivity under intrinsic and equilibrium condition at a given temperature

5.

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161

where the subscript X represents either I or V, SL and S; are the entropies of formation and migration, respectively, and H i and H," are the enthalpies of formation and migration. (Except in cases under high externally applied stress, we will use the internal energy, o r simply energy, in lieu of enthalpy.) Here, vo is the normal mode frequency, and r is the atomic jump distance. The asterisk denotes parameters under intrinsic (infinite dilution) equilibrium conditions. It follows that

Thus, the activation energy of self-diffusion Q is given by E.; + E," of whichever point defect species that dominates in a particular temperature range. 2 . SELF-DIFFUSION FROM ISOTOPEEXPERIMENTS Self-diffusion in silicon has been investigated experimentally over the years since the mid-1960s. The self-diffusion of silicon is very slow, so earlier experiments were usually carried out at temperatures 5 IIOWC. The activation energy of self-diffusion obtained from these experiments of varied methods falls in the rather narrow range of 4.8-5.1 eV (Peart, 1966: Masters and Fairfield, 1966; Mayer, Mehrer, and Maier, 1977). Later investigations extended to lower temperatures reported different activation energies. While Kalinowski and Seguin (1979) reported an activation energy of 4.7 e V in the temperature range 855-1175"C, Hirvonen and Antilla (1979) and Demond et al. (1983) reported activation of about 4.1-4.2 eV in the low-temperature range. Furthermore, Demond et al. (1983) also reported a break in the Arrhenius plot at about 1 100°C, with an activation energy of 4.9 eV in the high-temperature regime. A similar break in the Arrhenius plot for germanium diffusivity in silicon was reported by Hettich, Mehrer, and Maier (1979). There may be some similarity between germanium diffusion in silicon and silicon self-diffusion. The transition from the low-temperature to the high-temperature activation energy has been ascribed to a transition from a vacancy-dominated to an

162

S. M . HU

interstitialcy-dominated diffusion, a concept first introduced by Seeger and Chik (Seeger and Chik, 1968; Frank et al., 1984). This implies Efy -k E P - 4 e V E; -k E r

- 5eV.

This set of hypothesized relations has in many cases served as constraints for the seeking to separate EG, E;, E;, and E," by model fitting of diffusion profiles. In order for the interstitialcy mechanism to operate at high temperatures, it is necessary that the sum of entropies for formation and migration be much larger for the self-interstitial than for the vacancy. It is not possible to deduce from these experiments of self-diffusion to identify the point defect that represents the dominant term on the righthand side of Eq. (1). Only experiments of self-diffusion carried out under controlled conditions of point defect supersaturations can help resolve this issue. While so far no such experiment of silicon self-diffusion has been carried out, an indication of nearly equal vacancy and interstitialcy contributions to silicon self-diffusion may be inferred from the investigation of Fahey, Iyer, and Scilla (1989b) on germanium diffusion in silicon under separate conditions of vacancy and interstitial supersaturations.

3 . SELF-DIFFUSION FROM KINETICS OF EXTENDED DEFECTS The activation energy and the self-diffusivity from these investigations based on direct measurement of the diffusion of silicon isotopes generally agree quite well with those inferred indirectly from defect kinetics that are controlled by self-diffusion. Some examples include the kinetics of shrinkage of dislocation loops (Sanders and Dobson, 1974), the annealing of preexisting oxidation stacking faults (Hashimoto et al., 1976; Sugita et al., 1977; Shimizu, Yoshinaka, and Sugita, 1978; Claeys, Declerck, and van Overstraeten, 1979; Lin et al., 1981; Nishi and Antoniadis, 1985; Rogers and Massoud, 1991b),and dynamic deformation-recovery (Brion, Schroter, and Seithoff, 1979). The activation energy of self-diffusion from most of the annealing studies of preexisting stacking faults are in the range 4.6-4.9 eV. In the somewhat lower temperatures range investigated by Sanders and Dobson (1974) (970-1070°C) and Nishi and Antoniadis (1985) (950-1O5O0C), an activation energy of 4.1-4.3 eV was obtained. The dynamic recovery gives an even smaller activation energy of 3.6 e V in the temperature range 850-1100°C (Brion et al., 1979). The author is not aware of any data available for self-diffusion at even lower temperatures. While the activation energy obtained from defect kinetics quite

5.

INTRIN\I(

163

POINT DI-FFCTS IN SILICON

accurately represents the activation energy of silicon self-diffusion, the preexponential factor of self-diffusion so obtained is much less reliable. This is because the kinetics of defect shrinkage comprises many unknown factors, and its formulation relies on many simplifying assumptions in modeling. The only parameter modeled reasonably accurately is the driving force behind the shrinkage of extended defects. C ', the concentration of self-interstitial in equilibrium with a stacking fault, is given by (Hu, 1981b)

c' = c*exp{&,[

"'

y t 2Trr( 1

-

u ) (In:

-

I)]].

(6)

In this expression, within the outer pair of brackets, the first term, y, is the faulting energy per unit area of the stacking fault, R is the atomic volume, and h is the magnitude of Burgers vector of the dislocation loop. The second term represents the strain energy due to the stacking fault. G is the shear modulus and w Poisson's ratio. For the extrinsic stacking fault in silicon, y is about 70 ergs cm (Alexander et al., 1980), or about 0.026 e V per atom. For perfect dislocation loops, such as in Sanders and Dobson's (1974) annealing experiments, y = 0 and drops out from Eq. (61, and the strain energy is the sole driving force for shrinking. For stacking faults that are sufficiently large, the strain energy term becomes negligible compared to the faulting energy, and Eq. (6) reduces to

~'

( 7 '

=

c"exp(2.j

for y>>

Gh' 2lTy(l - v ) '

(7)

Thus, this expression should be good for r 5 1 k m . The kinetic parameter, on the other hand, could be formulated as either reaction-diffusion controlled as given by Hu (1981b) or diffusion controlled as given by Giisele et al. (Gosele and Frank, 1981: Tan and Gosele, 1982). In inert ambients, and in absence of bulk sources of point defects such as oxygen precipitation, the formulation of Gosele et al. simplifies to

where a c t is + a geometrical factor for the diffusion-limited case, given by 2 n/ln(8r/rc),which is a weak function of r . The value of (D,CT + D , CT ) obtained from stacking fault shrinkage kinetics differ slightly from self-diffusion measured from isotope diffusion because of the absence of correlation factors here (q.v. Eq. ( I ) ) .

164

s. M. nu

V. Coexistence of Vacancies and Self-Interstitialsin Silicon By coexistence of the vacancy and the self-interstitial, we mean the comparable dominance and roles of these two point defects in silicon. This can now be regarded as a firmly established fact. The reasoning of the inevitability of this conclusion is based on the experimental observation of oxidation-enhanced diffusion, oxidation-retarded diffusion, and oxidation generation of extrinsic stacking faults. Between 1969 and 1971, several groups of investigators (Will, 1969; Bean and Gleim, 1969; Chan and Mai, 1970; Kovalev et al., 1970; Okamura, 1970; Katz, 1970; Allen and Anand, 1971; Higuchi, Maki, and Takano, 1971) reported an interesting phenomenon that, in oxidizing ambients, the diffusion rate varies with the crystallographic orientation of the silicon surface, in the order { 100) > (1 10) > (1 11). What was observed is actually the phenomenon of oxidation enhanced diffusion, an effect that varies with the surface orientation. The diffusion enhancement is greater in wet oxidation than in dry oxidation. A separate phenomenon had been reported several years earlier, that thermal oxidation of silicon often caused the formation of stacking faults (Thomas, 1963; Queisser and van Loon, 1964; Jaccodine and Drum, 1966; Booker and Tunstall, 1966; Fisher and Amick, 1966). The growth rate of OSF is also dependent on the crystallographic orientation of the surface being oxidized, in the order (100) > (1 10) > (1 1 I). The growth rate is higher for oxidation in wet oxygen than in dry oxygen. The similarities between the two phenomena, OED and OSF, led Hu (1974) to suggest that these two phenomena are closely related and have a common origin. Connecting OED to OSF brought us to the crucial point on our way to understanding diffusion in silicon. This is because the nature of the stacking fault can be determined from image contrast in transmission electron microscopy (Hirsch et al., 1965; Hashimoto, Howie, and Whelan, 1962). The OSF in silicon has been determined to be extrinsic in nature, namely, of the interstitial type (Jaccodine and Drum, 1966; Booker and Tunstall, 1966). The model of point defects and diffusion that Hu put forth on the basis of the connection between OED and OSF contains the following important elements (Hu, 1974): A. The vacancy and the self-interstitial coexist as major thermal point defects in silicon. The diffusion of group I11 and V atoms in silicon occurs via a dual mechanism mediated by both the vacancy and the self-interstitial. The ratio between the interstitialcy and the vacancy components varies according to the atomic species. B. Thermal oxidation of silicon injects excess silicon interstitials into the silicon substrate. The rate of injection is assumed to be directly

5

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proportional to the rate of thermal oxidation. The excess selfinterstitials are assumed to be annihilated at the surface, via a regrowth process that is dependent on the surface orientation and especially the density of surface kinks. C. Some of the self-interstitials in excess of the thermal equilibrium value would condense to form OSF, when nucleation sites are available. D. At the same time, the supersaturation of self-interstitials would enhance the diffusion of those substitutional dopants that exhibit an affinity with the self-interstitial. The difference in OED among various dopants then reflects the difference in the dopant‘s affinity with the self-interstitial. At that time, observations of OED were available only for boron, phosphorus, and arsenic; but the difference in OED among these was already sufficient to establish the dual mechanism as the only logical explanation possible. The interstitial nature of the OSF is indisputable from the TEM fringe contrast. But some early vacancy-only advocates had contended that, while they could accept that thermal oxidation generate silicon selfinterstitials, the existence of the self-interstitials as an important native point defect at thermal equilibrium had not been proven. One indication of the self-interstitial as an important thermal point defect came from Foll and Kolbesen’s (1975) identificaticin of type A “swirl defects” as being interstitial type dislocation loops that can come only from the agglomeration of silicon self-interstitials during crystal growth. There is another phenomenon of OSF growth that can allow only the conclusion that the OSF are interstitial disks. The phenomenon is associated with the precipitation of oxygen in silicon. When interstitially dissolved oxygen atoms agglomerate into an SiOz precipitate, a unit volume of silicon is converted to approximately 3.25 unit volumes of the precipitate. One way to reduce strain energy incurred by the localized volume expansion is to provide the needed cavity volume via the emission of self-interstitials or the absorption of lattice vacancies. Consequently there will be a supersaturation of self-interstitials or an undersaturation of vacancies. The supersaturation of self-interstitials due to oxygen precipitation have been shown by Hu (1980b) and Rogers et al. (Rogers et al., 1989: Rogers and Massoud, 1991a) to feed the growth of preexisting OSF. Most crucially, a one-point-detect theory cannot explain why the diffusion of different dopants would respond differently to a supersaturation of one point defect species: the diffusion of some dopants is enhanced more than others, while the diffusion of still other dopants is retarded. In the years that followed, a number of related phenomena have been discovered, all of which have greatly reinforced the dual vacancy-

166

s. M. nu

interstitialcy mechanism. These include the observation, by Mizuo and Higuchi (Mizuo and Higuchi, 1981), and Antoniadis and Moskowitz (Antoniadis and Moskowitz, 1982), of the oxidation retarded diffusion (ORD) of antimony, for which there is a very natural explanation: A supersaturation of self-interstitials causes an undersaturation of vacancies. If the antimony diffusion in silicon is mediated predominantly by the vacancy, it will be retarded during oxidation. There is also a physically intuitive interpretation for antimony’s preference for the vacancy mechanism. The elastic interaction between a point defect and a substitutional atom is dominated by the mismatch of the sizes of the lattice and the substitutional atoms. A larger substitutional atom is attracted to a vacancy while a smaller substitutional atom is attracted to a self-interstitial. A complementary phenomenon was subsequently discovered (Mizuo and Higuchi, 1982; Hayafuji, Kajiwara, and Usui, 1982; Fahey, Dutton, and Moslehi, 1983; Mizuo et al., 1983; Fahey et al., 1985), that thermal nitridation of silicon injects excess vacancies. That interpretation comes from the observations of OED-ORD of various dopants in thermal nitridation. The diffusion of phosphorus is retarded, while the diffusion of antimony is enhanced. This trend is just the opposite of that in thermal oxidation. With the observation of the complementary effect of nitridation, the logics of a dual-point-defect system is now seamless: OSF are interstitial in nature as identified by TEM fringe contrast, and corroborated by their growth during oxygen precipitation in inert ambients. Therefore, the formation of OSF indicates there is a supersaturation of self-interstitials or an undersaturation of vacancies during thermal oxidation. From the OED of boron and phosphorus and, to a lesser extent, arsenic, we conclude that these elements can diffuse via an interstitialcy mechanism. From the ORD of antimony, we must conclude that it diffuses via a vacancy mechanism. The fact that the antimony diffusion is enhanced by thermal nitridation must then indicate that nitridation generates excess vacancies. Finally, since the phosphorus diffusion becomes retarded in the presence of these excess vacancies, one can conlude only that, under normal conditions, it takes place predominantly through the vehicle of the selfinterstitial, whose concentration is reduced by annihilation with the excess vacancies during the nitridation.

VI. Interstitial Configurations and Charge-Enhanced Migration 1. GEOMETRICAL CONFIGURATIONS A N D MIGRATION PATHWAYS OF THE SELF-INTERSTITIAL

The generally accepted configuration of a lattice vacancy is simply a regular lattice site with a missing lattice atom. In contrast, conjectures

5.

INTRIN\I(

POINI DFI-FCTS IN SILICON

n

F I G . I . The tetrahedral-interstitial configuration.

167

n

FIG. 2. The hexagonal-interstitial configuration.

for probable configurations of a n interstitial vary, with different claims of model calculations and experimental supports. The simplest conceptual picture of an interstitial is an atom sitting at a lattice interstice having the most ”open space” (in the hard-sphere model of the lattice atoms). In a diamond lattice, this interstice is the tetrahedral site (or the T site), with the four nearest neighboring atoms at the vertices of the tetrahedral (Fig. I). The interstitial atom can jump to any one of the four nearest tetrahedral sites by passing through a puckered hexagonal ring of atoms, of which three are at the vertices of a face of the tetrahedral. The center of this hexagonal ring, called the hr.urrgoncil sire (or the H site), is considered to be the saddle point (Fig. 2 ) . because the very little “open space.” The “hardness” of the spherical atoms (usually in terms of one of several forms of empirical interatomic potentials related to elastic properties) was used by a number of early researchers to determine the migration energy barrier of the interstitial. The larger is the interstitial atom, the larger would be the repulsive potential at the hexagonal site considered as the saddle point, and the larger would be the activation energy of migration. However, Weiser (1962) suggested that, for a small ionic interstitial, the tetrahedral site may not be the equilibrium site: it may instead be the saddle point. with the hexagonal site being the equilibrium site. He pointed out that an ion will cause a polarization of the lattice atoms surrounding it and that the magnitude of the polarization energy (which is negative) is larger for atoms closer to the ions. Therefore, one expects that the polarization would contribute a larger decrease to the energy of an ion at the hexagonal site than at the tetrahedral site. He calculated atomic polarizability from the macroscopic dielectric constant of silicon

168

s. M. HU

from Clausius-Mossotti’s relation, and obtained a polarization energy contribution of -4.67 eV for the tetrahedral configuration, and -5.43 eV for the hexagonal configuration. (A later, more accurate calculation by Hu and Weiser (Hu and Weiser, 1972; Hu, 1973) obtained -4.20 e V and -5.16 eV for the tetrahedral and the hexagonal site, respectively; but this would not materially affect the conclusion regarding an equilibrium site.) For small ionic interstitials, the repulsive overlap potential at the hexagonal site is small enough that it may be more than compensated for by the larger polarization energy at the hexagonal site. Weiser’s theory was motivated by the experimental observations that the activation energy of diffusion does not increase steadily with the radius of an ionic interstitial, as would be expected if the repulsive potential at the hexagonal site were the principal factor affecting the migration barrier. Weiser’s concept would afford an explanation of why the activation energies of diffusion are very small for some interstitial ions of intermediate size, e.g., copper. For such ions, the hexagonal and the tetrahedral sites may have nearly equal potential, resulting in very small migration barrier. It turns out, however, that this theory is not in accord with the experimental observations (Aggarwal et al., 1965; Watkins and Ham, 1970; Berry, 1970), which indicate lithium, a very small ion, to occupy the tetrahedral site in silicon. It was first pointed out by Seitz that the interstitial of the traditional view is not a counterpart of the vacancy. He proposed a configuration of an interstitial that would be a more logical counter part of the vacancy, and he called the interstitial of this configuration the interstitialcy (Seitz, 1950), now often called the split interstitial. Whereas the vacancy in a lattice is a lattice site with the lattice atom missing, the interstitialcy is a lattice site with an extra atom. There are some interesting characteristics that can be deduced for the interstitial of this configuration. Since an interstitialcy occupies a lattice site as does any host or substitutional atom, it is bound by the flux sum rule (Hu, 1992)

where subscripts A and B denote the impurity and the host atoms, and u ( t )is the velocity of the movement of the whole lattice relative to some stationary markers-the Kirkendall effect. When it moves from lattice site to lattice site, it exchanges positions with host lattice atoms as well as substitutional atoms, causing self- and impurity diffusion in a way that is analogous to a vacancy mechanism. A “regular” interstitial, on the other hand, will more likely migrate through the lattice all by itself, and the flux of this type of interstitial is not bound by the flux sum rule. It is

5.

n

FIG. 3. The hond-center-interstili~il configuration.

169

INTRIN5IC POINT Dt-FECTS IN SILICON

n

F I G . 4. The (100)-split-interstiIi~il configuration.

possible that a regular interstitial may displace a lattice atom when an interstitialcy saddle point energy i s lower than a “regular” (hexagonal or tetrahedral site) saddle point: but the flux of this interstitial is still not bound by the flux sum rule. A number of geometrical configurations of the interstitialcy can be conceived. Watkins ( 1966) speculated that a double-positive interstitial, with two dangling valence electrons, may bond with two lattice atoms in a bond-center configuration (or the B configuration) (Fig. 3 ) . Friedel (1967). on the other hand, proposed a (100)-split configuration (or the S configuration), as depicted in Fig. 4. From an internal friction investigation of boron-implanted silicon specimens, Tan, Berry, and Frank (1973) have speculated on a geometrical configuration of a ( 100)-split interstitial and a version of a (1 lO)-split interstitial (Fig. 3 ) . N o silicon self-interstitial has been identified by electron paramagnetic resonance (EPR) studies (although the EPR Si-G25 spectrum was tentatively identified as the isolated interstitial silicon (Watkins, 1975)). But Troxell and Watkins (1980) have reported a (100)-split configuration of a boron interstitial. Calculations based on the semi-empirical extended Hukel theory (EHT) (Watkins et al., 1971; Corbett. Bourgoin, and Weigel. 1973, Weigel et al., 1973), showed the (100)-split of Fig. 4 to be the lowest energy configuration for the neutral, single-positive, and single-negative charge states of the self-interstitial in both diamond and silicon. Next higher in energy was found to be the bond-centered configuration, then t h e hexagonal configuration, with the tetrahedral configuration being the highest. The finding that the tetrahedral site is the highest energy interstitial configuration of all charge slates is quite surprising. The reliability of the EHT calculations. however, has been criticized by Pantelides et al. (1983).

170

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M. HU

FIG.5. A (1 IO)-split-interstitial configuration.

On the other hand, from an angle-scanned channeling study of implanted boron in silicon, Swanson et al. (1981) concluded that about 40% of the implanted boron atoms are interstitial but are not located near tetrahedral or hexagonal interstitial sites. Rather, they have a bondcentered configuration. Nor can any of the interstitial boron aroms be characterized as having a (100)- or a (110)-split configuration. 2. CHARGE-ENHANCED AND ATHERMAL MIGRATION OF THE SELF-INTERSTITIAL Consider a neutral interstitial residing at a tetrahedral equilibrium site, with the hexagonal site being the saddle point. The potential energy at either site is decided largely by orbital overlap. If the interstitial atom now loses or captures an electron and becomes an ion, then, according to Weiser’s theory mentioned earlier, the energies at both sites will be lowered by an amount equal to the polarization energies for ions at the respective sites. The energy at the hexagonal site will be lowered by a larger amount (some calculated values are given in an earlier section). This is illustrated in Fig. 6 . It is possible that, if the energy of a neutral interstitial at the hexagonal site is only slightly larger than that at the tetrahedral site, the difference in polarization energy may tip the balance, making the hexagonal site the equilibrium site (Fig. 7), as proposed by Weiser for small ionic interstitials. Thus, after acquiring a charge, an interstitial at a tetrahedral site finds itself at an energy saddle point, with the neighboring hexagonal sites having become the equilibrium sites. It will then be able to move to a neighboring hexagonal site without thermal activation. It may subsequently capture an opposite charge and revert to

5.

INTHIN\I(

171

POIN1 DEFECTS IN SILICON

the neutral state, for which the hexagonal site is the saddle point. It can then move athermally to one of the neighboring tetrahedral sites. This is the uthermal migration mechanism proposed by Bourgoin and Corbett (1972). We should mention, however. that the tendency for an ion to prefer the hexagonal site as the equilibrium site is contrary to the results of first-principles calculation of Bar-Yam and Joannopoulos ( l984c), to be discussed in the last section. Their results show that the equilibrium sites for I " and I ' ' are the hexagonal and the tetrahedral sites, respectively . We have used the tetrahedral-hexagonal-tetrahedral transition as an illustration of an athermal migration mechanism because it is derivative of

H T H T H T FIG.6 . Charge-enhanced migration hy lowering of migration barrier energy. Solid curve: potential for a neutral intentitial: dashed curve: potential for an interstitial after capturing or losing an electron. 7 and H and the tetrahedr;rl and the hexagonal sites. respecficely.

..--..

,.--. .

. .

,.--..

. _ _ I

H T H T

. .

.---. . *.

*--.

H T

Pi(,. 7. The Bourgoin-Corbett mechanism of athermal migration: Ionization of an inter\titiid

fnr :in

c u w s the original \addle point t ( i hecome the equilibrium site. Solid curve: potential neutral interstitial: dashed curve potential for an interstitial after capturing or losing electron. r a n d H and the tetrahedral and the hexagonal sites. respectively. ii

172

s.

M.

nu

Weiser’s theory of ionic interstitials in silicon and because it is physically transparent. Other interstitial configurations such as the various splitinterstitials may also be capable of ionization-stimulated athermal migration. However, Frank, Seeger, and Gosele (1981) argued that athermal migration is not viable for the split configuration, because this configuration has no alternate location in a silicon lattice. Since they considered the split-configuration as the only likely self-interstitial configuration in silicon, they further suggested that the Bourgoin mechanism of athermal migration of the self-interstitial does not operate in silicon. Theoretical findings of the energies of point defects in various charge states and sites will be given in the last section. VII. Formation and Migration Parameters of Point Defects

There is a general acceptance of the activation energy of self-diffusion of between 4 and 5 eV, apparently because of the rather good agreement among results of very different experiments. However, there are very few direct ways to separate this activation energy into its component energies of defect formation and migration and the association of these energies with specific point defect species. The reliabilities of these few methods are also debatable. In the past decade, many investigators have attempted to obtain these parameters indirectly, by model-fittingdiffusion profiles of dopants and more particularly transition elements like gold and platinum. One cannot really say that any set of fitting parameters, including point defect formation and migration, that is uniquely suitable for one particular model represents the true physical parameters. Another attempted approach to determine defect (usually the self-interstitial) migration kinetics separately from its thermal formation is the study of flow of injected point defects from one surface across a silicon slice of varying thickness and measurement of its influence on the evolution of existing stacking faults or dopant profiles on the opposite surface.

I. STUDIES OF POINT DEFECTS FROM IRRADIATIONS In the section on thermal defects, we already mentioned the difficulty and failures of quenching from high temperatures in order to provide sufficiently high concentrations of point defects for study at low temperatures. In the early 1960s, EPR studies of silicon point defects were carried out, especially by Watkins (1965) and coworkers, at very low temperatures in silicon samples irradiated by MeV electrons. Thermally stimulated transient capacitance (TSCAP) and deep-level transient capacitance spectroscopy (DLTS) methods were introduced in the early 1970s (Sah et al., 1970; Lang, 1974). These techniques began to be used for the

5.

INTRINSIC POIN

r DEtFCTS IN SILICON

173

investigation of electron-irradiated silicon since the mid- 1970s (Brabant et al., 1976; Kimerling, 1977). Experimental investigations of radiationcreated point defects cannot produce such information as the enthalpies and entropies of formation. But they can yield such information as the activation energies of migration, the geometrical structure, and the electronic states of the point defects. One question that has not yet been resolved is whether the point defects created by energetic bombardment at low temperatures are the same point defects thermally created at high temperatures. And, assuming they are the same point defects, are their properties measured at low temperatures and in highly excited nonequilibrium states the same as at thermal equilibrium at high temperatures. It is expected that electron bombardment would create an equal number of vacancies and self-interstitials. It was somewhat of a mystery that, in low-temperature annealing of electron-irradiated silicon, only the vacancy and its various forms of complexes have been identified, the selfinterstitial and its various forms of complexes have not. In the case of aluminum-doped silicon, an explanation for the mystery came from the observation of aluminum interstitials (Watkins, 1965). In aluminumdoped silicon irradiated with I . S MeV electrons at 4.2 K , Watkins found a spectrum, Si-(318, that he identified as A l + ' . The production rate of these defects was high (-0.03 defect/cm', per electron/cm2)and similar to that of the isolated vacancies ( V and V - ) (Watkins, 1965). Watkins speculated that silicon interstitials produced by the irradiation had replaced substitutional aluminum atoms on lattice sites. The observation of boron interstitials has been interpreted in the same way (Watkins, 1975). All these processes were detected at 4.2 K when the self-interstitial must be mobile in order to produce these impurity interstitials. Such fast migration may be explained by the occurrence of the Bourgoin-Corbett mechanism of athermal migration mentioned in Section VI.2, as the system is highly excited under irradiation conditions. Another possibility is the absence or instability of states having odd number of electrons, making the interstitials invisible to EPR. Anderson (1975) has proposed a model to explain why defects in certain amorphous semiconductors are not paramagnetic, and hence undetectable by EPR. His explanation is that for deep-level defects within a semiconductor bandgap, the repulsive coulombic energy is more than offset by spin coupling and structural relaxation that may result from capturing (or expelling) a second electron at the defect. This property is now known as Anderson's negative-(/. Thus, I = (or I + ' ) may be a lower energy state than I - (or I + ) , and V' (or C ' ' + ) may be a lower energy state than V (or V' ). A question that has not been raised is: Have any extended interstitial defects, such as extrinsic stacking faults or the climbing of dislocations, +

174

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M. HU

ever been observed in Watkins's experiments? It may be noted that, while researchers using electron paramagnetic resonance see only vacancies in irradiated silicon, electron microscopists tend to see only interstitial-type ,stacking faults and dislocation loops, for example, in electron irradiated nickel (Makin, 1968; Makin, 1969). This is because each characterization technique has its own sensitivity limitations. The fast migration of the excess self-interstitials would likely allow them to agglomerate into interstitial-type dislocation loops. It is not clear, however, whether such loops have been observed (or examined) by Watkins and other researchers in their EPR studies. The silicon vacancy, while it could be frozen at 4.2 K, is also quite mobile at cryogenic temperatures, with migration energies of -0.33 and -0.18 eV in the neutral and doubly negative charge states, respectively (Watkins, 1965; Watkins, 1968). The migration energy of 0.33 eV was later revised to 0.32 eV (Watkins, Troxell, and Chatterjee, 1979). A defect that anneals out with an activation energy of 0.45 eV has not been firmly established, but is thought to be that of the doubly positive vacancy (Watkins et al., 1979). The vacancy charge states show an Anderson negative-U property and the levels are assigned as follows (Watkins and Troxell, 1980; Newton et al., 1983): 1. 2. 3. 4.

Vacancy Vacancy Vacancy Vacancy

donor level at E , + donor level at E , + acceptor level at E , acceptor level at E ,

0.05 eV for V o+ V + + e-. 0.13 eV for V + + V + + + e-. - 0.57 eV for Vo + e- + V - . - 0.11 eV for V - + e- + V = .

Because of the negative-U properties of the vacancy charge states, the V - species, mentioned earlier with a migration energy of 0.33 eV, is supposed to be unstable and does not exist normally. It can, however, be brought into existence in, for example, a photo-excited system, in which electrons from V = can be pumped into the conduction band. The charge state of a point defect is important because it affects not only the mobility of the defect, but also its thermal equilibrium concentration, which, of course, also depends on the Fermi level as shown by Shockley et al. (Shockley and Last, 1957; Shockley and Moll, 1960). For example, for defect Ex- having two acceptor states, the concentrations of its singly negative and doubly negative states are

5.

INTRINSIC POIN I DEE t C I S IN SILICON

175

Doubly negatively charged defects, assumed to be vacancies, have been found to be necessary for a satisfactory simulation of arsenic diffusion profiles by Chiu and Ghosh (1971). The equilibrium concentrations of Eqs. (10) and ( I I ) are based simply on statistical thermodynamics; according to the tenet of energy balance, the formation energy of the ionized defect is the same as that of the neutral defect plus the difference between the Fermi level and the defect state energy. Some theoretically calculated results of the formation energies of variously charged defects (Section VIII) appear to contradict this tenet. 2. VACANCY FORMATION ENERGY FROM POSITRON-LIFETIME MEASUREMENTS It has long been postulated that lattice vacancies, which represent localized volumes without positive nuclear charge, tend to trap positrons, thus delaying their annihilation with electrons. The lifetime of positrons trapped by lattice vacancies affords an estimate of the concentration of vacancies. Based on positron-lifetime experiments conducted in the temperature range between 300 and 1523 K . Dannefaer, Mascher, and Kerr (19861, reported an enthalpy of formation of 3.6 ? 0.2 e V , and an entropy of formation of 6 to 10 k. These values seem reasonable in view of other types of experimental results. However, many assumptions which are made in the analysis of such measurements, may influence the reliability of results . 3 . POINT DEFECT CONCENTRATIONS FROM

‘rHERMAL

EXPANSION

MEASUREMENTS At higher temperatures, more point defects are incorporated into a crystal and, depending on whether the dominant point defect is the vacancy or the self-interstitial, will cause the volume of the crystal to expand or contract by an amount that is in addition to the normal thermal expansion of the lattice. However. as we already mentioned in Section 111, the incorporation of “thermal point defects,” which are actually fastdiffusing metallic contaminants, will also expand the volume of a given crystal. There is a discrepancy between the thermal expansion coefficient from length measurements of Okaji (1988) and the thermal expansion coefficient from lattice parameter measurements of Okada and Tokumaru (1984). Okada (1989) assumed that the larger thermal expansion from length measurement is a direct result of a larger ( C , - C , ) and gave a value of I .8 x 10’6cm-3at 1300 K for (C,, - C , ) . However, some important points of his results are open to question. First, from the same figure (his Fig. I ; Okada, 1989) from which he drew the preceding conclu-

176

s.

M. HU

sion, one would obtain ( C , - C , ) of about the same value at 1073 K as at 1300 K, as if the formation enthalpy of the majority defect were essentially zero. The data and interpretation are even more problematic at lower temperatures: From 500 to 700 K, C v - C , (again from Okada's Fig. 1) would now become negative, but its magnitude on the order of 1016cm-3is still about the same as at 1300 K. Granted that a negative value may simply indicate that the self-interstitial is the predominant point defect at low temperatures. But we should also expect the concentrations of both the vacancies and the self-interstitials in silicon at 300500 K to be immeasurably low, not the same magnitude as at 1300 K according to Fig. 1 of Okada (1989).

4. ESTIMATION OF SELF-INTERSTITIAL CONCENTRATION FROM OXYGEN PRECIPITATION Oxygen at the level of = 10'8cm-3 dissolved interstitially in cruciblegrown silicon crystals will usually precipitate out as SiO, in thermal processings at temperatures lower than the silicon melting point (1410°C). The volume of an SiO, precipitate is about 2.25 times the volume of the silicon consumed locally by the precipitate. Thus, a precipitated SiO, inclusion gives rise to an immense local stress, which may be relieved in a number of ways (Hu, 1986a). At high temperatures, it is feasible and efficient for the stress to be relieved by emission of silicon self-interstitials (Hu, 1986a). The evolution of excess interstitials during oxygen precipitation have been found to affect the growth and shrinkage of preexisting stacking faults (Hu, 1980b; Rogers et al., 1989; Rogers and Massoud, 1991a). At high temperatures, for example, FI100°C, the oxygen precipitates take the form of octahedron, which is the geometry of minimum surface energy, but is also the geometry of maximum misfit strain energy. Yet, in TEM lattice images, the regions of the silicon lattice surrounding such octahedral SiO, precipitates are completely free of strain. The existence of a significant lattice strain would be incompatible with the octahedral precipitate morphology, and would have caused the SiO, precipitate to prefer a platelet morphology, thereby trading a smaller surface energy for a smaller strain energy (Hu, 1986b). The absence of any strain around octahedral precipitates can be interpreted only as due to the emission of self-interstitials at a rate of 0.58 interstitial per oxygen atom precipitated. Because the rate of the disappearance of interstitially dissolved oxygen can be accurately measured by means of infrared spectroscopy, the rate of bulk generation of self-interstitials can also be determined quite accurately (this is quite unlike the case of the generation of self-interstitials by the thermal oxidation of a silicon surface). Hu (1980b; 1981a) has

5.

177

INTRINSIC POINT DEFFCTS IN SILICON

12 10

3-. $

8

+-

z

2

6

i

u-

4

V-

v

2 0

0

10

20

30

40

so

Time, hours Fit,. 8 The evolution of cxceb\ wlt-inter$titial in a bilicon sample containing oxygen and annealed at I?O(K’.

found that the interstitial oxygen decays exponentially. By relating this precipitation kinetics to the kinetics of the growth and shrinkage of stacking faults, he was able to derive an analytical expression for the evolution of excess self-interstitials during oxygen precipitation. (A numerical solution may be required if the precipitation kinetics is more complex.) An example of the results of his analysis of the evolution of excess selfinterstitial at 1200°C is shown in Fig. 8. He also obtained the equilibrium concentration of self-interstitials through the following relationship (Hu, 1992):

5 . DIFFUSIVITY OF THE SEL.F-~NTERSTITIAL FROM MEMBRANE EXPERIMENTS

Several investigations have been made using a “membrane” method (Taniguchi, Antoniadis, and Matsushita, 1983; Taniguchi and Antoniadis, 1985; Griffin et al., 1985; Scheid and Chenevier, 1986; Ahn et al., 1987; Griffin et al., 1987; Rogers and Massoud. 1991b). In this method, silicon “membranes” of different thickness. tens to hundreds of km, are prepared. lnterstitials are injected from the back side of a specimen by thermal oxidation. while the front side is protected from oxidation by a nitride or nitride-oxide composite film. The injected interstitials will flow through the thickness of the membrane to the front side and get annihilated there. By measuring the evolution of preexisting stacking faults or

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s. M. HU

dopant profiles on the front side, the self-diffusivity can be obtained through appropriate modeling. The complications come from the frontside interface reactions, and the bulk trapping of the excess interstitials. The bulk recombination has been neglected in most analyses. As demonstrated by Griffin et al. (1987), the enhanced diffusion on the frontside differs between specimens from float-zone and Czochralski silicon crystals, with the enhancement reduced in the Czochralski specimen. ~ ) Since Czochralski silicon contains a high concentration (= 10l8~ m - of oxygen atoms, it may be concluded oxygen could act as traps for the injected interstitials. However, Rogers and Massoud (Rogers and Massoud, 1991b) reported no difference between float-zone and Czochralski silicon substrate in bulk trapping of self-interstitials migrating across the thickness of silicon wafers. The bulk generation-recombination of Frenkel pairs have also been neglected in these studies. The results obtained from these studies vary widely. 6. DEFECT PARAMETERS FROM MODEL-FITTING Au

AND

PT DIFFUSION

Gold diffusion in silicon was traditionally analyzed in the FrankTurnbull dissociative mechanism (Frank and Turnbull, 1956). In this model, the gold atoms diffuse interstitially very rapidly through the specimen and become saturated. Because gold has a larger substitutional solubility than interstitial solubility, further diffusion of gold will continue through the following reaction:

Aui

+ V*

Au,.

(13)

Gosele, Frank, and Seeger (1980) proposed an alternative mechanism through the following reaction Aui + Si,i+Au,

+ I.

(14)

In this mechanism, an interstitial gold atom takes up a substitutional site by “kicking out” a silicon lattice atom, Si,. This mechanism is now often referred to as the kick-out mechanism. (We may note that replacement is perhaps a more appropriate term, since it also states unambiguously the fact that this is a replacement reaction-a silicon lattice atom is replaced by a gold atom. The term kick-out does not simultaneously suggest that the gold atom takes up the position left by the kicked-out silicon atom. Kick-out will more appropriately denote the ejection of a lattice atom by an energetic agent, e.g., high-energy electrons or ions, photons, or electron-hole reaction events.) If both the vacancy and the selfinterstitial concentrations are maintained near their equilibrium value, due to the very large diffusivities of these two point defects, then there

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INTRINSIC POIN I DEFtCTS I N SILICON

179

is really no difference between these two mechanisms. However, if the diffusion of these point defects from or to the surfaces of the specimens cannot keep u p with the preceding two reactions, a difference arises not only in the point defect concentration profiles, but also in the gold concentration profiles, as shown by Cosele (1980) in an approximate analysis. They contended that the gold profiles from the kick-out model exhibit a U-shaped distribution, in agreement with experimental finding. This model has since been utilized by a number of investigators (Morehead et al., 1983; Morehead. 1988; Coffa et al., 1988; Boit, Lau, and Sittig, 1990; Zimmermann and Ryssel, 1992a; Zimmermann and Ryssel, 199%; Mathiot, 1992) to obtain the silicon self-diffusivity and even the diffusivity of the self-interstitial. Zimmermann and Ryssel (1992a; 1992b) have considered both the dissociative and the replacement mechanisms, as well as the bulk recombination between vacancies and self-interstitials in their analysis. Their results for the temperature range 700-950°C are summarized in the following:

CF

=

1.94 x lO”exp(

DI= 2.58

x 10

-

3.835 eV/kT)

’ exp( -0.965 eV/kT)cm’/s,

Ct

=

1.83 x IO”exp(- 1 . 1 6 2 e V / k T ) ~ m - ~ ,

D,

=

1.09 x lo3exp( - 2.838 eV/kT) cm’/s.

(15)

The vacancy formation enthalpy given by Eq. (IS) seems to be unreasonably small. Furthermore, according to Eq. (2). a preexponential factor of 1.83 x lof9for Ctr would imply a negative formation entropy, something that is not possible. Assuming that only the kick-out mechanism operates, and ignoring vacancy-self-interstitial generation-recombination, Boit et al. (Boit et al., 1990) have obtained from rapid optical unneufing of gold diffusion in silicon the following results:

D, = 1.03 x IOhexp(- 3.22 eV/kT) cm’/s, (16)

CF = 3. I 1 x 10”exp ( - I .58 eV/kT) cm-3.

VIII. Defect Energetics and Pathways from Theoretical Calculations

Theoretical calculations of the energies of formation and migration of the vacancy and the self-interstitial in silicon were made in the 1960s by use of empirical pairwise interatomic potentials (Swalin, 1961; Scholz and Seeger, 1963; Hasiguti. 1966). In the last several years, several new empirical interatomic potentials have been introduced for attempting better descriptions of covalent materials with some ad hoc terms to account

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S. M. HU

for environments beyond pairwise interactions. Such empirical interatomic potentials have been employed in a number of recent investigations for the calculations of the energetics of the vacancy and the selfinterstitial in silicon (Batra, Abraham, and Ciraci, 1987; Baskes, Nelson, and Wright, 1989; Ungar et al., 1993; Maroudas and Brown, 1993). Reasonable results, though not agreeing with each other, have been reported in all these investigations. But faith in such calculations would seem unwarranted, in view of the lack of theoretical basis in such empirical potentials. All scientists know that empirical formulas cannot be stretched too far. While some such empirical potentials are acceptable for calculating energies resulting from small changes from equilibrium lattice parameters, they cannot be expected to produce reliable predictions for drastic changes involving rearrangements of valence electrons in the formation of point defects. In particular, empirical interatomic potentials cannot provide means for calculating the energetics of point defects in their different charge states, which can be quite complex and unexpected (e.g., the occurrence of “negative-U” system mentioned in Section V1I.I). In the early 1970s, it is quite popular to calculate the energetics of point defects by use of semi-empirical extended Hiickel theory. Some of such calculations were mentioned in Section V1.I. The reliability of the EHT method has been criticized by Pantelides et al. (1983). Since the late 1970s, the energetics of the silicon vacancy and the self-interstitial have been obtained with first-principle calculations of total energy of a crystal containing a defect. In these calculations, the total energies of a perfect crystal and crystals containing a point defect at different lattice locations are calculated, and the appropriate differences then give the formation energy and migration energies along different paths. The Schrodinger equation is solved for a crystal containing a defect for a self-consistent pseudopotential (including the exchange-correlation energy). The self-consistency in the pseudopotential is achieved, by iterative computations, using the density-functional theory in the local density approximation for calculating the exchange-correlation potential (Kohn and Sham, 1965). These calculations are accomplished via two schemes: the use of self-consistent Green’s function method for a finite defect cluster (Baraff and Schluter, 1978; Bernholc, Lipari, and Pantelides, 1978; Lipari, Bernholc, and Pantelides, 1979; Bernholc, Lipari, and Pantelides, 1980; Baraff, Kane, and Schiilter, 1980; Caret al., 1984, Baraff and Schliiter, 1984; Car et al., 1985; Kelly and Car, 1992), and the method of supercell that contains 16 or 32 nearest atoms surrounding a defect and replicates by translations (Bar-Yam and Joannopoulos, 1984c; Bar-Yam and Joannopoulos, 1984b; Bar-Yam and Joannopoulos, 1984a;

5.

181

INTRINSIC POINT DEFECTS I N SILICON

Antonelli and Bernholc, 1989; Nichols, Van de Walle, and Pantelides, 1989). Up to 64 atoms are included in a supercell in a recent calculation (Sugino and Ashiyama, 1992)for the migration of impurity atoms, which would have to move away from the point defect to at least the third coordination site in order to return to the point defect at the nearest neighboring site that is different from the originating site. And it is also necessary to avoid the possibility of a percolation phenomenon (Mathiot and Pfister, 1982) in which [he point defect migration is short-circuited through closely spaced impurity atoms. The limitation on the reliability of these calculations is at present handicapped by the size of the supercell, or cluster, used, due to the limitation of present-day computer power. Thus, one problem with such calculations is that elastic relaxation and, particularly, electrostatic potentials are long range, occurring over many atomic shells. The effect is particularly evident in Weiser's (1962) calculations of polarization energy due to an interstitial ion. A typical supercell scheme would force these long-range effects to terminate at the third or the fourth coordination site, with unknown consequential errors. Bar-Yam and Joannopoulos ( 1984~)obtained from their calculations that equilibrium sites for I" and I ' are the hexagonal and the tetrahedral sites, respectively. This is just opposite to what one would expect from the effect of ionic polarization according to Weiser theory, as discussed earlier. The migration energies they calculated, with lattice relaxation, are I .O and 1.4 eV for I" and 1 ' , respectively. They later revised their results (Bar-Yam and Joannopoulos. 1984a) to 1.2 eV for the selfinterstitial in either charge state. They further differentiated the equilibrium geometrical figurations between p-type and n-type silicon, and reported that (Bar-Yam and Joannopoulos, 1984a), in n-type silicon. the tetrahedral site is the equilibrium site for I and the hexagonal site is the saddle point-i.e., the reverse of the p-type situation. Again, the hexagonal-tetrahedral configuration is the reverse for I" between p-type and n-type silicon. This finding is interesting, but does not seem to have an easy physical explanation. What differentiates n-type and p-type silicon is electrons in the conduction band that are not localized and are not originated from the neighborhood of the point defect. As such, why should they so strongly affect the potential energy at different sites'? One would intuitively suppose that the doping type, in terms of the Fermi level, would merely shift the formation energy of a charged defect uniformly in real space. In n-type silicon, the concentration of I would be low according to Fermi statistics as shown by Shockley et al. (Shockley and Last, 1957; Shockley and Moll, 1960). Bar-Yam and Joannopoulos (1984a) did not discuss this problem in their paper. Car et al. (1984) have also calculated the silicon self-interstitial energet+

+

+

+

+

+

182

S.

M. HU

ics for various geometrical configurations and charge states. They found that the tetrahedral site is the equilibrium site for Z , with the hexagonal site being its saddle point. This tetrahedral-hexagonal geometrical configuration is reversed for Zo, which is again in disagreement with the polarization energy concept of Weiser. Another peculiarity in the totalenergy vs geometrical location plot for Zo from the results of Car et al. (1984) is the existence of an energy cusp at the tetrahedral site. In the results of Car et al., the effect of the Fermi level is simply to shift the formation energy uniformly in real space by an amount equal to the Fermi energy (or twice that amount for doubly charged defects), up or down according to the sign of the charge. This is physically expected. They calculated the total energies for I + + , I + , and Zo. Their results suggest that the Bourgoin-Corbett mechanism may occur along the TB path: An I + + at the tetrahedral site (T) captures an electron and becomes I + , which then finds the neighboring bond-center site (B) to be at a lower energy and moves there without thermal assistance. Another possible path for the Bourgoin-Corbett mechanism was suggested to be the TBTH path. The BS path (bond-center to split-interstitial) of athermal migration, proposed earlier by Watkins et al., (1971), was found not to be possible. They found that I + is not a table charge state. In other words, Zo, I + , and Z + + form an Anderson negative-U system. Bar-Yam and Joannopoulos (1984~;1984b; 1984a), Car et al. (1984; 1985), and Kelly and Car (1992) did not report any negatively charged self-interstitials. This appears to be in conflict with the experimental evidence that phosphorus diffuses in silicon via a dominantly interstitialcy mechanism (Strunk, Gosele, and Kolbesen, 1979; Fahey, Dutton, and Hu, 1984; Nishi and Antoniadis, 1984; Fahey et al., 1989a), and that phosphorus diffusion is enhanced by electron concentration, almost to the second power (for example, see Fair, 1981; Fahey et al., 1989a), indicating that the self-interstitial may have a dominant double-negative charge state. (The concentration of neutral defects is independent of the Fermi level (Shockley and Last, 1957, Shockley and Moll, 1960).) The values of EC, Ei7, E;, and Ej" vary somewhat from different calculations. A summary of the results from various theoretical calculations is given in Table 1. The pressure dependence of defect energetics in silicon appropriate for self-diffusion, including the concerted-exchange mechanism of Pande y (1986), has been calculated by Antonelli and Bernholc (1989). The pressure dependence of defect energetics in silicon appropriate for impurity diffusion has been calculated by Sugino and Ashiyama (1992). They found that the activation energies for the diffusion of phosphorus, arsenic, and +

+

5.

183

INTRINSIC POINT DEFECTS I N SILICON

TABLE I

THEORETIC A1 F O R M A T I O N A N D MIGRATION ENERGIES (ev) OF INTRINSIC POINTDEFFCTS I N SILICON. ~~

E : or E :

Defect

I*'cT)

l"(T)

4.7 i- 0.5 4.0 3.6 4.4 4.3

~~~

~

E;"

Or

F"' -I'

References

0.4

2

0.2

2

0.5 0.2

2

0.5

Baraff and Schluter. 1984 Bar-Yam and Joannopoulos. 1984b Antonelli and Bernholc, 1989 Kelly and Car, 1992 Baraff and Schluter. 1984 Bar-Yam and Joannopoulos. 1984h Antonelli and Bernholc. 1989 Kelly and Car. 1992 Antonelli and Bernholc, 1989 Antonelli and Bernholc, 1989 Kelly and Car, 1992

I. 2

1.6

1.2 i- 0.3

4.3

0.3 I" ( € 3 ) \'I1

5.0 4.4 4.4 (unrelaxed)

antimony in silicon decrease with pressure for the vacancy mechanism, but increase with pressure for the interstitialcy mechanism. Taken together the experimental results of Nygren et al. (1985), which showed the diffusion of arsenic in silicon to increase with pressure, they (Sugino and Ashiyama, 1992)concluded that arsenic diffuses in silicon via a dominantly vacancy mechanism. However, they seemed to have neglected the fact that what Nygren et al. measured is the pressure effect on the activation enthalpy, rather than the activation energy, of diffusion. Sugino and Ashiyama (1992) reported a decrease of activation energy of diffusion by 0.6 eV at 60 kbar. Taking this value, the activation enthalpy, which includes a term of P A V of about 0.68 eV ( A V being approximately given by the atomic volume), would be +0.08 eV. A similar correction (but with an opposite sign) is needed for the activation enthalpy of the diffusion via an interstitialcy mechanism. In view of the accuracy of such supercell calculations, a definitive assessment of the diffusion mechanism is not warranted. While total energy calculations based on the local-density approximation have yielded remarkably good results, insofar as their compatibility with experimental data of self-diffusion is concerned, some of the limitations and reliability of such calculations should be noted. Kelly and Car (1992) have noted that for the calculation of the formation energy of silicon, a relaxation of the next-nearest neighbors would give such a huge change in value that a reliable first-principles calculation with a sufficiently large cluster is impractical for present-day computers. A similar

184

s. M. nu

problem occurs in the supercell method. A practical limit on the size of the supercell leads to very large dispersion in the gap state. Furthmiiller and Fahnle (1992) have noted that, for chalcogen defects in silicon, a significant dispersion occurs even for a supercell size of 128 atoms. Furthermore, the density-functional theory is a theory for the ground state. In the local-density approximation, it has proven unreliable for energies of excited states, such as the conduction band and conduction-band derived states. This caveat has indeed been noted by some authors of those calculations, of whom some would refrain from giving values for such energy states. However, the calculations of the total energy in terms of atomic arrangement have given some surprising good results, in view of the agreement reported among various research groups, as well as with experimental results.

IX. Summary In addition to their well-known roles on atomic diffusion and the formation and the dynamics of extended crystalline defects, vacancies and self-interstitials also affect the nucleation and precipitation of oxygen in silicon (Hu, 1977b; Hu, 1980a; Schaake et al., 1981; Craven, 1981; Oehrlein et al., 1982; Tan and Kung, 1986; Shimura, 1992). Conversely, oxygen precipitation causes excess self-interstitials and depletes vacancies, thereby affecting diffusion and defect processes (Hu, 1980b; Rogers et al., 1989; Kennel and Plummer, 1990; Rogers and Massoud, 1991a). With appropriate modeling, the kinetics of oxygen precipitation can provide an estimate of not only the supersaturation of silicon self-interstitials, but also their thermal equilibrium concentration (Hu, 1980b; Hu, 1992). Evidence from a wide variety of experimental observations indicates that both the vacancy and the self-interstitial coexist in silicon in almost equal roles. They have comparable energies of formation and of migration. They all contribute to the self-diffusion and the diffusion of substitutional impurities in silicon; but their relative roles vary for different impurities. The silicon self-interstitial has a number of different configurations, and moves through the lattice via different migration paths. Firstprinciples total-energy calculations, using local-density approximation to achieve self-consistency in defect potential, have given some surprisingly good results that are compatible with experiments. But there are some limitations and the question of reliability of such calculations. Possible errors, some quite large, arise from two main causes: (1) the size of clusters or supercells, sufficiently large to avoid the convergence and dispersion problems, cannot be handled by modern computers; (2) the inherent problem of the inability of the local-density approximation to

5.

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185

handle excited states. A rather unique feature of point defects in silicon, both the vacancy and the self-interstitial, is that the formation energy is very large. about 4 eV or more, and the migration energy is very small, about I eV or less. In spite of the probable errors, reasonably good values of the energy of formation and migration have been produced by theoretical calculations. On the other hand, attempts to produce separate values of formation and migration enthalpies by model-fitting experimental diffusion data, as well as other experimental approaches, e.g., diffusion of excess point defects through membranes, cannot at present be regarded as so successful.

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Sanders. I . R . . and Dobson. P. S. (1974). 1. Muter. Sci. 9, 1987. Schaake. H . F.. Barber, S. C., and PiniLzotto, R . F. (1981). In SL.miconduc/o,.Silicon 19x1, H. R . Huff. R. J . Kriegler. and Y . Takeishi (eds.). p. 344. Electrochemical Society. Pennington. N . J . Scheid. E.. and Chenevier. P. (1986). P17v.s. S r e r r . Solidi A 93, 523. Scholr, A . , and Seeger, A. (1963). Pliv.\. S t o r . Solidi 3, 1480. S t e r r i t s Solidi 29, 455. Seeger. A.. and Chik. K. P. (1968) t'lrr.~. Seitr. F . (1950). Actti Cryst. 3, 355. Shiniim. H.. Yoshinaka. A.. and Sugitir. Y . (1978). Jpn. J . A p p l . Phys. 17, 767. Shimura. F. (1992).J . Appl. P l r y s . 72, 1642. Shiniura. F..Dywn, W.. Moody. J . W., and Hockett. R. S . (1985). In V L S l Science und 7 6 . c k n o l o g y i l Y X 5 . W. M. Bulli\ and S. Broydo (eds.),pp. 507-516. Electrochem. Soc., Pennington. N.J. Shockley, W.. and Last. J. T. (1957). P h y s . Re\,. 107, 392. Shocklry. W.. and Moll. J . L. (196tl). Plrvs. Rei,. 119, 1480. Sorokin. L. M.. Sitnikova. A . A , . C'hervonyi. 1. F.. and Fal'kevich. E . S . 11991). Soi,. P/iv.\. Solid Sttrtr 33, 1824. Struck. H.. Gosele. U., and Kolbe\en. 13. 0. (1979). Appl. Phvs. Lett. 34, 530. Supino. 0.. and Ashiyama. A. (1992). P/rv.\. R ~ L B, . 46, 12335. Sugita. Y . . Shiniiru. H.. Yoshinaka. A . . and Aoshima. T. (1977). J . Vuc. Sci. Tec+~nol.14, 44.

Swalin. K. A . (1961). J . P h y s . Chrvti. S ~ l i d18, ~ 290. Swanwn. M . LA.. Howe. L . M., Saris. F. W.. and Quenneville. A. F. (1981). In Dyft,u.s in .S[,tt7ic,[,ndrrc,tor.\. J . Narayan and T. Y. Tan leds.). p. 71. North-Holland, New York. l'an. S . I . . Berry. B . S . . and Frank. W. i 1973). I n Ion Implantation in Srmiconducrors und Other Muteriirls. B. L . Crowdet (ed.), p. 17. Plenum Press. New York. l'an. T. Y . . and Cibsele. C . (1982).J . Appl. Phy.s. 53, 4767. Tan. T. Y . . and Kung. C . Y . (1980). In Setnic.ondrccior Silicon lYB6. H. R . Huff. T. Abe. and B. Kolbesen (eds.). p. 864. Electrochemical Society. Pennington. N.J. Taniguchi. K.. and Antoniadis. D. A . (1985). A p p l . Phys. Lett. 46, 944. Taniguchi. K.. Antoniadis. D. A. and Matsushita. Y . (1983). A p p l . Phvs. Lert. 42, 961. Thomas. D. J . D. (1963). Phvs. S t c r t . S,~lidi3, 2261. Troxell. J . R . . and Watkins. G . D. ( 19x0). P h y s . Re\,. B 22, 921. Tsuya. H . . Kondo. Y . . and Kananiori. M. (1983). Jpn. J . Appl. Phvs. 22, L16. Ungar. P. J . . Takai, T.. Halicioglu. 'I.. and Tiller, W. A. (1993). 1. Vuc. Sc,i. Techno/. A 11. 1-24.

Voronkov. V . V. (1981). J . Cpsr. G r o w t l r 59. 625. Wada. K . (1984). Phv.). Rci.. 30, 5x84. Wada. K . , and Inoue. N . (1986).In .Sc,nric.ondr~c.torSilicon lYX6. H. R. Huff, T. Abe, and B. Kolbesen (eds.), p. 778. Electrochemical Society. Pennington, N.J. Watkins. G . D. ( 1965). Rudiurion /)trrrrtiyr irr Sc,nric,ondr~ctors.p. 97. Dunod. Paris. Watkins. G . D. (1966). Quoted by ('orheit et al. (1973). Watkins, G . D. (1968). In Ruditrriori Dunicrgr iti .Srmic.onductors, F. L. Vook (ed.), p. 67. Plenum Press, New York. Watkins. G . D. ( 1975). In Ltittic.e I)t.fi.c I \ in Srniic,ondrrc,tor.s lY74. F. A . Huntly (ed.),p. 23. Institute of Physics, London Watkins. G . D.. and Ham. F. S. (1970). Pliys. Rev. B 1, 4071. Watkinh. G . D.. Mes5mer. K. P.. Weigel. C . , Peak. D.. and Corbett. J . W. (1971). Phvs. Re\.. L e t t . 27, 1573.

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Watkins, G. D., and Troxell, J. R. (1980). Phys. Rev.Lett. 44, 593. Watkins, G . D., Troxell, J. R., and Chatterjee, A. P. (1979). In Defects and Radiation ESferts in Semiconductors 1978, J. H. Albany (ed.), p. 16. Inst. Phys., Bristol. Weber, E., and Riotte, H. G. (1978). Appl. Phys. Lett. 33, 433. Weber, E., and Riotte, H. G. (1980). J . Appl. Phys. 51, 1484. Weigel, C., Peak, D., Corbett, J. W., Watkins, G. D., and Messmer, R. P. (1973). Phys. Rev. B 8, 2906. Weiser, K. (1962). Phys. Rev. 126, 1427. Will, G. N . (1969). Solid State Electron. 12, 133. Yamagishi, H., Fusegawa, I., Fujimaki, N., and Katayama, M. (1992). Semicond. Sci. Technol. 7, 135. Zimmermann, H., and Ryssel, H. (1992a). Appl. Phys. A 55, 121. Zimmermann, H., and Ryssel, H. (1992b). J . Electrochem. SOC. 139, 256.

St MlCONDliC rORS A N D SEMIMETALS. VOL 42

CHAPTER 6

Some Atomic Configurations of Oxygen B . Pajot CROUPE DE PHYSIQL'E DES SO1 I D t S U N I V E R S I T ~DE PARIS, PARIS. FRANCE

1. 11.

111.

IV.

V.

VI.

VI1.

INTRODUCTION . . . . . . . . . . . . . . . . . . . SPECTROSCOPY OF LOCALIZED MODESI N SEMICONDUCTORS . . I . Localized Mode.\ und Resonant Modes . . . . . . . 2. Intensities . . . . . . . . . . . . . . . . . . . 3 . Stress-Induced &ffects , . . , . . . . . . . . . . INTERSTITIAL OXYGEN, . . . . . . . . . . . . . . . I . Staric Properties . . . . . . . . . . . , . . . . . 1. Dynamic Properries . . . . . . . . . . . . . . . 3 . Perrurhation hy Foreign Atoms . . . . . . . . . , . Q~~ASI-SUESTITUTIONAI OXYGEN. . . . . . . . . . . . I . Spectroscopies o / rhc Oxygen-Vacancy Defect . . . . 2 . Thermal Stability , . . . . . . . . . . . . . . 3 . Other 0-Related Irradiation Defects . . . . . . . . COMPARISON W I T H OTHER LIGHTELEMENT IMPURITIES . . . I . C'urbon . . . . , . . . . . . . . . . . . . . . 2 . Nitrogen . . , . . . . . . . . . . , , . . , . . 3 . Hydrogen . . . , . . . . . . . . . . . . . . . OXYGEN I N OTHER SEMICONDUCTORS . . . , , . . . . . 1. Germanium . . , . . . . . . . . . . , . . . . . 2 . Gallium arsenidt. , . . . . . . . . . , . . . . . SUMMARY . . . . . . . . . . . . . . . . . . . . Acknondedgments . . . . . . . . . . . . . . . . . Referenc,es . , , . . . , . . . . . . . . . , ,

191 i94

194 196 196 200 200 210 21 I 217 217 220 222 224 224 226 228 233 213 236 243 244 245

1. Introduction

Oxygen is present in silicon crystals grown by the Czochralski 1CZ) pulling technique from a silica crucible (Chapters 2 and 7). It is also present in float-zoned (FZ) material refined under vacuum, but there the residual background is on the order of 10l3atoms/cm3 compared to about atoms/cm' in the CZ material. The affinity of oxygen for silicon can be explained by the strength of the Si-0 bond (-5.6 eV in molecules like HOSi (CHJ3), which i s stronger than the Si-Si bond ( - 2 . 3 eV in silicon). The infrared (IR) absorption measurements (Jastrzebski et a]. , 1982; Pajot et al., 1985) also show that most of the oxygen present in as-grown CZ 191 Copyright 0 1994 by Academic Pies\. Inc All nghts of reproductlon In any form reserved ISBN 0-12-752142.9

192

B. PAJOT

silicon at room temperature is in a dispersed form, labelled interstitial oxygen (O,), the structure of which will be presented in due time. Near the melting point of silicon (1412°C) the solubility of oxygen is estimated to be 2.1 x 10l8 atoms/cm3 (Carlberg, 1986). The temperature dependence of the solubility shows some scatter (Mikkelsen, 1986), but it none the less indicates that the equilibrium solubility at room temperature is smaller by several orders of magnitude than the concentration of dispersed oxygen in as-grown crystals. This means that as-grown CZ silicon is oversaturated with oxygen at room temperature and, as a consequence, annealing of the material can produce the precipitation of oxygen into various forms of silica (SiO,) precipitates. These precipitate forms can be considered globally as a second physical state of oxygen in silicon. From an initial state where oxygen is dispersed in silicon, it is possible to reach after annealing another state where the whole oxygen content is precipitated (the exact morphology of the precipitates depends on the annealing conditions). The situation is reversible and oxygen can be dispersed again by dissolution of the precipitates at very high temperature (- 1300- 1350°C) and quenching to room temperature. At high temperature, oxygen out-diffuses from the near surface regions so that the full 0,concentration is measured only in the bulk of the material. It has been observed by high-resolution X-rays diffraction measurements (Takano and Maki, 1973) that the presence in silicon of dispersed oxygen produces a small increase of the average lattice spacing, proportional to the oxygen concentration. This increase indicates a local expansion of the lattice near the isolated 0 atom. It has also been shown that the commonest form of silica found in the microprecipitates is the amorphous phase, with a density comparable to that of silicon. Hence, whatever its form, the presence of oxygen in silicon always leads to an expansion of the material and to built-in stresses. In the case of large precipitates, these stresses can be relieved by the growth of dislocations. The precipitates are characterized by their stoichiometry, their distribution, their structure and their size. These parameters depend on the annealing conditions. A discussion of the relationship between the shape of the precipitates and their infrared absorption has been given by Gaworzewski et al. (1984). Details on the properties of the oxygen precipitates can be found in other chapters of this book. Group VI doping elements S, Se and Te, are double donors in silicon (for a review, see Wagner et al., 1984). This electrical activity is explained by a substitutional location of these elements in the same way as the single donor electrical activity of P, As, Sb or Bi. As-grown CZ silicon displays an n-type electrical activity related to oxygen (Kaiser and Keck, 1957). This electrical activity comes indeed from a series of donor cen-

6.

SOME ATOMIC'('ONFIGURATIONS OF O X Y G E N

193

ters, the so-called thermal donors (TDs), which are also double donors (Wruck and Gaworzewski, 1979). Substitutional oxygen, which is also a group V1 element. could act as a double donor on a substitutional site. This location is unstable because of the small tetrahedral radius of the 0 atom (0.68 A), but it has been argued that TDs could be due to substitutional 0 surrounded by interstitial 0 to compensate an inward distortion by an outward distortion (Keller, 1984). The total concentration of these TDs is typically less than 1%) of the total oxygen concentration in the as-grown material. The TDs are thermally unstable, and they are destroyed by annealing the as-grown material above 550°C. The same TDs can be created again under annealing in the 400-500°C range and they are sometimes labelled 450°C TD. The singly ionized state of these TDs is paramagnetic because of the presence of an unpaired electron (Muller et al., 1978). The electron nuclear double resonance (ENDOR) results on the paramagnetic state in samples enriched with isotope "0 can be interpreted by assuming that the core of the TDs contains four oxygen atoms (Michel et al.. 1989) with a C2vpoint group symmetry. On the other hand, calculations by Deak. Snyder and Corbett (1992) lead to a model of TDs involving two 0 atoms and a self-interstitial. This seems to demonstrate that the core of the TDs is not an isolated on-center oxygen atom, but the maximum number of 0 atoms in the 450°C TDs is not known. Now, it can be said that despite substantial progress, a unified picture of these donors including a full microscopic description has not yet been reached. Annealing of as-grown CZ silicon wafers for a short time at between 650 and 800°C is done to destroy the 450°C TDs produced during the cooling-down of the crystal (the annealing time decreases when temperature increases). After the destruction of these TDs, the electrical activity of CZ silicon is the same a s that of FZ silicon with the same dopant concentration. and this can be considered as a proof that interstitial oxygen is electrically inactive. If the annealing time is increased beyond a few hours, the free-electron concentration starts increasing again as a new kind of thermal donors is produced (Capper et al.. 1977; Kanamori and Kanamori, 1979). This electrical conduction has been attributed to inversion layers surrounding some silica precipitates (Henry et al., 1986). In this introduction, I have attempted to give an overview of the different states where oxygen can be found in silicon when used for technological purposes, pointing out that the isolated form is interstitial oxygen. In the next sections, I will narrow the study to the structure and dynamics of isolated and nearly isolated forms of oxygen in silicon. I will therefore extend the description to the oxygen complexes created by irradiation with energetic particles, and it will be instructive to compare these prop-

194

B. PAJOT

erties and structures with those of other light and reactive elements in silicon. I will show in the last section that the structure of the oxygenrelated centers in other semiconductors have a great similarity to the forms in silicon, but that the relative strength of the bonds between 0 and the atoms of the crystal can allow for instance the formation of OH bonds not found in silicon. A wealth of information on the structure and stability of oxygen complexes in semiconductors has been obtained from their localized vibrational modes, I will henceforth start by trying to show how the information can be deduced from the infrared vibrational spectra.

11. Spectroscopy of Localized Modes in Semiconductors

1. LOCALIZED MODESAND RESONANT MODES In semiconductors, localized defects (LDs) can produce localized or resonant vibrational modes. Most of the LDs are isolated interstitial or substitutional foreign atoms, pairs of atoms or association of a foreign atom with a lattice defect. The frequencies of the modes induced by the LDs depend on the force constants between the foreign atoms and those of the host crystal as well as on their mass differences. Sketchily, when the differences between the force constants and the masses are small, the frequencies of the modes induced by the LDs fall within the allowed frequencies of the crystal, and they are resonant with some phonon frequencies. Conversely, for large force constants or for atoms with small masses, the frequencies are higher than the Raman frequency; they cannot propagate in the crystal and remain localized near the defect, hence their name of localized modes. Representative frequencies calculations have been made for impurity pairs in silicon (Elliott and Pfeuty, 1967) and for isolated substitutional impurities in semiconducting compounds with zinc blende structure (Vandevyver and Plumelle, 1977) using Green’s function techniques. Recently, ab initio calculations of LDs structures and vibrational modes have been undertaken starting from a crystalline molecular cluster and the results of such calculations will be discussed later. LDs at high densities can also alter locally the phonon density of states of the host crystal and such accidents are observed in silicon (Angress, Goodwin and Smith, 1965). Much information has been gained from the IR study of the localized vibrational modes (LVM) due to LDs in semiconductors because they can generally be observed as sharp lines on a monotonous background. Some of the bonds in LDs can also be found in other compounds or chemicals, and the LD can sometimes be considered as a small pseudomolecule interacting with the host crystal. In semiconductors, this is the

6.

S O M E ATOMIC (‘ONFIGURATIONS OF OXYGEN

195

case for the LDs involving a H atom bonded only to an atom X of the crystal (linear molecule XH)or for an atom like oxygen bonded to two atoms of the crystal. The small-molecule approximation is especially useful to calculate isotope shifts, as simple relations used in molecular spectroscopy can be used. In the valence bond approximation, the isotope shift for the antisymmetric mode v 3 of a nonlinear molecule X Y I with symmetry Czl is given by v;/v, =

{ [ ( M , / M , + 2 sin’a)/M,yJ’/[(M,/M, + 2 ~in*a)/M,I}”~,(1)

for the substitution of atom X or the two atoms Y (molecule ( X Y z ) ‘ ) .M , and M , . are the masses of atoms X and Y , and 2a is the apex angle of the molecule. assumed to be unchanged by the isotopic substitution. When only one atom Y is changed, the isotopic shifts for the t w o symmetric modes of (XY,)’ are required (DeWames and Wolfram, 1964). In practice, for moderate shifts, the arithmetic mean of the positions for X Y 2 and (XY,)’ is a good approximation. An interesting aspect of the measurement of an isotope effect is the possibility to identify one or more atoms of a center, knowing their masses and their isotopic abundances. As crude as it looks, expression ( 1 ) allows a determination of the value of 2a and the interaction between the LD and the surrounding lattice. This is obtained from a self-consistent fit using expression ( l ) , where the mass M , of the atoms of the lattice is replaced by M y + M ‘ or by x M , ( x > 1 ) where parameters M ’ or x represent the interaction of X Y 2 with the rest of the lattice (Newman, 1973; Pajot and Cales, 1986). A comparison between the predicted values and the experimental ones can inform us of the interaction between the pseudo-molecule and the host crystal. When light elements like hydrogen, carbon, nitrogen or oxygen are involved in a LD, the use of isotopically enriched samples can provide information on the number of atoms of this element in symmetric locations of the LD. This is because, if two or more identical atoms with the same mass vibrate at the same frequency, the change of the mass of one of these atoms by isotopic substitution will change the frequency. When the LD is electrically active, a change in its charge state occurs as a function of the Fermi level in the semiconductor. This can produce a change of the frequency of its LVM related to the change in the force constants and polarization of the LD. Hence, the observation of Fermilevel dependent LVMs related to the same LD indicates an electrical activity of this LD. The LDs have a well-defined symmetry. in silicon, the maximum symmetry of a defect is that of the tetrahedral point group Td.The corresponding LVM is a threefold degenerate as it transforms under the same irreducible representation as x. .v and z . For LDs with lower symmetry (C?,,

196

B. PAJOT

for a trigonal center), the threefold vibrational degeneracy must be partially removed into a nondegenerate and doubly degenerate LVM so that two lines should be observed. A consequence of the lowering of the spatial symmetry of the LD is the existence of equivalent orientations for this defect in the crystal. For instance, a defect oriented along a (1 1 I ) axis has four possible orientations, representing a fourfold orientational degeneracy of the LD distinct from the vibrational degeneracy of the LVM. The existence of the orientational degeneracy must be kept in mind as it will be the origin of most of the effects observed when a uniaxial stress is applied to the crystal containing the LD.

2. INTENSITIES In the SI system, the integrated absorption Ai of an isotropic oscillator with reduced mass p at concentration N in a solid with refractive index n is

where E” and c are, respectively, the permittivity of vacuum and the speed of light in a vacuum. The effective charge q (in electric charge units) can be considered as a dipole moment per unit of displacement (note that expression (2) corresponds to a spectrum plotted in wavenumber units). With p in atomic mass units and q expressed in units of electron charge, q

=

4.56 x 10’. (pnAi(cm-2)/N(cm-3))”2,

Expression (2) is deduced from that given by Newman (1973), and strictly speaking, it is valid only for a center with cubic symmetry like a substitutional isolated impurity. Once the effective charge is determined for a LVM at a given temperature, a calibration factor of the absorption can be obtained. Effective charges can also be obtained from ub initio calculations by computing the change in the dipole moment of the cluster when the atoms are displaced in proportion to the normal coordinates (Jones and Oberg 1992). 3. STRESS-INDUCED EFFECTS a. Stress-tnduced

Splitting of the LVMs

A uniaxial stress applied to a crystal containing LDs produces an elastic strain that can remove part or all of the degeneracies associated with these LDs. For a substitutional impurity in a cubic crystal, there is no

6.

S O M E ATOMIC CONFIGURATIONS OF OXYGEN

I97

urientational degeneracy and the stress can partially or totally remove the threefold degeneracy of the LVM because it lowers the symmetry of the LD. For an anisotropic LD, the main effect for most of the stress directions is the partial or complete removal of the orientational degeneracy. This produces a splitting of the LVM because of the angular dependence of the coupling of the electric dipole with stress. The physical separation between the dipoles vibrating with different frequencies implies a total o r partial polariLation of the stress-split components with respect to the stress direction. When stress is applied along simple crystallographic directions, the number of stress-split components, their relative intensities and polarizations can be obtained from simple geometrical arguments considering the initial orientations of the dipoles. In the actual cases, the orientations of the dipole moments are derived from the experimental data. The splitting of the components is a bilinear function of the stress and of the piezoyxctroscopic coefficients of thc LD. For crystals with a diamond or rinc blende structure. there are five possible kinds of LDs with distinct \ymmetries. Kaplyanski (1964) has tabulated the number of components, rhc relative intensities and the polarizations for these five groups for stresses along the (100). ( 1 10) and ( I I 1) directions. He has also calculated the number of independent piezo-spectroscopic coefficients and the shifts from the zero-stress value for these five groups. We are concerned here mainly with trigonal and rhombohedric I LDs where the dipole moments are along ( I 1 I ) and (I10) directions, respectively. The number of independent coefficients are two ( A , and A : ) for the trigonal centers and three ( A , . A ? and A , ) for the rhonihohedric I centers. Tables I and 11 adapted from Bosomworth et a]. (1970). give the shifts of the stress-induced components of a LD with one of these two symmetries as a function of the orientation of stress (T. h. Dic.hroism und Atomic Rcoric~ritutiori

Under stress, previously equivalent orientations of the same anisotropic L D are distributed i n t o classes with different energies (as a rule, the highest energy is for orientations parallel to the stress). With stress applied at a low temperature, there is no change in the population of the different orientations to minimize the LD energy because atomic reorientation requires energy taken from the lattice phonons. When stress is applied at a temperature where thermal energy allows reorientation of the LD and when the sample is cooled under stress, the low-temperature population of the orientations with the lowest energy is enhanced. The \tress can be released at a low temperature as the populations are frozen.

198

B. PAJOT

TABLE I REMOVING OF THE FOURFOLD ORIENTATION DEGENERACY OF A LVM RELATED TO A ( I 1 I)ORIENTED CENTER FOR DIFFERENT ORIENTATIONS OF A UNIAXIAL STRESS u (THE RESIDUAL DEGENERACY Is NOTEDR). THESHIFT A PER UNITSTRESS OF A COMPONENT WITH RESPECT TO THE ZEROSTRESS POSITION Is GIVENAS A FUNCTION OF THE INDEPENDENT PIEZO-SPECTROSCOPIC COEFFICIENTS A, A N D A2. THERELATIVE INTENSITIES I FOR DIPOLES P OR u AREGIVEN FOR 4 1 OR 1 TO u OR PARALLEL TO SPECIFIC ORIENTATIONS. 111 : I 1

u parallel to

A

R

[1101

A , + A2 A, - A2

2 2

P

U

P

U

2: 1:o 0:1:2

1:2:3 3:2:1

TABLE I1

REMOVING OF THE SIXFOLD ORIENTATIONAL DEGENERACY OF A LVM RELATED TO A (110)ORIENTED CENTER FOR DIFFERENT ORIENTATIONS OF A UNIAXIALSTRESS u (THE RESIDUAL DEGENERACY Is DENOTED R). THESHIFT A OF A COMPONENT WITH RESPECT TO THE ZERO STRESS POSITION Is GIVENAS A FUNCTION OF THE INDEPENDENT PIEZO-SPECTROSCOPIC COEFFICIENTS A , , A A N D A,. THERELATIVE INTENSITIES I AREGIVENFOR DIPOLES p PARALLEL TO (1 lo) OR TO (100) WITH THE ELECTRIC VECTOROF THE RADIATION Ell OR I TO u OR PARALLEL TO SPECIFIC ORIENTATIONS.

[lo01

[I111

11101

4 2 3 3

1

4 1

A2 A,

(A, (A,

+ 2 ’ 4 2 + 2AJI3 + 2A2 - 2A,)13

A2 + A3 (AI + A d 2 A2 - A3

2: 1 0: 1 4: 1 0:3

0: I

I:O:O

0:l:O 2:0:2 0:l:O

l:2:l 0:o: I

1

:o

1:l 1:l

6.

SOME ATOMIC CONFIGURATIONS OF O X Y G E N

199

The population difference reflects on the dichroism of the sample measured by 9 = (a1 - all)/(aL+ all), where a I and all are the absorption coefficients measured for radiation polarized respectively perpendicular and parallel to the initial stress. We consider as an example ( I 1 I)-oriented dipoles forced to reorient under a ( 1 10) stress: the four orientations with initial populations no are converted into two orientations with population H , , , ~ ~ ,and two with population n L ( o w )It. can be checked that here, 9 = ( n , - nL)/2n,,.After removing the strain, the dichroism is maximum (ao). Assuming a first-order kinetics for the return to equilibrium, &d/df = -4k,@,

(3)

where kR is a thermally activated reorientation rate. At temperature T . it can be written k, = vO exp[ - ER/k,T], where vo is an attempt frequency and ER is the energy required to reorient the LD. After annealing at temperature 7 during time t . the dichroism decreases to 9 = 9" exp[ - 4kRf]. Successive isothermal annealings allow us to determine k,. An independent determination of vo and ER is obtained by repeating the procedure at different temperatures. Atomic reorientation of the oxygenvacancy center has been observed by EPR and by IR absorption (Watkins and Corbett; Corbett et al.. 1961).The measurement of atomic reorientation of interstitial oxygen in silicon and germanium (Corbett et al., 1964a) enabled a spectroscopic determination of the diffusion coefficient of oxygen in these semiconductors as atomic reorientation is the first step of diffusion (see also Chapter 8 ) . c'.

Dicliroism und St ress-Depcnden t Currier Capt ure

In a semiconductor, an electrically active LD has at least one level in the band gap. The energy of this level is also stress sensitive. Let us consider an LD with an electron acceptor level deeper than that of shallow donors. If the sample contains shallow donors at a concentration smaller than that of the LD. all the donor electrons are trapped at the acceptor level of the LD, and some of the acceptor levels remain empty. If such a sample is cooled under stress from a temperature where the electrons are not yet trapped by the acceptor level, the electrons would be progressively trapped, starting at the levels made deeper in the band gap by the stress. Hence the more shallow levels will remain empty or partially filled. The measurement of a I and all at LHeT after removing the stress will also show a dichroism due to stress-dependent electron capture. An analysis similar to the one made for atomic reorientation gives the thermalization energy of the electron in the conduction band, which is a value close to that of the electron acceptor level. Such a

200

B. PAJOT

stress-dependent electron capture has been observed for the neutral oxygen-vacancy center in silicon (Watkins and Corbett; Corbett et al., 1961).

111. Interstitial Oxygen

1. STATIC PROPERTIES Direct evidence for interstitial oxygen in silicon comes from the observation of its vibrational modes. They have first been detected by infrared absorption (see also Chapters 3 and 4). Phonon spectroscopy using superconducting tunnel diodes has also been used, and a brief description of this technique and its possibilities is given at the end of the paragraph. The infrared studies of Hrostowski and Kaiser (1957) using "0-enriched samples (the normal percent abundances of the 0 isotopes are I6O:99.76, "0 :0.04, "0 :0.20) showed that three vibrational features were associated with oxygen in as-grown silicon. They were then attributed to the three modes of a nonlinear Si-0-Si pseudo-molecule with Cz,, symmetry embedded in the silicon lattice. The most intense line, located at 1136 cm-' at liquid helium temperature (LHeT), was ascribed to the antisymmetric mode v 3 of Si-I6O-Si. Two other lines at 517 and 1206 cm-' were ascribed to the two symmetric modes of this Si-0-Si pseudo-molecule. In this pseudo-molecule, the Si atoms were assumed to be nearest neighbors atoms of the crystal, and the bridging with the 0 atom resulted from breaking the Si-Si bond. In this configuration, the interstitial 0 atom is located in a (111) plane equidistant between the two Si, atoms and its exact position depends on the Si-0-Si angle (Fig. I). A confirmation of this kind of interstitial structure came from the observation of the Si isotope effect of the v3 mode. Figure 2 shows the absorption of this mode at LHeT in a sample enriched with "0 and "0: the main absorption features near 1136, 1107 and 1084 cm-' are due to the 0 isotope effect, and their intensities are proportional to the concentrations of the different 0 isotopes. The structure seen for each 0 isotope is due to the isotope effect (silicon has three isotopes, 28Si,29Siand 30Si,with respective percent abundances of 92.17, 4.71 and 3.12), and the relative intensities of the components correspond to 28Si20,28Si029Si and 28Si030Si.The intensities of the other Si isotopes combinations are too small to be seen here. Incidentally, this figure illustrates an interesting, but unexplained feature: while the lines for l 6 0 and "0 have a FWHP of 0.6 cm-', the one for "0 is -1.2 cm-I (the only difference between "0 and the other isotopes is its nonzero nuclear spin (5/2)). This observation first made on standard CZ samples is independent of the samples used (Pajot, 1986). When cor-

6.

20 1

SOME ATOMIC CONFIGURATIONS OF OXYGEN

tic,. I . Model of a silicon unit cell containing an interstitial 0 atom (dark gray). This representation takes into account the actual distortion of the first neighbors of 0 along a ( I I I ) axis.

L

1070

10%I

III 0

I130

1150

\ ~ ' 4 L ' I ~ N l ~ h l R l(cm-1) iR FIG. 2 . Absorption o f vl(Oi)at h K i n ;I silicon sample enriched with "0 and ''0. 'The low-energy satellites are due to 'xSiO"Si and "Si0'"Si combinations. Note the broadening of the "0,mode (Pajot 1988).

rected for the intensity of the wing of the 2xSi2'60 line at the position of the small lines. the experimental relative intensities of the components match the calculated ones. This comparison was considered by Pajot and Deltour (1967) as proof that the 0 atom was bonded to two Si atoms. A similar conclusion was also reached by Bosomworth et al. (1970). When the temperature is raised above 8 K. new lines appear on the low-energy

202

B. PAJOT

side of the 1136 cm-' line (Fig. 3). These lines were attributed to transitions from thermalized levels close to the ground state (Hrostowski and Alder, 1960), but no quantitative level scheme was provided at that time. At room temperature, only one broad absorption band is observed near 1106 cm-' with a FWHP of -30 cm-'. This band is probably the superposition of sharper thermalized components originating, as will be shown later, from the low-frequency vibration-rotation motion of the 0 atom in the (1 11) plane. This is substantiated by the asymmetric profile of the band and by a noticeable shift of the peak absorption with temperature (Schomann and Graff, 1989). The attribution of the line at 1206 cm-' to a symmetric mode of 0;was questioned by Chrenko, McDonald and Pel1 (1969, who suggested that it was indeed related to a combination of the v3 mode with the libration of the 0 atom about the (1 11) axis containing the two Si atoms. The confirmation came from the thorough investigation of Bosomworth et al.

FIG.3 . Absorption of u3(l6Oi)in silicon at between 15 and 100 K showing the progressive thermalization of the low-frequency excited levels (K. Krishnan and S. L. Hill (1981). In Fourier Transform Infrared Spectroscopy, H. Sakai (ed.), p. 221. S.P.I.E., Bellingham, Wash.). Compare with Fig. 2 .

6.

SOME ATOMIC CONFIGURATIONS OF O X Y G E N

203

WAVENUMBER (cm-1)

FIG. 4. (a) Low frequency absorption of "0,in silicon due to the transition from the ground state to the first excited state of the two-dimensional oscillator. The FWHP of 0.2 c m - ' is resolution limited. (b) The same absorption at 35 K , showing transitions from thernialized levels. ( c ) .4bsorption of a 'XO-enrichedsample (from D. R . Bosomworth, W. Hayes. A. R . L. Spray and G. D. Watkins (1970). Proc. Phys. Soc. London A 317, 133).

(1970), who reported the observation of a low O-related frequency vibration at 29 c m - ' for I6O and 27 c m - ' for I80at LHeT (Fig. 4a and 4c). The corresponding mode for "0 has also been observed at 28 cm-' (Pajot, 1988). Bosomworth et al. (1970) explained the mode at 29 cm-' by a lowfrequency vibration of the 0 atom in the ( I 11) plane perpendicular to the Si . . Si broken bond. The motion of the 0 atom in this plane can be

204

B. PAJOT

considered either as a perturbed two-dimensional (2D) oscillator vibration or as the combination of a nearly free rotation about the Si . * . Si axis and of a low-frequency vibration of the 0 atom in a (211) plane. In the first case, a given state is labeled by quantum numbers v = v , + v2 and I = v I - v2. The IR selection rules are Av = I , A1 = ? 1 and the transitions are polarized in the two-dimensional oscillator plane. In this framework, the low-frequency mode observed at LHeT is the 10, O> + I I , t I > transition. In the second case, the formalism for the vibrationrotation interaction can be used: the vibrational state is a symmetric mode u2 of the Si-0-Si quasi-molecule described by a vibrational quantum number n (to avoid the confusion with v used previously) and the rotation about the Si . . . Si axis by a rotational quantum number J . At LHeT, the only transition observed is A n = 0, A J = 1 . It corresponds to a one-quantum excitation of the rotational motion of the 0 atom in the ( 1 1 1 ) plane about the broken Si . . * Si axis. At temperatures above LHeT, Bosomworth et al. (1970) also observed far IR lines corresponding to thermalized levels for the low-frequency excitations (Fig. 4b). They related these transitions with the ones near 1136 cm-’, and they could derive from both sets of data a unique energy level scheme. These two models give nearly identical values of the apex angle 2a of the Si-0-Si group (= 162”). Assuming an unaltered bond length of I .6 A for Si-0, the distance between the two bridged Si atoms is then 3.16 A compared to a nearest neighbors distance of 2.35 A in the unperturbed silicon lattice. The expansion due to oxygen must be partially compensated by a compression of the neighboring Si-Si bonds, and this explains why an average increase of the lattice constant of silicon is observed with increasing concentrations of interstitial oxygen. A more sophisticated phenomenological model of the vibration of 0, in silicon (but physically equivalent to the preceding) has been worked out by Yamada-Kaneta, Kaneta and Ogawa (1990) using a Si, = Si-0-Si = Si, pseudo-molecule with point group symmetry D3d.These authors consider the Hamiltonians for the unperturbed motion of the 0 atom in the ( I 1 1) plane and for the antisymmetric 0 mode (irreducible representation A2,, of D3J along the ( 1 1 I ) axis coupled by an interaction term. In the interaction scheme, a state is described by Jk, I , N > , where k describes the radial dependence of the two-dimensional anharmonic excitation, I , its angular dependence and N , the high-frequency A , , mode. In this description, the 29, 1136 and 1206 cm-’ lines correspond, respectively, to the transitions from the ground state 10, 0, O> to the 10, I , O>, 10, 0, I > and 11, 0, 1 > states. The calculation of the eigenvalues of the Hamiltonian as a function of the adjustable parameters was performed self-consistently using experimental frequencies for I6O and l8O. The

*

6.

205

SOMF 4lOMIC' CONFIGURATIONS O F OXYGEN

IABLE 111

ASSOCIATED WITH BFTWEEN EXPFRIMFNTAI F R I QlJFNC I F 5 (Cm I ) FOR TRANSITIONS %1,0I N S i r r c o r u roR T H E DIFFFRFYT i)ISOTOPFS A N D THOSE ( I N B H A C K E T S ) CAICULATED B> Y ~ M A D A - K A N FFTTAAI (1990) T t r i S I X cm ' MODE Is NOT INCIUDED THE I N I T I ~ L ( I ) 4 h l ) F I N A l ( f ) S T A T E S OF THE TRANSIIIO ARE NSINDICATFD W H E N A V A I L A B L F , E X P E R I M E N T A I ERLQIIEMIFSFOR "0 H A V FALSO B E IN G I V F N ( OMPARIWN

1

10. 0. 0 >

10.

?

I. 0

'

10. 0. I-> /I.0, I>

29.33

28.P

27.2"

129.41 I 136.4 I 1135.7)

1109.5'

"7.51 1085.0' 11084.I I

[ 1203.8)

I IS I . I" [ I 148.51

37.8" 137.21

35.2" [34.7]

1203.7'

117f1.7~

128.3' 127.71

I 101.3d

216.7' 216.51

I192.6d

1077.6" 1077.7 I 1161.31

1071 8d [ 1072.hl "Bosomworth et al. (1970). hPa;ot I1988). 'Pajot and Cales (1986). "PdjOt (1986).

overall agreement with the experimental values of the frequencies of the transitions given in Table 111 is good. For N = 0, the equilibrium positions of the 0 atom with respect to bond-center (BC) location are 0.25 and 0.24 A for I6O and "0,respectively. For N = 1 , these values increase to 0.34 and 0.32 A. An interesting result of the calculations by YamadaKaneta et al. ( 1990) is that the phenomenological coupling constant between the A,,, mode and the 2D low-frequency motion (2DLFM), used to fit the data. is found to be negative. Now, in the interaction scheme, the radial dependence of the force constant of the Az,, mode (labeled u3 for convenience) is proportional to this coupling constant. It follows then that, when the distance of the 0 atom from the BC position increases. the frequency of ui should decrease. A best fit analysis of the Si and 0 isotopic shift of the u3 components has also been performed using a simple molecular model by adjusting the lattice interaction through an adjustable

206

B. PAJOT

mass M' added to that of the Si atoms and the Si-0-Si angle 2a (Pajot and Cales, 1986). A value of 3 amu is obtained for M' and the value of 164" for 2a is about the same as the one obtained by the other methods. The frequency of the Oi-related mode at 517 cm-' is less than the Raman frequency of silicon (524 cm-' at LHeT at the Brillouin-zone center). Piezo-spectroscopic measurements on this mode (Stavola, 1984) indicate that the components of its dipole moment transform like coordinates x and y in the (1 11) plane (coordinate z is chosen along the trigonal ( 1 1 1) axis). Consequently, this mode can be labeled by the doubly degenerate representation E,, of point group D3d. From the fact that (i) no O-isotope effect is observed for this E, mode and (ii) no Si-isotope effect is observed for the 2DLFM, it is assumed that the coupling between these two modes is negligible. It turns out that the 518 cm-' line is very close to the Raman frequency of silicon. The E,, mode (labeled uI for convenience) is attributed to an in-band O-induced resonance (Angress et al., 1968). A weak line at 1013 cm-' has been ascribed to an overtone of u I (Pajot and Cales, 1986). A weak 0,-related line is also observed at 1725 cm-' at room temperature (Lappo and Tkachev, 1970; Pajot et al., 1985), shifting to 1749 cm-' at LHeT (Krishnan and Hill, 1981; Pajot and Cales, 1986). The frequency seems too small to ascribe this absorption to an overtone of v3: this would imply an unusually large anharmonicity of u3 and an overtone/ fundamental intensity ratio larger than the intensity ratio observed (1.6 x lo-'). The temperature dependence of the structure of the new absorption is similar to that of uj: thermalized lines appear above 10 K and the absorption shifts to 1720 cm-' at room temperature. The energy difference ( ~ 6 1 3cm-') between the new absorption and v3 is constant and temperature independent. This value compares with the energy of the two-phonon TA + TO mode at the X point of the Brillouin zone of silicon. Therefore, it seems sensible to ascribe the 1749 cm-' line to a combination mode of u3 with the earlier lattice phonon combination (Pajot et al., 1985). The Si isotope shift of the new line is however -3.5 times larger than that of v3, and this implies a strong coupling of the lattice phonons with the nearest neigbors of the 0 atom that is not expected at first sight. The vibration of 0; in silicon has also been detected by phonon spectroscopy (Dittrich, Scheitler and Eisenmenger, 1987). In this method, a superconducting Al-insulator-A1 tunnel diode acting as an acoustic phonon generator is evaporated on one side of an O-containing silicon sample. The frequency of the phonons emitted is tuned by changing the generator voltage. An Sn-insulator-Sn superconducting junction evaporated on the opposite side of the sample acts as a detector (the typical sample thickness is 1-2 mm). With this combination of junctions, the useful

h.

800

SOME ATOMIC CONFIGURATIONS OF OXYGEN

900

1000

1100

1200

207

1300

PHONON FREQUENCY (GHz) FIG. 5 . Phonon absorption spectrum at I K of the ZDLFM of '*O,In nuturd silicon. The contribution of I6O,has been computer subtracted for clarity. The converted FWHP of the '*O, absorption is 0.13 cm-I. The high-energy satellites are attributed to 0, pairing ( E . Dittrich. W. Scheitler and W. Eisenmenger (19871. Japan. J . Appl. Phvs. 26, Suppl. 26-3,

R73).

phonon spectrum is 280-3000 GHz (9.3-100 cm-I). The acoustic phonons can be resonantly absorbed in the silicon sample, and this produces dips in the phonon power spectrum detected. Two absorption dips are observed with a standard CZ silicon sample: The stronger one at 875 GHz (29.14 c m - ' ) and a weaker one at 823 GHz (27.41 cm-I) corresponding respectively to the ZDLFM of IhOand I8O. In this spectral range, phonon spectroscopy is more sensitive by two orders of magnitude than IR absorption (Fig. 5 ) . An nh initio calculation of the LVM of interstitial oxygen in silicon has been made by Jones, Umerski and Oberg (1992) using a crystalline molecular cluster of reasonable size (OSi,H,2) centered on an interstitial 0 atom. After relaxation of the atoms of the inner Si, = Si-0-Si = Si, group, energy convergence is obtained for some values of the bond angles and interatomic distances. These are given in Table IV with the calculated frequencies. The agreement for the antisymmetric mode is very good. From this calculation, v l should correspond to the symmetric stretching mode calculated to vibrate at 554 cm I, as the displacement of the 0 atom for this mode is found to be negligible. This last result can explain why no 0 isotope effect is observed for this symmetric mode. The frequency of the 2DLFM is very sensitive to the size of the cluster, and it is outside the range of applicability of the method used. The effective ~

208

9. PAJOT

TABLE IV AB INITIOATOMIC PARAMETERS AND FREQUENCIES (cm-I) FOR INTERSTITIAL OXYGEN I N SILICON (Jones et al., 1992). EXPERIMENTAL VALUES AT LHeT AREGIVEN I N PARENTHESES. THEMODE LABELS ARERELATED TO THOSE OF A CzvMOLECULE FOR CONVENIENCE.

VI

1 I04 (1136)

1051 (1085)

I098 ( I 129)

554 (518)

553 (518)

534 -

Si-0 length: 1.59A Si . . . Si length: 3.19A SiNN-SiNNN: 2.26A Si-0-Si angle: 172" ( 162")

charge of the antisymmetric mode at 1104 cm-' is calculated to be 3.5 e for a dipole moment parallel to (11l), close to the experimental value of 3.8 e calculated using expression (2). Experimentally, for an integrated absorption of v 3 normalized to unity, approximate relative intensities at LHeT of v , , u3 + one 2DLFM at 1206 cm-' and of the 2DLFM excitation at 29 cm-' are 0.25, 0.034 and 0.005, respectively (Pajot et al., 1985; Pajot and Cales, 1986). The stability of structures containing more than one Oi has been calculated by Needels et al. (1991). They found that only two adjacent Oi in a staggered structure are more stable (by about 1 eV) than two isolated Oi. The calculations show that chainlike clusters of several adjacent Oi along ( I 10) directions can also be stable. The thermodynamic conditions for the production of two-atom clusters is a compromise between a minimum annealing temperature for appreciable hopping of Oi (>900 K) and a maximum temperature (= 1000 K) where dissociation reduces the clusters concentration. The separation between the isolated Oi v 3 mode and the one for the 0;pair is evaluated to =20 cm-', and it is suggested that the latter could be observed at a low temperature above the isolated Oi frequency. Satellite lines (Fig. 5) have been ascribed to the shift of the 2DLFM of Oi due to the statistically distributed Oipairs (Dittrich et al., 1987). The measurement of the stress-induced splitting of the Oi lines and of the polarization of the components have provided fundamental information on their origin (Bosomworth et al., 1970). These results have been implicitly used in the preceding description of the structure and vibration of Oi, and they have reconfirmed that the dipole responsible for v3 is a (1 1 1)-oriented T dipole. The splittings of the Oi mode at 1206 cm-' shown

6.

SOME ATOMIC CONFIGURATIONS OF OXYGEN

-1

209

onentat ions

0

20

40

STRESS (kgOrnm2)

FIG.6 . Stress-dependent splitting of the 1206 c m - ' line of 0,in silicon at 20 K: (a) ull[ l 0 l . (b) ~y(ll1101.( c ) nll[l I I]. The orientations of the contributing dipoles are indicated (D. R . Bosomworth. W . Hayes, A. R . L . Spray and G . D. Watkins (1970). Proc. Phys. Soc. London A 317, 133). I kgf mm-? is approximately 10 MPa.

in Fig. 6 differ from those for a u dipole perpendicular to the ( 1 11) axis (Table I), and they also confirm the attribution of this mode to a combination involving the IT dipole of the antisymmetric O imode. It is interesting to note that when the stress is applied along a given ( I 1 I ) axis, the frequency of the vibrating dipole oriented along this axis decreases. This can be related to the nonlinear structure of the Si-0-Si group as a stress along the Si . * . Si broken bond must decrease the apex angle. In the simple quasi-molecule model, a decrease of CY. in expression ( I ) without any change in the force constants must produce a decrease of the v3 frequency. The effect is also consistent with the negative value of the coupling constant obtained by Yamada-Kaneta et al. (1990) for the interaction between v 3 and the 2DLFM. These explanations are only phenomenological, and the physical reasons lie in the electronic properties of the center. The values of the piezo-spectroscopic coefficients for the different 0, lines obtained by Bosomworth et al. (1970) are given in Table V .

210

B. PAJOT

TABLE V PIEZO-SPECTROSCOPIC COEFFICIENTS A, AND A 2 FOR THE DIFFERENT O i L i ~ IN ~ sSILICON (Bosomworth et al., 1970). Line (cm-')

A,((cm-'/GPa)

A2 (cm-'/GPa)

518 (20 K) 1136 (20 K) 1206 (20 K) 29 ( 4 K)

-1.1 0.2 ? 0.1 -0.9 ? 0.2 -3.8 ? 0.3

-0.3 -0.2 2 0.1 -2.3 2 0.3 -3.8 2 0.3

2. DYNAMIC PROPERTIES Reorientation of Oi in silicon has been detected by measuring the stress-induced dichroism of the Oi lines (Corbett et al., 1964a; Stavola, 1984; Oates and Stavola, 1987). In these experiments, an oriented sample is annealed for typically 30 minutes near 400°C under a stress u of 280 MPa. The sample is then cooled under stress to room temperature, where reorientation is blocked (in this particular case) and the stress released. The results showed that the dichroism 9 defined previously (i.e., the reorientation) was maximum for oil( 111) (Fig. 7) and not detectable for u11(100). The absence of dichroism for u11(100) indicates that the defect

1040

1100

1140

WAVENLTMBER (cm-1) FIG. 7. Stress-induced dichroism of v3(Oi)in silicon at ambient for a 270 MPa ( 1 1 1 ) aligning stress. Elland E , indicate the polarization directions parallel or perpendicular to the aligning stress (J. W. Corbett, R. S. McDonald and G . D. Watluns (1964). J . Phys. Chem. Solids 25, 873).

6.

SOME A'IOMI( CONFIGURATIONS OF OXYGEN

21 1

has (1 I I ) symmetry. The sign of the dichroism depends on the orientation of the dipole p : it is positive for v7 (pII( I 1 I)) and negative for u , ( p l ( l I I)). The recovery of the stress-induced dichroism allowed to measure a reorientation energy of 2.56 eV for the jump of an 0 atom from one orientation to an equivalent one (Corbett et al., 1964a). This energy is in good agreement with the one (2.5 eV) derived from the internal friction measurements of Southgate (1960) in 0-containing silicon. In this particular experiment, the relaxation of a mechanical excitation was followed vs. temperature. A loss peak was found at high temperature (-1050"C), and it was absent for mechanical excitation along a (100) axis. The jump of the 0 atom is the first step of its diffusion, that leads to the production of centers with more than one O atom and to the precipitation of silica.

3 . PERTURBATION BY FOREIGN ArOMs Oxygen has an electronegativity of 3.44 in Pauling's scale, and it can interact with atoms with small electronegativity. It has also been shown that 0, produced a local outward distortion of the silicon lattice so that the lattice energy can be reduced by interaction with atoms having m a l l radii. Examples of these two situations follow. (1.

Lithirrin

In silicon, Li is a fast-diffusing element acting as a shallow interstitial donor. Isolated Li can pair with 0,to form LiO complexes (Pell, 1961). The hydrogenlike IR electronic spectra of isolated Li and LiO donors due to transitions from the ground state to excited states have been reported by Aggarwal et al. (1965). The existence of several shallow L i 0 donor complexes came from the observation by Gilmer, Franks and Bell ( 1965) of distinct IR electronic spectra in Li-diffused 0-containing silicon. These results showed also that these complexes were not stable with time at room temperature. In FZ silicon. where the 0 concentration is small, only one L i 0 complex containing one 0 atom is predominant (Fig. 8 ) . This complex is responsible for the ESR line measured at 27 K at g = 1.9985 reported by Goldstein ( 1966) in Li-diffused samples and for the LiO electronic spectrum studied by Jagannath and Ramdas (1981)in similar samples at LHeT. When Li is diffused in CZ silicon to study LVM absorption, p + starting material must be used. This is to avoid the excess n-type doping that produces the strong electronic background of the L i 0 donors in the spectral region where the 0, LVMs are observed. In this material, Chrenko et al. (1965) observed at LHeT ii strong and broad (FWHP = 3 cm I ) LVM at 1016 c m - ' and u3 of isolated 0, with a small intensity (Fig. 9 ) .

212

B. PAJOT

20

24

28

32

36

40

PHOTON ENERGY (rneV)

9- 8-

-

6

v

+

4.4 x 10"cm-'182%8")

Lit 4 . 4 ~ 1 0 ~ ' c m - ' ( 9 4 % ~ i ~ )

o

-7r10'~cm-' I = 0.205 cm 7 - PUMPED HELIUM

8-

-

G -

+I--

L

SAMPLE 4

6-

-

5-

Si-O

z

g 2 $ 3

1136.0

4--

I

3-

-

2-

11342

II

Li -0

1016.6

I

P

44

6.

SOME ATOMIC' CONFIGURATIONS OF OXYGEN

213

The new mode was attributed to u3 of 0; paired with a Li' ion as this center forms at the expense of isolated Oi. New lines at 525 and 537 cm - I were also reported and ascribed to 'Li and 'Li counterparts of v I . However, experiments by other groups (Spitzer and Waldner, 1965: Devine and Newman, 1970) have shown that the two low-frequency lines were actually due to a resonant mode of the Li ion of the Li+B- pair so that there is no LiO, analog of u , for Oi. The Li isotope shift of the LVM at 1016 cm-' is very small, indicating that the motion is mainly 0 related and confirming the perturbation of 0; by Li. The structure of the most abundant LiO complex is not yet known with certainty: Chrenko et al. (1965) suggested a Li ion located in the same ( 1 11) plane as the interstitial 0 atom. Such a location does not seem to be compatible with the result of the stress splitting of the electronic spectrum of the most abundant LiO donor complex (Jagannath and Ramdas, 1981) as it indicates a (100) symmetry of the complex when neutral. The binding energy of the average Li + 0 complex is 0.42 eV. and it is electrostatic. It must be less when Li is neutral. This should be the reason w h y the LiO complexes have been found to be more stable in B-doped silicon, where they are ionized, than in uncompensated material, where they are neutral (Chrenko et al.. 1965). In silicon, Mg is also an interstitial (double) donor (Franks and Robertson, 1967), and several Mg-related donor complexes are known (Lin, 1982). From the similarity of their properties with the LiO complexes. it is likely that some of these complexes are due to the electrostatic pairing of Mg with interstitial 0. h. H y d r o g e n It was shown previously that several kinds of LiO donors can be produced by the trapping of Li, by 0,.It can be thought that a similar interaction could also occur with hydrogen. A donor HO center of a different nature has also been reported to exist in germanium (Haller, 1978). However, a cluster calculation of the structure and stability of an OH center in silicon shows that no OH bond is formed (Artacho and Yndurain, 1989). This result is confirmed by the investigation of the interaction of H with 0; by Estreicher (1990) using a h i n i f i o Hartree-Fock methods. One of the results of this study is that if H is placed in one of the interstitial tetrahedral sites nearest to 0,.the minimum energy is obtained when y H (Fig. 10a). The comparison of different the 0 atom points u ~ w from structures shows that the most stable one is Oi with a BC H atom bonded to one of Si atoms nearest neighbors of 0 (Fig. lob) and that the configuration where a OH bond is formed (Fig. 1Oc) is unstable. Proportionality has been reported between the intensity of weak LVMs observed near

214

B. PAJOT

FIG. 10. Compared stabilities calculated for (0, H) configurations in silicon in a {IIO} plane (S. K. Estreicher (1990). Phys. Rev. B 41, 9886). Shaded circles: Si atoms; dotted circle: 0; solid circle: H. (a) The H atom displaced from a T site by 0.24 A and an interstitial 0 atom correspond to a local minimum of the potential energy surface (PES). (b) H near a BC position and 0 near its usual interstitial site show a minimum of the PES of -0.66 eV with respect to (a). (c) A threefold coordinated 0, it is not stable (5 eV above (a)). The dashed open circles are the locations of the Si atoms in pure silicon.

2123 and 2192 cm-' and the Oi concentration in FZ material grown under a H, atmosphere (Qi et al., 1985), and it is possible that one of these LVMs correspond to the BC H atom of Fig. lob. c . Carbon

Carbon has been for some time a major residual impurity substituting a Si atom at a level of =5 x 1016 atoms/cm3 in CZ silicon grown from pullers with unshielded S i c heaters. It produces a LVM at 608 cm-I at LHeT (Newman and Willis, 1965). Pairing of C with Oi has been reported to give a LVM at 1105 cm-' (Newman and Smith, 1969). No C-isotope shift has been observed for this LVM and it correlates with LVMs at 589, 640 and 690 cm-' ( X , Y and Z , respectively) that exhibit a C-isotope shift (Fig. 11). The 1105 cm-' LVM was ascribed to vj(Oi) perturbed by carbon. The existence of X , Y and Z was ascribed to the vibration of the perturbing C atom nearby of Oi in a site of low symmetry that can split the triply degenerate C LVM. The C atom has a small radius that produces a

6.

215

SOME ATOMIC' ('ONFIGURATIONS OF OXYGEN

local inward lattice distortion (Baker et al., 1968). Its substitution near 0, certainly reduces the outward distortion brought by 0,. and this can be the origin of this complex. Another carbon-oxygen complex is also present at a lower concentration than the preceding one, giving a perturbed 0, mode at 1052 cm and carbon modes at frequencies higher

'

WAVI:NIJM131 K ( c n - 1 )

1000

1040

1080

1120

1160

1200

1240

WAV1~;NIIMBIIK (cm-1)

FIG. I I . Absorption near L H e T of a C% silicon sample with 0, and either '*C or "C: (a) jhows the isolated 0, u , mode. the wbstitutional C (Cs) L V M and L V M s X , Y and Z due 10 0, perturbed by C,; (b) shows the first overtone of "CS, isolated 0, modes and lines A and B . due to 0, modes perturbed by carbon (Claybourn and Newman 1988). Line A at 1105 cm and modes X , Y and Z are due to the same center. All the concentrations are of the order of I x IOln atomsicm'.

'

216

B. PAJOT

11364 1 II

4.5 B

WAVENUMBER (cm-1)

FIG.12. Ge-concentration dependence of the perturbation of v3(Oi)in silicon by Ge. The two perturbed modes are labeled 0,-I1 and 0,-111 (H. Yamada-Kaneta, C. Kaneta and T. Ogawa (1992). Materials Science Forum 83-87, 419). 1 ppma corresponds to 5 x 10l6 atoms/cm3.

than those of X , Y and Z , but there is no microscopic model for this center.

d . Germanium Silicon and germanium form a mixed crystal in all proportions. In CZ silicon containing 3 x lo2' Ge atoms/cm3,new Orrelated LVMs at 11 18.5 and 1130 cm-I were observed at LHeT (Pajot, 1969; Newman, 1973). They were attributed to v3(Oi)perturbed by a Ge atom on a second neighbor site. Recent investigations by Yamada-Kaneta, Kaneta and Ogawa (1992) for Ge concentrations ranging from 6.5 x lo'* to 6.5 x lo2' atoms/ cm3have confirmed this point (Fig. 12). In this work, the same two modes were related to Oiperturbed by one Ge atom in two different sites, excluding the nearest neighbor of 0. The perturbation could also be observed in the Oicombination mode and on the 2DLFM. A conclusion drawn from these new results is that Ge alloying reduces the anharmonic coupling between v3 and the 2DLFM, and this causes a decrease of intensity of the combination mode resulting from this coupling with increasing Ge concentrations.

6.

SOME ATOMIC’ CONFIGURATIONS OF OXYGEN

217

IV. Quasi-Substitutional Oxygen I. SPECTROSCOPIES OF THE OXYGEN-VACANCY DEFECI

Irradiation of CZ silicon at room temperature with high-energy particles, for instance 2 MeV electrons, produces primary defects (vacancies, noted V , and Si, self-interstitials). These primary defects are mobile at this temperature, and they can recombine with each other. Vacancies can also combine with existing LDs. including other vacancies, to produce secondary defects that are stable at room temperature. The oxygenvacancy center ( A center or OV, used here for convenience) is formed when a nearest neighbor of the interstitial 0 atom is ejected. Formation of OV leads to a loss of 0, but a saturation in the production of OV occurs after electron doses of = S x 10’’ cm-’. This indicates a dynamic equilibrium between the trapping of V by 0; and the trapping of Si; by OV (Newman, 1973). OV can be seen as a vacancy in which one of the reconstructed bonds is “decorated” by an 0 atom. It can also be seen as a substitutional (unstable) 0 atom having undergone a (100) distortion that pushes this atom out of center with the breaking of the elongated bonds and the reconstruction of a Si-Si distorted bond (Fig. 13).The term suhsriturional oxygen is sometimes used for this defect by opposition to interstitial oxygen discussed in the preceding section. A difference between 0, and OV is that OV is electrically active. The origin of this activity can be depicted schematically by considering the reconstructed Si-Si bond, made up of two dangling bonds (atomic orbitals), having one bonding state filled by the two electrons and one empty antibonding state. The production of OV in n-type CZ silicon has shown that this antibonding state could trap an electron with an energy deeper than that of an electron binding on a group V dopants. This state was the cause of an acceptor level at E, - 0.17 eV reported by Wertheim (1957) and Hill (1959). The EPR spectrum (sometimes* labeled Si-BI) of this electron has been investigated in detail by Watkins and Corbett (1961). and they have shown that the extra electron density is shared by the Si atoms of the reconstructed bond. The neutral charge state OVo is diamagnetic, but optical excitation with = 1 . 1 eV photons can promote one electron from the bonding state into the antibonding state, producing spin one OVg=,, responsible for the Si-SI EPR spectrum (Brower. 1970 and 1972). An EPR spectrum (Si-I I ) observed also under white light illumination in n-type electron-irradiated C Z silicon has been tentatively ascribed to * W e follow the nomenclature where Si-BI means the EPR defect signature first obqerved in \ i k o n at Bell Telephone Laboratorie\. S o r SL stands for Sandia Laboratories. G for General Electric. etc.

218

B. PAJOT

FIG. 13. Model of a silicon unit cell containing an OV center. By comparison with Fig. I , the central atom has been removed and the 0 atom has rebonded to a second nearest neighbor. The four Si atoms nearest neighbors of V have been displaced inward to simulate relaxation.

OVf (Brosious, 1976). This last charge state could be produced by capture of a hole by OV!,, but no confirmation of this attribution has been reported so far. In OV, the 0 atom is bonded to two second nearest neighbor Si atoms. The stretching mode of this Si-0-Si structure gives LVMs at 836 and 798 cm-' for I60Voand of I80Vo,respectively (Corbett et al., 1961; Abou-el-Fotouh and Newman, 1974). The LVM of "OV- is shifted to 885 cm-' (Bean and Newman, 1971). The FWHPs of these LVMs are broad (=3 cm-') so that no Si-isotope effect is observed. The stress-induced splitting of the 836 c m - ' mode has been investigated (Bosomworth et al., 1970; Pajot et al., 1994). Figure 14 shows the splitting of this mode at 8 K for a 0.50 GPa stress along a [Olll axis. The results can be fitted to a center with a rhombohedra1 symmetry with a dipole along a ( 1 10) axis. The piezo-spectroscopic coefficients A , , A , and A , for OVo are respectively -2.4, 2.4 and 4.5 cm-IGPa-'. In samples with OV concentration much larger than the electron concentration available, Watkins and Corbett (1961) probed with EPR the energy-dependent redistribution of electrons among OV configurations with electronic energies shifted by a uniaxial stress applied at 77 K. They derived the stress-dependence of the electronic energy of OV- and, from the annealing of the effect, a thermalization energy of the electron from OV (0.20 eV) comparable to the position of the level given previously. For a stress along a (100) axis, they found a characteristic splitting of 42 meV.GPa-' for the electronic level. The atomic reorientation of the 0

6.

SOME ATOMIC CONFIGURATIONS OF OXYGEN

219

L--

825.0

$32 5

840.0

847.5

U A V I N L I M B L K (cni-1)

FIG. 14. Splitting of the OV" L V M in silicon at 8 K under a stress of 0.5 GPa along the [ I 101 direction. Polarization vector parallel to the stress (a) and parallel to [I101 (h). The bars show the positions of the three component\ and their relative intensities (Pajot el al.. 1994).

;itom of OV" was also measured after alignment with the stress applied at 125 K by probing again the reoriented fraction with the EPR of OV-. A reorientation energy of 0.38 eV was obtained and confirmed by IR dichroism recovery (Corbett et al.. 1961). Thermal emission of the electron trapped by OV can also be observed in DLTS as a single peak with an activation energy of 0.18 eV (Kimerling, 1977). Piezo-DLTS experiments on OV- have been made (Meese, Farmer and Lamp, 1984: Qin, Yao and Mou, 1984), and a splitting of the DLTS peak was observed. Their results have given an atomic reorientation energy of 0.38 eV and a stress-induced splitting of the electron acceptor level of 57 meV.GPa-' for mil( 100) that compare well with the values obtained from piezo-EPR and from piezo-absorption. A priori prediction of the distortion for an 0 atom placed in a substitutional site in a silicon crystal is difficult from cluster-type calculations including atomic relaxation with the modified neglect of diatomic overlap (MNDO) method. Apparently correct trends can arise from spurious effects related to the size of the cluster size and its SiH terminations (DeLeo, Fowler and Watkins, 1984). In the cih initio total-energy calculations by Ortega-Blake et al. (1989), a (Si,=Si)20, Si, cluster is used and the 0 atom and its four nearest neighbors are allowed to move. An off-center (100) distortion of 0.9 of the 0 atom and a reduction of the distance between the pairs of bonded Si atom are found that are supported qualitatively by experiment.

220

9. PAJOT

2. THERMAL STABILITY Watkins (1975) has observed in p - and n-type CZ silicon electronirradiated near 20 K an EPR spectrum (Si-G4) ascribed to a metastable OV-* center already present at 20 K. The conversion from Si-G4 to the Si-BI spectrum of the stable from OV- takes place near 100 and 45 K in p-type and n-type material, respectively. In this metastable OV-* center, the 0 atom undergoes a (100) distortion similar to the OV center stable at room temperature. In the p-type material, the annealing of the vacancies near 60 K produces another EPR spectrum (Si-G3) attributed also to a metastable OVI,;,, center that anneals near 90 K. In this last center, the 0 distortion is along a ( I 11) direction. On the high temperature side, the annealing of OV at 300°C produces a decrease of the EPR and 1R signals indicating an atomic modification or a dissociation of the defect. The loss of intensity of the OVo LVM is correlated with the growth of a new LVM at 889 cm-' at room temperature (Corbett et al., 1964b). These authors proposed that the new LVM could come from an 0,V center formed by the trapping by 0;of a mobile OV defect. This seemed to be substantiated by the quadratic dependence of the final intensity of the 889 cm-' LVM (896 cm-' at LHeT) on [Oil after complete annealing of OV (Lindstrom and Svensonn, 1986). A test for this interpretation is the 0 isotope effect of the LVM. Implantation in silicon of equal doses of I 6 0 and I8O producing directly I60V and "OV were performed by Stein (1986b). Annealing of the implanted samples at 300°C produced only the 889 cm-' LVM and its I 8 0 equivalent at 850 cm-'. No intermediate LVM was detected between these two modes. This point and the magnitude of the 0 isotope shift for the defect make unlikely the presence of two 0 atoms in this new defect (labeled A' center by Stein) unless these two atoms are weakly coupled. The A' center anneals out at -450°C and LVMs at 910,976,991 and 1005 cm-' (LHeT) are in turn observed in the samples. Because the annealing kinetics of the A' center is thermally activated with an energy of 2.6 eV, close to the activation energy for 0; diffusion (2.54 eV), it has been suggested by Lindstrom and Svensonn (1986) that these LVMs were related to 0; trapped near an A' center, but there is unfortunately no 0 isotope experiment here to tell how many 0 atoms are involved in this center. The above IR results on the annealing of OV should be compared to EPR studies on CZ silicon samples irradiated with high electron fluences near 100°C (Lee and Corbett, 1976). In these samples, two EPR spin-one spectra were attributed to 0-vacancies complexes: Si-A14 to OV, ( V , with a nearly substitutional 0 trapped on one of the V sites) and Si-P4

6.

SOME ATOMIC CONFIGURATIONS OF OXYGEN

22 1

ep. FIG. 15. Models for different polyvacuncy-oxygen complexes in silicon. The 0 atoms are represented as dotted circles and the dangling bonds as single-atom bonds: (a) OVq; th) O , V $ ; ( c ) OV:; ( d ) In 0,C‘T. not shown. the 0 atoms are 0’and 0”’of ( d ) (from Y . H . Lee and J . W . Corbett. (1976).P h y s . Re\,. B 13, 2653). The Si atoms labels are for EPR lines assignment and orbitals description not considered here.

to OV, (a nearly substitutional C ) trapped near one of the end vacancy of a V , chain along a ( I 10) axis). Models for these defects are shown in Fig. IS. From its production rate (0.05 center/electron.cm), OV, is assumed to be produced by a direct collision process, and it anneals out at about the same temperature as OV. It has been suggested (Davies et al., 1987b) that OV, could produce one of the aforementioned LVMs, observed at 991 c m - ’ after electron irradiation at 100°C. OV, is produced during the annealing of OV and OVz,and it anneals out in turn at -450°C. For these reasons, OV, could produce the LVM at 889 cm-’. Other EPR spin-one spectra observed after annealing are attributed to oxygen-vacancies complexes with more than one atom ( 0 , V 2 , OzV, and O,V,) when nearly substitutional 0 atoms get trapped near still “empty” vacancies (Lee and Corbett, 1976).

222

B. PAJOT

3. OTHER O-RELATED IRRADIATION DEFECTS a. Dejects with Interstitial Si

An LVM at 936 cm-' was first reported by Whan (1966) in n-type CZ silicon electron-irradiated at temperatures between 80 and 150 K, together with LVMs at 922,932 and 945 cm-'. Annealing sequences below 250 K under white light illumination or in the dark gave evidence of two charge states of the same defect, producing the LVM at 945 cm-I and a new one at 956 cm-'. The defects giving all the previous LVMs anneal out below 300 K except the defect giving the 936 cm-' LVM, which is stable up to 350 K. They were attributed to rather simple centers involving one defect and one 0 atom. The 936 cm-' LVM was also observed by Brelot (1973) who attributed it to Si,O, (an interstitial Si atom trapped The attribution was challenged by Lindstrom et al. (1984), who by Oi). found an annealing temperature near 300°C for this LVM observed after room temperature electron irradiation. New experiments by Stein (1989) show that if this LVM can also be produced by room temperature electron irradiation, it still anneals out at 350 K in agreement with the earliest results. A comparison of the creation rate of the related defect in C-doped and in C-free CZ silicon seems to support a SiiOi attribution and the experimental results can imply the existence of another LVM at the same frequency. b. Dejects with Carbon In C-containing CZ silicon, electron irradiation near ambient produces among other LVMs a set of five lines at 529,550,742,865 and 11 15 cm-' (LHeT), labeled C(3) that are related to the same center (Davies et al., 1985). C(3) is correlated with (i) an electronic line near 790 meV (C-line) observed at LHeT in photoluminescence (PL) or by transmission and (ii) with an EPR signature (Si-(315). Si-G15 has been correlated in turn with a hole trap at E, - 0.38 eV (Mooney et al., 1977). These are four manifestations of the same center assumed to be a CO complex. The C-line is due in absorption to the creation of an electron-hole pair (exciton) with the hole more tightly bound to the center than the electron (pseudo-donor) and in PL to the recombination of this exciton (Thonke, Watkins and Sauer, 1984). A vibronic structure is related with C-line: the local mode frequencies deduced from the position of the satellites are 528, 585, 1114 and 1172 cm-' (Wagner, Thonke, and Sauer, 1984) and the frequencies of two of them almost coincide with those of the LVMs measured by absorption. A C-isotope effect is observed only for the two high-frequency LVMs of the C(3) set and for the zero-phonon C-line

6.

SOME ATOMIC' CONFIGURATIONS OF OXYGEN

223

1'1 IOI'ON ENERGY (rnev) 789 8

15691

790 0

15690

WAVELENGTH (pm)

FIG. 16. C-isotope effect of the rero-phonon 790 meV line (here observed at LHeT by photoluminescence) in electron-irradiated CZ silicon. This line I S due to the recombination of an excilon bound to a C,O, complex ( K . Thonke. G. D. Watkins and R . Sauer (1984). Solid Sfare Commun. 51, 127).

(Fig. 16) while a weak O-isotope effect is found only in the PL spectra for the local modes at 528 and 585 c m - ' . This identifies the presence of C and 0 in the center. Stress splitting of the C-line indicated that the center had a low symmetry (CI)!).The presence of C, (interstitial carbon) in the center, deduced from a modeling of the radiation process (Davies et al., 1985) was confirmed by piezo-EPR studies by Trombetta and Watkins (1987), who also proposed a model of the center that met the symmetry requirements. However, the fact that the O-related LVMs are at much lower frequencies than the C-related LVMs was apparently not solved in this model. An ah initio cluster yields a model preserving the symmetry and accounting qualitatively for the frequencies observed (Jones and Oberg, 1992a). In this model, the presence of dangling bonds on three Si atoms frustrates the 0 atom as, whatever the Si pair bridged by 0, one of the dangling bonds is unsaturated. This dangling bond then tries also to form a bond with the 0 atom leading to a threefold coordinated

224

B. PAJOT

FIG.17. Proposed model for the CiO, complex in irradiated silicon shown embedded in a silicon unit cell. The 0 atom (small dark gray) and the C atom (medium gray) are threefold coordinated (R. Jones and S. Oberg (1992a). Phys. Rev. Lett. 68, 86).

0 atom (Fig. 17). The low frequency of the 0-related modes is due to the large Si-0 bond length (-1.85A) in this defect. An electronic line at 3942 cm-' (489 meV) is also observed by PL and in absorption in electron-irradiated CZ silicon (Davies et al., 1987a). The stress splitting shows that the related center has C,, symmetry. The 0and C-isotope sensitivity of the line indicates also that the related center (annealing out at 225°C) is also an (OC) complex, but no LVM has yet been correlated with this line. A strong argument for the presence of a vacancy in this center (COW has been given by Davies et al. (1987b). V. Comparison with Other Light Element Impurities 1. CARBON

The solubility of substitutional carbon in FZ silicon is -10I8 atoms/ cm3 near the melting point; it seems to be limited by the lattice shrinking due to the small atomic radius of C compared to Si. In CZ material, larger C solubilities can be achieved (-2 x 10I8 atoms/cm3) because carbon compensates the lattice expansion due to oxygen (Newman, 1986). The C atom sits on center, and it produces only one LVM at 608, 589 and 573 cm-l for 12C,13Cand I4C, respectively. The effective charge of C for this mode is q = 2.5 e. Due to a stronger coupling with the lattice, the anharmonicity of a substitutional atom is larger than that of an interstitial one and an overtone is observed at 1211 and 1175 cm-' for "C and 13C,

6.

225

SOME ATOMIC CONFIGURATIONSOF OXYGEN

respectively (Newman and Smith, 1969). C is isoelectronic to Si and electrically inactive. Interaction between C and 0 has been discussed in the preceding sections. C is not as reactive as 0, and only a few number of complexes with foreign atoms are known. With the group 111 acceptors, C can form acceptor complexes with an ionization energy -0.8 times smaller than that of the isolated acceptor. They have been investigated by several experimental techniques and also by extended Huckel calculations. The model that best fits the results is an acceptor surrounded by three Si and one C atoms (Jones et al., 1981). In C-containing silicon, electron irradiation below room temperature produces a characteristic EPR spectrum (G 12), attributed to a (100)-oriented C=Si interstitial defect (dumbbell) bonded to four Si atoms on regular sites (Watkins and Brower, 1976). This (CSi), defect is correlated with two LVMs at 922 and 932 cm-I (C(I) spectrum). I t anneals out at near ambient temperatures, and after an intermediate structure responsible for the C(2) IR mode, a new center is formed. It is responsible for a strong signal at 969 meV, observed by PL as well as in absorption (Fig. 18), and it can be used to detect carbon in FZ silicon with a better sensitivity (- IOl4 atoms/ cm') than by measuring the substitutional C LVM (Davies et al., 1984). A S = '/z EPR spectrum (GI I ) is related to this new center in the positive charge state, and it was identified by Brower (1978) as two nearsubstitutional asymmetric C atoms separated by an interstitial Si CC,Si,C,J. The C isotope effect of the vibronic sidebands of the 969 meV line gives evidence for the presence of only one C atom in the center

1

I

+

d

I L

1

~

96975

9695

96925

I'IiOTON ENERGY (mev)

FIG. 18. Absorption at 2 K due t o the 969 meV line in a nominally C-free and 0-free silicon sample irradiated with 5.6 x 2 MeV electronsicm!. That line is due to a C,Si,C, complex produced by the irradiation. IC) is estimated to be 2 x atoms/cm3. The IR path is 20 mm (G. Davies, R . Lightowlers. M . C. do Carmo. J . G . Wilkes and G . R . Wolstenholme (1984). Solid Stare Comrnrrn. 50, 1057).

226

B. PAJOT

(Davies, Lightowlers and do Carmo, 1983). This puzzle was solved by the ODMR observation of a S = 1 excited state of the neutral center (O’Donnel, Lee and Watkins, 1983). In this configuration, the structure of the excited neutral center at low temperatures would be somewhat similar to that of 0; when replacing the two equivalent Si atoms by two C atoms and the 0 atom by Si. Unfortunately, no LVM related to this center has been reported. 2. NITROGEN The solubility on nitrogen in silicon is much lower than that of carbon and [N] - 1015 atoms/cm3 in bulk-doped crystals is a representative figure. N doping is achieved by CZ growth in N, + Ar atmosphere or by adding Si3N4to the polysilicon charge prior to melting. O-free, but Ndoped Si has also been obtained by CZ pulling from a silicon nitride crucible (Watanabe et al., 1981). For research purposes, N implantation whether followed or not by annealing is also used, and in that case, N concentrations 1020 atoms/cm3 can be achieved by laser annealing (Stein, 1986a) as nitrogen solubility increases with the growth velocity of the solid phase. N is not a shallow dopant like the other group V elements, and this is related to its small atomic radius that seems to preclude an on-center substitutional location.

-

a. Isolated Nitrogen

In N-implanted laser-annealed silicon, an EPR spectrum (SL5) is observed to be stable up to 400°C, where it is replaced by SL6 and SL7 (Brower, 1982). These paramagnetic centers account only for a small ) the total N present. SL5 is attributed to a substitufraction ( ~ 0 . 0 5 - 0 . 1of tional off-center N atom with a (1 1 1 ) distortion. The hyperfine (hf) interaction indicates that the fifth electron is localized on one of the four surrounding Si atoms. The small reorientation energy of N among the four equivalent sites (=O. 107 eV) was interpreted by a location of the N atom near the center of rotation. This point was clarified by Murakami, Kuribayashi and Masuda (1988) who observed that the hyperfine splitting of SL5 increased with temperature from 150 K. They interpreted this fact by the existence of an on-center metastable minimum of the N atom intermediate between off-centers stable (1 1 1 ) locations. The observation conditions of SL5 are the same as those of a N-related LVM at 653/637 cm-l ( 14N/”N) reported by Stein (1985). Hence this LVM is attributed to off-center substitutional N . The comparison with the 14C LVM (573 cm-’) indicate an average bonding stronger between Si and N than between Si and C. From DLTS measurements (Tokumaru et al., 1982), a

6.

--.

227

SOME ATOMIC (‘ONFIGURATIONSOF O X Y G E N ~

“ ~ - 1 . 5 ~

T

-

f

A

’*N/crn’.

*

1

B=’5N/cm’

.

7 irN-~5N

B / A = 1 .O

crl

z E/A=O 5

0, E/A=0.2

I SI-N PAIRS FOR DIFFERENT ” N / l 4 N AABS.=O.Ol AFTER LASER ANNEALING

RATIO T_=80

700

770

840

1

I

9 10

980

WAVENUMBER (cm-1) FIG. 19. Absorption at 80 K after laser annealing of silicon implanted with overlapping profiles of I4N and ”N with different ”N/I4N ratios ( H . J . Stein (1986a). M a t . Res. S y m p . Proc. 59, 5 2 3 ) .

value of 0.3 e V seems to be the most probable for the position of the deep level associated with SLS. Total energy Hartree-Fock calculations by Hjalmarson and Jennison ( 198s) show that a trigonal distortion of the N atom in the preceding structure spontaneously occurs when the four surrounding Si atoms relax either outward or inward, but that the inward relaxation is more likely. PI, lines investigated in silicon samples containing C and N isotopes have been convincingly attributed to some kind of interstitial distorted CN pair due to the pairing of C with off-center N (Dornen. Sauer and Pensl, 1986). However, no CN-related LVM has been observed in samples where they could have been present (Stein, 1988). h. The Nitrogeri Pairs Two “N-related LVMs were observed at 747 and 963 c m - ’ at ambient temperatures in N-doped silicon (Abe et al., 1981) and also in implanted material (Stein. 1983). The comparison of I4N-implanted and I5N implanted samples with a I4N-’’N coimplanted sample by (Stein, 1986a) indicated an interaction between N atoms in the related centers because of the occurrence of an intermediate 14N-”N LVM (Fig., 19). Existence of N-N pairs bonded to Si atoms were then suggested to be responsible for the two LVMs. These pairs are stable up to 6 W C , but in samples

228

B. PAJOT

coimplanted with 0 (Stein, 1988) or taken from N-doped CZ crystal (Qi et al., 19911, new LVMs at 805-810, 1000, 1030 and 1064 cm-' are observed after laser annealing. They can be attributed to perturbation of the vibration of the N-N pairs by Oiand also to the inverse. From the intensities of the LVMs, the N pairs must be the most abundant N-related species in silicon. c'.

N-Related Shallow Donors vs. Thermal Donors

An N-related PL line at 1122 meV has been reported in N-doped silicon as well as the presence of a small concentration of N-related shallow donors with concentrations - 0 5 1 . 3 % of the total [N] (Tajima et al., 1981). It is not clear if these two observations are related and if the PL line does or does not come from excitons bound to the N-related shallow donors. Shallow donors ascribed to nitrogen-oxygen complexes have also been reported by Suezawa et al. (1986; 1988), who observed in Ndoped CZ silicon hydrogenlike spectra of seven centers with ionization energies ranging from 32.6 to 37.4 meV. Some of these centers were as-grown with a rather high stability compared with the 450°C TDs, and others were produced by annealing near 450-500°C. It has been suggested from a kinetic analysis that one of these complexes contains two pairs of N atoms and another three pairs. It is likely that some of these centers were also among the ones reported by Navarro et al. (1986) using photothermal ionization spectroscopy (PTIS) on supposed N-free CZ Si. This raises the case of nitrogen as a low-background residual impurity in silicon (a very small amount of oxygen-nitrogen complexes could be detected by PTIS). The same question is raised by the observation by Hara, Hirai and Ohsawa (1990) in N-doped Si samples after long annealing at 470°C of an EPR spectrum identified as NLlO (Muller et al., 1978), not present in the N-free samples. In this case, it seems that the presence of N in NLlO can be ruled out (Ammerlaan, private communication) so that the case is still open. The presence of C in the N-doped CZ samples modify the kinetics of formation of the previous shallow donors and other shallow donors are formed (Hara and Ohsawa, 1991) but experiments providing direct evidence of N in these shallow centers are still needed. 3. HYDROGEN

Hydrogen is introduced in bulk undoped silicon by FZ growth under a H, atmosphere and bonded H atoms are detected from the absorption of the SiH LVMs (Bai et al., 1985). The concentration of bonded H in the undoped material is difficult to estimate. A comparison with germanium (Haller, 1991) gives [HI = 1-3 x IOl4 atoms/cm3. The two strongest

6.

S O M E ATOM'( (ONFIGURATIONS OF OXYGEN

2220.0

2222.5

229

2225.0

W A V E N U M B E R (cm-1) Fib. 20. Si-H stretching mode at h K i n a vacancy "decorated" by four H atoms i n FZ silicon grown in a H, atmosphere t U . Cleriaud (1991). Phvsicrr B 170, 383). The relative intensities of the lines match the relative abundances of the Si isotopes.

L V M s in the as-grown material at 1952 and 2223 c m - ' have a fine structure characteristic of a Si-H bond (Fig. 20). The intensity of the L V M at 1953 c m - ' is correlated with that of two L V M s at 794 and 814 c m - ' (Pearton. Corbett and Shi. 19x7). On the other hand, H/D doping shows that only one H atom is related to the 1952 c m - L V M . So, the 794 or the 814 c m - ' L V M could be due to the wag mode and the 1952 c m - ' L V M to the corresponding stretch mode. The presence of a second lowfrequency mode could indicate a defect with two weakly coupled H atoms. The attribution of the 1,223 c m - ' L V M to a tetrahedral center with four H atoms (Bai et al., 1985) was confirmed from stress-splitting measurements by Bech Nielsen, Olajos and Grimmeiss (1989), who suggested a hydrogen-decorated vacancy VH4. The calculations predict that the most stable configuration for H and H" is the interstitial BC location where H is midway between two Si nearest neighbors. This produces a large outward relaxation of the two Si atom (-0.4 A), but it is compenu t e d by the energy gained in forming a Si . . . H . . . Si three-center bond (Van de Walle, 1991). This structure is reminiscent of O;, but the

230

B. PAJOT

bonding is different. BC Ho is paramagnetic and the AA9 EPR spectrum has been attributed to this center (Gorelkinskii and Nevinnyi, 1987). To obviate the low solubility of hydrogen in pure silicon, proton implantation has been used for a long time to study H-related defects (Stein, 1979). The presence in the implanted material of H-related defects is inferred from the many LVMs in the 2000 cm-’ region (see Pearton et al. (1987) for a list). The symmetry of some of these centers has been determined from the stress splitting of the LVMs and they seem to be related to vacancy- or divacancy-like centers “decorated” with one or more H atoms (Bech Nielsen and Grimmeiss, 1989). In H-implanted CZ silicon, LVMs at 870 and 891 cm-’ attributed to the vibration of 0 in an OV center decorated with H atoms (OVH, and to OVH-) have been reported (Mukashev et al., 1991). Configurations and electrical activities of the OVH, and OVH centers mentioned earlier have been calculated by cluster MNDO and Xa-DV methods (Gutsev et al., 1989). A structure with a chemical OH bond is obtained for O W ; for OVH,, the two H atoms bond to the broken Si-Si reconstructed bond of OV. Surprisingly, the O W , center is found to have a deep level in the gap so that it could not be said that hydrogen passivates OV. An electrical manifestation of the interaction between hydrogen and shallow dopants in silicon is their neutralization (see Johnson et al. (1991) for a review). The idea that hydrogen could interact with acceptors to form electrically neutral pairs was confirmed by the results by Pankove et al. (1985) and Johnson (1985): in B-doped silicon neutralized by hydrogen, they reported the existence of a LVM at 1870 cm-’ (ambient) that they attributed to the stretching mode of a BH complex. The existence of H-related LVMs with A1 and Ga acceptors was shown by Stavola et al. (1987). These complexes were formed in p-type material by Coulomb attraction between a proton (an H atom having captured a hole) and a negative acceptor ion. The difference with Li, which behaves similarly (Chrenko et al., 1965), is that instead of an atom pair stabilized by electrostatic interaction, a chemical bond is formed in the case of hydrogen. The solubility of hydrogen in p-type silicon in the form of acceptorhydrogen complexes has been studied mainly for the B acceptor, where it follows roughly the B concentration. [BH] lozocenters/cm3 on 3 k m beneath the hydrogenated surface have been reported by Herrero, Stutzmann and Breitschwerdt (1991). In these complexes, H is in a BC location along the (1 1 1 ) direction between B and one nearest neighbor Si atom (Fig. 21a). The main bond is between H and the Si atom (the stretching frequency is too low for a B-H mode), but a weak bonding exist also between H and the B atom, demonstrated by the existence of a small

-

6.

SOME ATOMIC C O N F I G U R A T I O N SOF O X Y G E N

23 1

FIG.21. Representation of a silicon unit cell with (a) an acceptor-hydrogen complex. The relaxation shown is approximately the one for the B acceptor (dark gray). The H atom is shown in black. 'The same cell with ( h ) a donor-hydrogen complex. The relaxation of the donor atom (dark gray) is small compared with that of the Si atom bonded t o H.

B-isotope effect of the Si-H . . . B L V M (Pajot et al., 1988).The reasons why a Si-H bond is formed instead of a B-H bond lie in the fact that, in this center, the atoms keep their natural coordination. The properties of the model calculated by DeLeo and Fowler (1985)agree with the experiments, and they predict a reasonable value of the stretching frequency

232

B. PAJOT

of the Si-H . A1 LVM. No wag mode of these complexes has been observed, perhaps because of the small displacement of the H atom in the (1 11) plane or of the low-frequency of this motion. Substitutional B in silicon reduces the average lattice spacing of the crystal as the tetrahedral B radius is smaller than that of Si. The formation of a BH complex relaxes partially the stress because it increases the distance between unbonded atoms (Herrero et al., 1991). A1 and Ga atoms have atomic radii equal to or larger than that of Si. At LHeT, only one line is observed for the LVMs of BH, AlH and GaH complexes, but above -40 K, a low-energy satellite appears for the AlH and GaH complexes (Stavola et al,, 1987). By analogy with the situation for Oi this can be an indication that in these complexes, the Si-H bond direction makes an angle with the (111) axis. The question of the respective stabilities of the BC and off-axis location of H in the acceptor-hydrogen complexes has been addressed by Amore Bonapasta, Giannozi and Capizzi (1992). The stress splitting of the LVM of the BH complex is consistent with a trigonal symmetry when measured by IR absorption at I5 K (Bergman et al., 1988b) in agreement with the preceding model, and a Si-H bond reorientation energy of 0.2 eV is measured (Stavola et al., 1988)that is the same as the one predicted (Van de Walle, 1991). However, the off-axis displacement of the H atom is relatively easy. For this reason and to explain piezo-Raman results at 100 K on the Si-H . B LVM, one has to assume that a (1 11) stress applied at 100 K can distort the Si-H bond out from the (111) axis (Herrero et al., 1991). The effect of a stress along the (1 11) axis of the acceptor-hydrogen complexes on the direction of the Si-H bond has been modeled by Estreicher, Throckmorton and Marynick (1989) using cluster calculations, and they point out the influence of the acceptor-hydrogen coupling with increasing stress. The results of channelling experiments at 30 K on the BH complexes are consistent with a BC location of H (Bech Nielsen et al., 1988). Deicher et al. (1991) present a review of the results on the location of H in BH and InH complexes using nuclear techniques. In n-type silicon, H can also form complexes that neutralize the donors (Johnson, Herring and Chadi, 1986) but neutralization is not as efficient as for acceptors. LVMs associated with the donor-hydrogen complexes indicate that the H atom is not bonded to the donor atom, but to one of the nearest neighbors Si, Bergman et al. (1988a), in agreement with the prediction of Johnson et al. (1986). Unlike the acceptor complexes, the H atom is interstitial along a (111) antibonding direction symmetric to the BC location just discussed (Fig. 21b). The frequency of the stretch mode of these Si-H bonds is near 1560 cm-' at LHeT, significantly lower than the ones in the acceptor complexes, because the antibonded H atom is not constrained by another atom as in the BC location so that its bond

-

6.

233

SOME ATOMIC CONFIGURATIONS OF O X Y G E N

FIG.22, Model of the double donor-hydrogen complex (S and H atoms shown dark gray and black) (after A . S . Yapsir. P. Derik. R . K. Singh, L. C. Snyder, J . W . Corbett and T.-M. Lu (1988). Phys. R e v . B 38, 9936). This configuration should be the same for the di-hydrogenated OV center.

length must be slightly longer. For the same reason, this Si-H bond has also a wag mode near 810 c m - ’ . Another LVM is observed about 100 c m - above the Si-H stretching mode, and there is no clear attribution for this mode (Bergman et al., 1988a). The stress-induced splitting of the As. Si-H stretching mode is consistent with a trigonal symmetry of the center (Bergman et al., 1988b). Recent cluster calculations on the P , Si-H centers confirm the location of H antibonded to Si while Si relaxes out from P by -0.6 A so that the Si-P bond can be considered broken (Denteneer et al., 1990). The frequencies calculated by these authors (stretch: 1460 c m - ’ and wag: 740 cm ‘ ) show a substantial improvement on preceding results (see for instance Stavola (1991) for a comparison). Hydrogen neutralization of S , Se and Te double donors measured by DLTS has been reported by Pens1 et al. ( 1988) and this surely means the binding of two H atoms in the vicinity of the chalcogen donor (Fig. 22). The same structure as this one is predicted by Yapsir et al. (1988) for an OVHz center.

’

VI. Oxygen in Other Semiconductors

I . GERMANIUM

Oxygen is not a residual impurity in germanium. Different methods have been used to dope this material with oxygen (maximum 101 7 x 10” atomsicm’) and 0-related absorptions have been reported (Bloem,

-

234

B. PAJOT

Haas and Penning, 1959; Kaiser, 1962; Stein, 1973). A LVM at 862 cm-' (LHeT) is observed that shift at 818 cm-' with IgO (Whan, 1965). It is attributed to the u3 mode of Ge-0-Ge (OJ.Another LVM has been reported near 1270 cm-' (LHeT) with an intensity proportional to that of u3 (Kaiser, 1962). 0-related TDs are also produced in germanium by annealing near 350°C and the relative Oi loss seems to be more important than in silicon while annealing at T > 600°C leads to the precipitation of GeO, (Kaiser, 1962). The TDs in germanium are double donors as in silicon; the energy of their electronic spectrum is shifted to lower energies with respect to silicon, as for all the hydrogenic spectra that can be observed in both semiconductors (Clauws and Vennick, 1984). By analogy with the Si isotope splitting of v 3 in silicon, 15 isotopic components are expected from the Ge-isotope effect for that mode in germanium in a spectral interval of about three wavenumbers (the percent of natural abundances of the Ge isotopes are 'OGe: 20.50, '*Ge: 27.40, 73Geand 76Ge:7.80, 74Ge:36.50). The average FWHP of the components of u3 in germanium is -0.04 cm-' (Pajot and Clauws, 1987), and they should be fully resolved under high resolution. The number of components actually observed at 6 K under high resolution is larger, and it indicates that transitions from thermalized levels already occur at this temperature (Fig. 23). For each isotopic combination, three components labeled L(ow), C(entra1) and H(igh) can be seen at 6 K using standard germanium material. The H-C and C-L separations are -0.067 and 0.229 cm- I , respectively. In monoisotopic germanium (74Ge),where extra components are due only to thermalized levels, a fourth low-energy transition, (N), distant of C by 0.48 cm-' has also been observed at LHeT, as shown in the inset of Fig. 23 (Khirunenko et al., 1990). The fit of the isotope shift used for Oiin silicon (Pajot and Cales, 1986) when repeated for germanium gives a value of the apex angle Ge-0-Ge of 140" and an interaction mass M' of 11.65 amu. As for silicon, it is found that the Ge-0-Ge angle is larger in the elemental material than in the oxide (Pantelides and Harrison, 1976). In germanium, the distance between Oi and the ( 1 1 1 ) axis is 0.6 A compared to 0.2 A in silicon, and this results in smaller energies related to the hindered rotation or tunnelling of the 0 atom. In the free-rotator approximation, the first excited level would be at 3.2 cm-I. Phonon spectroscopy, briefly described in the section on 0; in silicon, has provided spectacular results in the case of Oi in germanium (Gienger, Glaser and Lassman, 1993). Figure 24 shows the phonon spectrum of Oiin germanium at I K. At zero stress, above the 1.2 meV (9.7 cm- ') onset of Sn-insulator-Sn detector, eight transitions are observed between -10 and 22 cm-'. An analysis of the results shows that even at 1 K some of the transitions already arise from thermalized levels as the

6.

235

SOME ATOMIC'CONFIGURATIONS OF O X Y G E N

864.4

8634

862.4

861.4

860.4

WAVENl JMBEK (cm-1) Fic. 23. Absorption of v,(''O,) in germanium at 6 K. The fine structure is due to the Ge isotope effect and the thermalization of the first levels (Pajot, 1990). By comparison. a ~monoisotopic 0,) 74Ge(inset) shows only the fundamental and LHeT spectrum of ~ ~ ( 'in lhermalired components for ''Ge20 (L. I . Khirunenko, V. I. Shakovstov, V . K. Shinkarenko and F. M . Voroblako (1990). F k . Tekh. P o l u p r o r d n . 24, 1401: Sov. Phvs. Semiw n d . 24, 663). The asterisks denote the contribution of the components C , H and L of the inset.

/

c

0 , 2x1017~m-3 PI1 I l l O l

OMPo

J

c f

-

D

I

1

2

3

PHONON E N E K ( i Y (meV) Fici. 24. Phonon absorption spectrum at 1 K of 0, in germanium as a function of a (110) stress. Some of the lines arise from already thernialized sublevels. The transitions with the lowest energies cannot be observed because of the experimental cut-off at 9.3 c m I~. At bottom right are shown the Al-insulator-Al phonon generator and Sn-insulator-Sn detector evaporated on the sides of the Ge sample (Gienger et al., 1 9 3 ) .

236

B. PAJOT

first two excited levels are 1.45 and 5.40 cm-' above the 0 K ground state. The free-rotator analysis cannot account for such low energies, and it seems that in germanium, the lower value of 2a does not allow nearly free rotation as in silicon, but only hindered rotation. The potential barrier between the six equivalent minima about the ( 1 11) axis allows tunnelling between these minima that produces a splitting of the levels depending of the barrier height (Hrostowski and Alder, 1960). The stress-induced dichroism of Oiin germanium was also observed and the results are qualitatively the same as for silicon (Corbett et al., 1964a). The reorientation energy of Oiis smaller in germanium (2.08 eV), where the diffusion of 0 is thermally activated with a preexponential term Do = 0.40 cm2/s at room temperature. This means that in germanium 0; is mobile at a lower temperature than in silicon. Irradiation of l60/I80-dopedn-type Ge at 25 K does not produce new LVMs, but after annealing at 73 K, a LVM at 719/683 cm-' (160/'80) appears. The associated center contains only one 0 atom and it anneals out near 160 K. A new center is created with a LVM at 620/589 cm-' (160/180) containing also one 0 atom (Whan, 1965). The similarity in stability between this center and the one giving an EPR spectrum attributed to OV- (Baldwin, 1965) suggests that the 620 cm-' LVM is associated with OV- in germanium. Near 373 K, this center seems to transform into new ones producing LVMs at 808 and 715 cm-' ("0).A strong LVM at 780 cm-' (I6O)appears after annealing above 373 K and isotopic substitution with I8O shows that the associated center contains two 0 atoms. These annealing sequences are reminiscent of the ones for OV in silicon, but in germanium, much less EPR data are available so that information on the symmetry of the centers produced is scarce. A study of the annealing of O-doped n-type germanium irradiated with y-rays seems to show that the O p / O V - level is at E, - 0.27 eV (Litvinov, Urenev and Shershel', 1983). 2. GALLIUM ARSENIDE a . Interstitial Oxygen and OVA, It has been thought for some time that semi-insulating (SI) gallium arsenide (GaAs) could be obtained by doping with oxygen, hence the interest for the properties of this element in GaAs. Several doping techniques were then used like a partial pressure of O2 or the addition of Ga,O, or As,O, in the starting material (see Martin and Makram-Ebeid (1986) for a review). The maximum solubility of oxygen in GaAs measured by charged particles analysis (CPA) seems to be in the range of l x 10l6 atoms/cm3 (Shikano, Kobayashi and Miyazawa, 1985). The first

6.

SOME ATOMIC' CONFIGURATIONS OF OXYGi5.N

237

report by Akkerman. Borisova and Kravchenko (1976) of an 0-related LVM attributed to v3 of 0;at 8361790 cm- I ( 'hO/'XO)in GaAs doped with "0 enriched As@, went unnoticed for some years. Song et al. (1987) reported the observation in GaAs Si of photo-sensitive LVMs at 715 and 731 c m - ' they attributed to the deep defect EL2 but they recognized afterward (Zhong et al.. 1988) that these LVMs were due to an oxygenAs vacancy center ( O V A , ) . This point was confirmed by Schneider et al. (1989) using "0-enriched samples. This is a change with silicon and germanium as in GaAs, OVA,is a native defect. This is due to the fact that GaAs is a compound semiconductor where vacancies of both types can exist due to small differences to the exact stoichiometry. By analogy with silicon and in germanium, interstitial oxygen in GaAs is expected to be bonded to nearest neighbors As and Ga atoms. The vj mode must then be a doublet due to the Ga isotopes ("Ga: 60%, "Ga: 40%). This doublet (845.44 and 845.82 c m - ' at LHeT) was indeed reported by Schneider et al. (1989) and Song et al. (1990a), and it is shifted by 44 cm-l when '('0is replaced by "0. This frequency is not too different from the one reported earlier for 0, in germanium. In samples with low internal strains, the FWHP of the u3 isotopic components is 0.06 cm-I at LHeT (Song, 1992). Unlike germanium, there is no thermalized component at LHeT (shown later in Fig. 26b). The temperature broadening of the mode is rapid and barely detectable at 77K. The bonding of 0 to a Ga atom and to an antisite AsGa second nearest neighbor near VA, would also produce a doublet. However, the stress-induced splitting of u 3 shows that the dipole is oriented along (1 1 1 ) whereas Ga-0-As,, would have a ( 1 10) symmetry (Song et al., 1990b). There is no reason for 0 to be midway between As and Ga, and some asymmetry can be inferred from the absence of internal rotation about the ( I I I ) axis. An ub initio calculation finds that the 0 atom is nearer from t h e Ga atom (1.59 A) than from the As atom (1.88 A ) for a Ga-0-As apex angle of 158" and that the displacement of the As atom is very small (Jones and Oberg, 199%). The agreement between the predicted frequencies and the ones for h9Ga'60As/69Gai80As compared observed is fair: (924/875 cm An effective charge of 2.1 e is also obtained for uj to (846/802 cm-')c,bs,. and this value yields a maximum lo,]of 3 x 10"atoms/cm3 in the samples investigated. The calculation predicts another mode at 302 cm- but this frequency is located in the one-phonon strong absorption region of GaAs, and its observation would be very difficult. The stress splitting amplitude of v 3 is comparable to the one in silicon, but easier to measure because of the smaller FWHP in GaAs (Fig. 25). In GaAs, reorientation of 0, (Fig. 26a) is observed when cooling the sample under stress from room temperature (Song, 1992) whereas starting ~

238

B. PAJOT

.2

c

846.0

-1

845.2 0

F / l [OOII

0

TlT TI/

7 50

-_--100

150

STRESS (MPa) FIG.25. Splitting of ~ ~ ( in 0 GaAs , ) at 8 K as a function of a [I101 stress with a [OOI] viewing axis (C. Song, B. Pajot, and C . Porte (1990). Phys. Rev. B 41, 12330). H and L correspond to "GaOAs and 69GaOAs,respectively.

temperatures above 300°C are required for Oiin silicon and germanium (Corbett et al., 1964a). The reorientation energy of Oiin GaAs is between 0.8 and 1.1 eV, but it is not possible to know from the spectroscopic data whether the reorientation takes place about the As atom or the Ga atom. The dissociation energy for a diatomic Ga-0 molecule is 285 kJ/mole compared to 481 kJ/mole for As-0, but the cluster calculation of Jones and Oberg (1992b) indicate an inverse trend: they deduce a reorientation energy of 0.5 eV about the Ga atom (breaking of an As-0 bond) and of 1.84 eV about the As atom (breaking of a Ga-0 bond). Hence, actual reorientation must take place preferentially about the Ga atom. For this reason, care must be exercised when deducing an Oi diffusion coefficient from the experimental reorientation energy. In GaAs, three LVMs labeled A , B and C (italics are used to avoid confusion with chemical symbols) are attributed to different charge states of OVA,. The primary attribution comes from the observation of three components for each of these LVMs (Fig. 27). These components are

6.

SOME ATOMIC CONFIGURATIONS OF OXYGEN

239

due to the Ga-isotope effect, and they indicate that an 0 atom is symmetrically bonded to two Ga atoms. The simplest defect rendering this bonding possible is an As vacancy, hence the attribution. Two of the LVMs are observed under thermal equilibrium: mode A near 731 cm.-' corresponding to the most positive state is observed in Sl GaAs and mode B near 715 c m - ' in n-type material. In weakly n-type material, both modes are observed (Alt, 1989a; Song, Pajot and Gendron, 1990a). After a short illumination of S1 GaAs at LHeT with photons in the 1.25 eV range (-- 1 pm), a third mode, labeled C (Song et al., 1990a) or B" (Alt, 198Yb), can be observed to grow near 714 cm. at the expense of A (Fig. 27). In the S1 samples where EL2 and OVA,are both present, interconversion of A can occur under illumination with photons in the 1.25 eV range. Figure

'

WAVENUMBER (cm-1)

.

'

ldl i

WAVENUMBER (cm-1) 2h. (a) Stress-induced dichroism of ~ ~ ( 'in" GaAs 0 ~ )at 8 K due to atomic reorientation under a I101 stress of 120 MPd. Elland E , indicate the polarization directions parallel or perpendicular to the aligning stress. (b) Polarized reference spectrum of ~ ~ ( 'in~GaAs 0,) at 8 K of an unstressed sample showing n o dichroism. The Ell spectrum is shifted by 0. I c m - ' for clarity (Song. 1992). FIG.

240

B. PAJOT

0.40

0.32

z 0.24

2 0.16

0.08

0 .oo

73i.7

71

WAVENUMBER (cm-1) FIG.27. Modes A , B and C of I60VAsinGaAs at 6 K. H H , H L and L L stand for 71Ga10, 7'Ga069Gaand 69Ga,0, respectively (Song et al., 1992).

ILLUMINATION TIME (s) FIG.28. Change under illumination with 1.25 e V photons at 6 K of the concentration of the different charge states of OVA,in SI GaAs represented by the intensity changes of the corresponding LVMs (the component with two "light" Ga isotopes ( L L ) is used) (Song et al.. 1992).

28 shows the charge transfer from A to B followed by the inverse. The fast transfer from A to B is explained by the photoionization of EL2' in the conduction band and by the preferential trapping of the photoelectrons by OV,,. The second part of the interconversion is mediated by the photoionization of EL2' in the valence band. This photoionization

6.

S O M E ATOMIC' CONFIGURATIONS OF OXYGEN

24 1

produces holes in the valence band and their recombination with EL2" competes with the phototransfer of EL2" into the metastable state by photons within the same energy range (Martin and Makram-Ebeid, 1986). The metastable state of EL? is electrically inactive so that the holes left are available for trapping by negative OVA,( B )that returns to the positive state ( A ) . The two peaks of observation of C show that this mode must correspond to an intermediate state between those giving A and B. Hence, there is a charge difference of two between the stable states producing A and B and this i s characteristic of a center with negative ( J (Alt, 1990; Skowronski, Neild and Kremer, 1990). The charge states corresponding to A , B and C' are attributed to OV:,, OV:; and OVA,, respectively. The position in the gap of the levels associated with OV;; and with OV,,, ( E , - 0.6 eV and E, - 0.14 eV, respectively) has been determined from the intensity decrease under annealing of modes B or C created by illumination (Ah, 1990; Skowronski et al., 1990). In n-type 0-containing GaAs, several electron traps have been detected including EL2 and EL3. The similitude between the energy signature of EL3 and that of OV;; leads to ascribe electron trap EL3 to OVA,(Kaufmann et al.. 1991; Neild, Skrowronski and Lagowski, 1991). There is an uncertainty on the absolute charge state of OV in SI GaAs and the ab initio calculations of Jones and Oberg (1992b) predict that the charge state should be OV,, instead of OVX, so that all the charge states should be shifted. None the less, with these attributions, at least one of the OVA, states is paramagnetic, but no related EPR spectrum has been detected u p to now. This can be due to the large widths of the EPR lines in GaAs that require a rather large concentration of centers. The splitting of A , B and C' under stress is consistent with a dipole oriented along a ( I 10) axis and this confirms the structure of the center (Song, 1992). The splittings for A and B are similar and this seems to indicate that the relaxations of the corresponding charge states are comparable while the relaxation for OV?,; should differ. The atomic reorientation of OVA,follows qualitatively the one of OV in silicon; in particular, no dichroism is detected for a stress parallel to [ I101 applied from room temperature when the propagation vector of the radiation is along [0011 (Pajot et al., 1994). In samples containing OV;, and Ova;, a stress applied from ambient produces electronic reorientation and the formation of OVA,without illumination. This fact can be attributed to the trapping of a single electron by OV;,. OV,, is normally unstable above -95 K . but it is assumed that the stress stabilizes this charge state and allows its observation (Song et al., 1992). The annealing of OVA, between 650 and 750°C results in an increase of the 0,concentration (Skowronski and Kremer, 1991). Short-term anneal-

242

B. PAJOl

ing near 1200°C produces new 0-related LVMs that can coexist with the OVA, LVMs (Skowronski, 1992). The fine structure of these new LVMs resembles that of the OVA, modes. One near 733 cm-' is a triplet indicating again an 0 atom bonded symmetrically to two Ga atoms. Two other ones, close in frequency are quadruplets. The extra line results from the splitting of the "Ga0"Ga component (HL in Fig. 27) and this indicates that the two Ga atoms bonded to oxygen are no longer equivalent. Tentative models for these new centers have been proposed by Skowronski (1992). In 0-containing samples, a LVM near 604 cm-' is observed (Song et al., 1990a; Skowronski and Kremer, 1991). The triplet structure indicates a Ga-X-Ga structure for the center. No measurement on I80-enriched samples has been made (an I8O mode would be expected near 570 cm-'1. The frequency of this mode is comparable to the one reported by Whan (1965) for a center attributed to OV in germanium. This center is different from the one giving modes A , B and C as it is insensitive to near IR illumination. A possible attribution would be a Ga-0-Ga structure in an environment different from the previously discussed OVA, center. Carbon does not seem to be directly or indirectly involved in the 604 cm-' mode, as it is observed also in the Bridgman samples with a very low C concentration. Other LVM have been observed in 0-containing S1 GaAs (Song et al., 1990a; Skowronski and Kremer, 1991) but information on their structure is too scarce for a reasonable discussion on their origin. In short-term rapid thermal annealing (RTA), the A mode and the 604 cm-' LVM starts decreasing in intensity at -600°C with a correlated increase of the intensity of v,(O,), and these native centers seem more stable than OV in silicon. Long-term annealing indicates the formation of other 0-related centers and finally the precipitation of oxygen (Skowronski and Kremer, 1991). b. OH-Reluted Centers

In some 0-containing GaAs, high-frequency LVMs are observed between 2900 and 3500 cm-' (Pajot and Song, 1992a). Such frequencies imply the stretching of a NH or of an OH bond. The strongest of these LVMs (3300 cm-' at LHeT with a FWHP of 0.13 cm-') has a weak satellite at 3298.54 cm-I with a relative intensity of 0.03 (Fig. 29). The calculated frequency and the relative intensity of an "OH oscillator mode compared to 160H at 3300 cm-' are respectively 3298.14 cm-' and 0.037. For these reasons and because SI GaAs is known to contain hydrogen as a residual impurity (Clerjaud, 1991), it is inferred that OH-related centers are formed in GaAs. The stress splitting of this LVM does not fit the

6.

SOME ATOMIC CONFIGURATIONS OF OXYGEN

I

243

'

LINE 14 6K res. =0.06ciii-l

3285.0

3295.0 3305.0 WAVI:NlIMRER (cm-1)

FIG.29. Enlarged portion of the ahsorption of an OH LVM at 3300 c W ' (Line 14) in Sl GaAs showing the very weak '*OH \atellite ( B . Pajot and C. Song (1992a). Phys. R e v . B 45, 6484).

usual pattern for (100); ( 1 10) or ( 1 I [)-oriented dipoles. The fact that more components are observed than expected does not mean here a dipole with a low symmetry because of the full polarization of the components for simple orientations. This is interpreted as an OH radical weakly coupled to its environment, which can reorient under stress in directions different from the ones at zero stress (Pajot and Song, 1992a). This OH center is electrically active, and it can trap a hole, giving a new LVM at 3296 cm-' (Fig. 30). The small change in frequency suggest that the hole is not trapped by the 0 - H bond but by its environment. Among the other high-frequency LVMs, one at 2947 cm- has been related with certainty to N H in a trigonal site, but from their frequencies other LVMs must be related to other kinds of OH centers (Pqjot, Song and Porte, 1992b).

'

VII. Summary

Silicon, germanium and GaAs are three semiconductors for which relatively detailed information exists on interstitial oxygen, oxygen-vacancy centers and a few combinations of oxygen with impurities, dopants and lattice atoms. There is however a large variety of centers containing one or few 0 atoms for which no detailed microscopic information is available. This is especially true of the precursors of the thermal donors in silicon and germanium and of the complexes formed by migration of 0 or dissociation of simple 0-containing defects. The situation in GaP is not so clear and a LVM at 1020 cm- I has been tentatively attributed

244

B. PAJOT

b I

,

3293.0

,

,

,

1

3295.5

'

3298.0

'

'

'

I

"

3300.5

I ,

3303.0

WAVENUMBER (cm-1)

FIG.30. Absorption of OH LVMs near 3300 cm-' in SI GaAs: (a) under thermal equilibrium; (b) after 10 min. illumination with white light. Line 13 corresponds to the complex giving line 14 after trapping of a hole. The lines were labeled by integers in order of increasing energy ( B . Pajot and C. Song (1992a). Phys. Rev.B 45,6484).

(Barker, Berman and Verleur, 1973) to v3(Oi).In GaP again, the electrical and optical properties of 0 as a deep center have been discussed at length (Dean, 1986). The 0 atom related to this deep center is presumably substitutional. In II-VI compounds, because of the larger ionicity of the matrix, it seems possible for 0 to locate on an anion site, where it can behave as a deep isoelectronic trap in ZnTe (Merz, 1968), but it has been recently reported from PL data that it could also act as an acceptor in other II-VI compounds due to a charge transfer from the host lattice (Akimoto et al., 1992). Oxygen has been detected in diamond by fusion analysis and by CPA, and it is possible that a very small portion of this oxygen is present in the dispersed form (Walker, 1979). In that case, substitutional location seems more likely than interstitial. ACKNOWLEDGMENTS Some of the results described in this chapter were obtained in close collaboration with C. Song, and I wish t o acknowledge her competence and tireless activity. I am indebted to R. C. Newman for discussions and the communication of unpublished results. Discussions with C. A. J. Ammerlaan and R. Jones are also gratefully acknowledged. Special thanks are due to K. Lassmann for discussions on phonon spectroscopy and the communication of unpublished results. I take this opportunity to thank all the coauthors of our papers quoted in this chapter. Isotopically enriched samples were kindly provided by C. A. J.

6.

SOME A I O h l l ( (ONFIGUK4TIONS OF OX LGE N

245

Ammerlaan and J. M . Spaeth. I am a l s o indebted to P. Clauws and S. McQuaid tor discussions and for providing samples. Cutting w n p l e s for stress measurements was competently performed by C. Porte. 1 was greatly helped in computer-assisted drawing of defect models by V . Fabart and Y Zheng. Thi? work was supported in part by DRET.

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Sk,MICONDIl(' IOKS .AND S1:MIMElALS. VOL. 42

CHAPTER 7

Electrical Properties of Oxygen in Silicon J . Michel w i d L . C. Kitnerlitzg DFPARTMENT OF MATERIALS 'A I E N( F AND ENGINEERING MASSACHUSETTS INSTITUT€ OF 1 F( HNOLOGY, CAMBRIDGE, MASSACHUSETTS

. . . . . . 5 . Current Understonding and Unresolved Issues . 111. NEW DONORS . . . . . . . . . . . . . . . . Rejerences . . . . . . . . . . . . . . . . . .

I.

11.

INTRODUCTION . . . . . . . . . . THERMAI. DONORS . . . . . . . . . . 1 . Donor Introduction . . . . . . . . 2 . Spectroscop? . . . . . . . . . . 3 . Heut Trealment u r 35O-S(K)"C' . . . 4. Atomic und E/ec,tronic. Strucrure . .

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251 252 254

266 27 I 2x0 282 284

1. Introduction

Oxygen in its usual interstitial configuration in silicon is electrically inactive. For this reason, oxygen concentrations of 10'' cm-' in Czochralski-grown (Cz.) silicon can be used for the production of integrated circuits without influencing the electrical performance of the devices. Fuller et al. (1954) discovered that upon heat treatment in the temperature range of 300-550°C electrically active centers were formed in oxygen-rich silicon (lo,]- 10" cm '). These centers are donors (Kaiser, Frisch and Reiss 1958). and because of their generation under thermal treatment, were called Thermul Donors (TD). A second electrically active center in silicon was later associated with the presence of oxygen (Liaw and Varker, 1977). The so-called N e w Donors (ND) are formed in the temperature range of 650-850°C. There has been extensive research on the formation kinetics, the properties and the structure of the Thermal Donors. We will review this work in the first and major part of this chapter. The second part will review the limited information on the new donors. ~

11. Thermal Donors

Thermal Donor5 have been extensively studied during the past 30 years. The interest in understanding the formation mechanism and resolving the 25 I Copyright (c 1W4 by A c d e r n l c Pre,, Inc i r f reproduction in dny form rexrved I5HN 0 I? 752142 Y

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structure was fueled by the use of Czochralski-grown boules in silicon integrated circuit technology and the increasing requirements of dopant uniformity and process control with integration density. In addition, internal gettering (IG), with the formation of an oxygen denuded zone and bulk oxygen precipitates required a detailed knowledge of the early stages of precipitate nucleation. Much of the TD process research has focussed on defining the role of Thermal Donors as precipitates’ embryos. Because of the great interest in Thermal Donors the most sophisticated techniques for defects studies have been used. However, even after 30 years of intensive research, surprising new results, such as the bistability of TDs and the enhanced TD formation rate upon hydrogen plasma treatment, continue to be reported. In this section we shall review both established and controversial results, and present an integrated framework for understanding TD phenomena. 1 . DONOR INTRODUCTION

Thermal Donors are formed upon heat treatment of oxygen-rich silicon at temperatures near 450°C. Early experiments of isothermal annealing showed that the formation rate and the maximum concentration of TDs were dependent on the fourth and third powers of the oxygen concentration, respectively (Kaiser et al., 1958). Figure 1 shows the experimental evidence for these dependencies. These results established the involvement of oxygen in the formation process of TDs. The data, however, do not address the role of oxygen as an electrical active center in silicon. The important factors that control the formation of TDs are the annealing temperature and annealing time. Measurements of the added electron concentration by the TDs showed that at temperatures below 450°C the formation rate is decreased and the saturation concentration of TDs is less than for a 450°C thermal treatment. Above 450°C the saturation concentration of TDs decreases with increasing temperature (Oehrlein, Lindstrom, and Cohen, 1984). Detailed studies show that the TD concentration and the annealing temperature at which the maximum concentration is reached depend on the duration of the thermal treatment. Figure 2 shows the dependency of the T D concentration on annealing temperature and annealing time. These studies are characteristic of the early experiments, which used resistivity measurements to determine the TD concentration by calculation of the added electron concentration. It was assumed that TDs were one specific defect center. The formation kinetics yielded a conclusion that “the TD” is an [SO,] donor complex, containing of a central silicon and four oxygen atoms (Kaiser et a]., 1958).

7.

t L t ( T R l C 4 1 PKOI'I-RlltS 01 OXYGEN IN S I I ICON

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254

,

J . MICHEL A N D L . C . KIMERLING

1016

TEMPERATURE (OC)

540

5;

:4

4 7

3O :

[oll = 7.7

1017~~-3

[Csl = 4.0 x 10I6cm-3

i

B

F

.

B

llrc

@@o 1013

-

*.

'8 HEAT TREATMENT o 20min. 0 60min. o 300min. 1200min.

.

@o 0 . 0 0

:1 0

2. SPECTROSCOPY u . Injkured Absorption Spectroscopy

Hall effect and infrared (IR) absorption measurements shed new light on the structure and properties of TDs. A significant breakthrough was the discovery of several species of TDs and their behavior as double donors (Wruck and Gaworzewski, 19791, following the suggestion by

7.

ELFCTKICAI PROPERTIES OF OXYGEN IN SILICON

255

Bean and Newman (1972). Wruck and Gaworzewski (1979)demonstrated the existence of two distinct donor levels of TDs by using Hall effect measurements. Figure 3 shows the Hall effect measurements for two differently annealed samples. For a 0.75 h anneal at 450"C,two donor ionization energies at 60 and 130 meV were found. while for a 7.5 h annealed sample, the energies were 55 and 120 meV. This trend was found to be general that the donor ionization energies decreased with increasing annealing time. ldentical samples were used to measure IR absorption spectra. The spectra exhibited low-energy and high-energy absorption bands. These bands could be grouped into pairs of lines having approximately the energy separation of hydrogenic and helium-like donors in silicon, whose ground and excited states could be described by the effective mass approximation. The I s ground state energies were estimated to range from 62.5 to h9.S meV and from 137.6 to 154.9 meV for the first four pairs of the low-energy and high energy series, respectively. From their Hall effect and 1R measurements, Wruck and Gaworzewski (1979) concluded that TDs are double donors that exist as several different TD species. 1R spectroscopy has proved to be a powerful tool to extend the knowledge of the formation of TDs. Pajot et al. (1983) and Oder and Wagner (1983) used this technique to identify nine different TDs with slightly different binding energies. Both the neutral and the singly ionized TDs

-

cc,

c

C

i)

C

FIG.3 . Temperature dependence of the electron concentration of two Cz silicon samples:

o is sample annealed for 0.7.5 hr at 450°C. A is sample annealed for 7.5 hr at 450°C (Wruck and Gaworzewski. 1979).

256

J . MICHEL AND L. C. KIMERLING

were observed for each species. Figure 4 shows an IR spectrum of neutral TDs. The different TD species are denoted A to D . The spectrum consists of the superposition of similar donor spectra with different binding energies. Both groups observed that the different TD species are produced sequentially. As a possible interpretation for the decreasing binding energies, it was suggested that the TD complexes grow in size with increasing annealing duration. Table I gives the binding energies of 1 1 different species, so far identified (Wagner and Hage, 1989). Table 1 provided the basis for following the formation and annihilation kinetics of each TD species separately. Previously, experiments described only the integrated effects of the different defect centers. The sequential formation and annihilation of the different TD species with annealing time suggests a successive generation of each species by addition of oxygen impurities, leading to larger and larger centers. The 1R measurements confirm that the formation and annihilation of each species depends on its size (temporal position in the formation sequence). This concept is consistent with the increasing stability of precipitates nuclei with size.

i

T=8K

70

60

so 40

30

20

00' 4I0

'

I 430

'

' 450

'

I 470

1 490

I

I

510

530

550

WAVE NUMBER (CM-1)

FIG.4. Spectrum of the neutral TD obtained by pumping the sample with band gap light (Pajor et al.. 1983).

7.

ELEC TRICAI. I’KOl’CRlIES OF OXYGFN IN SILICON

257

The first extensive study of the formation of the different TD species was done by Wagner et al. ( 1984). The different species were labled TD,, where n represents a temporal position in the formation sequence. Figure 5 shows the absorption coefficients (TD concentration) of the TD transitions for six different TD species, TD I to TD6, as a function of annealing time. It is obvious that the TD with the largest binding energy, TDI, is formed first. The following TDs are generated consecutively with decreasing binding energies. This study was used to model the formation kinetics of the TDs as the growth of an oxygen cluster with a common core (Ourmazd, Schroder, and Bourret, 1984). h . De r p - Le vcl Trunsir n t S p oct r o s copy ID L T S )

Two defect states, E(0.07) and E ( 0 . IS) have been identified by DLTS as oxygen donor levels in silicon (Kimerling and Benton 1981). Figure h shows the current transient spectra for these two defect states. This identification was made as follows: ( 1 ) the states were observed only in silicon that contained high concentrations of interstitial oxygen, ([O,1) > 10’’ cm 7 ) ; ( 2 ) the states appear during 450°C annealing and disappear during annealing above 550°C: and ( 3 ) the ionization energy of the states decreased with applied electron field according to the Poole-Frenkel mechanism (-Ell’), confirming the shallow donor nature of the center. Further DLTS experiments showed a shift of the E(0.15) donor state (ionization energies) to lower temperatures as the annealing time is increased. The E(0. IS) donor state. additionally, exhibits an anisotropy in emission rate with an ionization energy dependence of the electric field direction. The DLTS method as the Hall effect measurement does not resolve the multiple TD species. However, the trend in decreasing ionization energy with time and evidence for an anisotropy in conduction band valley interactions are clearly evident. ~

c‘.

Ele ct ron Puru mug n e t ic . R oson ( i n ce (i nd Electron N r ~ c l i ~ c i r Dorrhlr R c s o n u n w

Magnetic resonance measurements have proven to be a very effective tool for learning about symmetry and local environment ofthe TDs. Electron paramagnetic resonance (EPR)measurements on oxygen-rich silicon annealed at 450°C revealed scveral defect centers (Muller et al.. 1978). Most of these centers exhibited donor behavior. Later measurements on carefully prepared samples showed that only two of the initial EPK centers, NL8 and NLIO, are oxygen related (Gregorkiewicz et al., 1987). The other centers were assigned to metal contamination. EPR signals of TDs should be observable only in p-type silicon. be-

TABLE I IR-ABSORPTION LINEPOSITIONS u - I N c m - ' A N D BINDING ENERGIES EB I N meV FOR THE VARIOUS TD SPECIES. THEBINDING ENERGIES EB WERE DETERMINED USING THE 3p,-OR, ALTERNATIVELY, THE 2pz-TRANSITION. RESOLUTION OF THE SPECTROMETER USED IS 1 Cm-l. TDI

TD2

TD3

TD4

TDS

TD6

TD7

TD8

TD9

TDlO

TDll

EMT

b

z

U

r 0 R

a. Neutral species: iJ @Po) EB GPO) iJ (2P, )

EB ( 2 ~ 2 ) iJ (3Pd EB UPO)

461 12.1

442 12.0

423 12.2

405 12.0

507 6.36

488 6.34

470 6.34

451 434 6.34 6.34

-

494 5.60

475 5.72

456 (423) 441 5.72 5.47 5.60

533 3.12

514 3.12

496 3.12

477 460 3.12 3.12

541 2.14

522 2.13

503 2.25

485 2.13

388 12.0

-

-

372 11.9

357 12.2

343 12.0

330 12.1

417 6.34

404 6.40

388 6.40

(363) (351) 376 6.40 6.40 6.40

(395) (383) 412 5.41 5.53 5.53

443 (429) 3.12 3.30

-

-

(319) 11.9

(307) 11.9

11.51

-

-

-

-

6.40 5.48

-

3.12

-

-

-

-

-

-

-

-

-

-

-

-

2. I 9

zF!

2 0

c, ( 5 ~ ~ ) c, (gs)

-

1.38

1.51

-

-

-

-

-

-

-

-

51.4

49.9

I .44

31.27 H 55.8 He

69.2

66.8

64.6

62.2

60.1

58.0

56.5

54.5

53.0

854 50.4

806 49.8

763 49.2

713 49.8

678 48.9

645 48.3

613 47.7

585 46.8

(559) 46.7

46.04

1044 26.9

991 26.9

945 26.6

889 28.0

846 28.1

804 28.6

769 28.3

(729) 28.9

(700) 29.2

25.60

iJ (?Pz,,) (2P,l,)

1048 26.4

998 26.0

951 25.9

904 26.1

862 26.1

825 26.0

791 25.6

(756) 25.6

(729) 25.6

25.60

iJ I ? p , , )

I156 13.0

1105

1057 12.8

1011

931 12.9

-

-

-

12.9

96X 13.0

-

12.8

-

12.48

c. t3pz,,j En ( ~ P ~ I , )

1160 12.5

1107 12.5

I059 12.5

1014 12.5

972 12.5

934 12.5

-

-

-

-

12.48

iJ ( 4 p 7 ) E , (4p,

I I87 9.13

-

8.76

EB (gs)

156.3

149.7

b . Sing/y ionized species: iJ (?P,,) €8 (2PO)

u (2Pr,) €8

(2P,/)

€8

€8

1 3 ~ ~ ~ )

-

1 090

8.66 143.8

-

-

-

-

-

-

-

-

-

-

-

-

138.2

133.0

128.3

123.6

119.3

116.0

126.8

260

J . MICHEL A N D L. C . KIMERLING

CZ-Si undoped

0.J 0.1

I

'

TA=46OoC

I

I

1

10

ANNEALING TIME (h) FIG. 5 . Absorption coefficients of the 2po-transitions as a function of annealing time at 460°C for TDJ'. i = 1-6 (Wagner et al., 1984).

cause the Fermi-level must fall below the TD energy level at the measurement temperature (-20 K) in order to singly ionize the double donors. NL8 and NLlO both were observed in p-type silicon only, and therefore both were candidates for the TD. Annealing studies revealed that NL8 is observed after short annealing times (0.5-40 hrs), while NLlO is observed only after extended annealing of the sample (>20 hrs). Both NL8 and NLlO have an anisotropic g-value close to 2.0 and exhibit CZvsymmetry. Figure 7 shows an EPR spectrum and the angular dependence of NL8. Both centers show no hyperfine interactions with silicon or the "O isotope after indiffusion of "O enriched oxygen (Muller et al., 1978). The formation behavior of NL8 was found to follow the integrated measure of the TDs, as detected by electrical measurements. Both EPR centers show a g-value shift with annealing time. While EPR, like the electrical measurements, cannot resolve the different TD species, electron nuclear double resonance spectroscopy (ENDOR) can distinguish between the different TD species (Michel et al. 1986). ENDOR detects the hyperfine interactions between the paramagnetic electron and the nuclei surrounding the defect. Five different TDs with decreasing hyperfine interactions, reflecting a delocalization of the defect wavefunction, were identified from ENDOR measurements of

7.

26 I

EI.F.CTRICAI I'KOI'EKTIES OF OXYGEN IN SIL.ICON

S I - A S - F Z - S8 n,,,. 4.5 i 1 0 ' 4 c m - 3

Si-P-CG-S8 * 7 I 10" ern-

n,,,

-

T, * 9 p s l l e h r s 450'C

E(0.07)7, '9Ps

-

t I

18hrs

400'C

-

5

-

!

30 50

O

8

-

EI0.07)

7-

30 5 0

n,,,=

4

i

I00

Si-P-CC-SB n, = 5 i 10" c m - 3

1014 c m - 3

T,*?pS As G R O W N

7, = 9 p s 2 4 h r s BOO'C

30 50 (K)

I00

TEMPERATURE

FIG. 6 . Current tran\ient spectra for ti-type \iIicon. Heat treatment of oxygen contatning ( C G ) material displays the E(0.07) and t(0. IS) donor fealures (Kirnerling. 1986).

262

J . MICHEL A N D L. C . KIMERLING

magnetic field / mT

(4 339.0]+/ I100 1

11111

1

angle degrees (b) FIG.7. (a)TD+ EPR absorption spectrum of NL8 for a Cz-Si sample annealed for 4 hrs at 460°C. (b) Angular dependence of the TD+ EPR spectrum for rotation of the magnetic field in a { I lo} plane. TD' has GI: symmetry (Michel, Niklas, and Spaeth, 1989).

NL8. The identification was accomplished by comparison of the ENDOR line intensities of the different ENDOR species with the signal intensities of the TD IR absorption lines. These results confirmed the earlier thermally induced depopulation measurements (Lee, Trombetta, and Watkins, 1985), which showed a correlation between NL8 and the TDs. ENDOR measurements also revealed the existence of oxygen as part of the defect for the first time. It is possible to identify the nuclei surrounding the defect by their nuclear g-value. Oxygen was identified in both, the NLlO (van Wezep et al., 1986) and the NL8 (Michel, Niklas, and Spaeth, 1988b) defect. Since only the oxygen isotope ''0 has a nuclear spin, the samples had to be enriched with this oxygen isotope. Furthermore, aluminum hyperfine interactions were detected in NL 10 (Gregorkiewicz, Bekman, and Ammerlaan, 1989). The NLlO center has

7.

EI.FCTKI( A 1 PKOPt KTIES OF OXYGEN IN SILICON

263

not been correlated directly with the TDs observed in IR spectroscopy. although their structure is very similar to that of the NL8 center (see Fig. 18).

In addition to the identification of nuclei, ENDOR gives information about the symmetry of the nuclei in the different neighboring shells around the defect core. ENDOR studies show that there are at least two oxygen neighbor shells of different symmetry. Each neighbor shell contains one or two oxygen atoms with approximately [ I I t]-symmetry (Michel et al., 1989). In addition to t h e neighbor shells of silicon on lattice sites. a single silicon atom in [ O O l ] symmetry was found. This silicon atom shows the strongest hyperfine interaction for all different NL8 species and therefore is expected to be part of the defect core. The structure of NLIO, determined by ENDOR (Gregorkiewicz. Beckman, and Ammerlaan. 1988). exhibits a central aluminum nucleus and two oxygen nuclei in a (01I ) mirror plane in positions close to their interstitial site. They suggest that the growth of NL,IO species occurs by adding single oxygens along the 101 I J direction. EPR and ENDOR have given significant insight into the structure of TDs. have narrowed the variety of possible structural models, and have unambiguously identified oxygen as a constituent of the center. These techniques, however, have not yet provided an unambiguous structural model of the TDs. The primary obstacle is the shallow, delocalized character of the defect wavefunction that inhibits, in particular, the observation of the weak hyperfine interactions of the oxygen nuclei, because of the superposition of many oxygen ENDOR lines in the same spectral region. d. Pizo tolir inin escen C P

Tajima, Kanamori, and lizuka (1979) reported the first observations of photoluminescence (PL) lines that could be correlated to Thermal Donors. After a 450°C annealing three new lines at 1.143. 1.124, and 1.085 eV were assigned to TDs (Fig. 8). The 1.143 eV line was identified as a zero-phonon line, and the other two lines as phonon replicas. Control measurements were done with low oxygen content ([O,] < 10'" crn '1, float-zoned (FZ) wafers, with and without an additional oxygen ion implantation. The unimplanted FZ samples showed no new PL lines. while the oxygen implanted FZ samples exhibits the same PL spectrum observed in Cz material. Steele and Thewalt (1989) studied these PL lines at high resolution and found at least 18 separate transitions for the 1.143 eV PL line in a sample in which nine TD species had been identified by 1R spectroscopy.

264

1. MICHEL A N D L. C . KIMERLING

r jT0 - bzJ

bl

TTO 1.16

1.14

1.12

1.10

1.08

PHOTON ENERGY (eV)

FIG.8. PL spectra at 4.2K from CZ wafers (B-doped, r annealed at 450°C for 64 hrs (Tajima et al., 1979).

- 1.5 Rcm): (a) as-received, (b)

Figure 9 shows their high-resolution PL spectrum. According to the authors, the emission lines represent an electron-hole pair added to a neutral TD. Two transitions for each TD result from the fact that the effective mass wavefunction for the TDs is constructed from a single pair of conduction band minima. These doubly degenerated electron states are separated by valley-orbit splitting in the ground-state manifold. An exciton that is localized a t a neutral TD requires the occupation of both valleyorbit states, since there are three electrons in the ground state. Recombination of an electron in either state with a hole will give two separate PL lines for a single bound exciton. A second group of PL lines, called 0 and 0' lines, was assigned to TDs by Weber and Queisser (1986). These lines are observable only after extended heat treatment at 450-500°C (>20 hrs maximum intensity at 100 hrs). The energetic position of these lines coincides with the ionization energies of TDs. Because of the observed asymmetric line shape, Weber and Queisser (1986) concluded that the 0 lines are due to free-to-bound (FBI transitions involving neutral TDs and free holes. Problems with this

7.

265

ELECTKICAL I'KOPFKTIES OF OXYGEN I N SILICON

interpretation are that FB transitions are very unlikely at 4 K , and they are much broader than observed for the 0 lines. In addition, the variation in lifetime among the different 0 lines (Thewalt et al., 1986) of four orders of magnitude makes this interpretation very unlikely. A second interpretation of these lines is based on time resolved and excitation density dependence studies by Dornen and Hangleiter (1986). I hey found a close analogy between these PL lines and the properties of donor-acceptor pair spectra. I t was concluded that the 0 lines are due to the recombination of TD-neutral acceptor pairs. Their model was able to explain the different lifetimes of the lines, but the correlation with the transition energies of the TDa was lost. Thewalt et al. ( 1986) used emission transient spectroscopy, excitation \pectroscopy. and temperature- and excitation density-dependent measurements to study the 0 lines. Their lifetime measurements revealed that within the 0 lines there are two different species with a lifetime variation of four orders of magnitude. Their interpretation explains the main 0 line as an isoelectronic bound exciton transition and the faster transitions as bound multiexciton complexes associated with the same 7

7

PNP

!

1075

l ' t : O T C l l ~ J tLbJERGY i,rneV)

1155

FK,. 9 , PL spectra from two a n n e d r t l S I samples: Cz Si (top). annealed for. 32 hrs at W ' C . and FZ Si tbottom). annealed hi-72 hrz ai 480°C tSteele and Thewalt. 1989).

266

J . MICHEL AND L. C . KIMERLING

binding center. Taking into account the annealing behavior of the 0 lines, which correlates with the population decrease of the TDs rather than with the TD formation, Steele and Thewalt (1989) concluded that these isoelectronic centers are remnant cores of the TDs after they lose their electrical activity.

3 . HEATTREATMENT AT 350-500°C As previously mentioned, isothermal annealing studies of added electron concentration show that the aggregate maximum concentration of TDs is dependent on the third power of the oxygen concentration. With the separate TDn species observed in IR spectroscopy it was possible to examine if the third power law for the maximum concentration of TDs was valid for each species. This law was confirmed by IR spectroscopy for TD3 and TD4, but does not hold for TD1 and TD2. For these species the dependency of the maximum TD concentration from the 0 concentraand [Oil’.’, respectively (Wagner, 1986). tion is The first study of the annihilation of the aggregate TDs showed an exponential decay at temperatures between 540°C and 565°C (Fuller and Logan, 1957). The activation energy for the decay was 2.7 eV. These results have been challenged by Kanamori (1979) and Oehrlein et al. (1984), whose experiments showed a much slower decay of TDs. The more recent results were attributed to a higher quality of the silicon material. All of the preceding studies used electrical measurements to determine the concentration of TDs. By measuring the 1R absorption of the TDns, Suezawa and Sumino (1984) found exponential decays for all of the different TD species. The activation energies for the TD species 3-6 was 4.3 eV. The activation energy for the sum of all TD species, including species 1 and 2, was found to be 3.4 eV, in better agreement with the early data by Fuller et al. (1960) (considering nearly 30 years of advances in silicon growth technology). u . Forrnution Kinetics

The formation kinetics of TDs present a significant problem for the direct involvement of oxygen. The diffusivity of oxygen, required by the formation kinetics of TDs, is two to three orders of magnitude larger than generally accepted. The oxygen diffusivity at 450°C is 6 x lo-’’ cm2s-’ (Stavola et al., 1983a) compared to the diffusivity extracted from the TD ern's-' (Kaiser et al., 1958; Fuller et formation rate, which is 2 x al., 1960). Based on the Kaiser model Gosele and Tan (1983) proposed the existence of a fast diffusing molecular oxygen ( 0 2 )Ourmazd . et al. (1984)proposed a kinetic model based on the successive formation of the

7.

ELECTRICAL PKOPPRTIES OF OXYGEN IN SII.ICON

267

different TD species. Their model requires an oxygen diffusivity of 4 x 1 0 ~l 6 cm’s I , which is similar to the early value o f 2 x 10- I‘ em's- I and in conflict with the properties of isolated (O,]. The primary problem in the kinetics studies is the diffusion of interstitial oxygen. A reevaluation can be done by taking into account that each TD introduces two states and two electrons into the system (Wruck and Gaworzewski, 1979; Kimerling and Benton, 1981). This result does not require reexamination of the 1O,I4 proportionality. It does, however. increase by a factor of two the effective oxygen diffusivity term in the rate equation. The increase in oxygen diffusion rate by two orders of magnitude in heat treated material (preanneal at SOOT) and under a hydrogen plasma ambient (Murray. Brown, and Newman, 1989) act to further enhance the TD formation rate, hence, do not resolve this paradox. The concentration of interstitial oxygen, as monitored by the intensity of the 9 pm and 16.5 pm absorption bands, decreases at a rate proportional to the square of the oxygen concentration, [Oil’. at 450°C during donor formation (Newman 1985). This result i s clearly inconsistent with dependence of the donor formation kinetics. The critical obserthe [0,l4 vation is the loss of the [O,] vibrational mode. Since no new vibrational modes result, t h e reaction product must be ( I )disconnected from the lattice. e.g., an 0’ molecule; ( 2 ) constructed of hybrid bonds of reduced strength whose modes are resonant with the continuum of lattice frequencies; or ( 3 ) not in possession of a dipole moment. The third possibility is highly unlikely, since oxygen possesses a strong electronegativity relative to silicon. A description of the Si : 0’ states is critical to understanding the 1 D formation process. An lo,]’ dependence requires that, with near 100% efficiency, two oxygens interact at a distance of approximately 5-10 A to yield a new structure. The relatively large interaction distance of 5-10 A is not physically attractive. The two approaching oxygen atoms should possess two repulsive interactions: Coulombic and compression strain. If R = 2 A is taken as a reasonable value and bimolecular kinetics are applied. one must conclude that [O,] was underestimated by LT. Possible sources for this discrepancy are ( 1 ) the calibration of the absorption band oscillator strength and ( 2 ) inhomogeneity in the spatial distribution due to growth striations or partial clustering related to the sample history. Since donor formation such an error in the concentration term would bring kinetics vary as [0,l4, theory and experiment closer by a factor of 25. These results have strong implications regarding the thermodynamics of oxygen aggregation. Precipitation of a second phase takes place in three steps: a local fluctuation in chemical potential (embryo); formation of a stable nucleus of critical size; and precipitate growth. The criterion

268

J . MICHEL A N D L. C . KIMERLING

for stability reflects the competition between a relatively constant positive free energy of interface formation and a volume-dependent, negative free energy for second-phase, SiO,, formation. Growth of macroscopic precipitate structures is observed at TD formation temperatures after times greater than 500 hrs (Bergholz, Pirouz, and Hutchison, 1985). Extrapolation of equilibrium nucleus concentrations from high temperature yields a critical radius at 450°C of about 3 A (Inoue, Wada, and Osaka, 1981; Livingston et al., 1984). The critical radius of the stable nucleus must be larger than that of an embryonic 0, cluster unless an intermediate phase (defect) is more stable for the small cluster. b. Stress-Induced Alignment

From IR absorption measurements it was concluded that the effective mass-like ground state of the TDs consists of a single pair of the six degenerate [ 1001 conduction-band minima (see later). The formation of TDs under uniaxial stress should, therefore, show preferential alignment (i.e., Thermal Donors would form only in a certain symmetry configuration). EPR and polarized IR absorption measurements were performed on identical samples (Wagner et al., 1987) to detect a preferential defect symmetry. EPR experiments were performed by observing the so-called NL8 center, which represents TDs (Pajot and von Bardeleben, 1984; Lee et al., 1985). The NL8 spectrum is characterized by a g-tensor with C Zv defect symmetry. Figure 10 shows that, formed under stress, an alignment of the TDs has been observed. It was found that the defects preferentially align with their g , axis ( 1 1 [OOl]) perpendicular to the compressed direction. In the IR absorption experiments the different TD orientations were observed by monitoring the polarization dependence of the optical transitions. Figure 11 shows the polarization dependency for the transition of the ionized donors TD2+ and TD3+. A polarization dependence of the optical transitions in the stress annealed samples was observed. From these measurements the relative concentration of the various TD orientations was estimated by specifying the orientation of the optical dipoles. The results are in agreement with the EPR data and lead to the following possible explanations of the preferential alignment: The core of the TDs can reorient and align in the applied stress field. 2. The alignment is a result of either preferential growth or activation (or annihilation) of electrical activity, for the differently oriented TDs, without orientation occurring at any stage. 1.

7.

269

ELECTRICAL, I’HOPI.Rl IES O F OXYGEN I N SILICON

GAIN x 4

A

0

ti

C

A

B

C

Fic,. 10. N L 8 EPK spectra with ti 1) I I 1 0 1 lor Thermal Donors grown with and without \ t r r \ s foi- 90 min at 4hO”C: ( a ) (r = 0: ( b ) ( r 11 [ 1101. 600 MPa: ( c ) u 11 [(K)I]. 600 MPa. The in\ets show [he defect orientations aswcinled with each of the three resolved EPR lines along with the stress and magnetic held orientations. (Wagner et al.. 1987). ~

A distinction between these two processes was not possible because reorientation of the TDs under uniaxial stress had to be done at temperatures, where TDs are also formed. I t is fact. however, that compression along (100) preferentially retards the formation of TDs with symmetry axes along the same direction. c. lnjlicrnc~to f C cind H

The formation of Thermal Donors is influenced by the presence of carbon and hydrogen. The influence of carbon on the TD formation was studied by Bean and Newman (1972). Optical and electrical measurements were used to monitor [he curbon and carbon-oxygen pair concentration as well as the T D concentration. The experiments showed that in samples with a carbon concentration of less than 3 x I O ” cm-’ there is only a small effect on the TI) generation. However, when the carbon concentration is higher, the maximum TD concentration is reduced by two or more orders of magnitude. This effect was explained by the forniation of carbon-oxygen pairs and other carbon-related defects that capture oxygen atoms and. therefore. inhibit the T D formation. Although carbon heterogeneously nucleates oxygen aggregation. its small size, relative to silicon, may prevent formation of the unique TD core structure. It was discovered that the T D formation is enhanced by exposure to a

t 4

(a) T, =460'C

4 0

TA= 460'C

riioi

tA= 90 rnin

tA = 110 min

STRESS = 600 MPa 11 riioi

STRESS = 600 MPa

I001 I

11101

#2

W U

U

L

z a

<

m

a

a

0

v,

m

a

1100

1000

900

WAVENUMBE RS

800

cml

1100

1000

900

800

cm'

WAV ENUMBE R S

FIG. 1 1 . Infrared absorption spectra of singly ionized Thermal Donors grown with stress for different stress and viewing directions. The lines are labeled according to the respective final states. The splitting of the 2p? and 3p? lines are clearly observed: (a) u 11 [-110], 600 MPa. Viewing direction k I) Ill01 and electric field vector E 1) I - l l O ] and E )I [OOl]. respectively; (b) u /I LOOll, 600 MPa. Viewing direction ! i 11 [ O l O ] and E 11 [OOI] and E I/ [loo], respectively (Wagner et al.. 1987).

7.

E l E C l R I C A l I'KOPFKllES OF OXYGEN IN SILICON

27 1

Time ( h ) Fir,. I ? Production of TD with nnnenlinp time at 400°C for hydrogen ( x ) , AriO? (U1 mixture. and helium ( A ) pla\rna. The point\ \hewn ( 0 1 are for a furnace anneal (Murray et dl . 1989)

hydrogen plasma during annealing (Brown et al., 1988). These experiments were performed at temperatures between 350°C and 450°C while exposed to different ambient gases and plasmas. Using the same annealing times and temperatures, the TD IR spectra for samples annealed in different atmospheres were compared. The hydrogen plasma annealed sample showed a significant increase in TD concentration. The sample heated in molecular hydrogen gas showed no enhancement of the TD concentration compared to a furnace anneal. For different annealing temperatures different enhancement factors for the TD formation were found. The strongest enhancement was found for an annealing temperature of 350°C: an enhancement factor of 300 compared with a furnace annealing at the same temperature (Murray et al., 1989). Figure 12 shows the generation of TDs for different plasmas at 400°C. The enhancement of the TD formation rate correlates with the accelerated loss of interstitial oxygen. The study supports long-range oxygen diffusion as a limiting step in TD formation. The rate enhancement under a hydrogen plasma environment reflects the hydrogen accelerated diffusion of oxygen described elsewhere in this volume (Newman and Jones). 3. A rOMlC

AND

ELECTRONIC s TRUC 1 LIRE

Perhaps the most elusive challenge in TD research is the description of the microscopic structure of this family of defects and correlation with

272

1. MICHEL A N D L. C . KIMERLING

its various properties. A proper model has to include the shallow double donor with an effective mass-like wavefunction, the different species with an identical or very similar core, the formation kinetics, the stress induced alignment, the metastability of TDl and 2, and a multitude of other experimental facts. The simple model of an SiO, cluster, derived by Kaiser et al., (1958) from formation kinetic data, cannot, for instance, explain the electrical activity of the TDs. In this section, we discuss experiments that address the TD structure. The “macrostructure” is fairly well understood; the core “microstructure” remains undefined. a . Electronic Structure

Two groups of effective mass-like IR absorption lines have been observed. Their compensation behavior and temperature dependence define the double donor character of neutral and singly ionized states from a single center. The electronic structure of the TDs was further studied using uniaxial stress (Lee et al., 1985; Stavola et al., 1985; Stavola and Lee, 1986). In addition to the 1R measurements that give information about separate TD species, DLTS and EPR measurements have probed the behavior of an average of all TDs that are present in the sample. All uniaxial stress measurements show splitting of the TD related features and the results have been interpreted consistently with effective mass theory (EMT). Figure 13 gives an example of the splitting of the IR lines of TDs upon the application of uniaxial stress. In EMT the Is ground state is sixfold degenerate and splits in Td symmetry to a singlet, a doublet, and a triplet state. For substitutional donors in Si the singlet state is the lowest lying ground state. Uniaxial stress removes the degeneracy of the conduction band and therefore allows determination of the irreducible representation of the different 1s states. By applying uniaxial stress along different crystallographic axis orientations, it was found that the ground state splittings for the TD centers are an order of magnitude smaller than expected and that the stress orientation dependence is different from conduction band-like splitting characteristic of effective mass states. The core of the TDs has a low symmetry that distorts the effective mass-like wavefunction through anisotropic “central cell” effects. According to Stavola and Lee (1986) this splitting pattern is characteristic of a CZvsymmetry for the first four TDs. The experiments show that the spectral features do not split for a [OOl] stress. The absence of a [OOl] splitting requires that the ground and the excited states each split identically. By studying the uniaxial stress effect under polarized light, it was shown that the ground state of the TDs is nondegenerate. Therefore, it was concluded tHat the ground state wave-

7.

ELECTRICAL PROPERTIES OF OXYGEN IN SILICON

273

a . 0-11 [OOI]

-

it

52 a

iz c

+!, Ellc

1

1

function for TD" and TD + is constructed from only a single pair of conduction band valleys. In this case the transition energies remain unchanged under [OOI] stress because both the ground and excited states split together like their associated conduction valleys (Stavola et al.. 1985). Furthermore, they concluded from their observation that only tension or compression along the [ 1 1 0 1 axis contribute to the stress response of the 1R spectra, that TDs are elongated along a [ I101 axis.

274

J . MICHEL AND L . C . KIMERLING

TEMPERATURE (K)

Fic. 14. DLTS spectra of the TD’ oxygen donor peak, E(O.15), under (a) no applied stress. and under uniaxial stress parallel to the (b) [ l l l ] , (c) [ I 101, and ( d ) [lo01 axes (Kimerling. 1986).

The DLTS piezospectroscopic studies provide an independent explanation of the TD electronic structure. Two defect states, E(0.07) and E(0.15),have been identified by DLTS as TD states. The splitting of the E(0.15)state under uniaxial stress is illustrated in Fig. 14. The maximum response exists for a (100) stress. The splitting is linear in applied stress and consists of both a shift in ground state energy and in the “center of mass” energy of the defect. The deformation potential of the “center of mass” and of the center are approximately equal (10-15 eV). The relative strengths of the ground state splitting, 2 : I for (IOO), I : 2 for ( I lo), and none for (1 1 1 ) are consistent with a (100) primary axis and D,,symmetry. The motion of the “center of mass” energy (weighted by the degeneracy for each splitting) can be explained by stress coupling to the six conduction band minima. The context for interpretation of the DLTS piezospectroscopy is as follows. The TD states exhibit a classic, helium-like ionization spectrum that closely matches the ground state energies predicted by effective mass theory. The relative intensities of the stress split peaks are independent of temperature, verifying that the ground state is a singlet. Both the

7.

ELk,CTRICAL PROPLKTIES 01. OXYGEN IN SILICON

~

Direction ( 1 11) (111) ( I 10) (21 I ) ( 100)

275

~~~

(Electric Field). { V i c m )

T'T. (K'sec)

At,. ( e v )

0 (extrap.)

4000 10. I 8.9 6.4 3.1

0 3.0 x l o r ' 3.1 x l o - ? 3.26 x lo-' 3.54 x lo-?

2.4 x 1 0 4 2.4 x 10" 2.4 x 10' 2.4 x 10'

ground state and conduction band couples to external stress. The relative intensities of the split peaks correspond to projections of the stress on the ground state symmetry. For EMT this symmetry is that of the band structure. The ionization energy of the TD states decreases as the square root of the applied electric field. confirming the donor (positive core, negative electron emission) nature of the centers. This field emission phenomenon, first described by Frenkel (l938), is uniquely anisotropic for the TDs: Table I1 lists the observed anisotropy in emission rate and shift in energy position with electric field position for the E(O.15)donor state (Kimerling, 1986). The data are interpreted a s a superposition of an isotropic, longrange interaction (as manifested by the differences if T with respect to ( I I I ) extrapolating zero field behavior, and a n anisotropic Stark interaction with a local dipole). The symmetry of the core structure is, thus, reduced by C z v ,in agreement with the EPR measurements. h . Bis t u hility

Recently it was reported that the first-to-form TDs I and TD2 show structural bistability. This property was originally concluded from Halleffect measurements (Tkachev et i d . . 1084; Makarenko. Markevich, and Murin. 1985) and later confirmed by IR absorption measurements (Latushko et al., 1986; Wruck and Spiegelberg, 1986). Two different states exist for these two species at low temperatures, which are derived from two different structural configurations. One configuration is associated with the known TD shallow \late, while the second configuration forms an Anderson negative-U system. The different states are created by different cooling conditions. For I K measurements cooling in darkness will keep the TDs in an Anderson negative-U state with the occupancy levels fi(0I' + + ) at E, - 0.32 eV and E, 0.22 for TDI and TD2. respectively. The same state can be reached when a diode, n-type sample is cooled ~

276

J. M I C H E L A N D L. C. KIMERLING

I

czsi 30MIN

n - 2 x 10'5cm-3 450°C

3

m

=5

1.0

I-

I 0 0.8 w

-

I Y

a W n

v)

-

0.6

-

0.4

-

0.2

-

Id

0

50

100

150

200

250

TEMPERATURE (K)

300

350

4M)

-

FIG.IS. Isochronal ( 5 min) annealing data for the transformations u b and b + a . For each point, the Schottky diode was cooled from 350 K with the appropriate bias. annealed for 5 min under the opposite bias condition, and the E(0.15) DLTS signal was monitored (Chantre, 1987).

down with no reverse bias as is the case for DLTS (Chantre, 1987)or Hall effect measurements. Chantre (1987) studied the reversible conversion of TDs to negative-U systems by measuring the temperature dependence of the DLTS spectra under different bias conditions. Figure 15 shows the results of this measurement. State a is the TD configuration while state h is the Anderson negative-U configuration. This experiment implies significantly different configurational conversion rates for the two transitions. This result may indicate a charge-state-dependent barrier to atomic motion. The negative-U states are only observable in Hall-effect measurements. In IR spectroscopy and DLTS spectroscopy only a loss of the intensity of the TDI and TD2 bands is observed with varying cooling conditions. No bistability has been found for the later TD, species. Wagner and Hage (1989) showed that the occurrence of the bistability is controlled by the Fermi-level position. Figure 16 shows the dependence of the TD absorption lines on annealing time in a p-type sample that changes to n-type during annealing. These results demonstrate that the bistability of the TDs is observable only in n-type material. It was shown that in order to observe the bistability, the Fermi level at room temperature has to be above E,. - 0.32 eV and E,. - 0.25 for TDI and TD2,

7.

LLECTRIC AI. I'KOPt K I l E S OF O X Y G F N IN SILICON

277

respectively. In this case band-gap illumination will put the TDs into the metastable TD and TD" configurations. Furthermore it was noticed that very weak band-gap illuminat ion was sufficient to transform all centers into their metastable configuration. The bistability transformations do not always involve 100% of the TDs. This behavior could result from Fermi-level inhomogeneities or randomly fluctuating stresses that influence the configurational transformations. Hydrogen passivation of TD electrical activity is a similar phenomenon (Pearton et al., 1986: Johnson and Hahn. 1986). The early donors, TDl and TDZ, which are also metastable, are selectively passivated relative to the later TDs (Chantre et al.. 1978). The two observations point to an enhanced stability of the later TDs with respect to bond reconstruction. +

01

1

10

100

h

ANNEALING TIME

Pic;. 16. Room-temperature Fernwlevel position (above) and abwrption coefficients of the ?p,,I-line\ of singly ionized TD\ versus annealing time for a p-type sample. Full lines refer to the results obtained when the \ample wii\ cooled under illumination. The dashed lines give the measured absorption coefficient\ when the sample was cooled in darkness (Wagner and Hage. 19x9).

278

J . MICHEL AND L . C . KIMERLING

0 Si

(b)

I

FIG. 17. Models for TDs: (a) ylid model (Stavola and Snyder, 1983); (b) OBS model (Ourmazd et al., 1984)

c . Theory und Core Structure Models One of the main goals of the study of TDs is to provide a structural model that fits the experimental evidence. The first model was proposed by Kaiser et al., (1958) and explained a number of important experimental features, especially the formation kinetics of TDs. Kaiser et al., (1958) proposed an Si04 defect core with a silicon atom in the defect center. But the model failed to explain later IR absorption data, which showed a series of TD species. Models that took these facts into account were the ylid (0,)model (Stavola and Snyder, 1983) and the OBS model (Ourmazd et al., 1984). These models proposed an oxygen chain in a [I101 direction and a central Si atom (Fig. 17). The OBS model suggests an (0,)3 complex in a vacancy where one oxygen saturates two dangling

7.

ELECTRICAL PKOPEKlIES OF OXYGEN IN SILICON

279

bonds of the vacancy while the other two oxygens saturate one dangling bond each. These two oxygens are bonded to a Si atom on a [OOI] axis, which acts as a double donor. The OBS model is consistent with the formation of a hierarchy of different TD species by adding single 0 atoms to a [ I 101 chain. Although these models explain some features of the TDs, they are inconsistent with the EPR data because they predicted a hyperfine interaction of the central nuclei that is ten times larger than observed (Robertson and Ourmazd, 1985). A modification of the OBS model was suggested by Michel et al. (1988a) based o n the ENDOR results of NL8. This model consists offour oxygen atom4 in a vacancy on perpendicular { 1 lo} planes and a self-interstitial on the l O O l ] axis close to the defect core (Fig. 1%). From calculations Snyder el al. (1989) found that this 0, complex is unstable compared with other oxygen complexes, while Chadi (1990) suggc3ted a V-0, cluster as a possible TD core. New experimental evidence acquired by ENDOR led to refinements of the ylid model. Because no oxygen atom was found on the twofold axis complex was suggested (Snyder et al., 1989; of the TD core, an ((I,,)?

ti(s

I X TD model5 from E N D O R

(d)

NLX. (h) NLlO (after Deak et al.. 1992)

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J . MICHEL AND L. C . KlMERLtNG

FIG. 19. Structure of the 10: complex by Deak et al. (1992).

Jones, 1990). A further modification was put forward by Chadi (1990) on the basis of tight-binding-based total-energy-minimization calculations. He suggested a complex of two oxygen atoms intercepting parallel Si-Si bonds in a (1 11) plane as a possible T D core based on the double donor character and bistability. Based on these criteria Chadi found two additional defect configurations, a V - 0 , and a V-O4 complex, as a possible TD core. Recently similar tight-binding-based calculations were applied to oxygen aggregation, which showed the possible formation of oxygen chains without ejecting silicon interstitials (Needels et al., 1991). Deak, Snyder, and Corbett (1992) studied a wide range of oxygen cornplexes by using molecular- and cyclic-cluster calculations. They came to the conclusion that the only oxygen complex that fulfills the experimental requirements is a complex of a silicon self-interstitial bonded to two neighboring oxygen interstitials (Fig. 19). This complex shows a shallow double donor character and the spin localizations for the donor wavefunction are in qualitative agreement with the ENDOR results on NL8. A fast diffusing oxygen-self-interstitial complex is suggested to explain the formation kinetics of the TDs. The calculations show an activation energy of - I .6 eV for the diffusion of this complex, significantly lower than the 2.1 eV, found for the diffusion of isolated oxygen.

5 . CURRENT UNDERSTANDING A N D UNRESOLVED ISSUES The Thermal Donor center is a defect complex that is introduced as interstitial oxygen leaves solution in a silicon matrix. The first level in the hierarchy of associates, the dioxygen pair (02), is not a donor.

7.

ELECTRICAL PROPE R r I E 5 OF OXYGEN IN SILICON

28 1

The TD donor state is a helium-like, effective mass center with O/ + and + + levels split off from the conduction band. The electrons bound to the positive core (central cell) occupy extended orbits that are determined to first order by the silicon band structure. The donor core has a low C,, symmetry (similar to a water molecule) that is characterized by a dipole oriented along the (100) direction. The core consists of at least two oxygen atoms and one interstitial silicon atom. The anisotropic core ((100) compression) lowers the energy of two of the six conduction band valleys in silicon and creates a unique (100) “pancake” shaped wavefunction for the bound electron. A series of TD centers form sequentially with a single, self-consistent set of kinetic parameters. The series, consisting of I 1 known centers, TDI-TDIl, is composed of the same core structure with (most likely) added oxygen atoms outside the core. The later TD centers have an increasing delocalized core and, consequently, more extended electron orbits and weaker binding potentials. The early TD centers TDI and TD2 can be reconstructed (bistability and hydrogen passivation) into deep, electrically neutral states. The core structure of the later donors is locked into a stable configuration. The large body of recent kinetic data reveal many nuances in the behavior of oxygen in silicon, but confirm the original essence of the oxygen aggregation models. +/

Interstitial oxygen in supersaturated concentrations approaches e qu i I i b r i urn b y aggre ga t i o n . 2 . The oxygen donor is a special class of structures that occur early in the aggregation process. 3 . At low temperatures, a high density of the small aggregates are stable with concentrations of 5 10’’ cm-3 characteristic of the temperature range 300-SOOT. 4. At temperatures higher than 500°C. smaller aggregates become unstable, and a coarsening reaction occurs yielding a lower density of larger aggregates. 1.

The key unresolved issues are the atomic structure and the formation mechanism. An average of .I2 interstitial oxygen atoms are lost from solution for each TD (Newman et al., 1000). Kinetic models are consistent with the requirement of an average of four oxygen atoms. The minimum energy aggregation morphology is a (100) chain. which can relieve stress by a local (core) band reconstruction along (100). The TD formation rate is too fast for a diffusion limited oxygen aggregation process unless the interaction length is large ( > 10 A) or a unqiue fast diffusion path for oxygen pairs exists.

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J . MICHEL A N D L. C . KIMERLING

Research on TD properties and formation reactions is important because it addresses the early stages of aggregation of oxygen in silicon. The donor activity must be controlled to maintain doping uniformity as circuit integrated levels increase. Control of oxygen precipitation nucleation and growth is key to processing defect-free devices and contamination gettering. TD research has, also, added fundamental insights into the understanding of shallow level impurities in semiconductors. TDs have provided both a source of new knowledge and a basis for process technology design. 111. New Donors

Donor states due to heat treatment of Cz silicon material at temperatures between 650°C and 800°C have first been reported by Liaw and Varker (1977) and Grinshtein et al. (1978). Kanamori and Kanamori ( 1979) demonstrated that TDs and the high-temperature donors, called N e w Donors (ND) show significantly different annealing behavior. TDs annihilate at 550°C while NDs are generated at temperatures above 550°C. The ND generation depends on the preannealing conditions. Only at 470°C to 550°C do preannealed samples produce ND in Cz silicon. It was found that a high carbon concentration ([C] > 2 x 10l6~ m - also ~ ) promotes the formation of NDs without a low-temperature preanneal. Annealing experiments with oxygen-diffused FZ silicon also produced NDs. This demonstrated that oxygen is essential for the ND formation. Figure 20 shows the donor generation in dependence of the annealing temperature. There are two temperature regimes in which donors are formed: at 450°C TDs are generated and around 750°C NDs appear. NDs can be partially annihilated at temperatures above 1000°C. A heat treatment of 10 hrs at 1000°C reduces the ND concentration by 50 to 80% (Cazcarra and Zunino, 1980). Cazcarra and Zunino (1980) also studied the formation kinetics of the NDs. They found that the formation kinetics of the NDs are closely related to the formation of oxygen precipitates. Therefore they suggested that NDs are related to Si,O,r clusters of a few hundred atoms of oxygen acting as nucleation centers for oxygen precipitation. Carbon was suspected to play a major role in the formation of new donors. Leroueille (1981) showed that with the formation of NDs the IR absorption band of carbon at 16.5 pm decreased indicating that carbon is involved in the formation of NDs. Gaworzewski and Schmalz (1983) suggested that carbon is involved in the nucleation process of NDs through formation of ( C , 0) complexes. They demonstrated the importance of carbon as a site of nucleation for ND formation and oxygen

7.

ELECTRICAL P K O t ' t R T IES OF OXYGEN IN SILICON

I

' A '

11

I

I

I

283

I

initial O x y g e n (pprna) 0 40

A 37 24

1

700

900

0 32 I

300

500

Anne;iling Tcmperature (OC) Ficj. 20. Maximum donor generation pel- h o w ( M . D . G . H . )of annealing at a given temperattire i n a nitrogen ambience. (C'arcarr;~and Zunino, 19x0).

precipitation. These (C, 0) complexes of different size were tentatively identified as NDs. A study of the formation of NUS by Kamiura, Hashimoto, and Yoneta (1991) shed new light on the nucleation of NDs. DLTS spectroscopy revealed three different traps connected with NDs. It was shown that different kind of NDs were formed depending on the carbon content and preannealing conditions. One DLTS band was correlated with the presence of carbon in the sample while another band existed only in connection with rodlike defects after a preannealing at 450°C. The third DLTS band was found in preannealed samples with high carbon content. These results show that depending o n the material and the annealing conditions different NDs are observed. They could also explain the different models that are proposed for NDs.

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1. MICHEL A N D L. C . KIMERLING

There are two models that explain the origin of the electronic states of NDs. Holzlein, Pensl, and Schulz (1984) developed a model based on the similarity of the DLTS spectra of NDs and Si-SiO, interfaces. This model proposes a continuous distribution of ND deep levels originating from states at the surface of SiO, precipitates. The donorlike behavior was explained by a fixed positive charge associated with the precipitate. Such a fixed positive charge was found in the oxide near the Si-SiO, interface of planar MOS structures. In a further study on hydrogenation effects on NDs, Holzlein et al. (1986) came to the conclusion that interface states at the surface of the SO, precipitates as well as bound states in the Coulombic well of a fixed positive charge contribute to NDs. A second model to explain the electrical activity was put forward by Babich et al. (1988). Based on EPR and Hall-effect measurement it was proposed that NDs are due to extensive fluctuations of the crystal potential on which electrons can localize. These fluctuations are caused by the formation of oxygen clusters that lead to a crystal lattice distortion near their boundaries. With these assumptions it was possible to explain the linear shift of the g-factor as well as asymmetry, anisotropy, and EPR line width and their dependence on the annealing conditions. From the DLTS experiments it becomes evident that NDs are a collection of several different defects. Oxygen is involved in these defects. There is little disagreement that NDs are due to extended defects, whether as oxygen clusters or as oxygen precipitates, but there is no agreement on the structure of the donor. Until now structure sensitive experiments like ENDOR have not been applied to NDs successfully.

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N.J. Johnwn. N. M . . and Hahn. S. K. (19x6). A p p l . PI7y.s. Lett. 48, 709. Junes. K. ( 1990). .Setnic.ond. S c , i TC,c/rnol 5 . 255. Kaiser, W.. l-'ri\ch. H . L.. and Reiss. H . (19%). Phys. Rev. 112, 1546. Kaniiura. Y.. Hashimoto. F.. and Yoneta, M . i 1991). PI7ys. Sttrr. S o l . ( N ) 123, 357. Kananiori. A . 11979). Appl. PIry5. f . c / t . 34, 287. Kanamori. A,. and Kanamori. M . (1979).J . Appl. PIrys SO, 809.5. Kirnei-ling. L . C . II986). In O.rygt,tr. C'trrhon. HvdrogPn crnd Nitrogen ir7 Silic.on. J. C. Mikkel\en. Jr.. S . J . Pearton. J . W . C'orbetl. and S.J . Pennycook. (eds.). MRS Sprnposia Proceedings Vol. 59, p. 83. Materials Rewarch Society. Pittsburgh. Kimerling. L . C.. and Benton. J . L.. 11981 I . Appl. Plrvs. Lett. 39, 410. 1-atushko. Y . I..Makarenko. L. F.. Markevich. V . P.. and M u m . 1,. I . (1986). Phy.\. S t t r t . Sol. ( ( 4 ) 93, K181. Lee. K. M . . Trombetta, J. M . . and Watkins. G . I). 11985). In Mic.ro.sc.oprc Ident!fictrrron c~,f Elc,cwnnic. D~:fkc.i.v in Svmicc~ndrrcI O U N. M .Johnson. S. G . Bishop. and G . D.Watkins (eds.). M R S Symposia Proceeding\ Vol. 46. p. 263. Materials Research Society. Pittsburgh. Leroueille. J. (1981). Phys. Stcrr. So/ ( t r j 67, 177. Liaw. H . M . . and Varker. C. J . (19771, In Srtr7ic~irrdrrcrorSilic.onl977. H. R. Huff and E. Sirtl. leds.), Vol. 2. p. 116. Electrochemical Society. Princeton. N.J. Livingston. F. M . . Mesolorab. S.. Newnian. R . C.. Pike B. C.. Stewart. K. J.. Binns. M . J , Brown. W . P.. and Wilke\. J . 6. (19x4). J . Phy.s. C. 6253. Makarenko. L . F.. Markevich. V. P . . and Murin. L. I.(1985). SOI,.Phys. Semic,ond. 19,

I 192. Michel. J . . Meilweh. N . , Niklaa. J . K.. ; m i Sparth, J . M. (1988a). In S h a l l o ~Impurrries , in S~,nric.otidrrc.tors.B . Monemar led.). Vol. 95, p. 201. IOP. Bristol. hlichel. J . Niklas, J . R.. and Spaeth. J . M . (IYXXb). I n 1)yfec.r~in Elecrronic. MrrrPrrtrl.s. M .

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Stavola, S. J. Pearton, and G. Davies (eds.), MRS Symposia Proceedings Vol. 104, p. 185. Materials Research Society, Pittsburgh. Michel, J., Niklas, J. R., and Spaeth, J. M. (1989). Phys. Rev. B 40, 1732. Michel. J.. Niklas, J . R., Spaeth, J. M., and Weinert, C. M. (1986). Phys. Rev. Lett. 57, 611. Muller, S. H., Sprenger, S . , Sievers, E. G., and Ammerlaan, C. A. J. (1978). Solid State Comm. 25, 987. Murray. R., Brown, A . R..and Newman, R. C. (1989). M a t . Sci. Engineering B4, 299. Needels, M.. Joannopoulos, J . D., Bar-Yam, Y., and Pantelides, S. T . (1991).Phys. Rev. B 43, 4208. Newman. R. C. (1985). 1.Phys. C 18, L967. Newman. R. C., Brown, A . R.. Murray, R., Tipping, A,, and Tucker, J . H. (1990). In Pruc. 6rh I n f . Symp. Silicon Muter. Sci. Technol.-Semiconducfor Sci. H. R. Huff, K. G . Barraclough, and J. Chickawa (eds.), Electrochem. SOC.Proc. Vol. 90-7,p. 743. Oder, R.. and Wagner, P. (1983). In Defects in Semiconductors 11, S. Mahajan and J . W. Corbett (eds.), MRS Symposia Proceedings Vol. 14,p. 171. North-Holland, New York. Oehrlein. G . S . , Lindstrom, J . L., and Cohen, S. A. (1984). In Proc. o f t h e 13th I n t . Cmf. ow Defiers in Semiconductors. L. C. Kimerling and J. M. Parsey, Jr. (eds.). p. 701. The Metallurgical Society of AIME, Warrendale, Pa. Ourmazd A.. Schroder, W., and Bourret, A. (1984). J. App1. Phys. 56, 1670. Pajot, B., Compain, H . , Lerouille, J . , and Clejaud, B. (1983). Physica 117B-l18B, 110. Pajot, B., and von Bardeleben, J. (1984). In Proc. of the 13th I n t . Conf. o n Defecfs in Sen7iconductors, L . C. Kimerling and J . M. Parsey, Jr. (eds.), p. 685. The Metallurgical Society of AIME, Warrendale, Pa. Pearton. S. J . . Chantre, A., Kimerling, L. C., Cummings, K. D., and Dautremont-Smith. W. C. (1986). Proc. Muter. Res. Soc. 59, 475. Robertson. J.. and Ourmazd, A. (1985). Appl. Phys. Lett. 46, 559. Snyder, L. C., DeBk, P., Wu, R. Z., and Corbett, J. W. (1989). In Proc. of the / 5 t h Int. Conf. on Defects in Semiconductors. G . Ferenczi (ed.), Materials Science Forum Vols. 38-41, p. 329. Trans Tech Publications, Zurich, Switzerland. Stavola, M . and Lee, K . M., (1986). In Oxygen, Carbon, Hydrogen and Nitrogen in Silicon. J . C. Mikkelsen, Jr., S. J . Pearton, J. W. Corbett, and S. J . Pennycook (eds.), MRS Symposia Proceedings Vol. 59, p. 95. Materials Research Society, Pittsburgh. Stavola. M., Lee, K. M., Nabity. J. C.. Freeland, P. E., and Kimerling. L . C. (1985). Phys. Rev. Lett. 54, 2639. Stavola. M.. Patel, J . R., Kimmerling, L . C., and Freeland, P. E. (1983). Appl. Phys. Leu. 42, 7 3 . Stavola, M..and Snyder, L. C. (1983). In Defects in Silicon. L. C. Kimerling and M. Bullis (eds.). p. 61. The Electrochemical Society, Pennington, N.J. Steele. A . G . , and Thewalt, M. L. W. (1989). Can. J. Phys. 67, 268. Suezawa, M.,and Sumino, K. (1984). Phys. Srat. Sol. ( a ) 85, 469. Tajima. M., Kanamori, A , , and lizuka, T. (1979). Jpn. J. Appl. Phys. 18, 1401. Thewalt. M . L. W., Steele, A . G . , Watkins, S . P., and Lightowlers, E. C. (1986). Phvs. R e v . Left. 57, 1939. Tkachev, V. D., Makarenko, L. F.. Markevich. V . P., and Murin, L . I . (1984). Sov. Phys. Seinic.ond. 18, 324. Wagner. P. (1986). In Oxygen. Carbon. Hydrogen and Nifrogen in Silicon,J . C. Mikkelsen, Jr., S . J . Pearton, J. W. Corbett, and S. J. Pennycook (eds.). MRS Symposia Proceedings Vol. 59, p. 125. Materials Research Society, Pittsburgh.

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ELECTRICAL f’KOPtRTIES O F OXYGEN IN SILICON

287

Wagner. P.. Gottschalk. H . . Tromhetta. I . . and Watkins. G . D. (19x7). J . Appl. PAY\. 61, 346. Wagner. P.. and Hage. J . (1989). A p p l . P/I?J.A 49, 123. Wagner. P.. Holm, C.. Sirtl. E.. Oeder. K . , and Zulehner. W. ( 19x4). In A d i ~ t i ~ it7 r sS o l i d Sicita Phvsic~s.P. Grosse (ed.). V o l . 24, p. 191. Vieweg-Pergamon, Braunschweig. i Nilrogczn in Weber. J.. and Queisrer. H . J . (1986). In O.rygun. Curbon. H y d r ~ g ~ rcind Silicon. J . C . Mikkelsen. Jr . S . J . Pearton. J . W. Corbett. and S. J . Pennycook leds.1. MRS Symposia Proceedings Vol 59. p. 147. Materials Research Society. Pittsburgh. van Werep. 0 . A , . Gregorkiewici. -1- . Lkkman. H . H . P. T.. and Ammerlaan. C. A . J . 1986). In Dqfc>cis in Srtnicondirt IIJU. H . J . von Bardeleben (ed.). Materials Science Forum Vols. 10-12, p. 1009. Tian\ Tech Publication Ltd.. Switzerland. Wruck. 0 . . and GaworLewski. P. (1979).P h \ > s . Stcii. Sol. ( t i ) 56. 557. Wruck. D.. and Spiegelberg. F. (1986). Pliv\. S i ( i r . S o l . ( b ) 133. K39.

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S t M l C O N D U ( IOHS A N D SEMIMETALS. VOL 42

CHAPTER 8

Diffusion of Oxygen in Silicon R . C. Newman INTERDISCIPLINARY RESEARCH

< FNTRE

FOR SEMICONDUCTOR MATERIALS

THE BLACKETT LABORATORY IMPERIAL COLLEGE O F SCIFNC I

, TE< HNOI OGY

AND MEDICINE

I O N D O N , UNITED KINGDOM

und R . Jones DEPARTMENT O F PHYSICS UNIVERSITY O F EXETER, l J N l l E D KINGDOM

1. 11.

INTRODUCTION . . . . , . . . . . . . . . . . . . . DIRECTMEASUREMENTY OF NORMAL OXYGEN DIFFUSION . . . I . Single D$fusion J u m p s . . . . . . . . . . . . . . 2 . Profiles . . . . . . . . . . . . . . . . . . . . 3. Summary . . . . . . . . . . . . . . . . . . .

111.

INDIRECTMEASUREMENTS OF NORMAL OXYGEN DIFFUSION. . I . D,,,, Determined ,from Oxygen Precipitation ut High Temperutures . . . . . . . . . . . . . . . . . . lit Intermediate Temperatures . . 3. Oxygen Aggregtrtion N I L O N ,Temperurures . . . . . . ENHANCED OXYGEN DIFFUSION NOT INVOLVING HYDROGEN. I . Effects Due to the Injrc.tion of Vacancies und I-Atoms h! 2 MeV Electron lrrudiution . . . . . . . . . . . 2 . The Effect of E.rt ('.\A I-Atoms . . . . . . . . . . . 3. Rtipid Diffusion of' Di-O.rygen De.fec,ts . . . . . . . . 4. Effects Due t o Curhon . . . . . . . . . . . . . . 5 . Fffects Due t o Mrtirllic. Conrumination . . . . . . . 6. S u m m u y . . . . . . . . . . . . . . . . . . . . SILICON CONTAINING HYDKOC~EN IMPURITIES . , . . . , . I . Silicon Heated in Hydrogen Gus . . . . . . . . , . 2 . Silicon Heated in uti RF Pltrstnu . . . . . . . . . . 3. A n Outline Model tincl S u m i n u p . . . . . . . . . . THEORETICAL MODEII N G ot OXYGEN DIFFUSION. . . . . . I . The.orrtica1 Methods . , . . . . . . . . . . . . . 2. Theory o f the D(ffii.rion Constunt . . . . . . . . . . 3. Intrrstitiul Oxvgen . . . . . . . . . . . . . . . . 4. Diflusion of 0, ('trtu1y:ed by Hydrogen . . . . . . . S. The 0.rygen Ditticr . . . . . . . . . . . . . . . 6. Other 0.rygen Aggregtrtes , . . . . . . . . . . . .

2 . C).rygen Aggregution

IV.

V.

VI.

V11. CONSTRAINTS ON MODFI.SOF THERMAL DONORCENTERS . . .

290 292 293 296 298 298

299 303

305 308 309 312 314 316 317

317 718 31Y

323 324 326

327 33 I 332 335 339 34 I 342

289 Copyright IE, 1994 hy Academic he\,. Inc All nght5 of reproduction in any form re\erved ISBN 0-1?-7S?14?-Y

290

R. C. NEWMAN A N D R. JONES

VIIl. SUMMARY . . . . . . . . . . . . . . . . . . . . . Acknowledgmenls . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . .

345 347 347

I. Introduction

Silicon grown by the Czochralski pulling technique contains oxygen impurities in a concentration close to 10" ~ 1 1 1Early ~ ~ . X-ray diffraction measurements showed that the lattice parameter, a,, was increased when oxygen was present, demonstrating that the atoms occupy interstitial sites (Bond and Kaiser, 1960). High-resolution infrared (IR) absorption measurements of the now well-known 9 km band and other associated bands due to the vibrations of the oxygen impurities then led to the conclusion that the atoms were located in off-axis bond centered positions, written as 0, (Chapter 5). The bonding to two silicon neighbors explains why there is no electrical activity of such atoms. However, diffusion of Oiatoms during annealing around 450°C leads to the formation of small clusters that act as double thermal donors (TD) (Chapter 6), while the precipitation of particles of SiOz at much higher temperatures (Chapters 9 and 12) is also a consequence of 0; diffusion. There was a clear need to determine the diffusion coefficient Doxyover a wide range of temperature (Section 11) but this has been no easy task. Electrical methods used for the determination of high-temperature indiffused profiles of group I l l and V elements (Fuller and Ditzenberger, 1956) are not applicable, and neither is there a suitable radio tracer, comparable with I4C used for diffusion measurements of electrically inactive carbon (Newman and Wakefield, 1961, 1962). Early measurements of Doxy,although well-conceived, ingenious and pioneering, particularly those obtained from measurements of internal friction (Southgate, 1957, 1960; Haas, 1960) and the relaxation of stress-induced dichroism of the 9 k m IR band (Corbett and Watkins, 1961; Corbett, McDonald and Watkins, 1964a), were therefore limited in number. It is only relatively recently that additional reliable values, determined from profiles measured by secondary ion mass spectrography (SIMS) have become available for T 2 650°C (Mikkelsen, 1982a, 1982b; Lee and Nichols, 1985; 19861, although other SIMS measurements in carbon-doped silicon have shown anomalies (Shimura, Higuchi and Hockett, 1988). It was then shown that the rate of precipitation of SiO, in the same temperature range was diffusion limited with the same value of Doxy(Section 111). In a middle range (400°C to 700°C) there are no microscopic measurements, while SIMS measurements have again shown anomalies (Lee and Fellinger, 1986; Fellinger and Chen, 1988; Gosele et al., 1989) (Section IV). At lower

8. DIFFIISION

O k O X Y G E N IN SILICON

29 1

temperatures (270°C to 400"c'), further determinations of Don) have been made from the rate of relaxation of stress-induced dichroism of the IR 9 pm absorption band (Stavola et al., 1983; Newman, Tucker and Livingston. 1983b). The values so obtained agreed with the extrapolation of the high-temperature internal friction and SlMS data, but only for certain samples. Stress-dichoism measurements made on samples given a postgrowth heat treatment have shown enhanced values of Doxy(Stavola et al., 1983). appearing to support other claims of much greater enhancements based on indirect evidence (Berghok, Hutchison and Pirouz, 1985: Gaworzewski and Ritter, 1981). These claims have given rise to attendant speculation, extending over some 35 years (Section IV). It is not sufficient to invoke enhanced diffusion to explain particular observations: the circumstances leading to the enhancement must be fully identified. followed by the proposal of a microscopic model. This model should be checked by ancillary experiments (Section V ) , and its plausibility should also be examined by theory (Section V1). Much progress has been made but we do not yet have definitive answers to certain k e y questions that have been raised. Much of the confusion ha3 arisen because interactions of 0,atoms with both lattice vacancies (Bemski. 1959; Watkins and Corbett, 1961; Corbett et al., 1961) and self-interstitials (I-atoms) (Brelot and Charlemagne, 19711 have been clearly demonstrated (Section IV), I-atoms are known to be generated during precipitation of oxygen for T > 500°C (Bourret. 1986),and there is long-standing but rarely quoted indirect evidence that 0; atoms interact with fast-diffusing hydrogen atoms (Fuller and Logan. 1957) (Section V ) . In addition, theory has indicated that oxygen pairs (O,)?,formed in the early stages of oxygen aggregation. have a diffusion coefficient greater than that of isolated 0; atoms (Sections 1V and V I ) (see also Gosele and Tan, 1982). centers have not been detected spectroscopically (Kinierling, 1986) although the formation of O2C, complexes, where C, i s an interstitial carbon atom (Kurner et al., 1989). provides some plausible indirect evidence for their existence. Interactions between 0, atom5 and C, atoms have also been invoked to explain enhanced 0,diffusion at high temperatures (Shimura et a\., 1988). It is important to point out that related first principles theory is gaining in importance as the strengthh and weaknesses of various procedures are evaluated. There is no doubt that the procedures have improved over the years. while the available computing capacity has increased to make calculations more realistic and hence more reliable. As this has happened, there has been a shift in the predictions relating to oxygen diffusion processes. This work is not yet definitive. and in that sense, it mirrors the experiments. A full discussion is given in Section V1.

292

R. C . NEWMAN AND R . JONES

0

SILICON ATOM OXYGENATOM

FIG.1 . Geometry of a bonded interstitial oxygen impurity in silicon showing the off-axis site, the mean diffusion jump distance d and the bond populations nl-n4.

After reviewing these various topics, we can state the most likely scenarios as they appear at present and give the consequences when there is more than one option (Section VII). In particular, the number of oxygen atoms that can aggregate to form a thermal donor in a given time will depend not only on D o x y but , on whether or not (Oi)* pairs diffuse more or less rapidly than single Oiatoms. Our overall conclusions are set out in Section VIII. 11. Direct Measurements of Normal Oxygen Diffusion

Oxygen diffusion jumps are presumed to be from one bond-centered site, a mean position when allowance is made for the rotational motion, to an equivalent adjacent site (Fig. I). The jump distance d is equal to (2/3)% = (2)”*u0/4 = 1.92 A, where a is the Si-Si nearest neighbor separation. Doxyis equal to d 2 / T , where the reorientation lifetime T (for a diffusion jump) is given by T~ exp (E,/kT) at a temperature T . Thus Doxy = Do exp ( - E,/kT), with Do = 2a2/37 = 4 / 8 7 , if the diffusion jumps are uncorrelated. The lowest measured values of Doxyat a given Tare taken

8.

293

DIFFLI\ION O F OXYGEN IN SILICON

to define normal diffusion. There is no evidence that intrinsic defects or other impurities are involved or that the rate is dependent on the position of the Fermi level F~ (Lee and Nichols, 1985: Hahn, 1986). Larger values of Dox,have been reported (Sections IV and V) and must be equal to the (normal) and D,,,, (enhanced), involving processes in which sum of Doxy defects or a second impurity interact with the 0, atom.

I . SINGLE, DIFFUSION JUMPS The fact that the local symmetry of an 0, atom is not tetrahedral has been used to great advantagc. In a strain-free crystal the four bondcentered sites along ( 1 1 1 ) directions are equivalent. and the four associated populations r i l - i i j of 0,atom3 are equal. However, if a uniaxial stress is applied along a [ I 1 I1 direclion, atoms with this bond axis experience an interaction energy three times greater than that of atoms in the other three ( I 1 I ) axes (a factor of cos (70.5')). The population ti, will decrease, ;is a result of diffusion jumps to the neighboring bonds, and n, = n , = t i j will increase, provided the temperature is high enough for the jumps to occur. The application of acoustic waves with a stress component parallel to ( I I I ) leads to an alternating jumping process that produces damping of the mechanical vibrations. The position of the damping peak 8 the occurs when COT* = 1, where w is the angular frequency, T* = ~ / is time constant measured experimentally and the shape of the curve provides further information about the resonance (Southgate, 1960; Haas, 19h0). From the geometry of the bonds (Fig. 1 j we deduce

dtlI/df =

(1/7)1 -

6t11 + 2r2,

+ 2n-3 + 2n41,

(1)

and three other equations with cyclic permutations of n,-tz,. The internal friction is proportional to ?' =

I?! - ( 1 / 3 ) ( t 1 ,

+ n , t n,)

= (Ill

-

n2),

(2)

for the stress parallel to ( I I I ) . We find dyldt = - @ / T = - Y / T * , so that Doxy = ~1'/127*or ~ $ 6 4 ~ ' Such . effects were measured as a function of temperature by Southgate (1957. 19601, who used either a 100 kHz or a 300 kHz source. These measurements also demonstrated that the axis of an 0, impurity was parallel to a Si-Si bond since no internal friction was found when the applied stress was parallel to a (001) axis. Haas analyzed Southgate's data to find the value of D,, and obtained Doxy= 0.21 exp ( -2.55eVlkT) em's-' for the range 1325°C > T > 850°C (Fig. 2 ) . These ideas were expanded and adapted to allow Doxyto be measured at much lower temperatures (33OT-40o"Cj from stress-induced dichroism in the oxygen 9 pm vibrational absorption band (Corbett and Wat-

294

R . C . NEWMAN A N D R . JONES

10.8

1000 800

Temperature "C 600 500 400

300

Doxy = 0.13exp(-2.53eV/kT)cm2s

0.6

0.8

1.0

1.2

1.4

1.6

1.8

1O O O / l (K-l)

FIG. 2. An Arrhenius plot of the oxygen diffusion coefficient, combining the internal friction data of Southgate (1957, 1960) and Haas (1960) (the solid line) (REFS h and i), the low-temperature stress dichroism data of Corbett et al. (1964a), Stavola et al. (1983). and Newman et al. (1983b) (REFS g, d and e), the high-temperature SlMS data for in-diffused profiles of Mikkelsen (1982a) and Lee and Nichols (1985, 1986) (REFS c and b), the X-ray data of Takano and Maki (1973) (REF f ) , together with the analyses of Gass et al. (1980) (REF a). The line Doxy= 0.13 exp ( - 2.53 eV/kT) cm2 s - ' is taken to define normal oxygen diffusion.

kins, 1961; Corbett et al., 1964a). Isotropic absorption occurs only if the 400°C for four populations ~ 1 - 1 1 4 are equal. Heating a sample to T 15-30 min while a uniaxial stress of 100 MPa is applied along a (1 1 1) axis leads to a decrease in n , and increases in n2 = n3 = n4 as explained earlier. This distribution is frozen in, on cooling the sample to room temperature with the stress still applied, at which stage the stress is removed. The absorption coefficients a , ,and aL for polarized light with the E-vector parallel and perpendicular to the stress axis respectively are proportional to ( n , 4 3 ) and (4n2/3),assuming that the dipole moment M I is , parallel to a bond axis. Expressions for a l / a I I(Table I) were given by Corbett et al. (1964a) for three stress axes, different viewing axes and

-

+

-

8. DIFFLI\ION

295

OF OXYGEN IN SILICON

IABLk I

1 H E DICHROIC RATIOa,/ulMFASLIRFO A 1 ROOMTEMPERATLIRE. FOR VARIOUS A N D ViFwih(I Axr5' (Corbett et al , 1964a) Stress Axis

Viewing Axis

< I 10>

rheory

MI. I I I

I y? 2 f

SlRrSS A X E S

0 1 /all

M

Expth

Predicted'

2 ( I + y?) 3y? + I

1.18

1.16

"'4stresh of 2700 kg c m - ' was applied for 30 min at 400°C. ? 0.07. '.4ssuming M < I I I >. 'Similar values were found for unstressed control samples. 'Used to predict the other value\

for M either parallel or perpendicular to ( 1 1 I ) . where p' = n z / n i and y' = t i 4 / ) i 3 . A discussion of the magnitude of the dichroism was also presented and shown to be consistent with that expected from Boltzmann statistics. On annealing, the normalized dichroism 3(a, - aI,)/(all+ 2a,) ( a , all)/a, of the 9 pm band decays exponentially with a time constant T * during a subsequent isothermal anneal, leading to the values of D,,, shown in Fig. 2 (Corbett et a l . , 196421; Stavola et al., 1983; Newman et al., 1983b). Alternatively. the induced dichroism and its loss can be measured for the weaker oxygen 19.5 pm band (517 c m - l ) . The frequency of this band falls in the continuum of lattice modes (Raman frequency 520 cm 1 and shows no isotopic shift when I6O is replaced by "0 and so, unlike the 9 pm band. it cannot be a true localized vibrational mode ( L V M ) (Newman, 1973). The absorption occurs because there is a dipole moment of the oxygen complex perpendicular to the Si-Si bond axis (Jones, Oberg and Umerski. 1992) and for a ( 1 1 I ) stress we have al,> a _ (Table I ) . The normalized dichroism i s smaller than that for the 9 pm band by a factor of two but the calculated relaxation time T * is the same. These conclusions were verified hy Stavola (l984), who demonstrated that the 19.5 pm (517 c m - ' ) band was indeed due to the presence of 0, atoms. rather than grown-in substitutional oxygen atoms, as proposed by

-

~

'

296

R. C. N E W M A N A N D R. JONES

TABLE 11

SUMMARY OF DATA FOR NORMAL OXYGEN DIFFUSION

’

D,(cm2s )

ED (eV)

Reference

0. I4 0. I3 0.23 0.21

2.53 2.53 2.56 2.55

Lee and Nichols, 1985 Mikkelsen, 1986 Watkins, Corbett and McDonald, 1982 Southgate, 1960; Hass, 1960

O’Mara (1983). The latter suggestion arose from the known sequence (Newman, 1973) of LVM frequencies for 1°B (644 cm-I), “B (621 cm-I), I2C (605 cm-I), 13C (586 cm-I), I4C (570 cm-I), and I6O (530 cm-’-540 cm-’) (extrapolated). In practice, it is better to make dichroism measurements of the 9 pm band because a superior signahoise ratio can be achieved. However, the 19.5 p,m band can be used, as in the work of Freeland (1980) and Newman et al. (1983a, 1986b), and there would be an advantage if there were absorption from precipitated S O , underlying the 9 p.m band. In summary, the results of the dichroism measurements are in complete agreement with those obtained from the internal friction measurements (Fig. 2; Table 11). 2. PROFILES Diffusion of oxygen into or out of as-grown material containing Oi atoms in a concentration c,, has been studied under conditions where the surface concentration has a constant value of c, corresponding to the solubility and resulting from a coating of SO,. Assuming that there is no surface rate limitation and that internal precipitation does not occur to any significant extent, the diffused distribution is given by c(x, t ) = c, e r f c [ x / ( 2 ~ t ) ~+’ ~~,erf[x/(2Dt)”~)]. ]

-

(3)

In float-zone silicon the value of co is usually less than 10l6 atom cm-3 and there will be a net in-diffusion at all temperatures for which the solubility c , exceeds co. On the other hand, if cois large, as in Czochralski silicon, there will usually be a net out-diffusion. To find values of Doxyit is necessary to determine the distribution c ( x , t ) . Logan and Peters (1957, 1959) had the ingenious idea of making hightemperature in-diffused oxygen profiles electrically active by giving such samples a second heat treatment at 450°C to produce small oxygen aggregates that acted as donors (thermal donors). The original oxygen distribu-

8.

DIFFII5ION O F OXYGEN IN SILICON

297

tion could then be quantified from subsequent measurements of the conductivity as a function of depth from the surface. In their second paper, they took account of the observations of Kaiser, Frisch and Reiss (1958) that the initial rate of donor formation and the maximum concentration that was attained varied as the fourth and third powers of the oxygen concentration, respectively. Similar measurements were carried out later by Hu (19811, Gaworzewski and Ritter (1981), and Isoma, Aoki and Watanabe ( 1984). Data obtained for high-temperature diffusions were in reasonable agreement with those obtained by internal friction, but it is now known that there could have been complications. The concentrations of the various types of donor (TDI, TD2, TD3, etc.) that are formed sequentially have different dependences on c , , (Wagner, 1986), while negligible rates of TD formation near a surface have been reported by Hahn (1986). Another early analysis was carried out by Takano and Maki (1973). who obtained depth profiles of the lattice parameter u,, from X-ray measurements after the successive removal of layers of material. Oxygen concentrations down to I O l 7 cm ~'could be detected in samples diffused in the range 1 100°C-1200"C, and values of Doxywere in excellent agreement with those obtained by internal friction and SIMS (Fig. ?). Indiffused oxygen has also been quantified by charged particle analysis (Gass et al., 1980; l t o h and Nozaki, 1985). Further discussion of these topics has been presented by Mikkelsen (1986). By far the most important measurements, covering a wide range of 7 (700"C-l40O"C) are those obtained by the SIMS technique, first for in-diffused profiles (Mikkelsen, I982a. 1982b) and then for out-diffused and further in-diffused profiles (Lee and Nichols. 1985. 1986). Mikkelsen used enriched "0 as a diffusant to improve the SIMS sensitivity, which is otherwise limited by residual "(1 contamination in the vacuum system. to give a background --loi7 c m - ': use of "0 reduced this level by a factor of -100. Measurements were possible only for 7 2 700°C because at lower temperatures the depth of the protile was limited by the low values of D,,,, and the surface concentration c , (see Section 111). The combined data are shown in Fig. 2 . Other out-diffusion measurements made by SIMS following annealing made at II0O"C (Heck, Tressler and Monkowski, 1983) were interpreted in terms of small enhancements or retardations of D o x ydepending . on the heating ambients. The small overall spread in the values of Doxyof 7.8 z 0.3 x lo-" em's-', where = 7.8 x l o - " ern's-' is the value quoted by Mikkelsen (1986). cannot in our opinion be considered to be sufficiently large to justify the claim nor the proposal that the diffusion occurs by a vacancy process. The source of the oxygen used by Mikkelsen was enriched water vapor

298

R . C. NEWMAN AND R . JONES

H2’*0so that there would have been simultaneous in-diffusion of hydrogen (McQuaid et al., 1991; Veloarisoa et al., 1991). There were no obvious effects on the oxygen diffusion rate arising from the presence of the hydrogen, although enhancements occur at temperatures T < 500°C (see Section V). Hydrogen-oxygen interactions in plasmas are also important as implied by Hansen, Pearton and Haller (1984), but the introduction of lEO into a plasma did not lead to in-diffused concentrations of oxygen that could be detected by SIMS (Mikkelsen, 1986).

3 . SUMMARY To conclude this section on “normal” oxygen diffusion, parameters for Doxygiven by various authors, including combinations of the low- and high-temperature data (see Watkins et al., 1982), are given in Table 11. The linkage of the high- and low-temperature microscopic measurements provides convincing evidence for the model of Oi jumps from one bond center to the next, without the involvement of an intrinsic defect or a second impurity, including a second Oi atom. The diffusion jumps occur, with an activation energy close to 2.5 eV, over the whole temperature range from the melting point of silicon down to 250°C. However, longrange diffusion is known to have this activation energy only for T 2 700°C. In the later sections we shall evaluate Doxyfrom the expression Doxy= 0.13 exp (-2.53 eV/kT) cm-? s-l given by Mikkelsen (1986). It is interesting to find that this expression does not differ in any significant way from that deduced from the work of Southgate and Haas in 1960 (Table 11). Measurements that have implied enhanced diffusion were made at temperatures T 5 650°C except for the results presented by Shimura et al. (1988) and Shimura (1991). For the proposals that are vindicated, it would be reasonable to infer mechanisms that have activation energies less than 2.5 eV.

111. Indirect Measurements of Normal Oxygen Diffusion

In Section II.2., the out-diffused oxygen profile to an external planar silicon surface was discussed. Measurements of c(x, t ) by SIMS led to values of Doxy,with the assumption that there was no rate limiting process at the surface. Alternatively, IR measurements of the 9 pm band could have been made and fitted to the expression [c, - JE c(x, t ) d x ] , to give the loss of Oifrom solution as a function of time, since the reduction in the integrated absorption coefficient of the 9 pm band can be converted to AIOj] using the calibration data of Baghdad; et al. (1989). Corresponding

8.

D I F F U S I O N OF O X Y G E N I N SILICON

299

measurements of A[O,] resulting from the growth of internal precipitates of SiO, will also lead to values of D,,,,. if the size and number density of the particles are known, and if it is assumed that there is no rate limiting interfacial process. Direct measurements of the rate of growth of SiOz particles can be made by TEM or SANS without ambiguity for Czochralski silicon heated to temperatures T 2 650°C. Some duplication of the information presented in Chapters 4 . 9 and 10, is necessary to show that values of D,,,, deduced from high-temperature precipitation kinetics agree with those for normal diffusion, so that extrapolations to lower temperatures might be justified. We shall discuss three temperature ranges: (a) high temperatures ( Z 2 SSOOC), where SiOz particles form, (b) intermediate temperatures 500°C 5 T 5 650"C, where ribbonlike contrast is found in transmission electron micrographs. and (c) low temperatures ( T 5 SOO"c'), where thermal donors are produced. The aim is to relate measurements of the rate of loss of oxygen from solution. A[O, ]/At. to models. to obtain a coherent and self-consistent overview for the whole range of temperature. For T < 650°C the known facts are limited and the validity of proposed interpretations remains subjective. 1. D,,xy DETERMINED FROM

O X Y G E N PREClPlTATlON AT HIGH

TEMPERATURES

The rate of growth of SiOz precipitate particles during the early strrges of high-temperature annealing ( 7 ' z 650°C) is easily quantified if 0, diffusion is the rate limiting process. The number of 0, atoms per unit time that cross a spherical surface surrounding a diffusion sink with a capture radius rr is then given by 47rc,)1',1). I f I', ( 1 ) is set equal to the radius r,, of a "large" growing (spherical) precipitate, we obtain 1'5 = (2c,)D/c,,11, where c'p = 4.6 x 10" cm- is the concentration of oxygen atoms in SiO,. The grown-in oxygen concentration co can be determined by IK spectroscopy, while the size of the particles, which have been shown to be nearly spherical in the early stages (Gupta et al., 1990), can be measured by TEM or SANS. The two methods give equivalent results. relating to real space and reciprocal space, respectively (Bergholz et al., 19891. but the latter is preferred as i t leads to an average value for the whole volume of the sample. Measurements made on a sample heated at 750°C (Fig. 3 ) led to a value of D equal to the normal value of Doxy (Fig. 4). within the experimental errors (Livingston et al.. 1984). Thus, it was demonstrated that long-range 0, diffusion controls the rate of precipitate growth at this temperature, rather than a surface reaction such as the formation and outward diffusion of self-interstitials (/-atoms) required to accommodate the local increases in volume at the sites of the precipitates

300

R. C . NEWMAN AND R . JONES

OY

100

200

300

Anneal Time (h)

FIG.3. The variation of the squared radius of growing precipitates in undoped Cz Si as a function of heating time at 750°C. measured by small angle neutron scattering (SANS), yielding D = 4.4 x lOI4 em's-' (Livingston et al., 1984).

(Bullough and Newman, 1970; Gosele, 1986; Tan, 1986; Taylor, Tan and Gosele, 1991). Values of Doxyhave also been obtained by examining the precipitation process over extended periods of time, which led to the loss of nearly all the oxygen from solution. The oxygen loss AIOi] was measured by 1R spectroscopy with the samples at 4.2 K and the number density of precipitates N was determined by SANS and defect etching (Livingston et al., 1984). N showed only small reductions with increasing anneal time, due to Ostwald ripening, but was very dependent on temperature (Newman et al., 1986a). For a set of samples cut from a particular as-grown boule, not given a prior postgrowth heat treatment, SANS measurements in the exp( + 3 eV/kT) temperature range 650°C to 1050°C led to N = 6 x (Fig. 5): the large increase in N as T was lowered was attributed to the increasing oxygen supersaturation. Conservation of oxygen atoms requires the quantity (4/3)rriNcp to be equal to the loss of oxygen AIOi] from solution at all stages of the annealing. Hence the number of oxygen atoms per particle was also determined for long annealing times (Fig. 6). It follows that the temperature dependence of rp must correspond to that of N i.e., exp( - 1.0 eV/kT) for the set of samples discussed.

8.

30 1

DIFFUSION O F OXYGEN IN SILICON

Somewhat different values would be expected for other samples with different grown-in oxygen concentrations. The important point is that the measured rate of oxygen loss will be given by the product 4 ~ rN, D I O , ] . and will have the temperature dependence of N2'3LI, that is -exp( -0.5 eV/kT), as r, - r,, and the activation energy E, of Doxyis -2.5 eV. Since N was known, the kinetics of the precipitation could be evaluated from least squares fits to the theory of' Ham (1958) to yield values of Doxy (Patrick et al.. 1979; Wada el al., 1980, 1982; Livingston et al., 1984) and the solubility of 0, atoms. c , ( T ) .DC,\? had normal values with El, - 2.5 eV for temperatures down to 650°C (Fig. 4). The values of c, determined

1

1

1

1

I

I

I

I

1

0 REF a

\ 0 HiOx

15~ 1 0 ' ~

Doxy= 0 13exp(-2.53eV/kT)cm2s

0.6

0.8

10

1.2 1OOOiT

1.4

1.6

1.8

(K I )

FIG.4. Arrhenius plot showing the line determined for normal oxygen diffusion (Fig. 2). Also shown are the values of Doh"obtained from the precipitation data of Livingston et al. (1984). who used IR and SANS measurements ( R E F a). the precipitation data of Wada et al. (1980. 1982) ( R E F d), the out-diffusion data o f Gosele et al. (1989) (vertical bars), the oxygen aggregation data of Bergholr et al. (1985) ( R E F b). the thermal donor data of Gaworzewski and Ritter (1981) ( R E F c ) and the oxygenoloss data of Binns (1994). using second-order kinetics and a dimer caplure radius of 10 A ( R E F e). 0, diffusion is clearly the rate-limiting process for precipitation lor 7 2 650°C. but the interpretation at the lower temperature data is still open to dehate.

302

R. C . NEWMAN AND R . JONES

1000 1017-

I

800

'

500

600

'

I

l

l

+

-

I ~

-

0

-

z

-

sr c ._ v)

-

a, c ~

I

FIG.5 . An Arrhenius plot of the number density N of SiOz precipitate particles for a set of samples cut from a common undoped Cz crystal with [O,],= 9 ? 1 x lo" given no postgrowth heat treatment prior to the anneal to induce precipitation (x). Data points ( A ) are for samples cut from a different crystal. These measurements were obtained from 1R and SANS. Points marked ( + ) were derived from IR measurements with the assumption that D,,,was normal (Messoloras et al., 1987).

Temperature ("C) 1 0 9 ~

-

+j107.-

r

. Q m

-

cn

S

c

105-

m L

a,

a

5 z

-

103-

10 8

I

10

I

12

I

14

16

IikT (eV') FIG.6. An Arrhenius plot of the number of oxygen atoms per precipitate particle deduced from the data shown in Fig. 5 (Messoloras et al., 1987).

8.

303

D I F F U S I O N O F O X Y G F N I N SILICON

-

in this way indicated a heat of solution of 1.4 eV at high temperatures but then passed through a broad minimum around 800°C to 700°C (Fig. 7) (Newman, 1988, 1992),due to the increasing importance of the interfacial energy as the precipitate size decreases. Heating for very much longer times, which are not achievable experimentally, should lead to a progressively lower density of larger particles and lower measured values of c J , reflecting the true solubility . In summary. these measurements provided a clear trend for a reduction of the particle sizes as the temperature was lowered to 650°C. The calculated values of c, supported this dependence, were physically meaningful and showed no anomalous behavior. Measurements of the rate of oxygen precipitation at 750°C in silicon highly doped with boron. carbon or antimony (Gupta et al., 1991. 1992a, 1993b) provided no evidence for enhanced or retarded oxygen diffusion. or effects due to changes in the position of E ~ - when , proper account was taken of differences in the number densities and sizes of the precipitate particles resulting from the presence of the second impurity. 3.

OXYGEN

AGGREGATION A T I N 1H:RMEDIAlE TEMPERATURES

At temperatures lower than 650°C. measurements of N by SANS have not been reported because of the lack of sensitivity for detecting small Tmperature ( C)

I

1

6

7

1

8

1

9 10 1 0 4 (K ~

I

I

11

12

I

FIG.7. The measured solubilitv 0 1 oxygen in silicon showing the flattening of the Arrhenius plot near 7 W C , followed by ;in upturn at lower temperatures. which is attributed to the effect of the interfacial energy and implies the presence of very tiny precipitate particles (cf. Fig. 6) (Newman, 1992)

304

R. C . NEWMAN AND R. JONES

SiOz particles (Messoloras et al., 1987). It follows that the number density of diffusion sinks cannot be determined, although values of d [ O , ] / d tcan still be measured. The use of Ham’s equations to analyze the kinetics of the oxygen loss for 500°C 5 T I600”C, with the assumption that Doxy was normal, led to physically unrealistic results, particularly at the lower end of the temperature range when calculated values of N were close to 10l8 ~ m - which ~ , would imply that a growing particle contained only one 0, atom, even at long annealing times. The procedure, or the assumption of normal values of D o x y was , obviously flawed. The capture radius r[ should be given by rc = rp + a , where a is the width of an effective capture zone surrounding the precipitate, which has an actual radius rp. At high temperatures ( T > 650°C) when rp is large we would have rc rp. However, once rp becomes small compared with a , r, would be essentially equal to a and independent of annealing time and temperature. After a rapid initial transient, the kinetics would have the form

-

( c - c , ) / ( c ,- c,)

=

exp( - t / ~ ) , where 7

=

( 4 ~ r D ~ ~ ~ N r( ~ 4 )) - ’ ,

allowing values of N and c, to be determined, again assuming Doxyhad its normal values. This revised procedure leads to an important prediction, not discussed by Messoloras et al. (1987). Since rr was assumed to be independent of temperature, the temperature dependence of d[O,]ldt should be that of the product DoxyN , namely, exp( +0.5 eV/kT). Thus d [ O , ] l d t should show an apparently anomalous increase as T is decreased. This prediction has been verified for samples cut from two boules with different grown-in oxygen concentrations (Fig. 8) (Newman, 1991; Brown, 1991). This result, together with the increasing values of c, as T is lowered in this range (Fig. 7) provide self-consistent evidence that SiO, particles could still grow at a rate limited by normal oxygen diffusion. However, their size was predicted to become very small and at 500°C the number of oxygen atoms per particle was estimated to be only 20 or 30 (Fig. 6). A consequence was that TEM “black dot” contrast was associated with these tiny precipitates. Coherent structures observed by direct TEM lattice imaging and originally assigned to coesite, a high pressure phase of silica would then have to be associated with some other extended defects. Bourret ( 1987) re-interpreted the TEM features in terms of hexagonal silicon, nucleated by the release of I-atoms during the oxygen aggregation. The need to invoke an enhancement of Doxyby a factor of lo4 at 485°C (Fig. 4) (Bergholz et al., 1985) to account for the growth of the “coesite” structure was thereby removed. These authors observed other TEM features that could be attributed to I-atom clusters, implying that these intrinsic defects had been formed. Unfortunately, the conclusions

8.

Temperature ("C) 650 550 450 350

10'

I

l

l

1

305

DIFFUSION OF OXYGEN IN SILICON

I

I

Temperature ("C) lo,316701 570 I 470 I 370

I

Oxyger

- 10'

Oxygen

1 0i7

Slope -0.6eV

-6 . 6

0

Slope

Slope

ij 10'

t u

- 10'

TD . Formation

5 .. T

0

lo9

t a)

1 ne

10

I

12 14 104/T(K')

I

16

lo8 I (b) 10

1

I

12 14 1041 T (K l )

I

16

FIG.8. Arrhenius plots showing the rate of loss of 0,atoms from solution for two b o d e s with ( a ) [O,],, = I .5 x lo'#c m - ' and ( b ) [O,],,= 9 x 10" cm-', respectively. At temperatures 7 2 .SSO"C, the slopes are -0.6 eV and 0 . 3 eV. followed by anomalous rises as the temperalure falls t o -475°C. At lower temperatures the slopes are expected t o become asymptotic to the activation energy for 0,diffusion. due t o the formation of O? dimers but the measured slopes are -1 eV and - I . 3 r V . respectively. Also shown are Arrhenius plots of the rates of formation of TD centers (Brown 1991).

have been confused again by the work of Pirouz et al. (1990) who have argued that the coherent TEM structures are not due to hexagonal silicon and are probably not due to coewe; however, no positive interpretation wa, advanced. We shall return to the subject of heat treatments in this temperature range in Section I V . 3. OXYGEN

AGGREGATION A T L,OW r r E M P E R A T U R E S

( 7 2 S00"c)

Extrapolation of the measurements shown in Fig. 6 to 450°C leads to the conclusion that oxygen loss would occur predominantly by the formation of oxygen pairs O2 up to quite long annealing times. Assuming that 0, defects are stable. we can write d [ O , ] / d r = -87rr,.D[O,]', since any A factor of diffusing 0, atom has a concentration of sinks equal to [Oil. 8 rather than 4 in the equation occurs because the "sinks" are also diffusing. A n analysis of the rate of oxygen loss should yield an activation energy of 1.5 eV, equal to lhat of Dc,xv.according to this mechanism. Measurements led to values o f I ) , , , that were in agreement with normal diffusion at 7 = 420°C and 7' = 450°C (Newman et al.. 1986a) (with r,

306

R. C . NEWMAN AND R. JONES

= 10 A). However, at a higher temperature of T = 500°C the value of Doxy estimated in this way was smaller than the normal value by a factor of -5 (Fig. 4). This result was explained by postulating that dimers would exhibit some degree of dissociation. The total loss of 0, atoms from solution would be smaller than expected from the simplified analysis used, leading to a too small value of Doxy.It would be logical to argue that dimers would become more stable as the anneal temperature was reduced. Meaningful measurements at low temperatures ( T 5 400°C) can be obtained only if the period of the annealing is extended to several thousand hours (at say 350°C) to obtain sufficiently large reductions in [O,].The first such results of Newman and Claybourn (1989) were not reliable and later data implied that calculated values of Doxywere somewhat greater than the normal values at 350°C (Brown et al., 1990a; Newman et al., 1990). Suggestions were made of ways of reconciling these data for long-range migration with those involving single atomic jumps where normal values of Doxywere obtained. It was argued that there may have been in-diffusion of some unknown species such as hydrogen, originating from water vapor in the ambience, but no real evidence for such a process had emerged. Subsequently, many further measurements have been made on samples with differing concentrations of grown-in oxygen (Binns, 1994). It was then found that the calculated values of Doxy increased for anneals at T > 400°C as the grown-in oxygen concentration became larger. This result is qualitatively explicable in terms of dimer dissociation described by

d [ O , ] l d t= -8.rrrcD[0,]2+ k,[O,],

(5)

since the second term would become more important as [O,] becomes smaller. The later data (Figs. 4 and 9) indicate that the measurements for samples with high and low oxygen merge at temperatures below 400°C. There is an implication that dimer formation and dissociation are quite closely balanced, according to these arguments. In that case, the slope of an Arrhenius plot for the rate of oxygen loss (and TD formation) over a limited temperature range would not correspond to an activation energy of a single process: this conclusion is supported by the low temperature data given in Fig. 8. It follows that the determination of the activation energy of Doxy from measurements of the rate of oxygen loss from solution is not a simple procedure. To evaluate numerical values of Doxy,it is necessary to assume a value for the capture radius rcr which should be essentially independent of the temperature. Newman et al. (1986b) argued that this might be as large as 10 A, but Kimerling (1986) thought that the smallest possible value of only 2 A would be more appropriate. We show in Figs. 9 and 10 values

8.

DIFFUIION OF O X Y G E N IN SILICON

307

FIG.9. Arrhenius plots, for furnace annealed samples. o f Dox)determined for low temperature\, according to a model o f stable dimer formation, with a capture raditib of 10 A for two houles with [O,] = 1.5 x 10'" cm ' ( H i Ox) and [ O , ] = 9 x 10" c m - ' ( M E D Ox). respectively. There I S reasonably good linkage to values o f D,>,, determined by stressdichroism measurements. Any enhancement in the rate o f long-range diffusion at 350°C would be no greater than a factor o f 3-4 according to this analysis. The dashed line corresponds to enhanced oxygen diffusion in the presence o f hydrogen (see Figs. I 6 and 17) (Binns. 19941.

of Dolr calculated from second-order kinetics and measured values of d10, Ildr using the two values o f I', to indicate whether or not there might be a linkage to the low-temperature stress-dichroism data. Such a linkage appears quite unreasonable if I', = 2 A but is possible for I', = 10 A . We shall comment further on the choice of this parameter in Section IV when we consider the diffusion of 0,atoms in samples given a prior heat treatment in hydrogen gas (see also Section V1). We simply note that if theory requires I ' ~ - 2 A there is still no implication that Do,) for longrange diffusion at low temperatures (,-,3So"C) is enhanced by more than a factor of about 10. More comprehensive kinetic analyses have been made by Tan et al. (1986) who took the formation of trimets and larger oxygen clusters into account, as well as allowing dissociation of dimers to occur in their model. They also found an apparent increase of Doxywith increasing [O,] but it is difficult to draw further conclusions as the comparison with

308

R. C. NEWMAN A N D R . JONES

FIG.10. Arrhenius plots for furnace annealed samples of Do,, determined for ol! temperatures, according to a model of stable dimer formation with a capture radius of 2 A for two boules with [O,] = 1.5 x lo’* cm-3 (Hi Ox) and [O,] = 9 x lo” cm--’ (MED Ox), respectively. The linkage to values of Doxydetermined by stress-dichroism shows a discontinuity corresponding to a factor of -15 (cf. Fig. 9). The dashed line corresponds to enhanced oxygen diffusion in the presence of hydrogen (see Figs. 16 and 17) (Binns, 1994).

experiments was for one temperature only, namely, 450°C. From measurements of d[O,]ldtalone, it is difficult to determine several parameters ( r , for dimers, r,. for other aggregates, k, for dissociation of dimers, D o x y , etc.) with any degree of precision. We end this section by pointing out that the analysis presented leads to the possibility that Doxyis normal, or only very slightly enhanced, for long-range migration at any temperature from the melting point of silicon down to 350°C. IV. Enhanced Oxygen Diffusion Not Involving Hydrogen

Enhancement mechanisms must involve interactions of Oiatoms with another diffusing species, which may be a vacancy ( V ) , an I-atom or an interstitial impurity that could be a metal such as copper, iron, etc. or nonmetallic carbon, nitrogen or even a second oxygen atom. It is implied that a complex, formed as a transient species, dissociates or is annihilated after a certain time and that one or more 0; diffusion jumps occur as a

8.

DIFFU5ION O F , OXYGEN IN SILICON

309

result of the interaction. We shall first consider interactions with vacancies and I-atoms introduced by 2 MeV electron irradiation. An inherent complication is that the two defects are produced simultaneously, and it has been established that they each form stable complexes with 0, atoms at low temperatures. It is also known that substantial recombination of the two species occurs at 300 K and that part of the process is due to their sequential trapping at 0, atoms (Davies et al., 1987). We have to consider the analyses of oxygen diffusion profiles by SIMS carried out by Shimura et al. ( 1988) for annealing temperatures of 750°C and 1000°C and those of Lee and Fellinger (1986). Lee et al. (1988). and Gosele et al. (1989) relating to temperatures in the range 450°C to 650°C. Effects due to the presence of f-atoms and vacancies were considered in the interpretation of this lattcr work, some of which involved ionimplanted oxygen sources but eventually they were ascribed to rapidly diffusing 0, pairs. The work of Gaworzewski and Ritter (1981) is closely related to these studies. At the end of this section we comment on the effects due to the presence of carbon and metallic contamination. The effects of exposing silicon to hydrogen gas at high temperatures or to atomic hydrogen generated in a hydrogen plasma at much lower temperatures will be discussed separately in Section V .

I . EFFECTS DUETO THE INJECI.ION OF VACANCIES A N D LATOMS B Y 2 MeV ELECTRON IRRAIIIATION Newman et al. (1983a) investigated the effect of room temperature 2 MeV electron irradiation on samples that had been stressed to induce dichroism in the 9 p m band. The irradiation led to the formation of stable oxygen-vacancy pairs (A-centers) that give an 1R absorption band at 836 cm I (77 K ) and a reduction in thc strength of the 9 p m band. There was also a loss of dichroism in the 9 p m band at a rate that depended on the 300°C. For an incident electron flux but not on temperature u p to T this rate (for samples maintained at T current density of 22 p A cm 50°C) corresponded to that for normal 0, diffusion jumps that occur in furnace annealed silicon at a temperature of 350°C. Confirmation that vacancies were involved in the process leading to the enhancement of the loss of dichroism was obtained by irradiating Cz Si doped with isoelectronic tin impurities present in a concentration of 10’’ cm-’. Tin atoms also trap mobile vacancies efficiently to form Sn-V pairs that are stable up to T - 150°C (Brelot, 1973; Watkins, 1975). There was a reduction in the rate of formation of A-centers by a factor of -6 compared with undoped Cz Si because of the competition for trapping the available vacancies and there was a reduction in the rate of l o s s of dichroism in

‘,

-

310

R. C . NEWMAN A N D R. JONES

the 9 pm band by the same factor (Oates et al., 1984). However, if the sample temperature were raised above 150°C during the irradiation, so that tin atoms no longer trapped vacancies to form stable Sn-V pairs, the rates of formation of A-centers and the loss of dichroism were the same as those measured in undoped samples irradiated at room temperature. The capture of a vacancy by an 0;atom could produce a diffusion jump due to the rapid re-orientation within the A-center (Watkins and Corbett, 1961) followed by either (a) its dissociation or (b) by the capture of a mobile I-atom, so that the final bonding of the Oi atom was to different neighbors from the original neighbors. Newman et al. (1983a) concluded that A-centers captured mobile I-atoms, in agreement with the model of radiation damage discussed by Davies et al. (1987). An alternative possibility that 0; atoms first captured a mobile I-atom and then a vacancy, which could also lead to a diffusion jump, was discounted, as O i l complexes have a small binding energy and they are formed only during irradiations below room temperature (Section IV.2). When undoped prestressed Cz Si was irradiated at temperatures above T - 300"C, A-centers were not detected in IR spectra, which was not surprising in view of their known annealing at these temperatures (Svensson and Lindstrom, 1986). Nevertheless, the rate of loss of dichroism increased dramatically (Oates, Newman and Tucker, 1985) and the possibility had to be considered that A-centers were produced as a transient species and that one or more diffusion jumps occurred before dissociation. Oates and Newman (1986) initially inferred that dissociation did occur by demonstrating that the loss of A-centers during an isochronal annealing was accompanied by a corresponding increase in the concentration of unpaired 0;atoms. However, later work showed that regeneration of isolated 0;atoms occurred only in samples that had been given a large (-5 X 10l8 cm-2) dose of 2 MeV irradiation and then only in the first stage of an isothermal anneal (Newman, Tipping and Tucker, 1986b; Svensson and Lindstrom, 1986) (Fig. 11). Dissociation of a complex cannot suddenly stop at some stage during an annealing, and so Newman et al. (1990) argued that the initial loss of A-centers occurred by the capture of I-atoms released from clusters of these defects that had also been formed during the extended irradiations. In the second stage of the annealing (Fig. 1 I ) , conversion of A-centers to another type of defect that gives IR absorption at 889 cm-' at 300 K (894 cm-l at T 5 77 K) is observed. The general consensus is that this defect should be assigned to an 0,-V complex (Corbett, Watkins and McDonald, 1964b) that is produced when a mobile A-center diffuses to an uncomplexed 0; atom. However, this interpretation has some shortcomings. During the forma-

8.

DIFbCI\IC)N O F O X Y G L N IN SILICON

311

Loss of iritegiated absorption from

the 835cm ' A band (cm ,')

FIG. I I . The loss in the integrated abwrption ( I A ) coefficient of the 835 c m - ' 1K line fi-om 0,-1' pairs (A-centerh) during an isothermal annealing of a sample at 300°C. following 2 MeV electron irradiation at room temperature to a dose of 6 x 10IKcm-:. In stage 1 the lost absorption reappears a s an increase in (he IA of the 9 pm 0, band. At a later stage (11) this process terminates. and there i h correlated growth of a line at 889 c m - ' (O?-V center) ( N e w m a n et al.. 1986b. 1990).

tion of 889 c m - ' defects there is no further loss of 0, atoms from solution (Svensson and Lindstrom, 1986; Newman et al., 1986b; Stein, 1986). In addition, there is no isotopic splitting of the LVM corresponding to Ih 0 I 8 0 V centers in samples containing the mixed oxygen isotopes (Stein, 1986; Abou-el-Fotouh and Newman, 1974). Finally, the effects of an applied uniaxial stress have shown that the defect symmetry is lower than the commonly assumed Dz,,(Bosomworth et a]., 1970). In spite of these uncertainties, it seems that the 889 c m - ' defect must incorporate at least one lattice vacancy. In that case, the fact that the defect is not generated in t h e early stages of the annealings of highly irradiated samples (5 x 10" cm ' 1 can be explained (Fig. 1 I ) . If I-atoms are released from large aggregates of the defects and are trapped by A-centers. they could also be trapped by the 889 c m - ' defects so that no detectable concentration builds up. At a later stage in the annealing. the flux of released I-atoms would he reduced but not to zero; thus there could be some continued annihilation of A-centers to regenerate 0, atoms. while simultaneously. other A -centers migrated to 0, atoms to form new 889 c m - ' defects leading to a loss of 0, atoms. Svensson and Lindstrom (1986)had to argue that there was a hularice of such processes to explain their observation that 10,] remained constant during stage 11 of the annealing. For low-irradiation doses ( 2 x lo" em-') only small

312

R. C. NEWMAN A N D R. JONES

aggregates of Z-atoms would be formed. If these clusters were relatively unstable and dissociated at the beginning of the annealing it is possible that there would be immediate formation of 889 cm-' defects as found by Newman et al. (1990); that is, stage I of the annealing was not detected (Fig. 1 1 ) . Further work is required to clarify the interpretation of the observations. The most important point to emerge is that there is no evidence for vacancy-enhanced diffusion of Oi atoms at temperatures below -300°C. The 889 cm-' defect is stable up to T 450"C, while at higher temperatures, aggregation of Oi atoms occurs and the diffusion rate is normal (Section 111.1).

-

2. THEEFFECT OF EXCESS Z-ATOMS It has been suggested that the presence of Z-atoms alone enhances Doxy (Ourmazd, Schroter and Bourrett, 1984). The irradiation experiments discussed previously provide no supporting evidence for this process but, on the other hand, they do not lead to its exclusion. From the measurements on the tin doped silicon it can be deduced that any direct enhancement of Doxyby Z-atoms is smaller by a factor of -6 than that arising from the recombination of Z-atoms with A-centers. In an earlier work, Brelot and Charlemagne (1971) showed that 0;atoms formed complexes with 1-atoms generated during low temperature (77 K) 2 MeV electron irradiation of Cz Si. This result is analogous to the formation of 0;complexes with interstitial carbon atoms (C;), which have been called C(3)centers (Davies and Newman, 1994). The latter defect is stable up to T 350°C (Ramdas and Rao, 1966) but the Oil defect that gives IR LVM lines at 956 cm-I, 944 cm-' and 935 cm-' (Brelot and Charlemdgne, 1971) dissociates near 50°C. The release of Z-atoms is unambiguous since they are retrapped by substitutional carbon impurities that are ejected into interstitial sites. Brelot (1972) determined an activation energy for the dissociation of O i l defects by carrying out an isothermal anneal at 333 K for a limited time, after which the sample was given further heat treatments at 348 K. From the measured tangents of the curves for the anneal of the 935 cm-' IR line at the point where the temperature was changed (Fig. 12), he determined Edlsof -1.0 0.1 eV. This energy should be the sum of the binding energy EB and the migration energy EM of the Z-atoms. He assumed that E M 0.2 eV to obtain EB 0.8 eV. These measurements lead to the view that Doxymight be enhanced due to the presence of Z-atoms and the activation energy would be (EF - EB + E M ) ,where EFis the formation energy of an Z-atom. For the formation of 1-atoms by a thermally activated intrinsic process, EF would be very

-

*

-

-

8.

10

313

D I F ~ U S I U NOF O X Y G E N I N SILICON

20

30 Anneal time (rnin)

0

4

0

FIG.12. Reduction in the strength o f the absorption coefficient of an 1R line at 935 c m - l ( 0 - 1 pairs) during an isothermal annealing at 333 K for up to 37 rnin. followed by further isothermal annealing at 348 K. leading lo a dissociation energy of 1.0 eV; the assumption that the migration energy of an /-atom I \ 0 2 eV leads to a binding energy of 0 8 eV (Brelot. 1972)

large ( - 5 e V ) but there is evidence that f-atoms are generated during the aggregation of 0, atoms at high temperatures when stacking faults and other defects grow adjacent to SiOZ precipitates (Bourret, ThisbaultDesseaux and Seidman, 1984). The initial rate of I-atom generation would then be controlled by the rate of loss of oxygen from solution for which the slope of an Arrhenius plot is quite low (Fig. 8). If f-atoms were similarly generated at low temperatures ( T < 500°C) this energy might rise to the activation energy of normal oxygen diffusion (2.5 e V ) , leading to a mechanism of enhanced diffusion of remaining isolated 0, atoms with activation energy of about 1.9 eV. The contribution of this process to the total diffusivity would depend on the concentration of f-atoms present. Newman et al. (1983a)argued that one /-atom is generated for every two Oi atoms that coalesce, even at these low temperatures (see also Section VII), but the rate of loss of uncomplexed f-atoms from a crystal is uncertain. and so it is not possible to estimate a concentration arising from a dynamic equilibrium between the two processes. Although substitutional carbon atoms are efficient traps for mobile I-atoms (Newman et a]., 1983a). the rates of loss of 0, atoms from solution in (a) carbon-free loi8 cm ~’are material and (b) material containing carbon with [C,] essentially equal. The latter measurements therefore provide no evidence

-

314

R. C . N E W M A N AND R. JONES

that the presence of I-atoms generated by the internal aggregation of Oi atoms enhances Doxy.Small variations in Doxyhave been observed, but these can be correlated with differences in the grown-in oxygen concentration (Tan et al., 1986; Newman and Claybourn, 1989) (see Section VII). In summary, enhancements of Doxywould be expected at low temperatures if mobile I-atoms were present but experimental evidence supporting this mechanism is essentially nonexistent. It could be inferred that this lack of evidence implies that the formation of I-atoms does not occur. There is a possible exception to this negative conclusion. In Section 111, it was shown that values of Doxydetermined from oxygen loss measurements at very low temperatures appear to be somewhat greater than those determined from stress-dichroism measurements. We point out that even if there were I-atom formation in the extended annealing required to measure the oxygen loss, no I-atoms would be generated during the short heat treatments required to effect single 0;jumps. Although discussion of these particular low temperature measurements has already been deferred, it is necessary to consider yet additional evidence, in relation to Si containing hydrogen impurities (Section V), before the discussion can be completed.

3. RAPIDDIFFUSION OF DI-OXYGEN DEFECTS In Section 111 it was assumed that stable immobile oxygen pair defects are formed during annealings at T 5 450°C. Various models for these defects have been proposed as a result of theoretical analyses, and it is concluded that there is a binding energy (Section VI.5). IR absorption from these defects has not been detected, either as LVM lines at frequencies different from those of isolated Oi atoms, or from modifications of the lines from the latter centers (Brown et al., 1990b). If two 0, atoms were present at adjacent Si-Si bonds with a common apex, the frequency of the 1136 cm-' Oi band (4.2 K) should be shifted. Second, the rotational motion about the [ 1 I I] bond axis should be quenched or severely modified. Changes in the rotational energy levels would be detected by making IR absorption measurements at T 10-20 K when the first excited rotational state is occupied (Bosomworth et al., 1970). Brown et al. (1990b) compared the spectra of heated and unheated samples but found no detectable difference. It has been stated by Stavola and Snyder (1983) that they made similar measurements, but again no differences were detected. Possible inferences of these negative results are that if close oxygen pairs form there are large changes in the local bonding so that the oxygen vibrational modes are shifted away from the 9 p,m region or the pairs are lost from solution by rapid diffusion to traps.

-

8.

DIFFUSION O F O X Y G E N IN SILICON

315

Rapid diffusion of di-oxygen "molecules" was proposed by Gosele and Tan (1982). who supposed that pairs of these defects combined to form 0, complexes. However. no detailed atomic structure was proposed for either the O2 or the 0, centers, and neither was the mechanism of the rapid diffusion of 0, explained. The main feature was that the model offered an explanation for the results of Kaiser et al. (19581, who found that the rate of formation of TD centers was proportional to 0:. Recently, 1,ondos et al. (1993) have shown that this power dependence is specific to an annealing temperature of 450°C and for T I 400°C, the rate is proportional to 0:. At these lower temperatures estimates of Doxy,determined from the rate of oxygen loss and the use of second-order kinetics, become independent of the grown-in oxygen concentration. Hence the relevance of the idea of Gosele and Tan (1982) to TD formation is now less obvious since it could be inferred that a TD center contains only two oxygen atoms. In a later work Giisele et al. (1989) again invoked the presence of rapidly diffusing O2 dimers to explain the SIMS measurements of Lee and Fellinger (1986) and Lee et al. (1988), which indicated rapid mass transport of oxygen out of surface regions of Cz crystals heated in the range 500°C to 65OoC, with enhancements of Doh).by factors of up to 10' (Fig. 4). Related SIMS measurements showing rapid in-diffusion of oxygen. ( I x 0 ) . from surface souIces produced by ion implantation were also explained in this way. The interpretation of the latter measurements may not be straightforward because of the large amount of lattice damage that would have been produced by the implantation and the observations that the presence of damage can lead to enhancements of Doxy(Section l V . I ) . In their analysis, Ciosele et al. (1989) postulated that there were two types of oxygen dimers. The first consisted of a pair of adjacent oxygen atoms that was highly mobile and could dissociate, while the second, 0;. was formed when an /-atom was ejected, so that 0: was considered to correspond to the first stage of precipitation. The emission of /-atoms was considered necessary to account for the family of TD centers that was formed for T < 500°C (see Claybourn and Newman, 1987). N o alternative explanation has been proposed for the anomalous SIMS data and so it would be imporiant for the measurements to be repeated. Superficially. the results of Gaworzewski and Ritter (1981) appear to bupport the rapid out diffusion of oxygen at 450°C. They estimated an enhancement factor of 10'' (Fig. 4) by measuring the depth profiles of thermal donors. However. if T D centers incorporate some other component such as an /-atom, these measurements could relate to the outdiffusion of that component rather than oxygen.

-

316

R. C . NEWMAN AND R. JONES

4. EFFECTS DUETO CARBON

Shimura et al. (1988) reported SIMS measurements of the out-diffused profiles of oxygen from Cz Si wafers heated for 64 hours in dry oxygen, either at 750°C or 1000°C. The oxygen concentrations were [O,] = 1.13 x lo’* ~ 1 7 (according 1 ~ ~ to the calibration of Baghadadi et al., 1989), and the crystals contained either a low carbon content, L(C) < 5 x loi5~ m - ~ , or a high carbon content, H(C) = 4 x 1017~ m - Heating ~ . a L(C) sample at 750°C led to negligible oxygen precipitation as determined from 1R measurements, while the out-diffused SIMS profile was stated to be “fairly in agreement” with that calculated from Eq. (3) using the normal value of Doxy(Table 11). In our opinion, the agreement was excellent. The validity of the measurement techniques was thereby established and Doxywas normal. After the L ( C ) sample had been heated at IOOO’C, the calculated outdiffused oxygen profile ran parallel to that measured by SIMS but was lower in concentration by a factor of -2. There was a similar but larger discrepancy for the H(C) sample heated at 1000°C. It was inferred that the oxygen diffusion was retarded by the presence of I-atoms generated by the internal precipitation of 50% ( L ( C ) )and 86% (H(C)), respectively, of the grown-in oxygen and by the formation of additional I-atoms at the surfaces due to the growth of SiO, layers (Shimura 1991). It was then argued that these results supported a vacancy mechanism for oxygen diffusion, as proposed by Heck et al. (1983). However, the use of Eq. (3) is not appropriate for the analysis of these samples as the precipitated oxygen would not be mobile and could not contribute to the out-diffusion although it would still be detected by SIMS. A more complex calculation is required to analyse the data before it could be concluded that Doxydid not have its normal value. On the other hand, the result of heating a L(C) sample at 750°C was interesting and could be important. This sample showed losses of oxygen of 9.3 x 1017 ~ r n and - ~ all the carbon atoms, 4 x 10” ~ m - from ~ , their normal lattice sites, and the formation of complexes involving interstitial carbon (C,) and two or more 0, atoms (C,O,n),which were designated as perturbed C(3) centers (Shimura, Baiardo and Fraundorf, 1985; Shimura, 1986). The relevant feature to the present discussion was the observation of enhancement in Doxyfrom the normal value of 4.47 x 10-l4 cm-, SKI to 1.51 x cm2 s-I and the diffusion coefficient of carbon was also enhanced. The latter effect can be understood as substitutional carbon atoms would be ejected into interstitial sites by the capture of Z-atoms and the resulting C, atoms have a high diffusion coefficient, D = 0.44 exp(-0.87 eV/kT) cm2 s - I (Tipping and Newman, 1987). It was then

8.

DIFFU\ION O F OXYGEN IN SILICON

317

proposed that C,-Oi complexes have a higher diffusivity than isolated 0, atoms, similar to the proposal that (0,). defects might also have a higher rate of diffusion (Gosele and Tan, 1982). It is interesting that 1R data for the unperturbed C(3) center imply that the oxygen atom is displaced from its normal bond-centered site (Davies et al., 1986) and this displacement is also predicted by uh initio calculations (Jones and Oberg, 1992). In summary. it has been shown that a heat treatment of L ( C ) material at 750°C in dry oxygen, which would lead to the injection of excess /-atoms at the surface, still led to a diffused oxygen profile with a normal . contrast, the presence of grown-in carbon led to envalue of D o x yBy Iiuticc~dout-diffusion of oxygen. with the implication that the presence of interstitial carbon atoms leads to the formation and rapid diffusion of O,C, complexes. I t is important to note that there was no enhancement during an anneal of a H ( C ) sample at I00o"C. but that 1R measurements then failed to reveal CiO,,,complexes. which are presumably unstable at the high temperature.

5.

EFFECTS D U E .TO

METALLIC. C O N 1 A M I N ATION

I t is well known that tranhition metals such as Ni, Fe and Cu diffuse rapidly in silicon as interstitial species. Consequently, transient complexes with 0; atoms could he produced, leading to a n oxygen diffusion jump upon dissociation. The experimental work of Newman. Tipping and Tucker (1985) and Tipping et al. ( 1986) appeared to support this view. Fe or Cu was diffused into Cz Si at 900°C and subsequently enhanced diffusion jumps were observed i n measurements of the relaxation of stressinduced dichroism. The transfer of Cu atoms from substitutional to interstitial sites during cooling from the 900°C treatment and the production of vacancies was also considered to be important. Woodbury and Ludwig ( 1960) found that vacancies formed by this process led to site switching of interstitial Mn impurities to substitutional sites. The possibility that the presence of vacancies might lead to enhanced oxygen diffusion has been discussed and shown nut to be very likely. In the work of Tipping et al. ( 1986). the metallic impurities were introduced by heating silicon in contact with their hydrated salts (nitrates),and the presence of hydrogen (Secimpurities would almost certainly have led to enhancements of Doxy tion V ) . Nevertheless the metals may have played a secondary role as will be explained in Section V . 3 . 6. SUMMARY

It has been shown that irradiation damage, involving the sequential capture of vacancies and then /-atoms by 0, impurities enhances D o x y .

318

R . C . NEWMAN AND R . JONES

The injection of vacancies or I-atoms alone could also lead to enhancements but their magnitudes cannot be estimated and there is no clear experimental evidence to support these mechanisms. Likewise, the presence of fast diffusing metallic impurities could enhance Doxybut again there is no supporting experimental evidence. It has been shown that the presence of grown-in carbon leads to enhanced out-diffusion of oxygen at 750"C, possibly due t o the rapid diffusion of CiOicomplexes. However, measurements were reported only for one sample and further work is needed to verify the result. This leaves hydrogen as the dominant catalyst (Section V), with the additional possibility that 0, centers diffuse more rapidly than isolated 0; atoms (Section VIII). The lack of experimental evidence for the existence of O2 centers in heated samples could support this view. If 0, centers do diffuse rapidly there are important consequences relating to the formation of TD centers for T < 500"C, and the rates of oxygen loss from solution in the range 500"C-600"C (see Section Vll). V. Silicon Containing Hydrogen Impurities Fuller and Logan (1957) found that the rate of TD formation in Cz Si grown in an atmosphere of hydrogen was ten times greater during subsequent heat treatments at 450°C than that in material grown in the same equipment but in a helium atmosphere (Fig. 13). It has now been demonstrated from electron nuclear double resonance (ENDOR) measurements made on Si containing enriched "0 (Michel, Niklas and Spaeth, 1989) (Chapter 6) that TD defects incorporate small oxygen clusters. The measurements of Fuller and Logan therefore provided the first evidence that long-range enhanced diffusion of oxygen can occur during oxygen aggregation at low temperatures. Previously van Wieringen and Warmholz (1956) showed that hydrogen may be introduced into Si by heating crystals in hydrogen gas to temperatures close to 1200°C. Diffusion occurred throughout material with a thickness of -1 mm, the solubility was -10'' ~ m - and ~ , the activation energy for diffusion was estimated to be -0.5 eV. The validity of extrapolations to low temperatures ( T < 500°C) is unclear because of (a) the formation of complexes of hydrogen with impurities and defects, and (b) the likely formation of H, pairs and perhaps larger hydrogen clusters. Recently, the effects of the presence of hydrogen, introduced into Cz silicon by high-temperature annealings in H, gas, on the long-range diffusion of 0;atoms during subsequent annealing at T 5 500°C has been examined (Section V. 1). Alternatively, hydrogen may be introduced as the atomic species at low temperatures by exposing samples to a hydro-

8.

1

319

DIFbtISION O F O X Y G E N IN SILICON

100

10

1000

Anneal time (h) F I G . 13. A compariwn of the introduction rates of added electron carriers. from resislivitv measurements, due to the formalicin of thermal donors for two Cz silicon crystals. ( a ) grown i n H, gas, and (h) grown in He gas in the same puller, showing the enhancement due to the presence o f hydrogen (Fuller. and Logan, 1957).

gen (or deuterium) RF plasma (13.56 MHz, 50 W, 1-2 Torr) (Section V.2). 1.

SIL.I(.ON

HEATED IN

HYDRO(iEN

GAS

McQuaid et al. (1991) demonstrated that samples preheated in H, gas at 900°C for 2 hrs and quenched to room temperature, showed enhanced rates of relaxation of dichroism of the 9 pm band following an intermediate stressing treatment at 420°C. An Arrhenius plot (Fig. 14) for the range 250°C 5 T 5 350°C indicated that Do,.).had a reduced activation energy of -2.0 eV, in agreement with the earlier measurements of enhanced oxygen diffusion (Stavola et al., 1983) for which there was no adequate explanation at that time. The samples used in the latter work had also been given a postgrowth treatment at 900°C for 2 hrs that was carried out in the crystal growing chamber in an atmosphere of argon-hydrogen (Kimerling. private communication). The introduction of metallic impurities would have been avoided (Section 1V.4). but the presence of hydrogen gas in the ambience was a common feature of the two investigations. By measuring the concentration of passivated H-B pairs in quenched Si samples by precalibrated 1R LVM spectroscopy, McQuaid et al. ( 1991. 1992, 1993) and Veloarisoa et al. (1991, 1992) showed that the concentration of dissolved hydrogen increased monotonically in the range 900°C to 1300°C up to c m - j (Fig. IS). McQuaid et al. (1991) also demon-

320

R. C. NEWMAN AND R. JONES

FIG.14. Arrhenius plots of Doxyshowing normal diffusion (dashed line) and enhancements with a lower activation energy (-2 eV) for samples preheated in H2gas at various temperatures in the range 600”C-1250”C, followed by a rapid quenching to room temperature. The measurements were made by the relaxation of stress-induced dichroism. N . B . : The enhancements increase up to a quenching temperature of 900°C but then saturate (Newman et al., 1992).

strated (a) that the H-B pairs were distributed uniformly throughout Samples -1 mm in thickness and (b) that the hydrogen originated from the gas, since replacing H, by D , led to the formation of D-B pairs but not H-B pairs. The concentration of [H-B] pairs saturated for a given heat treatment as the concentration of boron was increased beyond lo” ~ m - ~ . These data have now been confirmed by direct SIMS measurements made on both boron doped and undoped deuterated material and “hidden” (non-IR active) hydrogen has been revealed (McQuaid et al., 1993). The presence of hydrogen in n-type quenched silicon (Veloarisoa et al., 1991) can be revealed by subjecting samples to 2 MeV electron irradiation but pairing of hydrogen with phosphorus impurities in such material was not detected. Thus, two independent groups have shown that hydrogen dissolves in silicon at high temperatures but further work is required to determine the solubility because of the recent detection of hidden hydrogen. Nevertheless, the numerical data are close to those of van Wieringen and Warmoltz (1956) and Ichimiya and Furuichi (1968) (Fig. 15) but the validity of extrapolations to temperatures below 500°C is again unclear.

8.

32 1

DIFFUSION OF O X Y G E N IN SILICON

The effect of using different initial hydrogenation temperatures on the subsequent rate of oxygen diffusion jumps was examined by Newman et al. (1992). Samples quenched from 600°C showed enhancements in Doxy but only for annealings at T 5 325°C. Increasing the temperature of the pretreatment up to 900°C led to increases in D o x y ,consistent with an increase in t h e pre-exponential factor, Do (Fig. 14). Further increases of the pre-annealing temperature to 1250°C led to no further increase in D o x y . This result was surprising in view of the measured increasing hydrogen solubility in this temperaturf, range, since it had been proposed that the presence of atomic hydrogel1 was responsible for the enhancement. It should be pointed out, however, that the effects of the intermediate heat treatment at 420°C required to induce the dichroism are not fully understood. Tipping et al. (1986) have shown that the cooling rate from 420°C has a large effect on measured enhancements of Doxythat are small if the rate is either very high or very low. In addition, the enhancement is sometimes found only as a transient effect, depending on the procedure adopted (Brown et al., 1990b). Other samples heated at 1300°C in H, gas and quenched to room temperature have been annealed at temperatures in the range 325°C 5 7' 5 Temperature ("C)

-

0.6

07

0.8

09

1000 i T (K.')

FIG. IS. Measurements of the solubility of hydrogen in silicon obtained by heating samples in hydrogen gas. quenching to room temperature and measuring the concentrations of H-B pairs (H. 0 and solid line. McQuaid et al., 1992). Also shown are the permeation data ( + 1 of van Wieringen and Warmolrr (1956) and ( x and dashed line) measurements relating to tritium radioactivity of Ichimiya and Furuichi (1968). Figure taken from McQuaid et al., (1997).

322

R. C. NEWMAN AND R. JONES

Temperature (“C)

N

10-2’ -

-

A

Dichroisrn

w

ME DO^ 0.9x

1018

A LoOx 0.65 x

cm 3 cm-3

\\\\

‘\\ \

I 0-23 1.2

I

I

1.4

I

I 1.6

I

\\.

I

1.8

103 i T (K-’)

FIG.16. Arrhenius plot of Doxy (enh), determined from a model of stable dirner formation with a capture radius of 10 A for samples quenched in H2 gas. There is a clear linkage to values of Do,, determined by the stress dichroism technique leading to Do,, (enh) = 2.3 x exp( - 1.7 eV/kT) cmz s-I (cf. Fig. 9) (Binns, 1994).

470°C to determine the rate of oxygen loss from solution (Binns, 1994). Values of Doxywere calculated on the basis of second-order kinetics, assuming that there was no dissociation of (0i)2 pairs. The results are shown in Figs. 16 and 17, with the assumption of capture radii of 10 A and 2 respectively, as used for the analysis of furnace annealed samples (Section 111.3). The values of Doxyso obtained were all enhanced, as can be seen from the diagrams where the dashed line shows normal oxygen diffusion. There was an overlap in the temperature range used for these samples with the range used for the dichroism measurements for which the quenching temperature was 1200°C. If the capture radius was set equal to 10 A there was continuity between the two sets of data exp( - 1.7 eV/kT) cm2 S K I over the leading to Doxy(enh) = 2.3 x range 275°C to 400°C so that the value of ED was somewhat lower than that derived from the stress-dichroism data alone. However, large errors are expected because of the limited temperature range used. For r, 2 A there is a discontinuity between the two types of measurements (Fig.

A,

-

8.

323

DIFFII\ION O F O X Y G t N I N SILICON

Temperature ("C)

Assumed capture radius rc = 2A

8

10"

-

A

Dichroisrn

A LoOx

0 65

10"cm

'\ \

1

1023

1.2

1 14

I

I

I

1.6 10' / T (K ' )

'.

I 1 .a

FIG. 17. Arrhenius plot off),,, ( r n h ) determined from a model of stahle dirner formation with a capture radius of 2 A for samples quenched in HIgas. There is a discontinuity to values of D,,,, determined by the sire\\ dichroism technique icf. Fig. 16) (Binns, 1994).

17). In these samples, any small enhancement effects that might have been produced in furnace annealed samples for long heating times would have been completely overridden because of the hydrogen pretreatments. I t would seem, therefore, that a choice of Y 10 A has to be made to obtain self-consistency, if the analysis of di-oxygen formation is valid.

-

3. SILICON HEATED IN

AN

R F PI.ASMA

Prior to the work on quenched samples, measurements had been made on Cz Si that had been treated in an inductively coupled radio-frequency hydrogen plasma ( 1 Torr, 40 W . 13.56 MHz) (Brown et al., 1988, 1990a; Murray, Brown and Newman, 1989; Newman et al., 1990, 1992). The rate of thermal donor formation was increased for sample temperatures in the range 250T-4So"C and there were enhanced rates of (a) formation of carbon-oxygen complexes. (b) loss of Oiatoms from solution, and (c) loss of substitutional carbon in magnetic Czochralski (MCz) crystals. It

324

R. C. NEWMAN AND R. JONES

was known that the plasma treatment leads to the introduction of atomic hydrogen at the low temperatures used, because of the formation of passivated H-B, H-A1, H-Ga, H-P, H-As, H-Sb pairs etc. in doped crystals (Stavola and Pearton, 1991). Consequently it was inferred that the presence of hydrogen led to enhancements in Doxy. Enhanced rates of loss of dichroism were then demonstrated. Initially, it was supposed, erroneously, that the process occurred uniformly throughout the total thickness ( 2 mm) of the samples (Newman, 1990). Later, it was recognized that it would take time for the hydrogen to diffuse into the silicon and that this time scale might be comparable with the time intervals used for the measurements of the loss of dichroism. These ideas were shown to be correct by Newman et al. (1991), who found that the dichroism was lost rapidly in surface regions of samples but not in their interior. The thickness of the surface region increased with the time of heating and allowed estimates to be made of the depth to which the hydrogen diffused as a function of time. These data led to values of an effective diffusion coefficient for hydrogen in this lowtemperature range, but the nature of the diffusion process was unclear and was almost certainly trap-limited (see, for example, Leitch et al., 1 992). Heat treatments were also carried out in deuterium, helium, argon, argon-oxygen and nitrogen plasmas. Enhancements of Doxywere found only when deuterium was used or if the nitrogen was deliberately contaminated with water vapor (Fig. 18). Plasma treatments were also extended to long times and enhanced rates of oxygen loss and thermal donor formation were found. Enhancement factors of -5, 30 and 200 were found at 45OoC, 400°C and 350"C, respectively (Murray et al., 1989). These observations were consistent with independent studies of TD formation made by spreading resistance measurements by Stein and Hahn (1990a, 1990b, 1990c, 1992) to determine the depth profiles (Fig. 19). These workers also investigated the formation of TD centers in Cz Si beneath buried SiO, (SIMOX) or Si,N, (SIMNI) layers. Enhanced rates were found for the former samples, but not the latter. It is known that SiO, is permeable to hydrogen but Si,N, is not, when the thickness exceeds -100 A (Chevallier et al., 1991). It is clear from all the experimental data that hydrogen plays a key role in the process leading to the enhancement of Doxy. 3 . AN OUTLINE MODELAND SUMMARY

Estreicher (1990) put forward a model whereby H-atoms diffused rapidly in the Si matrix and made random collisions with 0; atoms. It was

8.

325

D I F F t I \ I O N O F O X Y G E N IN SILICON

Anneal time (h)

FIG.18. Thermal donor formation in uiidoped C r Si heated at 400°C in nitrogen plasmas with increasing water vapor content and comparison with ii furnace heated sample and another heated in a hydrogen plasrna (Newman et al.. 1991).

5 After a hydrogen plasma anneal C

0 ... E

c

C a 0 0 0 L

a, L

rc 0

Background doping level

0

100

200 300 Depth iprn)

400

500

t i c , . 19, Thermal donor profile measured by spreading resistance for n-type silicon sample\ with (O,l0= LO" cm-' heated in a deuterium (or a hydrogen) plasma for 2 hrs at 400°C. illustrating the limited depth of the deuterium diffusion (Stein and Hahn, IY90bl.

326

R. C. NEWMAN AND R. JONES

assumed that close 0-H pairs formed as a transient species and that a diffusion jump of the 0,could occur when the complex dissociated. Thus the hydrogen acted only as a catalyst. The probability per unit time P of a collision with one 0, atom is P = 4rC.rrD,[H], where rc 5 A is the interaction radius. It was then assumed that Doxy(enh) = Pd’, where d is the oxygen diffusion jump distance. If both D, and [HI were known, it would be possible to calculate Doxyfor this model which presumes a spontaneous diffusion jump of 0,.The permeation measurements of van Wieringen and Warmoltz (1956) yielded a value of 2.3 eV for the sum of the activation energy of D, and the heat of solution of atomic hydrogen. The activation energy of Doxy(enh) should then be equal to this value. However, if there were a binding energy for the pair (Newman et al., 1991) (see Section VI), this estimate should be reduced and might give a value consistent with the experimental value of 1.7 to 2.0 eV, although the validity of extrapolations from high to low temperatures has already been questioned. Finally, we comment that there may have been some metallic impurities (copper) in the as-grown material and further limited amounts of contamination may have been introduced during plasma treatments. There is no evidence that fast diffusing metallic impurities lead directly to enhancements in Dpxy but it has been proposed that the presence of copper catalyzes the dissociation of H, (tritium) molecules in Ge crystals so that the concentration of atomic hydrogen is increased (Hansen, Haller and Luke, 1982). If the same process occurred in Si, indirect enhancements of Doxycould also result (Newman et al., 1991).

-

VI. Theoretical Modeling of Oxygen Diffusion

In spite of the colossal number of experimental studies of oxygen aggregation in silicon, there have been comparatively few fundamental theoretical studies of oxygen complexes and their migration. In part, this is because of the complexity of the problem. One needs a method that is capable of describing the way in which 0 atoms push themselves into Si-Si bonds, enlarging and possibly breaking them. The method must also be able to handle 0-vacancy, Oi-Oi and 0,-self-interstitial interactions as well as saddle-point geometries where over- and undercoordinated oxygen and silicon atoms might exist: some of these defects have gap levels and might diffuse as a charged species. It is clear that empirical interatomic potentials that have been developed for a number of isolated defects cannot be relied on to predict, with confidence, the properties of these oxygen complexes. Instead one requires a method that solves the many-body Schrodinger equation for the electrons and nuclei, within the

8.

DIFFUSION O F OXYGEN I N SILICON

327

Born-Oppenheimer approximation, computing the total energy and then moving the atoms until this energy is minimized. It is only recently that efficient methods of dealing with this Schrodinger equation and the substantial computational resources they require have become available, as discussed in Section VI. I . In Section VI.2 we describe reaction rate theory that is at the heart of any calculation of 0 diffusion at temperatures much lower than barrier heights. We then describe in Section V1.3 results that have been obtained for interstitial oxygen. 0 , ,including its activation energy for a diffusion jump to an adjacent bond centered site, and in Section V1.4 how the presence of atomic hydrogen can catalyze this motion. The first stage of oxygen aggregation probably involves a pairing of two 0, defects. This does not result in an oxygen molecule but an Si-0,Si-Oi-Si unit. Its structure and binding energy is contentious, and there is only one work that describes its diffusion, as discussed in Section V1.5. Finally, in Section V1.6 a discussion is given of several other oxygen complexes. 1. THEORETICAL METHODS

The two standard methods of calculating the energy and structure of a defect by solving the many-body Schrodinger equation are based on Hartree-Fock (HF) and local density function (LDF) theories (Lundqvist and March, 1986; Ihm, 1988). ‘They are not devoid of approximations and assumptions but they have been found to be particularly useful for ground-state molecular and crystalline structures. They are both variational procedures with H F theory assuming the wavefunction to be the variational variable whereas LDF theory, applicable only to nondegenerate ground states. takes it to be the charge density. The former variable is a function of the coordinates of all the electrons whereas the latter is a function of just three coordinates. In the spin-polarized version. the variational variables include the magnetization density. Both theories can be written in terms of single-particle Schrodinger equations with the potential acting on an electron arising from an effective field due to all the others. Thus both require a self-consistent equation to be solved. However there are important differences-especially in the treatment of exchange and correlation. HI; theory ignores the latter and its inclusion i.ia, say, Moller-Plesset perturbation theory is unwieldy. LDF theory includes an exchange-correlation term derived from the homogeneous electron gas but its utility in multi-atomic systems, where the charge density varies rapidly, is well proven. The exchange energy in H F theory is a four-center integral and its

328

R. C. NEWMAN AND R. JONES

evaluation requires the computation of O(N4)integrals, where N is the basis size. This is to be contrasted with LDF theory where the exchangecorrelation energy is an integral of a function of the electron density n ( r ) and its evaluation requires O ( N * M )computations where M is the number of points or operations involved in estimating this integral. The development of pseudopotentials (Yin and Cohen, 1982; Bachelet, Hamann and Schluter, 1982) that remove core electrons from the problem, leaving only the valance electrons to be considered, has been essential in allowing systems containing large numbers of Si atoms surrounding oxygen to be treated. The total electron density is composed of two parts, namely, a core density, which is the sum of contributions from different atomic cores and is large near each nucleus but falls off rapidly to zero outside the core, and the valence charge density, which although varying rapidly near the core (because of the constraints imposed by orthogonalization) is relatively smooth round the centers of chemical bonds. Norm-conserving pseudopotentials (Bachelet et al., 1982) have pseudowavefunctions that agree exactly with those of the true atom outside the core. Thus the charge density, exchange-correlation potential and Hartree potential derived from the pseudopotential are exactly the same as those given by a full atom calculation. Inside the core, the pseudopotential has a repulsive part making the pseudo-wavefunctions smooth and nodeless and this makes it easier to represent them with a simple basis-although the 2p 0 orbital causes problems when a basis of plane waves is utilized. This repulsive potential is chosen so that (a) the energy levels agree with the valence levels of the atom, (b) the scattering phase shifts are the same for the atom and pseudo-atom and (c) the core of the pseudo-atom contains the same charge as the true atom. These properties make the repulsive potential dependent on the orbital angular momentum and consequently the pseudopotential is a nonlocal operator. The belief is that these pseudopotentials can correctly describe different types of bonding between atoms but there is no formal proof of this. The nature of the exchange energy in HF theory involving the product of four orbital functions, some of which may be core ones, has made it more difficult to develop reliable pseudopotentials. It is for this reason that few calculations on large systems have been carried out (but see Mark et al., 1989; Nada et al., 1990) and instead a multitude of approximate methods have been developed. Those with the abbreviations CNDO and M I N D 0 ignore integrals representing matrix elements involving a pair of basis functions at distinct sites. Of course, there is no compelling mathematical reason for this, and it is then necessary to adjust the diagonal contributions. This is done by using fits to an empirical data base consisting usually of equilibrium geometries, ionization potentials and

8.

DIFFU5ION O F OXYGEN IN SILICON

329

other spectroscopic information. It is difficult to be persuaded that these methods can consistently model oxygen defects correctly, especially those far away from the fitted data base at a saddle point or other unusual bonding configurations. Nevertheless, there has been an accumulation of wisdom in using these methods extending over a decade, and the method, in the right hands. can yield great insight into complex defects and processes. It appears, for example, that the geometries predicted by the method are often very good; the frequencies of local vibrational modes are invariably overestimated, but often by a constant amount that allows systematic scaling. Deak and Snyder (1987) employ a variant of the M I N D 0 / 3 scheme, namely, ;t cyclic-cluster scheme, in which the wavefunction is forced to be periodic within the cluster. The method seems to give surprisingly good formation and migration energies. Nowadays, however, the emphasis is on using ab initio or more correctly parameter-free methods. There is no appeal to any empirical data base but the main deficiencies lie in The simplistic treatment of exchange-correlation; B . The incompleteness of the basis sets used to represent the wavefunction or charge density; c. The size of the cluster or supercell; D. The difficulty in assessing whether the relaxation procedure has produced a global or local energy minimum (i.e., one corresponding to a metastable structure); E. The convergence of the difference in the energy of the stable and saddle-po'int structures for the determination of migration energies; F. The accurate location of donor and acceptor levels that control the charge states of the diffusing species; G . The limitation to zero-temperature that prevents thermal expansion effects from being included.

A.

In practice, it seems that the methods can yield excellent structures and fair vibraticinal modes, but the errors in defect energies are much greater. For example. the oxygen molecule has been studied by spinpolarized LDF 1:heory (Kutrler and Painter, 1992). The O2 bond length was found to be I .21 A compared with an experimental value of 1.207 A . The frequen'cy of the stretch mode is calculated to be 1606 c m - ' compared with ;in observed one of I580 c m - ' , but the binding energy. 7.53 eV, is 44'3greater than that observed (5.21 eV). This can be substantially improved lo 5.4 eV if gradient contributions to the exchange correlation energy are used. Up to now, these have not been used to treat oxygen diffusion. It is uxually considered, however, that much of the

330

R. C . NEWMAN AND R. JONES

error in the binding energy occurs for the dissociated structure and that energy differences between similar structures are given more accurately. For H F itself, the method of PRDDO (partial retention of diatomic overlap) developed by Halgren and Lipscomb (1973) has given useful results in a number of problems involving impurities in Si-especially hydrogen and oxygen (Estreicher, 1992). Here one is judicious in the neglect of products of basis functions by requiring the basis functions to be orthogonal. Only the four center integrals involving distinct sites are neglected. In this way no parameters are necessary and the method seems efficient at giving sensible bond lengths. There are difficulties for saddle point energies-invariably too large (an effect that can happen in any theory where a seriously incomplete basis is used) and in determining vibrational modes. Gaussian basis functions have been a popular choice for both CNDO and MINDO, as well as LDF theories. Saito and Oshiyama (1988) as well as Jones ( 1988) describe methods of implementing LDF schemes, using such orbitals, for clusters. In the cluster method it is necessary to terminate the cluster in such a way that the properties of the inner part are insensitive to this surface. Most workers have used H atom saturation. The idea here is to passivate surface dangling bonds that would otherwise draw charge from the inner part of the cluster to the surface and interfere greatly with the properties of the defect lying there. It is important to choose a short H-surface length as this depresses the H-bonding states below the bulk valence band top and elevates the H-antibonding states to energies above the bulk conduction band. However, since the host feels a confining potential from the surface H atoms, its valence and conduction bands are also depressed and elevated, respectively, resulting in an increased band gap. However, it seems that this band gap widening does not significantly affect structural or vibrational properties, although it does lead to defect levels lying deeper in the gap than observed. It is known that small Hterminated molecules have structures and vibratory modes close to those of the bulk. For example, disiloxane, (SiH,), 0, has an 5-0 length of 1.634 A and vibrational modes at 1107 cm-' and 606 cm-I, which lie close to those parameters for interstitial oxygen in Si, namely, 1.6 A, 1136 cm-l and 515 cm-' (Stavola, 1984). Saito and Oshiyama (1988) use clusters containing up to 36 atoms, whereas Jones, Oberg and Umerski (1991) as well as Estreicher (1990) use clusters up to 86 atoms. There are two ways of avoiding the use of clusters. One uses either a Green function technique or a supercell. Kelly and Car (1992) describe a Green function approach using Gaussian orbitals and incorporating pseudopotentials. The advantage of this method is that one treats an isolated

8.

DIFFCI5ION O F O X \ G E N IN SILICON

33 1

defect in an infinite Si lattice. The usual problem with the Green function method is the difficulty of including the relaxation of a large number of atoms. The more atoms one relaxes. the greater the number of elements of the Green function that are required and this makes the method very time consuming. Other LDF calculations have been carried out using plane waves and a supercell sometimes with the molecular dynamical method of Car and Parrinello (1984). Here one treats the degrees of freedom of the electrons, namely, the coefficients of the expansion of each orbital in terms of plane waves, together with the positions of the ions as a set of generalized coordinates in analytical dynamics. The Lagrangian for this system can then be written down together with the equations of motion. These can be solved as in the usual molecular dynamical method. The ion temperature is then gradually reduced to enable the system to assume the lowest potential energy. This technique allows very large numbers of plane waves to be used in the basis. Needels et al. (1991) adopt it to relax unit cells containing up to 65 atoms with the Kleinman and Bylander (1982) form of the pseudopotential.

2.

T H E O R Y OF T H E

DIFFUSION cONSIAN'I

The standard amlytical tool for an evaluation of the hopping rate. for, say, 0;from one bond center to the adjacent one, is provided by reactionrate theory (Vinyard, 1957). Here the adiabatic potential energy surface plays a fundamental role. Thc Born-Oppenheimer approximation is used at the outset to describe the cnergy of any assemblage of atoms in terms of their positions only, the electrons being assumed always to occupy the ground state, The theory assumes that this potential surface, in the neighborhoods of both the stable and saddle points of the diffusing species, can be approximated by a Taylor series expansion up to secondorder terms. Of course the first-order terms are absent as the energy derivatives vanish at the stable and saddle points. The second derivatives of the energy at these points determine, via the dynamical matrix. the vibrational frequencies of atoms. At the saddle point, at least one of these frequencies is imaginary as the energy is locally a maximum along the corresponding normal mode. We suppose that the real frequencies at the stable and saddle points are i',and w,'. respectively. It is further assumed that, as a result of thermal fluctuations. the system visits each of these points as time evolves but if it enters the saddle surface then it always crosses it so that a diffusion event occurs. The ergodic assumption of statistical mechanics tells us that the relative probability of the system being in each of these points is related to the free energy of each. The

332

R . C. NEWMAN AND R . JONES

jump rate from the stable to the saddle point is then given by (Vinyard, 1957) rIVi

-exp( - AE/kBT). IIV,!

Here AE is the adiabatic potential energy difference between the saddle point and the stable one. Strictly speaking, this energy should include the effects of thermal expansion. If we identify the pre-exponential factor as a Debye frequency scaled by motion entropy, this rate is written as v exp(ASlk,

-

AE/k,T).

(7)

Now, the pre-exponential factor observed for the diffusion constant is 0.13 cm2 s - ' (Table 11) (Mikkelsen, 1986) and leads to a jump attempt rate of 3.5 x I O l 4 s - ' , which is about 35 times the Debye frequency, suggesting a motional entropy of about 3-4kB. There are several ways in which this entropy can be greater than zero (Stoneham, 1989). A. A saddle-point structure could have one or more very low frequencies. We shall discuss this later and suggest that the saddle surface does appear to be quite flat; B. It could result from thermal expansion. Stoneham (1989) finds a large effect due to thermal expansion on the cation mobility in MgO and it is not unreasonable that a similar effect would occur for Oimigration in silicon. C. The occupied gap levels at the saddle point may be temperature dependent. The Si band gap decreases quite rapidly with temperature leading to an effective entropy of about 5 k B . If there were an occupied gap level in the saddle-point configuration that also became shallower with increasing temperature, then one would expect the effective activation energy, A E ( T), to be temperature dependent. This follows from the fact that this occupied energy level also contributes to the total energy. Writing AE(T)

=

AE(0) - akBT,

(8)

shows that the entropy includes the term a . None of these effects has been properly discussed in relation to oxygen diffusion.

3. INTERSTITIAL OXYGEN Interstitial oxygen, O i , is not found at any high symmetry site in the Si lattice but it is customary to refer to its location as the nearest such

8.

333

DIFFLI5ION O F O X Y G E N I N SILICON

FIG. 2 0 . Location of various high-symmetry 4tes in the diamond structure. T is the tetrahedral interstitial site. H is the hexagonal interstitial site, BC is the bond center. and C is at the center of a rhombus formed by three adjacent Si atoms and the nearest T \ite. The M site is midway between two c' sites; it is also located midway between BC and a neighboring H site (Van de Walle. 1991 1.

Calculat iori

Snyder. Wu and Deiik. 1989 Ebtreicher. 1990 Jones et al.. 1991 Saito and Oshiyarna. 1988 Kelly and Car. 1992 Needels et al.. 1991 Bowmworth el al.. 1970 Newman. 1973

SI-0 Length (A)

Modes.

Barrier'

Angle (deg.)

(ern-')

(SV)

I80

1275. 699

SI-0-SI

I61 I $66 I 5Y I 6x I 77 I h4

I64

I72

1104. 554

152

I I87

I40 140 162

1136. 518

2.5 3. I 2.X I. ? 2.5

I .x 25

~~~~~

'The barrier for a diffusion jump relet\ to the C site

site. Thus oxygen at a bond center (BC) site refers to 0; near the center of neighboring Si atoms. Other important sites are t h e center of next-tonearest neighboriing Si atoms (the C site), and the antibonding (AB) site found midway between a Si site and the nearest interstitial tetrahedral (T) site. There is general agreement that 0,is stable at a BC site (Fig. 20). Table 111 shows the properties of this defect as calculated by different groups. Most workers allow the 0, atom and perhaps two shells of host atoms to relax. Kelly and Car (1992) allow the 0, atom to move perpendicular to the Si-Si bond from its BC site. while this bond, together with its neigh-

334

R. C . NEWMAN AND R. JONES

bors, can expand along their lengths. Their calculated length of the Si-0 bond seems to be too large to explain the high-frequency asymmetric Si-0 stretch mode, as it is recalled that the observed Si-0 length in disiloxane is 1.634 A, yet the frequency is close to that of 0;. The general consensus is that the Si-0 bond length for 0; is around I .6 rather close to that found in a-quartz, 1.60-1.61 p\ (Levien, Prewitt and Weidner, 1980). There is greater variation in the Si-0,-Si angle. It seems quite difficult to calculate this as there appears to be a rather flat potential energy surface for greater Si-0 lengths and smaller angles. Bosomworth et al. (1970) estimated this angle by fitting overtones of the 29.3 c m - ' bend mode to a simple potential for which they deduced a Si-0,-Si angle to be 1 6 4 , supposing a Si-0 length of I .6 A. The symmetric and asymmetric stretch modes are well reproduced by most calculations. Jones et al. (1992) also found their isotopic shifts to be in good agreement with experiment. The energy barrier for a diffusion jump of Oihas been calculated by a number of groups, who often assume that the saddle point occurs near the C-site. Jones et al. (1991) explicitly verified this assumption by mapping out the potential energy surface obtained by their LDF cluster approach. Saito and Oshiyama (1988) also showed that the C-site is unstable. The saddle-point structure is relevant to understanding how the barrier can be reduced by the presence of other defects. Jones et al. (1991) find the Si( 1)-0, Si(2)-0 and Si( I)-Si(2) bonds (see Fig. 21) have lengths 1.54, 2.31 and 2.86 (broken) A, respectively, together with an occupied low gap level. Saito and Oshiyama (1988) give 1.74, 1.9 and 2.62 A for these lengths with mid-gap occupied and empty levels. Snyder and Corbett (1986) give 1.67, 2.02 A for the first two 0-Si lengths, whereas Kelly and Car report 2.0, 1.93 A and Needels et al. (1991) find

A,

FIG.21. Oxygen at the C-site

8.

DIFFUSION ( I F O X Y G F N IN SILICON

335

1.69 and 1.93 A . Kelly and Car find only an acceptor state low in the gap. Thus there are very great differences between the calculations. This may be because the potential energy near the saddle point is rather flat, and this in turn might lead to low vibration frequencies there explaining the large entropy factor mentioned previously. Turning to the diffusion jump energies given in Table 111, we note the wide disparity of values. Snyder. Wu and Deak (1989) and Jones et al. ( 1991) report barriers close to that measured (2.5 eV). Estreicher's barrier is too large but this is not unexpected, as the barriers are sensitive to the sizes of basis sets. Other barriers straddle t h e measured value, and the differences are usually regarded as reflecting the technical deficiencies of the calculation, e.g., the inadequate size of the cluster, basis or relaxation method used. A counterview is taken by Ncedels et al. (1991) who believe that the adiabatic saddle point is indeed 0.7 eV lower in energy than the measured value of 2.53. This deficiency would then imply the breakdown of reaction rate theory. They argue that although an 0; atom, provided with about 1.8 eV of kinetic energy moves close t o the saddle point, it fails to open up the attacked Si-Si bond and returns to its starting point. They suggest that the 0, atom must develop kinetic energy of around 2 . 3 eV to avoid this return. However. it is not clear that the 0 atom will invariably return to its starting point and especially so if the attacked Si-Si bond is provided with at least a share of the 1.8 eV, allowing it to open up and permitting the energetic 0 atom to enter its bond center. The deficiency of 0.7 eV found by these authors might arise from the method employed. the pseudopotential used or indeed the use of LDF theory. This is a serious charge against the theory and further work is called for. 4. DIFFUSION OF 0, CA.I.ALYZEU HL HYDROGEN

There are two theories for the enhancement in the diffusion jump rate of 0, in the presence of H. We emphasiLed previously that in the saddlepoint structure one of the silicon atoms, Si(l) of Fig. 21, possesses a dangling bond. A nearby H atom may form a strong bond with this Si atom. leading to a reduction in the saddle-point energy. This assumes that, in the starting structure, when 0 is at BC site, the hydrogen is only weakly bound. Estreicher (19990) found that a H atom in the starting structure was most stable at a BC site adjacent to 0,.The energy for a metastable state with H near one of the three equivalent T sites (Fig. 2 2 ) was 0.66 e V higher. He argued that. when H is located near this metastable T site, it is able to lower the barrier for 0 migrating to the C site through the

336

R. C. NEWMAN AND R. JONES

FIG.22. The configurations of atoms according to Estreicher (1990) for 0, diffusion in the presence of hydrogen: (a) BC sited H , (b) H at T site, (c) saddle point, involving 0, with normal coordination and H overcoordinated, (d) final state with same energy as (a).

formation of the Si( 1)-H bond and leaving 0 bonded to two atoms. This barrier, when H is initially at the T site (Fig. 22), is 1.25 eV and is much lower than that in the absence of H. The final configuration then consists of H and 0 at adjacent BC sites. It seems to us, however, that the true activation energy must include the energy necessary for the H atom to get to the T site from the lowest energy configuration, i.e., a BC one, provided that thermal equilibrium prevails. This simply adds 0.66 eV to the preceding barrier and still provides a significant reduction of the 4.1 eV barrier found in the absence of H (Table 111). However, Estreicher argued that thermal equilibrium is not established and that an H atom is unable to enter the BC site, in the absence of O i , because of a high barrier between it and the T site. Thus, when H is introduced into the crystal, it diffuses by jumping between T sites and rarely enters a BC site; if it did enter a BC site it would remain trapped there. The diffusing Oiatom, however, promotes a movement of H into the BC site. He argued that a muon spin rotation experiment in oxygen-rich Si provides support for this viewpoint as no signal is observed due to muons located at T sites, in contrast to 0-free Si (Patterson

8.

DIFFU5ION (Ib OXYGEN IN SILICON

337

et al.. 1984). This view, that H is unable to reach its lowest energy site is not universally shared, as other calculations show rather low barriers for H to transfer from BC and to T sites (van de Walle et al., 1989; Buda et al., 1989; Briddon and Jones 1990). The energy profile during the migration is sketched in Fig. 2 3 . There is a problem with this model concerning what happens during subsequent oxygen jumps because i t is not clear whether the 0 - H complex dissociates or whether another H atom promotes the later 0,jumps. Jones et al. (1991). however, did not find the BC site adjacent to 0, to have the lowest energy for H but instead t h e AB site opposite Si-0-Si (Fig. 34). They believed the stability of this site was caused by polarization of the H atom originating from the Si-0-Si unit. The Si-H length was 1.5 A. and there was ;I hydrogen-related singly occupied mid-gap level. Relative to this structure. the energy of the BC site was higher by 1.5 eV and there were increases of 0.75 eV at the other three T sites. With H at the AB site and with 0 moved to the C-site, the energy increase is only 0.2 eV. Thus the previous barrier of 2.8 eV (Table 111) has been effectively eliminated. This is because the Si(I)-H bond has strengthened and reduced in length to 1.45 A. A H-related gap level is now filled and lies close to the valence band, E, . There remains a partially filled mid-gap state that is localized on 0 and has some overlap with the H atom. Now, when 0 moves away from the C-site, the energy increases because the Si(l)-H bond starts to weaken and a bond is formed between Si(I) and Si(2). The new activation barrier is found to be 1.4 eV, somewhat lower than the observed barrier. When the 0 atom moves to its

(a)

(b)

(c)

(d)

FIG.2 3 . Energy profile during 0, migration. according to Estreicher (1990):(a). ( h l . ( c ) . and ( d ) refer to the sites 5hown in Fig. 22.

338

R. C . NEWMAN A N D R. JONES

(c)b

Si

Si #'

0''

FIG.24. Configuration of atoms during 0,migration in the presence of hydrogen according to Jones et al. (1991): (a) H at AB site to Si-0,-Si, (b) saddle point with overcoordinated 0 only. ( c ) T site, (d) final structure with same energy as (a).

new bond-centered site, H is now no longer in the lowest energy configuration and must jump to a new antibonding site. It has to move to the further one if long range Oi migration is to occur. The energy profile is sketched in Fig. 25. It is not possible to say which of these two models is correct at the present time. Both of these theories assume that H is in a neutral charge state. Consider now the diffusion of Oiin the presence of H + or H - . Here, the starting structure possesses donor and acceptor H-related gap levels at, say, E d , and E,, , respectively. If the saddle point involves a strong Si-H bond, the H-related level must be full and low lying. There are likely to be higher gap levels, Ed2 and E,, associated with trivalent 0, which are empty and filled in p-type and n-type Si, respectively. The activation energy is then changed from the neutral case by (Edl-EdZ) in p-type Si and (E,,-E,,) in n-type Si. If Ed2 > E d , , and E,, > E,, in p-type Si, we would expect the rate of diffusion jumps to be further enhanced, but H - would inhibit the process. However, it is possible to think of other mechanisms not involving a strong Si-H bond at the saddle point. It may

8.

339

D I F F U S I O N ofi O X Y G L N I N SILICON

be that H' forms a direct bond with O,, weakening the two Si-0 bonds and hence promoting diffusion of 0 - H but this needs to be investigated. In either case, one expects that the catalytic effect of H upon 0 diffusion to be Fermi-level dependent. 5 . THEOXYGEN DIMER

The first stage of 0, precipitation is considered to be the formation of a dimer. It appears that a pair of nearest neighbor bonded interstitial oxygen atoms is a more stable arrangement than one involving the formation of an oxygen mo/rcu/r (Kelly. 1989; Snyder et al., 1988; Needels et al., 1991). This result is in conflict with the idea of Gosele and Tan (1982) that rapidly diffusing mo/e.c.u/rslead to enhanced oxygen diffusion. Derik, Snyder and Corbett ( 1992) reported that Si, generation is endothermic at least for aggregates of less than four 0, atoms. Thus, there is no theoretical support for the old idea. based on the volume of SiO,. that Si, must be generated during the initial stages of precipitation. The current view is that the dimer consists of a di-oxygen interstitial defect bonded to the Si lattice. Snyder et al. (1988) found that a buckled dimer (Fig. 26) was stable with a binding energy of 0. I eV. Jones (1990), Umerski and Jones (1992) and Kelly (1989) found that a pair of oxygen atoms placed at two adjacent bond-centered sites buckled outwards from each other, although Kelly reported a small binding energy. Needels et al. (1991) found a binding energy of I eV (for an unexpected geometry of the two 0 atoms lying above and below the plane of the two Si-Si bonds they break). The defect has no gap states. Umerski and Jones (1993) found

(a)

(b)

(c)

(d)

FIG 2 5 . Energy profile during 0, migration in the presence of H . according to Jones e t al. (1991): ( a ) . ( b ) . ( c ) and ( d ) refer 10 the bites \hewn i n Fig. 24.

340

R . C. NEWMAN A N D R . JONES

FIG.26. Buckled oxygen dimer structure (Snyder et al., 1988).

that the 0-Si-0 lengths are shortened to 1.53 A, whereas the other two 0-Si bonds are 1.6 This implies that there should be two asymmetric stretch modes with at least one lying above the 1136 c m - ' mode of 0,. N o experimental evidence for these modes has been reported from IR measurements. This may be understood if the defect was rather mobile forming a trimer. Indeed Snyder et and diffused quickly to another Oi, al. (1988) found an extremely low migration energy of the dimer of only 1.36 eV. They argued that the saddle point or its migration is close to a four-membered ring of two trivalent 0 atoms and a pair of Si atoms (Fig. 27). In essence, one 0 atom pulls the other through the barrier. Presumably the reason for the low migration barrier is that the saddle-point structure is stabilized, perhaps by a mechanism similar to that discussed earlier for the H atom. The essential point is that the silicon atoms are always fourfold coordinated and no Si dangling bond is created. Few details are given in the calculation and it would be useful to have this result confirmed by others.

A.

0 FIG.27. Saddle-point structure for oxygen dimer migration (Snyder et al.. 1988).

8.

DIFFUSION O F OXYGEN 1N SILICON

34 I

There has been considerable theoretical work on a vacancy containing a single 0 atom. The V 0 defect (A-center) (Watkins and Corbett, 1961: Corbett et al., 1961 1. and this has been discussed by DeLeo, Fowler and Watkins (1984). using MIND0 and X-a methods applied to H-terminated clusters containing up to 53 atoms. They found that 0 moved off-site along [IOO], as is observed, by about I A for a smaller 17 atom cluster and much less so for a largei- one. For the smaller cluster, t h e barrier to a reorientation of the oxygen atom within the VO defect is 0.47 eV. close to the measured value of 0.38 eV. Using a large cluster and modified spring constants for more remote atoms, they deduced the 0 stretch mode frequency to be 806 cm I. in excellent agreement with that of 836 cm (77 K ) observed experimentally but no attempt was made to calculate the migration barrier of the A-center. Snyder et al. (1989) and Deik et al. (1989) reported MIND013 calculations on 53 atom clusters and found that 0 moved off-site by I .22 A along a [ 1001 direction. The Si-0 bond lengths were I.66 A. and the 0 stretch mode occurred at 908 cm I . The upper region of the gap contained a bonding and antibonding pair of defect states, rather close together. N o information was given about the reorientation energy. Chadi ( 1990) reported that the Si-0 bond lengths, the weak Si-Si lengths and the Si-0-Si angle for the negatively charged defect were 1.7 A, 2.61 A and IW. respectively. Kelly (1989) found that the 0 atom lies along a [ I I I ] direction in contradiction to experiment. DeLeo. Milsted and Kralick ( 1985) and Snyder et al. (1989) have also investigated VO:. They both reported structures with Dld symmetry. in conflict with the observations of Bosomworth et al. (1970). However their calculated E vibrational modes at 847 c m - ' and 951 c m - ' . respectively, are in excellent agreement with that observed at 889 c m - ' . Snyder et al. (1989) calculated Si-0 lengths of 1.67 A and the 0-0 separation to be 2.66 A for this defect.

'

~

6 . Oxy-vgeti Conip1exc.s bt9ith S ~ . l f l l ~ ~ ~ . r - s t i t i a l s

Deak et a]. (1989. 1991, 1992) discussed O i l and ( 0 , ) : I complexes. They found that the 0 atoms readily formed over coordinated defects just as at the saddle-point structure (Fig. 21). If 0 forms a third bond, from the overlap of an 0 lone-pair orbital with an occupied sp3 Si hybrid. then an antibonding state must be occupied. The level associated with such a state must lie high up in the gap, and the defect would readily act as donor. They suggested that the defect shown in Fig. 28 is a candidate for

342

R . C . NEWMAN A N D R. JONES

tZ

Silicon atom

0 Oxygen atom FIG.28. 0,Ithermal donor model (Deak et al., 1992).

the thermal donor. There is support for oxygen over coordination from theoretical investigations of the Cj-Oj defect (Jones and Oberg, 1992) and from instabilities in simple models of thermal donors as mentioned earlier (Jones, 1990). In the former case, the 0 atom is bonded to a third Si atom, which is positively charged, having lost its electron to an adjacent carbon interstitial atom. This interaction stabilizes the overcoordination so that the defect thermally dissociates at a relatively high temperature of 300°C. Two important and unanswered questions concerning this model of the donor by Deak et al. are (a) whether its binding energy is sufficient to allow it to remain stable at 350-450°C and (b) what is the origin of the silicon interstitials that form the defect. It is essential to obtain accurate answers to these questions before the model can be accepted as a serious candidate for the thermal donor. VII. Constraints on Models of Thermal Donor Centers

Unless hydrogen impurities are present, the evidence for enhancements in Doxyin as-grown samples is minimal for 500°C 2 T 2 400°C: there may be an enhancement not exceeding a factor of -10 at 350°C during very extended heat treatments (Section 111.3) but a negligible enhancement at 450°C. These conclusions have important consequences relating to the maximum size of oxygen aggregates that can form at low temperatures, which in turn places severe constraints on models of TD centers. The set of coupled differential equations describing the aggregation of Oiatoms to form oxygen clusters O,, O,, etc. with the assumption of diffusion limited kinetics has been given by Tan et al. (1986) and related

8.

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DIFFUSION Oi- 0 X Y G L . N IN SILICON

to measurements of the rate of loss of 0, atoms from solution during furnace annealings at 450°C. It was first assumed that there were no oxygen clusters present in the as-received material and calculations then led to the evolution of the various aggregates as shown in Fig. 29. A normal value of Do,y was required to explain the rate of oxygen loss, leading to the conclusion that loz] IO" cm-' and [O,] - 1Olh c m - ' after some 100-300 hrs of annealing. An important point is that [O,] is much greater than the concentration of [TD] 10l6cm13, while [TD] is much greater than LO,]. It follows that if TD centers involve only O2 defects in their cores, not all O2 defects can be TD centers. On the other hand, the possibility that TD centers contain 0, cores would be excluded on the basis of this model. However. if 0, defects were significantly more mobile than 0,atoms (Gosele and Tan. 1982; Gosele et al., 1989) it would be possible for them to be trapped by remaining 0, impurities to form 0, centers at a rate effectively equal to the previous rate of formation of O2 defects. It follows that the rate of loss of 0, from solution would be greater than originally calculated by -SO%, but this change could be accommodated by reducing the estimated value of Do,, (or the capture radius, r, , Section 111.3) by 33%. The resulting O3 defects would then be converted to 0, defects in a concentration of -10" cm-3 after -200 hrs by the capture of another diffusing 0,atom. However, it would be difficult to identify an 0, defect with a thermal donor, as the formation rate of

-

-

0

1

2 3 4 Anneal time ( 1 Oz h)

5

FIL. 79. The evolution of oxygen aggregates 0:.01,04.etc.. with annealing time at 450°C' calculated for a normal value of I),,,, (Tan el al., 1986).

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R . C . NEWMAN AND R. JONES

the latter defect has now been shown to be proportional to [0,12 at T < 400°C (Londos et al., 1993). In their second model Tan et al. (1986) assumed that there were grownin O2 centers in a concentration of 9 x loi6 cm-3 in their as-received silicon bodes. The existence of a low concentration of such pairs is to be expected since there would be diffusion and aggregation of 0, atoms as the growing Cz crystal cooled to room temperature (Fraundorf et al., 1985). Measurements of the strength of the 9 pm band in heated samples sometimes show an increase compared with the strength in the asreceived material, implying that the heat treatment leads to the redissolution of very tiny oxygen aggregates (see, for example, Hahn, Shatas and Stein, 1986). Tan et al. (1986) went on to show that this second model could also explain their measurements of d[O,]ldr at 450°C. The calculated concentration of 0, centers remained close to 10'' cm-3 throughout the heat treatment, while the concentration of 0, clusters increased progressively and accounted primarily for the loss of 0,atoms from solution with a normal value of Doxy.It was again found that the calculated values of Doxyincreased linearly with [O,],. The possibility that 0, complexes might be identified with TD centers appeared to be less favorable than for the first model. The possibility that 0, defects were mobile was not considered, but if they were, there would be formation of larger oxygen clusters. There have been various measurements of the ratio of the loss of oxygen from solution to the number of donors generated A[O,]/A[TD]. Some of the reported variations relate to changes (28%) that have been made to the IR calibration coefficient of the 9 pm IR band (see Baghdadi et al., 1989), which in turn lead to changes in the estimated value of A[O,]. Other variations can be attributed to the presence of residual carbon impurities in samples, leading to values of A[O,]/A[TD] that are larger than for more pure samples. Taking an average for all samples, including those examined most recently (see Fig. 8 and Binns, 1994) the numerical value of the ratio is close to 10 ? 2 (using the calibration of Baghdadi et al.) for samples heated at any temperature T I450"C, irrespective of whether Doxywas normal or enhanced by the presence of hydrogen. The ratio was also constant for all heating times from zero up to the stage where [TD] became close to its maximum value. This result again demonstrates that not all 0, defects can be TD centers, but it is difficult to understand how TD centers could be associated with aggregates of oxygen atoms with no involvement of other components even if 0, pairs had a high diffusion coefficient. Thus, the formation of TD(N) from the similar double donor TD(N - 1) would require the incorporation of additional oxygen atoms, without increasing the number of donors, contrary to the

8.

DIFEU$ION O b O X Y L F N IN SILICON

345

almost constant value of AIOi]/AITD]. A possible defect is an /-atom, generated at some stage during the oxygen precipitation (see Mathiot, 1987, 1988). VIII. Summary

Microscopic measurements of Do,, derived from measurements of internal friction and the relaxation of stress-induced dichroism show that normal oxygen diffusion occurs by a single process over the whole temperature range from 1400°C to 300°C, with an activation energy close to 2 . S eV (Table 11). This result is in accord with first principles theory relating to diffusion jumps from one bond-centered site to the next. without the involvement of a vacancy. self-interstitial or a n y other impurity. These results have been supported by measurements of oxygen diffused profiles at high temperatures, and it has also been shown that the rate of oxygen precipitation is controlled primarily by the rate of diffusion. even though there is generation of self-interstitials at the matrix-precipitate interface. However, similar generation of /-atoms at the surface may lead to enhanced out-diffusion of 0, atoms at 750°C in carbon doped silicon. Further measurements are required to confirm this process. It is at lower temperatures (7' < 650°C) that there have been claims of enhanced oxygen diffusion which have gained wide recognition. One suggestion of an enhancement by a factor of lo4 to explain t h e formation of the structure originally believed to be coesite has been withdrawn, and the structure has been reassigned to hexagonal Si nucleated by I-atoms released during aggregation of 0, atoms. Subsequently, the reassignment has been questioned but no positive alternative interpretation was ad. vanced. Published SIMS measurements have implied values of D o x yenhanced by factors of up to lo4. and have been interpreted in terms of the rapid diffusion of Oz pairs. For 7 < 500"C, the evidence for enhancements in Doh!from direct measurement is in no sense overwhelming, unless samples contain hydrogen impurities or are subjected to 2 MeV electron irradiation. The latter process when there is sequential trapping of vacancies and 1-atoms by 0, impurities is easily understood, while two models have been proposed for interactions of hydrogen with 0, atoms and provide a basis for underInteractions of 0; impurities standing observed enhancements in with either vacancies or /-atoms alone have been examined by theory. and there is also experimental evidence that demonstrates the existence of binding energies with both types of defect. A central problem is to know whether or not there is a constant supply of vacancies or I-atoms present in heated samples. Contrary to an earlier suggestion. there is now

-

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R. C. NEWMAN AND R. JONES

no evidence that the presence of metallic contaminants leads directly to enhanced 0;diffusion, but they may be lead to dissociation of H, pairs to generate atomic hydrogen so that Doxyis enhanced indirectly. We are then led to the following basic questions that still need to be answered. A. Do stable 0, defects form? These defects have not been observed by IR spectroscopy but they play the predominant role in proposed models of low temperature oxygen aggregation. B . If stable 0, centers form by two 0;atoms diffusing together, what is the magnitude of the capture radius? This result is important to the understanding of possible links between long-range diffusion and single diffusion jumps. In previous studies, Davies et al. (1987) have reported experimentally determined ratios of capture radii for various defect reactions involving V and I-atoms with numerical values up to 10.0 s 5.0. Since a minimum value of r, is 2 A, it is implied that larger values of rc = 20 k 10 A can sometimes occur. We have implied that a value of r,. = 10 A is appropriate to dimer formation but better fits of our data can be obtained with r, = 15 A. It would appear that these values cannot be dismissed as being physically unreasonable without further investigation. C. Are 0, defects more mobile than single Oiatoms? The answer to this question is of paramount importance with respect to the type of oxygen clusters that may form and to possible assignments to TD defects. In Section 111.2, we quoted the conclusions of Messoloras et al. (1987) that the measured rates of loss of oxygen from solution as a result of annealing in the range 500°C 5 T I600°C cannot sensibly be described by the theory of Ham (1958). In fact, the fitting of the data to theory yields two parameters, namely, c, and a rate constant K . The latter parameter is proportional to N"' Doxyand consequently, if the effective value of Doxywere enhanced by a factor of lo4, as shown in Fig. 4 (Gosele et al., 1989), the number density of oxygen aggregates would be lowered by a factor of lo6. In that case, the theory would be physically meaningful, because each particle would be predicted to contain -lo6 oxygen atoms after long anneals at SOOT, and it might be possible to identify the ribbonlike defects with oxygen aggregates (Bergholz et al. 1985). A clarification of the TEM data is required as a consequence of the work of Pirouz et al. (1990). D. Is there continuous generation of I-atoms during 0;atom aggregation at low temperatures when 0, formation would appear to be the dominant process for the loss of oxygen from solution? Evi-

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DIFFU\ION O F OXYGEN I N SILICON

347

dence relating to the loss of carbon from solution has been cited in favor of the process. but it is difficult to reconcile this proposal with first principles calculations for the formation of the I-atoms (Deak et al., 1992). If /-atoms are generated, they may be a major constituent of TD centers. If rapid diffusion of O2 occurs, so that there is formation of 0, aggregates, it could alternatively be proposed that there is f-atom emission at that stage. Further studies of TD centers by the ENDOR technique are required to distinguish oxygenlf-atom clubters from pure oxygen clusters.

In conclusion, it is now apparent that heat treatments of Si in hydrogen with E, = 1.7-2.0 eV that make ambients lead to enhancements in themselves apparent for 7 5 500°C. As a result, all the processes that depend on Doxq as the rate-limiting process are also enhanced by the same factor, including the formation of TD centers. The principal outstanding questions appear to be related to the properties of O2 defects. Further understanding will be difficult until answers are forthcoming to the questions that have been listed.

A(

KNOWLEDGMENTS

The authors would like to thank M . J . Binns, A . K. Brown. C. A . Londos. S. A . McQuaid. and J . H . Tucker for allowing their re\ult\ to he published prior to puhlication and a l w for their comment5 on the manuscript. C'. F.'. Dale I\ thanked for the preparation for the manuscript and N Powell for preparing the illu\ti-ations. The Science and Engineering Research Council of The United Kingdom are thanked for their financial support of this work

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Newman, R. C . , and Wakefield. J . (1962). I n Merallrrrgy of' Srmiconducror Mtrraricrls. 1 . B . Schroeder ( e d . ) . Vol. 15, p. 201. Interscience. New York. Oates. A . S . . Binns. M. J . . Newman. K . C . . Tucker. J . H.. Wilkes. J . G . . and Wilkinson. A . (1984). J . Pliv.\. c': Solid .S/cr/c, P / r ~ ' . s17, 5695. Oates, A . s.. and Newman, R. C . (I9X6\. A p p l . P h y s . [ - e f t . 49, 262. Oates. A . S.. Newman. R . C.. and Tucker. J . H. (1985). In 13rh /nr@rncrfiona/Con/i,reric,e on Drfrc.r.s iri .Sc,,,iic.c,nc/rrctc,r\ I Y X J . L. C'. Kimerling and J . M . Parsey. Jr. (ed5.l. p. 709. AIME, New York. O'Mara. W. C. (1983). In f r o ( w d i i i g . \ ( ~t hf e Svrnposicrm on Defecrs in Silicon. W . M . Bullis and 0. C . Kimerling ( e d s . ) . p. 120. The Electrochem SOC.. Pennington. N.J. Ourmard. A , . Schroter, W . . and Bourret. .4. (1984). J . A p p l . Pl1y.r. 56, 1670. Patrick. W.. Hearn. E., Westdorp. W . , and Bohg. A. (1979).J . A p p l . P h y s . 50, 7156. Patterson. B. 0.. Bosshard. A,. Strdumann. 11.. Truol. P.. Wuest. A , . and Wichert. T. (1984). Phvs. Re\,. Lett. 52, 938. Pirouz, P.. Dahmen. U., Westmacott. K. H., and Chaim. R. (1990). Acru M c r d l . M u t e r . 38, 329. Kamda\. A . K . . and Kao. M. G . (1966). Phv.~.K c v . 142, 451. Saito. M.. and Oshiyama. A. (1988). /'liv.\. R e i , . B 38. 10711. Shimura, F. (1986). J . Appl. Pliys. 59, 3251. Shimura, I-'. (1991). In Solid Sfcite P l i r ~ r i o n i c ~ r i19 u and 20, M. Kittler and H. Richter (ed\.), p. I . Trans. Tech. Pub.. Switrerland, Zurich. Shimura. F.. Balardo. J . P.. and Fraundorf. P. (1985). Appl. P h y s . Lrrr. 46, 941. Shimura. F.. Higuchi. T.. and Hochett. K . S. (1988).A p p l . Phys. Lett. 53, 69. Snyder. L . C., and Corbett. J . W. (I9Xh). Mu/ Kcs. S y m p . Proc. 59, 207. Snyder. L . C., Corbett. J. W . . Deak. f'., and Wu. R. (1988).Mar. Rex. S y m p . Pro(,. 104, 179. Snyder, L. C., Wu, R., and Derik. P. (1989). Rudinfion E.ffkcts und De&xt.s in Solids lll-ll2,393. Southgate. P. D. (1957). Proc. P h v c . So(.(London) B 70, 804. Southgate. 1'. D. (1960). Proc . Pliy\. .So( . iLondon) 36, 385. Stavola. M. (1984).Appl. Phys. Lcrt 44, 514. Stavola. M.. Patel. J . R.. Kimerling. 1.. C.. and Freeland. P . E. (1983). A p p l . Phy.c. L c t r . 42, 73. Stavola. M.. and Pearton, S . J . (1991). In I f y d r o g r n in Serniconduc.tor.c. J . 1. Pankoce and 3 . M. Johnson (eds.). Srrtiic.orrtlrr( /t,rc und Seinirnctol.s 34, p. 139. Academic Press: San Diego. Stavola. M.. and Snyder, L. C. (1983). I n I k f i . c r s in Silicon. W . M . Bullis and L C. Kimerling (eds.). p. 61. The Electrochemical Soc., Pennington. N.J. Stein. H . J . (1986). Mtrrcr. .S(.i. Fortrni 10-12, 935. Stein. H . J . . and Hahn. S . (1990a) A p p l . P h v ~ Lett. . 56, 63. Stein. H . J.. and Hahn. S . (199Oh). In Itit. ('orif: o t i Science and Trc lznol. of'Dcfert ( ' o n r r o l in Sc>rtiic.ond.. K . Sumino ( e d . ) . Vol I . p. 21 1. North-Holland. Amsterdarn. Stein. H . J . . and Hahn, S. ( 1 9 9 0 ~ )J. . E l w r r r d w t n . Soc. 137, 138. Stein. H . J.. and Hahn. S . (1992).,Murvr S c i . f.cwrrrn 83-87, 10.5 Stoneham. A. M. (1989). Physicu .Cc ripro T25, 17. Svensson. B. G . . and Lindstrom. 1 1,. (1986). P h v s . Re\.. B 34, 8709. Takano. Y . . and Maki. M. (1973). In Sc,rnic.onduc/or Silicon /Y7-?, H. R. Huff and K . R . Burger5 teds.). p. 469. Electrochein. Soc.. Pennington. N J . I an. T. Y. ( 1986). M a t e r . Re.\. So( . . S v r t i p Pro( . 59, 2h9. Tan. T. Y.. Kleinhenz, R.. and Schneider. c'. P. (1986). Muter. R e s . S M . S y m p . Proc 59, I

,

195.

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Taylor, W. J., Tan, T. Y., and Gosele, U. M. (1991). In Defects in Silicon 11, W. M. Bullis, U . M. Gosele and F. Shimura (eds.), p. 255. The Electrochem. SOC.,Pennington, N.J. Tipping, A. K., and Newman, R. C. (1987). Semicond Sci. and Techno/. 2, 315. Tipping, A. K . , Newrnan, R. C., Newton, D. C., and Tucker, J. H. (1986). Muter. Sci. Forum 10-12, 887. Urnerski. A., and Jones, R. (1993). Phil M a g . , A 67, 905. Van de Walle, C. G. (1991). Physica B 170, 21. Van de Walle, C. G., Denteneer, P. G. H., Bar-Yam, Y., and Pantelides, S. T. (1989). Phys. R e v . B 39, 10791. van Wieringen, A , , and Warmoltz, W. (1956). Physica 22, 849. Veloarisoa. 1. A., Stavola, M., Kozuch, D. M., Peale, R. E., and Watkins, G. D. (1991). A p p l . Phys. L e t t . 59, 2121. Veloarisoa, 1. A., Kozuch, D. M. Stavola, M., Peale, R. E., Watkins. G. D., Pearton, S. J . , Abernathy, C. R., and Hobson, W. S. (1992). Mater. Sci. Forum 83-87, 1 1 I . Vinyard, G. H. (1957). J . Phys. C h e m . Solids 3, 121. Wada, K. Inoue, N., and Kohra, K. (1980). J . Crystal Growth 49, 749. Wada. K., Nakanishi, J., Takaoka, T., and Inoue, N. (1982). J. Cryst. GroM,th 57, 337. Wagner, P. (1986). M a t . Res. S o c . S y m p . Proc. 59, 125. Watkins. G . D. (1975). Phys. Rev. B 12, 4383. Watkins, G. D., and Corbett, J. W. (1961). Phys. Rev. 121, 1001. Watkins, G. D., Corbett, J. W., and McDonald, R. S. (1982). J . Appl. Phys. 53, 7097. Woodbury, H. H., and Ludwig, G. W. (1960). Phys. Rev. Lett. 5, 96. Yin, M . T., and Cohen, M. L. (1982). Phys. Rev. 25, 7403.

S E M I C O N D I I i IONS 4NI) S k M I M E T A 1 . S . V O I . 42

CHAPTER 9

Mechanisms of Oxygen Precipitation: Some Quantitative Aspects T. Y . Tun

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W . J . Tuylor MOTOROLA

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AUSTIN. TEXAS

I. 11.

INTRODUCTION

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ASSO( IATI-D W I T H O X Y G E N PRECIPITATION

PRECIPITATE NLKIE A T I O N . . . . . . . . . . . . . . I . The Horriogenroir \ N i r c letition Model . . . . . . . 2 . The Strtiin Relief Mriclc,/c . . . . . . . . . . . IV. PRECIPITATE GROWTH . . . . . . . . . . . . . . I . The 0, l ) i f ~ r s i o t ; - / , r ~ r i i / ~Pre.c~rpi/ti/e ,t/ G r o w t h Behatior 2. Thr Doniinunt Srrtrrn R c / r c : / ’ Mwhani.\m: I-Emission .

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. . . . . . . D E ~ E CGENERATION T . . . . . . . . . . I . .Si .Sr./f-lri/er.~rititi/(;cJnc,rrition . . . . 2. Prismutil. Dis/oc~(rrirjril.oop P i t r i i . h i n ~ ~. E F F E C T OF C4RHoIU

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.

1. Introduction

Because of intrinsic getteririg (1G) (Shimura in this volume; Tan, 1991; Tan, Gardner and Tice, 1977). the process of SiOz precipitate formation in Czochralski (CZ) Si has heen (and still is) an active research subject (Bullis and Kimerling, 1983; Fair. Pearce and Washburn, 1985; Huff et al., 1981, 1986. 1990; Mahajan and Corbett. 1983; Mikklesen et al., 1986; Nardyan and Tan, 1981). Grown from molten Si contained in a fused quartz crucible, a CZ Si crystal contains interstitial oxygen atoms (0;)to a concentration ( C , ) that is supersaturated at typical device processing temperatures. During device processing or a preannealing treatment, the Si surface region 0, out-diffuiion can be sufficiently prominent so that the supersaturation in C i can decrease to the extent that no SiOz precipitates need to form to a depth of typically a few to -10 IJ-m. This leaves a defect-free zone (DFZ), or precipitate-free zone. or denuded zone suit353 Copyright G 1994 hy Academic Pres,, Inc

All right, of reproduction in any form rmerved I S B N 0-12-752142-9

354

T. Y. TAN AND W. 1. TAYLOR

able for device fabrication. In the meanwhile, deeper in the wafer bulk, SiO, precipitates and their associated defects, including punched-out dislocation loops and stacking faults, form. Such precipitate-defect complexes serve as effective gettering sites for removing metallic contaminants, unintentionally introduced during device processing, away from the wafer surface region. Intrinsic gettering improves device fabrication leakage limited yield and is therefore now a part of the integrated circuit fabrication technology. The SiO, precipitate formation process includes two aspects, that of nucleation and that of growth. The first systematic effort to model the S O z precipitate nucleation process is that of Inoue, Wada and Osaka (1981). They reported that, in some CZ crystals, the process may be described on a homogeneous nucleation basis. However, the complexities associated with Oiprecipitation in apparently normal CZ Si materials are seemingly beyond the description of the classical nucleation theory just on a homogeneous or heterogeneous basis. A large number of complexities have been observed in association with the creation of the DFZ and the wafer bulk IG gettering sites, all directly related to the SiO, precipitate nucleation and growth behaviors. A brief summary of the responsible experimental factors and the associated complexities is given in the following. Carbon During CZ Si growth, graphite is used as the crucible heating element. Though under a partial vacuum, there is sufficient oxygen in the growth chamber that reacts with C to form CO to dissolve in the Si melt. In turn, C is incorporated in the Si crystal to a concentration of - I ppm, slightly more, or substantially less. When present at a concentration above -0.5 ppm, C enhances the SiO, precipitate nucleation and hence its density tremendously (Shimura, Tsuya and Kawamura, 1981; Yamamot0 et al., 1980), when compared to wafers containing much less C but the same amount of 0;. Annealing Ambient

For wafers with the same Oiconcentration, compared to the results obtained using the inert ambient N,, a dry or wet 0, ambient reduces Oiprecipitation in the Si bulk (Hu, 1980a; Oehrlein, Lindstrom and Corbett, 1982; Schaake, Baber and Pinnizzotto, 1981) and enlarges the DFZ width (Craven, 1981). While the smallest DFZ width has been obtained from the use of 0, containing HCl in one experiment (Craven, 1981), in others the addition of HCl to 0, either enlarges the DFZ

9.

ME( HANISMS OF OXYGFN ['RE( IPII

ATION:

SOME QUANTITATIVE ASPECTS

355

(Peibst and Raidt, 1981: Rozgonyi and Pearce, 1978) or has no effect (Hu, 1980a). Phosphorus Diffusion ln-diffusion of P from the wafer surface has been found to enlarge the DFZ width in some experiments (Fair. 1983). but to shrink it in others (de Kock, 1983). Annealing Time in Lo-Hi Pregettering Treatment In the so-called Lo-Hi type pregettering treatment, the phenomena of S O z precipitate nucleation retardation-recovery has been observed (Kennel and Plummer. 1990; Ogino. 1982; Tan and Kung, 1986). For an illustration of these phenomena, we use as an example a case observed by Tan and Kung ( 19x6) for which the Lo-annealing is carried out at 650°C and the Hi-annealing at 1050"C, the Lo-annealing is a nucleation step to generate nuclei suitable for precipitate growth to occur at the Hi-annealing temperature. In this example. for Loannealing times shorter than -8 hrs. the nuclei density increased with the increase in annealing time. As the Lo-annealing time increased from -8 to -32 hrs, however. the nuclei density has decreased as the annealing time is increased. This is the retardation phenomenon. As the Lo-annealing time becomes still longer, the nuclei density starts to increase again from a minimum value obtained at -32 hrs with the increase in annealing time. This is the recovery phenomenon. Morphology of SiO, Precipitates Well-grown SiOz precipitates have been found to exhibit the shapes of platelets (Maher et al.. 1976; Tan and Tice, 1976; Tempelhoff et a]., 1979). spheres or rhombohedra (Ponce and Hahn, 1984; Tempelhoft et al.. 1979; Yang. Anderson and Kappert, 1978a) and needles (Tempelhoff et al.. 1979; Bourett, Thibault-Desseaux and Seidman, 1984). The platelet and spherical or rhombohedra1 precipitates have been fairly satisfactorily identified as amorphous SO2. The nature of the needleshaped "precipitates" is, however, still controversial. It has been thought that they may either be coesite (Bourett et al., 1984; Ponce and Hahn, 1984). a high-pressure phase of S O z , or hexagonal Si (Bender and Vanhellemont. 1988; Bourett. 1987; Tan, Foil and Hu. 1981) accompanying the formation of small but numerous spherical or rhomhohedral S O , precipitate5 (Tempelhoff et al., 1979). In the orientations accessible for high-resolut ion transmission electron microscopy observations, coesite and hexagonal Si produce nearly identical structure images and diffraction patterns.

356

T. Y . TAN AND W . J . TAYLOR

Banded and Swirl Distribution of Precipitates As driven by intrinsic gettering needs, the Si crystal growth community has devoted a large effort (Benson, Lin and Martin, 1981; Lin in this volume; Lin and Benson, 1989) to produce large diameter C Z Si crystals with predictable-controllable SiO, precipitation behaviors (Bullis and Kimerling, 1983; Fair et al., 1985; Huff et al., 1981, 1986, 1990; Mahajan and Corbett, 1983; Mikklesen et al., 1986; Narayan and Tan, 1981). One result is that large-diameter Si crystals with radially and longitudinally uniform 0, and C concentrations have become available since some time ago. Even for these crystals, however, the precipitate distribution is banded (longitudinally) or swirled (radially) on a millimeter scale. This is seemingly due to the crystal growth rate adjustment, in response to temperature fluctuations in the Si melt, for maintaining the growing crystal at a constant diameter. Such fluctuations or adjustments have been thought to influence the point defect concentrations in the crystal and hence the formation of the so-called swirl defects, which are distributed in swirl patterns radially and banded longitudinally (Tan and Gosele, 1985). In turn, the swirl defects are believed to influence the S O , precipitate nucleation behavior, leading to the distribution of the precipitates in the same patterns. For swirl defects in floating zone Si, at least the so-called A-type has been identified as interstitial dislocation loops (Foll and Kolbesen, 1975; Petroff and de Kock, 1975),which are therefore point-defect aggregates formed essentially independent of the influence of an impurity. For CZ Si crystals, however, the swirl defects are elusive in that none has been found to be independent of the influence of 0,. Wafer Thermal History Another elusive factor is the so called wafer thermal history. Since early times, it has been known that the Oiprecipitation behaviors of wafers from different sections of a crystal are different, with the seed end and tail end wafers exhibiting the largest difference. Part of the reason is the Oiand C concentrations between the wafers. The difference in precipitation behaviors, however, also exhibits even with Oi and C concentrations being apparently the same. Thermal history, i.e., the times the different crystal sections spent at higher temperatures during growth can apparently count for part of it: tail end wafers have spent a much shorter time than the seed end wafers and should hence precipitate less O i . The problem is that the results are not consistent.

9

M€CHAYISMS OF OXYGEN PKF( I P I T A I I O N : SOME QUANTITATIVE ASPFCrS

Precipitation in p

and

17

'

357

Si

In most 0, precipitation studies lightly doped Si wafers were used. Interesting 0, behavior- occurs at high doping levels: p+-doping enhances (Bains et al.. 1990) while II * -doping retards (de Kock and van de Wijgert, 1981) the precipitation process for wafers with the same C, values. Since the 0, diffusion mechanism in heavily and lightly doped 1 1 - and p-type Si are very similar. a difference in the SiOz precipitate growth kinetics cannot bc thc cause. Thus, heavy doping apparently influences the precipitate nucleation process (Oates and Lin, 1988) via. e.g.. complexing of charged point defects and 0, atoms (Gupta et al., 1993: Shimura et al.. 1985). Detailed knowledge is, however, unavailable. In view of the existence o f the extremely complicated experimental results. such a s those .just listed, for which some are self-contradicting without a readily discernible reawn, it can be expected that the search tor o i i c theory that can explain all the acpects should be unfruitful. What we could hope for is the identification of one to a few most basic physical factor(s)that can account for the majority of the experimental results. In this chapter a couple of such factors will be identified, and their effects on both the SiO, precipitate nucleation and growth aspects discussed. thereby explaining some of the outstanding features mentioned. In most experimental results, the role of precipitate nucleation is not distinguished from that of precipitate growth. By observing precipitate sizes. however, it has been tound that. within experimental accuracy. the Sic>?precipitates exhibit the 0,diffusion limited growth behavior (Livingston et al.. 1984; Yang et al.. I978b). 11. Volume Shortage Associated with Oxygen Precipitation

The most fundamental physical factor. which is believed to be responsible for most of the complexities in the experimental results, has been identified since earlier times. This is the volume shortcrge associated with 0,precipitation (as well as with the oxide film growth on the wafer surface in an oxidizing ambient), tint noticed in defect studies, and subsequently rationalized (Gosele and Tan, 1982: Hu. 1980a; Mahajan. Rozgonyi and Brasen, 1977: Maher et al.. 1976; Patrick et a].. 1979; Schaake et al.. 1981; Takako, Osaka and Inoue, 1978: Tan and Gosele, 1985; Tan and Kung. 1986; Tan and Tice. 1976). Being an interstitial species. each 0, atom in Si does not occupy a unit volume associated with a crystal \ubstitutional site. The observed crystal lattice expansion due to 0,incor-

358

T. Y. TAN AND W . J . TAYLOR

poration in Si (Takano and Maki, 1973) is caused by a small elastic strain incurred to the lattice by the O iatoms. This strain disappears if the 0; atom is removed from the interstitial position it occupies in Si. Upon the removal of an O iatom, there shall be no unit volume associated with a substitutional site, i.e., a vacancy, left behind. Upon precipitation, the 0;atoms leave their bond-centered interstitial positions and appear in the SiO, precipitate structure. The volume of each SiO, molecule, no,,is about 2.25 times that of a Si atom, nsi.For the formation of each SiO, molecule, only one Si atom in the matrix is consumed, therefore, there is a volume shortage of approximately 125%. Because of this volume shortage, the growth of a precipitate or embryo is associated with a negative strain accompanied by a compressive stress in the surrounding Si matrix. 111. Precipitate Nucleation

Classical nucleation theory describes the precipitate nucleation process in terms of being either homogeneous or heterogeneous. The influence of a strain in the matrix material, generated by a volume change associated with precipitate formation, has also been discussed. In the homogeneous nucleation process, only the chemical energy changes associated with the precipitating atomic species are considered, i.e., influences due to other atomic species, defects and strain i r e assumed to be absent. Incorporating the influence of other atomic species and defects, the nucleation process becomes heterogeneous. Heterogeneous nucleation leads always to a higher nucleation rate than that of homogeneous nucleation, because the influence of these heterogeneous factors, in particular that of defects such as dislocations and other kinds of precipitates, is always to decrease the critical Gibbs free energy for nucleation to occur. On the other hand, strain leads always to a lower nucleation rate than that of homogeneous nucleation, because the strain energy resulting from the volume change is always to increase the critical Gibbs free energy for nucleation to occur, irrespective of whether the stress associated with the strain is compressive or tensile. For some metal and ceramic systems, for which the strain energy constitutes but a small fraction of the chemical energy change, the influence of strain on nucleation phenomena have been extensively treated. In these cases the strain producing volume change associated with the precipitation process is much less than 100%. Thus, to study oxygen precipitation in Si, it is expected that knowledge available from studies of other material systems can offer only limited help.

9.

M E C H 4 N I S M S 01- O X Y G F N P K t C IPITATION: SOME QUANTlTATlVF ASPLCTS

359

TABLE I EFFKTIVF

RAI)lLl\ ref'

I-OK V 4 R I O U S

PRECIPITATE S H A P E S

Precipitate Shape Sphere with radius r

I' all

I

2rIn

Disk with radiu\ r Square-shaped platelet with \ide lengths I and thicknes\ d << I

V i

=-/

1T

1.

THE

HOMOGENEOUS NLTI F.AT10N MODEL

In the homogeneous nucleation process, the precipitate nucleation rate is. in the simplest case, given by the Volmer-Weber nucleation rate equation (Burke, 1965; Christian. 1965) J

= %c',,,w.

(1)

where Z is the Zeldovich factor. C,,, is the critical nucleus density and w is the 0, impingement frequency onto a critical nucleus. The Zeldovich factor is for all purposes a fitting parameter usually on the order of but smaller than 1. The quantity Ccr,is given by

where C , is the 0, concentration in the Si matrix. k , is Boltzmann's constant, T is the absolute temperature and AG,,, = AG(rE;) is the Gibbs free energy for forming a critical nucleus with the critical radius r $ . Generally, is an effective radius that is not only restricted to that of a spherical precipitate. Some examples of are listed in Table I (Cosele and Tan, 1982) for precipitates with different shapes. In the rest of this chapter the superscript eff will be dropped for the sake of simplicity, with the understanding that 1- generally refers to an effective radius of a precipitate whose shape is not necessarily that of a sphere. The quantities r,,, and AG,,, are given by

360

T. Y . TAN AND W . J . TAYLOR

where u is the interfacial energy density between the SiO, precipitate and Si, and AG, is the chemical energy change in forming a SiOz molecule from Oi. The quantity AGv is given by

$:(

AG,, = -2knTIn - , where Ceq is the Oi thermal equilibrium concentration at the precipitation temperature, and the numerical factor 2 is present because a SiO, molecule contains 2 Oiatoms. The impingement factor is given by

where D is the Oi diffusivity and d is the interatomic distance in Si, 2.35 A. According to Craven (1981 j, the Oi thermal equilibrium concentration in Si is

for which the Fourier-transform infrared (FTIRj measurement calibration standard due to Graff et al. (1973) has been used. According to Corbett, McDonald and Watkins (1973), the Oi diffusivity is Di

=

0.2 ex,(

--)2.57 eV

cm2s-1.

k,

The J curve as a function of 1/T is bell shaped when plotted in the linear scale, and exhibits a downward concave shape when log J scale is used, see Fig. 1 for a schematic case. It is easy to understand the reason that J has a maximum value at a certain temperature. When the temperature is very high, the Oi supersaturation is smaller or even not existing, leading to a smaller or even zero nucleation rate. When the temperature is very low, the Oi supersaturation can be very high, but 0, diffusion becomes very slow, leading to also reduced and even vanishing nucleation rates. Inoue et al. (1981) have performed experiments using Si wafers with the same C ivalues to observe the SiO, precipitate nucleation rates at different precipitation temperatures. Their nucleation data can be described by the homogeneous nucleation model using a u value of -430 erg cm-2.

9.

MECH4NISM) Of OXYGFN P K t ( IPITATION: SOME QUANTITATIVF ASPECTS

361

h

c

w v

7

ul

-

I t i < ; . I . ‘The hypothetical precipitate nucleation rate according t o classical nucleation theory. ( a ) for J plotted in linear scale. ;ind ( b ) for J plotted in log scale

Generally. however, the homogeneous nucleation theory cannot be used to describe the 0, precipitation process. For heterogeneous nucleation, the same expressions ohtained for homogeneous nucleation also apply in an essential mannet. and hence the temperature-dependent nucleation rate curve also exhibits the same shapes as for homogeneous nucleation. The differences are only in the numerical values w , rcr,and Therefore. based on the temperature-dependent nucleation rate, it is rather difficult to judge whether homogeneous nucleation or heterogeneous nucleation is involved. One reason is the extreme sensitivity of J on the value of (r. Available values of u are from -80 to 500 ergs cm Examining Eqs. ( I ), ( 2 ) , and ( 4 ) . it is seen that J depends on u exponentially to the cubic power. Therefore. the value of u influences the value of.1 extremely critically. and the wide range of the available u values can lead only to .I values with little reliability. This means that the reliability of an apparently satisfactory data fit is questionable when used to judge the precipitate nucleation mechanisms. More important, however, is that

’.

362

T . Y . TAN AND W . J . TAYLOR

the homogeneous nucleation model does not provide explanations to the observed complexities associated with the 0; precipitation phenomena, such as those mentioned in Section I. 2. THESTRAIN RELIEFMODELS For the SiO, precipitate nucleation process, influences of some heterogeneous factors should exist in general, which tend to enhance the nucleation process. On the other hand, the strain resulting from the volume change accompanying the formation of a SiO, molecule can be extremely large, which will yield an effect in retarding the nucleation process. Here we will ignore the influences of the heterogeneous factors and concentrate on the volume change or strain issue. If the number of molecules in the SiOz is very small, e.g., a few, the volume shortage can probably be accommodated by strain. As the precipitate embryo grows larger, e.g., reaching the size of a critical nucleus suitable for high temperature growth to occur, the strain will become too large and therefore must be relieved o r else neither nucleation nor growth of the precipitate can occur (Hu, 1986). There are three ways the strain may be relieved: (i) by emitting Si self-interstitials (I) into the Si matrix; (ii) by absorbing vacancies ( V ) from the Si matrix; and (iii) by punching out interstitial-type prismatic dislocation loops into the Si matrix. The I-emission process leads to an I-supersaturation in the matrix, the V-absorption process leads to a Vundersaturation in the matrix and prismatic punching leads to a stored elastic energy in the matrix. Any process is in balance with a residual strain that is still left in the Si matrix material surrounding the oxide precipitate. As a digression, we mention that the same volume shortage phenomenon also occurs in the Si surface oxidation process. However, in this case the main stress-strain relief mechanism is the viscoelastic flow of the newly grown oxide, accompanied by only a small amount of I injected into the Si matrix (Tan and Gosele, 1985). Such injected Z cause oxidation-enhanced and -retarded diffusion of dopants to occur and can also lead to the generation of oxidation-induced stacking faults at the wafer surfaces, if nucleation becomes easy, e.g., due to the presence of metallic impurities or mechanical damages. Models invoking some means to relieve the strain associated with 0; precipitation constitute strain relief models. It will be shown that V absorption is not an effective strain relieving process during precipitate growth. It will also be shown that prismatic dislocation loop punching is also an ineffective process for strain relief even for a well-grown precipitate during its growth process. Therefore, here we will assume that Zemission is the primary means of compensating for the volume shortage

9.

MFCHANISMS OF O X Y G F N PHFC I P I I A T I O N : SOME Q U A N T I T A T I V E ASPECTS

363

associated with 0, precipitation in the Si interior. For this process, the combined law of mass and volume conservation reads 2Si

+ 2 0 , e SiO, + y r l + ( I

-

yI)Si,traln.

(9)

for the oxide to grow by one SiO? molecule. In reaction (9) the simplifying assumption that n,, = 2OS, has been used. The quantity y, is the number of I emitted for the precipitate to grow by one SiOz molecule, while ( 1 - y,)Si,,,,,, is the fractional volume shortage for forming one SiO, molecule that has been converted into strain. Note, under the assumption that Q , , = 252,, holds, the volume shortage in forming one SiO, molecule will be exactly compensated by the emission of one I . However, because the SiO, precipitate must be associated with a residual strain, the emitted I number is a little less than I per SiO, molecule formed. Thus y , < 1 and y , - 1 can hold but not y, = I. Reaction (9) does not apply for the surface oxidation case for which emission of I into Si matrix accommodates but only a very small fraction of the volume shortage (Tan and Giisele, 1985). Noting the presence of strain and that Si is an anisotropic elastic medium, Hu (1986) and Tiller, Hahn and Ponce (1986) explained the observed morphology differences of the SiO, precipitates. Dependent upon the annealing temperature, precipitates with shapes of needles, platelets, and rhombohedra can be obtained in the order of increased annealing temperature (Bourett et al., 1984; Maher et al., 1976; Ponce and Hahn. 1984; Tan and Tice, 1976; Tempelhoff et al., 1979; Yang et al., 197th). We note that the existence ot’ needle-shaped precipitates is still rather uncertain (Bender and Vanhellemont, 1988: Bourett, 1987: Bourett et al.. 1984). Assuming that the strain makes a negligibly small quantitative contribution. Giisele and Tan (1982) found that the critical size for nucleation to occur is given by I’crl, =

ks 7’ In

%(J

c , / c ’):(~c ; ~ /’”c1’, )

(10)

where C, and C:q are the actual and thermal equilibrium 0, concentrations, respectively, and C, and <.;q are the actual and thermal equilibrium I concentrations. respectively. With I’,,, known, the nucleation rate J can be calculated using Eqs. ( I ) ;tnd (4)-(8). Qualitatively, the majority of the experimental results on the DFZ width and IG site density are consistent with the description of Eq. ( 10). Surface oxidation induces an I-supersaturation in the Si matrix. Therefore, rLr,becomes larger and the precipitate density is reduced when the

364

T . Y. TAN A N D W. J . TAYLOR

ambient is changed from N, to O,, just as have been observed (Hu. 1980a; Oehrlein et al., 1982; Schaake et al., 1981), and the DFZ is enlarged, as has been observed by Craven (1981). Addition of HCI to the oxidizing ambient reduces the oxidation induced I-supersaturation and even can lead to an I-undersaturation (Shiraki, 1975; Tan and Gosele, 1985), which is consistent with the observation of a very small DFZ (Craven, 1981). Similarly, P in-diffusion generates an I-supersaturation in the Si matrix (Morehead and Lever, 1986), which leads to the observed DFZ enlargement (Fair, 1983). The precipitation nucleation retardation-recovery phenomena observed in the Lo-Hi pregettering treatment process (Kennel and Plummer, 1990; Ogino, 1982; Tan and Kung, 1986) can be basically explained in the same manner. The retardation phenomenon is seemingly caused by an I burst during the temperature rise before reaching the Hi-annealing temperature, when too many nuclei have been generated in the Lo-annealing step. The recovery phenomenon is seemingly caused by the condensation of the emitted-I at the Lo-annealing temperature already when still more nuclei are generated. The I-condensation removes the I-supersaturation and allows more nuclei to grow at the Hiannealing temperature. Physically, however, a residual strain must exist, since otherwise an I-supersaturation in the Si matrix cannot be maintained by the SiO, precipitate during either nucleation or growth. In a recent study, Taylor, Tan and Gosele (1991) have obtained an analytical solution to this problem. In accordance with reaction (9), the Gibbs free energy of the Si crystal containing O;, I , one SiO’ precipitate and its associated residual strain can be written as

The first three terms on the righthand side (RHS) of Eq. (1 1) are, respectively, the contributions of O;, I , and the Si0,-Si interface, and G, is that of the strain. Here N j is the number of 0;atoms in the Si crystal, N , is the number of I and r is the radius of the precipitate. The strain energy G, stored in a material due to the existence of a spherical precipitate in the matrix with a misfit 6 is given by (Mott and Nabarro, 1940; Nabarro, 1940) 6pm s’v, = f,S’V,,, (12) (1 + 4pr,/3K,) where prn is the shear modulus of the matrix material, K , is the bulk modulus of the precipitate, V,, is the initial unconstrained volume of the

G,

=

9.

MECHANISMS OF O X Y G F N PKI C I P l r A T I O N : SOME Q U A N T I T A T l V r ASPEC r5

365

matrix and.f, is simply an abbreviation of the factor 6p.,,,/(1 + 4p.,,,/3KL,). The misfit 6, which results from fitting a precipitate with an unconstrained radius of r,, (volume V,) to a cavity in the matrix with an unconstrained radius of r,,, (volume V,,,),is

I n the matrix, the precipitate is compressed to its final constrained radius r,

=

I

r ”

+ (6iX) I t 6

’

(14)

if a relaxation by other means did not occur. Here X = 1 + 4p.,,,/3KP = 4 for Si02 in Si. The numher of Si atoms in the precipitate, n,p, is the same as the number of SiO, molecules in the precipitate. Since il,,, is ?IZ,,. Thus, C’[, = I I , ~ K L ~ , The , . Si atoms about twice 12,,, we let {Ic,, consumed in forming the precipitate leave behind a cavity of volume V,,, = n,,{2,,,/2. The generation of I is a thermally activated process that is assisted by the compressive stress. Thus, in the presence of a strain, this process will be operative as long as the strain energy exceeds that due to the I-supersaturation so generated. For each I generated, V,,, is enand N , is increased by one. Thus, for I generated in the larged by a,,, amount of A n l , the relaxed matrix cavity volume becomes :

v,,, = ( I l , p

-t &2/)flOX/2,

(15)

which replaces V,,,in Eqs. ( 1 I ) and (17). With Eq. (14), G, and therefore also G become functions of the two independent variables n s pand An,. The minimum G value is obtained when aG/aAn, = 0 and dGldn,, = 0 hold simultaneously. Using Eqs. (lo)-( 13) to solve for dG/dAn, = 0, we obtain

The last term on the RHS of Eq. (16) is significant only during nucleation (small r,). Equation (16) shows that there is a direct relationship between the strain and the I-supersaturation. Without the strain, i.e., for 6 = 0 holding. the I-supersaturation reduces to that maintained by the surface energy IT only: C , = C;q exp(oll,,,ir,,k,T). For 6 = 0 to hold, it is necessary to assume that the precipitate is very soft so that K, = 0. and hence also l/X = 0, hold. Solving for dG/dn,, = 0 and ignoring higher

366

T. Y . TAN A N D W . J . TAYLOR

order terms, we obtain the critical nucleus radius for nucleation to occur as 1

\-,

11

I

for 6 << 1 holding. Substituting Eq. (16) into (17) yields, for a soft matrix for which X 1 holds,

-

UR,.

Here r,,,r,l is the radius of the critical nucleus in the unconstrained state, and the values of C , and C;q are that in the bulk of the matrix. The radius of the constrained critical nucleus, rfcnl,can be calculated from Eqs. (13), and rfCnlboth reduce to Eq. (10) for (14) and (18). The expressions of rpCn1 an incompressible precipitate ( X = 1). Assuming that strain relief is impossible, one obtains

which is of a similar form as that obtained by Hu (1986). Numerical results for typical cases for which Ci is -10'' c r r 3 showed that neither nucleation nor growth would be possible for T 2 700°C, which is quite contrary to common observations. Thus, a strain relief mechanism, e.g., Z-emission, must be operative. Upon knowing the Z-supersaturation, the residual strain can be calculated using Eq. (16). One can instead assume that absorption of V from the Si matrix is the strain relief mechanism. The results are the same as those expressed by Eqs. (lo), (11) and (16)-(18) but with C,/Cbq now replacing CjqlC,.These results are also obtained by simply assuming that in the Si matrix the dynamical equilibrium condition C , C , = C;qCt!, which ignores the role of u and 6 to some extent, has been fulfilled between Z and V . The assumption that Z and V can both relieve the strain in an independent manner is not valid, since at the matrix-precipitate interface a dynamical equilibrium condition C , C , = f(C;q, C g , cr, 6 ) is always satisfied.

9.

ME< H A N I S M S O F O X Y G E N PKk( l P l l A T I O N : SOME Q U A N T l T A T l V t ASPECTS

367

I V . Precipitate Growth 1 . THE0; DIFFUSION-LIMITED ~ ' R t C I P I T A ~ i EGROWTH BEHAVIOR

The SiOz precipitates exhibit 0,diffusion limited growth behavior (Livingston et al., 1984; Yang et al., lY78b). That is, within experimental accuracy, for growth time f the precipitate sizes are described well by reff =

[ s ~ , , D-, ~( :cq ),t ] ' ' ' ,

(20)

if C, ha5 not been significanlly depleted during the precipitate growth process. This indicates that the strain must have been relieved quite effectively, most likely by /-emission, which, however, generates an I-supersaturation in the Si matrix. For the SiO, precipitate growth process to appear to be limited by 0, diffusion, it requires that this I-supersaturation did not exert B large effect to retard the precipitate growth. This has been shown to be the case by Tiller and Oh (1988) and Taylor. Giisele and Tan ( I Y Y I . 1YY2b, 1Y93a). In the following the discussion follows closely that of Taylor et al. During growth, the dynamical equilibrium reaction P, t-2Si

+ 2 0 , @ P , + ,+ y,/ + ( I

-

y,)Si,,,,,,,

121)

holds. In reaction (21) P , is a precipitate containing j SiO, molecules. The value of y , . when known. offers ;I means for judging whether the I-emission process is an effective means of relieving the strain on a quantitative basis. For instance. a y, value of - 1 indicates that the process is very effective since almost all the volume shortage is accommodated by the I-emission process. while a y, value of 0. I indicates that the process is very ineffective, since 90% of the volume shortage has to be accommodated by the strain. Now, the mas$ action law between 0, and I

holds. Equation ( 2 2 ) reflects also the effect of strain via the y,/2 power of the C,(r,)/C;qterm on the KHS. In order for reaction (21) to hold. it also requires that the integrated fluxes of the 0; atoms flowing into the precipitate and that of / flowing into the matrix is in balance at the precipitat e - Si interface :

where

C ' , ( x )and

C , ( r ) are concentration values in the matrix.

368

T. Y. TAN AND W . J . TAYLOR

Equations (13), (16), (22) and (23) allow us to determine the values of yI and C,(m)lC;q,which in turn allows the determination of the precipitate growth rate compared t o that of the 0;diffusion limited case. While most of the expressions in Section I11 are applicable only during the precipitate nucleation process, it is noted that Eqs. (13) and (16) are not similarly restricted: Eq. (13) contains only geometric definitions, and Eq. (16) is also applicable during precipitate growth provided C, is regarded to be that at the precipitate-Si interface, i.e., C,(rf). Adopting the same assumptions leading to Eq. (15), it is easily shown that Eq. (13) leads to 6 = [2/(1 Y ) ] ' ' ~- 1. Equating this with that given by Eq. (16) in which the rightmost term is ignored, one obtains

+

which contains the two unknown variables y, and CI(rf)IC;q. On the other hand, Eqs. (22) and (23) yield

which contains the same two unknown variables. Equations (24) and (25) can be solved to obtain the y, and C,(q)/C;q values. The computed y, values for the case of C i = 1 x l o i 8cm113and u = 0 are shown in Fig. 2, and that of C,(cr)/C;q = S, in Fig. 3 by the curve labeled S,. Here the value of C,(m)IC;q is assumed to be 1, the values of C:q and D iare given, respectively, by Eqs. (7) and (8), and D,C;q

=

( 4.i:~v) cm-Is-1,

4.57 x lOZ5exp -~

(26)

holds for I (Stolwijk, Schuster and Holzl, 1984). For u # 0, significantly different results are obtained only for very small precipitates, e.g., rp 1 nm. From Fig. 2, it is seen that the y , values are all on the order of 1, but with those at very low temperatures relatively small: e.g., y , 0.5 at 400°C. For comparison to that of the vacancy case, however, we assume that this y, value is still acceptable but it constitutes the lower limit. The S , curve in Fig. 3 shows that, at a growing precipitate interface, the I-supersaturation can be quite high at a temperature lower than 1000°C even if the Si bulk I-concentration is at the thermal equilibrium value.

-

-

-

T ("C)

800

1200

400

10

08

06 al

m x

04

02

0.0

06

OH

10

12

14

16

1 0 ~ (1 K - '~)

Fic;. 2 . Values of

Y,

and v, a s a function of 7 for the c', = 10" c m - ' and (r

=

0 caw.

T ("C)

1200

800

400

10

10

10 m

m

10 O

v)

10

-3

10

10

-9

06

08

1.0

12

1 4

16

l @ 3 / T( K - ' )

F.ic,. 3 . Value5 o f S , and S C as a function of 7 for the C, = 10'' c m - ' and u = 0 case

370

T. Y. T A N A N D W . J . TAYLOR

T ("C) 1200

800

400

1.o

0.8

0.6

0.6

0.8

1.0

1.2

1.4

1.6

1 0 ~ (K-' 1 ~

FIG.4. Values of Q, and Qv as a function of T for the C ,

=

C I T - ~and

u = 0 case.

The y , values shown in Fig. 2 are close to 1 at higher temperatures, indicating that the I-emission process should be an effective strain relief process. On the other hand, the S, values shown in Fig. 3 seems to imply that, at lower temperatures, the SO,-Si interface I-supersaturation may change the SiO, growth process from that limited by 0; diffusion into one apparently limited by a reaction burrier. A quantitative examination showed, however, that the effect of S, is relatively small throughout the entire considered temperature range. This is shown in Fig. 4 by the curve Q I , which is the ratio of the (volumic) growth rate of the I-emission limited case to that of the Oi diffusion-limited case, plotted as a function of 1/T under the assumption cr = 0. To calculate Q, it is assumed that the precipitate growth rate is proportional to the 0; flux reaching the precipitate. For the I-limited case, the integrated Oi flux is

9.

MECHANISMS OF O X Y G E N P R t ( ' l P l 1 ATION: SOME Q U A N T I T A T I V E ASPECTS

371

in which the second equality obtains from Eq. ( 2 2 ) or ( 2 5 ) . For the 0, diffusion-limited case, the integrated flux is

The quantity Q , in Fig. 4 is the ratio of .I,,,,. to J , , for the case for which the y, and S , values are taken. respectively, from those shown in Figs. 2 and 3 . At all temperatures, QI is smaller than 1 but not by a significant amount. Furthermore. the experimentally observed quantity is not the precipitate volume, but its effective radius. The ratio of the growth rate of the radius varies even less, proportional to QI". Therefore, within experimental accuracy, one can still expect to observe an apparent 0, diffusion-limited precipitate growth behavior. For cr f 0. Q / values become lower than that of the (J = 0 case. but not by much. For example, for a precipitate as small as r = 2 nni, CI (7 value as high as SO0 ergs cm and a temperature as low as 400°C. Q, = 0.4 is still obtained. It is seen from Fig. 4 that, in the temperature range of -800-900°C. the Q , value exhibits a minimum which. however, is still larger than 0.9. This minimum exists because at higher temperatures the 0, supersaturation becomes smaller while at lower temperatures the 0, flux becomes substantially smaller than that of I . We conclude this section h y mentioning that in experiments the SiO, precipitate growth behavior is apparently limited by 0, diffusion (Livingston et al., 1984: Yang et al.. 197Xh) because /-emission is an effective means of accommodating the volume shortage. This conclusion is arrived in two ways. First. the y, values shown in Fig. 2 indicate that during precipitate growth the volume shortage is substantially accommodated by I-emission at all temperatures. Second, the Q, values shown in Fig. 4 indicate that the /-supersaturation at the precipitate-Si interface did not retard the precipitate growth process excessively, because its diffusion into the matrix is quite rapid. These two aspects ( y , and Q,) are related and t l o r independent of each other. ~

2 . T H EDOMINANT STRAIN RE1 I I ' F

MEC'HANISM:

',

/-EMISSION

Via native point defect mediations, there are two possible ways to relieve the strain accompanying the precipitate growth process, I emission and V-absorption. Taylor et al. (1992b, 1993a) have recently compared the efficiencies of the two mechanisms and concluded that I-enii s\ ion dominates.

372

T. Y. TAN AND W . 1. TAYLOR

The fact that invoking the I-emission dominating assumption can explain the observed Oidiffusion limited SiOz precipitate growth behavior has been discussed already in the last section, see the y , and Q, curves shown, respectively, in Figs. 2 and 4 . Assuming that V-absorption is the dominating strain relief mechanism, the reaction

Pj + Si

+ 20, + yvV@Pj+, + (I

- yv)Sistrainr

(29)

holds. In reaction (29) y v is the counterpart of yI in reaction (9) or (211, and hence has also an analogous meaning as yI. The mass action law reads now

The balance of the integrated Oiand V fluxes at the precipitate-Si interface yields

where Cv(m) is the actual V concentration in the Si matrix. Equations (131, (301, (31) and

which is the counterpart of Eq. (16), holding for V for large precipitate cases, can be used to calculate y v and Cv(cp)lC;q. Equations (13) and (32) yield

which contains the two unknown variables y v and C v ( ~ f ) l C ; qEquations . (30) and (31) yield

which contains the same two unknown variables. The values of y, and

9.

MECHANISMS OF O X Y G E N PRECIPITATION: SOME QUANTITATIVE ASPECTS

373

C,(r,)IC:q can be obtained by wlvlng Eqs. (33) and (34). The computed v L values for the case of C , = I x lot8c m - 3 and CT = 0 are shown in Fig. 2 and that of Cv(r,)/CEq = S, in Fig. 3 by the curve labeled S , . Here the value of Cv(.;)/Ciq I S a5wmed to be 1 , the values of C:q and D ,

are given, respectively, by Eq\. ( 7 ) and ( 8 ) , and

holds for V (Gosele and Tan, 1985; Tan and Gosele, 1985). For (r # 0, significantly different results are obtained only for very small precipitates, e.g., rL, I nm. From Fig. 2 it is seen that the y , values decrease rapidly as the tempervalue in close to 1 only at 1200"C, and at other ature is lowered. The ?;, temperatures the y r values are much smaller than the corresponding J ' , values. Since y , represents the efficiency of relieving the strain by V absorption while y I represents that by f-emission. the y I and y v values shown in Fig. 2 indicate that V-absorption is not as effective a process as f-emission in relieving the strain. The S , curve shown in Fig. 3 indicates that at the precipitate-Si interface the V-undersaturation is very severe at a temperature lower than - 1200"C,even if the Si bulk \,'-concentration is at the thermal equilibrium value. The S,, curve in Fig. 3 implies that, below -1200°C. the V undersaturation at the Si0,-Si interface will change the SiOz growth process from that limited by 0, diffusion into one apparently limited by a rrcictiori brrrricir. A quantitative examination showed that this is indeed the case, see the curve Q b in Fig. 4, which is the ratio of the precipitate (volumic) growth rate of the V-limited case to that of the 0, diffusionlimited case, plotted as a function of l / T under the assumption CT = 0. To calculate Q v it is assumed that the precipitate growth rate is proportional to the 0, flux reaching the precipitate. For the V-limited case. the integrated 0; flux is

-

in which the second equality obtains from Eq. (31) or (34). For the 0, diffurion-limited case. the integrated flux is given by Eq. ( 2 8 ) . The quan-

374

T . Y . TAN A N D W . J . TAYLOR

tity Q , in Fig. 4 is the ratio of J 0 , , to J , for the case for which the y , and S , values are taken from those shown in Figs. 2 and 3, respectively. At a temperature lower than 1200"C, Q , is substantially smaller than 1. Obviously, the V-absorption limited precipitate growth kinetics cannot appear to be limited by 0,diffusion, which is contrary to the experimental results. Therefore, V-absorption cannot be the dominant strain relief mechanism associated with SiO, precipitate formation at these temperatures. Physically, the difference in the effectiveness of relieving the strain in the I-emission and V-absorption mechanisms results from the difference in the nature of emitting an I and that of absorbing a V at the precipitatematrix interface, and the difference in the ability of the matrix in maintaining an I flux and a V flux. For I-emission, even if the I concentration in the immediate vicinity of the precipitate is already highly supersaturated, more I can still be generated provided they can flow away and C,(r,)is still a small fraction of the Si lattice site density. At any temperature, the C;q value should be small so that even if highly supersaturated C , ( r / )should still be a small fraction of the Si lattice site density. Insofar as the I concentration gradient is very large, the supersaturated I can flow into the matrix quite effectively to allow the precipitate growth process to appear as limited by 0, diffusion. This is the case, because in J , 0~ ACI - C I ( r l )- C,(x), the quantity AC, can be larger than C,(=) by many orders of magnitude due to the fact that C I ( r f )is many orders of magnitude of C;q while C,(m) C;q holds. The condition C , ( m ) C;q can be satisfied because in the matrix the precipitate concentration is low or I-sinks exist. For V-absorption, a severe V-undersaturation at the precipitate-matrix interface means there simply do not exist a sufficient number of V to relieve the strain, and consequently the precipitate growth process becomes limited by the supply of V from the matrix. The indiffusing V may not be associated with a sufficiently large flux for the reason that a very large V concentration gradient may not exist, because in J , ACv - C,(=) - Cv(rf), the quantity AC, can at best be equal to C g , not many orders of Cbq. The upper limit of AC, is Cbq, which obtains for C,(x) = C g and Cv(rf) = 0 holding. The conditions that in the Si matrix the precipitate concentration is small or V-sources exist can only maintain C,(.a) to the value of C g . Thus, insofar as the involved I and V diffusion distances, A x , are about the same and Cbq is not larger than C;q by many orders of magnitude, the in-diffusion process of V from the Si matrix to reach the precipitate-Si interface should be a much less effective process than out-diffusion of I from the precipitate-Si interface to disperse into the Si matrix.

-

-

9.

MEC'HANISMS OF OXYGEN PRECIPITATION: SOME QUANTITATIVE ASPECTS

375

V. The Effect of Carbon

Carbon enhances 0, precipitation, as revealed by an increased precipitate density as well as a decreased C concentration in the Si matrix (Gaworzewski et al., 1984; Kung, Forbes and Peng, 1983; Shimura, 1986; Shimura et al.. 1981. 1985: Sun et al., 1990; Yamamoto et al., 1980) in high C concentration CZ Si wafers. Giisele and Tan (1985) pointed out that this is due to the fact that C atoms can help to accommodate the volume shortage, i.e., to relieve the strain, associated with Oi precipitation, because the covalent C atom size is small. The lattice constant of diamond is 0.356 nm while that of Si is 0.543 nm. Therefore, it can be assumed that. in Si, the substitutional C atom volume is only -28% of that of a Si atom. There are several ways a C atom can help to relieve the strain associated with 0, precipitation. In the first, a C site can provide u p to 73% of the volume for trapping an 1. Once trapped at the C site, the I atom is effectively removed from the I-supersaturation generated by 0, precipitation. This will permit the 0, precipitation process via f-emission to relieve the strain, e.g., during nucleation, to proceed at a faster rate. I n the second, the same holds if the C atoms are diffused to the surrounding of the precipitate to directly relieve the strain. In the third, the C atoms may themselves be incorporated into the SiOz precipitate either as a covalent substitution for Si atoms or as a gaseous species, e.g., C 0 . In reality probably all three mechanisms are operating to some extent. Treating the role of C using the simplifying assumption that each C atom is able to provide -100% of II,, (instead of the more realistic -72%). it is a straightforward matter to obtain

where C,- and C;q are the actual and thermal equilibrium C concentrations. respectively. Comparing Eqs. (10) and ( 3 7 ) .it is seen that the role of C is just the opposite of that of I : a supersaturation in C enhances the nucleation while the opposite holds for I . Since, at least at t h e nucleation temperatures, C exists in Si in supersaturation in high C content wafers, an enhancement of 0, precipitate nucleation can be expected. In high C content CZ Si, C coprecipitates with Oi at lower temperatures. The precipitated out C and 0, atoms are approximately in a C : 0 == I : ? ratio in most cases (Gaworzewski et al., 1984; Kung et al., 1983; Shimura, 1986; Shimura et al.. 19x1, 1985; Sun et al., 1990). This indicates that the role of C precipitation is most probably that of accommodating

376

T. Y . TAN AND W. J . TAYLOR

the 0;precipitation-induced strain. However, the state of the precipitated out C atoms constitutes a puzzling factor. First, due to the existence of a very high interfacial energy density (Taylor, Gosele and Tan, 1993b), the formation of S i c precipitates is very unlikely. Second, the Si-0-C ternary phase diagram does not contain a ternary phase showing a 1 :2 C to 0 atomic ratio. Third, the percentage seems to be also too large for C to exist in SiO, as an impurity species. This puzzling factor aside, Taylor et al. (1993~)have recently shown that the 1 : 2 coprecipitation behavior of C with Oican be interpreted to be due to the role of C to relieve the strain during SiO, precipitate growth, via a comparison of the magnitudes of the C and I fluxes. The flux argument applies only during precipitate growth and not during precipitate nucleation. While C atoms are participating in both the precipitate nucleation and growth stages, it is assumed that only those precipitated out during the growth stage are of a sufficiently large amount to be measured by FTIR. Figure 5 shows the FTIR measured C-0 coprecipitation data of Shimura (1986) obtained by annealing as-grown CZ wafers for 64 hrs. The interesting point to note is the sudden cease of C precipitation above -850"C, while in the lower temperature range of -450-800°C the precipitated out C and 0 are in a ratio of -1 : 2 . Invoking the idea that, in addition to I-emission, C precipitation is a parallel means of relieving the

4

I

5

h

3

-0 v c

c

.L

2

:

c V

0-

1

s

v

0

400

600

800

1000

FIG. 5 . The experimental C and 0, precipitation data of Shimura (1986) obtained by isochronal annealing.

9.

MECHANISMS OF OXYGEN PRECIPITATION: SOME QUANTITATIVE ASPECTS

377

strain during precipitate growth, the problem can be analyzed in terms of the appropriate fluxes. The flux of C flowing into the precipitate is

where D,. is the diffusivity of C, Ctq is the C thermal equilibrium concentration, C , ( = ) is the actual C concentration in the Si matrix, and C c ( r , ) is the C concentration at the precipitate-matrix interface. In Eq. (38) the second equality obtains under the simplifying assumption that there is no C supersaturation at the precipitate-matrix interface, i.e.. CC(rl) = C>q. Using the FTIR measured C ( . ( x )value, and the quantities D , and C;P given by (Bean and Newman. 197 I ; Newman and Wakefield. 1961)

J , . can be easily evaluated. The flux of I flowing away from the precipitate is given by

In contrast to the C case, the 1 flux is not as easily calculated, since C,(r/) is a function of the strain surrounding the precipitate. If the C flux is low. then I will be responsible for the strain relief, and therefore a large I-supersaturation will be generated. see Fig. 3. If the C flux is high, then C is capable of relieving most or all of the strain, so that little or no I-supersaturation will be present. Therefore, in order to compare the two fluxes, it is assumed that C,(r/)/C;q = I . I constitutes a lower bound for I-supersaturation. which is a very low value for an I-emission dominating case. Now, the I flux can be taken to be J,

=

4 n ~ I ~ ~ C ~-" (I ) l. . I

(42)

In Fig. 6 t h e fluxes J , and .I, (ignoring the 4 n r terms) in accordance with Eqs. (41) and (42) are plotted. A relatively high-bulk carbon concentration. 2.5 x 10'' cm-3, appropriate for the experimental data of Shi-

378

T. Y . TAN AND W . J . TAYLOR

T ("C)

1000 800

400

600

10-l6 10

-1 8

10 -20

10 -22

10

-24

10 -26 0.6

0.8

1.0

1.2

1.4

1.6

1 0 ~ (K-' 1 ~

FIG.6 . Comparison of the fluxes of the strain relief species substitutional carbon (C) or self-interstitials ( I ) , under the assumptions stated in the text.

mura (1986) shown in Fig. 5, has been used. It is worth noting that at lower temperatures much larger values of C,(rf)lC;qis expected, which would shift the Z-flux curve in Fig. 6 upward. However, since enhancements in C diffusivity are directly proportional to f-supersaturation (Kalejs and Ladd, 1984; Ladd, Kalejs and Gosele, 1985), the C flux curve should shift up as well, preserving the relative positions of the curves. From Fig. 6 it is seen that, for lower temperatures, the C flux is higher than the f flux, and therefore C should dominate the strain relief. This means that, as 0;precipitates are growing, C concentration in the matrix should be simultaneously decreasing. At high temperatures even the very low f-supersaturation assumed for Eq. (42) allowed the f flux to become larger than the C flux, so that f-emission should dominate the strain relief process. This allows the C concentration to remain essentially unchanging. The critical temperature at which the dominant strain relief species changes depends upon the C concentration and the C,(Y~)/C;~ value. In Fig. 6 the C-f dominant regions compare favorably to the data of Shimura (1986) shown in Fig. 5, wherein it is seen that C precipitated out at the lower temperatures but not at the higher temperatures. It is important to note that the two flux curves in Fig. 6 do not remain static during an annealing. As C precipitates out of the matrix, the C flux will naturally decrease, so that the C flux curve would shift down. Therefore, a system

9.

MECHANISMS OF OXYGEN

PRCCIPITATION: SOME QUANTITATIVE

ASPECTS

379

that initially finds C-absorption favorable would switch to I-emission after C is exhausted. VI. Defect Generation Associated with well-grown SiOz precipitates, interstitial-type prismatic dislocation loops and stacking faults (SF) are routinely observed (Maher et al., 1976; Ponce and Hahn. 1984; Tan and Tice, 1976; Yang et al.. I978b: Tempelhoff et al., 1979). The prismatic dislocation loops have ( I lo)/? burgers vectors and are generated by prismatic punching. The SF grow by the climb motion of the (111)/3 Frank partial dislocations bounding the fault layers.

I . SI SEI-F-INTERSTITIAL GENERATION Since SF grow via the climb motion of the ( I I1)/3 Frank partial dislocations by either absorbing I from or emitting V into the Si lattice, they constitute evidence that, associated with the 0;precipitation process. an I-supersaturation is present. The alternative possibility that a V undersaturation is present needs not be further considered, since it has been shown that this cannot explain the observed apparent 0, diffusion limited SiOz precipitate growth behavior (Taylor et al., 1992b. 1993a. and Section IV.2). A large effort has been made to measure this I supersaturation on a quantitative basis. The results are, however, quite elusive. Only two kinds of experimental techniques are available, those invoking measurements at the wafer surfaces and those invoking measurements in the Si bulk. Pregrown S F (generated by wafer surface oxidation) or implanted dopant layers have been used in the wafer surface type experiments. lrrespective of whether capping layers are used, however, the wafer surfaces behaved as I-sinks. Therefore, the Si bulk fsupersaturation induced by 0, precipitation is significantly decreased or even diminished at the Si surface regions. This renders the quantitative data reliability into serious doubts. For bulk-type of experiments, only the SF size can be monitored. Since nucleation of SF in the Si wafer bulk cannot be controlled. the data is similarly unreliable on a quantitative basis. Consequently, there i \ no acceptable measured I-supersaturation value associated with the 0, precipitation process up to now. 2 . PRlSMA-rlC DISLOCATION L O O P PtJNCliINC

The interstitial-type ( I 10)/2 prismatic dislocation loops associated with the SiO, precipitates are generated by the mechanism of prismatic punching. which was identified on a qualitative basis since early times (Maher

380

T. Y . T A N A N D W. J . TAYLOR

et al., 1976; Ponce and Hahn, 1984; Tan and Tice, 1976; Yang et al., 1978b; Tempelhoff et al., 1979). In contrast to the case of I-supersaturation, Taylor, Gosele and Tan (1992a) have recently obtained quantitative information on the prismatic punching process. Prismatic dislocation punching occurs as also a stress-strain relief mechanism, in parallel with I-emission and C-absorption. The fact that the punched out loops are interstitial-type is consistent with the presence of a compressive stress associated with the SiO, precipitate growth process. In dynamical equilibrium with the emitted I , there is a residual strain left at the precipitate (Taylor et al., 1991, 1992a, 1992b). This growth residual strain constitutes a measure of the effectiveness of 1-emission in relieving the precipitate growth strain. Because the thermal expansion coefficient of Si is larger than that of SiO,, a compressive cooling strain also develops during cooling after precipitate growth. As an additional means of strain relief, prismatic dislocation loops can be punched out into the Si matrix by the stress accompanying the precipitate strain. Prismatic punching can occur only if the strain energy is large enough for loop nucleation to occur, otherwise I-emission will remain as the only means of strain relief. Thus, prismatic dislocation loop punching occurring or not is a measure of the strain level. The cooling strain is straightforward to calculate, and the calculation of the growth residual strain can be carried out using Eqs. (16), (24) and ( 2 5 ) . After the cooling strain and the growth residual strain are both calculated, the theory of Ashby and Johnson (1969) for nucleation of prismatic dislocation loops can be used to determine, as a function of the precipitate size rr, the critical strain level 6cr'(rf)above which prismatic punching can occur. The calculated growth residual strain values are in the order of to indicating that the precipitate growth strain is relieved via Z-emission by -90% to 99%. This is, of course, quite consistent with our earlier calculated y , values shown in Fig. 2 in the appropriate temperature range. Experimental results on whether prismatic punching has or has not occurred fit the calculated critical strain level fairly well, thereby indicating that the calculated strain and 6"'(r,) values are in acceptable accuracy ranges. Without relief, the cooling strain is given by 6,

=

1 - a,,AT - 1, 1 - aSiAT

(43)

where a,, and aSiare respectively the thermal expansion coefficients of SiO, and Si, given by 5.5 x lo-' K - ' and 5.0 X K - ' , respectively, and A T is the cooling range taken to be T, - 300"C, with T, being the precipitate growth temperature and 300°C taken to be the minimum tem-

9.

MCCHAYISMS OF OXYGEN PKtClPITATION: SOME QUANTITATIVE ASP€CTS

800

900

1000

1100

381

1200

Fit;. 7 . Some calculated C / ( r , ) / C yvalues ' a s ii function of the SiO, growth temperature / < . The parameters ( a . p) aw)ciated with each curve denote the Si matrix oxygen concen, a as in C , ( = ) = a x 10" c m - ' . tration. C',IX). and I-wpersaturation. C / ( r ( ) / C ; qvalues: and a s in C ' , ( r , = p. To avoid overcrowding. only p values of I and 10 are included. Each ( ( 1 . 10) curve terminate5 at a temperature for which the precipitate will cease to grow under the given oxygen concentration and the I-5upersaturation valueb.

perature at which a dislocation is still mobile. The results so calculated represent the maximum attainable cooling strain since the dislocation may already not be mobile at ;I temperature higher than 300°C. In Eq. (43) and in subsequent expressions. 6 represents the unconstrained strain values. i.e., the "misfit." To calculate the growth residual strain, Eqs. (24) and ( 2 5 ) were solved for C,(x)/C;'qvalues in the range of I to 10 to obtain the corresponding C',(Y,)/C';~values, see the results 5hown in Fig. 7. These values were then used in Eq. (16), with the rightmost term neglected. to obtain the corresponding growth residual strains. 6,. The results are shown in Fig. 8. The sun1 of the appropriate 6, and 6, values, S , , are shown in Fig. 9. For the results shown in Figs. 7 to 9, the matrix C , ( r )value was also used as a parameter. It is seen from Fig. 8 that 6, attains values in the range of l o - ' to lo-'. Considering that the unrelieved strain is -0.26, this demonstrates that /-emission is a very effective strain relief mechanism during precipitate growth: by -90% to 99%. Of course, without strain relief. neither precipitate growth nor precipitate nucleation can occur. The total strain is on the order of lo-', see Fig. 9. I n 0, precipitation experiments in CZ Si. for wafers with the same C , ( x )value and annealed at the same temperature, precipitate densities

382

T. Y. TAN AND

1(

W . J . TAYLOR

.l 800

900

1000

1100

1200

T, ("C)

FIG.8. Some calculated values of the growth residual strain 6,. The parameters (a,p) have the same meaning as in Fig. 7 . 10.'

I

00

1

FIG.9. Some calculated values of the total strain 6,. The parameters (a,p) have the same meaning as in Fig. 7 .

can vary widely because they are strongly dependent upon the nucleation treatment. Thus, the Z-supersaturation in the Si matrix, C,(m)lC,eq,may range from 1 to some larger values. While many experimental results have attested to the existence of an I-supersaturation in the Si matrix qualitatively (Maher et al., 1976; Ponce and Hahn, 1984; Tan and Tice,

-

9.

MECHANISMS OF OXYGEN PRFCIPITATION: SOME QUANTITATIVE ASPECTS

383

1976; Tempelhoff et al., 1979; Yang et al., 197%). no usable quantitative data exist. Therefore, C,(=)/C;q needs to be used as a parameter within a restricted value range, say. from I to 10. The resulting C,(r,)/CEqvalue range and hence also the 6, range are both fairly narrow. In particular, that of 6, is within a few times, see Fig. 8 . Aside from the intrinsic interest for knowing the strain and precipitate size levels for prismatic punching to occur, it is obvious that such a study will also offer a check on whether the preceding calculated strain values are sufficiently accurate. For precipitate strain relief by dislocation loop punching, the nucleation theory of Ashby and Johnson (1969) is used. They considered the system energy change when a shear nucleator loop of radius r , is formed by the strain around a spherical precipitate of radius r, in an isotropic matrix:

where the first term on the righthand side describes the increase in energy due to the dislocation generation while the second term describes the decrease in energy due to strain relief. A stable shear loop is nucleated when AE 4 0 holds. In Eq. (44) p,,, is the Si (matrix) shear modulus, 4.4 x 10’’ eV cm-3; u is Poison’s ratio of Si, 0.26; K,, is the SiO, bulk h is the Burgers vector of a 1/2(110) modulus, 2.3 x 10” eV cm dislocation, 3.84 A; 6 is the strain; x, y and z are spatial coordinates: c’ = r/2 - z’; and z = 0.707r,. By inserting values for 6, and rp into Eq. (44) and testing a variety of values for r , (0 < r, < 2r,), the feasibility of punching out a dislocation loop has been determined numerically. For a given r , , the minimum strain value 6 ” ’ ( r , ) that allows a stable nucleator loop t o be punched out is plotted in Fig. 10. I n the upper (shaded) region of Fig. 10 strain relief via prismatic punching can occur, while in the lower (open) region strain can only be relieved by I-emission. Some available experimental results (Hasebe, Corbett and Kawakami, 1992; Inoue et al., 1981; Lawrence and Tsai, 1986; Maher et a]., 1976: Shimura. Tsuya and Kawamura. 1980; Tan and Tice, 1976; Tempelhoff et a]., 1977, 1979; Tsai, 1986: Yang et al., 1978a. 3978b) on prismatic ) shown in Fig. 10. The punching can be described by the t i C r ’ ( r , criterion strain values were as those shown in Figs. 8 and 9. For each case the strain value from the overall strain curves such as those shown in Fig. 8 according to the growth temperature and oxygen concentration were

‘;

384

T. Y. T A N AND W. J. TAYLOR

.01

.l

1

10

r f (Pm)

FIG. 10. The dependence of the critical strain, 8cr’(rf),on the precipitate radius r, for prismatic punching to occur. In the upper (shaded) region, strain relief via prismatic punching can occur. In the lower (open) region. strain can be relieved only by I-emission.

determined. The data points so determined are plotted in Fig. I I in accordance with the observed precipitate size. The punched and notpunched data shown in Fig. 11 fit the 8cr’(rf)criterion fairly well. Here f i t means that the datum point lies in the appropriate region defined by the ?jcr’(rf)curve as indicated in Fig. 10. It is not necessary that the datum is lying on the curve. For the not-punched cases, results for which the precipitates are existing alone, i.e., without dislocations, are included. For the punched cases, only results for which a lone precipitate is existing with a set or sets of its punched-out loops were included. For these punched cases, the loops are of the same size, which also equals the size of the precipitate. On an experimental basis, this indicates that they are all generated in a narrow time range near the onset of cooling or during cooling. Each datum point in Fig. 11, in the form of a vertical bar with intersecting horizontal tick marks, contains two kinds of uncertainties. The first arises from the reported oxygen concentration value uncertainties, which is represented by the length of a portion of the datum bar: from the bar bottom position to that of the first tick mark upon moving upward. The second is due to the lack of a more precise knowledge of the C,(m)/Crq values in the experiments. In Fig. 11 this is represented for each case by up to four tick marks intersecting the datum bar. From the bottom to the top of the datum bar, the tick marks are, respectively, for C,(=)/C;q values of 1, 2, 5 and 10. Each tick mark position denotes the

9.

MECHANISMS OF OXYGEN PRECIPITATION: SOME QUANTITATIVE ASPECTS

385

10 O

10

10

10

1

-2

-3

0.01

0.1

1

r f (vm)

F I G .I I . Experimental data. for which prismatic punching has not (filled bars) and has (open bars) occurred. fitted to the total \train f i . The upper and lower regions separated hy the ?jCr'(rf) curve have the same meanings a \ in Fig. 10. See Taylor et al. (1992a) for the origin of the experimental data.

top position of the data uncertainty due to the oxygen concentrations. It is seen from Fig. 1 I that generally the different data points satisfy the 6"'(r,) criterion with different C,(x)/c';qvalues. Each datum point may satisfy the S Y r , ) criterion for the whole considered C,(x)/C;qvalue range of I to 10, the lower portion of the C,(x)IC;q value range (the second rightmost datum of the not-punched category, filled bars), or the higher portion of the C,(=)/C;q value range (the five leftmost data of the punched category, open bars). Such variations are quite reasonable since it can be expected that in the different experiments the C,(=)lC;q values in the Si matrix are in general different and most of them should be larger than I . Using the C,(x)/C;qvalue range of from I to 10, the resulting 6, values are confined in a range of within a factor of -3. In three cases (Tan and Tice, 1976; Tempelhoff et al., 1079; Yang et al., 1978a) the innermost loop is of the same size of the precipitate, but away from the precipitate the prismatic loops in the same set monotonically decreased in size, indicating that they are punched o u t by the growth residual strain at different times in situ during t h e precipitate growth process. These data are plotted in Fig. 12 and compared to the 6"'(r,) curve. The data bars and the horizontal tick marks have the same meanings as those in Fig. 1 I . These data were not included in Fig. I I , since the strain component involved here is only the growth residual strain 6,. For each datum point, the precipitate size i s that inferred from the size of the smallest loop situated

386

T. Y. T A N A N D W. J. TAYLOR

10

0

3

lo-' 0 0 "

10

10

-* -3

0.01

0.1

1

10

r f (Pm)

FIG. 12. Data of in situ punched loops fitted to the growth residual strain 6,. The upper and lower regions separated by the 6cr'(r,)curve have the same meanings as in Fig. 10. See Taylor et al. (1992a) for the origin of the experimental data.

at the outermost position of the set, regarded as being generated at the onset of the in situ loop punching process. As in the case of Fig. 11, the needed C,(m)/C;q values for obtaining the good fit in Fig. 12 are also in

the range of 1 to 10. The satisfactory fits in Figs. 1 1 and 12 indicate that the model for calculating the precipitate growth residual strain (Taylor et al., 1991, 1992a, 1992b) and the model of Ashby and Johnson (1969) for dislocation loop nucleation are in acceptable accuracy ranges. The results showed that prismatic punching is also not an effective means of relieving the strain during precipitate growth. In most cases, punched out dislocation Loops are generated during cooling or at the end of the annealing. In the few cases prismatic punching seems to be operative during precipitate growth, the precipitate size was already fairly large. Thus, I-emission constitutes the only effective strain relief mechanism during precipitate growth. VII. Summary: The Free Energy and Flux Balance Treatment of the Oxygen Precipitation Problem

Based on considerations of Gibbs free energy, on the one hand, and flux balance, on the other, this chapter addresses some aspects of the oxygen precipitation problem in Si on a quantitative basis. These include

9.

MECHANISMS OF OXYGEN PRECIPITATION: SOME QUANTITATIVE ASPECTS

387

precipitate nucleation, growth, and defect generations. The approach is primarily that of Taylor et al. (1991, 1992a, 1992b, 1993a, 1993b, 1993~). In their treatment t h e strain associated with the oxygen precipitation process has been directly correlated to either I or V, which serves as a strain relieve mechanism. However, the effects of I and V cannot be treated together with the strain. The Gibbs free energy formulation was first used by Vanhellemont et al. (1987) who obtained an expression of the critical nucleus for nucleation to occur, which contains contributions from both I and V. The relative contributions of I and C’ are, however, left as parameters. They have obtained no quantitative correlation between the point defect concentrations and strain, which is ;I task that cannot be accomplished by the formulation. The Gibbs free energy and flux concepts have been first used together by Tiller and Oh (1988) to examine the SiO, precipitate growth properties. Some of their results are quite similar to those obtained by Taylor et al. (1991). For example, their calculated C,(r,)lC;q values are nearly identical to the S, values shown in Fig. 3 , and they also concluded that the precipitate exhibits an apparent 0, diffusion-limited growth behavior. In order to treat the roles of I-emission, V-absorption and strain together, however. the mathematical complexity has prevented other information to be clearly discerned. For example, it was not possihle to compare the efficiencies of strain relief between the OV-absorption and the 01-emission mechanisms. Furthermore, the formulation cannot he used also for nucleation studies. Also based on Gibbs free energy. Schrems et al. (1990) developed a computer simulation model, which includes contributions from both I and V. Again, the relative I and V contributions are left as parameters, and in actual simulations the V contribution has been neglected. N o direct relationship between strain and the point defect concentrations has been obtained. It is clearly desirable to find a formulation capable of yielding clear results on the problems of oxide precipitate nucleation, growth and defect generations by considering t h e roles of I , V and strain simultaneously. It i s also clearly desired to know more about the effects of other factors, such as ti and p + doping, which has not been discussed here. +

RWFRENCES Ashhy. M . F.. and Johnson. L. (1c)hC))./ ’ / i i / o s . M t r g . 20, 1009. Hain$. S . K . . Griffiths, D. P.. Wilke\. J . 6.. Series. R . W . , and Barraclough. K . G . (1990). .I. t/ec.tr.ocl~etn.Soc. 137, 647 Bean. A . R . . and Newman, R. C. 11971 ). J . f’hy.~.Cheni. Solid.\ 32. 121 I . Bender. H . , and Vanhellemont. J . ( I Y X X ) . Phy.,. S c c i r . S o l . ( ( 1 ) 107, 455. Benssn. K . E.. Lin. W . . and Martin. t.P. (1981). In Huff et al.. p . 33.

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Bourret, A. (1987). Inst. Cof. Ser. No. 87, p. 39. Bourret, A., Thibault-Desseaux, J., and Seidman, D. N. (1984). J . Appl. Phys. 55, 825. Bullis, W. M., and Kimerling, L. C. (eds.). (1983). Defects in Silicon. The Electrochem. Soc.. Pennington, N.J. Burke. J. ( 1965). The Kinetics q f Phase Transformations in Metals, Chapter 5 . Pergamon Press. London. Craven, R. A. (1981). In Huff et al., p. 254. Christian, J . W. (1965). The Theory of Transformations in Metals and Alloys. Chapter 10. Pergamon Press, Oxford. Corbett, J . W., McDonald, R. S.. and Watkins, G. D. (1973). J . Phys. Chem. Solids 25, 873. de Kock, A. J . R. (1983). In Aggregates Phenomena of Point Defects in Silicon. E. Sirtl, J. Goorissen and P. Wagner (eds.), p. 58. The Electrochem. SOC.,Pennington, N.J. de Kock. A . J . R., and van de Wijgert, W. M. (1981). Appl. Phys. Lett. 38, 888. Fair. R. B. (1983). In Bullis and Kimerling. p. 61. Fair, R. B., Pearce, C. W., and Washburn, J. (eds.). (1985). Impurity Dgfusion and Gettering in Silicon. Mat. Res. SOC.Proc. 36, Mat. Res. Soc., Pittsburgh. F611. H., and Kolbesen, B . 0. (1975). Appl. Phys. 8, 319. Gaworzewski, P., Hild, E.. Kirscht. F.-G., and Vecsernyes, L. (1984). Phys. Stat. Sol. A 85, 133. Gosele. U.. and Tan, T. Y. (1982). Appl. Phys. A 28, 79. Gosele. U . . and Tan, T. Y. (1983). In Mahajan and Corbett, p. 45. Gosele. U . . and Tan, T. Y. (1985). In Fair et al., p. 105. Graff. K., Gallrath, E., Ades, S . .Goldenbach, G., andTolg, G. (1973). Solid-Stale Electron. 16, 887. Gupta. S.. Messoloras, S., Schneider. J. R., Stewart, R. J., and Zulehner, W. (1992). Srrnicond. Sci. Techno/. 7, 443. Hasebe, M.. Corbett, J. W., and Kawakami, K. (1992). Muter. Sci. Forum 83-87, 1475. Hu. S. M . (1980a). Appl. Phys. Lett. 36, 561. Hu. S. M . (1980b). J . Appl. Phys. 51, 3666. Hu, S. M . (1986). In Mikklesen et al., p. 249. Huff. H . R.. Kriegler, R. J., and Takeishi, Y. (eds.). (1981). Semiconductor Silicon 1981. The Electrochem. Soc., Pennington, N.J. Huff. H . R., Abe, T., and Kolbesen, B. (eds.). (1986). Semiconductor Silicon 1986. The Electrochem. Soc., Pennington, N.J. Huff. H. R., Barraclough, K. G., and Chikawa, J.-I. (eds.). (1990). Semiconductor Silicon IYYO. The Electrochem. Soc., Pennington, N.J. h u e , N . , Wada, K., and Osaka, J. (1981). In Huff et al. (1981). p. 282. Kalejs, J. P., and Ladd, L. A. (1984). Appl. Phys. Lett. 45, 268. Kennel, H. W.. and Plummer, J. D. (1990). In Huff et al., p. 496. Kung. C. Y.. Forbes, L . , and Peng, J. D. (1983). Mat. Res. Bull. 18, 1437. Ladd. L. A,. Kalejs, J. P., and Gosele. U . (1985). In Fair et al., p. 89. Lawrence. J. D., and Tsai, H. L. (1986). In Mikklesen et al., p. 389. Lin. W., and Benson, K. E. (1989). Microelectronic Materials and Processes, Chapter 1 . Kluwer Academic Publishers, Norwell, MA. Livingston. F. M., Messoloras, S., Newman, R. C., Pike, B . C., Stewart, R . J., Binns. M . J.. and Wilkes, J. G. (1984). J . Phys. C : Solid State Phys. 17, 6253. Mahajan, S . . and Corbett, J . W. (eds.). (1983). Defects in Semiconductors I I . Mat. Res. Soc. Proc. Vol. 14, North-Holland, New York. Mahajan. S.. Rozgonyi, G. A , , and Brasen, D. (1977). Appl. Phys. Lett. 30, 73.

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Maher. D. M . . S t u d i n g e r . A . . a n d Patel. J . R . (1976).J . Appl. Phvc. 47, 3813. Mikkelsen. J . C . , Ji-.. Pearton, S . J . . Corbett. J . W., and Pennycock, S. J. (eds.). (1986). O.vvgc,ii, Curbon. Hydrogen und Nitrogrri in Cnstcrllinc. Silic.on. Mat. Res. Sot. Proc. 59, Mat. Res. Soc.. Pittsburgh. Moreheud. F. F.. a n d Lever. R . F (1986). Appl. Phvs. Leri. 48. 151. Mort. N . F.. a n d Nabarro. F. R . N ( 1940). Prot . Plivs. Sot,. 52, 86. Nabarro. F . R . N (1940). Pro(.. K I I V So(,. A 175. 519. Narayan. J . . a n d T a n . T. Y . ( e d s 1. (1981). 1kfec.t.s in Semiconductors. Mat. Reh. S o c . Proc. Vol. 2, North-Holland. N e u York. N e w m a n . R . C.. a n d Wakefield. J . I 1961). J . P / I M .Charn. Solids 19. 230. Oate\. A . S . . a n d Lin. W . ( 1988). ,4ppl. I'hys. f . t * t t . 53, 2660. Oehrlein. 6. S.. L.in&trom. J . L... and ('orbe!:. J . W . (1982).Appl. Phys. Leti. 40, 241. Ogina. M. (1982). Appl. Phy.s. Lett. 41. 817. Patel. J . R . . J a c k w n . K . N . . and K e i \ \ . H . (1977). J . Appl. Phys. 48. 5279. Patrick. W . . H e a r n . E . . We5tdorp. W . . and Borg. A . (1979). J . A p p l . Phys. 50, 7156. Peihst. H . . a n d Kaidt, H . (19811. P / i v \ . . S i u . Sol. A 68, 253. Petroff. 1'. M . . a n d de Kock. A . J . K (19751, J . (.r>,.st. Gro\t,t/i 30, 117. l'once. F. A , . and H a h n . S . (1984). I n f
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Templehoff, K., Spiegelberg, F., and Gleichmann, R. (1977). In Semiconductor Silicon 1977. H. R. Huff and E . Sirtl (eds.), p. 585. The Electrochem. Soc., Pennington, N.J. Tempelhoff. K., Gleichmann, R., Spiegelberg, F., and Wruck, D. (1979). Phys. Star. Sol. A 56, 213. Tiller, W. A.. Hahn, S., and Ponce, F. A. (1986). J. Appl. Phys. 59, 3255. Tiller, W. A.. and Oh, S. (1988). J. Appl. Phys. 64, 375. Tsai, H. L. (1986). In Huff et al., p. 790. Vanhellemont, J., and Claeys, C. (1987). J. Appl. Phys. 62, 3960. Yarnarnoto, K.. Kishino, S., Matsushita. Y.. and Lizuka, T . (1980). Appl. Phys. Lett. 36, 195. Yang. K. H.. Anderson, R., and Kappert, H. F. (1978a). Appl. Phys. Lett. 33, 225. Yang, K. H., Kappert, H. F., and Schwuttke, G. H. (1978b). Phys. Star. Sol. ( a ) 50, 221.

SF.MICONDII("IOKS AND SEMIMETALS. VOL 42

C H A P T E R 10

Simulation of Oxygen Precipitation M . Schrrms INSTITUT FUR ALLCEMEINE TI EKTROTFCHNIK l l N D ELEKTRONIK TECHNISCHE UNlVERSlTAT WIFIU. VIE N N A . AUSTRIA

1. 11.

111.

IV.

V.

VI.

. . . . . . . . . . . . . . . . MODELTYPES . . . . . . . . . . . . . . . . . I . Nucleution Mode/.\ . . . . . . . . . . . . . . . 2 . Dererminisric Gnibt 1h Mode1.c. . . . . . . . . . . 3 . Combined Nucdrtrrion und Growth Models . , , , . 4. Monte C(irlo Model., . . . . . . . . . . . . . . 5 . Models Bused o n R u f e or F'okktr-Plnnck Eyrturions . MODELSA N D EXPERIMINTAI KESLIITS . . . . . . . . . I . Generul Remurk.\ . . . . . . . . . . . . . . . 2 . One-, Tuzo-, und lhrer,-.Step Thermal CvcleJ . . . . 3 . Miclrisrep Thermul C'vc~les . . . . . . . . . . . . COMPUTER-AIDED DF,SKAOF O X Y G EPRECIPITATION N . , . I . Substitiitionul Anneulin,y.c . . . . . . . . . . . . 2 . 1njluenc.e of Proc.e\.r Vtrricrrions . . . . . . . . . ON T H E INTERACTIOMOF OXYGEN WITH OTHER DEFECTS . 1 . Currenr Models . . . . . . . . . . . . . . . 2 . Generuli,-rd Prec rpirution Eqirirrions . . . . . . . . SUMMARY . . . . . . . . . . . . . . . . . . . . REFERENCES. . . . . . . . . . . . . . . . . . INTRODUCTION

. . . .

39 I 397 393 396 4 0

.

402

. .

404 413 4 1 416

.

. . . .

.

. .

414 428 428 431

.

435 435 44 I

.

443

.

444

.

1. Introduction

The recently growing interest in the use of computer simulation for investigating oxygen related phenomena in silicon is like in many other fields catalysed by the continuously decreasing cost to performance ratio of modern computer equipment. which allows the development of increasingly sophisticated and accurate models. Apart from the scientific interest modeling and simulation of oxygen precipitation and related phenomena offer the economic perspective of minimizing costly and time consuming annealing experiments. which are necessary for designing oxygen precipitation during thermal device processing steps in order to optimize internal gettering and denuded zone depths. The goal of this chapter is to outline the use of computer simulation for calculating numbers and sizes of oxygen precipitates in thermally 39 I Copyrighr (9 I 9 4 by Academic Pres5. Inc. All right\ of reproduction in any form reserved. ISBN 0-1?-75?14?-9

392

M. SCHREMS

treated silicon crystals and to relate the calculation results to experimental findings. Other topics such as ab initio calculations of cluster energies of very small precipitates containing only a few oxygen atoms as well as the issue of thermal donor modeling lie outside the scope of this review. From the experimental findings analysed in the other chapters of this book it can be seen that oxygen precipitates may occur in a number of different sizes and shapes in thermally treated CZ-Si. The fundamental quantity for describing the growth and dissolution processes of all precipitate sizes is the precipitate size-distribution function. For a given processing time and a given volume in the crystal, it yields the number of precipitates as a function of a precipitate size related quantity, which may be, e.g., the precipitate radius or the number of particles in the precipitate. In a more general formulation (Section V.2) the precipitate distribution may depend not only on the size parameter, but on the composition (i.e., the set of the numbers of particles of each species S in the precipitate) as well as the geometrical configuration of the particles, which determines the precipitate shape. Even simplified distribution functions like the oxygen precipitate size-distribution depending on the spherical radius or the number of oxygen atoms in the precipitate are hardly accessible experimentally. Comparisons between calculated and experimental results will therefore be performed for weighted sums over the size-distribution function like the total precipitated oxygen concentration, the total density of precipitates or the average precipitate radius. Frequently used oxygen precipitation models will be classified according to the degree to which they provide information on the sizedistribution function of the oxygen precipitates (Section 11). For working out the basic differences between the model types, Section I1 discusses only those models that neglect the interaction of oxygen precipitation with other phenomena such as intrinsic point defects, mechanical stress or concentrations of other dopants. If not stated otherwise, the models also assume spherical precipitate geometries for model simplicity, although other shapes such as platelets are frequently observed experimentally. Generalized models, which also address the interaction of oxygen precipitation with other defects, will be discussed in a separate section later (Section V). In spite of the simplifications some models from Section 11, especially the model based on chemical rate equations in combination with a Fokker-Planck equation, will be shown to give a good description of oxygen precipitation observed for a number of one-, two-, three- and multistep annealing experiments (Section 111). Examples for using simulation to design the oxygen precipitation behaviour during thermal cycles and to analyse the influence of processing parameters on the amount of

10.

SIMULATION OF OXYGEN PRECIPITATION

393

precipitation observed are given in Section IV. Finally both current and potential future modeling approaches addressing the interaction of oxygen precipitation with other phenomena will be outlined in Section V. 11. Model Types

I . NUCLEATION MODELS (I.

ConcYpf

The steady-state theory of nuclei formation from supersaturated solutions was originally developed by Vollmer and Weber (1926). With its extensions introduced by Becker and Doring (1935) it is called VWBDtheory according to the initials of its developers. Further extensions were reported by Kaischew (1957). The theory assumes that the precipitate size distribution function equals the equilibrium distribution function .f'q(n)

=

C', exp[ - b G ( n ) / ( k ,T ) ]

(1)

which is proportional to the concentration C,yof nucleation sites and an exponential factor. It contains the Gibbs energy A C ( n )for the formation of a precipitate with n oxygen atoms, which is divided by the Boltzmann constant k , times the absolute temperature T . The critical number ti, of oxygen atoms follows from the condition dAG(n)ldn = 0. For precipitates with II > n , . called sfcible precipitates, growth is more probable than dissolution. while for n < n , (rrnstable precipitates) the opposite is true. The nucleation theory calculates the number of precipitates (nuclei) that grow per unit time from subcritical to supercritical precipitate sizes. The resulting (steady state) nucleation rate is given by (Hirth and Pound. 1963)

The dimensionless Zeldovich factor Z equals

For the frequency W of attachment of atoms to the nucleus

is set. with c0 denoting the surface condensation coefficient. D o the diffusivity of oxygen, (I the atomic .lump distance in the lattice and Co the

394

M. SCHREMS

concentration of interstitial oxygen. For spherical oxygen precipitates the critical radius r,. is related to the critical number of oxygen atoms by 4n -r: 3vo with v o being the precipitate volume per oxygen atom. n,.

=

b. Examples and Basic Results

Most of the oxygen precipitation models proposed until now are based on the VWBD theory, which is also called steady state nucleation theory. The models differ mainly in assumptions on the concentration of sites C , (Eq. (I)), the term used for the Gibbs energy of precipitate formation AG(n) and the value of the Zeldovich factor 2. In the homogenous nucleation models C, is set equal to the interstitial oxygen concentration (Freeland et al., 1977; Inoue, Wada and Osaka, 1981; Inoue, Wada and Osaka, 1987; Reiche and Nitzsche, 1985) by most authors. However, Voronkov et al. (1989) claim that by this assumption the mass action law is violated and suggest setting the concentration of nucleation sites C , equal to the total density of interstitial lattice sites in the crystal. Heterogenous nucleation models assume that C, is equal to the concentration of some other defect such as carbon (Kishino et al., 1982; Usami, Matsushita and Ogino, 1984; Isomae, 1991) or vacancy clusters (Ravi, 1974). The Gibbs energy AG(n = n,.) occurring in Eqs. (1) and (3) is frequently assumed to be equal to the sum of volume energy accounting for the formation of the precipitate from oxygen atoms in solid solution and interfacial energy of the precipitate due to interaction with the surrounding crystal atoms: AG(n,.)

=

-n,.k,Tln

i:;) + -

4nrf.a.

The interfacial energy parameter a (a = 0.43 J/rn2; Inoue et al., 1981)and the Zeldovich factor 2 are usually determined from matching calculated nucleation rates J (Eq. (I)) to values obtained from experimental results. For Z either a constant value (2 = 0.01; Inoue et al., 1981) or Eq. (3) (Reiche and Nitzsche, 1985) is used. Cbqdenotes the equilibrium concentration of oxygen in the crystal. The basic calculation result of the steady state nucleation models is the nucleation rate Eq. (2). The total precipitate density Copfollows from integrating the nucleation rate J with processing time Cop = J J d t

(7)

for a given thermal sequence. Examples of calculation results obtained by Inoue et al. (1981) can be seen from Figs. 1 and 2. A strong increase

10.

SIMU1.A I ION O F OXYGEN PRECIPITATION

395

Oxygen Content C, ( lOt7atoms/crn3) FIG. I. Nucleation rate at 750°C V.I initial oxygen concentration. Calculations were performed with a model based on steady htate nucleation theory. The expenmental oxygen concentration values in this figure were determined using a FTlR spectra conversion coefficient o f h ppma . cm. When compared to the other figures (DIN conversion coefficient of 4.9 ppma . em) the oxygen concentrations in thih figure have to he multiplied by 4.916. (After Inoue el al.. 1981. This figure wi15 originally presented at the Spring 1981 Meeting of the Electrocheinical Society held in Minneapoli\.)

of the nucleation rate with the initial oxygen concentration is observed both experimentally and in the calculated results for a processing temperature of 750°C. The nucleation rate as a function of temperature shows a peak for temperatures typically between 600°C and 800°C. It descends both for lower temperatures. which is determined by the lowering of the valuc of the oxygen diffusivity, and for higher temperatures, where the increase in the equilibrium concentration of oxygen is dominant. The values of the equilibriiim size-distribution function (Eq. ( I ) . Fig. 2 ) were found to decrease with increasing temperature (Inoue et al.. 1981). c. Applicability

Despite the good agreement between experimental and calculated precipitate densities found for a number of cases (Inoue et al., 1987; Reiche and Nitzsche, 1985; Voronkov et al., 1989; Babitskii et al., 1990), the steady-state nucleation models have substantial deficiencies in describing the oxygen precipitation process: 1.

The loss in interstitial oxygen due to oxygen precipitation and the average precipitate radius as a function of processing time cannot be calculated.

396

M. SCHREMS

\

104

lo6 104

loz

I1

loo LL 1

1

~~

2

1200 \ \llOO\’O‘ \ ‘, , 1 1 I 5 10 20 1

1

, ,u

\ I

50

100

Number of Oxygen Atoms in Embryo FIG.2. Equilibrium distribution functions of small precipitates (embryos) for various temperatures and an initial interstitial oxygen concentration of 1 1 . 10’’ cm-) (calibration as in Fig. 1) calculated with the same model as in Fig. 1. (After lnoue et al., 1981. This figure was originally presented at the Spring 1981 Meeting of the Electrochemical Society held in Minneapolis.)

The experimentally observed reduction in the total precipitate density for longer annealing times (e.g., Bergholz et al., 1989) cannot be described, since this would require negative values for the nucleation rate. From Eq. (2) it follows, however, that this cannot be achieved by the steady-state nucleation theory. 3 . The model is based on the assumption that the size-distribution function can be approximated by its equilibrium value.

2.

A transient nucleation theory containing the VWBD steady-state approach as a special case (Kashchiev, 1969; Toshev and Gutzow, 1972) may resolve problem (2), while problem (1) remains in any case.

2. DETERMINISTIC GROWTH MODELS u . Concept

All the models summarized by the term deterministic growth models share the assumptions that the precipitates can be regarded as equal in size and that their number is constant with processing time. The oxygen precipitation process is thus described only by the variation with time of a “deterministic” average precipitate size instead of using the more general

10.

SIMULATION OF OXYGEN PRECIPITATION

397

size-distribution function. which is based on the picture of statistical growth and dissolution processes for all precipitate sizes. With the additional assumption that the precipitate dimensions are small compared to the interprecipitate distance, direct diffusional interaction between precipitates can be neglected. The silicon crystal can then be divided into a number of cells each containing one oxygen precipitate with the net diffusional fluxes between individual cells canceling each other. An equation for the variation with time of the average precipitate size, which is also known as g r m l t h IuM’. is obtained by solving the diffusion equation for a single precipitate and its surrounding matrix area. Growth laws were reported for different precipitate shapes such as spherical (Wert and Zener. 1950; Ham, 1958). cylindrical discs (Flynn, 1964; Seidman and Balluffi, 1966; Hu, 1981; Wada and Inoue, 1985; Hu, 1986a, 1986b). oblate and prolate spheroids (Ham. 1958, 1959). Frequently models based on Ham’s theory of diffusion limited precipitation (Ham, 1958) are used. For spherical precipitates with an average radius f ( t ) as a function of time t an approximate solution of the transient diffusion equation yields the following growth law (Wert and Zener. 1950; Ham, 1958):

denote the oxygen concentration in the The symbols C,(t), C; and C,, bulk at the precipitate-matrix interface and in the precipitate. Considering the conservation of total oxygen an equation for evaluating the time dependent interstitial oxygen concentration C,(t) can be derived from Eq. (8) (Ham, 1958; Yatsutake, Umeno and Kawabe, 1984):

by assuming that the interfacial oxygen concentration is equal to the bulk equilibrium concentration C:;. C’,, denotes the total concentration of oxygen precipitates. The righthand side function H is given by

h. Esurnplrs uiid Basic Rrsults

Deterministic growth models were successfully compared with experimental data by a number of authors. For platelet-shaped precipitates (Wada, Inoue and Osaka, 1983) some experimental data for the increase

398

M. SCHREMS

1013

I

'

' """I

'

" " " q

800°C

~

0

.s Y

101'

a

.r

Ea 1010

1

10

100

1000

time [h]

FIG.3 . Precipitate densities vs. annealing time for two different temperatures. Calculations were made by using a deterministic growth model (solid lines). Experimental results (circles) were obtained from TEM investigations. (After Yatsutake et al., 1984.)

of precipitate size with annealing time could be explained by adjusting the value of the oxygen diffusivity until calculations meet the experimental data. Using Ham's theory for spherical precipitates, values for the oxygen diffusivity and the equilibrium concentration of oxygen were determined over a temperature range 500"C-l050"C (Livingston et al., 1984; Messoloras et al., 1987) based on experimental results for the loss of interstitial oxygen and the precipitate density after long-time thermal anneals. Earlier applications of Ham's theory calculated the total density of precipitates from given values of the oxygen diffusivity and the experimental data for the loss of interstitial oxygen (Newman et al., 1983; Binns et al., 1983; Wilkes, 1983). Yatsutake et al. (1984) determined values for the precipitate density from fitting experimental data for the loss of interstitial oxygen as a function of the annealing time by using a model based on Ham's theory for oblate spheroidal precipitates. The analytic equation used by Yatsutake et al. differs from Eq. (9) only by an additional lefthand side geometry-related factor, which approaches 1 when the oblate spheroid approaches spherical shape. The example in Fig. 3 shows that the calculated precipitate densities for two one-step anneals agree well with data from TEM observations. The average precipitate radii (Fig. 4) were determined from the conservation of total oxygen and are also well represented.

10.

SIMUI.ATION 01: OXYGEN PRECIPITATION

399

L

ec 10’

1

100

10 tinif,

1000

[ti]

FK, 4. Sire of platelet shaped oxygen precipitates vs. annealing time obtained from the w n e modeling and experimental study referenced in Fig. 3 . (After Yatsutake et al.. 19.84.)

c’.

Applicuhility

Contrary to the classical nucleation models discussed in Section 11. I . the deterministic growth models account both for growth and shrinkage of precipitates (see Eq. (8)). However, the concentration of precipitates Cop and the Loss of interstitial oxygen cannot be calculated simultaneously, since only one equation (e.g. Eq. (9)) is available. Furthermore, the concentration of precipitates is regarded as constant with annealing time. For a given annealing step with a fixed temperature. this may be valid after an initial transient period (Ham, 1958; Livingston et al.. 1984). For very long annealing times this assumption is also proven inadequate by experimental results (Livingston et al., 1984; Bergholz et al.. 1989) showing a reduction in the precipitate density with increasing processing time. which may be attributed to the growth of larger precipitates at the cost of smaller ones (“coarsening”). The assumption that all precipitates are equal in size may be considered a good approximation only if the precipitate size-distribution function is sharply peaked, which becomes more likely with longer annealing times and higher processing temperatures. In this context it is emphasised that precipitate size-distributions are not a pure theoretical concept, but that their existence is also observed experimentally (oxygen: Fraundorf and Shimura, 1985; antimony: Brabec et al., 1989; stacking faults: Patel, Jackson and Reiss, 1977). Therefore, a more detailed picture of the precipitation process can be

400

M. SCHREMS

given only by those models, which allow calculating the transient evolution of the oxygen size-distribution function. 3 . COMBINED NUCLEATION AND GROWTH MODELS a . Concept

The previous discussion has shown that nucleation models (Section 11.1) can calculate only the total concentration of precipitates during a

given annealing sequence, but not the total loss of interstitial oxygen or the average precipitate size. On the other hand, the loss of interstitial oxygen or the average precipitate size can be determined by using deterministic growth models (Section 11.2), if the value of the total precipitate density is known. Therefore, a combined use of the two model types seems desirable.

b . Examples and Basic Results Among the first published models suggesting a combined use of nucleation and growth models is the work by Usami et al. (1984). Oxygen precipitate nucleation (Eqs. ( 1 ) and (2)) was assumed to occur only at the site of a carbon atom. Oxygen precipitate growth was described by Eq. (8). Good agreement was reported between experimental and calculated oxygen reduction for a set of two-step annealing sequences using wafers with different carbon contents. Pagani and Huber (1987) proposed a model using homogenous nucleation by setting the concentration of sites in Eq. ( I ) equal to the interstitial oxygen concentration. Precipitate growth is described using Ham’s theory in the form of Eq. (9) from Section 11.2. For a multistep CMOS and a NMOS annealing sequence a correct prediction of trends in the experimental loss of interstitial oxygen as a function of initial oxygen was reported. Yang et al. (1987) formulated a model combining the use of nucleation theory and Ham’s theory with a one-dimensional diffusion equation. For several three-step HI-LO-HI annealing sequences the model could be applied to calculating the precipitated oxygen concentration and the density of precipitates in the bulk as well as in the near surface region of the wafer, where both precipitation and outdiffusion of oxygen contribute to the total loss of interstitial oxygen. Additionally, experimental and theoretical denuded zone depths were found to be in good agreement. Recently Isomae (1991) applied a model similar to the one proposed by Usami et al. (1984) for simulating oxygen precipitation both in three-step and in multistep CMOS-type annealing sequences. Experimental results could be satisfactorily explained only

10.

S I M U L A l I O N O F OXYGEN PRECIPITATION

1

40 1

10 100 Radius ( n m )

F I G 5 Size-distribution function
after replacing the growth law from Eq. (8) with an equation, proposed by Greenwood (1956). that also takes into account diffusional interaction betweeen neighbouring precipitates leading to precipitate coarsening. As in the work by Schrems et al. (I991a). which is based on a different method, discussed later (Section 11.5). multipeaking is observed in the calculated precipitate size-distribution function (Isomae, 1991) after a multistep CMOS-type thermal anneal (Fig. 5). c . Applicability

The combination of nucleation and growth models allows the simultaneous calculation of the oxygen l o s s , the total precipitate density and the average precipitate radius during thermal annealings. By special iterative numerical calculation schemes (Isomae. 1991) a precipitate sizedistribution can also be evaluated (Usami, Matsushita and Ogino, 1984; lsomae, 1991). However, for all precipitate radii smaller than the critical radius an equilibrium size-distribution function following a Boltzman distribution has to be assumed. If the critical radius rapidly increases with annealing time (e.g., due to ii rapid change of temperature during ramping) it has to be expected that even the size-distribution function in the regime of subcritical precipitate radii will not follow an equilibrium distribution immediately, but deviate from i t due to the finite period of time required for dissolving those precipitates, which become subcritical.

402

M . SCHREMS

4. MONTECARLOMODELS

a. Concept Work on applying Moc-2 Carlo xhniques for modeling oxygen precipitation was reported by Lavine, Hawkins and coworker. In earlier work a two-dimensional (Lavine and Hawkins, 1986) and later a threedimensional (Lavine, Russel and Hawkins, 1989) model was proposed. In the latter version oxygen diffusional jumps and oxygen aggregation was described in three spatial dimensions with the simulation domain typically being a cube of 0.4 km side length. Periodic boundary conditions were used. The number of oxygen atoms in the cell followed from the oxygen concentration times the cube volume. Randomly selected lattice sites served as heterogenous nucleation centers. At the beginning of a simulation, each nucleation site started with a randomly chosen number of two or more oxygen atoms. The remaining oxygen atoms were randomly distributed over the other lattice sites. When an oxygen atom approached a nucleation site it was either captured or jumped away depending on whether the value of a random number was greater or smaller than the value of the Boltzmann factor

B.F.

=

).

exp( - AGn-rn+l k, T

The Gibbs energy barrier AGfl-rfl+, for the incorporation of an additional oxygen atom into a precipitate with n oxygen atoms was given by AG,,,,,,

1

=

max{(AG(n + 1) - AG(n) + AGactivatlon,AGaCtivationl. (12)

The Gibbs energy AG(n) of an individual precipitate was modeled as the sum of volume and interfacial energy similar to the term used in the nucleation models. It was assumed that the total energy barrier cannot be smaller than an activation energy of AGaCtivation = 0.25 eV (Turnbull and Fischer, 1949). Escape of an oxygen atom in the precipitate may also take place. It is governed by a similar function as Eq. ( 1 1) with an attempt frequency used to control the rate of escape attempts. h. Examples and Basic Results

The basic calculation result of the Monte Carlo models is the sizedistribution function for oxygen precipitates. Some calculated results (Lavine and Hawkins, 1986) are shown in Fig. 6. Quantities like the concentration of precipitated oxygen and the total density of precipitates may be calculated therefrom. Studying the decrease of the total number of oxygen precipitates (precipitate coarsening) during single-step thermal

10.

SIMUl A710N 0 1 ; O X Y G E N PRECIPITATION

403

FIG.6 . Precipitate size distribution\ for annealing times at 750°C in 10 hr intervals as (After calculated by Lavine and Hawkins for an initial oxygen concentration of 10'" Lavine and Hawkins. 1989b.)

annealings was one of the main model applications (Lavine and Hawkins, 1986, 1989, 1992a. 1992b; Lavine et al.. 1989). The 2D Monte Carlo model (Lavine and Hawkins, 1986) was also applied for estimating the reduction in the density of precipitates due to a preceding rapid thermal anneal (RTA), by fitting calculated results for loss of interstitial oxygen after a two-step LO-HI annealing to experimental data (Hawkins and Lavine. 1989). c . App/icuhility

Unlike the model types discussed in the previous sections, the Monte Carlo models fully account for the transient evolution of the oxygen precipitate size-distribution function. However, a frequent problem of the

404

M. SCHREMS

Monte Carlo methods in general and their application to oxygen precipitation in particular is their excessive computational demand (Lavine and Hawkins, 1992b) when trying to increase the number of particles in the simulation domain in order to minimize statistical errors. A model that consumes only a “reasonable” amount of computation time was reported by Lavine and Hawkins (1992b) recently. However, according to my knowledge the term reasonable was not yet quantified and some of the calculated precipitate size-distributions were very “noisy,” which made a comparison to predictions by other methods such as the LSW theory (see Section 11.5) rather difficult. The models suggested until now (Lavine and Hawkins, 1986, 1989, 1992b) have been used mainly for fundamental studies of coarsening phenomena. Model calculations and a comparison to experimental results for oxygen precipitation in multistep device manufacturing cycles have not yet been performed. Consequently, it is not clear if there is practical limit in applicability to more complicated annealing sequences due to the demand in computation time.

5. MODELSBASEDON RATEOR FOKKER-PLANCK EQUATIONS a. Coricept

Similar to the Monte Carlo method outlined in the previous section, growth and dissolution of all precipitate sizes is described statistically. However, instead of using random numbers for deciding on growth and dissolution of individual precipitates in the simulation domain, the growth and dissolution of each entity of equally sized precipitates is described by one chemical rate equation. In the simplest case, a precipitate with ( n ) particles (oxygen atoms) may either incorporate (“growth”) or emit (“dissolution”) a single particle ( I ) following the quasi-chemical reaction

(n) + (1)%

+ 1)

dn

(n)+(n

-

1)

+ (1).

The statistical nature of precipitate growth and dissolution is introduced by the growth and dissolution rates g, and d,. The translation of Eq. ( 1 3) into a chemical rate equation (CRE) is straightforward and results in a single differential equation

for every precipitate size n . Equation (14) is often called the muster equution of the quasi-chemical process of Eq. (13). It is worth noting that by a stricter definition the name muster equation is reserved for those cases

10.

S I M U L A T I O N O b O X Y G E N PRECIPITATION

405

when f,, is a probability (van Kampen. 1981). Here. however, the functions I;,denote the numbers of precipitates containing n particles per unit volume. The set of functions,/;,for all values of n is the size-distribution function. With oxygen precipitates containing typically up to tens of millions of particles a similar number of CREs (Eq. (14)) has to be solved simultaneously. This computational problem can be resolved by approximating the set of CREs with a single partial differential equation called the Fokker-Plutick equation (FPE). I t is obtained by expanding the master equation with respect to the number of particles n , which is then regarded as quasi-continuous (Kramers-Moyal expansion (Gardiner. 1985)). Since the assumption of quasi-continuous particle numbers is a bad approximation for the smallest precipitates containing only a few atoms, a combination of CREs for the smallest precipitates up to a size n,,with a single approximating FPE for all larger precipitates was suggested (Schrems et al.. 1990b. 1991a: Schrems, 1991). The goal of this approach is to allow an accurate description of all precipitate sizes. while keeping the computational demand (Schrems et al.. 1991d) manageable. CREs and the FPE only provide the framework for modeling precipitation phenomena. Practical application requires the additional modeling of the growth and dissolution rates of the precipitates, which occur as coefficients in the equations. I n order to illustrate this, two examples of models. one using a FPE only (Schrems et al., 1989) and the other based on CREs in combination with ii FPE. are reviewed in more detail. h. E.ratnples und Busic. Rrsinlts Fokker-Planck equations have already been used in the modeling of a variety of physical and chemical problems (Gardiner. 1985). Nevertheless. the application for simulating oxygen precipitation in silicon was not reported until recently (Hartzell. Schaake and Massey, 1985; Schrems et al., 1989, 1990b: Schrerns, 1991, 1993).The basic calculation result of the method is the size-distribution function. Other quantities like the concentration of precipitated oxygen. the precipitate density and the average radius can be evaluated (Schrems et al., 1989. 1991a; Schrems, 1991). The models can be divided into approaches using a FPE only (Hartzell et al., 1985; Schrems et al., 1989, 1990a, 1990b) and those using chemical rate and Fokker-Planck equations in combination (Schrems et al., 1990~.1991a, 1991b, 1 9 9 1 ~ 1991d: . Schrems, 1993). i . Fohher-Planck eyuation on1.v. Hartzell et al. (1985) reported the first attempt to model oxygen precipitation by using a FPE. Comparison

406

M. SCHREMS

of calculated and experimental loss of interstitial oxygen after a variety of different anneals as well as calculated precipitate densities and sizedistribution functions for a two-step annealing were presented. An evaluation of the results is difficult, since the paper contains specific information on neither how the coefficients of the FPE were modeled nor the annealing conditions for obtaining the experimental results shown. Therefore, later work (Schrems et al., 1989; Schrems, 1991) is reviewed in more detail. The model is based on the Lifshitz-Slyozov-Wagner (LSW) theory (Lifshitz and Slyozov, 1961; Wagner, 1961; Landau and Lifschitz, 1983). Spherical precipitates with radius r were assumed. The FPE obtained from the Kramers-Moyal expansion uses the number of oxygen atoms n and the time t as independent variables ( n representation). A representation with r and t as independent variables was obtained by substituting the relation vo

=

vsio2/2 = 2.25.

cm3

with v o being the volume per oxygen atom in the precipitate with average stochiometry SO,. This yielded the following FPE:

with f ( r , t ) and j ( r , t ) being the transformed size-distribution function and precipitation flux. For statistical equilibrium [ a f ( r , t ) l d t = 01 the coefficients A and B can be related (Lifshitz and Slyozov, 1961; Landau and Lifschitz, 1983). Assuming a similar relation for the case of nonequilibrium (Schrems et al., 1989; Schrems, 1991) yielded

dr as a function of the absolute temperature T , the derivative a A G l d r of the Gibbs energy of a precipitate with respect to its radius r , and the other coefficient A ( r , t ) . The Gibbs energy was described as the sum of volume energy and interfacial energy: 4rr3 A G ( r , t ) = -k B T h 3vo with the interfacial energy parameter a and the equilibrium concentration C:; being determined from comparison of calculations to experimental

10.

SIMULATION OF OXYGEN PRECIPITATION

407

results (Schrems et al.. 1989).The interstitial oxygen concentration C,,(t) follows from the conservation of total oxygen C y ' :

assuming that out-diffusion can be neglected in the bulk. The term rz = 0 . 2 2 nm corresponds to the equivalent spherical radius of one SiOz molecule. While the coefficient B ( r . I ) is known to be most important for the growth kinetics of smaller precipitates (fluctuations), the coefficient A ( r , t ) is more dominant for larger precipitates. A(,, t ) can be approximated by the growth law of an individual precipitate, which is obtained by solving the diffusion equation outside a spherical precipitate (Lifshitz and Slyozov. 1961; Landau and Lifschitz. 1983):

For the oxygen diffusivity thc value by Stavola et al. (1983) was used. The concentration of oxygen atoms at the interface-precipitate matrix C ; ( r ) was obtained by assuming that thermodynamical equilibrium at the interface is restored quickly compared to mass transport ( d A G / d r = 0). This resulted in the relation

Initial and boundary conditions for the FPE (Eq. (16)) are formulated asuming a quasi-equilibrium diwibution function at the lower boundary (r? = 0.22 nm): j l r , t = 0 ) = Jo(r. t = 0 ) . ar,?,

(22)

(23) (24)

(25) The simulation parameter p accounts for the effects not considered in the model such as the influence of other impurities than oxygen (heterogeneous nucleation, coprecipitation with other dopants), or the differences in thermal history between different wafers. The solution of the FPE yields the size-distribution function (Fig. 7) of the oxygen precipitates

408

M. SCHREMG

loi2

-

r

+

:Annealing: 750°C/4h 1000°C/16h? :O-concentration: 15 1017 cm-3

7

1

10'1

j

2

-time: time: - -time: - time:

4h? 8h i

16h: 20h i 3 3

CI

-

\ \

lo3

I

1

; I

102

I '

;

'

'

"

','I

' '

1,- ,

,,,I

, , , , , , ,,

radius r at , 1989.)

as a function of annealing time. It is the basis for calculating the total precipitated oxygen, the average precipitate radius and the total density of precipitates (Section 111.I). ii. Rute equations in combination with a Fokker-Planck equation. Modeling of oxygen precipitation by combining chemical rate equations and a Fokker-Planck equation was reported (Schrems et al., 1990b, 1990c, 1991a; Schrems, 1991) and applied to simulating both bulk oxygen precipitation (Schrems et al., 1990c, 1991a, 1991b, 1991c, 1991d) and denuded zone formation (Schrems, 1993). The model's latest version (Schrems, 1993) is reviewed in the following. A small volume dV at an arbitrary depth z perpendicular to the wafer surface was chosen. According to Eqs. (13) and (14) growth and dissolution of the oxygen precipitates containing up to no oxygen atoms is described by a set of CREs: df,

-a( tz ,

t ) = g ( n - 1, z , t ) .f,-,- d ( n , z , t ) *f,

( n = 2 , . . . , n o ) (26)

10.

409

SIMULATION O F O X Y G E N PRECIPITATION

with g ( n , z , t ) and d ( n , i, t ) again denoting the growth and dissolution rates of oxygen precipitates. For all precipitates with more than tz = no oxygen atoms the set of CREs (Eq. (26)) is approximated by the corresponding FPE: B.f'+ A

.f

dn

d d(n,z.t) - - E . dn

(28)

Equation ( 2 7 ) with the number I I of oxygen atoms in the precipitate as one of the independent variables is called the Fokker-Planck equation in pcirticle number representation ( FPEPR) in the following. Accordingly, Eq. (16) is the FPE in radius representation (FPERR). Using Eq. ( 1 5 ) the FPERR can be related to the FPEPR (Schrems, 1991) yielding transformation rules for the size distribution functions f- f , the precipitation flux J -+ j and the coefficients A -+ A . R + B:

dn dr

f = J'. -,

J

=

J.

From Eq. (28) it becomes clear, that due to being the average of the precipitate growth and dissolution rate, B may be interpreted as the coefficient governing precipitate growth by fluctuations (Gardiner, 1985; Landau and Lifschitz, 1983). In the limit of larger precipitate sizes (Schrems, 1991) the value of the coefficients A or A in the FPE is determined by the difference between the growth rate Kin, . . .) and the corresponding dissolution rate d ( n . . . .). The term g - d can be approximated by the derivative with time dnldt of the number of oxygen atoms in a precipitate with size n . Also, dnldr was set proportional to the difference between the concentration C:; of oxygen atoms at the interface precipitate matrix and its equilibrium value (Cr;eq)(Schrems et al., 1991a; Schrems. 1991, 1993). Therefrom

resulted. 11 was further assumed that the dissolution rate depends only on the equilibrium concentration of oxygen atoms in the interfacial

410

M . SCHREMS

layer ( d rate:

=

K ~ ~ ~ ~ which C : ~ relates ~ ) , the dissolution rate to the growth

For the growth rate (Schrems et al., 1991a; Schrems, 1991, 1993) the ansatz

was used. The precipitate radius r and the number of oxygen atoms n in the precipitate are again related by Eq. (15). The growth rate depends on the number NE of oxygen atoms in the precipitate’s interfacial layer (thickness 6 0.235 nm). iV: is equal to the product of the volume of the interfacial layer and the concentration of oxygen atoms in the layer CC:). With a frequency -’I

v =

D0/a2

(34)

estimated from the diffusivity D o in the undisturbed lattice the oxygen atoms in the interfacial layer attempt to jump across the energy barrier AG,,,+,

=

max{AG(n -

+ I, z, t)

(35)

AG(n7 2, t ) + AGactivatim?AGactivation)

for incorporation into the precipitate. The energy barrier was modeled in the same way as in the Monte Carlo approach by Lavine and Hawkins (1989) (see Eq. (12)). The Gibbs energy AG(n, z , t ) of a precipitate with n oxygen atoms was also set equal to the sum of volume energy AGO and the interfacial energy AGif: 113

AGO= -n.kTln

,

AGif=4nr2-a.(I

+ (i) n

).

(36)

The symbols C , and C g denote the average concentration of interstitial oxygen atoms in the silicon lattice and its equilibrium value taken from the literature (Craven, 1981). The difference to previous approaches is due to an empirical correction factor ( I + (5/t1)’’~)in the interfacial energy AGif.Containing the free parameter = 0.22 (Schrems et al., 1991a) the correction term will compensate the inadequate description of the energies of the smallest precipitates due to extrapolating the Gibbs energy relation, which is strictly valid only for the larger precipitates. It can be

<

10.

SIMULAI ION OF OXYGEN PRECIPITATION

41 1

seen that with increasing precipitate size the correction term approaches a value of 1 and the interfacial energy then follows the commonly assumed macroscopic behaviour. The nonequilibrium interfacial oxygen concentration Cg occurring in Eq. (33) was obtained by inserting the growth law drldt for spherical precipitates (Eq. (20)) into Eq. (31) and considering Eqs. (32)-(34) and Eq. (15). The result was

with the coefficients

K,,,,

and

given by

K~~~~

The equilibrium interfacial concentration of oxygen C:eq was determined from the condition dAG07, z . t ) / d n = 0. The concentration C , ( z . t ) = j , of single not precipitated oxygen ( n = I ) in a given volume dV at a depth z inside the wafer was determined by considering both oxygen diffusion into dV (C,,,difl)and oxygen consumption or generation due to the precipitation process. This yielded (39)

The diffusion term was modeled by using Fick's law

In the actual calculations (Schrems, 1993), however, an approximation method based on analytical error function solutions for the diffusion problem was used instead of Eq. (40) in order to reduce the model's computational demand. The term for the variation with annealing time of the total in Eq. (39) reflects the consumption amount of precipitated oxygen C,,,prec (generation) of interstitial oxygen atoms if a precipitate grows (dissolves) according to the reaction Eq. (13). " ,1111,

412

M. SCHREMS

- 10'8

'?

E

INITIAL

OXYGEN: 8.04017cm-3

1015

- THERMAL

h

HISTORY

lo9

800°C/2h _ _ .. 800"C/2h+1050"C/8h 800°C/2h+10500C/16h -

106

-

2 1012

-

L Y

L

a

E Z w

0

g

-

lo3

1-p

0 I

100

; ,'J

\

FIG. 8 . Examples of size-distribution functions of oxygen precipitates after different stages of a two-step LO-HI annealing calculated with a model combining five chemical rate equations and a Fokker-Planck equation (Schrems et al., 1991d; 0 1991 IEEE).

J , denotes the net precipitation flux between the precipitates with ( n I ) and ( n ) oxygen atoms, respectively. The term nmaxis the maximum number of oxygen atoms in the precipitate. Boundary conditions for the precipitation flux J ( n , z , t ) link the FPE (Eq. (27)) to the CRE (Eqs. (39) and (26)) and terminate the precipitation flux at n = n,,, (n,,, + x).

An,, + 1, Z , t )

=

Jn0+,(z, t ) -

J ( n m a x 7 Z,

d(n,

= g,,,(z,

t)fno(z,

t)

+ l , z , t ) f ( n , + 1,z,t)

(42)

t ) = 0.

For the diffusion-precipitation Eq. (39) the value of the oxygen concentration on the wafer surfaces was prescribed (Schrems, 1993). As for the models using an FPE only or the Monte Carlo approaches, the fundamental calculation result is again the size-distribution function of oxygen precipitatesf(n, z , t ) . An example for the case of bulk precipitation (depth z set to 300 Fm) is shown in Fig. 8. The size-distribution function comprises both the solutions of the rate equations (26) and (39) visualized by the steps and the solution of the FPE (Eq. (27)) shown by the continuous line in Fig. 8. The precipitated oxygen concentration, the total precipitate density and the average radius can be calculated therefrom (see Section 111.1). Among the two free model parameters determined from fitting calculated to experimental results for the loss of inter-

10.

S I M U L A l ION OF OXYGEN PRECIPITATION

413

stitial oxygen after LO-HI anneals (Schrems, 1991a)the value 5 = 0.22 in the interfacial energy had the same value in all the calculations performed (Schrems et al.. l99la, 1991b. 199Ic, 199ld; Schrems, 1993). The other parameter was the time for exponential decrease of temperature with time during crystal growth, which is an important part of the wafer's thermal history. Since in most cases data for the thermal history of the wafers used in the experimental investigations are not provided, this value also had to be determined from matching calculated to experimental values. c'.

Appliccihility

Both from the physical and the practical point of view the model using CKE; and a FPE (1I.S.b.ii) may be considered as an improvement compared to the model based on a FPE only (lI.S.b.i). Apart from a more accurate description of the smallest precipitate sizes. it also offers more flexibility for modeling the precipitation in the regime of small precipitate sizes in future work. Instead of extrapolating the macroscopic Gibbs energy (Eqs. (18), (36)) towards small precipitate sizes the use of the rate equations also offers the possibility to include discrete values of energies for the smallest oxygen precipitates as obtained from quantum mechanical cluster calculations. The assumption that thermal donors (TD) are nuclei o f oxygen precipitates may be tested by comparing calculated and experimental results for TD-kinetics and the formation of larger oxygen precipitates. The use of the Fokker-Planck equation in particle representation (11.5.b.ii) is favourable compared to the radius representation (11.5.b.i). because it does not depend on the precipitate shape and also provides a link to the growth and dissolution rates, which reveal the atomistic nature of the precipitation process. It may be once again emphasized that an important limitation of all the modeling approaches reviewed in Section I1 is the neglect of precipitate stress and the interaction of oxygen precipitates with other defects. Including these phenomena into the models from Section 11 will be discussed in Section V. 111. Models and Experimental Results

1.

CiENERAL

REMARKS

In the following subsections a number of experimental and calculation results for oxygen precipitation will be compared. The main emphasis will be put on the results obtained either by the model using a Fokker-Planck

414

M. SCHREMS

Table I POTENTIAL CALCULATED QUANTITIES REFERRING TO OXYGEN PRECIPITATION I N SILICON AND EXPERIMENTAL METHODS FOR THEIR VERIFICATION Quantity

Symbol

Experimental Method

Size distribution function lnterstitial oxygen Total oxygen concentration Total concentration of oxygen precipitates Average oxygen precipitate radius Denuded zone depth

f ( n , 1)

TEM FTIR, PPBlR IGFA, VFA, SIMS CE, TEM. SANS TEM, SANS CE, SIMS

CO

CY' COP TOP

dDZ

equation only (Section IIS.b.i, Schrems et al., 1989) or by the model based on chemical rate equations in combination with a Fokker-Planck equation (Section 11.5.b.ii). A number of interesting results by other authors is briefly referenced in this section, if not already quoted previously. Table 1 summarizes quantities that may be obtained from calculations and lists corresponding measurement methods. Details on the experimental methods may be found in Chapters 2 and 3 of this book. Few experimental data on oxygen precipitate size distributions after thermal annealings (Fraundorf et al., 1985; using transmission electron microscopy (TEM)) have been reported so far. Usually only weighted averages of the size-distribution function such as the precipitated oxygen concentration (Co.prec), the total precipitate density (Cop)and the average precipitate radius (rap) are experimentally accessible. When using models assuming spherical precipitate geometry the calculated radii have to be interpreted as equivalent sphere radii. Comparison with experimental precipitate sizes should be performed for the corresponding number of oxygen atoms in the precipitate or the corresponding precipitate volume, since experimental precipitate shapes are often rather plateletlike than spherical. The equations for evaluating other quantities from the size-distribution function may be written by using a summation operator S Cop(t)= S[1 .fh01

(43)

CO,prec(f)= SLn * f ( n , f)l

(45)

with r again denoting the equivalent spherical radius of an oxygen precipitate containing n oxygen atoms. For the model from Section 11.5.b.i based

10.

SIMULATION O F O X Y G t N PRtCIP17ATlON

415

on a Fokker-Planck equation in radius representation the summation operator becomes

In the case of the model using t i , ) rate equations in combination with a Fokker-Planck equation in particle representation we have “0

The number n,,, and its equivalent spherical radius rre,refer to the minimum number of oxygen atoms in a precipitate and its minimum experimentally detectable size (resolution limit). Obviously. a dependency of the experimental resolution limit on the type of the characterization method used has to be expected. When simulating the concentration of determined from FTIR results ti,,, = 2 or r,,\ precipitated oxygen CC,,prrc = r2 has to be set. For the total concentration of oxygen precipitates evaluated from counting defect-related pits revealed by cross-sectional chemical etching (CE) the values of I?,,, will be in the order of lo7 (Schrems et al., 199lb). The following subsections also show some simulation results for the critical radius r ( .of oxygen precipitates. I t is a theoretical quantity characterizing the Gibbs energy of an oxygen precipitate. It is calculated from dAGldr = 0 and must not be confused with real precipitate radii, which are confined to finite nonnegative values. From Eq. (18) we obtain

(48)

if only oxygen precipitation is considered. A generalization including the influence of precipitate stress and intrinsic point defects was reported, e.g.. by Vanhellemont and Claeys (1987). Most of the experimental data, which are compared with simulation results in the succeeding subsections, refer to the change in the interstitial oxygen concentration due to precipitation during thermal annealings. Experimental values are determined from FTIR absorption spectra. As pointed out in more detail in Chapters 2 and 3 , FTIR yields absorption

416

M . SCHREMS

coefficients, which have to be converted into concentration values using a calibration factor determined from other methods such as CPAA (charged particle activation analysis) or VFA (vacuum fusion analysis) with reported values in the literature ranging from 4.9 0.3 to 12.0 ? i.4 ppma . cm. A new standard (International Oxygen Coefficient 1988 (IOC-88)) of 6.28 k 0.18 ppma . cm (Baghdadi et al., 1989) proposed in 1988 is not yet commonly used. Most FTIR results as well as the corresponding calculated oxygen concentrations shown in this chapter are based on the DIN or new ASTM value of 4.9 ppma cm for the conversion coefficient.

*

2. ONE-,Two-,

AND

THREE-STEP THERMAL CYCLES

Simple one-step and two-step low-temperature-high-temperature (LOHI) thermal treatments can be used for obtaining a basic knowledge on oxygen precipitation phenomena or for estimating the bulk oxygen precipitation behaviour during more complicated device-manufacturing cycles (Chiou, 1987; Swaroop et al., 1987). In a similar manner three-step high-temperature-low-temperature-high-temperature (HI-LO-HI) annealings are often applied for testing bulk precipitation and the formation of a defect denuded zone (DZ) near the wafer surface. The occurrence of a DZ is mainly influenced by out-diffusion of oxygen and precipitate dissolution during the first anneal, for which a higher temperature than in the succeeding steps is chosen (Isomae, Aoki and Watanabe, 1984). One-step, two-step or three-step annealings may also be used as a pretreatment in an attempt by the wafer manufacturers to adjust the internal gettering (IG) efficiency and the DZ depth according to the device manufacturers needs. In the experimental investigations the most frequently monitored parameter is the change in the interstitial oxygen concentration during thermal treatments, which is due to both oxygen precipitation and outdiffusion through the wafer surface. The graph of the oxygen loss as a function of the initial interstitial oxygen concentration after thermal annealings typically follows an S-curve-like behaviour. This can be seen from both calculated and experimental results in Figs. 9 and 10 for a number of one-step and two-step annealings. For the annealings studied in these figures, the loss of oxygen due to out-diffusion was negligible compared to the loss due to precipitation. It is obvious that with increasing initial oxygen concentration the amount of precipitated oxygen in the wafer increases. The three characteristic regions are the low precipitation region in the flat parts of the curve for the lowest initial oxygen values, the regime with the steepest gradient known as the partial precipitation region and the 100% precipita-

-

15

7

i

1

,

-

r

7

750 c'/411 -750 r / 4 h

+ 1000 C / 4 h + 1000 C/4h

-750 C'/4h

+

0

c

I

n

,

,

(exp.) (sini.)

15

0 -- -

i

r: M

x 0

*

1000 C/16h (sim.)

1000 ('/16h ( e x p . ) 1000 C / l 6 h (siin.)

c,= C ' ,

II

selected for analysis

0 0

(b)

5

10

itiitial oxygrn

15

20

[III'. ~ I I I - ' ]

FIG. 9. Precipitated vs. total oxygen concentration. Square symbols are experimental results and dashed lines are simulations for a IO00"C single-step anneal (4 hr: (a). I6 hr: ( b ) ) .Circles and solid lines are experimental and theoretical results for similar I000"C annealings. which were preceded by an additional 750"/4 hr nucleation annealing. Points labeled A , . . . , , C , are selected tor further analysis in Figs. 14 and I S . (Schrems et al., 1989.)

418

M . SCHREMS

-

10

*)

-0

5

x-lOh

...._....+ x-16h

2

2

----O

x-30h

v)

s

'"5 Z w m > X

0

0

5

10 I N I T I A L OXYGEN [1017cm-31

FIG. 10. Calculated (lines) and experimental (symbols, Schrems et al., 1990a) oxygen loss as a function of the initial oxygen concentration in a two-step thermal cycle for various growth times x at 1050°C. (Schrems et al., 1991c.)

tion region (Chiou, 1987; Swaroop et al., 1987). In the 100% region the interstitial oxygen concentration has reached the bulk equilibrium value. Any further increase in the initial oxygen concentration leads to a similar increase of the precipitated concentration. Consequently, this part of the S-curve becomes a straight line. The calculation results in Fig. 9 were obtained by adjusting the free parameters of a model using a FPE only (II.S.b.i, Schrems et al., 1989) to reproduce the experimental data available. In the calculations, however, the S-curve could then be easily completed for the whole regime of initial oxygen concentrations. After parameter extraction (Schrems et al., 1991a) simulations with the model based on CRE in combination with a FPE (II.S.b.ii, Schrems et al., 1991a, 1991b, 1991c, 1991d) yielded good predictions for data from FTIR measurements after one-step and two-step annealing as can be seen from Figs. 10 and 11. As shown in Fig. 12 experimental precipitate densities (curve for tcooling= 3 hr) could also be explained quite well. The characteristic time fcooling varied in the simulations shown in Fig. 12 accounts for the cooling phase during crystal growth and all other thermal pretreatments, which are known as thermal history. The thermal history of the wafers already results in a significant formation of small precipitates influencing succeeding anneals. For the case of a two-step LO-HI annealing, Fig. 12 shows an increasing influence of the thermal history on the calculated precipitate densities the shorter the duration of the LO anneal at 750°C. A typical distribution of interstitial oxygen after three-step HI-LO-HI

10.

SlMUL A [ I O N O F O X Y G E N PKECIPlTATlON

419

10

-

800°C/2h*10500C/16h 800"C/lh+1050"C/8h

n

E 0

>0 P I

Z W

9 X

0

0

5

a

7

4 INITIAL

9

10

OXYGEN [1017cm-31

F I G . I I . S-shaped curves showing oxygen l o s s vs. initial oxygen for a HI and three different LO-Hl annealings. Experimental results-symbols: Swaroop et al.. I987 (circles and r ) . Chiou, 1987 (stars: squares and diamonds represent averages over a larger number ofmeasurements). Schrems et al.. IWOa ( t )-are shown in order to check the calculations. (Schrems et al., l99lb.)

-

1013

h7

E V

I

~

1012

I

m

z

W

W

lo1' 10'0

w Ly

a

10-1

100

lo1

lo2

lo3

TIME t at 750°C [hl F I ( i . I ? . Calculated (lines) and experimental (lnoue et al.. 1981; circles) density of oxygen precipitate, as a function o f the 7 W ( ' nucleation-annealing in a two-step thermal process. for cooling during Thc \tar\ mark experimental error h i \ . I n the calculations the time r,l crv.;tal growth from 1400°C to 4CO'C' wah varied. (Schrems et al.. 1991c.)

420

M . SCHREMS

1100°C/16h+6500C/16h+ 1000°C/16h

1100"C/3h+650"C/l6h+ 0-

INTERSTITIAL OXYGEN PRECIPITATED OXYGEN

Y

Li

z

0

U

z W

5x

1

t 0

(a)

20

40 60 DEPTH [pml

80

0

100

0

20

40 60 DEPTH [pml

80

(b) FIG.13. Calculated interstitial (solid line) and precipitated oxygen concentrations (dotted line) as a function of depth from the wafer surface after two different three-step HI-LO-HI annealings (initial bulk oxygen concentration: 9.5 . 10'' cm-'). Circles mark the error bars for the experimental results reported by lsomae et al. (1984). The dotted lines show the calculated precipitated oxygen concentrations. (Schrems, 1993.)

annealings as a function of depth from the wafer surface is illustrated in Fig. 13(a), (b). In both cases the interstitial oxygen concentration declines from a peak value towards the surface and towards the inside of the wafer, where it reaches a constant bulk value. Due to the shorter HI anneals the peak value is less pronounced for the results in Fig. 13(a). The characteristic curve shape is due to the interaction of oxygen outdiffusion dominating in the surface near region left of the peak and an increasing loss of interstitial oxygen caused by increasing precipitation for larger depths, which finally approaches a constant bulk value. The denuded zone depths (Isomae et al., 1984; Yang et al., 1986; Schrems, 1993) may be estimated from profiles showing an increase of the precipitate density with the greater depths in the wafer. Alternatively analytical models for a direct calculation of DZ-depths were suggested (Wijaranakula and Matlock, 1991). The DZ depths were found to increase both with annealing temperature and the duration of the first HI annealing, but to decrease with increasing initial oxygen content in the wafer. When performing a detailed analysis of oxygen precipitation during a given thermal sequence computer modeling can be a very powerful method in providing additional data, which are not accessible to experimental investigations or only with difficulty. As an example bulk precipitation for the HI and LO-HI sequences from Fig. 9 was analyzed using

100

10.

SIMUI.ATION OF OXYGEN PRECIPITATION

42 1

the model based on a FPE only (Section 11.5.b.i, Schrems et al., 1989). For three representative points from the low ( A ) ,the partial ( B ) and the 100% precipitation region (C’)precipitated fractions. precipitate densities, average radii, size-distribution functions and critical precipitate radii were evaluated (Schrems et 31.. 1989). Some of the results are shown in Figh. 7. 13 and IS. By comparing Figs. 14(a) and 14(b) as well as 14(c) and 14(d)and the calculated precipitate radii (Schrems, 1991) for the HI and the LO-HI annealing, i t was found that the L O annealing leads to a 4ignificant acceleration of the precipitation process. If the initial oxygen concentrations are equal (data points C in Figs. 9, 14, 15) the additional LO annealing leads to a larger number of precipitates with smaller average size. when the curves i n Fig. 14 approach a quasi-stationary value. The additional precipitates observed in the LO-HI anneal (Fig. 14(d)) form during the LO annealing. but their growth rate during the LO anneal is small. Consequently, the precipitated fraction of oxygen remains very \mall (0-4 hr total annealing time in Fig. 14(b)). During the succeeding HI annealing the number of precipitates remains constant or decreases slightly (Fig. 14(d)).At the same time the precipitate radius (Schrems, 1991) grows significantly, which causes the reduction in the interstitial oxygen content found in Fig. 14ib). This illustrates why a L O and a succeeding HI anneal are frequently called nucletrrion crnnra/in,q and g r o ~ > t l az n t z r t r l i n ~ ~respectively. , From Fig. 14(c) and (d) an exponential dependence of the precipitate density on the value of the initial interstitial oxygen concentration and on the preceding anneals is appai-ent. This holds, even whcri the system approaches the quasistationary state. For the highest initial oxygen concentration (dashed lines in Figs. 14 and IS) an approach to the stationary state can be seen, while for the lower oxygen concentrations this was only observed for longer high-temperature annealing times than the value of 16 hr shown in the figures. In the initial phase of precipitation during the HI annealing, the average precipitate radius increases. while the critical radius (Fig. 15) increases at a much smaller rate (Schrems, 1991; Fig. 6.18). As the precipitated fraction (Fig. 14(h))approaches a value close to I , the critical radius almost reaches the value of the average radius. The increase of the critical radius leads to a gradual dissolution of an increasing number of larger sized precipitates, which now become subcritical. This dissolution process causes the temporary repopulation of smaller precipitate sizes observed in the calculated size-distribution function in Fig. 7, especially for 16 hr and 20 hr total simulation time. Those precipitates, which are larger than the critical radius. continue to grow. They consume the oxygen, which becomes available due to the dissolution of the smaller precipitates (coarsening). The growth rate (Eq. (20)) has now become very

422

M. SCHREMS

1.5

P Y

* ..-au 0.5

0.0

0

5

10

(4

time [h]

(b)

time [h]

15

20

FIG. 14. Precipitated fraction, (a) and (b), and precipitate density, (c) and (d), vs. total annealing time for A,, B , , C3 and A,, B , , C , from Fig. 9(b). (Schrems et al., 1989.)

10.

SIMULATION OF OXYGEN PRECIPITATION

1015 1014

108

10'

1015

r-r' '

'

Annealing: 750 c'/41i

1014

- 1013

10'

(d)

"

"

I

'

'

''1

+ 100OCC/16h

423

424

M . SCHREMS

(01: 5 s 10"cm 3 ) (0,: 8 0 10"cm ') ---c, 15 0 10"cna 1 ) -A,

8 4

(o<:

0 Y

2 .-

10'

a .U

i

______ 10-1' ' ' ' '

0

I

5

'

'

'

'

'

'

'

10 time [h]

'

'

I

15

'

'

'

'

'

20

FIG.15. Critical radius r,(t) vs. total annealing time t for A , , B , , C , in Fig. 14. (Schrems et al., 1989.)

small, since the value of the interstitial oxygen concentration is already very close to the equilibrium interfacial concentration (Eq. ( 2 1)). Therefore, the calculated values for the precipitated fraction and the average precipitate radius already seem stationary for C4,although there are still changes observed in the size-distribution function. However, the theoretical equilibrium state in the process is reached only when all the precipitated oxygen is concentrated in one single precipitate (Landau and Lifschitz, 1983).

3 . MULTISTEP THERMAL CYCLES Compared to the number of papers dealing with the simulation of oxygen precipitation during one-, two- and three-step annealings, only few attempts to simulate oxygen precipitation during multistep thermal cycles such as those occurring during device manufacturing are known until now. Pagani and Huber (1987) reported good agreement between calculated and experimental loss of interstitial oxygen after a CMOS and a NMOS process for 5-in. wafers using a combined nucleation and growth model (Section 11.3). A preceding 7OO0C/4 hr nucleation annealing was

10.

S I M U l . A l ION OF OXYGEN PRECIPITATION

425

found to increase the loss of interstitial oxygen after the CMOS as well as the NMOS process both in experiment and in the calculations. lsomae (1991) also used a combined nucleation and growth model for studying the influence of a one-step preannealing on the oxygen loss after a simplified CMOS process. The largest increase of the oxygen loss was found for preannealing temperatures between 700°C and 750°C both experimentally and theoretically. In these cases the preannealing time was kept at a fixed value of 2 hr. Increasing the preannealing time at 725°C also led to an increase of the oxygen loss. Other recent work (Schrems et al., 1991a. 1991b, 1991c, 1991d) reported simulation studies of three different CMOS-type thermal annealings using the model combining rate equations and Fokker-Planck equation as described in Section 11.S.b.ii. The same model was also used for obtaining the majority of the other sirnulation results shown in this chapter. The annealing sequences of the three processes named CMOSI. 2 , 3 are shown in Table 11. Important differences between the three processes are the amount of consideration of low-temperature processing steps and the type of annealing prior to the CMOS-type process. While CMOSI and CMOS3 neglect processing steps below 700"C, even steps at lower temperatures are considered in CMOS2. The process preceding CMOSI is a high-temperature annealing at 12Oo"C, which was aimed at dissolving precipitates formed during the thermal history of the wafers used in experiment. The preannealing for the CMOS2 sequence is not a high-temperature precipitate dissolution step, but a low-temperature nucleation step, which shall provide a sufficient number of oxygen precipitates for internal gettering of metals during processing. Calculations for CMOSI, CMOS2 and CMOS3 could predict a set of experimental results for the loss of interstitial oxygen and the precipitate density in CMOSI-3 (Figs. 16 and 17) reasonably well. Since there was no information on the temperature ramping conditions between the individual processing steps available for CMOS3 (Chiou, 1987), two choices were compared in the simulations. For all processing steps with a holding temperature higher than 800°C a ramp up rate of 1O"Cimin and a ramp down rate of 5"Cimin was assumed (dashed lines in Figs. 16 and 17). When assuming there is only ramp up and down for temperatures above a threshold of 1000°C (dash-dotted line in Fig. 16) the calculated values especially for initial oxygen concentrations higher- than 8.0 . 10" c m - j become too low in comparison to the experimental results. The example shows that for reproducibility of experimental results a detailed knowledge of the complete thermal cycle is necessary. In the simulated precipitate densities as a function of the initial oxygen content (Fig. 17) qualitative differences in the results for the different CMOS-type anneals were found (Schrems

426

M. SCHREMS

Table 11 PROCESS DATAFOR THREECMOS-TYPETHERMAL ANNEALINCS Step

Temperature (“C)

CMOS1 (Schrems et al., 1991b) I Precipitate dissolution

850

-

1200 1200 1200 850 850 -+ 950 950 950 + 1100 1100 1200 I200 1200 850 800 800+ 1000 -+

2 Oxidation

-+

3 Well drive-in 4 Nitridation

5 Oxidation

1000

850 800 800 950 950 950 + 850

1000 -+

6 Nitridation

--j

7 ...

CMOS2 (Huber and Pagani, 1990) 1 Nucleation 2 Pad oxide 3 Nitride 4 Field oxide 5 Well drive-in 6 Gate oxide 7 Polysilicon gate 8 SID diffusion 9 P-glass 10 Densification II Alloying 12 Passivation

Time (min) 70 120 70 20 60 30 50 300 175 200 40 780 75 60

30 300 50

415 900 450 415

240 120 60 I60 960 60 120 30 30 35 70 30

925 800 I IS0 925

300 45 I200 840

700 I100 780 950 1150 900 650 1000

Ambient 95% NI + 95% N? + 95% NI + 95% N 2 +

5% 02 5% 0 2 5% 0 2 5% O2 100% 0, 95% Nz + 5% 0 2 95% NI + 5% 0, 95% N2 + 5% 0 2 95% N2 + 5% 0 2 95% Nz + 5% 0 2 95% NI + 5% 0 2 Wet 0, 95% Nz + 5% 0 2 95%N2 + 5 % 0 2 95%Nz + 5 % 0 2 95% N? + 5% 0 2 95% Nl + 5% 0 2

CMOS3 (Chiou, 1987) 1

2 3 4

et al., 1991d). After CMOS2 a monotonous increase of the precipitate density with the initial oxygen content is found. The results for CMOS1 and CMOS3, however, show a kind of plateau for initial oxygen concen~ . may be explained by the trations between 7.0 and 8.0 . 10” ~ m - This dominance of two succeeding LO-HI type thermal annealings in CMOS 1

10.

S I M U L A I ION O F OXYGEN PRECIPITATION

427

Z W

2 !X

0

0 5

7

6 N IT IA IL

8

9

10

OXYGEN [1017cm-31

FIG. 16. Calculated oxygen loss (line\) as a function o f the initial oxygen concentration for three differenl CMOS-type thermal anneals \pecified in Table 11. Squares (Chiou. 1987) and croses (Schrems et al., 1991b) are experimental results. The dash-dotted line shows the calculated result for C M O S . if the w n p l e s are not loaded into the furnace at 800°C. but at IoO0"C. (Schrems et al.. 1991d: icl 1991 IEEE.)

1013 10'2

I-

-- -----

101'

CMOS1 CMOS2 CMOS3

0

W F

Q

c

1O'O

loq z 108 W

!X 2 0

lo7

5

6

N I TIA IL

7

8

9

10

OXYGEN [1017cm-31

FIG. 17. Calculated precipitate densities (lines) as a function of the initial oxygen concentration for three different CMOS-tvpe thermal anneals specified in Table II. The circle (Huher and Pagani. 1990) is an experimental result. The dash-dotted line shows the calculated precipitate densities after the \tep\ 1-3 of C'MOSI. (Schrems et al.. 1991d; C, 1991

IEEE.)

428

M . SCHREMS

and CMOS3. For CMOS 1 (Table 11) a monotonous increase of the precipitate density with initial oxygen is observed after steps 1-3, which is typical of a LO-HI annealing sequence. The cooling in crystal growth and other parts of the thermal history have a similar effect like a single LO annealing, which introduces smaller precipitates. Steps 1-3 are all HI annealings, leading to growth of the larger precipitates. The process steps 4 and 5 can be regarded as a second LO-HI annealing, which also forms precipitates for lower initial oxygen concentrations (Schrems et a]., 1991a, 1991b, 1991d). The superposition of the two curves for the precipitate density with each one originating from one of the LO-HI type sequences can explain the formation of the plateau region. For CMOSl the characteristic plateau shape is not changed by the final processing steps 6 and 7, which are also LO-HI type, but do not influence oxygen precipitation significantly (Schrems et al., 1991a). Similar considerations hold for CMOS3. Again the thermal history corresponds to the first LO annealing. Process step no. 1 for CMOS3 in Table 11 may be interpreted as the first HI anneal. The second LO anneal is step 2, while steps 3 and 4 correspond to the second HI anneal. It was already mentioned that contrary to CMOS1 and CMOS3 the CMOS2 sequence is preceded by a 700"C/4 hr nucleation anneal. This anneal covers the effect of shorter LO sequences occurring later in the process flow. In effect, the whole sequence may therefore be described as being LO-HI type and consequently there is no plateau region. A more detailed analysis of CMOSl (Schrems et al., 1991a) showed that the size-distribution function had not only one, as in the LO-HI anneals, but three characteristic precipitation peaks for a given intermediate initial oxygen concentration. A similar multipeaking effect in the calculated size-distribution function was found by lsomae (1991) for another multistep process applying a combined nucleation and growth model (Fig. 5). IV. Computer-Aided Design of Oxygen Precipitation 1. SUBSTITUTIONAL ANNEALINGS

For routine experimental tests of the oxygen precipitation behaviour in commercial CZ-Si wafers, the manufacturers have to use a series of time consuming and expensive annealing experiments. Therefore, it is desirable to develop shorter two-step or three-step thermal annealings resulting in similar precipitation, but with a lower thermal budget as the multistep device manufacturing processes. These abbreviated annealing sequences may also be called substitutional processes or substitutional

10.

-

n

S I M U L A r l O N OF OXYGEN PRECIPITATION

429

- CMOS1 - - _ 1200°C/5h+

annrtilitzgs. By definition a substitutional process has to yield the same

size-distribution function as the original process at any location in the wafer at a given time during processing. In practical applications, however, similar loss of interstitial oxygen, similar precipitate densities and average precipitate sizes will be regarded as sufficient. Usually the development of substitutional processes for multistep device manufacturing sequences is performed by extensively using experimental methods. Recently, however, attempts for using computer modeling in order to reduce the number of required experiments during process development were reported (Schrems et al., 199ld). It was attempted to design a substitutional two-step or three-step process for the bulk oxygen precipitation observed after CMOSl, which was analyzed in the previous section (111.2). A three-step 1200"C/S hr + 800OC13.3 hr + 1000"C/13 hr HI-LO-HI annealing was extracted by omitting all processing steps, which did not significantly influence the final results. From Figs. 18-20 it can be seen that the substitutional anneal (dashed line) gives a good approximation with respect to the oxygen loss, precipitate densities and average radii calculated for CMOSl (solid line). Nevertheless. performing the three-step substitutional annealing can already save 30-40% of processing time compared to CMOS l . Attempts for deriving LO-HI processes are also shown in Figs. 18-20. Although both annealings were fitted to match the S-shaped curve of CMOSl in Fig. 18. the LO-HI annealings fail both quantitatively and qualitatively

430

M . SCHREMS

CI

cn

1012 r - - - 120OoC/5h+ 800"C/3.3h+1000"C/13h

7

CMOSl 120OoC/5h+ 800"C/3.3h+1000"C/13h .......... 800"C/lh+1000"C/25h 800"C/4h+1050"C/8h

.....

......

---_ ... W

2 [Y

W

10'

5

6 7 8 9 10 INITIAL OXYGEN "1017cm~31

FIG. 20. The calculated average precipitate radius as a function of the initial oxygen concentration is shown for CMOS1 of Table I1 and three potential substitutional processes. (Schrems et al., 1991d; 0 1991 IEEE.)

10.

S l M U l ATION OF OXYGEN PRECIPITATION

43 1

at describing the precipitate densities for CMOS1 as obtained in the previous part. From the discussion there, it is clear that a two-step LO-HI annealing cannot account for the characteristic plateau region in the precipitate density curve after CMOS 1 . The calculated results for the two LO-HI anneals in Figs. 18 and 19 indicate that matching the S-shaped curves is not enough to guarantee that the precipitate densities i n the original and the substitutional processes are in the same order of magnitude. Unlike some attempts in the past (Chiou. 1987), it seems therefore necessary to measure at least both the loss of interstitial oxygen and the precipitate densities for experimentally developing substitutional anneals. ?.

I N F L U E N C E OF PROCESS V A R I A I I O N S

For controlling oxygen precipitation during thermal annealings it is mandatory to have both a good qualitative and quantitative understanding of the influence of variation3 in the processing parameters. Important examples of such parameters are the

I . Initial oxygen content, 2. Annealing temperature, 3 . Annealing time, 4. Parameters affecting the thermal history (e.g., crystal diameter and pulling rate in crystal growth, thermal pretreatments such as thermal donor annealings), 5. Concentrations of other impurities such as C, Sb, P, B, N , . . . or metals, 6. Ambients and surface layers. Since it has the potential of performing systematic parameter variations and analyzing their impact on the process in detail, the use of computer modeling also seems desirable in this case. The models described in Section 11, however. consider only oxygen precipitation, but not the influence of related defects such as silicon self-interstitials and vacancies, stacking faults. and other dopants. Therefore, those models can be used only to study the influence of the parameters (1)-(3), and some aspects of the thermal history (4). Applications within the limits of the models from Section 11.5 will be discussed in the following. Current and future modeling approaches for addressing the other items will be discussed in Section V . Despite the importance of the other processing parameters, the initial oxygen content may be regarded as the most important one. Its influence

432

M. SCHREMS

on the amount of oxygen precipitation observed after a given annealing sequence is visualized by the S-curves showing oxygen loss vs. initial oxygen and the related curves for precipitate densities and average radii. These curves showing an increase of oxygen precipitation with initial oxygen content with three characteristic regions (low, partial and 100% precipitation) have already been discussed in detail in the previous Sections 111.1 and 111.2. Systematic variations of annealing times and temperatures were studied recently (Schrems et al., 1991d) for the case of LO-HI anneals. With respect to a 800"C/4 hr + 1050"C/16 hr process a reduction in the growth time at 1050°C by a factor of 2 resulted in a reduced amount of oxygen loss. This was due to smaller precipitate radii, while the precipitate density remained almost unchanged. Reducing the growth temperature by 50°C had a similar effect. Halving the duration of the low-temperature nucleation annealing led to a reduced precipitate density and consequently a reduced oxygen loss. Simultaneously an increase in the average precipitate radius was found. A decrease in the nucleation temperature from 800°C to 750°C resulted in an increased oxygen loss due to an increase in the precipitate density, while the average precipitate radii tended to decrease. Nucleation temperatures near 750°C yield the maximum loss of interstitial oxygen for a given initial oxygen concentration. A further decrease in the nucleation temperature now leads to a decrease in the loss of interstitial oxygen, which can be seen from Fig. 21. It has to be remembered at this point that this dependency of oxygen precipitation on annealing temperature and time may in some cases be completely changed by other influences such as significant supersaturations of point defects. These effects were not included in the model used for performing the preceding calculations (Section II.S.b.ii, Schrems et al., 1991a, 1991b, 1991c, 1991d). An example for such a case is the precipitation retardation-recovery phenomenon (Tan and Kung, 1986), which is discussed briefly in the next section. An essential part of the thermal history of CZ-wafers is the cooling of the grown crystal during pulling. At this stage formation of oxygen precipitates is already taking place. In the calculated size distribution functions (Fig. 22) precipitate formation is predominantly found during cooling from 1000°C to 700°C. From Fig. 12, where a characteristic time rcooling for exponential decrease of temperature during crystal growth is varied, it can be concluded that by extended nucleation annealings the influence of variations in the crystal growth related part of the thermal history can be covered due to additionally formed precipitates. Although the influence of mechanical stress, intrinsic point defects and dopants on oxygen precipitation in CZ silicon wafers are not included in

10.

SIMULATION O F O X Y G E N PRECIPITATION

433

oxygen loss

temperature ["(

initial oxygi'ii

[ IIPi

C?I1

'1

'1

FIG.2 1 . Calculated oxygen loss as a function of the nucleation temperature T and the oxygen concentration in a T14 hr t 105OoC/16hr LO-HI annealing cycle. (Schrems er al.. 1991b.l inilial

initist

oxygen:

1200°C

-- looooc 700°C

10'

102

103

NUMBER OF 0-ATOMS n

F K . 22. Calculated size distribution function for four succeeding temperatures during cooling i n crystal growth. (Schrems et al., 1991:~)

434

M . SCHREMS

10 9

1 D -

6

5

NITAIL

7 8 9 10 OXYGEN [ 1 0 1 7 ~ ~ - 3 1

FIG.23. Experimental (Chiou. 1987) and calculated S-shaped curves for a 80O0C/2 hr

+

1O5O0C/16hr LO-HI annealing. The effect of variations of the cooling time tcoolingin crystal

growth from 1400°C to 450°C is compared to variations tration of oxygen. (Schrems et al., 1991b.)

x in the effective equilibrium concen-

the model, the influence can be roughly estimated by using the concept of an effective equilibrium concentration of oxygen. All these effects are usually modeled by additional terms (Vanhellemont and Claeys, 1987; Tiller and Oh, 1988) in the Gibbs energy of oxygen precipitates. Rewriting the total Gibbs energy of the precipitate in a way that the additional terms are included into the volume energy term of Eq. (36), an effective equilibrium concentration depending from point defect and dopant supersaturations as well as precipitate stress can be isolated. In Figs. 23 and 24 (Schrems et al., 1991b), the sensitivity of oxygen loss on variations in the characteristic cooling time tcoolingand in the effective equilibrium concentration are investigated. Comparatively small variations in the effective equilibrium concentration (20%) were found to have a much more pronounced effect on both the oxygen loss and the precipitate densities than much larger variations in the cooling time. This does not suggest that the thermal history is unimportant, since it may also lead to superor undersaturations of intrinsic point defects, which will in turn influence the precipitation behaviour significantly. These effects are, however, not included in the model used for performing the calculations. The changes in oxygen loss caused by varying the effective oxygen equilibrium concentration are so significant that the scattering of experimental data can be explained easily (Fig. 23). Therefore, it can be concluded that for better model predictions it is necessary to account for those effects which

10.

435

S l M U l A l I O N OF O X Y G F N PRECIPITATION

- loy3

I

'

I

'

I

I

I

'

0

v

800"C/2h+1050"C/16h

-:

IOU

- L,,9-10h.

v)

z

8

,

x-1.0

-

1

1

10"

W

+ a 1o'O t,

r

5

Y lo9 [Y

a

5

:/

108

9 E

lo7

5

4

7

a

9

10

INITIAL OXYGEN [10'7cm-31 24 C d k u h t e d precipitate denbitie+ a\ a tlinction of initial o%ygenfor d 8oo'c 12 h r I0W"C'iIh hr LO-HI annealing A \ in Fig 2 7 the effect of variation5 of the time for cooling in cry5raI growth trom 1400 C to 470"(' 15compared to vdrintion5 in the effective equilibrium concentration of oxvgen hv ,i f x t o r ot x (Schrern., et a1 1991b.l bit,

t

.

affect the value of the effective equilibrium concentration of oxygen such as precipitate stress and point defect or dopant concentrations.

V. On the Interactions of Oxygen with Other Defects 1. CURRENT MODEL.S

An experimental and a fundamental theoretical analysis of the physical phenomena associated with diffusion and precipitation of oxygen has been performed in detail in t h e other chapters of this book. Therefore, the reader will already be familiar with concepts like volume shortage during SiOz particle growth leading to lattice stresses, which may be released by silicon self-interstitial emission, absorption of vacancies, punching of prismatic dislocation loops or a counterpart stress field generated by other defects. Interaction with other defects such as dislocations and stacking faults as well as the wafer surface may take place via stress fields or intrinsic point defects. Until now the modeling of the complex interaction of phenomena during oxygen precipitation has focused mainly on formulating Gibbs energies for individual precipitates (see Chapter 9 for more details). A review of earlier approaches can also be found in a work by Hu (1986b). More recently Tiller, Hahn and Ponce ( 1986) and Tiller and Oh (1988) proposed

436

M. SCHREMS

a predominantly thermodynamical model of oxygen precipitation and successfully used it for qualitative interpretations of oxygen precipitate nucleation and growth as well as the experimentally observed precipitate morphologies. The effect of high carbon concentrations (Hahn et al., 1988a) or heavy boron doping (Hahn et al., 1988b) were also investigated using the same model. As basic reaction equation for precipitate formation (1

+ 2Jy,l)Si(s)+ 2 0 + 2y,,V*SiO,(s) + 21y,lI + stressa,

(49)

was assumed. It takes into account that the formation of SiO, precipitates from interstitial oxygen and silicon lattice atoms (Si(s)) is assisted by the generation of silicon self-interstitials (I) and stress u , as well as the absorption of vacancies (V) at the precipitate-matrix interface. Here, y, (50) and y v (LO) denote the average numbers of I or V absorbed for each precipitated 0-atom according to a notation introduced by Vanhellemont and Claeys (1988). Generation and recombination of intrinsic point defects takes place via the Frenkel pair mechanism I

+V

e Si(s).

(50)

From their experimental findings on the defect structure in high carbon material, Hahn et al. (1988a) concluded that the major role of carbon in enhancing oxygen precipitation is that of providing a source for vacancies due to S i c precipitation. This was described by Si

+ C e S i c + -32 V + stress u,.

(51)

It has to be noted, however, that the importance of this mechanism for the enhancement of oxygen precipitation due to the presence of carbon is not generally agreed upon. There are also arguments for the dominance of the formation of C - 0 bonds (Taylor, 1992). The total thermodynamic driving force for oxygen precipitation (Tiller and Oh, 1988; Tiller et al., 1986) was split into the excess Gibbs energy storage in the interface area between precipitate and matrix (AGE), a contribution for the transport of diffusing species (AG,) including terms for interstitial oxygen as well as intrinsic point defects and a contribution for interface attachment (AG,), which was related to the growth law of a precipitate with radius Y by an analytical equation (Tiller and Oh, 1988 (Eq. 4a)). In summary this yields the Gibbs energy

AGE + AG,

+ AG,,

+ AG,,. (52) AGE = AG,f + AGStreSS The excess energy storage AGE summarized the contributions of interfacial energy AG,, precipitate stress AG,,,,, and intrinsic point defect genAG

=

10.

SIMUI ATION Of OXYGFN PRECIPITATION

437

eration-recombination AG,, . The interfacial concentrations of oxygen and intrinsic point defects appearing in AG, were obtained from the pre) D cipitate growth law using Peclet numbers ( P = r . ( d r / d r ) / ( 2 D )with denoting the respective diffusion coefficient for each species). For different temperatures the optimum Peclet number for oxygen after long annealing times and from that the interface supersaturations of silicon self-interstitials and undersaturations of vacancies were determined. High supersaturations of self-interstitials at the Si02-Si interface were calculated for temperatures below I ISOT, and the interface was found to be far from thermodynamical equilibrium. In a theoretical study of the critical radius of oxygen precipitates. Vanhellemont and Claeys ( 1987) also addressed the influence of stress and point defects on the precipitation process, but used a partly different fcmnulation of the total Gibhs energy, which did not include oxygen or intrinsic point defect transport. I t may be summarized by (Schrems et al.. 199Oa, 1 9 9 0 ~ ) hG = AGO + A(;,

+

+ AG,,,,,, + AG,,.

(53)

For spherical precipitates with radius r containing n oxygen atoms the contributions of the Gibbs energy difference AG,, between the oxygen atoms in the precipitate and the same number of nonclustered interstitial oxygen atoms. the energies due to generation of self-interstitials AG, and vacancies AGv, precipitate stress AG,tre,,and the interfacial energy AGIf were modeled by (Vanhellemont and Claeys. 1987, 1988; Schrems et al., 1990a, 1990b) AG,, = - nkT ln(Co/C:;), (54) AG,

=

-y,n/iTln(C,/C~q),

(55)

AGv

=

-yvnk71n(C,./C~q),

(56)

AG,trc,r= (47rr3/3).6 k e , r , ,

A<;,,

= 47rr'

.a.

(57) (58)

C,,, C , . C , . and C:;, Cleq. C;" are the bulk concentrations of interstitial oxygen, silicon self-interstitials and vacancies and their thermodynamic depends from the shear equilibrium values. The stress energy ACstre5s modulus k of SiOz as well as the constrained strain r,- and the stress free transformation strain (linear misfit) e Here a denotes the interfacial energy per unit surface. Vanhellemont and Claeys (1987) obtained an expression for the critical radius for the case of spherical oxygen precipitates by solving ijAC/dr = 0 for the precipitate radius r . Further assuming an exponential distribution of precipitate radii. they also reported excel-

,.

438

M . SCHREMS

lent agreement between calculated and experimentally based estimates of the subcritical oxygen content as a function of initial oxygen. Gibbs energy terms like Eq. ( 5 3 ) describe the thermodynamic driving forces leading to precipitate formation, but for calculating transient changes in the numbers and sizes of oxygen precipitates other approaches such as those summarized in Section 11have to be used. The model types from Section 11.1 and 11.3-5 depend explicitly on the Gibbs energies of individual precipitates, which contain volume and interfacial energy terms similar to Eqs. (54) and (58). Obviously, a first simple step in generalizing the models from Sections 11.1 and 11.3-5 is the inclusion of Gibbs energy contributions like Eqs. (55)-(57) for point defects and stress caused by oxygen precipitate formation. Another, equally important step has to focus on formulating additional kinetic equations for transport and aggregation of intrinsic point defects and impurities other than oxygen. Steady-state nucleation models, including energy terms for selfinterstitial emission and precipitate stress, may be found in the work by Jablonski, Wojciechowsky and Kucharski (1988) (platelike oxygen precipitates) or Voronkov et al. (1989) (spherical precipitate shapes). An early attempt of combining deterministic growth laws for a spherical oxygen precipitate and its related stacking fault was made by Patel et al. (1977) in order to show a t3’4dependence of the stacking fault radius on the annealing time t. Hartzell et al. (1985) using a Fokker-Planck equation for modeling oxygen precipitation proposed the use of a Gibbs energy term additionally including contributions for self-interstitial emission precipitate stress and even for carbon. However, the paper does not clearly state if all these effects were also included in the calculations. Extensions of the oxygen precipitation model from Section 11.5.b.i. which is also based on a Fokker-Planck equation were reported by Schrems et al. (1990a, 1990b). In both cases the Gibbs energy terms as described by Eqs. (53)-(58) for spherical precipitates were used. In order to reduce the number of unknown parameters, the coefficient y v for the absorption of vacancies was set equal to zero. This assumption should be carefully reconsidered in future calculations in view of recent investigations by Zimmermann and Falster (1992) showing evidence that vacancies might directly be consumed at the precipitate-matrix interface during oxygen precipitation. According to Vanhellemont and Claeys (1987) the number of silicon self-interstitials yI emitted per oxygen atom in the precipitate was related to the stress-free transformation strain. This in turn was obtained by minimizing the total Gibbs energy of the precipitate with respect to the stress free transformation strain. In the earlier model version (Schrems et al., 1990a) the growth of extrinsic Frank-type stackingfault loops due to the silicon self-interstitials emitted from growing oxy-

10.

SIMUI.AT1C)N O F O X Y G E N PRECIPITATION

439

gen precipitates was estimated by Gibbs energy-related considerations only. The energy of a silicon self-interstitial was compared to the energy of a silicon atom in a stacking-fault (SF) loop. The term for the S F energy was taken from a paper by Schoeck and Tiller (1960). The number of stacking faults was assumed to be proportional to the number of oxygen precipitates. In its further improved version (Schrems et al., 1990b), the Fokker-Planck equation-based oxygen precipitation model from Section 11.S.b.i was supplemented by a deterministic growth model (Wada et al., 1983) for the kinetics of the Frank-type stacking-fault loops. Furthermore. Frenkel-pair generation-recombination and the formation of Sic precipitates according to the reaction Eq. (51) proposed by Hahn et al. ( I9X8a) was considered. Oxygen precipitation was coupled with Frenkelpair generation-recombination. stacking-fault loop formation and carbon precipitation via the equations for the change with time of interstitial oxygen (I?()). silicon self-interstitials ( C , ) ,vacancies ( C , , )and carbon ( C ( . ) (59)

selfThe model also accounted for diffusion of oxygen (CO,diR), vacancies (CL,L,lfi.) and carbon (C,,diff)between the interstitials (Cl,diff) wafer surface and the bulk. C,,,,,.,,, C,,,,,, and C,,, denote the total concentrations of precipitated 0 , 1. and C in the bulk. Best fit model calculations (Schrems et al., 1990b) could represent experimental results by Tan and Kung ( 1986) showing the precipitation retardation-recovery phenomenon reasonably well (Fig. 2 5 ) except for the significant deviations for the longest growth times (x = 36 hr). In the experiments wafers with a nonnegligible initial carbon concentration of 1 . S . 10'' cm- were exposed to a series of LO-HI annealings. Three regimes were observed for the interstitial oxygen concentration as a function of the low-temperature annealing time. First it decreased, then it increased (precipitation retardation) and finally it decreased again (precipitation recovery) with increasing duration of the low-temperature annealing. In a similar experiment with carbon lean samples (Tan and Kung, 1986)and the corresponding calculations (Schrems et a]., 1 9 9 0 ~no ) retar-

'

440

M . SCHREMS

10 750°C/t

F

+

1O5O0C/x

5

5

0, Y

5 h Y 4

0"

0

0

2

32 t(750"C) [hl

8

128

FIG.25. Interstitial oxygen concentration Co(t) after x = 0 hr, 8 hr, 16 hr, 36 hr at 1050°C as a function of the preannealing time I at 750°C. Experimental values by Tan and Kung (1986) are connected by dashed lines. The other lines are simulations. (Schrems et al., 1990b. This figure was originally presented at the Spring 1990 Meeting of the Electrochemical Society held in Montreal.)

dation effect, but only a monotonous decrease of interstitial oxygen due to increasing precipitate formation, was observed. In the simulations the retardation effect was explained by a temporary dominance of precipitate dissolution, which was already noticeable for the one-step LO annealing. The model combining rate equations and a Fokker-Planck equation reviewed in Section II.5.b.ii can be extended in a similar manner (Schrems et al., 1990~).Calculation results were fitted to experimental values by Hawkins and Lavine (1989), who showed a retardation of oxygen precipitation in a two-step thermal sequence due to a preceding rapid thermal annealing (Fig. 26). In the simulations the retardation effect due to the rapid thermal annealing was explained by the dissolution of small preexisting oxygen precipitates, which formed during the wafers' thermal history. The preceding summary indicates that, despite experimental evidence (see, e.g., Chapters 4, 8 , 9, 12, 13) and theoretical indications (e.g., Section IV.2) for the significant dependence of the amount of oxygen precipitation observed on the interaction with other defects and mechanical stress, only a modest number of models is currently available. All of them have a very limited predictive capability. Even the most complicated approaches suggested so far (Schrems et al., 1990a, 1990b) cannot address a variety of important experimental findings such as enhancement or retardation of oxygen precipitation due to dopants like B , P or metals,

10.

SlMULAl ION O F O X Y G E N PRECIPITATION

6 1

I

I

1

441

I

12OO0C/x (RTA) + 950°C/lh + 12OO0C/y A EXPERIMENT - SIMULATION

/’

5

6 INITIAL

7

a

9

OXYGEN [1017cm-31

FIG.26. Oxygen loss vs. initial oxygen for LO-HI annealings without and with a preceding rapid thermal annealing. (Schrems et al.. 199Oc.)

as well as the existence of and transitions between different precipitate shapes, size-distributions of stacking-fault loops (Patel 1977). etc. Therefore, the next section will outline a generalized set of precipitation equations that can serve as framework for describing the complicated interactions between the different diffusion and aggregation phenomena in more sophisticated future models of oxygen precipitation and its related phenomena.

2 . GENERALIZED PRECIPITATION EQUATIONS Details of the kinetic theory of interacting precipitation phenomena, which is summarized in the following. can be found in Schrems et al. (19Yla) or Schrems (1991). The theoretical considerations are based on generalizing the term prccipitate. It is defined as any particle or compound that differs in its composition from the undisturbed crystal lattice. For oxygen in silicon this means that not only extended defects such as oxygen-silicon agglomerates with millions of atoms, stacking-fault loops or dislocations but even single oxygen atoms. silicon self-interstitials or vacancies are included in this generalized definition of a precipitate. The definition provides the basis for a unified theory of interacting precipitation phenomena starting from single atoms up to the formation of extended defects with millions of particles. The fundamental properties of a precipitate are its “type” and the “position” of its center of mass with respect to a coordinate

442

M. SCHREMS

system fixed against the crystal lattice. The precipitate “type” T is determined by the “composition” (i.e., the number of particles n i of the species S i (i = 1, . . . ,s) the precipitate contains) and the spatial “configuration” of the individual atoms: T

= ( n , a,),

Iz =

(Hi,

n,,

. . . , ni, . . . , n s ) .

(63)

A particle species Si can be a single atom, a vacancy, a silicon selfinterstitial or a molecule either with or without electrical charge or even a single free electron. The integer number a, accounts for the different geometric configurations, which also determine the precipitate shapes. A volume d ’ x with the center 2 = (x,, x2,x3) is assumed, in which the concentration of those precipitates, which can move in the lattice, is approximately constant with space. On the other hand, d’x shall be large compared to the sizes of the precipitates. The concentration f, of precipitates in the volume d 3 x changes with time either by precipitate motion (diffusion) into or out of d 3 x or due to a transition of its type from IJ- to T , which is determined by the continuity equation

a

at -f,G, t ) = -Vj, +

2

+ QT

I*+,

-

-fkwF+T

-f,wT4,,

(64)

I*

where j , denotes the diffusion flux into the volume d 3 x . The generation of precipitates T in d’x is equal to the sum over all type transitions between and T described by precipitation fluxes IF+, and an additional term Q,. which accounts for the fact that the precipitates T may be generated or consumed as by-products in other type transitions. Q, is obtained from equations for the conservation of particles (Schrems et al., 1991a; Schrems, 1991). The quantities wT+* and wIL+Tdenote the transition rates between the precipitate types. From Eqs. (64) (there is one equation for each precipitate type T ) and the conservation of particles, simplified cases can be derived by systematically introducing additional assumptions (Schrems et al., 1991a; Schrems, 1991). For example, the set of Eqs. (14) follows by regarding only oxygen as precipitating species (s = 1) and a change of the particle number n = n , by ? 1 at any type transition. Furthermore, single oxygen atoms are regarded as the only diffusing species ( Q , = 0 a n d j , = b for n # 1). Additionally, the initial oxygen content is assumed to vary only along an axis z = x3 perpendicular to the wafer surface. If oxygen molecules are also mobile, s = t 1, ? 2 has to be specified resulting in four instead of two precipitation fluxes originating from the sum in each Eq. (64), and the diffusional term and the Q term may be unequal to zero both for n = 1 and n = 2. The kinetic equations as well as the correspond-

10.

S I M U L A I ION O F O X Y G E N PREClPITArlON

443

ing Fokker-Planck equation for coprecipitation of two species like oxygen and silicon self-interstitials can also be found in earlier work (Schrems, 1991). As a final example an improved model of oxygen precipitation in interaction with one dopant will he outlined. I t addresses point defect mediated interaction between oxygen precipitation and an other dopant, which may be, e.g., carbon, boron, phosphorus or a metal atom species. The approach may be considered as a further refinement of earlier models (Schrems et al.. 1990b, 1990c), since not only oxygen precipitation. but also the precipitation of the silicon self-interstitials and the other impurity, will be described by precipitate distribution functions rather than deterministic growth laws. Instead of different precipitate configurations. macroscopic precipitate shapes such as spheroids and cylindrical discs are used. There are four precipitating particle species 0 , I , V, and the second dopant X ( = Me, C. €3. P, . . .) and thus s = 4 has to be set in Eqs. (64). It is further assumed that only single particles are mobile. As in Section II.S.b.ii, the number of equations is reduced by using Eqs. (64) only for the smallest precipitates with a few atoms and a single approximating Fokker-Planck equation for all larger precipitate sizes. The resulting size-distribution function depends on the four particle numbers ) I , , . . . , )id. At least one additional spatial coordinate and the simulation time have to be considered. too. In order to scale down the model to a manageable computational demand, further simplifications are introduced by assuming that not all arbitrary combinations of 0. I , V and X , but only the stochiometry SiOz (for the oxygen precipitates) and Xc,Si,,O((for the X precipitates with constants u , b, c ) can occur. Furthermore. only extrinsic stacking-fault loops composed of condensed silicon self-interstitials ( I ) are considered. The Fokker-Planck equation then splits up into three decoupled equations, which depend on only one particle number each and thus become identical to Eq. (26) from Section 11.S.b.ii. The oxygen precipitates. the precipitates of the other dopant X and the stacking faults can now be modeled in a similar manner as in Section 11.5.b.ii. Only the Gibbs energies and the growth laws are replaced by expressions for spheroidal shapes for oxygen and X precipitates or for cylindrical discs for t h e stacking-fault loops. The coupling of the precipitation phenomena is effected by the equations for the single mobile particles 0, I , V and X ,which resemble Eqs. (591462). VI. Summary

Current models of oxygen precipitation and the specific simulation re\ult\ obtained have been $urnmarued Early models such as nucleation

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models or deterministic growth models are valuable in obtaining overall trends for a number of experimental annealings, but they cannot completely describe oxygen precipitation during arbitrary thermal sequences. This is due to the fact that these models do not allow the determination of the transient evolution of the size-distribution function of oxygen precipitates. Furthermore, the amount of precipitated oxygen and the precipitate density cannot be calculated simultaneously. By combining both approaches the latter problem can be resolved and experimental loss of interstitial oxygen in two-step, three-step and multistep CMOS-type annealing experiments could be explained. However, the change with processing time of the precipitate size-distribution function is still not calculated, but assumed to follow a sequence of equilibrium values. The consequences of this assumption especially for the case of rapid changes in the annealing temperatures may need further investigations. Monte Carlo approaches and models based on rate equations or a Fokker-Planck equation both yield the transient precipitate size-distribution function as basic calculation result. Models were successfully applied to fundamental studies of precipitate coarsening. However, the authors of the Monte Carlo models reported that computation times were rather large and that some results were statistically very noisy. A model combining rate equations and a Fokker-Planck equation was shown to have predictive capability for a number of experimental results, and its use for analyzing and designing oxygen precipitation in multistep annealing cycles was demonstrated. Calculation results show a very significant dependence from variations in the effective equilibrium concentration of oxygen, which can be interpreted as a function of influences such as silicon self-interstitial and vacancy concentrations, the interactions with other impurities or precipitate stress. First attempts of taking into account these effects as well as the interaction of oxygen precipitation with the formation of other extended defects such as bulk stacking faults have been reported within recent years. However, these approaches seem not yet sufficient for predicting the complicated interaction of diffusion and aggregation phenomena associated with oxygen precipitation in silicon. The formulation of generalized precipitation equations was found to be useful in systematically deriving special kinetic models, which provide the framework for more sophisticated future modeling approaches.

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Baghdadi. A . . Bulli\. W. M . , Croarhin. M C.. Li. Yue-zhen. Scace. K. I . , Series. K . W.. Stallhofer, P.. and Watanabe. M . (1980).J . Electrochem. Soc. 136, 2015. Becker. K..and L>Aring. W. (1935). A t r t r . f'hys. (Leipzig) 24, 719. Bergholr. W . . Binns. M. J . . Booker. J . R . . Hutchinson, J . C.. Kinder. S. H . . Messoloras. S.. Nrwman. R . C . . Stewart. K J . . and Wilkes. J . G. (19891. Phil. Mng. B 59, 499. Binn\. M . J . . B r o u n . W. P . . Wilkes. J . G . . Newman. R. C . . Livingston. F. M.. Messoloras. S.. and Stewart. K. J . (19x3). Appl. f'/ry,\. Lrrr. 42, 5 2 5 . Bi-;+hec. I ' . . Schrems. M.. Hudil. M . . Potil. H . W . Kuhnert. W . . Pongratr. P.. Stmgeder. ( i . . and G r a s w b a u e r . M. lI9X9i. J ElwfrocI7rr7i. .Sot,. 136. 1542. Chtou. H . II9X7i.Solid Srtrrr 7 d i r r o l o q y (March). 77. Craven. K . A . (1981). I n Scmic.otidrrc / o r S / / i i , r v r , H. R . Huff. K . J . Kriegler and Y Takeishi 1. p. 254. ?-he Electrochemical Society. Pennington. N . J . . P . (1964). P/rv,\, R e \ . . il 133, 5x7. traundoii. P . . Fraundorf. G. K.. and Shimmini. F (1985). J . A p p l . Pliys. 58, 4049. Ereeland. P. E.. Jackson. K . A , . L.owe. (', W.. and Patel, J. R. (1977). A p p l . Phyt 1,err. 30, 31. <',Iddiner. . . C. W. (19x51. I n Handhool, o / Sroc.lrii.s/ic, Merlrods. H . Haken (ed.). Springer Serie\ in Synergetics, Vol. 13, Springer-Verlug, Berlin and Heidelberg. Greenwood. G. W . (1956i.,4c,rtr t t w r o l l 4. 242. Hahn. S . . Arst. M.. Kitr. K . N . Shataz. S..Stein. H. J . . Kek. Z. U . . and Tiller. W . A . 1 I98Xal. 1.A p p l . P l i y . ~ 64, . X49 Hahn. S . . Ponce. F. A . . 'filler. W. A . . Slol;lnoff. V . . Bulla. D. A . P.. and Castro. W. E.. Jr. l198Xbi.1.Appl. Phyc. 64. 4454 Ham. F. S . (1958). J . f'/iv.\. C'ht,tn. Sold.\ 6 . 3 3 5 . Hum. F. S . (1959). J . A p p l . Phvc. 30. I 5 I X . Hartrell. K . A , . Schaake. H. F . . m d Mkissey. K. ( 3 . 119x5). In lrnprrrirv Djfjirsion cind Gcvicritig in S i l i ~ ~ o t R i , . B. Fair. c' W Pearce and J. Washburn (eds.), p. 217. Mat. Re\. Soc. Synip. Proc.. Vol. 36. Pittsburgh. Hauhin\. G . A , . and Lavine. J . P. 11989) J . A p p l . Phys. 65, 3644. Hirth. J. P.. and Pound. G . M. (1963). "(:ondens. and Evaporation." In Proqr. in M t r t . .5c,i.. B. Chalnier\ ( e d . ) .pp. I I . 1.Pergarnon Press, Oxford. Hu. S. M. (1981). In f k f r . c . f . \ in Sr,rricfJ,lclrcc.ror.\.J . Naravan and T. Y. Tan (eds.). p. 3 3 3 . North-Holland. New York. 48. I IS. Hu. S. M. (I986a). .4ppl. f'/ry.\. h f / H u . S. M. ( 198hb). I n 0.kygc.n. C u r l u w , H!.dr.ouc,ii und Nitrogen in C'rvsttrlline .Silic.on. J . C. Mikkelsen. Jr.. S . J . Pearion. J . W . C'orbett and S . J . Pennycock (eds.). p. 249. Mat. Res. Soc. Symp. Proc . V o l 59. Pittsburgh. Huber. W . . and Pagani. M. (1990). J . Elcc troc./icvn. Soc.. 137, 3210. h u e . N . . Wada. K.. and Osaka. J (19x1). In S~~miconducior Silicon. H. R. Huff. R . J . Kriegler and Y . Takeishi (eds.1. p . 2x2. .The Electrochemical Society. Pennington. N.J. Inoue. N . . Wada. K . , and Osaka. J (19x7). In Dcfecrs und Properritv ofSrmiconduc.ror.s: I k f ; ' c ' r Enginerring. J. Chikawa. K. Suniino and K . Wada (eds.). p. 197.KTK Scientific Publishers. Tokyo. Iwmae. S . (1991). J . A p p l . Pliy.\. 70, 4217 I\om;ie. S.. Aoki. S . . and Watanabr. K . (19x41. J . A p p l . Phy.s. 55, 817. Jahlonski, J . . Wqiciechowzky. J . . and Kucharski. K. (19x8). P11y.t. Srcrr. S o l . f u ) 105. 113. Kaisshew. R. (1957).Z.Ele.Atroc~lrrm 61, 35. Kashchiev. I>. ( 1969). .SurJ .Scienc.v 14, 209. Ki5hino. S . . Matsushita. Y., Kanamori. M . . and lizuka. T. (1982). J p n . J . A p p l . Phys. 21, I.

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Landau, L . D., and Lifschitz, E. M. (1983). Lehrbuch der Theoretischen Physik, P. Ziesche (ed.), Vol. 10, Physikalische Kinetik, p. 458. Akademie Verlag, Berlin. Lavine, J. P., and Hawkins, G. A. (1986). In Oxygen, Carbon, Hydrogen and Nitrogen in Ciystalline Silicon. J. C. Mikkelsen, Jr., S. J. Pearton, J . W. Corbett and S. J. Pennycock (eds.), p. 301. Mat. Res. SOC.Symp. Proc., Vol. 59, Pittsburgh. Lavine, J. P., and Hawkins, G. A. (1989). In Atomic Scale Calculations in Materials Science. J . Tersoff, D. Vanderbilt and V. Vitek (eds.), p. 267. Mat. Res. SOC.Syrnp. Proc.. Vol. 141, Pittsburgh. Lavine, J. P., and Hawkins, G . A. (1992a). In Kinetics of Phase Transformations, M. 0. Thompson, M. Aziz, G. B. Stephenson and D. Cherns (eds.), p. 345. Mat. Res. SOC. Symp. Proc., Vol. 205, Pittsburgh. Lavine, J. P., and Hawkins. G . A. (1992b). In Strucfure and Properfies of Interfaces in Materials. W. A. T. Clark, C . L. Briant and U. Dahmen (eds.), p. 285. Mat. Res. SOC. Symp. Proc., Vol. 238, Pittsburgh. Lavine, J. P., Russel, J. T., and Hawkins, G . A. (1989). In Atomic Scale Calculations in Materials Science, J . Tersoff, D. Vanderbilt and V. Vitek (eds.), p. 261. Mat. Res. SOC.Synip. Proc., Vol. 141, Pittsburgh. Lifshitz, 1. M.. and Slyozov, V. V. (1961). J . Phys. Chem. Solids 35. Livingston. F. M., Messoloras, S., Newman, R. C., Pike, B. C., Stewart, R. J., Binns, M. J.. Brown, W. P., and Wilkes, I. G . (1984). J . Phys. C: Solid State Phys. 17,6253. Messoloras. S.,Newman, R. C., Stewart, R. J., and Tucker, J . H. (1987). Semicond. Sci. Techno/. 2, 14. Newman. R. C., Binns, M. J . , Brown, W. P., Livingston. F. M.. Messoloras, S., Stewart, R. J . , and Wilkes, J . G . (1983). Physica 116B, 264. Osaka. J.. Inoue, N., and Wada, K. (1982). J . Electrochem. Soc. 129, 2780. Pagani. M.,and Huber, W. (1987). In Proc. ESSDERC’87. P. U . Calzolari and G. Soncini (eds.), p. 339. TECNOPRINT, Bologna. Patel, J . R., Jackson, K . A., and Reiss, H. (1977). J . Appl. Phys. 48, 5279. Kavi, K . V. (1974). J . Electrochem. S o c . 121, 1090. Reiche, M.. and Nitzsche, W. (1985). Proc. Ist f n t . Autumn School on Gettering and Defect Engineering in Semiconductor Technology (GADEST), H. Richter (ed.),p. 174. Institute for Physics of Semiconductors, Frankfurt an der Oder, Germany. Schoeck. G.. and Tiller, W. A. (1960). Phil. M a g . 5 , 43. Schrems. M. (1991). Ph.D. thesis. Technical University of Vienna, Austria. Schrems, M . (1993). In Proc. o f the 5th Intern. Conf. on Shallow Impurities in Semiconductors, G . E. Murch (ed.),p. 231. Materials Science Forum, Vols. 117-118,Trans. Tech. Publ., Switzerland. Schrems, M., Brabec, T., Budil, M., Potzl, H., Guerrero, E., Huber, D., and Pongratz, P. (1989). Materials Science and Engineering B4, 393. Schrems, M., Brabec, T., Budil, M., Potzl, H., Hage, J., Guerrero, E., Huber, D., and Pongratz, P. (1990a). In Defect Control in Semiconductors, K . Sumino (ed.), p. 245. Elsevier Science Publishers B.V. (North Holland), Amsterdam. Schrems, M.. Budil, M., Hobler, G., Potzl, H., and Hage, J. (1991a). In Simulation of Semiconductor Devices and Processes, W. Fichtner and D. Ammer (eds.), Vol. 4, p. 113. Hartung-Gorre, Constance, Germany. Schrems. M.. Guerrero, E., Hage, J., and Potzl, H. (1991b). In the symposium on Advanced Science and Technology of Silicon Materials, Japan Society for the Promotion of Science. p. 40. Schrems, M., Hobler, G . , Budil, M., Potzl, H., and Hage, J. (1991~).Microelectronic Engineering 15, 57.

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p. 1 1 0 . Schrem, M . . Pongratr. P . . Budil. M., Potrl. H.. Hage. J . , Guerrero, E., and Huber. D. (IYWhl. In S[.rriic,onditc.tor S i l i c o n . H. R . Huff, K. G. Barraclough and J . Chikawa (ed\.). p. 144. The Electrocheniical Society. Pennington. N.J. Schrem.;. M.. Pongratr. P.. Budil. M . . f'otrl. H . . Hage. J . , Guerrero. E.. and Huber. 0. ( 1 9 9 0 ~ )I .n 7 h c Phvsic,.~c!fSenii~ondrtt for.\, E. M . Anastassikas and J . D. Joannopoulos (eds.). Vol. 1, p. 557. World Scientific, London. Seidman. D. N.. and Balluffi. R . W f l9h6). Phil. M u g . 13, 649. Stavola. M . . Patel. J . R . , Kirnrnerling. I . . C . . and Freeland. P. E. (1983). A p p l . P h y . Lett.

42. 73. Swaroop. K . . Kim. N . . Lin. W.. Hulli\. M . Shive. L.. Rice. A.. Castell. E . . and Christ. M . (1987). Solid Srare 7 w h r i o l o w v (March). 85. Tan. T. Y.. and Kung. C. Y . (1986). ./. A p p l . Phv.s. 59, 917. Taylor. W. J.. Jr. (1992). Ph.D. the\i\. [hike University, Durham. N.C. Tiller. W . A . . Hahn. S.. and Ponce. k-.A . (1986).J . A p p l . Phvs. 59, 3255. Tiller. W . A , . and Oh. S . (1988). J ,4pp/ P h v . ~64, . 375. Tmhev. S . . and Gutzow. I. (1972). k'ri.srtrll rtrid T ~ h r r i k7( 1-3). 4 3 . Turnbull. D.. and Fi5her. J . C. (1949) J ( ' h e m P h y s . 17, 71. Usami. T.. Matsushita. Y .. and Ogintr. M . (1984).J . Crysr. Growth 70, 319. Vanhellemont, J . . and Claeys. C. (19x7). J . Appl. Plly.5. 62, 3960. Vanhellemont. J . , and Claeys. C . (1988). Solid S / t i / r D r ~ , i c e sG. . Soncini and P. U . Calfolari (ed5.). p. 451. Elsevier Science Puhlijhrrs B.V. (North Holland), Amsterdam. van Kampen. N . G . ( 1981). .Sroc~hu.tricProc.~~s.sc~.v in Physk.c rind Chemisrry. North-Holland. .kn.;terdarn. Volrner. M.,and Weber. A . (1926) Zr\c h r . f'. Pliys. Chcm. 119, 277. Voronkov, V . V.. Mil'vidskii. M. G . . Grinshtein. P. M . , and Babitskii, Y . M . (1989). SOL.. PhyA. Crisrrrllo,qr.34(I).I 15. Wada. K.. and Inoue. N . (1985). J . C t v . \ l . Growth 71, II I. Wada. K . . Inoue. N.. and Osaka. J . (1983) M t i r . Re.\. Sot,. Sytnp. Proc-., Vol. 14, S. Mahajan and J. W. Corhett (eds.1. p. 125. El\evier, New York. Wada. K.. Nakani\hi. H.. Takaoka. t i . . and Inoue. N . f 1982). J . Ctysr. Growrh 57. 1535. Wagner. C. 11961). Z. Elekrroc.hc.ni. 65, 5 x 1 Wert. C . , and Zener. C . J . (19.50). J . A p p l . P h w . 21, 5. Wijaranakula. W.. and Matlock. J . t l 11991). J A p p l . Pliys. 69, 6982. Wilkes. J. G . (1983). J . Cp.sr. G'roit,tll 65. 214. I'ang. K . . Carle. J.. and Kleinhenr. K . 11987). J . Appl. Plivs. 62, 4890. Yatwtake. K . . CJnieno. M . . and Kawabe. H. 11984). Phvs. Slur. Sol. ( ~ I83. J 207. Zimmermann. H . , and Falster. K . ( 1992). 4 p p l . P/ivs. L e i / . 60, 3750.

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CHAPTER I 1

Oxygen Effect on Mechanical Properties K . Surnino anti I . Y o n t ~ n a g t r INSlITLITE FOR MATFRIAL9 R I \ E ARC t i TOHOKU CINIVFRSITY SLNDAI. JAPAN

INTRODUCTION . . . . . . . . . . . . . . . . . . PLASTIC DEFORMATION , \ N I ) I ~ X X A T I O NI SN SILICON CRYSTAI s . . . . . . . . . . . . . . . . . . . . 111. INFLUENCE OF DISP~RCI U O X Y G E N A r o M s ON THE MOBII.ITY OF DISLOCATIONS I N SII ICON . . . . . . . . . . . . . . I . Methodologic trl f'roblettr,s 111 t h e Mecrsuremeiit o f

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K. SUMINO A N D I . YONENAGA

VIII. EFFECTS OF NITROGEN A N D CARBON IMPURITIESON MECHANICAL PROPERTIES OF SILICON . . . . . . . . . . 1 . Nitrogen Effect . . . . . . . . . . . . . . . . . 2 . Carbon Effect . . . . . . . . . . . . . . . . . . IX. SUMMARY . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . .

499 499 504 507 5 10

I. Introduction

It is well known that wafers of Czochralski-grown silicon (CZ-Sij are much more resistive against the generation of dislocations or the occurrence of warpage than wafers of floating-zone-grown silicon (FZ-Sij during thermal cycling in device production processing. This is one of the main reasons why CZ-Si is used almost exclusively as the materials for VLSl or ULSI despite its lower purity compared with FZ-Si. It is natural to attribute such difference between CZ-Si and FZ-Si in the mechanical stability to the effect of oxygen impurities in CZ-Si on the dislocation processes occurring under stress at high temperatures. Oxygen impurities in CZ-Si are supersaturated in the temperature range below about 1250°C. Oxygen atoms in such a state effectively inhibit the dynamic activity of dislocations under stress. Supersaturated impurities naturally precipitate within a crystal when the crystal is held at temperatures at which the impurities move by diffusion at appreciable rates. Precipitation of oxygen in CZ-Si generally accompanies generation of various kinds of defects. Such defects are often reported to degrade the device function when they thread through device-active regions. They can also be utilized positively as effective gettering sites for harmful impurities incorporated by contamination. As to the effect on mechanical property precipitation of oxygen in CZ-Si leads to the softening of wafers. Understanding the effects of oxygen on mechanical properties of Si is, thus, very important in developing the production technology of Si devices. On the one hand, the mechanical properties of Si bear an important meaning also in basic study of crystal plasticity. The development of crystal growth technology in the last few decades has made it possible to grow Si crystals of high quality that are substantially free from dislocations. Dynamic properties of dislocations in Si have been studied experimentally in detail by observing the behavior of individual dislocations under stress, which were introduced intentionally into such high-quality crystals. Mechanical properties of Si measured by macroscopic mechanical tests can be analyzed on the basis of a microscopic model using the

1 1 . O Y Y - G I lu I I

I I ( 1 O N M E C H A N I C A L PKOPFRTIFS

45 1

dynamic properties of individual dislocations clarified in such a way. As it consequence, understanding the niacroscopically observed mechanical behavior of crystals in term5 of dislocation dynamics on a microscopic s a l e has now advanced the furthest in Si of all materials including impurity effects. This chapter reviews both the macroscopic and microscopic aspects of oxygen effects o n the mechanical behavior of Si. Effects of other light element impurities, such a 4 nitrogen and carbon, are also mentioned. Section 11 gives some basic aspect of plastic deformation of a crystal and also a brief description on the nature of dislocations in Si. Section I11 \bows the influence of oxygen atoms that dispersed within a Si crystal o n the dislocation motion. Section IV shows segregation of oxygen on dislocations and the resulting effect o n the dynamic activity of dislocations. Section V illustrates dislocation generation in Si as affected by oxygen. The experimental ol-wrvation is interpreted with the effect claritied in the preceding section. The effect of oxygen on macroscopic mechanical properties of Si I S described in Section V1. A description of the macroscopically observed mechanical behavior of Si crystals in terms of dislocation processes is also given there. Softening of Si caused by oxygen precipitation is described in Section VI1. Section VlIl gives the effects of nitrogen and carbon o n the mechanical strength of Si. 11. Plastic Deformation and Dislocations in Silicon Crystals

Si is completely brittle at low temperatures and becomes ductile gradually as the temperature is r a i d . This is common for all kinds of semiconductors. The temperature of the hrittlc to ductile transition can never be defined exactly. I t shifts to a high temperature when the crystal is stressed at it slow rate and shifts to ;I low temperature when stressed at a high rate. A rough measure for the tranbition temperature in Si may be taken to be about 500°C. All of w c h features reflect the dynamic property of dislocations in Si, which will be mentioned in later sections of this chapter. As in other kinds of diamond-type crystals, plastic deformation o f Si at high temperatures takes place hy means of a slip along the { 1 I I } planes in the ( I i0) directions. Such plastic deformation of Si by a slip is brought about by the glide motion of di\locations having t h e Burgers vectors of I!? ( I ( I i0) type, where (1 is the lattice parameter. along the { I 1 I } planes. During the plastic deformation of a crystal on a macroscopic scale, a high density of dislocations undergo glide motion at some appreciable velocity .

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K . SUMINO AND I . YONENAGA

To characterize the mechanical property, a crystal is usually subjected to a mechanical test by tensile or compressive deformation under a constant strain rate, and the so-called stress-strain curve is measured. In the case of a single crystal, the stress is referred to the shear stress component of applied stress, while the strain to the shear strain with respect to the slip system operating in deformation. The strain of a crystal consists of both elastic strain and plastic strain. The main part of the strain is elastic in the beginning of deformation of a crystal, namely, when the strain is small. Stress increases rapidly with increasing strain in such a deformation stage. After some amount of strain, plastic strain suddenly becomes predominant, and the stressstrain curve shows a break. This point is called the yield point. The stress at the yield point, called yield stress, is often taken as a quantity characterizing the mechanical strength of the crystal. The characteristics of the stress-strain curve of any crystal observed macroscopically are determined by a number of microscopic processes related to dislocations, such as generation, multiplication, motion, interaction with each other and with impurities. The basic equation which relates macroscopic deformation of a crystal with the dynamic state of dislocations inside it is given by ipl = NCb,

where 8,, is the plastic strain rate of the crystal, N is the density, V is the mean velocity, and b is the magnitude of the Burgers vector of dislocations in motion. The dislocation density is defined to be the length of dislocations contained in a unit volume of the crystal and has the dimension of c m - 2 . A dislocation in a Si crystal is energetically favorable when it lies along the most closely packed direction, which is one of the (1iO) directions. Thus, a stable dislocation in Si on the (1 11) plane is either a 60" dislocation o r a screw dislocation, which are the dislocation lines making the angles 60" and o", respectively, with the Burgers vector. Observations of dislocations by transmission electron microscopy have revealed that glide dislocations in Si are extended (Ray and Cockayne, 1971; Gomez, Cockayne, Hirsch and Vitek, 1975; Wessel and Alexander, 1977; Gomez and Hirsch, 1978; Foll and Carter, 1979; Sato and Sumino, 1979; Sato, Hiraga and Sumino, 1980). Namely, any such dislocations dissociate into two Shockley partial dislocations with the Burgers vectors of the (1 16) a ( 1 12) type, which bound a strip of stacking fault of the intrinsic type. The widths of the strip of stacking fault are 5.8 nm and 3.6 nm for a 60" dislocation and a screw dislocation, respectively, in Si (Gottschalk, 1979) under no stress. This means that such dislocations are

453

t I ( , . I . End-on high-resolution iniiigr\ of ( a ) ii in SI

cib\t,il

tSalo et

id..

h0' dislocation and ( b ) il screw dislocation

1980).

of a glide set. in the terminology o f Hirth and Lothe (1982). End-on high-resolution images of a 60" and a screw dislocation in Si are shown in Fig. 1 (Sato et a].. 1980). A dislocation loop generated f r o m ii source inside a crystal or a surface wurce assumes a shape of hexagon or half-hexagon, as shown schematically in Fig. 2 , when the di\lociition is isolated from other dislocations and the crystal does not contain a high concentration of impurities. 'The loop consist5 of segments of 60" dislocation and screw dislocation. The hO" segment consists of a 90' Shockley partial and a 30" Shockley partial hounding a strip of stacking fault. while the screw segment consists of two 30" Shockley partials. Atomic configurations at { h e core\ of a 30" Shockley partial and a 90" Shockley partial are shown in Fig. 3 . Geometrically, dangling bonds may

454

K. SUMlNO AND 1. YONENAGA

60° FIG.2. Schematic picture of a hexagonal-shaped dislocation loop on the ( I 11) slip plane in Si crystal. The hatched region shows stacking fault of intrinsic type.

be aligned along the dislocation core. However, such geometrical dangling bonds are now believed to be reconstructed to form bonds between two neighboring atoms along the dislocation line on the bases of electronic state of dislocations and theoretical calculations. A review on the dynamic behavior of dislocations and the characteristics of plastic deformation in various kinds of semiconductors is given by Sumino in a forthcoming issue of the Handbook on Semicouductors (North-Holland). 111. Influence of Dispersed Oxygen Atoms on the Mobility of

Dislocations in Silicon 1 . METHODOLOGICAL PROBLEMS I N THE MEASUREMENT OF

DISLOCATION VELOCITIES

Many papers have so far reported experimental results on dislocation velocities in Si as functions of stress and temperature. In most works dislocation velocities have been measured by means of intermittent technique; namely, the positions of dislocations are determined at room temperature by the etch pit technique or X-ray topography, while they are displaced by stress at elevated temperature. The intermittent technique has several origins for error in determining the accurate velocity of dislocations as pointed out by Sumino (1987). The most important and unavoidable origin of the error is the immobilization of dislocations by impurities. As demonstrated later, dislocations in a crystal act as very effective

1 1.

O X Y G E N F I t F( 1 ON ME C HANIC A 1 PKOPERTIES

455

(b)

(a)

F I G .3. Atomic configuration\ a l Ihe coi-es of (a1 a 30" Shockley partial dislocation and Ib1 >I 9 0 Shockley partial dislocation in 51crystid.

gettering sites for impuritie\ at elevated temperatures. Dislocations are locked when they getter impurities. In some cases t h e effect brings about ;L critical stress to start dislocations moving. In other cases a locked dislocation spcnds some incubation period before starting after application of stress. In the latter c a w the stress dependence of t h e dislocation velocity is measured to be htronger than the real one. Impurities are incorporated into the crystal with various origins, as residual impurities or by contamination. Dislocation\ are unavoidably held at rest at elevated temperatures in the intermittent technique. which leads to gettering of impurities by the dislocations. Thus. it is difficult to obtain the velocity of dislocation in motion avoiding the locking effects by impurities in the intermittent method. 'The most reliable experimental technique for measurements of dislocation velocity is thought to be that by means of in situ X-ray topography developed by the Sumino group (Sumino and Harada. 1981; lmai and Sumino, 1983) utiliLing a high-power X-ray source. a high-temperature tensile stage. and a highly sensitive T V system. Motion of isolated dislocations in a crystal introduced from some sources can be followed by real time observation as functions of the temperature and the applied stress with this technique. 'The technique is free from the ambiguity related to the locking effect o f irnpurities in determining the dislocation velocity.

2 Vtmcirv

OF

DISLOCATION\ I N HILH-PURITY SILICON

F i i \ t . experimental datd o n velocitie4 of di\locatlon\ i n a high-purity FZ-Si cry\tal are \hewn. The velocitie\ of i\olated 60"and \crew di\loca-

456

K . SUMINO AND 1. YONENAGA

tions at various temperatures measured by means of the in situ X-ray topographic technique are plotted against the shear stress in Fig. 4(a) (Imai and Sumino, 1983). Figure 4(b) shows the dislocation velocities under various stresses plotted against inverse temperature. It is seen that the velocities of the both types of dislocations in high-purity FZ-Si are linear with respect to the shear stress in the stress range 1-40 MPa and that the activation energies are independent of the shear stress in the temperature range 600-800°C. The dislocation velocity v is expressed well with the following equation: u =

v,,(7/To)exp(- Q / k , T ) .

(2)

The magnitudes of u,, are 1.0 x lo4 and 3.5 x lo4 m/s and those of Q are 2.20 and 2.35 eV for 60" and screw dislocations, respectively (Imai and Sumino, 1983). The shape of moving dislocations is observed to be a regular hexagon or a half-hexagon. The stress exponent of u has been determined to be higher than unity by various groups with the intermittent technique, ranging from 1.2 to 1.4, or not to be constant but to depend on the stress range where the measurements were conducted (Suzuki and Kojima, 1966; Patel and Freeland, 1967; Erofeev, Nikitenko and

3

FIG.4a. Dislocation velocity in high-purity FZ-Si crystal plotted against shear stress for various temperatures (Imai and Sumino, 1983).

1 1.

OXYGEN t t FFC T ON MECHANICAL PROPERTIES

457

2 1 0 ~ ,1 ~K"

t-'icl. 4b. Di\localion velocity in high-puritv FZ-Si crystal plotted against i n v e n e temperashear \tre\,s (Irnai ,ind Surnino. 1983).

tui-t' t'm barious

Osvenskii. 1969; George, Fscavarage. Champier and SchrBter. 1972: Fisher, 1975, 1978). The resulls obtained with the intermittent technique are not in quantitative agreement among different groups. Such disagreement may be attributed to the drawback involved in the intermittent technique.

3.

VEL.OC17 Y 01'DISLOCATIONS I N sII.ICON

CONTAINING OXYGEN

I M P U K I l IES

Figure 5 shows the relations between the velocity of a 60" dislocation and the shear stress at various temperatures in a Si crystal containing oxygen impurities at a concentration o f 7 . 4 x lo" atomsicm' obtained by means of the in situ X-ray topographic technique (Imai and Suniino, 1983). Data for high-purity FZ-Si are also shown in the figure. Dislocations in the crystal containing oxygen impurities move at velocities that are equal to those in the high-purity FZ-Si crystals in a high-stress range. However, dislocations originally in motion under high stress cease to move when the stress is reduced t o lower than about 3 MPa in the Si crvstal containing oxygen impurities. 'The velocity of dislocations in the crystal containing oxygen decreases more rapidly t h a n in the high-purity

458

K . SUMINO AND I . YONENAGA

0

0

High purity FZ 101 Z4x10'5m-3

I I

1

/

732°C

'

I 10

Shear stress,

I

1c MPa

FIG.5 . Velocity versus shear stress relations at various temperatures of 60" dislocations in a Si crystal containing oxygen impurities at a concentration of 7.4 x 1017 atomsicm'. Open circles indicate the data for high-purity FZ-Si (lmai and Sumino, 1983).

FZ-Si as the stress is decreased toward such a critical stress for the cessation of dislocation motion, shown by vertical broken lines in the figure. The stress exponent of the dislocation velocity is determined to be apparently larger than unity in the low-stress range in such a Si crystal. Figure 6 shows the velocity versus stress relations for 60" dislocations at 647°C in Si with dissolved oxygen impurities at various concentrations (Imai and Sumino, 1983). Broken lines drawn vertically bear the same meaning as those in Fig. 5, namely, the critical stresses below which dislocations originally moving under a high stress become immobile. Again, the dislocation velocities in the crystals containing oxygen impurities at a n y concentration are almost the same as those in high-purity FZ-Si under high stress. Both the deviation of the velocity from that in the high-purity FZ-Si with decreasing stress in the low-stress range and the critical stress for the cessation of dislocation motion increase with an increase in the concentration of dissolved oxygen impurhes. The magnitudes of the critical stress for the cease of dislocation motion are shown in Table I for Si crystals containing the various types of impurities.

OXYGLN F l l € ( I ON M L C H A N I C A L

10

PROPFKTIF5

459

-

Shear stress,

1c I

MPa

Fic;. 6. Velocitv v e r w s shear
Primary Impiiitv

Critical Sti-esh for Cessation of

Concentration Element

(;itoni\

~ciii')

___

Boron Carhon Nitrogen

2.0

Phosphoru<

1.2

Oxygen

I

1.0 5 4 5

10" 1011

IOI" :

2.5

7.4 v 2

lI)l<

1

Dislocation Motion (MPa) <:

1.2


.z

4.2 8.5

10'-

.--I.? I .x

10" 10'.

8.0

10''

3.0

460

K . SUMINO AND I . YONENAGA

Essentially, the same effect of dissolved oxygen impurities on the dislocation velocity is observed also for screw dislocations. 4. MORPHOLOGY OF DISLOCATIONS IN MOTION

The shape of moving dislocations in high-purity FZ-Si crystals is observed always to be a regular hexagon or half-hexagon of which segments are straight along ( 1 10) directions over the wide stress range investigated. This is true also in Si crystals containing oxygen impurities when dislocations are moving at the velocities equal to those in the high-purity FZ-Si in the high-stress range. However, whenever the velocities of dislocations deviate from those in the high-purity FZ-Si under relatively low stresses, the shape of the moving dislocations is observed to be perturbed from the ( I 10) straight lines and to become irregular. Figure 7 shows the X-ray topographs of dislocations moving in the low-stress range in Si crystals containing oxygen impurities at various concentrations (Imai and Sumino, 1983). The impurity-related perturbation in the shape of moving dislocations is found to be reversible. When the crystal in which moving segments are perturbed from (1 10) straight lines under low stress is subjected to high stress. the segments restore the straightness along ( 1 10) directions. Upon reducing the stress, the shape is perturbed again. Further reduction of the applied stress leads to the halting of dislocation motion. Extra stress is needed to restart such an immobilized dislocation. It increases with increases in the duration and temperature where the dislocations have been kept at rest, depending on the concentration of the dissolved oxygen atoms. This phenomenon is treated in the next section. In situ observations of dislocations in motion with a high-voltage transmission electron microscope equipped with a high-temperature tensile stage have also revealed interesting features in the dislocation motion in silicon crystals on a microscopic scale (Sato and Sumino, 1977, 1979: Louchet, 1981). Dislocations in silicon crystals were observed to move in a viscous manner at elevated temperatures on the microscopic scale. In accordance with the results of in situ X-ray topography, fast-moving dislocations are observed to consist of straight segments parallel to ( 110) directions when they are isolated. In CZ-Si crystals the shape of dislocations becomes irregular when they move at low velocities. They seem to be retarded locally by impurity-related obstacles. Once the retarded portion of dislocation overcomes the obstacle, the whole dislocation has a strong tendency to become straight along ( 1 10). As a result, segments of the dislocation are observed to move by repeating the local depression and quick recovery of it.

11.

O k Y G L N L l I I ( I ON M t ( H4NIC A 1 PROPFRTlt5

46 1

FIG.7. In \itu X-ray topographs 01 dislocation half-loops in motion at h47”C in Si crystals containing oxygen impurities at conLentr;ilion\ of la) 1.5 x (hl 2.5 x IO”’, ( c ) 7.5 x 101’. and (d) 9 x l o i 7 atomsicm’. Except for ( a ) . the topographs were taken under l o w stress. where deviations of the velocit) from that in high-purity FZ-Si were rernarkahle (Imai and Suniino. 1983).

5.

~ N T E R P R E T A T I O OF N THE

O Y \ C , FENF F ~ COTN DISLOCATION VELOCITY

A dislocation interacts with impurities through the overlap of their strain fields or electrostatic fields. Theoretically, such kinds of interaction:, result in the reduction of the dislocation velocity since extra energy is spent when the dislocation overconies the potential barrier related to the interaction. We have seen in Section 11.3 that oxygen atoms dispersed in a Si crystal

462

K. SUMINO A N D I . YONENAGA

retard the motion of a dislocation only when the dislocation moves at low velocity under low stress but not when the dislocation moves at relatively high velocity. The retardation of dislocation motion is accompanied by the perturbation in shape of the dislocation in motion. The perturbation in the shape of the dislocation means per se that the obstacles against dislocation motion did not develop uniformly along the dislocation line on a macroscopic scale. Overcoming such an obstacle of dislocation is achieved by bowing out of dislocation segments around the obstacle under stress. Under such circumstance the whole dislocation keeps moving at a constant velocity, which is lower than that of an unperturbed dislocation. On a further reduction of stress the dislocation ceases to move. Immobilization of the dislocation is thought to be caused when the obstacles develop closely along the dislocation line. When a dislocation is highly mobile in the matrix region of the crystal, the theory of thermally activated motion of a dislocation overcoming pointlike obstacles leads to the stress T / , needed to keep a constant velocity v given below in its simplest formulation (Seeger, 1958): T,, =

[ E - kgTIn(Lu/u)]/b2L,

(3)

where E is the energy of interaction between the dislocation and the obstacle, L is the mean separation of the obstacles, and v is the frequency of dislocation vibration. The important interaction between a dislocation and an obstacle at high temperatures is through their strain fields. The magnitude of E for such interaction is inversely proportional to the separation between the dislocation and the obstacle. The interaction energy between a dislocation and an impurity atom is calculated to be less than 0.5 eV, even when the impurity atom with a large misfit is located at the closest position to the dislocation. For such a magnitude of interaction energy and for impurity concentrations typical in semiconductors the magnitude of T,, becomes zero at a temperature well below room temperature. This gives the theoretical reason for why oxygen atoms dissolved in the matrix crystal of CZ-Si have no appreciable effect on the dislocation velocity under high stress. Dispersed obstacles can give rise to an appreciable effect on the dislocation velocity in the temperature range where Si is ductile if the interaction energy is higher than 3-4 eV. Such obstacles are thought to be clusters or complexes of oxygen atoms in Si crystals containing oxygen impurities. We reach the following picture. In Si crystals containing oxygen impurities oxygen atoms catch up to a slowly moving dislocation and develop clusters on the dislocation line that have a high interaction energy with

I I.

OXYGEN F I I I C I ON M E C H A N I C A L PROPERTIFS

463

the dislocation. This results in both the perturbation of the line shape and retardation of the dislocation. A dislocation ceases to move when such clusters or complexes of impurities are developed closely along the dislocation line. IV. Immobilization of Dislocations by Oxygen 1.

R E L E A S E S T R E S S OF

Dlsr.oc',AI I O Y S

l M M O B I L l Z E D BY O X Y G E N IMPURITIES

When a dislocation originally moving under high stress is halted under no applied stress in a Si cryctal containing oxygen impurities at a high temperature, where the diffusion of impurities is appreciable, it is immobilized due to the development of oxygen clusters on it. Extra stress i s necessary to start such a dislocation moving. It increases with an increase in halting duration. Such stress is termed the release ,stress or uniockirig strrss of the dislocation and i s interpreted to be the stress to release the dislocation from impurity iitoms segregated on the former. Dislocations free from segregation of impurity atoms are called .fresh disloccrrions while those immobilized by impurity segregation are called riged dislocu tion s . Figure 8 shows the variation of the release stress for originally fresh 60' dislocations at 647°C in Si containing oxygen impurities at various concentrations against the duration of halting at the same temperature (Sumino and Imai, 1983). N o appreciable release stress is detected for

Fic,. 8 . Variation of the relea\e stre\\ a( h j 7 Y for initially fresh 60"dislocations against the duration of aging at M7"C in Si ci-v\t;ils containing oxygen impurities at concentrations 5hown in the figure (Sumino and 1rn;ti. 1981).

464

K . SUMINO A N D I . YONENAGA

40 -

*

30-

v)

2

;20-

c

v)

2

c

!2

10-

*\

fa 5 min 0

I

I

I

\10 I

FIG.9. Temperature dependence of the release stress for 60" dislocations in Si crystals atoms/cm3that were annealed containing oxygen impurities at a concentration of 1 .O x at 730°C for various durations between 5 and 20 min (Sato and Sumino, 1985).

dislocations in a high-purity FZ-Si crystal even after a prolonged halting at high temperatures. The increasing rate of the release stress increases with an increase in the concentration of oxygen impurities. The release stress of a dislocation that is immobilized by any given heat treatment decreases as the stressing temperature is raised. Figure 9 shows the temperature dependence of the release stress for originally fresh dislocations in Si crystals containing oxygen impurities at a concentration of 1.O x lo'* atoms/cm3after annealing at 730°C for various durations between S and 30 min (Sato and Sumino, 1985). The release stress and temperature is in a linear relationship with the same slope for all the crystals in the temperature range higher than lOS0 K while another linear relationship seems to hold in the low-temperature range. 2. STATE OF OXYGEN SEGREGATED ON DISLOCATIONS Immobilization of a dislocation in an impure crystal is often related to the development of the Cottrell atmosphere around the dislocation. We first discuss the Cottrell atmosphere in a Si crystal containing oxygen impurities. Any given impurity atom occupies some definite site in the crystal, and each site is occupied by only one impurity atom. The distribution of impurity atoms within the crystal in thermal equilibrium, then, obeys the Fermi-Dirac statistics. The probability p with which an impurity occupies the site where the energy of interaction between the impurity atom and a dislocation is E ,

11.

OXYbEW Ft t F ( I ON MFC HANICAL PROPERTIES

465

T , 'C

Fit,. 1 0 . Occupation probability p i n thermal equilibrium of an impurity atom at the site having the interaction energy E , plotted against temperature T f o r an impurity concentration of 1 ppm. E , being taken a\ a parameter (Sumino. 198%).

is given approximately by the following equation as a function of ternperature 7 (Sumino, 198%): p = 1 / 1 1 t- ( l i ( : , ) e ~ p ( - E , i k , T ) ] .

(4)

where ('(, is the mean concentration o f the impurity in the crystal. The impurity distribution around a dislocation related to the Cottrell atmosphere is governed by Eq. ( 4 ) . Figure 10 shows p calculated a s a function of T (in "C) for a mean concentration of C,, = l o - " ( = I pprn) for various values of E,. The occupation probability p changeb from unity to C,, within a rather narrow temperature range as the temperature increases, depending on the magnitude of E , . At temperatures where diffusion of most impurity atoms takes place at appreciable rates, impurities of a concentration of I pprn are known to be effectively trapped by the sites where the magnitude of the interaction energy is higher than about I .5 eV. The dependence of p on 7 is influenced also by the magnitude of C ( , .The temperature range in which impurities are trapped effectively by the sites of any given value of E , is shown to become wider ;IS the impurity concentration increases. The interaction of a dislocation with an impurity atom that plays an important role at high temperatures is that through their elastic strain fields. As has already been mentioned. the magnitude of the maximum interaction energy at the smallest separation hardly exceeds 0.5 eV even for a typical impurity atom accompanying a large misfit strain. The interaction energy decreases rapidly a s the impurity atom is separated from thc dislocation. 'Thus. an oxygen-rich or -lean region (the Cottrell atmo-

466

K . SUMINO A N D I . YONENAGA

sphere) never develops around a dislocation at the typical oxygen concentration in CZ-Si. We are led to the conclusion that the immobilization of dislocations due to oxygen segregation in Si is not related to the development of the Cottrell atmosphere around dislocations. Oxygen atoms or, more generally, impurity atoms are thought to be gettered by dislocations at high temperatures by the following two mechanisms (Sumino, 1989b): ( 1 ) impurity is supersaturated and dislocations act as preferential nucleation sites of precipitates of the impurity; ( 2 ) some special reaction that incorporates impurity atoms from the matrix region takes place at the dislocation core. Special reactions that never take place in the matrix region may occur at the dislocation core because of the peculiarity of atomic arrangement there. The reaction product may have a high interaction energy with the dislocation. Occurrence of such special reactions incorporating oxygen impurities at the dislocation core has indeed been observed in CZ-Si (Koguchi, Yonenaga and Sumino, 1982; Yonenaga and Sumino, 1985). On the basis of the conclusion that impurity gettering by a dislocation proceeds by means of preferential precipitation or development of special reaction products at the dislocation core, we can treat the kinetics of the gettering by a dislocation with a simple assumption that the dislocation core is a perfect sink for impurity atoms that arrive there. The change rate of the impurity concentration C at any place in the stress field of a dislocation is given by dCldt

=

DV[VC

+ (C/ksT)VE,],

where t is the time, D is the diffusion constant of impurities, and E , is the energy of interaction of an impurity atom with the dislocation. The first term on the righthand side of Eq. (5) is related to the diffusion flow of impurities that originates from the inhomogeneity in the impurity concentration while the second term is the drift flow due to the interaction force between the impurity atom and the dislocation. Taking the dislocation line to be straight, we have the problem in the two-dimensional space. Again considering the elastic interaction through strain fields, the problem is solved numerically with the initial condition that the impurity distribution is uniform at t = 0. The time variation of C at any position in the crystal together with the number of impurity atoms absorbed at the dislocation core can be traced numerically as a function of the aging duration at any temperature (Sumino and Imai, 1983; Yonenaga and Sumino, 1985). The results of the simulation done for the gettering of oxygen impurities by dislocations in silicon are shown in Fig. 11 together with experimental results (Yonenaga and Sumino, 1985). They are in good

11.

O X Y G E N kFI I

<

I ON M t ( H A N I C A L PROPERTIEF

467

I

t ,

5

I I . Variation of the fraction / o f oxygen atoms segregated o n dislocations in C'Z-Si containing oxygen impurities at a concentration of' 6 x 1 0 ~ ' atomsicnil and involving dislocation.; at den\itie\ shown in the figure ( i n c m ') against the duration I of aging at 900°C. Murk\ and solid line\ show expenrnent;il data and broken lines results of calculation ( Y o nenaga and Surnino, 1985). Fit,.

Fii,. 12. T E M micrograph? \bowing the debelopment of oxygen precipitate5 along a di\location in CZ-Si due to aging at 9OtY'(' l o r v t i r i o i i \ durations shown in the figure.

agreement with respect to the time law and the dependence on the dislocation density. Oxygen atoms that are gettered by a dislocation are usually not distributed uniformly but discretely along the dislocation line as clusters or particles, as shown in the T E M micrograph of Fig. 12. This observation agrees with the picture we have already obtained with respect to the locking of a dislocation in a Si crystal containing oxygen impurities.

468

K. SUMINO A N D I . YONENAGA

3

L

“ 2

*Lu’

1

0

I

0

I

10 20 Aging duration, min

I

3(

FIG.13. Variations of the interaction energy E* and the line density N * of locking particles along dislocations in CZ-Si containing oxygen at a concentration of 1 .O x lo’* atoms/ an’ against the duration of annealing at 730°C (Sato and Sumino, 1985).

Suppose that locking particles are arranged discretely along the line of an immobilized dislocation with a line density N* and each particle has the interaction energy E* with a dislocation. On the assumptions that the interaction is of a short-range nature and that free portions of the dislocation are highly mobile, the theory of thermal activation leads to the following expression for the release stress T R : TR

=

N*[E* - kgTIn(LN*~*/T)]/b2,

(6)

where L and u* are the length and vibration frequency of the dislocation, and r is the releasing rate of the dislocation from the locking particles. The theory predicts the linear relationship between the release stress and the temperature when the locking particles are of only one kind, the slope being determined by N* and the magnitude of T R extrapolated to the absolute zero temperature by N * * E ” . Such a linear relationship is seen in Fig. 9 for dislocations immobilized by gettering of oxygen impurities in all the crystals in the temperature range higher than about 1050 K. Figure 13 shows the magnitudes of E* and N * of the locking particles deduced from the results in Fig. 9 using Eq. (6) against the duration of aging at 730°C. The density of the locking particles along the dislocation line is determined to be about 0.8 x lo6 cm-’ and is almost constant

I 1.

O X Y G E N E k k t C 1 O N M E C H A N I C A L PROPERTIES

469

against the duration of aging at 730°C. The magnitude of the interaction energy increases from 2.9 to 3 . 3 eV as the aging duration increases from 5 to 30 min. This seems to reflect the fact that the locking particles grow with aging. Figure 9 shows that another linear relation holds in the lowtemperature range in crystals aged for short durations. This may be interpreted as that some other kind of locking particles also develop along the dislocation line in addition to those mentioned previously. The interaction energies determined for the both kinds of particles are much higher than the interaction energy for a single oxygen atom in silicon. The separations of locking particles are determined lo be larger than the mean separation of individual oxygen atoms in the matrix crystal. These results accord well with the picture that oxygen atoms gettered on the dislocation line are in the state of clusters or complexes.

V. Effect of Oxygen on Dislocation Generation I. G E Y € , . K I I O N

OF

DISL.OC.ATIONS

When a Si crystal initially free from dislocation is stressed at a high temperature, dislocations are generated heterogeneously under stress lower than the ideal strength for dislocation nucleation by orders of magnitude (Sumino and Harada. 19x1 ). Then, macroscopic deformation of the crystal takes place by means of the propagation of Luders bands from the place where dislocations itre generated. The ideal strength is the stress necessary to cause slip in a perfect crystal and has theoretically been evaluated to be about 0.24 G tor ;I diamond-type crystal, where G is the shear modulus of the crystal. Cisually, dislocations are observed to be preferentially generated at the surface region of the crystal and to penetrate into the bulk if the crystal contains no structural irregularities inside which facilitate dislocation generation. Such an observation naturally leads to the idea that any real crystal has some irregularities on the surface that act as the preferential generation centers of dislocations under stress at an elevated temperature. The irregularities are thought to be microscopic regions with a strongly disturbed atomic structure that mity be formed by some energetical stimulation such as mechanical shock or chemical reaction at the surface. which i 4 inevitably or accidentally involved during the surface preparation. I t has been reported that several kinds of damaged structure on a microscopic scale are introduced by abrasion or indentation of Si surfaces (Stickler and Booker. 1963; Gridneva. Milman and Trefilov, 1972: Erernenko and Nikitenko, 1972). Recently an extremely tiny region of amorphous silicon surrounded by a dislocated crystalline region has been

470

K . SUMINO AND I . YONENAGA

FIG. 14. (a) Cross-sectional TEM micrograph of a scratch made on Si surface at room temperature together with the diffraction pattern, and (b) that after annealing at 600°C for I hr. Dark lines are images of dislocations (Minowa and Sumino, 1992).

found around a scratch or an indentation made on a silicon surface at room temperature by TEM observations (Clarke, Kroll, Kirchner, Cook and Hockey, 1988; Minowa and Sumino, 1992). Figure 14(a) shows a cross-sectional TEM micrograph of a scratch made with a 2 gram load on the surface of a Si crystal at room temperature. A region with a round periphery having uniform and dark contrast is the amorphized region produced by scratching. The crystalline silicon changes to amorphous silicon abruptly across the interface of the two regions. This suggests that the amorphous region was formed not as a result of heavy plastic deformation of the Si crystal but by means of phase transformation of crystalline Si under a highly localized stress. Dislocations developed around the amorphous region are on the (1 1 l} planes and have Burgers vectors parallel to the ( 1 10) directions. The magnitude of the shear stress realized in the region beneath the scratch is estimated to be close to the ideal strength of the crystal. Thus, these dislocations are thought to be generated by spontaneous nucleation under such high stress. The amorphous region is observed to transform to a heavily dislocated crystalline Si when the crystal is brought to a tempera-

47 1

FIG. I S , Changes in the imagc c o n t i i i \ t \ o f X-ray toPograph\ of indented region\ made on k%-Si \uil'ace w i t h the increase iii leniper;tlure under stresb (Sumino and Harada. I Y X I ) .

ture higher than about S0O"C a s 4hown in Fig. 14(b) (Minowa and Sumino, 1992). A scratch or an indentation on the surface of a Si crystal accompanies a strained region around it that is extended over a macroscopic scale observable with X-ray topography. Such a strained region shrinks in size when the amorphous micro-region transforms to the dislocated microregion due to annealing. When the crystal is under stress, some of the dislocations that have the maximum Schmid factor come out ot'the microregion and penetrate into the matrix and expand on a macroscopic scale (Sumino and Harada. 19x1). At this stage dislocations are usually recognized to be generated. This p r o w s is demonstrated in Fig. 15, in which X-ray topographs showing the change in the contrast around indentations on the surface of a FZ-Si crystal under stress with an increase of the temperature are shown (Sumino and Harada, 19811. The contrast at room temperature under no applied stress i s shown in Fig. 15(a). White dots show distorted regions around the indentations. The contrast under a shear stress of 10 MPa at room temperature is shown in Fig. 15(b). It is recognized that indentations have no significant stress concentration effect. In Fig. IS(c) the contrast of the indentations when the crystal is heated to 600°C under a stre44 of 10 MPa is shown. The contrast of the image5 of the distorted region4 i s seen to diminish strikingly. Figure IS(d)

472

K . SUMINO A N D 1. YONENAGA

--_---____---

_____ _-_____ 0.__----. -._._ 0-_.-------__ I I 600 650 700 Temperature, "C

''

~

FIG. 16. Critical stress for dislocation generation from a Knoop indentation plotted against temperature in FZ-Si and CZ-Si (Sumino and Harada, 1981).

is the topograph when the crystal is further heated up to 650" under the same stress. Now, the size of the white dots is seen to recover. Figure 15(e) is the topograph of the crystal that is subsequently heated to 690°C. The image size is further enlarged and dislocations in such regions are seen. The diminishing of the size of the white dots seen in Fig. 15(c) may be attributed to the release of the strain around the indentations related to the recrystallization of amorphous Si and the recovery in the size from Figs. 15(c) to 15(e) to the generation of dislocations from the indented area. 2. OXYGEN EFFECT ON DISLOCATION GENERATION Dislocations are easily generated from a flaw, such as an indentation or a scratch, in high-purity silicon crystals even under extremely low stresses at high temperature. However, in a crystal doped with a certain kind of impurities no dislocations come out of the flaw until the applied stress exceeds a critical stress even though the flaw accompanies a dislocated micro-region. The effect of oxygen impurities on the generation of dislocations on a macroscopic scale in CZ-Si has been investigated, making use of intentionally introduced surface flaws such as indentations. Figure 16 shows the critical stress for dislocation generation from a Knoop indentation made at room temperature in a FZ-Si crystal and a CZ-Si crystal as a function of the temperature (Sumino and Harada, 1981). The CZ-Si crystal contains oxygen impurities at a concentration of an order of 1OI8 ~ m - The ~ . crystals were heated quickly to test temperatures in the abscissa under stress. In high-purity FZ-Si dislocations are generated under a stress lower than 1 MPa over the whole temperature

1I.

OXYGEN EFFt ( I O N MECHANICAL PROPERTIES

473

range tested. On the other hand, in CZ-Si fairly high magnitudes of the critical stress are measured. The critical stress increases with an increase in the temperature. It has been shown in the preceding section that oxygen atoms dissolved in a Si crystal do not affect the velocity of a dislocation moving under a high stress. The velocity of a dislocation increases with an increase in the temperature. From these facts it is concluded that the critical stress for dislocation generation is not related to the resistance against the dislocation motion due to oxygen atoms dissolved in the crystal. Thus, the critical stress for dislocation generation is related to the release stress of dislocations in the flaw region that are immobilized during heating of the crystal due to the gettering of oxygen atoms. When stress is low enough to allow the development of clusters or complexes of oxygen atoms along dislocations in the recrystallized dislocated region at a flaw. the dislocations ar-e immobilized and do not come out of the flaw region until the applied stress exceeds the release stress. This is

FIG. 17. X-ray topographs showing the generation of dislocations from scratcheh and peripheries of wafers due 10 thermal cycling in C‘Z-Si containing oxygen impuritieh at a c o n c e n t i d o n of 1.7 x 10’x.a high-purity FZ-SI and FZ-Si containing nitrogen impurities at a concentration of 1.5 x I O ” a t o m ~ / c n i (Ahe ‘ et al.. 1981).

474

K. SUMINO AND I . YONENAGA

thought to be the mechanism of suppression of dislocation generation in the CZ-Si crystal. Figure 17 shows dislocation generation due to thermal cycling at a scratch and the periphery of wafers of CZ-Si, high-purity FZ-Si and FZ-Si doped with nitrogen impurities (Abe, Kikuchi, Shirai and Muraoka, 1981). Dislocations are abundantly generated in high-purity FZ-Si while generated less in CZ-Si and nitrogen-doped FZ-Si. This observation demonstrates oxygen and nitrogen impurities are effective in suppressing dislocation generation in device production processing of wafers. The effect of nitrogen impurities on the dynamic activity of dislocations is given in a later section. VI. Mechanical Properties of Silicon as Influenced by Oxygen Impurities 1. MECHANICAL PROPERTIES OF HIGH-PURITY SILICON CRYSTALS

First in this section, we show the characteristics in mechanical behavior of high-purity FZ-Si crystals that are free from the effect of oxygen impurities. They are the mechanical properties inherent to Si. Oxygen effects are then described in following sections. Figure 18(a) shows the stress-strain curves of high-purity FZ-Si crystals subjected to tensile deformation along the [123] direction at various temperatures under a shear strain rate of 1.1 x s - ' . The crystals initially contain dislocations at a density of 2 x lo4 cm-2 (Yonenaga and Sumino, 1978). Figure 18(b) shows stress-strain curves of the same FZ-Si crystals at 900°C under various shear strain rates. The stress-strain curve of FZ-Si is characterized by a noticeable drop in stress from the upper to the lower yield points. The magnitudes of the upper and lower yield stresses and the amount of the stress drop after the upper yield point depend sensitively on the temperature and strain rate. They all decrease rapidly with an increase in the temperature and increase markedly with an increase in the strain rate. There is another important parameter that affects the characteristics of stress-strain curve in the yield region; namely, the density of generation centers or multiplication centers for dislocations initially contained in the crystal. Figure 18(c) shows how the upper and lower yield stresses and the stress drop diminish with an increase in the density of dislocations initially contained in FZ-Si crystals in the deformation at 800°C under a shear strain rate of 1.1 x s-' (Yonenaga and Sumino, 1978). Specimens with initial dislocation densities higher than 2 x lo6 cm-* show no stress drop in yield deformation. Most dislocations originally contained in high-purity FZ-Si crystals are observed to be mobile even under an extremely low stress and to undergo self-multiplication during their motion along the slip planes.

I I.

475

OXYGEN F f F F ( 1 O N M F C H A N I C A L PROPFRTIES

0

lo

20

30

1

Shear strain, Yo

(h)

Shear strain, "/. (CI }I(,. I X Stre\s-\lrain curves of high-puritv FL-SI crystals in tensile deformation along the 11231 direction as dependent on ( a ) temperature. ( h ) shear strain rate and ( c ) inilial dcn\ity of dislocations (Yonenaga and Sunllno. 1978).

476

K. SUMINO AND I. YONENAGA

The upper yield stress T , , ~and the lower yield stress T~~ depend on the temperature T and the strain rate i: in such a way as described with the following relation: T,,~

or

(7)

T , CK~ ~ ‘ “ e x p ( U l k , T ) ,

where the magnitudes of n and U for T , are ~ reported to be 2.1-2.5 and 0.94-1.25 eV, respectively, and those for T~~ to be 2.9-3.3 and 0.80-0.92 e V , respectively (Patel and Chaudhuri, 1963; Siethoff and Haasen, 1968; Yonenaga and Sumino, 1978; Schroter, Brion and Siethoff, 1983). EFFECTON MECHANICAL PROPERTIES OF 2. OXYGEN DISLOCATION-FREE CRYSTALS Figure 19 compares stress-strain curves of dislocation-free Si crystals with various concentrations of interstitially dissolved oxygen atoms together with that of high-purity FZ-Si deformed at 900°C under a shear strain rate of 1 . 1 x s - ’ (Yonenaga, Sumino and Hoshi, 1984). All specimens have been subjected to annealing at 1300°C followed by rapid cooling to homogenize them before deformation tests. The stress-strain curve of the crystal with any oxygen concentration is characterized by an extremely high upper yield stress and a sharp stress drop after the upper yield point. The shape of all the curves from the upper yield point to the lower yield point is rather irregular. This reflects the fact that

N

OL

I

I

1

I

10

20

30

40

Shear

strain , %

FIG. 19. Stress-strain curves of dislocation-free crystals of Si containing oxygen irnpurities at various concentrations shown in the figure and high-purity FZ-Si deformed in tension along the [I231 direction at 900°C under a shear strain rate of 1 . 1 x s - ’ (Yonenaga et al.. 1984).

11.

O X k C L Y I=f 1.1

(

I O N MI C H A N I C A I PROPFRlIES

477

deformation proceeds by nucleation and propagation of Luders bands. It may be said from the figure that both the upper and lower yield stresses and the amount of yield drop a s well as overall stress-strain characteristics show no systematic dependencies on the oxygen concentration: namely, they are almost independent of the oxygen concentration. Several groups reported that the yield stress of dislocation-free crystals of usual CZ-Si was almost the same a s that of usual FZ-Si (Mahajan. Brasen and Hassen, 1079; Sumino, Hiiracla and Yonenaga. 1980; Doerschel and Kirscht. 1981). It is concluded that individually dispersed oxygen atoms have little influence on dislocation processes occurring in the deformation of a Si crystal. This agrees with the ohservation that oxygen impurities at any concentration do not affect the velocities of dislocations in motion as seen in Figs. 5 and 6.

3 . OXYGEN EFFLCTON

ME(.HANI(’AI.

PROPERTIES OF DISLOCATED CRYS.TA1.S

Figure 20(a) shows stress-strain curves of dislocated CZ-Si crystals in deformation at various tempct-atures under a shear strain rate of 1 . 1 x 10 5 I , while Fig. 20(b) those under various strain rates at 900°C. The crystals are originally dislocated at a density of 2 x lohcm-’ and contain oxygen impurities at a concentration of 7 x to” atoms/cm3. I t is seen that the dislocated CZ-Si crystals show the same type of dependencies of the yielding behavior on both the temperature and the strain rate as those in dislocated high-purity FZ-Si crystals seen in Fig. 18. Essential difference between C Z S i and FZ-Si is in the dependence of the yield behavior on the dcnsity of dislocations initially contained in the crystals. Figure 21 show\ the stress-strain curves of CZ-Si crystals dislocated at two different densities deformed at 800°C under a shear strain rate of I . I x 10 s - I together with those of FZ-Si crystals dislocated also at two different densities. A CZ-Si crystal with a dislocation density of 5 x 10‘ c m - ’ shows the yield behavior similar to that of a dislocation-free crystal in Fig. 19. A FZ-Si crystal dislocated at a density of 1.7 x 10‘ c m - shows no stress drop in yielding, while a CZ-Si crystal dislocated at 9 x 10‘ c m - ? shows a more remarkable stress drop than that of a FZ-Si crystal dislocated at 2 x lo4 cm-’. Thus, dislocated CZ-Si crystals show yield behavior that corresponds to that of a FZ-Si crystal with tin initial dislocation density more than two orders of magnitude lower. The effect becomes increasingly remarkable as the concentration of oxygen impurities increases. Figure 22 shows stress-strain curves in the yield region of Si crystals dislocated at densities of approximately 1 x 10‘ c m - ’ , containing at a variety of concentrations of oxygen impurities. deformed at 800°C under a shear strain rate of 1 . 1 x s - ’ (Yonenaga

’

478

K. SUMINO A N D I . YONENAGA

N

E 2

r-

1

0 3ln

?

+ m

Shear

strain

.

1

10

20

30

40

50

Shear strain , %

FIG.20. Stress-strain curves of CZ-Si crystals dislocated at a density of 2 x lo6 cm-? and containing oxygen impurities at a concentration of 7 x 10” atoms/cm3 as dependent on (a) temperature and (b) shear strain rate.

J

N

E

cz 5x10'crn\

m

_. oL-L-..L

0

10

20

LO

30 Shear

50

60

70

strain , Yo

Fic,. 2 I . Stress-\train curves of dislocated c q s t a l s of CZ-Si and FZ-Si i n tensile deiorinaInitial lion along the 117-31 direction at 800Y' undei- a 5hear strain rate of 1 . 1 x l o - ' di5location densitie\ of the cry\tal\ are \hewn in the figure (Surnino et al.. 1980).

0

5

lo

Shear strain, '10

Fic;. 22. Stres\-strain curves of S I crystals dislocated at densities of about I x I O h c m - ' and containing oxygen at various concentration\ shown in the figure deformed at 800°C under a shear strain rate of 1 . 1 x I0 ' \ (Yonenaga et al.. IY84).

'

480

K . SUMINO AND I . YONENAGA

60 -

$

50-

$ 40k v)

P .g 30\

B

3

2010 -

01

'

1 o4

I

!

I I 106 Dislocation density, cm-2 /

lo5

I

I

I

lo7

FIG.23. Upper yield stresses of Si crystals containing various concentrations of oxygen shown in the figure in the deformation at 800°C under a shear strain rate of 1 . 1 x SC' plotted against the density of dislocations contained in the crystals prior to deformation (Yonenaga et al., 1984).

et al., 1984). All the specimens were annealed at 1300°C and cooled rapidly to avoid the precipitation of oxygen. The upper yield stress is seen to increase with an increase in oxygen concentration. Figure 23 shows the upper yield stress in the deformation at 800°C under a shear strain rate of 1.1 x s - ' for crystals with various concentrations of oxygen impurities plotted against the density of dislocations initially contained in the crystals (Yonenaga et al., 1984). For any values of the oxygen concentration, the upper yield stress is affected noticeably by the initial density of dislocations. It is seen that the upper yield stress of crystals with an oxygen concentration of 1.5 x 10'' atoms/ cm3 is approximately equal to that of a high-purity FZ-Si crystal of which dislocation density is lower than that in the former by about one order of magnitude, and that in the crystals with an oxygen concentration of 9 X lOI7 atoms/cm3 is equal to that of the high-purity FZ-Si crystal of which dislocation density is more than two orders of magnitude lower. Figure 24 shows the dependence of the upper yield stress in the deformation of 800 and 900°C on the oxygen concentration for crystals with dislocation densities of 2 x lo5 cm112and 1 x lo6 cm-2 (Yonenaga et al., 1984). For both dislocation densities, the upper yield stress is seen to increase with the oxygen concentration, the increasing rate being enhanced at high oxygen concentrations.

11.

OXYGEN F1FI-C 1 O N MECHANICAL PROPERTIES

48 1

G 5
k

4-

Z t-

o ,-

.3-

x 1

IJ

21 -

t IC 24 Dependence of the uppei vield \tres\ T", at 800°C and 900°C o n the concentrdtion C of oxygen a t o m i n cry\talc with initirll di\location densitie5 of 2 x 10' and I x 106 cni ' (Yonenagd ct dl , 1984)

,4s has been demonstrated in preceeding sections, in situ X-ray topographic observations have verified that the mobility of dislocations in a Si crystal is little influenced by dispersed oxygen atoms but that the locking of individual dislocations takes place pronouncedly in the crystals with high concentrations ot' dissolved oxygen (Imai and Sumino. 1983: Sumino and Imai. 1983). Thus. it i s natural to think that high upper yield stresses of crystals with high oxygen concentrations are closely related to the immobilization of d i h c a t i o n s initially contained in the crystals due to the development of oxygen clusters or complexes along them. Dislocations initially contained in oxygen-doped Si crystals are locked firmly by oxygen impurities and t h e locking strength increases with an increase in the concentration of oxygen. In the next section it is shown how such dislocation immobilization gives rise to the effect that corresponds to an apparent decrease in the initial density of dislocations. 4.

T H t O R E T I C A L D E R I V A T I O N OF Y I L l I) C H A R A C T E R I S T I C S

u . Si Crystctls in the Ahsrnc.r,

I)i.vlocutioti Locking by I m p u r i t i t ~ s

Plastic deformation of' a crystal proceeds by means of the motion of a high density of dislocations in the crystal. Yielding of a crystal may be regarded as the transient \t:ige during which the internal state of the crystal changes from the static one t o the dynamic one when the crystal

482

K. SUMINO AND I . YONENAGA

is subjected to deformation of a constant rate. Both the upper and lower yield points as well as the stress-strain curve of the crystal in yield deformation are determined by various dislocation processes that take place during such transience. The basic equation that relates the dynamic state of dislocations in a crystal to macroscopic deformation of the crystal is kp, = NGb,

(8)

which is identical to Eq. (I). In Eq. (8), it is assumed that deformation of the crystal takes place by means of a single slip along the primary slip plane and, as a consequence, dislocations of only the primary slip system contribute to deformation. The total shear strain rate i: is the sum of the plastic shear strain rate given by Eq. (8) and the elastic shear strain rate iel. Thus,

.

&

=

.

+ kel.

(9)

The flow stress T , of a crystal is equal to the stress needed to move dislocations within the crystal at a certain velocity, which is determined by the strain rate and the density of dislocations in motion. It is proportional to the elastic strain. Thus, the time derivative of the flow stress is given by where 5 is the elastic constant of the system consisting of the specimen and deformation apparatus. In deformation under a constant strain rate, Eq. (10) turns to be dT,/d&

=

.$(&- N G b ) / i .

(11)

The flow stress consists of two components: One is the effective stress which is necessary to make a dislocation overcome the intrinsic resistance of the crystal lattice at some given rate, and the other is the athermal stress T ~ which , is necessary to overcome the interaction between dislocations. Namely,

Teff,

The mean velocity of dislocations moving in the crystal during defor~ ~ Eq. (2): mation is obtained by substituting T , into

According to the dislocation theory, T~ =

T~

is given by

GbN;"/P,

II

O Y Y b F N t F I kC 1 O N h l l ( HANIC A 1 PROPERTIES

483

where G is the shear modulus, h is the magnitude of the Burgers vector, N , is the density of all dislocations in the crystal and p is a constant of about 3-4. Dislocations multiply thenisclves during motion and a simple model of self-multiplication leads to the following multiplication rate of dislocations (Peissker. Haasen and Alexander. 1961): clNldl = Kr,,NV, (15) where K is a constant. Equation (IS)is valid when the dislocation multiplication process is controlled by dislocations of only the primary slip \ystem and is deduced on the physical model that the multiplication takes place by means of a double cross glide of screw dislocations or a local pinning of dislocations by a fixed number of obstacles. We assume N = N , in the following; namely, that all dislocations in the crystal are in motion. This assumption may he valid in the beginning stage of deformation such as yield deformation. The stress-strain curves of a Si crystal are calculated by solving simultaneous differential equations ( 1 1 ) and (15) with Eqs. (13) and (14) in a numerical way. The initial condition is taken to be T ~ = , GbNA”/p for F = 0. where N,, is the density of dislocations initially contained in the crystal. Derivation of the stress-\train curves on the preceding model have been performed by Suezawa, Sumino and Yonenaga (1979). Only K is the fitting parameter of the model, the value of which has been determined from the magnitude of the upper yield stress of a specimen with a certain value of N,) in the deformation at some fixed temperature and strain rate. The stress-strain curves of a Si crystal calculated for various deformation conditions are in good agreement with the experimental ones with respect to the dependencies of the both upper and lower yield stresses on the temperature and the strain rate. However, the calculated magnitudes of the lower yield \tress are systematically lower than the experimental ones. Further. t tic calculated upper and lower yield stresses both show weaker dependencies on N,, than experimental ones. This ahove discrepancy between calculation and experimental is removed by taking into account of activity of dislocations of the secondary slip system (Sumino and Yonenaga, 1991, 1993). It is commonly observed that dislocations of slip systems other than the primary slip system are i i l s o active in yield deformation of a Si crystal. When two slip systems are active in deformation of a crystal, the total plastic shear strain rate is given by the following equation instead of Eq. (8):

t,,, = N , i ) , b t yN,C,b,

(16)

484

K. SUMINO AND 1. YONENAGA

where N , and N 2 are the densities of dislocations of the primary and secondary slip systems, respectively, V , and V 2 are the mean velocities of dislocations on the primary and secondary slip systems, respectively, and y is a geometrical factor that is smaller than unity. The velocities V , and V , are obtained by substituting the following effective stresses on the primary and secondary slip systems into Eq. (13): T , ~ I~ ,= T ~I ,

GbN!‘2/f!- GbN:I2/P*,

(17a)

~ = T~, , ~ ~

GbN;”/P* , ~ - GbNii2/P,

(1%)

T

where T , , , ~and T , , ~ are the resolved shear stresses of the applied stress with respect to the primary and secondary slip systems, respectively, and P and p* are constants characterizing the interaction between dislocations of the same slip system and that between dislocations belonging to different slip systems, respectively (p > p*). In situ observations of dislocation multiplication processes by means of X-ray topography (Sumino and Harada, 1981) and transmission electron microscopy (Sato and Sumino, 1977; Sumino and Sato, 1979) have revealed that dislocation multiplication takes place by two basically different mechanisms in Si crystals: one is spontaneous multiplication of gliding dislocations, for example, by means of double cross slip and the other multiplication through interaction of dislocations belonging to different slip systems. The multiplication rates of dislocations of the primary and secondary slip systems are then given by dN,ldt

=

K N l ~ l ~ e f+f ,K, * N I N : ! v I T ~ ~ ~ , I ,

( 18a)

dN,ldt

=

K N 2 v 2 ~ e K+, 2K * N 2 N I v 2 ~ e f f , 2 ,

(18b)

respectively, where K and K* are constants that characterize the two multiplication processes. Stress-strain curves calculated with Eqs. (16) through (18) are shown in Fig. 25, which is in good agreement with experimental observations shown in Fig. 18. Figure 26 shows the calculated upper and lower yield stresses with solid lines as functions of various parameters. Experimental data are shown by open and filled circles. The agreement between calculation and experiment is excellent. b. Effect of Dislocation Locking by Oxygen Impurities

We have seen in Sections VI.2 and 3 that an increase in the oxygen concentration in Si results in a significant increase of the strength of the

11

OX’rCrFlu t l I t ( I O N MF( H A N I C A L PROPtRTIF\

900°C I .L I 5 10 IS Shear strain

30

r--

o/o

-

485

L

I I 10 15 Shear strain , ‘lo

5

~

T- 600°C

Shear strain, Yo (C)

Fiti. 7 5 . Calculated \li-e\\-\trdin ctine\ o f high-purity si crystals a\ dependent o n ( a ) temperature. (h) sheai- strain rate ,ind I C ) initial density of dislocations. which corre\pond t o experimental strea\-strain curve\ in Fig. I X ( a ) . ( b ) . and ( c ) . respectively (Sumino and Yonenaga. 1993).

486

K . SUMINO AND 1. YONENAGA

T , 'C 850

800

L 0.85 0.9 0.95 1 0 3 / ~ K-' ,

1 10-5

10-4 € , s-'

Ir 3

(b)

E

-

0

lo4

105 lo6 N o , cm-2

107

(C)

FIG.26. Upper yield stress T , and ~ lower yield stress T , of ~ high-purity Si crystals as dependent on (a) temperature, (b) shear strain rate and ( c ) initial density of dislocations. Solid lines show the results of calculation while open and filled circles show experimental points for T~~ and T , ~ ,respectively (Sumino and Yonenaga, 1993).

crystal only when the crystal is initially dislocated. We have concluded that the strengthening of Si crystals due to oxygen impurities is not related to the resistance of oxygen atoms dispersed within the crystal against the dislocation motion but to the locking of dislocations due to the segregation of oxygen atoms on the dislocation core. Here, we discuss how such locking of dislocations affects the yield behavior of the crystal. Let us consider a simplified case in which dislocations of only the

II

O X Y G E N Et I-f

(

I O N M F C H A N I C A L PROPFRTltS

487

primary slip system are activated in deformation and they multiply themselves, being controlled by Eq. ( 1 5 ) . Suppose that the applied stress T , , increases at a constant rate q ; namely. T , = q t . When the dislocation density N is low enough that T , in Eq. ( 14) is much lower than T,,.~. T , , is approximately equal to T,,,. Assuming that all dislocations in the crystal are in motion. Eqs. (13) and ( 15) lead to N as a function of^,, to be given as follows (Sumino. I989a): N

=

N,,exp(
(19)

with

<=

(

vi, K/3qTo)exp(- Q / k , T ) .

where N,, is the density of mobile dislocations initially contained in the cry st al. When dislocations are locked by impurities, a stress T , . is needed to release the dislocations from the impurities and to start them moving. In such a case N turns o u t t o be its follows:

It is known that once applied stress exceeds the release stress the density of dislocations increases with stress in such a way as if the initial density of mobile dislocations were reduced by locking by a factor of ~ X P ( < T < ' ) This . is just the explanation for our observation in Section V1.3. The magnitude of T , increases with the oxygen concentration and also depends on the period and temperature where the dislocations are kept under no stress. We can estimate the magnitude of release stress of dislocations from the magnitude of the upper yield stress if the deformation condition and the initial density of dislocations are known. Figure 27 shows the release stress as a function of the oxygen concentration, which is obtained from the analysis of data in Fig. 14 with the model that dislocations of the primary and secondary slip systems are activated. It is seen that the release stress increases with the concentration of oxygen impurities and that the magnitude of the release stress at 900°C is lower than that at 800°C:. The latter reflects the fact that the release process of dislocations from impurities is thermally activated. Oxygen segregation along dislocations in the specimens of Fig. 14 IS thought to have taken place while the specimens are heated to deformation temperature o r they were kept at that temperature before the deformation test.

488

K. SUMINO A N D I. YONENAGA

I I

B

5ot

= 40ffl-

ffl

gul

30-

al ffl

-3 2

2010-

5 10 Oxygen concentration, 10’ 'ern-3 FIG.27. Release stress of dislocations in CZ-Si crystals estimated from the upper yield stress in Fig. 24 shown as a function of the oxygen concentration.

5 . WAFERSTRENGTHENING BY OXYGEN IMPURITIES In the following, an explanation is given of why CZ-Si wafers are more resistive than FZ-Si wafers to warpage caused by thermal-stress-related thermal cycling even if they are free from dislocations (Sumino, 1986). Any real wafer used in device fabrication processing is never free from some structural irregularities, especially at the edge of the wafer, which are effective generation centers for dislocations. In fact, dislocations are observed to be generated from such surface irregularities during device production processing. Once generated, dislocations multiply during motion and, as a result, increase their density as described by Eq. (15) or (18).

We consider the simplified case of a wafer that is subjected to stress cycling with the amplitude T~ at a constant temperature T , as shown in Fig. 28 and dislocation multiplication controlled by Eq. (15). The density of dislocations increases with stress in each cycle in such a way as described by Eq. (19) where No in the first stress cycle is taken to be proportional to the density of generation centers for dislocations in the crystal. After the first stress cycle the density of dislocations attains a certain magnitude determined by T and T ~ In . the absence of locking by oxygen impurities, as in FZ-Si, dislocations of such a density all act as dislocation sources. Thus, the density of dislocations starts increasing from such a value in the second cycle and attains an increased magnitude after the second cycle. After repetition of some number of cycling, the density of dislocations increases up to a magnitude that is high enough to cause appreciable warpage of the wafer. In Fig. 29 curves marked

11.

OXYGEN EFFkC'l ON MECHANICAL PROPERTIES

489

Time

FIG.28. Stress verws lime relation in stress cycling.

I

Nc

-

Cycling number

FIG. 29. Variation in the dislocation density aga~nstthe number of stress cycles calculated for F-Z-Si and CZ-Si wafers. Calculafion wah done for stress cycling at 900°C with a stressing rate of 5 x l o - ? MPaIs and stress :implitude\ of 7.5 and 10 MPa (Sumino. 1992).

490

K . SUMINO AND 1. YONENAGA

FZ-Si show how the density of dislocations increases with the number of cycling at 900°C for stress amplitudes T~ = 7.5 and 10 MPa and a stressing rate of -q = 5 x lo-* MPa/s. The case of thermal cycling is more complicated. Thermal stress is induced by inhomogeneous distribution of temperature during the heating and cooling course of the cycling. Thus, the temperature as well as the stress varies with time. In the case of a Si wafer containing impurities, such as oxygen, which immobilize dislocations effectively, there are two effects that prevent dislocations from increasing their density. First, dislocations are not generated from the dislocation sources if the amplitude of stress cycle does not exceed the critical stress for generation of dislocations seen in Section V.2. In such a case the wafer is kept practically free from dislocations, even after a number of stress cycling. Second, in actual device production processing a wafer is kept under no stress at high temperatures for a certain duration, since the temperature is uniform throughout the wafer. Even if dislocations are generated from the dislocation sources and move into the wafer during the preceding heating or cooling course of the cycling, they are immobilized due to gettering by oxygen atoms when the wafer is kept at the high temperature. Thus, the density of dislocation sources after each cycle returns to the initial value before the cycling is started. As a consequence, the density of dislocations keeps a low value even after a number of cycles. Curves marked CZ-Si in Fig. 29 show the variation of the dislocation density against the number of cycles on the simplified assumption that the temperature is a constant 900°C (Sumino, 1992). This is the reason why wafers of CZ-Si are more resistive to warpage due to thermal cycling than wafers of FZ-Si.

VII. Influence of Oxygen Precipitation on Mechanical Strength

1. GENERAL FEATURES IN THE SOFTENING OF SILICON RELATED TO PRECIPITATION OF OXYGEN

It is known that the high resistance against wafer warpage in CZ-Si is lost when the wafers are kept at temperatures around 1000°C for a rather long period. This phenomenon is related to the precipitation of supersaturated oxygen in CZ-Si. Interstitially dissolved oxygen atoms in CZ-Si crystals become supersaturated in the temperature range below about 1200°C. Figure 30 shows the effect of annealing at 1050"C, 1175°C and 1320"C, each for 24 hr on the stress-strain curves of originally dislocation-free CZ-Si crystals with an oxygen concentration of 9 x lo" atoms/cm3 in tensile deformation at s - ' (Yonenaga and Sumino, 1982). 900°C under a strain rate of 1 x

1I

49 1

O X Y G E N F F b F C IO N M l ( H A N l C A l PROPERTIES

~~

q-

I

0

I

10

30

20 Shear strain

,

40

50

'1.

FIG. 30. Stress-strain curves of originally dislocation-free CZ-SI crystals annealed at varioub temperatures shown in the figure measured each for 24 hr deformation at 900°C under a shear Strain rate of 1 x 10 s (Yonenaga and Surnino, 1982).

'

Annealing at 1175°C or 1320°C does not affect the magnitude of the upper yield stress significantly. Deformation of crystals that are subjected to such heat treatment and that are in the as-grown state all proceed by means of the propagation of 1,iiders hands in the yield stage. Annealing at I0So"C drastically reduces the magnitude of the upper yield stress and t h e flow stress throughout all deformation stages. as has been first demonstrated by Patel (1964). The deformation of a crystal annealed at 1050°C proceeds homogeneously like a FZ-Si crystal containing dislocations at a density higher than lo4 cmVarious types of defects as well as SiOz precipitates are developed in the crystals due to annealing at 1050°C. Figure 31 shows an extrinsic stacking fault and punched-out dislocation loops developed around precipitate particles in such crystals (Yonenaga and Sumino. 1982).The details of the generation of defects induced by oxygen precipitation are given in another chapter. Annealing of precipitation-softened crystals at temperatures higher than 1200°C leads to the restoration of the high upper yield stress and large stress drop in the yield defcmnation, as shown in Fig. 32 (Yonenaga and Sumino. 1982). SiO, precipitates its well as various kinds of defects around them are observed to be diminished by such dissolution treat-

'.

492

K . SUMINO A N D I . YONENAGA

ment. The change in the stress-strain curve is similar to that caused by the decrease in the density of the dislocation sources. The stress-strain curve of the crystal subjected to dissolution treatment at 1320°C for 1 hr is almost the same as that of the crystal subjected to no precipitation treatment. It may, thus, be concluded that the precipitation softening in CZ-Si crystals is caused by the generation of defects that can act as effective dislocation sources under stress. A CZ-Si crystal that is annealed at 1320°Cfor 24 hr and cooled directly to 1050°C and held there for 24 hr shows upper and lower yield stresses higher than those of a crystal in the as-grown state. N o defect related to precipitation of oxygen is observed to be developed. Contrarily, in crystals that are annealed at 1320°C and cooled to room temperature, drastic reductions in both the upper and lower yield stresses take place on subse-

FIG. 31. TEM micrographs of (a) an extrinsic-type stacking fault and (b) punched-out dislocations developed around oxygen precipitates in CZ-Si annealed at 1050°C for 24 hr (Yonenaga and Sumino, 1982).

1I

0'

493

OXYGEN € I f k < 1 O N M F C H A N I C A L PROPFRTIES

I

10

20 30 Shear strain

.

40

50

"/.

FIG.3 2 . Stress-strain curves of CZ-SI crystals precipitation-treated at 1050°C f o r 24 hr a s influenced by dissolution treatments at 1240. 1280 and 1320°C each for 5 min. and also by that at 1320°C for 60 min, meawred in deformation at 900°C under a shear strain rate S C ' (Yonenaga and Sumino. 1982). of 1 x

quent annealing at 1050"C, and at the same time, numerous defects were observed to be developed. This observation implies that the nuclei of precipitates o r defects causing the softening of CZ-Si crystals are formed during the cooling to room temperature from 1320°C or during the heating from room temperature to 1050°C. Thus, we know that the development of precipitates and associated defects is strongly influenced by the thermal history of the crystal. Usually, different ingots of CZ-Si follow different precipitation processes and, as a consequence. show different softening kinetics. Thus, in order to study the process of precipitation softening in detail, we must choose the crystals that have identical thermal hi stories.

2.

YIELD

STRENGTH OF CZ-SI

Wl' lH

OXYGEN

PRECIPITATION

In this section we show the characteristics in precipitation softening that proceeds at 1050°C in dislocation-free CZ-Si crystals all homogenized initially by annealing at 1300°C followed by rapid cooling. Figure 33 shows the stress-strain curves of crystals containing oxygen at various concentrations after annealing at 1050°C for 24 hr (Yonenaga et al.. 1984). It is seen that the magnitude of the upper yield stress and

494

K. SUMINO AND I. YONENAGA

N

0’

1

1

I

I

10

20

30

40

Shear strain

,

%

FIG.3 3 . Stress-strain curves of originally dislocation-free CZ-Si crystals containing oxygen impurities at various concentrations shown in the figure after annealing at 1050°C for 24 hr measured in deformation at 900°C under a shear strain rate of 1 x s - ’ (Yonenaga et al.. 1984).

the amount of the stress drop from the upper yield point to the lower yield point are reduced drastically upon such heat treatment in crystals with high concentrations of oxygen atoms. The reduction becomes increasingly significant as the concentration of dissolved oxygen atoms increases. The upper yield stress and the general characteristics of the stress-strain curve of a FZ-Si crystal with an oxygen concentration lower than 10l6atoms/cm3and those of a CZ-Si crystal of which oxygen concentration is as low as 2.5 x lo’’ atoms/cm3 are not influenced by annealing at 1050°C. Figure 34 shows how the stress-strain behavior of CZ-Si with an oxygen concentration of 9 x 10” atoms/cm3 changes with the duration of annealing at 1050°C (Yonenaga and Sumino, 1982). The crystals are softened rather rapidly with an increase in the duration of annealing in agreement with the work by Pate1 (1964). The softening is seen most drastically in the magnitude of the upper yield stress. The yield deformation proceeds by means of the propagation of Luders bands in the crystals subjected to annealing shorter than 3 hr. Figure 35 shows how the upper yield stress changes with the duration of annealing at 1050°C for the crystals with various oxygen concentrations (Yonenaga et al., 1984). Variation in the concentration of interstitially dissolved oxygen atoms due to the annealing is also shown in the bottom of the figure. It is confirmed that the softening of the crystals is related closely to the increase in the density of SiO, precipitates with direct

I 1.

O X Y b C N F I I 1 C I O N MFCHANICAL PROPERTIFS

495

observation of precipitates. I t is also related to the decrease in the concentration of interstitially dissolved oxygen atoms as seen in the figure. It is interesting to note that the concentration of interstitially dissolved oxygen atoms in the crystal with an original oxygen concentration of 9 x lo’’ atomsicm7 decreases rapidly in the early stage of annealing and becomes lower than those in the crystals with lower concentrations of oxygen for annealing durations longer than about 5 hr. This suggests that the density of nuclei of precipitate\ depends strongly on the concentration of oxygen atoms even in crystals having been subjected to the homogenization treatment. Figure 36 shows the relation hetween the upper yield stress and the amount of precipitated oxygen atoms for crystals with different concentrations of oxygen atoms (Yonenuga et al.. 1984). For a given amount of precipitated oxygen atoms, t h e upper yield stress is measured to be higher for the crystal of a higher oxygen concentration than for the crystal of a lower oxygen concentration. I t is also to be noted that the magnitude of upper yield stress decreases very rapidly against the amount of precipitated oxygen atoms. These ohw-vations give clues to clarify the mechanism of precipitation softening of CZ-Si as described in the next section.

SHEAR STRAIN ( % )

FIG. 34. Stress-strain curves of (11-iginally dislocation-free CZ-Si crystals annealed at 105O’C for various durations shown in the figure. measured in deformation at 900°C under a shes \train rate of I x I W 4s - ’ IYonenaga and Sumino, 1982).

496

K . SUMINO AND I . YONENAGA

-

*b-.

10 3

E

kU

5

P 6

0

10 20 Annealing duration, h

0

FIG. 35. Variations of upper yield stress T , ~and the concentration 0,of interstitially dissolved oxygen atoms against the duration of annealing at 1050°C in Si containing oxygen ~ measured in deformation atoms at various concentrations shown in the figure. Here T , was at 900°C under a shear strain rate of 1 x s - ' (Yonenaga et al., 1984).

3. MECHANISM OF PRECIPITATION SOFTENING

The stress-strain curve of a CZ-Si crystal softened due to oxygen precipitation is characterized by a low magnitude of the upper yield stress and a small stress drop in yield deformation, which is characteristic of that in a FZ-Si crystal with a rather high density of dislocations. Thus, we may suppose that some defects are induced in CZ-Si in connection with oxygen precipitation that can act as effective dislocation sources under stress. Figure 37 shows a row of etch pits of dislocations around a SiOz precipitate observed after slight deformation of a crystal subjected to precipitation treatment (Yonenaga and Sumino, 1982). At first sight, this micrograph seems to suggest that precipitates act as dislocation sources by themselves, which leads to the precipitation softening.

I 1.

O X Y G E N EFf I-( 1 O N ME( HANlCAL PROPERTltS

497

FIG. 36. Variation of the upper vield s ~ i e \ \T , , ~against the amount of precipitated oxygen atom\ O,, in Si crystals with differznt concentrations C,, of oxygen atoms. measured in deformation at 000°C under a shear strain irate of I x I O - ' s - ' iYonenaga et al.. 19x4).

Fit,. 37. Rows of dislocation etch pit\ around a SiO: precipitate observed after slight deformation of a crystal rubjected t o precipilalion treatment (Yonenaga and Sumino, 1982).

498

K . SUMINO AND 1. YONENAGA

On the assumption that SiO, precipitates act as dislocation sources, an analysis in terms of dislocation dynamics has been done to describe quantitatively the experimental relation in Fig. 36. With the model that the decrease in the upper yield stress is related to the increase in the density of precipitates, it turns out that the density of precipitates has to increase more than six orders of magnitude against the change in the amount of precipitated oxygen atoms of a factor 2-2.5 to account for the experimental results. This result is unreasonable, and thus, the model is concluded to be inadequate. With the alternative assumption that the density of precipitates is constant in the intermediate stage of precipitation and also during the dissolution of the precipitates, the nucleation rate of dislocations at a precipitate under a given applied stress has to increase by more than 10 orders of magnitude against the change in the size of the precipitate of a factor 2 to account for the experimental result. This result is again unreasonable. From elasticity calculations, Kayano (1968) reported that the magnitude of the stress concentration coefficient at a rigid inclusion in a crystal was 2 at maximum. Similarly, Yasutake, Umeno and Kawabe (1982) reported that the stress concentration coefficients at a sphere-shaped particle of amorphous SiO, and a platelet of cristobalite SiO, in silicon were 1.25 and 2, respectively. Such low magnitudes of the stress concentration coefficient are insufficient to nucleate dislocations under ordinary applied stresses. In any event, it is concluded that SiO, precipitates themselves are not dislocation sources that bring about precipitation softening in CZ-Si. Now, we discuss the possibility that prismatic loops of dislocations developed around precipitates owing to large misfit strain are dislocation sources responsible for the precipitation softening. As seen in Fig. 38, the prismatic loops of punched-out dislocations are elongated around a SiO, precipitate after slight deformation (Yasutake et al., 1982). This TEM micrograph corresponds to the observation in Fig. 37. In an early stage of precipitation each precipitate is small in size and a low density of dislocations are punched out from it owing to a small misfit strain. The punched-out dislocations are quickly locked by oxygen and immobilized, since a rather high concentration of dissolved oxygen atoms remain in the matrix at this stage. As the precipitation process proceeds, precipitates grow and the number of punched-out dislocations increases as the misfit strain increases. Locking for such dislocations is less effective because rather low concentrations of oxygen atoms remain in the matrix now. At the same time, the oxygen atoms segregated along dislocations that have been punched out in the earlier stage change to precipitate particles. Oxygen atoms, originally distributed uniformly along the dislocations, are now concentrated at discrete positions, as

1 1 OXYGtN

EFFI

(

I O N M t C H A N I C A L PROPFRTIES

499

FIG.38. TEM micrograph of punt hed-oul dislocations elongated by slight deformation (Yawtahe et

21..

1982).

shown in Fig. 12. leaving oxygen-free portions on the dislocations. Such portions are free from locking and are able to act as dislocation sources under applied stress. The occurrence of these phenomena has indeed been observed by TEM. With this picture, the relations in Fig. 36 are reasonably understood. The concentration of oxygen atoms remaining dissolved in the matrix crystal is higher in the crystal with a higher oxygen concentration than in that with a lower oxygen concentration for a given amount of precipitated oxygen atoms. Such oxygen atoms remaining at a high concentration are thought to lock dislocations punched out from precipitate particles and the locked dislocations cease the function as dislocation sources. Thus, a higher upper yield stress may be attained in the crystal with a higher oxygen concentration than in the crystal with a lower oxygen concentration for a given amount of precipitation. VIII. Effects of Nitrogen and Carbon Impurities on Mechanical Properties of Silicon 1 . NITROGEN EFFECI (I.

Effc3ct.v on the

Dynumic BcJliuisior of' Individuul Dislocutions

Nitrogen atoms are reported to be electrically inactive and thought to be located on the interstitial sites in Si lattice (Tokumaru, Okushi, Masui

500

K . SUMINO AND 1. YONENAGA

and Abe, 1982). The effect of nitrogen on the dynamic behavior of individual dislocations in Si crystals has been investigated by the Sumino group with nitrogen-doped FZ-Si by means of in situ X-ray topography (Sumino, Yonenaga, Imai and Abe, 1983; Imai and Sumino, 1983; Sumino and Imai, 1983). Dislocations originally in motion at elevated temperatures under rather high stress in nitrogen-doped FZ-Si cease to move when the applied stress is lowered beyond some critical stress as have been observed in the case of Si containing oxygen impurities in Section 111.3. Such cessation of dislocation motion is never observed in usual FZ-Si of high purity. The critical stress for cessation in a crystal with a nitrogen concentration of 5.4 X lo'-' atoms/cm3 has been measured to be 3.0 MPa at 600°C and 5.5 MPa at 800"C, increasing monotonically with the temperature. The velocities of dislocations in crystals of this nitrogen concentration are measured to be the same as those in high-purity FZ-Si under stresses higher than the critical stress for the cessation of motion. When a dislocation ceases the motion in the nitrogen-doped crystal, the stress necessary to start the dislocation increases with the period during which the dislocation is kept at rest, as we have seen with crystals containing oxygen impurities. Figure 39 shows the release stress of 60" dislocations at 647°C in Si doped with nitrogen at the preceding concentration plotted against the duration of aging of dislocations at the same temperature. Data for Si

0

I

I

I

1

I

10

20

30

40

50

Aging duration,

min

FIG.39. Variation of the release stress at 647°C for initially fresh 60" dislocations against the duration of aging at 647°C in FZ-Si doped with nitrogen at a concentration of 5.4 x 10" atorns/cm3. Data for CZ-Si with two different oxygen concentrations of 1.5 x and 7.5 x IOl7 atorns/crn' and FZ-Si doped with phosphorus at a concentration of 1.2 x IOl9 atomsicm' are also shown (Surnino and Irnai, 1983).

II.

OXYGEN EFI r

cr

.~

LO

50 1

O N MFCH A N I C A L PROPFRTIES

/ .'

h

. = I

N

€

1

"CZ

I1

5: W

a: I

0

10

I

I

I

20 30 LO SHEAR STRAIN ( 7 0 )

0

FIG.40. Stresh-atrain curves of initially dislocation-free crystals of nitrogen-doped FZ-SL (.YF%)b i t h a nitrogen concentration of 5.4 x 10'' atomsicm'. high-purity FZ-Si and CZ.-Si uith an oxygen concentration o f 9 10'' a t o m s / c r n ' in deformation at 900°C under a shear \train rate of 1 x 1 0 j - 't s u m i n o et d.. 19x3).

'

doped with two different concentrations of oxygen at I.S x 10'' and 7.5 x 10" atoms/cm3and that doped with phosphorus at a concentration of 1.2 x 10" atomsicm? are also shown in the figure for comparison. Nitrogen impurities at a concentration as low as 5.4 x 10" atomsicm' has a locking effect on dislocations approximately equal to that of oxygen impurities at a concentration higher by a factor of about 30. The locking strength of individual impurity atoms has been compared for different kinds of impurities from the number of the impurity atoms accumulated on a unit length of a dislocation during aging. It has been shown that an individual nitrogen atom has ii much stronger locking effect than an individual oxygen atom. b. Ejfcct on M r c h a n i c d Str.c*rrgtli

Abe et al. (1981) reported that wafers of a FZ-Si crystal doped with nitrogen at a concentration as low as 1.5 x atoms/cm3 were less susceptible to thermal slip than those of normal FZ-Si or CZ-Si crystals. This seems to reflect a strong locking effect o n dislocations due to nitrogen in Si. The stress-strain characteristics of a nitrogen-doped FZ-Si crystal in the as-grown state at elevated temperatures are similar to those of a usual FZ-Si crystal and a CZ-Si crystal when they are all free from dislocations

502

K. SUMINO AND 1. YONENAGA

I

SHEAR STRAIN ('1.1

FIG.41. Stress-strain curves of FZ-Si crystals doped with nitrogen at a concentration of 5.4 x 10'' atoms/crn3 containing dislocations at various densities prior to deformation in deformation at 800°C under a shear strain rate of I X s - ' . Numerals attached to the curves show initial densities of dislocations in unit of cm-' (Sumino et al., 1983).

prior to deformation. Figure 40 shows the stress-strain curve of a nitrogen-doped FZ-Si crystal (denoted NFZ in the figure) with a nitrogen concentration of 5.4 x lo" atoms/cm3deformed at 900°C under a strain rate s-l together with those of a high-purity FZ-Si crystal and a of 1 x CZ-Si crystal with an oxygen concentration of 9 x lo" atoms/cm3 (Sumino et al., 1983). They are all characterized by a marked stress drop and the deformation by means of propagation of Luders bands during yielding. Though the upper yield stress and the flow stress over a whole strain range are somewhat higher in the CZ-Si crystal than in the others, the difference among the three kinds of crystals is not significant, being much smaller than that found in dislocated crystals, which will be described next. Figure 41 shows stress-strain curves of the nitrogen-doped FZ-Si crystals with various densities of dislocations between 4 x lo4 and I .O x lo6 cm in deformation at 800°C under a strain rate of I x s - I (Sumino et al., 1983). The specimens in the figure all deform homogeneously during yielding. In comparison with the stress-strain curves of high-purity FZ-Si crystals in Fig. 18(c), we see that the stress-strain curves of the nitrogen-doped FZ-Si crystals show high magnitudes of the upper yield

-'

1I.

OXYGEN EFFb( 1 ON MFC HANICAL PROPERTIES

LO

503

L 0

,

I

in

FZ

\

2 20wt

0,

',

'0.

LI W

g 103

- 0

0

10 20 AGING DURATION ( h )

FIG.42. Variations of the upper yield $tress against the duration of annealing at IOSOT in initially dislocation-free crystals of nitrogen-doped FZ-Si ( N F Z ), high-purity FZ-Si and CZ-Si measured in deformation at YO0"C under a shear strain rate of I x S C ' . The crystals are the same as those in Fig. 40 (Sumino el al.. 1983).

stress and large stress drops from the upper yield point to the lower yield point. which are the characteristics of silicon crystals with low initial densities of dislocations. This suggests that a considerable part of dislocations initially existing in the nitrogen-doped FZ-Si crystals are locked effectively by nitrogen impurities and are inactive during deformation. We have already seen in the preceding section a quite similar phenomenon in CZ-Si crystals. We show the thermal stability of mechanical strength of nitrogen-doped FZ-Si crystals in the following. The variation of the upper yield stress of the nitrogen-doped FZ-Si crvstal against the duration of annealing at 1050°C is shown in Fig. 42 together with those of a high-purity FZ-Si crystal and a CZ-Si crystal. Tensile tests were conducted at 900°C under ~ upper yield stress of the nitrogen-doped a strain rate of I x 10 ~ ' I .s The FZ-Si crystal exhibits a peculiar behavior against the annealing duration; namely. a maximum is attained after about 6 hr of annealing. The origin of such increase in the yield stress has not yet been clarified. The strength of the crystal after annealing at I0SO"C for 24 hr is no lower than that before the annealing. No development of defects due to annealing at 1050°C was detected by etch pit observations.

504

K . SUMINO A N D 1. YONENAGA

It is concluded that nitrogen atoms in silicon crystals immobilize dislocations effectively on segregating along them and do not bring about the softening related to precipitation. 2. CARBON EFFECT Carbon impurities in FZ-Si at concentrations up to I x 10” atoms/ cm3 reveal neither a locking effect on dislocations nor an enhancementretardation effect on the dislocation velocity (Imai and Sumino, 1983). It is natural to suppose that the interaction between carbon atoms and a dislocation in a silicon crystal is so weak that no appreciable effect appears on dynamic behavior of dislocations since a substitutional carbon atom accompanies a rather small misfit strain and is electrically neutral in Si lattice. On the other hand, carbon atoms dissolved in CZ-Si are known to facilitate the precipitation of oxygen impurities in the temperature range between 600 and 1000°C. In comparison with carbon-lean CZ-Si, precipitate particles developed in carbon-rich CZ-Si are characterized by their small size and abundant density (Leroueille, 1981; Kishino, Matsushita, Kanamori and Iizuka, 1982). These observations lead to the supposition that carbon atoms or their clusters play the role of nucleation centers for oxygen precipitates in CZ-Si (Kishino et al., 1982). Since the strengthening of CZ-Si is achieved by the segregation of oxygen impurities on dislocations, it is interesting to know how carbon impurities affect such a process and, consequently, the mechanical strength of CZ-Si. Figure 43 shows the stress-strain curves in the yield stage of FZ-Si crystals containing carbon impurities at a concentration of 1.7 x l o i 7 atomsicmi with various dislocation densities in deformation at 800°C under a strain rate of 1 x s - ’ (Yonenaga and Sumino, 1984). The yield behavior, the magnitude of the upper yield stress and their dependencies on the dislocation density in the carbon-doped FZ-Si are almost identical to those in high-purity FZ-Si seen in Fig. 18(c). Thus, it is confirmed that carbon atoms dissolved in a silicon crystal play little role in locking dislocations by themselves alone, in accordance with the result of direct observation (Sumino and Imai, 1983). Next, we compare the mechanical strength of carbon-doped CZ-Si with that of carbon-lean CZ-Si. It has been reported that the upper yield stress of carbon-rich CZ-Si crystals is almost the same as that of carbon-lean CZ-Si crystals when the crystals are free from dislocations (Yasutake, Umeno and Kawabe, 1980). Figure 44 shows the upper yield stresses of dislocated crystals of CZ-Si doped with carbon at various concentrations together with those of car-

11.

OXYGEN E F F t ( 1 O N MECHANICAL PROPERTIFS

-

505

2x10~

N

E

1 3

r Y

'"

In

w

[L

I-

'"2 [r

Q I m

W

n W

3 1' z1 W Lz

I

A 5 SHEAR STRAIN

10

(Yo)

FIG.43. Stress-strain curves of F%-Sicrystals doped with carbon at a concentration of I.7 x I O " atom>/cm' that contain didocations at various densities shown in the figure ( i n cm :) in deformation at 800°C under a shear \train rate of I x IW4 5 - ' .

FK,.44. Upper yield stress T " , of carbon-doped FZ-Si and CZ-Si crystals with dislocation densitieb of about I x loh c m - ' plotted against the concentration 0 , of dissolved oxygen atoms. Open circles are the dala for carbon-lean Si. Filled marks are for carbon-doped Si at the carbon concentrations shown in thc figure. The upper yield stresses are for defcormation at X(WC and 900°C under a shear strain rate of I x s (Yonenaga and Sumino. 1984).

'

506

K . SUMINO A N D I . YONENAGA

-

0

0

1 2 3 4 Ic, 1 , 10‘ 7 a t 0 ~ i i 3

FIG.45. Upper yield stress T , and ~ lower yield stress T , of ~ CZ-Si crystals with dislocation densities of about 1 x lo6 cm-? and dissolved oxygen concentrations of about 6 x lo” cm-’ plotted against the concentration C , of dissolved carbon atoms. The yield stresses are for deformation at 800°C and 900°C under a shear strain rate of 1 x s - ’ (Yonenaga and Sumino. 1984).

bon-lean CZ-Si plotted against the oxygen concentration for deformation at 800°C and 900°C (Yonenaga and Sumino, 1984). Data for usual FZ-Si and carbon-doped FZ-Si crystals are also shown. The initial densities of dislocations in all the crystals are about 1 x lo6 ern-'. Open circles and solid lines are the data for carbon-lean FZ-Si and CZ-Si (Yonenaga et al., 1984). Filled triangles, circles and squares are for CZ-Si doped with carbon at concentrations of 0.9 x lOI7, 1.7 x loi7and 2.5 x lOI7atoms/ cm’, respectively. It is seen in the figure that carbon impurities at concentrations of the order of lOI7 atoms/cm3 have almost no influence on the magnitude of upper yield stress of Si crystal when the concentration of oxygen is lower than about 4 x 1017 atoms/cm3. However, the upper yield stress is enhanced distinctly by the presence of carbon impurities if the crystals contain oxygen at concentrations higher than about 5 x loi7atoms/cm3. Figure 45 shows the upper and lower yield stresses of CZ-Si crystals at 800 and 900°C plotted against the concentration of carbon atoms (Yonenaga and Sumino, 1984). All the crystals are dislocated at densities of about 1 x lo6 cm-* and contain oxygen at concentrations of about 6

I 1.

OXYGEN E l I F C 1 ON M F C H A N I C A L PROPERTIE5

507

x lo” atoms/cm3. The upper yield stress increases monotonically with increase in the carbon concentration. Carbon atoms dissolved at a concentration of 2.5 x IO” atomsicrnj enhance the upper yield stress of the crystal by a factor of 1.4. From these results, it is concluded that carbon impurities bring about the increase in mechanical strength of silicon crystals if they coexist with oxygen impurities the concentration of which is higher than about 5 x l o ” atoms/cm’. Since it has been clarified from direct measurements (Sumino and Lmai. 1983) that carbon impurities by themselves have no appreciable effect on the dynamic property of dislocations. carbon atoms in CZ-Si are thought to promote the dislocation locking due to oxygen atoms. It is conceivable that such promotion of dislocation locking is caused by carbon atoms that are incorporated in the core region of a dislocation and act as the preferential nucleation sites of oxygen clusters. IX. Summary

The characteristics in mechanical behavior of a Si crystal on a macroscopic scale are determined by dynamic processes of dislocations in the crystal that take place on a microscopic scale under stress. Important among such processes are the generation, multiplication and motion of dislocations as well as interaction of dislocations with each other. The effect of oxygen on mechanical properties of Si is interpreted in terms of knowledge on how oxygen impurities affect such dislocation processes. Difficulty appears in measuring the dislocation velocity when oxygen impurities are dissolved in Si. ‘This is related to immobilization of dislocations caused by segregation of oxygen atoms on the latter. The difficulty has been overcome by adopting the technique of in situ X-ray topographic observation . Dislocation mobility in Si increases very rapidly as temperature increases. The dislocation velocity in high-purity FZ-Si depends on the stress linearly down to a very low stress. The linear dependence of the dislocation velocity on the stress holds also in Si containing oxygen impurities at a concentration of the level in CZ-Si when a dislocation moves at a rather high velocity under a high stress. The dislocation velocity in CZ-Si under such a high stress is the same as that in high-purity FZ-Si. On the other hand, the dislocation velocity in Si containing oxygen impurities is lower than that in high-purity Si when the dislocation moves at a low velocity under a low stress. The retardation of dislocation motion caused by oxygen impuritie\ is accompanied by the disturbance in the shape of moving dislocations. Under a stress lower than some critical

508

K . SUMINO A N D I . YONENAGA

stress, a dislocation ceases to move in Si containing oxygen impurities. The magnitude of the critical stress for cessation of dislocation motion increases with an increase in the oxygen concentration. Such observations together with theoretical analysis lead to the conclusion that oxygen atoms individually dispersed in a Si crystal do not affect the dislocation velocity in the concerned temperature range. However, they catch up to slowly moving dislocations and develop clusters on the dislocation line. The development of oxygen clusters results in the perturbation in the line shape and retardation of the dislocation in motion. An originally fresh dislocation is immobilized in Si containing oxygen impurities when it is halted at high temperatures under no applied stress. A theoretical treatment shows that the immobilization of dislocation is caused not by the development of the Cottrell atmosphere of oxygen atoms around the dislocation but by the development of clusters of oxygen atoms on the dislocation line. Oxygen atoms or, more generally, impurity atoms are gettered by dislocations by means of (1) preferential nucleation of precipitates of supersaturated impurities on the dislocation line or (2) some special reaction that takes place at the dislocation core to incorporate impurity atoms from the matrix region. Oxygen impurities effectively suppress the dislocation generation in Si under stress. The mechanism of suppression is closely related to the generation process of dislocations in a Si crystal. Dislocations are generated heterogeneously from some structural irregularities in the crystal under stress. Surface damage in a Si crystal such as scratches and indentations acts as effective generation centers for dislocations. Small amorphous Si regions are developed around such damages made at room ternperature. Such an amorphized region recrystallizes into a dislocated region when the crystal is brought to high temperatures. Dislocations come out of such a region and penetrate into the matrix if the crystal is under stress, leading to the dislocation generation. Dislocation generation from the damaged region takes place even under a very small stress in high-purity FZ-Si. However, dislocations are not generated under stresses lower than a certain critical stress in CZ-Si. This is caused by the locking of dislocations in the recrystallized regions due to gettering of oxygen atoms while the crystal is heated up. The yield strength and stress-strain characteristics of Si are well understood on the basis of a theoretical model using various dislocation processes observed in experiments. Oxygen impurities give no appreciable influence on the mechanical strength of Si if the crystal is initially free from dislocations. The oxygen effect appears in initially dislocated Si crystals. Oxygen impurities in Si give rise to the same effect on mechani-

11.

OXYGEN E r t t ( I

o~

ME( H A N I C A L PROPERTIFS

509

cal behavior a s the decrease in the density of dislocations initially contained in the crystal does. These are successfully described with the theory by taking account of the locking of dislocations by oxygen impurities. The high resistance of CZ-Si wafers in comparison with FZ-Si wafers to warpage due to thermal cycling is well interpreted with the idea of dislocation locking by oxygen impurities. Precipitation of supersaturated oxygen in Si results i n a decrease in the mechanical strength. The mechanical behavior of a precipitation-softened Si crystal is very similar to that of a Si crystal with a high density of dislocations initially contained in the crystal. Dislocations punched out from precipitate particles act a s dislocation sources and bring about the reduction in the yield strength of the crystal. Dissolution of precipitates in precipitation-softened Si at high temperatures results in restoration of the high yield strength. Nitrogen impurities in Si effectively immobilize dislocations even though nitrogen atoms dispersed within the crystal have no appreciable effect o n the velocity of dislocations in motion. The immobilization of dislocations is related to gettering of nitrogen by the dislocation core. The strength of locking per one nitrogen atom is about 30 times higher than that of an oxygen atom. Nitrogen impurities enhance the yield Ytrength of a Si crystal when the crystal is initially dislocated. It does not give rise t o precipitation softening due to annealing at temperature around 1 ooooc.

Carbon impurities in Si at concentrations up to I x 10’’ atomsicm’ do not give rise to any appreciable effects on both dislocation mobility and yield strength. However, they enhance the mechanical strength of Si when they coexist with oxygen impurities. Oxygen impurities in Si are amphoteric in nature from the view of its effect on the mechanical strength. Oxygen atoms individually dissolved in Si enhance the mechanical stability of Si at elevated temperatures. This effect originates from gettering of oxygen atoms by dislocations. which leads to immobilization of the dislocations. The effect becomes increasingly remarkable as the oxygen concentration in Si increases. On the other hand, precipitation of supersaturated oxygen impurities accompanies the generation of defects that act as dislocation sources and leads to the softening of Si. However. such precipitation-related defects can be effectively utilized as gettering sinks for heavy metallic impurities in device production technology. In conclusion. i t is empha\ired that defect control in Si technology is most effectively accomplished on the basis of correct understanding of oxygen effects on various dislocation processes in Si.

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REFERENCES Abe. T., Kikuchi, K., Shirai, S . , and Muraoka, S. (1981). In Semiconductor Silicon, H. R. Huff, J . Kriegler, and Y. Takeishi (eds.), p. 54. Electrochem. Soc., Princeton. N.J. Clarke, D. R.,Kroll, M. C., Kirchner, P. D., Cook, R. F . , and Hockey, B. J. (1988). Phvs. R e v . L e t t . 60, 2156. Doerschel, J.. and Kirscht, F.-G. (1981). Phys. Stat. Sol. ( a ) 64, K85. Eremenko. V., and Nikitenko, V. 1. (1972). Phys. Stat. Sol. ( a ) 14, 317. Erofeev. V . N., Nikitenko, V . I . , and Osvenskii, V . B. (1969). Phys. Stat. Sol. 35, 79. Fisher, A. (1975). Expl. Tech. Phys. 23, 617. Fisher, A . (1978). Kristall und Technik 13, 1217. Foll. H.. and Carter, C. B. (1979). Philos. M a g . A40, 497. George, A , , Escavarage, C., Champier, G.. and Schroter, W. (1972). Phys. Stat. Sol. f b ) 53, 483. Gomez, A , , Cockayne, D. J . H., Hirsch, P. B., and Vitek, V. (1975). Philos. M a g . 31, 105. Gornez. A , , and Hirsch, P. B. (1978). Philos. M a g . A38, 773. Gottschalk, H. (1979). J. Physique 40, C6-127. Gridneva, I. V., Milman. Y. V., and Trefilov, V. I. (1972). Phys. Stat. Sol. ( a ) 14, 177. Hirth, J . P., and Lothe J . (1982). Theory of Dislocations. John Wiley & Sons, New York. Imai. M . , and Sumino, K. (1983). Philos. M a g . A47, 599. Kayano, H. (1968). Trans. Jpn. Inst. M e t . 9, 156. Kishino. S.. Matsushita, Y., Kanamori, M., and lizuka, T. (1982). Jpn. J . Appl. Phvs. 21, I . Koguchi, M . . Yonenaga, I . , and Sumino, K. (1982). Jpn. J . Appl. Phys. 21, L411. Leroueille. J . (1981). Phys. Stat. Sol. ( a ) 67, 177. Louchet. F. (1981). Philos. M a g . A43, 1289. Mahajan, S . . Brasen, D., and Haasen, P. (1979). Acta Metall. 27, 1165. Minowa. K.. and Sumino. K. (1992). Phys. R e v . Lett. 69, 320. Patel. J . R. (1964). Discuss. in Furaday Soc. 38, 201. Patel, J. R . . and Chaudhuri, A. R. (1963). J . Appl. Phys. 34, 2788. Patel, J . R., and Freeland, P. E. (1967). Phys. R e v . B 13, 3548. Peissker, P., Haasen, P., and Alexander, H. (1961). Philos. Mag. 7, 1279. Ray. 1. L. F.. and Cockayne, D. J. H. (1971). Proc. R o y . Soc. A325, 543. Sato, M.. Hiraga, K., and Sumino, K. (1980). Jpn. J. Appl. Phys. 19, L155. Sato. M.. and Sumino, K. (1977). Proc. 5th Int. Conf. on High Voltage Electron Microscopv. p. 459. Sato. M., and Sumino, K. (1979). Kristall und Technik 14, 1343. Sato, M., and Sumino, K. (1985). In Dislocations in Solids. H. Suzuki, T. Ninomiya, K . Surnino and S . Takeuchi (eds.), p. 391. University of Tokyo Press, Tokyo. Schroter. W . , Brion, H. G . , and Siethoff, H. (1983). J . Appl. Phys. 54, 1816. Seeger. A . (1958). In Handbuch der Physik V11/2, S . Fliigge (ed.), p. 114. Springer, Berlin. Siethoff. H . . and Haasen, P. (1968). In Lattice Defects in Semiconductors, R. R . Hasiguchi (ed.). p. 491. University of Tokyo Press, Tokyo. Stickler, R., and Booker, G. R . (1963). Philos. M a g . 25, 1429. Suezawa, M . , Surnino, K., and Yonenaga, 1. (1979). Phys. Srar. Sol. ( a ) 51, 217. Sumino, K . (1986). Muter. R e s . Soc. Symp. P r o c . , Vol. 59, Oxygen, Carbon, Hydrogen and Nitrogen in Crystalline Silicon, J. C. Mikkelsen, Jr. (ed.), p. 369. North-Holland, New York, Amsterdam and Oxford. Sumino, K . (1987). Proc. 7th Inr. School on Defects in Crystals, E. Mizera (ed.) p. 495 World Scientific, Singapore.

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Surnino, K . (198%). M u t e r . Sci. E n g . 84. 3 3 5 . Surnino. K. (1989b). I n Point und b,’.rrc,nclcd Dc;fi.cts in Semic~o,7duc./or.s.G . Benedek. A . Cavallini and W. Schroter ( e d \ . ) .p. 77. Plenum Press, New York and London. Surnino. K. ( 1992). In P r o ( . . lsr Puc.ific RIM Internail. Conf. oti Advunc.ed Muteriuls und Proc,e.s~ting,C. Shi. H. Li and A . Scott (eds.). p. 49. The Minerals. Metals & Material.; Soc.. Warrendale. P.A. Sumino. K., Harada, H..and Yonenaga. I . ( I Y X O ) . J p n . J . Appl. Phy.~.19, L49. Sun~ino.K., and Harada. H. (1981). phi lo^. Mtrg. A44, 1319. Suniino. K . . and Irnai. M . (1983). P / i i l ( ~ aMtrg. . A47, 753. Surnino. K.. and Sato. M . (1979). Krr.sttr// r r ! 7 d Icclrnik 14, 1343. Sumino. K . . and Yonenaga. I . ( 1991 .Yo/rd Stcrtc’ Phenotnenu lYi20. Gettering trnd l)efr,c/ Etigineering in .Semiccindrrc./or I , c . h t i ( ~ l ~Y gl . ~M. Kittler and H.Richter (eds.). p. 295. Sci-Tech Publication. Liechten\tein Sumino. K . . and Yonenagn. 1. (1997). fJ/iv.s. S t u t . Sol. f u ) . 138, 573. Sumino. K . . Yonenaga. 1.. Irnai. M . arid Abe. T. (1983). J . Appl. Pl7vs. 54, 5016 SuLuki. T.. and Kojinia. H.(1966) 4 c . t ~Mutull. 14, 913. Tokurnaru. Y., Okushi. H..Masui. T . . and Abe. T (19x2). J p n . 1.A p p i . P k v s . 21, L443. We<sel. K., and Alexander. H . (1977). Philo.\. Mtrg. 35. 1523. Yawtake. K . . Urneno. M.. and Kawabe. H.(1980).Appl. Plivs. Lctr. 37, 789. Yasutake. K . . Urneno. M . . and Kawahe. H.(19x2). Ph.vs. Stut. Sol. fu) 69, 333, Yonenaga. I . . and Surnino, K . (1978) !%v,\. S l u t . Sol. f u ) SO, 6x5. Yonenaga. I . , and Surnino, K . (19x2). Jpn J . A l ~ p l .Phys. 21, 47. Yonenaga. 1.. and Surnino. K. (19x4). J p n . J. 4ppl. P h y s . 23, LS90. Yonenuga. 1.. and Sumino. K. (1980. In I)is/oc.eirions i n Solids. H.Suzuki, T. Ninomiya. K. Sumino and S . Takeuchi ( r d s . ) . p 385 University of Tokyo Pres5. Tokyo. Yonenaga. I.. Suniino. K.. and Ho\hi. K (1984). J . A p p l . PAy.5. 56, 2346.

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SEMICONDIII IOKS A N D S E M I M E T A L S . V O L 42

C H A P T E R 12

Grown-in and Process-Induced Defects W. Ber
I. Introduction

The enormous practical importance of oxygen in Si is, to a large extent, due to the fact that oxygen precipitates and secondary defects act as gettering sites and that it is possible t o control both the density of these precipitates and the width of the defect-free denuded zone near the surface (Jastrzebski. 1990; Aoshima, Kosaka and Yoshinaga, 1990). It is the purpose of this chapter to give a comprehensive review of the morphologies and phases of oxygen precipitates and provide some insight into the mechanisms that give rise to a large variety of oxygen-related defects that have been observed both in experiments and device manufacturing. In Section I1 the focus will be o n simple one-step or multiple-step 513 Copyright 'C 1W4 by Academic Preaa. Inc. All right\ of reproduction in any form re\erved I S B N 0-12-752 142-9

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W . BERGHOLZ

high-temperature processes. It will be explained how the volume expansion during SiO, precipitate formation influences the morphology and phase of the oxygen precipitates. The key role of self-interstitials in the relief of strain around the expanding precipitates and their aggregation into extended defects will be elucidated for different temperature ranges (Section 11.1-11.3). This knowledge is then applied to the more complicated situation of multiple temperature annealing and CMOS or bipolar process sequences (Section 11.4). Those factors that affect the oxygen precipitation in a device manufacturing environment (initial oxygen content, carbon content, resistivity, etc.) are reviewed in Section 11.5. The full implication of oxygen precipitation including the formation of detrimental process-induced defects and a brief note on intrinsic gettering are outlined in Section 11.6. Oxygen precipitates and secondary defects, of course, form not only during high-temperature processes after the wafer has been cut and shaped, but also already during the cool-down of the ingot from the Si melt temperature of 1450°C. Both “macroscopic” evidence for the formation of oxygen precipitates in as-grown material and results of microscopic studies are reviewed in Section 111.1. Naturally, the aggregation of intrinsic point defects (self-interstitials and vacancies) during the cooling process of the crystal ingot will also leave their imprints on the asgrown material (Section 111.2). This has been studied in great detail for FZ-material where, due to the absence of oxygen, the intrinsic defect aggregates are essentially the only extended defects (Subsection III.2.b). After the interest in experimental studies of grown-in intrinsic defects has been relatively moderate for a long time (Subsection III.2.b), recent evidence on a correlation between gate oxide quality, crystal pulling speed and the density of a certain type of grown-in defect has transformed this area into one of the most exciting arenas of research in the field of defects in silicon. In Section 111.3 a review of the experimental facts about those defects is given. Although it appears quite certain that these defects are aggregates of intrinsic defects, their identification as, e.g., D-defects (known from FZ-material) has to be regarded as hypothetical. There is a certain amount of overlap with Chapters 4, 6, 8, 9, 10, 11, 13 and 14. As a prerequisite for this chapter, the key facts of Chapters 4, 5 , 6, 8 and 9 should be known. Some of the salient facts of this chapter are essential for a good comprehension of Chapters 10, 1 1 , 13, 14 and 15.

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11. Oxygen Precipitation During High-Temperature Processes

1.

0Vt:KVIEW: M O R P H O L O G Y A N D P H A S E S OF O X Y G E N PRECIPITATES

What is known about the morphology and structure of oxygen has been derived mainly from numerous 'I'EM-studies, however many important conclusions could not have been reached if it had not been for additional information from the following techniques:

IK (infrared spectroscopy for the measurement of the residual dissolved oxygen content. Schomnnn and Graff. 1989); Defect etching ( a very fast and time-efficient way to study precipitate densities and distributions, Secco d'Aragona. 1972; WrightJenkins, 1977; Bergholr. 1989): XRT (X-ray topography. for a tast overview of the precipitation in the whole wafer, Tanner. 1976); SlRM (for destruction-free characterization of oxygen precipitation, in particular at low precipitate densities, Lascik et al.. 1989): Neutron scattering (for good statistics on size and shape for large sample volumes. Messoloriis et al., 1989); Resistivity, 1R at cryogenic temperatures, photoluminescence. deep transient spectroxopy (DL'I'S)and electron paramagnetic resonance (EPR) (for the study of thermal donors). As a result of more than 20 years of detailed studies of oxygen precipitation by these analysis tools:. at least six different precipitate moiphologies in at least two different structures have been observed and characterized. The main types of oxygen precipitates are the following: 0

0

Spherical amorphous Si02precipitates (Fig. la): Polyhedral amorphou\ 50, precipitates (Fig. I b); Octahedral amorphou4 SiO, precipitates (Fig. Ic); Platelike amorphous SiO, precipitates (Fig. Id); Ribbonlike crystalline precipitates (coesite structure. controversial) (Fig. l e ) .

FIG.I . HKTEM direct lattice image\ (except c ) of (a) a spherical amorphous SiO, pi-ecipitale t Bergholr et al., 1989a): ( b ) a polyhedral amorphous SiOz precipitate (Ponce. 1985): ( c ) ;I weak-beam TEM image of an octahedral amorphous SiO: precipitate (note that the precipitate 1 5 viewed from the top) (Tsai. I Y 8 S ) : Id) ;I platelike amorphous SiO: precipitate (Bergh o k . Hutchison and Booker. 1986). ( e ) a crozc section of a ribbonlike cristalline SiQ precipitate elongated along a <: I10 direction (Hergholr et al.. 1986). The identification as coe\ite I \ controversial. ;in alternative interpretation is hexagonal Si IBourret. 19873.

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FIG. 1. (Continued).

518 W . BERGHOLZ

12.

GROWN-IN AND PROCESS-INDUCED DEFECTS

519

I n addition, the process of oxygen precipitation brings about the formation of the following intrinsic defects: I13 < I 1 I > type extrinsic stacking faults (Fig. 2a); Prismatic dislocation loops (Figs. 2b, 2c; Tan and Tice, 1976); Extrinsic dislocation dipoles in the < I 10> direction (Fig. 10); Small circular extrinsic stacking faults of non-1/3 < I 1 I > type (Fig. 2d. Bergholz, Hutchison and Pirouz, 1985); Dark spot defects (Fig. 9); Ordinary 60" dislocation (which nucleate on oxygen precipitates; Tempelhoff et at., 1970).

FIG.2. Secondary defects associated with oxygen precipitation: (a) '/I < I II>-type stacking faults (SFs) delineated by Secco defect etching o f a { 110) cleavage plane in the hulk of a Si-wafer (SFs that are Liewed end-on are denoted as SFe. those that are inclined to the cleavage plane are denoted as SFil; ( h ) prismatically punched dislocation loops delineated by Secco defect etching. etched surface i s the (100) wafer surface, the loops are marked by arrow heads: (c) prismatically punched dislocation loops delineated by Secco defect etching, etched surface i s a (I10) cleavage plane; (d) small circular extrinsic stacking fault o f a non-'/x< I I 1 >-type (high-resolution lattice image. the extra {III} plane is marked by arrow heads. Bergholz et al., 19851.

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GROWN-IN A N D PROCESS-INDUCED DEFECTS

52 1

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W . BERGHOLZ

2. FACTORS THATDETERMINE THE TYPEOF OXYGEN PRECIPITATE u . Volume Expansion

The key to this puzzling scenario is the fact that the formation of SiO, precipitates is accompanied by a volume expansion of about a factor of 2. In other words, the space taken up by one Si atom increases by a factor of 2 as the Si is transformed into S O , (Bourret, Thibault-Desseaux and Seidmann, 1984). b. Surface, Elastic, and Chemical Energies (Tiller, Hahn and Ponce, 1986)

To accommodate this additional volume the crystal can respond in different ways, which are depicted schematically in Fig. 3: Precipitate + intrinsic defect

v v A A

FIG.3. Schematic representation of the size of the surface energy E S ,of the elastic energy

.

E,, chemical energy E, (from the formation of self-interstitials) and the ratio of the volume

of the precipitate (which is a measure of the number of oxygen atoms removed from supersaturated solution) to the surface as a function of temperature and of the predominant defect in that temperature range. The first three quantities make the precipitate nucleation more difficult (symbolized by a minus sign), whereas the larger is the ratio volume/surface, the larger is the gain in chemical energy in relation to the energies in connection with the surface. The shape of the oxygen precipitates are drawn as open figures in the RHS of the figure, the intrinsic defects agglomerates are hatched. The triangles represent the stress of the Si-matrix on the precipitate.

12.

GKOWN-IN 4")

PKOCESS-INDUCED DEFECT5

523

Lattice strain. which puts the growing precipitate under compressive stress, at t h e expense of elastic energy E,, (both of the crystal and the precipitate); 'To reduce the strain, the precipitate can, in principle, assume a shape that reduces the strain (e.g., platelike instead of spherical morphology. at the expense of surface energy E , ): The growing precipitates can push Si-atoms onto interstitial sites. Thus. Si self-interstitial\ are created, at the expense of additional chemical energy E,; T o reduce the chemical energy, the self-interstitials can agglomerate to extended intrinsic defects (e.g., stacking faults). which. of course is not "free of charge" either. but entails formation energy E, for these defects. The whole process is driven by the tendency of the crystal to reduce i t x total energy E,,,:

EtL,,= E,, t t,,t E ,

+

E,

+ E,.

where E,, is the energy of solution for the dissolved oxygen precipitate.

c . Kiri 6)tics Which of the various precipitate types and secondary defects are formed depends not only on the energies involved. but, to a considerable extent, on the kinetics of the process: 0

0

The transport of oxygen atoms to the precipitates. i.e., the oxygen diffusion coefficient; The transport of self-interstitials away from the precipitates. the diffusion coefficient of %elf-interstitials

Just to give an example. the growth of ribbonlike precipitates may be favoured at low temperatures. where the oxygen diffusion coefficient is small due to the large migration enthalpy of 2.5 eV. This can be understood by the fact that the precipitate keeps growing into regions in which no oxygen precipitation has taken place; i.e., in a way the precipitate moves to the oxygen atoms rather than the atoms to the precipitate (Fig. 4). In the end. only small cylindrical regions around the principitate have been depleted of oxygen.

d . 7he Rolt) oj'lntvinsic Poitit I 1 i ~ f t ~ c ~tirid t . v Stwindrivy Dqfects As mentioned under b, the emission of self-interstitials (or the absorption of vacancies) is a n important avenue for the crystal to satisfy the

Z 1 0 H 9 8 3 9 'M

PZS

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GROWN-IN A N D PROCE 55-INDUCED DEFECTS

525

particular, if oxygen precipitates act as nucleation centers for such defects. Figures 2b. 2c and 6 are examples for such a situation. From the high-resolution TEM images o f a large number of oxygen precipitates formed after annealing at 750°C. it could be concluded that a large percentage of the precipitates had a stacking fault attached to them (Bergholz et al.. 1989a). In fact, it appears worth mentioning that a similar coexistence of impurity atom precipitates and stacking faults as a sink for intrinsic defect has been reported by Seibt (1990) for Cu in Si; i.e.. such a state of affairs seems to be quite typical for the precipitation in silicon

FIG.5 . Lang X-ray topograph of ii typical IS0 m m wafer after a standard device process. The bright rings are regions of strong oxygen precipitation. the dark rings are area\ o f retarded oxygen precipitation. (The feature5 opposite the wafer flat are dislocations cauzed by the \lits in the quartL wafer boat\.)

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W . BERGHOLZ

FIG. 6. High-resolution TEM micrograph of a platelike oxygen precipitate on {loo} with a stacking fault on { I 1 I} attached to it. The orientation of the stacking fault plane is marked.

and is presumably ultimately due to the properties of self-interstitials (equilibrium concentration and diffusion coefficient at low and medium temperatures).

3, OXYGEN PRECIPITATION I N DIFFERENT TEMPERATURE REGIMES It is the aim of this subsection to bring some order and systematics into the puzzling multitude of oxygen precipitate morphologies and secondary defects in order to enable the reader to make at least inspired guesses as to what kind of precipitate to expect at what temperature. a. T

< 550°C

Very few results from the literature exist for this temperature range as far as extended oxygen-related defects are concerned (Bergholz et al., 1985; Reiche, Reichel and Nitzsche, 1988). A large number of studies exist, on the other hand, on the subject of the formation of thermal donors, i.e., entities of 3 to 10 oxygen atoms (see, e.g., Ourmazd, Schroeter and Bourret, 1984, and references therein). Such studies have been, however, normally limited to comparatively short annealing times, below about 100 hours; for such times no detectable oxygen precipitates are formed. If, on the other hand, annealing times are prolonged to 500 hr to 5000 hr, not only does a sizable fraction of the oxygen disappear from solution, as monitored by IR (Fig. 7 shows an example), but several types of defects are found by TEM:

12.

527

GROWN-IN A N D PROCESS-INDUCED DEFECTS

Ribbonlike defects, which can be several micrometers in length (Fig. 8a). with a very small cross section of a few nm and crystalline structure (Fig. 8b); Stacking fault-like loop defects, most of which are associated with a ribbon defect (in fact, more than one ribbon defect can be attached to one loop; Fig. Ze is a high resolution image of a loop defect ) ; Defects that in a high-resolution image appear dark, that are unstable under an electron beam and that sometimes display an internal structure on { 1 1 1)-planes (Fig. 9). One self-consistent interpretation of these defects is that the ribbon defects are oxygen precipitates in a metastable crystalline structure (namely. coesite; Bourret et al., 1984). The loop defects and the dark bloblike defects are interpreted as agglomerates of self-interstitials, where the latter appear to be a prestage of the former. This defect identification is in quantitative agreement with the loss in dissolved oxygen, since the total volume of the ribbon defect is within the error limits (of about 3096) of what is to be expected if they contain the oxygen lost from solution. It is in order to mention that Bourret (1987) and Reiche et al. (1988) have, in the meantime, given an alternative interpretation. According to these authors, the ribbon defects are hexagonal Si, in which case the loop and blob defects have to be regarded as oxygen precipitates. Although this alternative defect identification cannot be ruled out completely at present. there are several difficulties: 0

0

Fig. 2d shows that the loop defects are extra (lI1}-planes, which implies problems in picruring the bonding arrangement of the oxygen atoms. The diffusion constant of oxygen is exceedingly low at this temperature. For such low diffusion coefficients, the ribbon shape is kinet-

*\

08061

0

300

GOO

900

Fic, 7 Rewiu,il oxygen concentmlion IOltr)
528 W. BERGHOLZ

12.

GROWN-IN A N D PROCESS-INDUCED DEFECTS

529

ically favoured in comparison to the sphere or disc shape (a$ explained in subsection 2 ) . The coesite hypothesis has two further points in its favour. As pointed out by Ourmazd et al. (1984). the structure of thermal donors can quite naturally be extended into the coesite structure for symmetry and structural reasons. The fact that coesite is a high-pressure phase of SiO, fits well into the scenario of lack of space due to the SiO, volume expansion and the resulting high lattice strain.

I?. T

=

.5.50-700”(‘

In this temperature range. appreciable loss of oxygen atoms from solution already occurs after 10-20 h r of annealing time. In addition to the defects listed in a , two further types ot crystal defects can be found for this temperature range: The ribbon defects. which for this temperature. are longer, “fatter” and on { 100) instead of { I 1 3 } habit planes (Fig. IOb and Fig. le) have sections of extrinsic dislocation dipoles colinear with the ribbon defects in < I 10> directions (Fig. 10a);

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W . BERGHOLZ

FIG.9. High-resolution TEM image of a "bloblike" defect observed after annealing at 485°C for 921 hr with an internal structure on (111) (Bergholz et al., 1985).

0 0

Platelike amorphous oxygen precipitates are observed in addition to the ribbon defects (Fig. Id); The loop defects are much larger and occur without ribbon defects attached to them (Bourret et a]., 1984; Bergholz, Pirouz and Hutchison, 1984, Fig. 1Oc).

12. GROWN-IN ,ANI) PRO( ESS-INDUCED DEFECTS

53 I

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17.

GROWN-IN A N D PKOCFSS-INDUCED DEFECTS

533

The simultaneous occurrence of plate and ribbon oxygen precipitates can be understood qualitatively as follows. As before, the ribbon defects are kinetically favoured (they are in fact the first defects to be formed: Bergholz et al., 1984). For longer annealing times. the fraction of plates increases, presumably because the nucleation and growth rates for the two kinds of precipitates do not differ by a large amount. The plate precipitates are favoured over the polyhedral or spherical precipitates be-

534

W. BERGHOLZ

cause the strain due to the volume expansion is smaller. Another fact is noteworthy. The temperature range 550-700°C is the preferred temperature for the so-called thermal donor kill annealing treatment carried out by the wafer manufacturer. It is plausible that, due to the simultaneous occurrence of several defects in this temperature, the balance between these defects and their influence on the oxygen precipitation in further processing can be strongly influenced by the details of the thermal donor kill treatment. c. 700-900°C

This temperature range derives its importance from the fact that it includes the temperature of maximum nucleation rate for oxygen precipitates. (This means that precipitate densities are determined mainly by process steps in this temperature range; e.g., nitride or poly deposition steps or intentional nucleation ,annealing.) Fortunately the scenario is made simpler by the fact that in this temperature range ribbon defects are no longer stable, because the pressure of the lattice is no longer sufficient to stabilize the high-pressure coesite phase (Bourret et al., 1984). in fact, in the study of specimens annealed at 750°C cases have been found where 5-10 plate precipitates were lined up along directions (Bergholz and Hutchison, 1988). The obvious interpretation of this finding is that these are the debris of an ex-ribbon defect that grew too large to be stabilized by the lattice any more. The plate precipitates are square, with edges along the <110> directions, the habit plane is {loo}, with a varying edge length to thickness ratio (Fig. Id). As before, the excess self-interstitials condense into loop defects on { 11I} planes. As mentioned before, the loop defects are very often attached to precipitates (the obvious benefits being that the nucleation of the loops on defects is easier and maybe just as important that the diffusion distance for the self-interstitials is small). Both for short and for long annealing times (compared to the time of, say, 50% oxygen precipitated) interesting phenomena can be observed. For a short annealing time (48 hr at 750"C), a toothlike structure on { 100) has been found (Bergholz et al., 1989a) in high-resolution TEM lattice images. The defects occur either isolated or attached to a small plate (Figs. 11 and 12). The appearance of this structure is similar to the regular structure observed at the interface of Si and thermal oxide (Ourmazd, Taylor and Berk, 1987) or in fact similar to the interface between 50, precipitates and the Si. it is hence concluded that the nucleation of plate precipitates takes place via a structure that has been interpreted by Ourmazd et al. (1987) as tridymite, which has however been strongly con-

12. GROWN-IN A N D PROCESS-INDUCED DEFECIS

L W Q

535

i.

-

536 W. BERGHOLZ

C

K

I?.

GROWN-IN A N D PROCESS-INDUCED DEFECTS

537

tended by several other authors. At any rate, this structure appears to minimize the surface energy. which explains its role as a kind of precursor phase for the amorphous plate precipitates. It appears also possible that this structure is kinetically favoured in a manner similar to Nisiz in the nucleation of Ni-silicide precipitates, which has been described in detail by Seibt (1990). For long annealing times. the plate precipitates can start to develop “shark’s fins” on the two {loo}planes perpendicular to the principal { 100) habit plane. Figure 14 is a schematic representation of the sequence of different geometries, Fig. 13 shows examples of such defects. It is quite obvious that it is only a small step from this kind of defect to octahedral amorphous precipitates which have been observed for higher temperatures (Fig. Ic). d. T

=

900-1100°C

For this temperature range, the shape of the precipitates gets more and more compact. the octahedral shape appears to be quite common (Fig. Ic. Rivaud, Anagnostopoulos and Erikson, 1988; Tsai, 1985). This fact can be understood in terms of the following two arguments: The surface energy is decreased by this more compact shape. the { 1 I I} surfaces of the octahedra obviously being low energy planes; The strain can be reduced by a more effective emission and condensation of self-interstitials compared to lower temperature, hence the volume/strain requirement is not of paramount importance any more, as it is at lower temperatures. In fact, the stacking faults that can be observed at this temperature are much larger than at lower temperatures; i.e., the diffusion of self-interstitials is more long range. One important phenomenon that is observed in this temperature range is the punching of prismatic dislocation loops by the growing precipitates as a new way to relieve the strain (Figs. 2b, 2c; Tan, Gosele and Morehead, 1983). In fact, experience shows that in many device processes this is a typical occurrence. It is in order to emphasize already at this stage that there is some evidence that a prerequisite for the formation of dislocation loops on oxygen precipitates may be the presence of metal impurities like Cu and Ni. These impurities form precipitates very easily and could help to nucleate the dislocation loops. This has been worked out in detail by Falster et al. (1092).

538 W. BERGHOLZ

12. GROWN-IN A N D PHOCESS-INDUCED DEFECTS

539

540

W. BERGHOLZ

I

< F > .. . .. . .. . . . . .. .:.. . : . . . .. . . . ’

Fic;. 14. Schematic drawing of the different stages of the development of platelike precipitates with fins (Bergholz et al., 1989a). P.

T > 1100°C

For this temperature, the amorphous precipitates get even more compact, namely, polyhedral or nearly spherical, to further minimize the surface energy (Fig. lb). There is hardly any strain around the precipitates, an indication that the removal of excess interstitials is even less of a problem than between 900 and 1100°C. In fact, giant stacking faults larger than 200 pm in diameter have been observed by X-ray topography (Patel, Jackson and Reiss, 1977).

To briefly summarize Section 3, it can be stated that at low temperatures the slow oxygen diffusion and the volume expansion of the SiOz precipitates favour the formation of crystalline ribbon precipitates or amorphous plate precipitates, which at first sight would not appear to be the energetically most favourable precipitate structure or morphology, but those that are favoured by kinetics. At high temperatures, on the other hand, the easy removal of excess volume makes a more compact crystal morphology more favourable. 4. MULTIPLE-STEP TEMPERATURE ANNEALINGS

It is the aim of this section to demonstrate how the basic understanding of the oxygen precipitation-defect phenomena can be applied to more complicated realistic situations.

12. (1.

GROWN-IN A N D PROCESS-INDUCED DEFECTS

It?flueni,t)of' Lori2-uiid

54 1

Hi~iliTrmper~itri,.e Preurinidings

In general, a preannealing a t a temperature below the main precipitation temperature will increase the precipitate density, and the precipitate density will be reduced for a higher preannealing temperature. (Figure 15 shows the loss of oxygen from solution for an annealing temperature of 635°C and preannealing temperatures of 920°C and 485°C. a s measured b y 1R. Comparison with TEM data shows that in the different oxygen precipitation rates are due to different precipitate densities (Bergholz el al.. 1984). The interpretation is simple. At the lower preannealing temperature additional nuclei are formed, some of which are above the critical radius for the main precipitation temperature. A higher preannealing temperature, on t h e other hand, will dissolve all grown-in nuclei (from the crystal growth) below the critical radius for that temperature. hence a lower precipitate density . It should be borne in mind, though. that for very short preannealings at comparatively high temperatures transient phenomena. presumably in

I

.*-

-t/h 0

-100

ZOO

300

F i b . 15. Amount of precipitated oxygen h [Ol a s a function of annealing time at 635°C for pwinnealing at 925'C. 2 hr: JU'C'. 24 h r and no preannealing.

542

W. BERGHOLZ

connection with grown-in intrinsic defects and defect clusters, can show a different behaviour (Hawkins and Lavine, 1989). b. HiLoHi Annealing

In the device processing or even at the stage of wafer manufacture for some applications, annealing programs are carried out to “engineer” certain oxygen precipitation properties into the wafer. The most popular of these is the so-called HiLoHi annealing, which consists of three steps, each of which has a special purpose: 0

0

0

Hi: annealing at comparatively high temperatures (>1 100°C) for a few hours does not lead to appreciable precipitation, but due to oxygen out-diffusion the top 20-100 pm under the wafer surface are oxygen depleted; Lo: the purpose of this annealing is to nucleate a sufficiently high density of precipitates in a temperature range of 650-800°C; Hi: the third temperature step at typically 1000°C is the precipitate growth step to stabilize the precipitate nuclei.

The result of this temperature treatment is a very low precipitate density near the surface, the denuded zone (Fig. 16) and a high defect density in the bulk, i.e., the defects in the bulk can getter metal contamination, but do not interfere with the devices near the surface.

c . CMOS and Bipolar Process Sequences A typical CMOS process consists of more than 10 high temperature steps, Fig. 17 is an example picked at random from the literature. In spite of such complexity, the influence of an oxygen precipitation is relatively easy to understand:

0 0

A s a rule, not much happens during the initial well oxide step (900- 1000°C); The well drive-in step(s) is (are) equivalent to a Hi-step, i.e., an oxygen-depleted zone near the surface is created, the prerequisite for the formation of a denuded zone; The poly-Si and the nitride deposition steps (700-900°C) for the LOCOS isolation can be regarded as nucleation steps; The field oxidation at 1000-1100°C leads to oxide precipitate growth, just like the second Hi step.

All subsequent high-temperature processes are usually at lower temperatures and result in a moderate further growth of the precipitates.

12.

GROWN-IN AND PROCESS-INDUCED DEFECTS

543

denuded zone1

F=

Fic,. 16. ( a ) Oxygen precipitate den\itv

;I\

a funct~onofdktance from the surface for two

uafers after a CMOS device proce\\ (data from Jastrzebski et al.. 1987); (b) defect-etched c r m s section with a well-developed denuded lone (marked by a double arrow) after a

CMOS-process.

544

W . BERGHOLZ

PROCESS TIME (HOURS) FIG. 17. Temperature-time diagram for a typical CMOS-process (data from Fraundorf et al., 1985b).

Bipolar processes are dominated by the buried layer diffusion, which is well above 1200°C for several hours. In our experience, this temperature step is the only one really relevant for oxygen precipitation. The details of the ramp-up and stand-by temperatures can be quite important for which of the oxygen precipitate nuclei can grow above the critical precipitate radius for the high annealing temperature. d . Size and Density of Oxygen Precipitates After-Device Processes

Typical densities of oxygen precipitates after-device processes are between lo3 and 10’O crnp3, this quantity is determined not only by the details of the thermal process (including the thermal history during crystal growth) but also by the factors to be described in section 5. A straightforward calculation shows that for these densities and common device processes each precipitate has its own “region of influx” around it, without much overlap, on average, since the average diffusion distance during the precipitate growth is smaller than the average distance between precipitates. This implies that, for a given process, the size of the oxygen precipitates is nearly independent of the precipitate density (in fact it varies with the third root of the initial oxygen concentration, which is usually between 7 and 8 x 10” cm-3 (new ASTM standard) for typical device processes. 5 . OTHERFACTORS THATAFFECTOXYGEN PRECIPITATION

Unfortunately, matters are not quite as simple as one might be tempted to conclude from Sections 3 and 4. For a given device process, the density of oxygen precipitates can vary over the full range mentioned in Section 4 by the choice of the starting material alone. In this section, material-

12.

GROWN-IN AND PROCESS-INDUCED DEFECTS

545

related parameters that affect the oxygen precipitate density are very briefly reviewed. (1.

lnitiul Oxygrn Content

The oxygen precipitate density as a function of the initial oxygen content appears to obey a kind of universal S-curve, which is shifted along the [O]-axis by variations of the device process. Figure 18 shows an example. In region 1 the amount of precipitated oxygen is below or at the detection limit. In region I 1 there is a steep increase in the amount of precipitated oxygen. In region 111 the precipitate density increases more slowly and is essentially proportional to the initial oxygen concentration. Typical device processes aim at precipitate densities in region 11; i.e.. the initial oxygen content is a parameter that needs to be tightly controlled. b. C'urbon Content

The influence of carbon that can be present in CZ-Si in concentrations between some 10' and 10'' c m - j (Kolbesen and Muehlbauer. 1982) is an increase in the precipitate density for C-concentrations larger than about 1-3 x 10'' cm-'. This can be understood qualitatively by the fact that C contracts the Si lattice in its vicinity, and thus it is plausible that it can alleviate the excess volume requirements of a nucleating oxygen precipitate. A particularly clear experiment on this subject has been reported by Shimura et al. (1985), who have shown by SIMS that the regions of high-carbon and high-oxygen precipitate density coincide.

"I0

12 1L I 6 18 20 22 INITIAL OXYGEN CONC (ppma,new ASTM]

E K ; . 18. Typical dependence of the amount of precipitated oxygen as a function of the initial oxygen concentration (data f r o m Swaroop et al.. 1987).

546

W. BERGHOLZ

c. Resistivity The oxygen precipitation density has been found to depend appreciably on the resistivity (see, e.g., Matsumoto et al., 1985, or Hahn et al., 1988). d . Epitaxy

Epitaxy is an additional high-temperature process and is therefore bound to influence the oxygen precipitation compared to wafers from the same crystal ingot. In addition, a poly-Si backside, which is very often deposited for gettering, entails not only an additional low-temperature annealing step (nucleation), but also enhances the oxygen precipitation in the vicinity of the poly-Si layer (Dyson et al., 1983). The reason for this is not clear. It can only be speculated that the interface to the Si substrate acts as a particularly good sink or source for intrinsic defects in such a manner as to reduce the supersaturation of self-interstitials. e . Metal Contamination

Obviously any defect will have the potential to act as a nucleation site for oxygen precipitation. Hence, metal contamination with Cu or Ni, both of which form precipitates very easily, can enhance oxygen precipitation. For an example see Kolbesen, 1985. It had been found that material abraded from metal tweezers to handle wafers had locally enhanced the oxygen precipitation. .f. Dislocations Sumino. Harada and Yonegawa (1980) and others have shown that the plastic deformation at elevated temperatures is strongly influenced by the oxygen content via the interaction of dislocations with dissolved oxygen atoms or oxygen precipitates. A particularly striking finding has been that during deformation at 900°C the oxygen can disappear from solution without oxygen precipitate formation; i.e., the oxygen atoms have apparently decorated the dislocations introduced by plastic deformation. g . Amhien t

Numerous workers have shown that the annealing ambient can have a strong influence on the oxygen precipitation (see, e.g., Hu, 1980). The most obvious interpretation of this state of affairs is that there is an interaction via the concentration of intrinsic point defects, e.g., via the self-interstitial supersaturation, created during oxidation.

12.

GROWN-IN AN11 PROCESS-INDUCED DEFECTS

547

TED DEFECTS A N D PROCESS-INDUCED DEFECTS 6 . OXYGEN-RELA

The phenomena described in this section are in a way at the perimeter of this chapter, since the main factor is not defect formation during crystal growth or simple annealing treatments to manipulate the oxygen precipitation. Rather. the main influence results from the complete device proccss. which. of course, is a very wide field. In this section. this complex field can, of course, not be treated comprehensively. but the essentials will be briefly touched upon. For a n up-to-date review see. e. g. , Kolbewn et al.. 1991. ( I . BlllX S l ~ l d i l l gFrilrlls

The formation of stacking faults in the bulk has already been mentioned. The additional aspect hei-e is that surface-near bulk-nucleated stacking fault5 can grow dui-ing oxidation (Fig. 19. Zulehner. 1989) and can eventually reach the surface and interfere with the devices.

Fit,. 19. Etch figure\ of oxidation-induced $tacking faults (OISFs) nucleated in the hulk. The broad lengths diatrihution i$typical lor !hi5 nucleation mechanism. B y contra\t. hurface-nucleated OISFc have ii well-dstinrd length distribution (Zulehner. 1989).

548

W.

BERGHOLZ

, 10 20 AMOUNT OF PRECIPITATED OXYGEN (PPm)

FIG.20. Wafer warpage as a function of the amount of precipitated oxygen [O] (old ASTM units) for a CMOS process (data from Jastrzebski et al., 1987).

h. Generution of Dislocations and Wafer Warp

The nucleation of dislocations during oxygen precipitation at or on oxygen precipitates is presumably the most important single cause for excessive wafer warpage during a normally well-behaved device process. For a given process, there is a correlation between the wafer warp and the amount of precipitated oxygen (Fig. 20). Above a critical limit the wafer warp rises sharply with increasing oxygen precipitation. Figure 21 shows a particularly drastic example. The deformation is so strong (a few 100 Fm) that only some areas of the wafer fulfill the diffraction condition for the X-ray topograph. A cleaved and etched cross section reveals a high density of oxygen precipitates, stacking faults and, most important dislocation etch pits. Details of the nucleation of dislocations on oxygen precipitates have been described by Tempelhoff et al., 1979. As a remedy against accidental oxygen precipitation Aoshima et al. (1990) have proposed “soft” intrinsic gettering; i.e., a lower amount of oxygen precipitation during intrinsic gettering than has been common practice up to now and special preannealing to make the oxygen precipitation relatively independent of the thermal history during crystal growth.

c. Nucleation of Metal Precipitates and Intrinsic Gettering A comprehensive and full treatment of the subject of metal precipitation would require a full chapter of its own, in this chapter we have to

12.

CROWN-IN A N D PROCESS-INDUCED DEFECTS

549

restrict ourselves to a brief description of the key features and principles. Metal decoration of crystal defects or metal precipitates are a most frequent cause for device failure, if the defects are located at or near the device at the wafer front surface. The principle of intrinsic gettering is to enhance the metal precipitation in the bulk of the wafer so as to reduce the probability for precipitate formation near the surface.

F K . 21. ( a ) X-ray ropograph of a wafer with a massive wafer warp due to excessive oxygen precipitation.

550

W . BERGHOLZ

FIG.21. (b) Secco defect-etched cross section of the same wafer. Note the etch pits of dislocations marked by arrow heads.

Several mechanisms for intrinsic gettering have been proposed:

I.

Nucleation of metal precipitates on oxygen precipitates (Falster and Bergholz, 1990) and secondary formation of dislocations (Falster et al., 1992); 2 . Nucleation of metal precipitates on bulk stacking faults (Graff, Hefner and Hennerici, 1988); 3 . Nucleation of metal precipitates enhanced by self-interstitial supersaturation (Seibt, 1990); 4. Diffusion of dissolved impurities from the denuded zone into the bulk during each cooling cycle (Gilles, Weber and Hahn, 1990). Irrespective of which model is correct, it is a well-established fact that intrinsic gettering not only reduces the defect-precipitate density near the surface, but also results in enhanced yields and improved reliability.

12.

GROWN-IN AND PROCESS-INDUCED DEFECTS

55 1

111. Grown-in Defects: Precipitation and Defect Aggregation During Crystal Growth

Every wafer has been subjected to a rather complicated thermal history during the crystal pulling process (Fig. 2 2 , Fraundorf et al., 198Sb). Depending on the technical details of t h e crystal puller and the position in the crystal ingot. a wafer has "seen" different times between 1400 and 1000°C. There is also a difference in the time spent in the temperature range of maximum oxygen nucleation. Whereas the high-temperature region is more important in connection with the agglomeration of intrinsic defects (see Section 2), the lower temperature interval is a more important factor for oxygen precipitation (Section 1). 1 . OXYGEN PRECIPITATION D L I K I N G CKYYI-AL GROWTH (I

.

' Mac r(I sc op ic ' '

E.rp r rim i,I I t ( I I E \id( Jticc.

Although the exact microscopic structure of the thermal donors is still a highly controversial subject (Ourmazd et al., 1984). there is no doubt that these defects that are already found after crystal growth contain oxygen atoms. This has been concluded indirectly from the dependence of the maximum thermal donor concentration on the third power of the initial oxygen concentration and a comparison of the thermal donor formation rate with the rate at which oxygen disappears from solution. as monitored by IR. Comparatively recently, direct evidence for oxygen atoms in thermal donors has come from ESR and ENDOR studies (van Wezep et al., 1986).

5 11

2

12

s1 08

=f 06 w QL I02 +0

=

1250

SHIELD

x150

850

65

TEMPERATURErl

L50

250 0

RAMP

F K , . 11. Thermal history of a C Z L,ry\tal for t w o different puller configurations (data from t raundorf et al.. 19XSb).

552

W. BERGHOLZ

The effect of “homogenization annealings” at temperatures above 1300°C provide further macroscopic evidence for the presence of oxygen precipitates in as-grown crystals: Jastrzebski et al. (1982) have shown that for some wafers the concentration of dissolved oxygen goes up after such annealings; i.e., an appreciable number of oxygen atoms must have been “hidden” in oxygen precipitates. As mentioned before, the effect of preannealings at a temperature higher than the main precipitation temperature is a significant reduction in the density of oxygen precipitates. In other words, existing precipitates (precipitate nuclei) smaller than the critical radius at the precipitation temperature are redissolved. As the thermal history of a given wafer varies strongly with the position along the crystal ingot axis, there should be a marked dependence of the precipitate density on that position, which is indeed observed. Inoue, Osaka and Wada (1982) have presented a technique that is claimed to be capable of determining the density and size of the oxygen precipitates in as-grown CZ silicon.

0

0

6 . Microscopic Evidence for Grown-in Oxygen Precipitates The density of large grown-in oxygen precipitates that could lend themselves to a straightforward TEM analysis is, unfortunately, rather small, so that to the author’s knowledge no substantial studies of this kind exist. According to the macroscopic evidence just described, smaller oxygen aggregates must be more abundant, but these are so small that a microanalysis is virtually impossible. Fraundorfer et al. (1985a) have postulated the existence of “precursors” to oxygen precipitates and have also presented some microscopic studies. More conclusive evidence about the structure and size of grown-in oxygen precipitates is still needed. 2.

INTRINSIC

DEFECTS

a . Vacancies and Interstitials As in any crystalline solid, there is an equilibrium concentration of intrinsic point defects at a given temperature. What makes the situation complicated in the case of silicon is the fact that there are both selfinterstitials I and vacancies V , which, in principle, can react according to the “chemical” equation I

+

V

t,

Si

(Si stands for a Si atom on a normal lattice site)

12.

GROWN-IN A N D PROCESS-INDUCED DEFECTS

553

and which have different equilibrium concentrations and diffusion coefficients (see, e.g., Tan et al., 1983; Voronkov. 1982; Seeger and Chik, IY6X: Frank, 1981). As a consequence. a variety of different intrinsic defect agglomerates have been found. which are going to be described in the next sections. h . FZ-Materiiil

Due to the low oxygen content of float zone (FZ)-Si, this material does not possess the complications of oxygen precipitation during the pulling proces\. Hence it is a more clear-cut case for the study of intrinsic defects during the crystal growth process (although it should be kept in mind that the details of the pulling process and the thermal history are quite different from the CZ crucible process). The understanding gained from the study of FZ-material will then be applied to the more complicated situation of CZ-material. i . A . B. C .slt*irl di.fi>ct.s uiitl l)-dqfiji,tS The existence of "swirl" defects that are distributed in t h e crystal in a swirllike pattern (Fig. 2 3 ) was recognized by several groups almost simultaneously (Foe11and Kolbesen. lY75: de Kock. Rocksnoer and Boonem, 1974; Petroff and de Kock, 1975) at a time when dislocation-free crystals became available as a standard product. The explanation why these defects were discovered at that particular time is rather straightforward. In the presence of dislocation4 in the bulk of the crystal, the intrinsic defects could easily establish their thermal equilibrium concentrations during cool-down from the melting temperature to room temperature. since these defects act as efficient sinks and sources for intrinsic defects. The situation is completely different for dislocation-free crystals. The advance of the solid-liquid interface and the gradual cool-down to lower temperatures are too fast for the excess defects to diffuse to the growth front or to the other crystal surfaces in order to annihilate at these sinks. Therefore. most of the intrinsic defects find themselves "trapped" within the interior of an almost perfect crystal (except for those areas in the outer few mm near the cry4tal surface). In the end, most of the trapped intrinsic defects form extended defects, namely, the swirl defects. The origin of the swirllike pattern is rooted in the fact that the crystal is rotated during the growth proceus. which entails periodic small temperature fluctuations, possibly in combination with the fact that an important impurity. carbon. has a very low distribution coefficient ( k = 0.07: Nozaki et al.. 1974).

554

W. BERGHOLZ

FIG. 2 3 . Swirllike distribution of A-defects as visualized by defect etching (Zulehner. 1989).

The largest of these defects, the A-swirl defects, can be several micrometers in their maximum dimension. The defects have been identified by Foell and Kolbesen (1975) to be extrinsic dislocation loops; Fig. 24 shows an example. From the extrinsic character of the defects it has been concluded that the swirl defects are aggregates of self-interstitials. The A-defects occur for a certain pulling speed range (compare to Fig. 25b) in most of the crystal cross section. The defects can be delineated either by defect etching or by Cu-decoration and X-ray topography (Fig. 2Sa). It should be noted that the A-defects can be avoided for very low pulling speeds (<0.25 mm/min for small crystal diameters), the obvious interpretation being that the cooling and the advance of crystal growth front are sufficiently slow for the defects to reach thermal equilibrium. It is also possible to avoid the A-defects by faster pulling (>4.5mm/min) (Fig. 2Sb; Rocksnoer and van den Boom, 1981). For pulling speeds between 4.5 and 5 mm/min B-swirl defects are the only defects that can be observed (Rocksnoer and van den Boom, 1981).

12.

GROWN-IN AND PROCESS-INDUCED DEFECTS

555

They cannot be detected by T E M but are usually detected by defect etching or Cu decoration and X-ray topography. There is no conclusive identification, one assumption is that the defects are precursors for A defects (Foell and Kolbesen, 1975, 1981). In some cases defects have been observed next to the B-defect region. The main difference to the B-defects being that the Cu-precipitates induced by the Cu-decoration technique are much smaller than for the B-defects (Rocksnoer, Bartels and Bulle. 1976). The defects also occur in a striated pattern. Both B - and C-defects are eliminated for pulling speeds above some 5 mm/min (or below .2 mmimin), Fig. 2%. It is important to note that most of the studies on A - , B - and C-defects have

Fiti. 24. TEM micrograph of an .4-\wirl defect (Kolbesen. private communication. and Foell and Kolbesen, 1976). 'The defect I \ ii complicated agglomerate of extrinsic dislocation loop>.

556

W. BERGHOLZ

GROWTH RATE

v

(mm/rnin-’~

-

12.

GROWN-IN A N D PROCESS-INDUCED DEFECTS

0

0

25

557

SWIRL FREE

50

75

100 125 150

CRYSTAL DIAMETER (mm) Fit,

31 Occurrence of A . B ~ w i t dcfecfs l ds

\peed Id.itd trom Abe et al

. I983d)

‘I

function of cry\tal diameter and pulling

been conducted on material o f comparatively small diameters and for carbon contents of 2-3 x IOihcm ‘. Furthermore, t h e minimum growth rate for which A and B swirl defects are suppressed is reduced as the diameter of the crystal is increased (Abe, Harada and Chikawa, 19X3a. 198%. Fig. 26).

ii. D-dc:fiJc,fs For low-carbon material ( <1 c m - ’) a new type of defect is observed for pulling speeds above 6 mmimin (Rocksnoer and van den Boom, 1981). It is most remarkable that the defect distribution. as visualized by the Cu decoration technique is no longer striated. but homogeneous (Fig. 27). As for the S - and C-defects the identification is handicapped by the lack of TEM investigations. It has been concluded by Rocksnoer and van den Boom, 1981 and by Abe et al.. 1983b that the D-defects are agglomerates of vacancies. Provided that this interpretation is correct, the vacancies ought to be significantly faster in establishing their equilibrium value, and larger pulling speeds are required to ”outrace” these defects, in other words to induce enough supersaturation for the condensation of these defects (note though that a larger nucleation barrier for the formation of the D-defects could also be a valid explanation). The absence of striations could mean that, e.g.. C has no part in the defect nucleation. Fiti. 25. ( a ) X-ray topograph of an F% wafer after Cu-decoration. The swirllike striated distribution of A-defects and B-defects i \ visible (de Kock. private communication. and de Kock. 1980): ( b ) occurrence of defects ;I\ a function of crystal pulling speed (data from de Kock. 1980).

558

W . BERGHOLZ

FIG.27. X-ray topograph of an FZ-wafer that contains D-defects. after Cu-decoration. Note that the topograph is of a section cut parallel to the growth axis. An obvious difference between the A-swirl section (introduced by a break in the pulling process) and the D-defects is the absence of strong striations in the D-defect regions (Abe and Kimura, 1990).

Recent studies of state-of-the-art FZ-Si with diameters up to 150 mm by Abe and Kimura (1990) have shown that both A - and D-defects occur in such material. Figure 28 shows the distribution in typical wafers: The A-defects occupy the outer perimeter of the wafer. At about 3/4 radius there is a neutral zone where no defects are visible. The interior of the wafer is occupied by D-defects. Indirect, but further strong evidence as to the extrinsic-intrinsic nature of the A-D-defects has been reported by Abe and Kimura (1990). If a wafer is annealed in different ambients and is then cut parallel to the growth direction, the A-region is observed to have expanded in an oxidizing ambient, whereas the D-region has shrunk (Fig. 29). The conclusion is that the D-defects must have a vacancy character since they are annihilated by the self-interstitial supersaturation (oxidation), whereas the extrinsic A-defects are enhanced, as expected. The behavior in an argon and in a nitrogen atmosphere has also been investigated and is consistent with the above identification. It is most important to keep in mind the following two facts:

12.

CROWN-IN AND PROCESS-INDUCED DEFECTS

559

For higher pulling speeds. i.e., stronger thermal gradients, the D defect region grows at the expense of the A-defects, again with a neutral zone in between (Abe and Kimura, 1990). 2 . The FZ material that is actually produced for device manufacture does not show up A - and D-defects in the Cu decoration test (Abe and Kimura, 1990).This is accomplished by adding a small amount of nitrogen to the puller ambient, which results in an Nconcentration of about I x 10'' em-]. It has been hypothesized that the nitrogen atoms interact with the intrinsic defects or with their agglomerates and render them "unattractive" for the decoration by Cu-precipitation. This passivation is presumably equivalent to the defects being harmless in a device process. By contrast. FZ-material without N-doping has an inferior gate oxide quality (Mohr and Gentsch, private communication).

I.

FIG. 28. Di\tribution of defects i n a wafer from typical FZ-material a s delineated by X-ray topography after Cu-decoration. 'I he A-detect\ a r e found in the wafer perimeter. whereas the [)-defect5 are ohrerved i n the wafer center. T h e two regions are separated by ;i neutral Lone ( A h e and Kimura. 1990)

560

W . BERGHOLZ

A

N

D

FIG.29. X-ray topographs after high-temperature treatments and Cu-decoration of samples from an FZ crystal. The samples are strips cut from 3 mm slugs vertical to the slug surface; i.e.. the images are cross sections of the wafers (the LHS of the strips are close to the crystal edge, the RHS are nearer to the crystal center): (a) as-grown: (b) dry oxidation, I000"C, 20 min; (c) wet oxidation, IOOOT, 20 min; (d) nitrogen annealing, I IOWC, 40 min: (e ) argon annealing, 1 lOWC, 40 min.

Although the common Cu-decoration test does not show up the A and D-defects in N-doped material, there is a Ni-based decoration test (Heizmann, Bergholz and Dellith, 1994) that appears to be more sensitive, since it shows up regions in the wafer that resemble those of the A and D regions. Figure 30a shows an example from a 125 rnm Fz wafer from FZ-Si. The exterior region of the wafer appears bright from a high density of surface-near precipitates ( = Ni-haze from an intentional Ni-

FIG.30. Ni-decoration test of a 5 in. FZ-wafer (see text for details: (a) the wafer surface after Secco defect etching (note the haze-free region in the wafer center); (b) etch figures observed on the defect etched cleavage planes show that large platelike NiSi>-precipitates have formed in the bulk of the wafer (note the feature in the center of each etch figure marked by arrowheads; Heitzmann et al., 1994): (c) etch figure of a particularly large Nisiz precipitate with a flow pattern etch feature in its vicinity.

12.

GROWN-IN A N D PKOCESS-INDUCED DEFECTS

561

562

W . BERGHOLZ

FIG.30. (Continued).

12.

GROWN-IN A N D PROCESS-INDUCED DEFECTS

563

contamination of the wafer's back surface). By contrast, the interior of the wafer is haze free, instead the Ni has formed large precipitates in the bulk (Fig. 30b). The interpretation of this observation is simple. In the interior of the wafer there are efficient nucleation sites for the Niprecipitate nucleation o r sinks-sources for intrinsic defects in those regions of the wafer in which the !)-defects are normally detected. I t is remarkable that these defects are not stable above about 1000°C. since rapid annealing above this temperature prior to the decoration test destroys the effect. c'.

CZ-Mutc.riul

As already mentioned, the situation in CZ-material is complicated by the simultaneous oxygen precipitate formation and intrinsic defect aggregation during the cool-down from the melting temperature during the crystal growth process. The interaction between the two phenomena can be many: 0 0

0

Nucleation of oxygen precipitates on intrinsic defect clusters; Direct interaction of oxygen atoms with intrinsic point defects; Indirect interaction via a supersaturation of intrinsic defects; Indirect interaction via electrical effects (presumably marginal)

In spite of this complicated scenario, a few facts appear to be firmly established. Similar to FZ-material, A-defects are found in the outer perimeter of the wafer, provided the pulling speed of the wafer is in the range around 1 mmimin (Fig. 3 I . Fusegawa et al., 1991a). At the borderline to the interior of the wafer, there is a small region in which a high density of stacking faults develops during oxidation at, e.g., I000"C. (For standard device grade material. the pulling speed is usually chosen high

O D A

FIG. 31. Schematic distribution of etch pits on ii slowly pulled CZ-wafer: in the wafer perimeter shallow etch pits of A-defects are observed. whereas in the center a kind of flow pattern IS observed (compare to Fig. 37al.

564

W . BERGHOLZ

enough for the OSF ring to be outside those parts of the crystal ingot that are within the final wafer diameter). There are fewer A-defects in the wafer center, within the OSF circle. There is, however, another type of defect within the OSF circle that can be delineated by a novel technique (details in the following section). The similarity in the distribution of A-defects and the ring-shaped transition region for FZ and for CZ material is apparently quite remarkable and has led to conjecture that the defects in the wafer interior are, as for FZ Si, D-defects, a view that is not shared by all workers active in the field. Observations of the Si-material dependent gate oxide quality to be described in Section 3 further underline the similarities in the defect scenario in FZ- and in CZ-material. 3. GROWN-IN DEFECTS AND GATEOXIDE QUALITY a . G a t e Oxide Quality Dependence on the Starting Material

Among the most striking phenomena in device processing are the differences among different CZ-materials and the superiority of FZ- over CZ-material as far as gate oxide quality is concerned (Bergholz et al., 1989b). Figure 32 shows a comparison of the gate oxide quality for two CZ-materials in a voltage ramp test (Yamabe, Taniguchi and Matsushita, 1983). CZ-material has a significant fraction of fails of test capacitors at electric field strengths between 2 and 8 MVcm-'. By contrast. FZ-

50

50

kl n

ti

n

5

E

2

C

0 0

5

E I (MVlcm)

10

0 0

5 EI (MVlcm)

FIG.32. Voltage ramp test of the gate oxide integrity ((301) for CZ-materials from two different vendors. The difference in B-mode failure in the histogram of the electric field strength at which gate oxide breakdown occurs correlates with a defect density test in the bulk of the wafer as described in detail by Yamabe et al. (1983).

12.

565

GROWN-IN AND PROCESS-INDUCED DEFECTS

FZ with pretreatment

retreatment

" 8 9 'O 900I

ae

Y

>

JOt. 60

40

a.

I

A

C

P

E

F

FIG.3 3 . Gate oxide yield for 8 mm-' test capacitors in a two-stage constant current test (Bergholr et al.. 198%) for FZ-material from two vendors and four CZ-vendors. The circle5 denote the percentage of functional lest c,ipacitor\ after the first test stage 60 kA!crn-' for 100 nis. the 5quare\ after the second \tage 2 rnA lor 500 r n b .

material has a virtually 100% yield of intrinsic gate oxide failure (i.e., failure at an electric field strength around 10 MVcm-' (Fig. 3 3 ) . It is also noteworthy that the gate oxide quality of the epitaxial material is comparable to that of FZ-Si. 1). M o d e I: I n t c' rac.1ion o j Gro \\In -in Dqfic.1s un d M r t d ConI u rninii t ion

Based on a large body of experimental observations, a model to explain the differences in gate oxide quality between FZ- and CZ-Si has been put forward (Fig. 34, Bergholz et a l . . 1989b). The essence of the model that is schematically explained in Fig. 34 was that the gate oxide breakdown sites for B-mode failure are the surface near oxygen precipitates decorated by metal impurities. The essential point is that for a poor gate oxide quality. a high density of gate oxide breakdown sites, "enough" metal contamination must be present to "activate" the potential breakdown sites. A reasonable gate oxide quality i s thus possible even for a poor starting material with a high density of potential breakdown sites, if processing is carried out with little contamination or very efficient gettering.

566

W . BERGHOLZ

GROWN-IN I hqh

0

* METAL IMPURITY

DEFECT DENSITY I

n 0DEFECT

IW

-

I

I MDECORATO, DEFECT

FIG.34. Schematic representation of the Si-material dependent gate oxide degradation mechanism. The Si crystal contains defects that will be activated in the case of metal contamination-decoration. Therefore, reasonable gate oxide quality can be obtained for either low metal contamination or a low defect density. (The superiority of FZ-material is thus due to the low density of defects, i.e., potential gate oxide degradation sites.)

FZ-material, on the other hand, is more tolerant of metal contamination due to the low density of possible breakdown sites. In the light of new evidence on the defects in CZ-Si gathered in the last 1-2 years (to be described in detail in subsections c-e), the model is modified and put forward as the following hypothesis. Instead of an oxygen precipitate as the potential site for gate oxide failure, it is postulated that the potential breakdown site is initialized by an intrinsic defect agglomerate, the exact nature of which is yet to be determined. This model is at variance with an alternative explanation, namely, that the ultimate cause for the gate oxide weakness is a surface flaw generated, e.g., by an SC1-cleaning step. c. Correlution with the Crystal Pulling Speed Presumably the first step in the recent progress in establishing a correlation between defects in Si substrate and the gate oxide quality was the observation that for crystal pulling speeds below about 0.7 mm/min the gate oxide quality improves dramatically and is essentially comparable to that of FZ- or epi-material (Fig. 35, Tachimori, Sakon and Kaneko, 1990). Even more exciting is the observation that for an intermediate pulling

12.

GROWN-IN A N D PROCESS-INDUCED DEFECTS

567

speed most of the defective gate oxide test capacitors are located within the OSF-ring that occurs somewhere at an intermediate radius for pulling speeds around I mmimin (Fig. 36). Thus the gate oxide quality is good in the A-defect region and poor in the interior, in the case of FZ-material this would correspond to the region of the D-defects.

:I. Ctpeririicntcil L'i.idericc7f b r

Intrinsic Dt
(;i.ou.ii-iii

The geometric similarity of the distribution of defects and the pattern o f gate oxide failure has led to the conjecture that the defects responsible tor the CZ-material specific gate oxide problems are in fact the D-defects recognired to be present in the interior of FZ-wafers (Tachimori et al.. 1990: Abe and Kimura. 1990). However. there is as yet no conclusive evidence that this is really the c;ise or that the defects are of a different nature and happen to have the w n e distribution in a wafer as the D-defects in FZ-Si. All the same, there exist a number of experimental observations for the defects in the center of CZ-Si wafers that are summarized here and further support the identification (for simplicity we call the defects I)t1ofi.c.t.s even though their identification is still doubtful): 1.

SC I cleaning of CZ-waters (i.e.. the alkaline part of the well-known RCA-clean) results in a \mall number of light point defects (LPDs)

02

06 Growth

10 rate

Pic, 35. Gate oxide yield for a voltage ramp (Tachimonet al.. 1990).

le\l

14

I rnrn/rnin) as a function of crystal pulling rpeed

568

W.

BERGHOLZ

FIG.36. Topography of gate oxide breakdown for a slowly pulled CZ-crystal. The interior of the crystal still contains D-defects, therefore, most of t h e test capacitors fail. By contrast, the D-defect free region in the outer wafer areas contains only a few failed test capacitors (data from Tachimori et al.. 1990).

as detected by a particle counter (Tachimori et al., 1990). If the cleaning is repeated several times, the number of LPDs that are not particles but holes increases proportional to the number of cleaning cycles (Fig. 37a). Since the density of the LPDs showed a correlation to the pulling speed and the gate oxide quality, it was suspected that the SC1 clean acted in fact as a defect delineation etch. 2 . Fusegawa et al., 1991a, showed that protracted Secco defect etching for 30 min results in characteristic “flow patterns” (Fig. 37b) the density of which correlates well with that of the SCl cleaning holes (Fig. 37c). 3. Furthermore, Fusegawa et al., 1991b, 1 9 9 1 have ~ reported that the Secco flow pattern density correlates with the crystal pulling speed (Fig. 38a) and that the gate oxide quality decreases as the density of flow pattern increases (Fig. 38b) (Fujimaki et al., 1991). 4. Flow patterns have also been observed in the D-defect region of FZ-material (Takeno, Ushio and Tanekada, 1992). FIG.37. number of delineated density of

(a) Density of light point defects (LPDs = etched holes) after SCl cleans as a SCI cleans (Tachimori et al., 1990); (b) light optical micrographs of Row patterns by 30 min Secco etching; (c) the density of flow patterns correlates with the LPDs after multiple SCI cleaning (data from Fusegawa et al., 1991~).

600

0 0

500

0 0

- LOO m

c

C

4

0 0

n

300

0

n I

6 200

5

0 0

0

100

0

C

0 0 1

(a)

v

0

0

2

0

3

v

*

+

A

T

1

I

I

L

5 6 7 8 9 1 No of SC-1 Cleans OZprn-O25pm 0 025pm-03prn 03pm-

9 8'

,'

x

I

.'

n o

0

A

c

m

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a, U c .-

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1.

'

0

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u

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8

'

"

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W. BERGHOLZ

, x 103 103

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.-L

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10

I:

0 2 01 06 08

0

1

12

1 L 1 6 10

2

I

Crystal growth rate (rnrn/min)

lil

(a)

-n a x

0

90

100

500 I300

3000

Secco pit density (lcm"21

(b)

FIG.38. (a) Secco flow pattern density as a function of crystal pulling speed (data from Fusegawa et al., 1991b); (b) gate oxide yield as a function of the Secco flow pattern density (data from Fujimaki et al., 1991).

5 . There have been several attempts to identify the defects: a. TEM observations have identified extrinsic dislocation clusters in the locations of shortly etched flow patterns (Takeno et al., 1992). This observation appears to be, at first sight, to be at variance with the identification as vacancy clusters. It is, however, not unlikely that the dislocation clusters are not the original defects but secondary defects nucleated on the original intrinsic defects with vacancy character. b. A Ni-decoration test as described for FZ-material did not show up a haze-free region in the wafer center. This could mean that the defects in the wafer center are not identical to the Ddefects in the center of FZ-wafers.

All in all it has to be realized that there is as yet no sound identification of the defects in the wafer center of standard CZ-material. 4. SPECULATIONS ON THE ORIGIN-FORMATION MECHANISMS OF GROWN-IN DEFECTS Putting together the information on FZ-material gathered mainly between 1974 and the mid 1980s and the recent evidence on CZ-material some obvious common features can be noted:

0

There are the two main defect regions in a wafer (center and ring) separated by a narrow transition region. For slow pulling speeds in FZ- and CZ-material the diameter of the inner zone shrinks to zero.

12.

0

GROWN-IN AND PROCESS-INDUCED DEFECTS

57 I

For large pulling speeds the interior zone takes over nearly all of the wafer. According to Abe (1992) the A-type defects form in regions of high thermal gradients, whereas the D-defects are observed mainly in regions with low thermal gradients. The oxygen precipitation is significantly slower in the interior of the stacking fault ring than outside, and there are anomalies in the ring region (Ogushi, Hourai and Shigematsu, 1992).

The obvious possibility to model the phenomenon is to take into account that there are two kinds of intrinsic point defects with different enthalpies of formations-concentrations and significantly different diffusion coefficients. A more detailed and quantitative model is beyond the scope of this chapter. Furthermore, it is to be expected that within the next few years there will be a rapid increase of experimental evidence on the defects in the center of CZ-material.

IV. Summary

The formation of grown-in and process-induced defects in CZ-Si is governed not only by oxygen. the most abundant impurity in the material, but is the result of a complex interplay among three defect types; namely, oxygen impurities, intrinsic defects and, last but not least, metal impurities. There are a great variety of morphologies and structures that the oxygen precipitates can exhibit. The main factor that leads to this multitude in oxygen-containing defects is ultimately not due to the oxygen itself, but due to the fact that the volume requirement of the Si02-precipitates are difficult to satisfy because of the low equilibrium concentration of intrinsic defects in Si. In addition to the oxygen-containing defects the precipitation of oxygen also gives rise to secondary extended defects, mainly stacking and dislocation loops. Again, the defect formation is a combination effect of oxygen and the intrinsic defects. The grown-in extended intrinsic defects. mainly the A - and D-defects appear to be present in both CZ and FZ silicon, and their occurrence in the perimeter wafer regions (A -defects) or in the wafer center (D-defects) appears to be due to the detail5 of the thermal history during crystal growth, independent of whether a crucible o r a float zone technique is employed. What appears to be of primary importance is the fact that there are two kinds of intrinsic defects in silicon, interstitials and vacancies. The occurrence of two kinds of extended defects can, in principle

572

W. BERGHOLZ

be rationalized in terms of the differences in the respective equilibrium concentrations and diffusion coefficients of these two kinds of intrinsic point defects. It is certain that the current research activities in the field will shed light onto this still very “dimly lit’’ area. The formation of metal precipitates is a very common occurrence in device processes, and it presumably also occurs to a small extent during crystal growth. The real importance of the metal impurities in the present context lies in their interaction with oxygen and intrinsic defects: Metal impurities can enhance oxygen precipitation. The formation of secondary defects during oxygen precipitation, namely, the formation of dislocations, could be influenced or catalyzed by the presence of metal impurities. The formation of defects that impair the gate oxide integrity, which is mainly a problem in CZ-material, appears to be a combination effect of the grown-in intrinsic A - and D-defects and metal impurities. It is not quite certain, at present, that the oxygen does not play a role in that game. Finally, intrinsic gettering can be viewed as an interaction between metal impurities and oxygen precipitates, however, the intrinsic gettering scenario is probably a more complicated one, in which the intrinsic point and extended defects couple the two systems oxygen in silicon and metal impurity in silicon.

REFERENCES Abe, T. (1992). MRS Spring Meeting, San Francisco, Abstract No E1.1. Abe, T.. Harada, H . , and Chikawa, J . (1983a). Physicu 116B, 139. Abe. T., Harada, H., and Chikawa, J. (1983b). In Defects in Semiconductors 11, S. Mahajan and J. W. Corbett (eds.), p. 1. Elsevier North-Holland, New York. Abe. T.. and Kimura, M. (1990). In Semiconductor Silicon 1990, H. R. Huff, K. J. Barraclough and .I.Chikawa (eds.), p. 105. Electrochem. Soc., Pennington, N.J. Aoshima, T., Kosaka, Y., and Yoshinaga, A. (1990). In Semiconductor Silicon 1990, H . R. Huff, K. J. Barraclough and J. Chikawa (eds.), p. 724. Electrochem. SOC., Pennington, N.J. Bergholz, W. (1989). In Semiconductors: Impurities und Defects in Group IV Elements und Ill-V Compounds, 0. Madelung and M. Schulz (eds.), p. 126. Landolt Boernstein New Series III/22b, Springer, Berlin. Bergholz, W., Binns, M. J., Booker, G. R., Hutchison, J. C., Kinder, S. H., Messoloras, S . , Newman, R . C., Stewart, R. J . , and Wilkes. J. C. (1989a). Philos. M u g . B59, 499. Bergholz, W .. Hutchison, J . C . , and Pirouz, P. (1985). Inst. Phys. Con$ Ser. 76, 11. Bergholz. W., Hutchison, J. L.. and Booker, G . R. (1986). In Semiconductor Silicon 1986. H . R . Huff, T. Abe and B. 0. Kolbesen (eds.), p. 874. Electrochem. Soc.. Pennington. N.J.

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tiROWN-IN AND PROCESS-INDUCED DEFECTS

573

Bergholz, W . , and Hutchison. J . L . (1988). In Proc. 36/h Annrrcrl M ~ r r i n gqf'rhe Elccrron Mic,rrj \ copv of' A,t?rric,tr, p. 478. Bergholz. W.. Mohr. M.. Drewes. W . . and Wendt. H. (lY8Yb). Marrrinls Scirncr titid Gigirrc.c,ririg B4. 359. BergholL. W.. Pirour. P.. Hutchison. J . I . . (19x4). J . Elecrron Marcviuls 14a, 717. Bourret. .4. ( 1987). I n s f . P/f!s. Cant. .{er. 87, 39. Bourret. A . . Thibault-Desseaux, J.. and Srrdmann. D. N . (1984). J . Appl. Phys. 55, 825. L)!wn. W . . Hellwig. L., Moody. J . . and R o b s i . J . (1983). In D t f ~ r sin Silic,o/i. W. M. Bulli\ and L. C . Kimerling (eds.1. p . 14h. Electrochem. Soc.. Pennington. N . J . Falster. R.. and Bergholz. W . (1990). J . l . J / ~ ~ r r o c ~ / r cSoc. ~ v r . 137, 1548. €-':tI\tcr, K..Lacrik. Z.. Booker. G . R.. Hhiitti. A . R . . and l'oeroek. P . (1992). In MRS S v m p Proc .. Vol. 262, S. A5hoh. J . Chevallier. K. Sumino and E. Weber ( e d s . ) . p. 945. Foell. H . . and Kolbesen. B. 0. (19751 A p p l PIrvs. 8, 319. toell. H . . and Kolhesen. B. 0. i 1976) J ~ l i r h r r ~elcr h AAtrdrrnir der Wissrtischqfi in ( h c f r i t r g m , p . 27. Vandenhoeck und Kuprecht. Goettingen. Germany. Foell. H . . and Kolbewn. B 0. (1981) J . C'r-vsr.C;row//r 52, 907. Frank. W . (19x1 ) , I n A d i ~ r n c in Solrd S r t r r c , P/rv\rc..\ X X f . J . Treusch (ed.). p. 281. Vieweg. Braunxhweig. Gel-many. Fvaundorf. G . . Fraundorf. P.. and C'raveri. R . A . (1985a). In Proc.. J r t l f n r . C'on,f: otr b'LSf. The Electrochem. Soc.. Pennington. N . J . t'raundorf'. G . . Fraundorf. P., Craven. R . .4..Frederick. R . A , . Moody. J . W.. and Shaw. R . W (l985h). J . El~,c,rro[./ic'rn., S o t 132. 1701. tujiinaki. N . . Fusegawa, I . . Matsu\hima. H.. Katayama. M.. and Yamagishi. H. (1991). 4bstr. No. 2XP-ZL-4. 3Xth Meeting Jap. Appl Physics Society. F ~ \ e g a ~ . : I+. .. Karasawa. Y . . Fujiniaki. N . . and Yamagirhi. H. (1991a). Abstr. N o . ZXPZL-I. 38th Meeting Jap. Appl. Phy4 Society. Fiiwgawa. I . . Lino. E.. Fujimahi. N . . and Yamapishi. H . (1991b). Abstr. No. 28P-LL-2. 38th Meeting Jap. Appl. Phys. Society. Fusegaha. I . . Takano. K.. Kobayashr. S., kuruse. S.. Kudo. H.. Fujimaki. N . . and Yamagi\hi. H . i1991c). Ahstr. N o . 28P-LI.-?. 38th Meeting Jap. Appl. Phys. Society. Gilles. D.. Weber. E. R., and Hahn. S.( I Y Y O ) . P h v s . Rriz. Lefr. 64, 196. Graff. K . . Hefner. H. A , . and Hennenci. W. (1988). J . Eltvtroc~hern.Sot.. 135, 952. Hahn. S..Ponce. F. A , . Tiller. W . A . Stojanoff. V . , Bulla. 0.A . P.. and Castro. W . E. (198XJ.J . Appl. Phv.r. 64, 445. Haukins, G. ,4., and Lavine, J . P. (19891, J . Appl. Phys. 65, 3644. Heitimann. M.. Bergholz. W . . and 1)ellith. M . 11993) J . A p p l . Plivs.. to be published. H u . S. M . (I98OJ. A p p l . P/iv.v. Lerr. 36, $61. Inoue. N . . Osaka. J . . and Wada. K . (1982).J . E'lc~.rroc./ic~rn. Soc,. 129, 2780. Jastrzebzki. L . (1990). In Seniic.onclrrt ! o r .Stlic.ow 1990. H . R . Huff. K. J . Barrdclough and J . Chikawa (eds.).p. 614. Electrochem. Soc., Pennington. N . J . Jastrzeb4i. L.. Zanrucchi. P.. Theh;iult. I > . . and Lagowski. J . (1982).J . Elecrrochrm. Sot. 129, 1638. Jasti-Leb\ki. L.. Soydan. R.. McGinn. J . . Kleppinger. R., Blurnenfeld. M., Gillespie. G . . Armour. N . . Goldsmith. B., Henry. W.. and Vecumbra. S. (1987). J . Elec.trcwhc~m. S w . 134. 1018. Vol. 3, S. P. Keller led.). de Kock. A . J . R. (1980). In Htrnclhocd ou .Sr/~trc~onduc~rors. p. 247. North-Holland, Amsterdam. de Kock. A . J . R.. Rocksnoer. P. J . . and Boonem. P. G . T . (1974). J . C 211. c7.s

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Kolbesen, B. 0. (1985). Summer School on Semiconductor Physics, Sao Paulo, Brazil. Kolbesen. B. O., Cerva, H., Gelsdorf, F., Zoth, G. and Bergholz. W. (1991). In Defects in Silicon 11, W. M. Bullis, U . Gosele and F. Shimura (eds.), p. 371. Electrochem. Soc., Pennington, N .J. Kolbesen, B. O., and Muehlbauer, A. (1982). Solid State Electron. 25, 759. Lascik. 2.. Booker, J. R., Bergholz. W.. and Falster, R. (1989). Appl. Phys. Lett. 55, 2625. Livingston, F. M., Messoloras, S . , Newman, R. C., Pike, B. C . , Stewart, R . J., Binns, M. J . , Brown, W. P., and Wilkes J. G. (1984). J . Phys. C: Solid St. Phys. 17, 6253. Marioton, B. P. R., and Gosele, U. (1988). J . Appl. Phys. 63, 4661. Matsumoto. S . , Ishihara, I., Kaneko, H., Harada. H., and Abe, T . (1985). Appl. Phys. Lett. 46, 957. Messoloras. S . , Schneider. J . R., Stewart, R. J., and Zulehner, W. (1989). Semicond. Sci. and Techno/. 4, 340. Nozaki, T . , Yatsurugi, Y ., Akiyama, N., Endo, Y ., and Makide, Y. ( 1974). J . Radioanal. C h e m . 19, 109. Ogushi, S . . Hourai, M . , and Shigematsu, T. (1992). MRS Spring Meeting. San Francisco, Abstract No. E1.4. Ourmazd, A., Schroeter, W., and Bourret, A. (1984). J . Appl. Phys. 56, 1670. Ourmazd, A., Taylor, 0. W., and Berk, J. (1987). Phys. R e v . L e f t . 59, 213. Patel, J. R . , Jackson, K. A,, and Reiss. H. (1977). J . Appl. Phys. 48, 5279. Petroff, P. W., and de Kock, A. J . R. (1975). J . Cryst. Growth 30, 117. Ponce. F. (1985). I n s t . Phys. Conf. Ser. 76, I. Reiche. M.,Reichel, J., and Nitzsche, W. (1988). Phys. Srat. Sol.(a) 107, 851. Rivaud. L..Anagnostopoulos, C. N . , and Erikson, G. R. (1988). J . Electrochem. Soc. 135, 437. Rocksnoer, P. J . , Bartels, W. J., and Bulle, C. W. T. (1976). J . Cryst. Growth 35, 245. Rocksnoer, P. J . , and van den Boom, M. M. B. (1981). J . Cryst. Growth 53, 563. Schomann. F., and Graff, K. (1989). J . Electrochern. Soc. 136, 2025. Secco d’Aragona, F. (1972). J . Electrochem. Soc. 119, 948. Seeger, A,. and Chik, K. P. (1968). Phys. Stat. Sol. 29, 455. Seibt. M. (1990). In Semiconductor Silicon 1990, H. R. Huff, K. J . Barraclough and J. Chikdwa (eds.), p. 663. Electrochem. SOC.,Pennington, N . J . Shimura, F.. Hockett, R. S. , Reed, D. A , , and Wayne, D. H. (1985). Appl. Phys. Lett. 47, 794. Swaroop, R.. Kim, N., Lin, W., Bullis, M., Shive, L., Rice, A ,, Castel, E . . and Christ, M. (1987). Solid State Technology (March), 85. Stavola, M.. Patel, J. R., Kimerling, L. C., and Freeland, P. E. (1983). Appl. Phys. Lett. 42, 73. Sumino, K., Harada, H., and Yonegawa, I . (1980). Jpn. J . Appl. Phys. 19, L49. Tachimori, H . , Sakon, T., and Kaneko, T. (1990). 7th Keitusho Kohgaku Syrnp. of Japan SOC.of Appl. Phys., JSAP Catalog No: AP 902217. Takeno. H.. Ushio, S. , and Tanekada, T. (1992). MRS Spring Meeting. San Francisco, Abstract No. E1.6. Tan, T. Y.. and Tice, L. K. (1976). Phil. M a g . 34, 615. Tan, T. Y Gosele, U . , and Morehead, F. F. (1983). Appl. Phys. A31, 97. Tanner, B. K. (1976). X-Ray Diffraction Topography. Pergamon Press, Oxford. Tempelhoff. K.. Spiegelberg, F., Gleichmann, R., and Wruck, D. (1979). Phys. Star. Sol.(a) 56, 213. Tiller, W. A., Hahn, S . , and Ponce, F. A. (1986). J . Appl. Phys. 59, 3255. .1

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Tsii. H . L. (1985). J . A p p l . P h n . 58. 377.5. Voronkov. V. V . (1982).J . C n . \ r . ~ ; t - o w r / i59, 625. van Werep. D. A . . Gregorkievicz. ‘I.. Hrkman H . H.. and Ammerlaan. C . A . J. (1986). M o f e r . Scieric c F o r u m . Vol. 10-12. p 1009 Trans Tech Publications Ltd.. Aederinannsdorf. Switzerland. Wright-Jenkins, M. (1977). J . Elec / r ( ~hcm. t . S ( J ( , . 124, 757. Yamabe. K.. Taniguchi. K . . and Mictw\hita. Y . (1983). In Defrcfs in Silicon. eds. W . M. Bull15 and L . C. Kimerling. p. 629. The Electrochern. S O C . , Pennington. N . J . Zulehner. W . ( 1989). In Srw7ic.e~r7dtr~ lor.\ . /wiptrrl/rc.s clnd Dyfc.c.r.5 in Grorrp / v Elernen/.$ t i n t / ///-V (‘ornponer7/.\. 0. Madelung and M . Schulz (eds.). p. 391. Landolt Boernstein Yew Series I I I ~ 2 2 b .Springer. Herliri

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SEMICONDU( I O K S A N D SEMIMETALS. VOL 42

C H A P T E R 13

Int rinsidhternal Get tering F . Shimura DEPARTMENT OF MATERIALS ScII;N('E SHIZUOKA INSTITUTE OF SCIENCE AND TECHNOLOGY, SHIZUOKA, JAPAN

I. 11.

INTRODUCTION

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SURFACE A N D INTERIOR

. . . . . . . . . . . . . MICRODEFECTS . . . . I . Surfuce Microdej~c.tc . . . . . . . . . 2. Interior Microde/iv.i.\ . . . . . . . . . 3. Summary of Proc-c~.~s-lndrct~rd Microdeferis

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. . . . . . . . . . . . . . . . . I . General Remurk.\ . . . . . . . . . . . . . . 2. E/irninution oJ'u C'iinitrtnination Source . . . . . 3. fntrinsicllniernul Getrering . . . . . . . . . . 1v. O X Y G E N BEHAVIOR IN SII.I('ON . . . . . . . . . . . I . 0.rvgen 6fec.i on Silk o n Wqfer Properties . . . . 2. Oxygen Precipitution crnd Redissolution . . . . . 3. Oxygen Oui-Dijfi/.\ion and Denuded Zone Formation v. INlERNAL. GETTERING PROCESS A N D MECHANISM. . . . I , Thermul Cycle . . . . . . . . . . . . . . . . 2. Geirering Mechanism . . . . . . . . . . . . . 3. Geriering Sinks . . . . . . . . . . . . . . . VI. SUMMARY . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . .

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577 579 5 80 583 590 593 593 596 596 599 599

599 606 610 610 61 I 612 614 615

1. Introduction

A modern VLSI/ULSI fabrication process includes hundreds of various steps. The process involves mainly subjecting polished Czochralski (CZ) silicon wafers to a variety of chemical, physical, and thermal treatments to fabricate active and passive device elements in the wafer surface region. Thermal oxidation and diffusion are usually performed at temperatures around 900°C or higher. Thus silicon wafers experience severe steps starting from the crystal growth through t h e complete device fabrication via wafer shaping processes. Even in recent high-quality silicon crystals, which are grown without any threading or observable dislocations. various kinds of microdefects are induced during thermal processes. Contamination, particularly with transition metals, during thermal processing initiates surface microdefects, while interior microdefects in

577 Copynght Q 1994 hy Acddemlc Press. Inc All rights of reproduction in any form reserved. ISBN 0-1?-752142-9

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CZ silicon wafers are caused exclusively by oxygen precipitation, which depends on various factors as discussed later in this chapter. Although there are many possible causes for device yield loss, the electronic device properties are greatly degraded by transition metals (e.g., Fe, Ni, Cu, Cr), when these impurities and the secondary defects are located in the device regions (Shimura, 1989) as extensively discussed in Chapters 12 and 14 in this volume. These elements are ubiquitous in a silicon processing environment, and unfortunately from the electronic device point of view, they have (i) extraordinary high diffusivity, (ii) low solubility and steep temperature dependence, and (iii) deep levels in the silicon forbidden band gap (Bergholz, et al., 1991). It is thus necessary to eliminate the detrimental effect of these impurities in order to ensure the high performance of electronic devices. In the fabrication of VLSI/ULSI devices, dry etching processes have been replacing wet etching processes in which silicon wafers are immersed in liquid etching reagents. Wet etching offers a low-cost, reliable, high-throughput process with excellent selectivity for the most processes; however, it is not capable of reproducible and controllable transfer of patterns in the micrometer or submicrometer range, which is required for VLSIKJLSI fabrication. Dry etching processes, which are based primarily on physical sputtering, ion-beam etching, or plasma etching, offer several advantages over the counterpart wet processes. However, dry processing has a tremendous contaminating capability and provides local heating and kinetic energy for contamination of the silicon wafer surface. Since reactive-ion etching (RIE) can selectively etch one chemical species in favor of another, it is possible to concentrate the residual species on the surface of the substrate, which is then driven into the circuit. i n particular, metallic impurities (e.g., Fe, Ni, Cu, Cr) can be sputtered from the chamber surfaces or components that consist of these elements and can then be deposited on the surfaces being etched. The intentional components of thin films (e.g., metal films or silicides) can also be the source of metallic contamination. Furthermore, reduced dimensions, particularly when a trench structure is used, are proving to be very difficult to clean, both from a particulate point of view and from a chemical solubility point of view, since the surface tension of the cleaning fluids is quite high in their pure states. Consequently, the contamination problem due to impurities has become more serious in the VLSI/ULSI era. The elimination of the effects of defects and impurities can be achieved through three steps: (i) suppression of the sources that may generate defects, (ii) annihilation of existing defects, and (iii) removal of impurities from the device regions in a silicon wafer. The process that accomplishes

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( i ) and ( i i i ) , particularly ( i i i ) in a narrow sense, is generally referred to as Krttrring. The term grftrring was originally used by Goetzberger and Shockley (1960)for the process of removing metallic impurities from the device region by a predeposited surface layer of either boron oxide or phosphorus pentoxide on a silicon wafer. Since metallic impurities are highly mobile, they diffuse from the surface of a wafer through the silicon lattice into the device regions very easily at processing temperatures. Gettering thus concerns mainly the removal of transition metals that diffuse quickly. cause surface microdefects (Shimura, Tsuya, and Kawamura, 1980a), and make lattice defects electrically active. The purpose of gettering is primarily to create a defect-free surface region in a silicon wafer used for electronic device fabrication. The gettering process involves three steps: ( i ) impurities are removed from the surface of a wafer, ( i i ) they then diffuse through the silicon lattice into certain gettering sinks at a position away from the device region, and ( i i i ) they are grttrred or captured by the gettering sinks. The gettering technology is one of the keys in the scheme of drjecr enginerring (Gatos, 1990; Rozgonyi, 1981; Rozgonyi, et al., 1987; Rozgonyi and Kola, 1990). 11. Surface and Interior Microdefects

Silicon microelectronic circuit devices are fabricated through various procesfes from the crystal growth through device formation processes. Figure 1 shows the steps for silicon device fabrication and the defects that can be induced into the silicon wafer. For convenience, these defects are classified into two categories: (i)grown-in defects and ( i i ) processinduced defects, which will be further classified into surface and interior defects. The major grown-in defects in high-quality silicon crystals for VLSliULSl are intrinsic point defects and impurities and their clusters. It should be emphasized that those defects listed in Fig. 1 may interact strongly with each other. Dislocations or stacking faults are not observed in the as-grown silicon crystals; however, their origin may inherently exist there and those lattice defects can be actualized by the subsequent thermal processes. In that case, the process-induced defects may more suitably be called process-grnrrated defects. Although process-induced defects are discussed in Chapter 12 in this volume. this section reviews briefly the surface and interior microdefects in terms of their origin and behavior, since it might be important to learn them for the understanding o f the gettering phenomenon which will be discussed in this chapter.

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I

I

Polvsilicon ’

I

impurities

I

6

I Crystal Growth 1

impurities point defects Grown-in Defects

. dopant striations oxygen donors microdefects -

dislocations

6 contamination Processes

mechanical damage

--.warpage

0 slip dislocation

I-}

Process-induced

surface microdefects stacking faults dislocations oxygen precipitates warpage

FIG.I . Semiconductor silicon manufacturing and device fabrication processes, and defects induced into silicon (Shimura, 1989; reprinted with the permission of Academic Press, Inc.).

I . SURFACE MICRODEFECTS a . General Remarks

Surface microdefects that manifest themselves as small saucer etch pits (S-pits) with a typical density of about 106/cm2are commonly generated in the surface of polished silicon wafers or epitaxial silicon films subjected to thermal oxidation at temperatures higher than 1100°C in a “not clean” furnace (Tsuya and Shimura, 1983). These surface microdefects have been attributed to contamination with transition metals during thermal processes (Pearce and McMahon, 1977; Shimura, et, al., 1980a). Figure 2 shows chemically etched figures of surface microdefects revealed by the Sirtl etchant for CZ silicon wafers subjected to different heat treatments in a “not clean” furnace. These figures indicate that ( i ) surface microdefects generated by wet 0, oxidation are larger in size than those generated by dry 0, oxidation, and (ii) these microdefects grow into large stacking faults by prolonged or repeated heat treatment at high temperatures. Moreover, it has been found that the density of

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IN1 KINbIC / I N T E R N A I GETTERINC

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surface microdefects greatly depends on the cleanliness of the furnace used. b. Nutiire

The characterization by means of TEM and AEM suggests three different stages of surface microdefects that manifest themselves as S-pits by preferential chemical etching. but not as linear etch pits, which commonly correspond to stacking faults. The first stage is a tiny cluster of predominantly transition metals, which is so small that it does not show any visible contrast in the TEM image (Tsuya and Shimura, 1983). The second

F I G .2. Etched figures of surface defects delineated by Sirtl etching for ( 5 1 1 ) CZ silicon wafer3 subjected to different heat treatment (Shimura. 1989; reprinted with the permission 0 1 .Academic Press, Inc.).

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FIG.3. TEM micrograph of surface microstacking fault in CZ silicon subjected to heat treatment at I100"C for 2 hrs in wet O2 (Shimura, et al., 1980a).

stage is a small stacking fault with the impurity clusters at the central region of the fault plane as shown in Fig. 3 (Shimura, et al., 1980a). The stacking fault is extrinsic in nature and is bounded by a Frank partial dislocation loop, i.e., the same nature as a common OSF. The third stage is a small stacking fault whose Frank partial loop is heavily decorated with impurity clusters, often whiskers, as shown in Fig. 4 (Shimura, et al., 1980a). The impurities, which are located in the central region of the stacking fault and decorate the Frank loop, have been identified as copper or a copper-containing compound by STEM-EDX analysis (Shimura, et al., 1980a). Other transition metals such as Ni, Fe, Co, and Cr have also been observed to cause different types of surface microdefects (Stacy, Allison, and Wu, 1981).

c . Formation Mechanism The morphology of surface microdefects depends on the extent of contamination and on the nature of contaminants, as well as on the heat treatment conditions. A schematic model for the formation and growth of surface microdefects that result in the three different stages is shown in Fig. 5 (Shimura and Craven, 1984).Transition metals are supplied from the heat treatment environment and agglomerate in the surface region of

13. I N T R I N S I C / I N T E R N AGETTERING L

583

F I G . 3 . TEM micrograph of s u r f x e microstacking fault in CZ silicon subjected to heat treatment at I I(WC for 2 hrs in wet 0:. Frank partial dislocation loop IS decorated with whisker precipitates of Cu (Shirnura. et al.. 19XOa).

a wafer during a thermal process at a high temperature. At this stage, these agglomerates may cause elastic strain around them. but lattice defects such as stacking faults are not formed yet. After further agglomeration of impurities, with the resultant formation of larger clusters and proceeding oxidation. extrinsic stacking faults are generated at these sites as in the way of common OSF formation (Hu, 1974). If the contamination continues after the formation of stacking faults, the contaminants will be trapped preferentially at the Frank partial loop or decorate the stacking fault, resulting in stabilization of both the stacking faults and the contaminants themselves. By absorbing self-interstitials, these small stacking faults can grow into larger ones. which can be observed as linear etch pits by preferential chemical etching. 2.

~ N ERIOR I

DEFECTS

u . Origin

Thermally induced interior defects or bulk defects in CZ silicon crystals are primarily and most exclusively caused by oxygen precipitation. As

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transition metal contamination

I wafer

/

transition metal contaminant

e l 0

transition metal

luster

extrinsic-type stacking fault

O

transition metal decoration

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1-7 FIG.5 . Schematic illustration showing formation and growth of surface microdefects in a silicon wafer (Shimura and Craven, 1984).

discussed in Chapter 2 in this volume, since oxygen is usually supersaturated in CZ silicon at modern processing temperatures, heat treatment leads to oxygen precipitation, which results in the formation of SiO, (x = 2 ) precipitates. Oxygen precipitates consists of amorphous or crystalline SiOz with a volume V,, per SiO, unit of roughly two times the atomic volume VSi in the silicon lattice. Accordingly, the precipitate growth can proceed either by relieving the excessive stresses by inducing plastic deformation of the silicon matrix, or by emitting one silicon selfinterstitial for every two oxygen atoms incorporated into the precipitate

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in the surrounding silicon matrix (see Chapter 9 in this volume for details). The process of self-interstitial emission is, in principle, similar to the process that occurs during surface oxidation at the Si0,-Si interface (Hu, 1974). The main difference is that the overwhelming part of the volume expansion during SiO, formation due to surface oxidation is accommodated by viscoelastic flow toward the surface of t h e oxide film (Tan and Gosele, 1981), whereas such a process is not possible within a silicon crystal. As in the case of surface oxidation, self-interstitials generated by oxygen precipitates may condense into extrinsic-type dislocations or stacking faults. The straightforward correlation between oxygen precipitation and interior defect generation is made by referring to Figs. 6 and 7. The [Oil change shown in Fig. 7 was obtained for the same CZ silicon samples that indicated interior defects revealed by chemical etching shown in Fig. 6. It is quite obvious that a higher oxygen precipitation results in a higher density or larger volume of interior defects.

Fit, h la) Etched figures of internal defects delineated by Wright etching for I I I I ) CZ \iIicon octant samples subjected t o heat ti-eatmrnt for 64 hrs at temperatures shown: optical photograph of octants (Shimura. I W Y : Reprinted with the permission of Academic Press. Inc )

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FIG.6 ( b ) . Etched figures of internal defects delineated by Wright etching for (111) CZ silicon octant samples subjected to heat treatment for 64 hours at temperatures shown: optical micrographs of etch pits in each octant (Shimura, 1989: Reprinted with the permission of Academic Press, Inc.).

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INTRINSIC'/INTERNAL GETTERING

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FIG 7 lntervtrtial oxygen concentrdtiim change in CZ silicon samples as a function of heat treatment temperature for 64 hr, in dry O? (Shimura and Tsuya. 1982a)

h. Natrrre The nature of interior defects depends primarily on the annealing temperature and heat-treatment sequence and has been extensively characterized by TEM (Bender, 1984; Bourret. Thibault-Desseaux and Seidman. 1984; Maher, Staudingher. and Patel, 1976; Matsushita, 1982; Ponce, Yamashita. and Hahn, 1983; Shimura, et al., 1980a; Shimura and Tsuya. 1982b; Tan and Tice. 1976). The first stage of thermally induced interior microdefects in CZ silicon is S O , precipitates, which are categorized into roughly three groups in terms of the precipitate morphology according to the precipitation temperature: ( i ) low-temperature range (<750"C), ( i i ) medium-temperature range (850-10WC), and (iii) hightemperature range ( 1 100-1200"C). After a long period of heat treatment at 650-750°C. SiO, microprecipitates are generated in CZ silicon. The TEM contrast analysis characterizes the shape of these microprecipitates as a tiny platelet. Among dense microprecipitates, dislocation dipoles such as shown in Fig. 8 are frequently observed (Shimura. et al.. 1980a). The dipoles consist of two parallel dislocations in the (I10) directions. Heat treatment at a temperature in the medium range for CZ silicon generates large square-shaped platelike precipitates on (100) planes with (110) edges such as shown in Fig. 9 (Shimura, et al., 1980a). Large precipitates often give rise to prismatic punching of dislocation loops and precipitate-dislocation com-

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Fic. 8. TEM rncirograph of oxygen precipitates and dislocation dipole in CZ silicon subjected to heat treatment at 750°C for 64 hrs in dry O2 (Shirnura and Tsuya, 1982b; reprinted with the permission of The Electrochemical Society, Inc.).

plex (PDC) (Tan and Tice, 1976). A typical TEM image of PDC observed in CZ silicon annealed at 1000°C for 64 hrs is shown in Fig. 10. In this temperature range, stacking faults associated with oxygen precipitates at the central region, such as shown in Fig. 11 (Shimura, et al., 1980a), are also frequently observed. Heat treatment for CZ silicon at a temperature in the range between 1100 and 1200°C forms large octahedral amorphous SiO, precipitates, which often generate punched-out dislocation loops (Matsushita, 1982; Shimura, 1981b; Shimura, et al., 1980a). Figure 12 shows TEM micrographs of two different views for an octahedral precipitate observed in CZ silicon annealed at 1150°C for 64 hrs (Shimura, 1981b). A TEM picture of prismatic punched-out dislocations generated by an octahedral precipitate is shown in Fig. 13 for example. This dislocation raws, denoted D , , D,, D,, and D,, are located along <110> directions. As just described, the nature of oxygen precipitates and interior defects, as a whole, induced in CZ silicon depends greatly and primarily on

FIG.9. T E M micrograph of platelike oxygen precipitate in CZ silicon subjected to heat treatment at 950°C for I6 hrs in dry 0: (Shimura. et al.. 1980a).

FIG. 10. TEM micrograph of precipitate-dislocation complex in CZ silicon subjected to heat treatment at IO00"C for 64 hr\ in dry O?(Shimura and Tsuva. 1982a: reprinted with the permission of The Electrochemical Society. lnc.).

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FIG. I I . TEM micrograph of bulk stacking fault with oxygen microprecipitate colonies in CZ silicon subjected to heat treatment at 950°C for 16 hrs in dry O2 (Shimura, et al., I980a).

the annealing temperature; however, for the formation of different types of oxygen precipitates, the variation of Gibbs free energy of the crystal during the heat treatment should be also considered by taking into account the elastic strains due to precipitates and the relaxation from emitting silicon self-interstitials (Yasutake, et al., 1984). Consequently, the type and density of internal defects induced in CZ silicon wafers depends greatly on various factors, including the concentration of oxygen, extrinsic and intrinsic point defect, subsidiary impurities such as carbon, and heat treatment conditions.

3 . SUMMARY OF’ PROCESS-INDUCED MICRODEFECTS Process-induced microdefects in CZ silicon wafers, excluding OSFs and slip dislocations, can be classified as either surface or interior (bulk) defects as summarized in Fig. 14. Contamination, particularly with transition metals, initiates surface microdefects. On the other hand, interior

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59 1

P I ( # I 2 TEM micrograph of oct,ihedi,il oxygen precipitate in CZ \illcon subjected to heat treatment at 1150°C for 64 hi\ in dry 0: ( a ) dark-field weak-beam image viewed from I I I I I nnd tb) bright-field image viewed tiom I 1101 (Shimura. 1981b. reprinted with the permi\sion ot North-Holland Publishing C ompany)

microdefects are caused exclusively by oxygen precipitation, which depends on various factors as discussed later in this chapter. Oxygen precipitates, SiO?. can be interior microdefects by themselves, or can originate secondary lattice defects such as dislocations and stacking faults by emitting excess silicon self-interslitials. These interior defects play a key role as internal gettering sinks t o r surface microdefects. On t h e other side of this double-edged knife, the interior defects may degrade the mechanical strength of silicon wafers when too many are generated (see Chapter I 1 in this volume): this result\ in serious warpage of silicon wafers. Consequently, it is essential to control oxygen precipitation to an optimum level during the thermal processes in order to maximize both the gettering effect and mechanical strength and, in turn, the device performance and fabrication yield.

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FIG. 13. TEM micrograph of octahedral oxygen precipitate and punched-out prismatic dislocation loops in CZ silicon subjected to heat treatment at I1OO"C for 16 hrs in dry 02: (a) viewed from [121], and (b) viewed from [ I l l ] (Shimura, et al., 1980a).

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Process-Induced Microdefects

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INTRINSIC /IN TEKNAI. GETTERING

-

Transition-Metal _____I__. -___Contamination ._________

LMetal Cluster w G S t a c k i n g Fault

Dislocation

Nitrogen

Stacking Fault

kvd 14. Summary of process-induced microdefects in CZ silicon wafer (Shirnura. 1989; reprinted with the permission of Acxieniic Prehs. Inc.).

111. Gettering

1. G E N E R AREMARKS L A gettering technique may therefore eventually be defined as a method to supply effective sinks for harmful impurities. Until now, various types of gettering techniques have been investigated for application to silicon wafers (Shimura, 1989). Thesc techniques can be classified into three categories for convenience: ( i extrinsic or external gettering (EG). ( i i ) intrinsic or internal gettering ( I G ) . and ( i i i ) chemical gettering (CG). External gettering involves the use o f r.urrrnri1 mruns to introduce gettering sinks into a silicon lattice, predominantly at the back surface region o f a silicon wafer. One of the disadvantages of EG is that the EG process itself can introduce additional contamination into the wafer including the front surface. In contrast, internal gettering uses thermally induced intrrior d s f i ~ c t as s gettering sinks in a silicon wafer. therefore the 1G process is clcan in principle. This gettering can be called intrinsic since the gettering will occur nutiirtilly or i n f r i i i s k c i / l y to some extent in CZ silicon wafers that are thermally processed. 'Therefore this gettering phenomenon was first called in-situ g d r c r i n g (Korgonyi. Deysher, and Pearce, 1976). and then intrinsic, ,q:cttcring (Tan, Gardner, and Tice. 1977). Since then the terms intrinsic gortrring and internti1 gottering have been used equivalently in the related community. However, some investigators prefer in-

594

F. SHIMURA

ternal gettering, which occurs internally to intrinsic gettering in order to avoid possible confusion with the terms of intrinsic semiconductor, intrinsic point defects, intrinsic stacking fault, and so on (Weber, private communication; Tan, 1991). This allows the author to intentionally use intrinsiclinrernal gettering (Shimura, 1991) for the title of this chapter. According to the definition of intrinsiclinternal gettering, the traditional EG can be referred to as extrinsiclexternal gettering. In this chapter, however, the gettering techniques are called IG and EG, respectively, for convenience. In addition, a new EG technique using a uniform network of interfacial misfit dislocations that are deliberately introduced at epitaxial-layer (Si)-epitaxial-layer (Si-Ge)-substrate interfaces has been recently developed (Salih et al., 1984). The lattice dilation required for misfit dislocation formation is obtained by incorporation of electrically inactive germanium during the silicon epitaxial growth. This is readily accomplished by adding GeH, to a flowing gas mixture of SiH,/H, in a CVD reactor. The controllability of the misfit dislocation density is achieved by adjusting the Ge content in the silicon matrix after a critical thickness of the lattice mismatched layer is surpassed. Moreover, Rozgonyi has recently proposed another way to introduce dislocation loops as gettering sinks by low- and high-energy ion implantation in the vicinity of a wafer surface particularly of an SO1 structure (Rozgonyi, private communication). Since these gettering sinks are extrinsically introduced into the internal region of a silicon wafer, this technique can be referred to as extrinsiclinternal gettering. On the other hand, chemical gettering (CG) does not provide gettering sinks as EG and IG do, and instead is performed during oxidation or heat treatment in chlorine-containing ambients. In this case, the elimination of metallic impurities is by their evaporation as a result of chemical reaction with chlorine, resulting in volatile metal chloride (Robinson and Heiman, 1971). Figure 15 depicts various gettering techniques that have been categorized into three groups (Shimura, 1989). It should be noted that most gettering phenomena may involve more than one category since the phenomena can affect each other more or less. For example, oxygen precipitation, which results in IG sinks, can be affected by externally induced damage (Takano et al., 1981) and deposited films (Shirai, Yamaguchi, and Shimura, 1989) on the back surface. In both the cases of EG and IG, for the formation of defect-free surface regions impurities must migrate from the front surface through the silicon lattice toward the gettering sinks. The diameter of silicon wafers used for electronic device fabrication has been steadily increased with the development of silicon technology. The increasing diameter is generally

13.

595

INTRIN\I( / I N I E R N A L GETTERING

HCI, TCE

Extrinsic/lnternal Gettering

I

(

I

detects

"

Stress Defects

111 I I , i I I

P diffusion

Ion implantation Laser irradiation

Sand-blasting Mechanical abrasion

I Extrinsic/External Getterind FIG. IS. Schematic illustration 5howing various gettering techniques for silicon wafers.

accompanied by increasing thickness (e.g.. 525, 725, and 775 Fm for loo-, 200-, and 300-mm-diam wafers. respectively); that is, in the case of EG, the contaminant impurities to be gettered must migrate a longer path from the front surface toward the backside gettering sinks in a larger-diameter wafer. I n addition, the potential advantage of reduced-temperature device processing has been widely recognized for the VLSI/ULSI technology. However, the diffusivity as well as the solubility of impurities to be gettered drastically decrease with a decreasing temperature. Under the preceding circumstances. it is desired that the gettering sinks be located close t o the wafer front surfacc, but far enough from the critical device regions. as is performed by 1G. The aforementioned rxtrinsiclinternal gettering technique using a uniform network of interfacial misfit dislocations can be an alternative or complement. Although the effectiveness of the technique has been well demonstrated. the complicated process and high cost might be a serious barrier to the VLSI/ULSI production. Consequently, the disadvantages of EG techniques, in addition to various limitations of individual ones. and the advantages of 1G will become more apparent as we approach the ULSl era.

596

F. SHIMURA

2. ELIMINATION OF A CONTAMINATION SOURCE Various gettering techniques have been investigated, and some of them have been extensively utilized in the silicon semiconductor industry. It should be noted at this point, however, that the primary effort undertaken to eliminate the detrimental effect of metallic impurities is to remove the sources of the harmful impurities that contaminate silicon wafers during the entire fabrication processes. Such contaminant sources that have been identified in silicon processing include (i) chemicals used in etching and cleaning processes, (ii) stainless steel parts of processing equipment, (iii) heating coils, (iv) graphite susceptors, and (v) metallic tools such as tweezers. In order to minimize the level of metallic contamination from these sources, the “super clean technology” (Ohmi, 1991) has been of great interest. The technology may include the following procedure that has been established as effective: (i) reducing process temperatures, (ii) subjecting furnace tubes to frequent chemical cleaning, and (iii) use of a double tube configuration in furnaces. Moreover, cassete-to-cassette operations in handling wafers has reduced the contamination originating from the human body and human handling. The ideal situation would be the establishment of perfectly clean processes, which do not need any gettering techniques; however, the practical silicon device fabrication processes at present seem to require some gettering treatment for the processing wafer, since gettering studies in increasing number have consistently shown that gettering operations are capable of overcoming defect and impurity problems arising during device processing. In fact the gettering techniques used in IC processing have been widely found to be beneficial to device performance and device manufacturing yield as discussed in Chapter 14 of this volume. In addition, it has been recognized that no single gettering may be adequate for all processes, and a tailored gettering program is required for the particular technology that utilizes a sequence of many processes. In any case, however, the limit of gettering capability should be recognized.

3. I N T R I N S I ~ ~ N T E RCETTERINC NAL As shown in Fig. 15, IG utilizes internal defects as gettering sinks. Therefore, IG effectiveness depends on the type and density of interior defects (Shimura, Tsuya and Kawamura, 1981; Craven, 1985; Nauka et al., 1985a), which in turn depend on several parameters as discussed later. Figure 16 shows surface and interior microdefects delineated by chemical etching for (1 11) CZ silicon wafers subjected to the two-step heat treat-

13.

INTRINSIC / I N TERNAI. GETTERING

597

Fic;. 16. Surface and intenor microdetects in ( I 1 I ) CZ silicon wafers with different [O,],, wbjected to two-step heat treatment (9SOTi16 hrsidry O2 + 11OO"C/2hrsiwet 0 : )tShimiira. 1989: reprinted with the permi\$ion of Academic Press. Inc.).

ment described in the caption. These three silicon wafers have different initial interstitial oxygen concentration (lo,],,1 values shown in the figure; that is, they are called low, medium, and high [O,],, wafers for convenience. In the low [O,],, wafer shown in Fig. 16(a), no interior defect is generated but dense microdefects appear in the surface because of no 1G effect. In the high [O,],,wafer shown in Fig. 16(c), dense interior defects are generated through the front surface to back surface. Because of the strong lG effect. no surface microdefect appears; however, the interior defects themselves do appear in the wafer surface. On the other hand, in the medium [O,],,wafer, a considerable amount of interior defects (i.e.. 1G sinks) and a denudcd zone ( D Z ) of about 30 pm depth where no defect is observed are formed, as shown in Fig. 16(b). As a result, no defect is observed in the surface of the wafer. With Figs. 16(a), 16(b), and 16(c). the depth (or width) of denuded zone ( W,,) can be defined as W,, = x , = 30 K r n (a finite value), and = 0, respectively. Electronic devices are fabricated in the denuded zone with a finite depth or in an epitaxial layer formed on the denuded zone. Figure

598

F. SHIMURA

Fic. 17. Cross section of IG-treated ( 1 11) CZ silicon wafer used for fabrication of shallowjunction bipolar transistors (Shimura, 1982; reprinted with the permission of The Electrochemical Society, Inc.).

17 shows, as an example, a cross section of shallow-junction bipolar transistors fabricated in an IG treated epitaxial silicon wafer (Shimura, 1982). Although the primary role of interior defects generated by oxygen precipitation is to provide gettering sinks in a silicon wafer, another important function of the interior defects is to capture and recombine minority carriers (Huff and Shimura, 1985; Craven, 1985). This capability may be disadvantageous for some device circuits, such as photovoltaic devices, but is generally very advantageous for specific device application such as CCD imagers (Ogino et al.. 1983) and CMOS devices (Anagnostopoulos et al., 1984). As symbolically illustrated in Fig. 16, the key scheme in IG is to form sufficient, but not too many, interior defects under the optimum depth of denuded zone where electronic devices are fabricated. Since interior defects are generated by oxygen precipitation, it is ultimately the key to control the [O,], and the behavior of oxygen in silicon wafers in order to utilize IG for the electronic device fabrication.

13.

599

INIRlN\lC /IN rFRNAl G E r T E R I N G

IV. Oxygen Behavior in Silicon

I . OXWENEFFECTON SILICON WAFERPROPERTIES Crochralski silicon usually contains oxygen on the order of 10”atoms/ 1 in this volume. N o matter how much oxygen is incorporated in CZ silicon wafers used for device fabrication, the impurity atoms critically affect the properties and yield of electronic devices because of the following three factors (Shimura. 1982): ( i ) interior (bulk) defects generated by oxygen precipitation benefit the 1G effect, ( i i ) mechanical strength of silicon wafer greatly depends on the oxygen concentration and state (degraded by oxygen precipitates or enhanced by dissolved oxygen atoms) (see Chapter I I in this volume), and (iii) oxygen “old“ and “new“ donors are formed by annealing at a specific temperature range (see Chapter 7 in this volume). Figure 18 summarizes the effect of oxygen on silicon wafer properties and the affecting factors. From the I(; point of view it is crucial t o understand the behavior of oxygen, i.e., prccipirtrtion, rcdissolirrion, oirr-di0irsion. and d ~ n u d e d:,one formarion, in silicon wafers in order to postulate enough 1G sinks and mechanical wength simultaneously.

cm) as discussed in Chapter

2.

O X Y G E N P R t ( ’ l P l T A T l 0 N A N D Rt.I)ISSOL.UTION

(I.

Prrciyitution und Redissolririon

The behavior of oxygen precipitation and dissolution in CZ silicon crystals has been extensively investigated. Figure 19(a) shows the IR spectra ranging from 1000 to 1300 cm for as-grown and heat-treated CZ silicon

’

Mechanical Strength /Warp Interstitial Atoms - Dlffuslon

I

I

SiOx Precipi-

1

t I

Bulk Defects

-

IG

Donors l-;:OId“ ([04],[Si04], ...?) New” (SOX)

Si lnterstitials Vacancies Impurities (C, N, H) FIG. 18. Oxygen effects on !he properties o f silicon wafer (Shimura, 1991)

600

F. SHIMURA

WAVELENGTH (pn) 8

9

10

I

I

1 .*,OW"

BOO'C. 16H

WAVELENGTH (p.m)

WAVELENGTH (pm)

8 I

9

10

1

1

1230°C. 2H 1230"C, 2H + W C , 16H

750%. 16H

12WC. 2n +7M'C. 16H

050°C. 16H

1230°C. 2H + 9 W C . 1611

11WC. 16H

1230°C. 2H + l l W C . 16k

11225 cm ' )

1 I

,

,

,

1300 1200 1100 1WO

1300 1200

1100

1000

1300 1200

1

,

1lW

1000

WAVE NUMBER (cm-1)

WAVE NUMBER (cm-1)

WAVE NUMBER ( c m - 1 )

(a)

(b)

(4

FIG. 19. IR absorption (relative transmission) spectra for as-grown and heat-treated CZ silicon at different temperatures in dry 0,. (Shimura et al., 1980b).

crystals (Shimura et al., 1980b). It clearly shows that oxygen precipitation occurs depending on the heat treatment conditions, which results in the decrease in uo3 absorption at 1106 a n - ' due to interstitial oxygen atoms and the increase in us,,absorption at 1225 cm-' due to SiO, precipitates (see Chapters 3 and 4 in this volume). The amount of SiO, precipitates, or precipitated oxygen, strongly depends on the heat-treatment temperature. If those silicon samples with oxygen precipitates are subjected to a subsequent heat treatment at a high temperature such as 1230°C SiO, precipitates are dissolved and oxygen atoms redistribute at interstitial sites (Glowinke and Wagner, 1977; Kaiser, 1957) as shown in Fig. 19(b). The IR spectra for the samples subjected to heat treatments of an inverse order to those shown in Fig. 19(b) are presented in Fig. 19(c). N o oxygen precipitation is observed in the samples that were subjected to a high-temperature heat treatment first, even after the heat treatment that resulted in oxygen precipitation as shown in Fig. 19(a). That is, it is indicated that oxygen precipitation is governed not only by the supersaturation ratio of oxygen (Freeland et al., 1977; Osaka, Inoue, and Wada, 1980), since the first-step high-temperature heat treatment does not affect the oxygen concentration of the samples as shown in Fig. 19(c). Accordingly, it has been suggested that oxygen precipitation occurs dominantly by the heterogeneous nucleation process in silicon (Shimura,

13.

60 1

I N T R I N S I ( . / I N T E R N A L GETTERING

0

1

2

3

4

5

6

7

8

ANNEALING STEP

FIG 20. Interstitial oxygen concentration change in CZ silicon subjected to multistep heat treatment temperature in dry O1(Shiniura and Tsuya, 1982b; reprinted with the permission of The Electrochemical Society. Inc ) .

Tsuya. and Kawamura, 1980b; Inoue. Osaka, and Wada, 1982; Usami. Matsushita, and Ogino. 1984). The change in interstitial oxygen concentration LO,] for CZ silicon crystals subjected to multistep heat treatments is shown in Fig. 20. Group I samples were heat treated at low (750°C). or medium (1000°C) temperature first, then at a high temperature (1230"C), while Group 11 samples were heat treated inversely. In Group I samples, oxygen precipitation (odd-numbered steps) and oxygen redissolution (even-numbered steps) repeat regularly from step 1 through step 8. The [O,] in the samples after even-numbered steps, namely. oxygen redissolution step, is consistent around 10 ppma, which approximates the effective oxygen solubility in silicon at 1230°C. Oxygen precipitation behavior in Group 11 samples differs distinctly from that in Group I samples. It is noteworthy that even during a high-temperature heat treatment, considerable oxygen precipitation occurs in later steps, such as step 3 , when the size of precipitates grown by previous heat treatment is larger than the critical size at 1230°C and the existing oxygen concentration exceeds the solubility at 1230°C. Consequently. the necessary condition for oxygen precipitation in a silicon crystal is the existence o f both nucleation active centers and super-

602

F. SHIMURA 20

o v

aa-grown after 750"G256h anneal. after lOMI'C-256h anneal.

0

-z

n

15-

-

-

E -

iI- 10-

0

-

0 0

-

z W

-

z

F 5

5 -

l

0

,

,

I

I

I

,

,

1

2

'*

saturated oxygen atoms. If either is missing, precipitated oxygen redissolves, and therefore oxygen precipitation does not occur.

b. Redissolution Rate of Precipitated Oxygen In practical device fabrication processes, which usually include thermal processes at a high temperature (> 12OO0C),redissolution of precipitated oxygen may also occur in processing silicon wafers. It is important to understand the redissolution phenomenon as well as oxygen precipitation, since both can critically affect the properties of silicon wafers as shown in Fig. 18. Figure 21 shows the change in [Oil as a function of time of redissolution heat treatment at 1230°C for CZ silicon crystals preannealed at 750°C or 1000°C for 256 hrs in order to precipitate the same amount of oxygen (Shimura, 1981a). As a result of high-temperature annealing, precipitated oxygen redissolves and the oxygen atoms redistribute into interstitial sites, and thus [Oil increases up to the effective solubility at 1230"C, as discussed earlier. However, the oxygen redissolution behavior in the 750°C preannealed silicon distinctly differs from that in the 1000°C preannealed silicon. That is, in the former silicon, the redis-

13.

IN I'RINSI( / I N r E R N A L G E T T E R I N G

603

solution completes in only 15 min or less of annealing with a dissolution rate estimated at >3 x 10'* atomsicm'hr. In the latter silicon, however, the dissolution proceeds gradually for 2 hr with the average dissolution rate estimated at -3 x 10'' atoms/cm'hr. In both the cases, the oxygen dissolution rate is much larger than the oxygen precipitation rate (e.g., -5 x 10" atoms/cm3hr at 750°C). The TEM observations have revealed that dense { 100) platelet microprecipitates of approximately xoo x 800 x 200 A in average size were generated in the silicon sample annealed at 750°C for 256 hrs, whereas in the sample annealed at 1000°C for 256 hrs, precipitate-dislocation complexes consisting of {loo} platelike precipitates of about 4800 x 4800 x 2000 A in average size were generated. Based on t h e TEM observation results, the difference in the oxygen redissolution rate in the CZ silicon first annealed 750 and 1000°C has been described mainly by the difference in the total surface area of oxygen precipitates for the identical AIOi], which dominates the flux of diffusing oxygen. and partly by the dislocation pinning effect on dissolving oxygen atoms. It should be emphasized again that the dissolution rate of precipitated oxygen greatly depends on the precipitation conditions but not on AIOj] itself. c. E''fectii-e Factors of Prcxipittrtion

It has been widely accepted that oxygen precipitation practically requires a nucleation active center and depends on various factors including heterogeneous ones. The amount of oxygen precipitation, A[O,], , during finite annealing can be qualitatively described by the following simplified function (Shimura et al., 1981; Shimura and Tsuya, 1982a):

h[OiI,

=

.f'(uyx7 S , , N,,

F , f),

(1)

where 7 is the annealing temperature, D';."is the diffusion coefficient of oxygen in silicon at 7 ,S, is the supersaturated oxygen ratio at 7,N , is the number of nuclei precipitates larger than the effective critical radius at T . F is the factor characterized by the density and type of existing lattice defects and impurity clusters, and t is the annealing time period. The heterogeneous factors (i.e.. N , , and F ) in Eq. ( 1 ) depend greatly on the concentration of intrinsic point defects and impurities incorporated into the silicon crystals concerned. as shown in Figs. 14 and 18. That is, oxygen precipitation is enhanced by the presence of ( i ) vacancy, ( i i ) an agglomerate of self-interstitials ( i.e., dislocations and stacking faults). ( i i i ) subsidiary impurities such as carbon. nitrogen, and hydrogen. and ( i v ) acceptor impurities. These can provide heterogeneous nucleation centers or enhance oxygen diffusion. On the other hand, it is retarded by

604

F. SHIMURA

( i ) dissolved self-interstitials, and (ii) donor impurities (Shimura, 1989; Shimura, 1991). It should be emphasized that oxygen precipitation does not occur in a silicon wafer when the [O,], is less than a certain threshold or critical concentration [O,], (- 14 ppma in general). As discussed later, the critical concentration plays a very important role in the formation of denuded zone and varies depending on various factors such as intrinsic point defects and impurities in the silicon crystal. It would be a realistic explanation that the oxygen supersaturation plays the determining role in oxygen precipitation in higher supersaturated circumstances (i.e., at a low temperature or for high [O,], wafers), while at low supersaturation (i.e., at a high temperature or for low [O,], wafers) heterogeneous factors play the dominant role. With regard to the growth of oxygen precipitates, it is well established that growth is governed by a diffusion-limited process (Ham, 1958; Wada, Inoue, and Kohra, 1980). Considering the scheme of Czochralski silicon crystal growth (see Chapter 2 in this volume), one may find that every portion of a CZ silicon crystal was grown under different growth conditions. Both the longitudinal and radial, particularly longitudinal, impurity variation is inherent in the CZ batch growth process because of the segregation phenomenon of impurities whose effective segregation coefficient is not unity. Moreover, every portion has been exposed to a different thermal history as a result of its different position along the crystal length and radius. This difference in thermal history greatly affects N , and F in Eq. (1) and, in turn, the oxygen precipitation behavior in silicon wafers prepared from different portions of a silicon ingot (Tsuya et al., 1982; Fraundorf et al., 1985). The effect of prior thermal history of a silicon crystal in the crystal puller on oxygen precipitation is strikingly demonstrated in Fig. 22 for sample wafers prepared for different portions of a CZ silicon ingot that was grown with a continuous feeding CZ method (see Section V.3 in Chapter 2 in this volume) that keeps the melt depth and melt convection constant and ensures the longitudinal uniformity of impurities including oxygen and dopant from the seed to tail ends. Note that the [O,], of all the samples shown in Fig. 22 is identical. The difference in thermal history results in the variation in the size and density distribution of grown-in SiO, precipitates, impurities, intrinsic point defects, and their clusters, which all can be effective heterogeneous nucleation sites, see Eq. ( l ) , for oxygen precipitation. The oxygen precipitation behavior that can be qualitatively described with Eq. ( I ) is depicted in Fig. 23 (Chiou, 1987; Shimura, 1991). Three characteristic regions as a function of [O,], are indicated: (i) zero precipitation, (ii) partial precipitation, and (iii) 100% precipitation (Chiou, 1987).

13.

INTRINSIC / I N T E R N A L GETTERING

605

as-grown

, f

/-

-

750 C 16H 0, + 1000 C 16H O2

50

INGOT POSITION (cm)

Eic, 22 Interstitidl oxygen concentidtion change as a function o f ingot position for continuous-leeding CZ d i c o n ~ t i j e c t e dto different heat-treatment temperature5 in dry O2 (Shirnura IY8Y. reprinted with the perrni\sion o f Academic Press, Inc )

A critical oxygen concentration [O,], that varies depending on various heterogeneous factors is also shown in the figure. Ideally, from t h e IG point of view, precipitated oxygen AlO,] during a finite thermal cycle could be controlled simply by 1 O;],,as a homogeneous nucleation process model claims: however, unfortunately there is considerable variation in AIO,], i.e., AAIOj], for wafers with identical [O f ] ,in , the partial precipitation region, which occurs mostly in practical device fabrication processes. The variation is, as discussed previously, indisputably due to the heterogeneous factors in Eq. ( I ) . In order to minimize AA[O,], and in turn the IG effectiveness, conducting a homogenizing heat treatment at a high temperature ( > 1200°C) on as-grown silicon crystals has been proposed (Shimura, 1982), and it has been demonstrated that the effect of prior thermal history in the crystal puller can be erased to a large extent by a short-time heat treatment at 1320°C for silicon wafers (Fraundorf et al.. 1985).

606

F. SHIMURA

Precipitation

i

.

Partial , 100% precipitation Precipitation

i

INITIAL OXYGEN CONCENTRATION o oil^)

FIG.2 3 . Generic curve showing critical oxygen concentration [O,], and the relation between oxygen precipitation as a function of initial oxygen concentration [O,], (Shimura, 1991).

3. OXYGEN OUT-DIFFUSION A N D DENUDED ZONEFORMATION Generally a denuded zone (DZ) is defined as a surface depth zone where no interior defect is delineated, most commonly by a preferential chemical etching technique. Therefore the DZ does not necessarily mean a defect-free zone. Some interior defects can be observed with other techniques, such as TEM, that are more sensitive than the chemical etching or can be electrically detected even in the denuded zone (Rath et al., 1985). Strictly from the device operational point of view, a DZ should be defined as a wafer surface area that is free of electrically active defects as well as structural defects. For convenience in this chapter, however, a DZ is discussed as a wafer surface zone that is free of interior defects generated by oxygen precipitation. Accordingly a DZ can be formed by oxygen out-diffusion from the wafer surface, resulting in an oxygen-lean region, where the oxygen concentration is not high enough to generate oxygen precipitates (i.e., [O,] < [Oil,), since the critical radius dramatically increases with decreasing oxygen concentration. Such oxygen outdiffusion occurs in the wafer surface region during heat treatment in any ambient (Tice and Tan, 1981). The diffusion of oxygen in silicon is extensively discussed in Chapter 8 in this volume. Assuming that the thickness of the wafer is much larger than the corresponding length of oxygen out-diffusion and that there exist neither oxygen precipitates nor any traps for oxygen atoms, the concentration of

13.

I N I K I N W / I N T E R N A L GETTERING

607

oxygen atoms [O] (not necessarily be intcJrstitialoxygen atoms) at depth x from the surface for annealing temperature T for time t has been well given by the following error function (Ruiz and Pollack, 1978):

101( x , 1 )

=

101, + CIOI,,- [oI,~) erf(xi2W)

(2)

where [O],yis the solid soluhility of oxygen in silicon at T and [O], the initial oxygen concentration in the wafer. The [0],and D y are given by the Eqs. ( 3 ) and (4).respectively (Mikkelsen, 1986):

[O], = 9 x 10" exp( - I .S2/kT) (atoms/cm3).

(3)

D'f'

(4)

=

0.13 exp( - 2.53ikT) (cm?/sec).

in the The oxygen concentration at the SiOz/Si interface reaches case of annealing in an oxygen ambient, and oxygen out-diffuse to the interface where the oxygen may help SiOz growth, while the oxygen concentration at the wafer surface reaches zero in an inert ambient. The out-diffusion of oxygen for both cases is depicted in Fig. 24, where l O~ ~ S. ~l ~, and ~ ~ I0,1,,s,,,2 ) ~ , ~ are the equilibrium concentra[O,,ls, [ O , . ] S ~ O OXYGEN

INERT AMBIENT

I

,

:sll

FIG 24 Schematic illustration rhowing oxygen outdiffuwm (a) in oxygen ambient, and cb) in inert gds ambient (Tice and T . i n , 1981)

608

F. SHIMURA

100WC/64h

>

3

0

10

20

30

DEPTH (pn)

115WCi2h

40

DEPTH (pm)

DEPTH (pm)

FIG.25. Calculated depth profiles of oxygen concentration for silicon wafers with [O,],, of 10. 15, and 20 ppma: (a) (7SOoC/64 hr/02) heat treatment, (b) (100O0C/64 hr/O,) heat treatment, and (c) (11SO0C/2 hr/02) heat treatment (Shimura, 1989; reprinted with the permission of Academic Press, Inc.).

tion of oxygen in Si, in SiO, at the SiO,/Si interface, in SiO, at the ambient-SiO, interface, and in ambient at the ambient-SiO, interface, respectively (Tice and Tan, 1981). Thus, strictly speaking, [O], in Eq. (2) should be replaced with [O,],, and zero for heat treatment in oxygen and inert ambients, respectively. Figure 25 shows the depth profiles of oxygen concentration calculated using Eqs. (2)-(4) in three different heat-treatment cases for silicon wafers with three different [O,], values. Assuming a certain critical oxygen concentration [O,], (e.g., 14 ppma) for the occurrence of oxygen precipitation, the denuded zone depth depending both on [O,], and annealing conditions are obtained as depicted in Fig. 25. Oxygen precipitation occurs in the wafer region deeper than the denuded zone-in other words, in the region whose [Oil is higher than [O,],. It is obvious that the W,, is infinite or equal to the wafer thickness in silicon wafers whose [O,], is less than [O,], (see the case with [O,], = 10 ppma shown in Figs. 25 and 16 (a)). In addition, in the case that the [O,], is extremely high or the diffusion of oxygen is negligibly small, the W,, is nearly zero as shown in Fig. 16(c) and 25(a). It is noteworthy that, in principle, denuded zones are symmetrically formed in both the front and back surfaces of a silicon wafer, and internal defects as IG sinks also distribute symmetrically in the wafer bulk region. Accordingly, in principle an IG treatment will not cause wafer warping or bowing, which can be a serious problem in device patterning, as most EG treatments do. It should be emphasized that, as depicted in Fig. 23, a critical concentration [0,1, may vary with various heterogeneous oxygen precipitation

13.

INTKINSI(./INTERNAL GETTERING

609

factors. Moreover, the diffusivity of interstitial oxygen D F can be influenced by the presence of point defects (Heck, Tressler, and Monkowski, 1983; Gosele and Tan, 1985). subsidiary light impurities such as carbon (Shimura, Higuchi, and Hockett, 1988) and hydrogen (Fuller and Logan, 1957; Newman, 1991 ; Zhong and Shimura. 1993), metallic impurities (Newman, Tipping, and Tucker. 1985), and dopant species (Gass et al., 1980). For example, the effect of carbon on oxygen out-diffusion is shown in the following. The out-diffusion behavior of oxygen and carbon in CZ silicon wafers with and without carbon doping ([C,] = 6 ppma) was investigated by SIMS, and the experimental results were compared with the counterpart ones calculated using the diffusion coefficient in literature (Mikkelsen, 1986; Newman and Wakerfield. 1961). The results showed that oxygen diffusion is greatly retarded by oxygen precipitation in both the cases of carbon-doped and undoped silicon and strongly support a vacancydominant diffusion mechanism for oxygen in silicon (Heck et al., 1983). In Fig. 26(a), it is found that the diffusion of both oxygen and carbon is significantly enhanced in carbon-doped silicon subjected to heat treatment at 750°C. Moreover, it should be noted that the obtained diffusion constants of oxygen and carbon are in good agreement (Shimura, 1991). This result was attributed to the formation of fast-diffusing 0-C complexes, i.e., perturbed C(3) centers that consist of a few oxygen atoms per carbon atom (Shimura. Baiardo, and Fraundorf, 1985; Shimura,

(a)

EiQoW

(b) 1 Q M O U 6 4 . h

FIG. 26. SIMS and calculated depth profiles of oxygen and carbon concentrations in carbon-doped DZ silicon subjected to different heat treatments (Shimura et al.. 1988; Shimura. 19911.

610

F. SHIMURA

1986). This is similar to the fast-diffusing gaslike molecular oxygen in silicon proposed by Gosele and Tan (1982). On the other hand, the diffusion of both oxygen and carbon is significantly retarded at 1000°C as shown in Fig. 26(b). The retardation of both oxygen and carbon diffusion has been primarily attributed to the oxygen precipitation that results in dense self-interstitials and the formation of slow-diffusing complexes such as Si-0-C (Shimura et al., 1988). Consequently, as summarized in Figs. 18 and 23, the DZ width in silicon wafers depends on (i) initial oxygen concentration ([O,],), (ii) heat treatment conditions ( T , r ), (iii) critical oxygen concentration ([O,],), and (iv) oxygen diffusivity (DF). The [O,], and DF greatly depend on heterogeneous factors in addition to [O,], and ( T , t ) . V. Internal Gettering Process and Mechanism

I . THERMAL CYCLE

For the purpose of forming an optimum denuded zone and interior defects, several thermal cycles for IG have been proposed (Kishino et al., 1984; Nagasawa, Matsushita, and Kishino, 1980; Peibt and Raidt, 1981; Tsuya, Ogawa, and Shimura, 1981). The IG thermal cycle commonly used is called a high-low-high (or-medium) sequence, which in principle consists of the following three steps: 1. Oxygen outdiffusion heat treatment at a high temperature (>I IOOOC) for DZ formation. In order to prevent OSF generation, this heat treatment is usually carried out in an inert ambient. 2 . Heterogeneous SiO, nucleation site formation at a low temperature (600-750°C). Since preannealing at a high temperature suppresses oxygen precipitation during the subsequent heat treatment, annealing at a low temperature is required to grow SiO, embryos. 3 . Gettering-sink introduction at a medium or high temperature (1000-1 100°C). During this heat treatment, SiO, precipitates grow larger and lattice defects as IG sinks are induced in the region under the denuded zone.

Furthermore, a multistep heat treatment consisting of several steps at temperatures from low (-500°C) to high (-1150°C) has proved its effectiveness on IG in low [O,], or heavily doped n + silicon wafers where oxygen precipitation rarely occurs (Tsuya, Ogawa and Shimura, 1981). However, in general, IG heat treatment requires a long period of furnace operation in addition to the time for device fabrication processes. This time-consuming heat treatment is a major disadvantage of an 1G tech-

13.

I N T H I N W / I N T E R N A L GETTERING

611

nique. In order to utilize 1G in practical device processing, silicon wafers must be treated so that inrrirrsic, gettering occurs simultaneously during devicc processes without any additional IG heat treatment.

3.

GE-TTERING

MECHANISM

The fundamental understanding of gettering mechanism has been well described in recent reviews by Weber and Gilles (1990) and Tan (1991). In principle, all metallic impurities dissolve in the silicon lattice both on interstitial and substitutional sites, i.e.. M , and M , , respectively (Tan, 1991). Because of t h e smaller diffusivity of M , under practical thermal conditions. M , is more difficult to getter than M I . Fortunately, the most prominent metallic contaminants (e.g., Cu, N i , and Fe) dissolve in silicon predominantly as M I . ,4 mechanism for IG is qualitatively illustrated in Fig. 27 in terms of diffusion of metallic impurities into the bulk region of a silicon wafer which is subjected to thermal treatment (Weber and Gilles, 1990). In the figure the concentration of M , is presented as function of wafer depth (x/ W L I L )for three stages. When metallic contarninants are introduced onto the wafer surface, the metal atoms will diffuse rapidly into the bulk region in order to establish an equilibrium concentration (C,,) at a processing temperature (T,,; usually at 850°C or higher), Fig. 27(a). Upon lowering the temperature to T , , the metallic impurities become supersaturated since the concentration exceed4 the solid solubility ( C , ) at T , , and they precipitate very rapidly in the interior region. The precipitation should occur preferentially at internal defects in gettering region since crystalline defects can provide low-energy heterogeneous nucleation sites. This is the reason to call such internal defects IG sinks. While in the denuded Lone. the precipitation is much more difficult since homogeneous nucleation, which requires high energy and high supersaturation, can be only the process of precipitation. This stage is depicted in Fig. 27(b). Once the metallic impurities precipitated in the bulk region, the impurities in the DZ may diffuse rapidly into the bulk region by a driving force due to the concentration gradient generated between the two regions as shown in Fig. 27(c). The metallic impurities may diffuse toward defects and segregate preferentially in the defect region even when they are not supersaturated at a high temperature. Thus, no metal precipitation or segregation occurs in the DZ, while metallic impurities precipitate or segregate in the internal defect region of a silicon wafer. The diffusion process in the denuded zone can be characterized by a parameter 0 = D y / WbZ where I)" is the diffusion coefficient of metallic impurity. M . According to t h e model shown in Fig. 27 (Weber and Gilles,

612

F. SHIMURA

1.0

1

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0.0

n

.

CO

0.8

0.4

1.2

1.6

. . I

L

0

0.0

0.8

0.4

1.6

1.2

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,

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FIG.27. Change in the metallic impurity concentration in denuded zone and bulk region of silicon wafer showing a model of internal gettering (Weber and Gilles, 1990; reprinted with the permission of The Electrochemical Society, Inc.).

1990), the gettering temperature and time for a given impurity species and concentration level can be optimized. If there is a sufficient capability of IG sinks for impurity precipitation, the gettering process can be uniquely determined by D', W,,, and the cooling rate or temperature. The concentration of M drops to 10% of its initial value when 0 becomes 1. It should be noted that the gettering of metallic impurities, such as Cu and Ni, that have the significantly larger solubility starts at considerably lower temperatures than that for others, such as Fe, Cr, Co, and Mn. It might be needless to say that a longer gettering time is required for slow-diffusing impurities such as Ti and M , . 3. GETTERING SINKS

It has been recognized that internal defects can be effective IG sinks. As to the question of the dominant gettering sites, however, several dif-

13.

INI HINSIC/INTEKNAI.

613

CETTERING

ferent models have been proposed until now as depicted in Fig. 28 (Shimura, 1989). It has been observed that low densities of dislocations or stacking faults are effective gettering sinks for Cu-related surface microdefect, but dense microprecipitates of SiO, are not (Shimura et al., 1981; Tsuya and Shimura. 1983). Accordingly, it has been proposed that dislocations or stacking faults are required for effective 1G sinks (Shimura et al., 1981; Tan et al.. 1977). It has been also reported that the density of stacking faults correlated well with gettering efficiencies (Graff, Hefner, and Hennerici, 1988). The effect of these lattice defects on gettering impurities is explained primarily by the Cottrell effect. in which solubility of a foreign atom will be greater in the vicinity of a dislocation (Nabbaro, 1967). Moreover, dangling bonds introduced by edge dislocations or stacking faults have been considered to be closely spaced acceptors since a dangling bond has an unpaired electron (Read. 1954). Therefore, dislocations may directly attract negatively charged species. Oxygen precipitates themselves have been considered effective gettering sinks for Ni and Fe atoms. Using high-resolution TEM, Ourmazd and Schroter (1984) detected Ni precipitates, Nisi?, near oxygen precipitates that show neither dislocation nor stacking faults. Accordingly, the formation of Nisiz near oxygen precipitates, namely, the gettering of Ni. was explained on the basis of the emission of silicon self-interstitials from the oxygen precipitates that condense with Ni to form a silicide (Ourrnazd and Schriiter, 1984). Moreover oxygen precipitates without any association of self-interstitials can he effective heterogeneous nucleation sites Contaminants

0

P

0

* *;* * .** *

v

* * *

Strain field

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Si-0 precipitates

Oxy. ppt-induced lattice defects

.i;.i A‘

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h

a

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f 16 ZX Schematic illustration 5hon ing possihle sinks for internal getterinp (Shirnura. 1989. reprinted with the permission ot Academic Press, Inc.).

614

F . SHIMURA

for metallic impurities by forming a new phase directly connected to a redissolution of oxygen precipitate (Colas and Weber, 1986; Gilles, Weber, and Hahn, 1990; Weber and Gilles, 1990). In addition, more strikingly, the denuded-zone formation and internal gettering in oxygen-free FZ silicon wafers have been reported as well (Nauka et al., 1985b). Eventually the process has been explained by the out-diffusion and precipitation of silicon self-interstitials, instead of oxygen, which can act as gettering sites for metallic impurities (Nauka et al., 1986).It has been identified by analytical TEM observation that internally gettered centers are three-dimensional butterfly-shaped complexes consisting of multiply extended dislocation loops and a high density of microprecipitates, which are mostly Cu-, occasionally Ni-, and very rarely Fe-silicides (Ueda et al., 1986). Moreover, an IG phenomenon has been found in oxygen-Iean MCZ silicon wafers where oxygen precipitates are rarely found, and there is a mechanism by which metallic impurities can be gettered by combining with interstitially dissolved oxygen atoms (Futagami et al., 1986). Consequently, all the internal defects, including oxygen atoms, depicted in Fig. 28 can be effective gettering sinks for specific impurity atoms depending on their physical and chemical properties. VI. Summary

The IG process is clean in principle and can provide effective gettering sinks in the region close to the surface where electronic devices are fabricated. These schemes of IG are more favorable than the counterpart EG techniques to the VLSI/ULSI technology. However, IG requires the strict control of various oxygen-related processes in order to perform uniform and consistent gettering. For this goal, the silicon wafers used for the device fabrication must satisfy the following major requirements: ( I ) they must have a specific [O,], with uniform radical distribution across the wafer diameter, and (2) they must result in a uniform and reproducible A LO,], DZ, and interior defects. The control of oxygen incorporation into growing silicon crystals has been well established as discussed extensively in Chapter 2 in this volume; however, oxygen precipitation and resulting interior defects have not necessarily been controlled well at this moment, since they are greatly influenced by various factors that are not easy to control. Moreover, additional thermal cycles required for IG are not desired from the device fabrication cost point of view. Therefore silicon wafers and the device fabrication sequence must be designed so that the IG effect can be expected in the processed wafers during ordinary device processes without any additional IG thermal cycle.

13.

INTRINSIC /INTERNAL GETTERINC

615

In order to eliminate the cumbersome oxygen-related phenomena including mechanical problems and 1G thermal cycles, an approach that uses silicon wafers with [O, I,, far below [O,], might be viable if an alternative gettering technique will remain effective throughout entire device fabrication processes or if the entire process is clean enough to require no gettering technique. Finally, i t is emphasized that ( i ) the device zone must be free of unwanted impurities, structural imperfections, and wafer strain, i.e., a real defect-jroe zone instead of a conventional denuded zone must be prepared by gettering or other treatment, and ( i i ) the primary effort undertaken to eliminate the detrimental effect of contamination is to remove the sources. but not to getter them.

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Kaiser, W. (1957). Phys. Rev. 105, 1751. Kishino, S.,Aoshima, T., Yoshinaka, A., Shimizu, H . , and Ono, M. (1984). Japan. J . Appl. Phvs. 23, L9. Maher, D. M., Staudinger, A., and Patel, J. (1976). J . Appl. Phys. 47, 3813. Matsushita, Y. (1982). J . Crystal Growth 56, 516. Mikkelsen, J. C., Jr. (1986). In Oxygen, Carbon, Hydrogen and Nitrogen in Crystalline Silicon, J . C. Mikkelsen, Jr., S. J. Pearton, J . W. Corbett, and S. J . Pennycook (eds.), p. 19. Materials Research Society, Pittsburgh. Nabaro, F. R. N. (1967). Theory of Crystal Dislocations. Oxford University Press, Oxford. Nagasawa. K . , Matsushita, Y., and Kishino, S. (1980). Appl. Phys. Lett. 37, 622. Nauka, K.,Lagowski, J., and Gatos, H . C. (1985a). In Impurity Diffusion and Gertering in Silicon, R. B. Fair, C. W. Pearce, and J . Washburn (eds.), p. 175. Materials Research Society, Pittsburgh. Nauka, K.. Lagowski, J., Gatos, H. C., and Li, C . J. (3985b). Appl. Phys. Lett. 46, 673. Nauka. K.. Lagowski, J., Gatos. H. C., and Ueda, 0. (1986). J . Appl. Phys. 60, 615. Newman, R. C. (1991). In Defects in Silicon I I . W. M. Bullis, U. Gosele, and F. Shimura (eds.). p. 271. The Electrochemical Society, Pennington, N.J. Newman, R.C., Tipping, A. K., and Tucker, J. H. (1985). J . Phys. C; Solid State Phys. 18, L861. Newman, R. C., and Wakerfield, J. (1961). J . Phys. Chem. Solids 19, 230. Ogino, M., Usami, T., Watanabe, M., Sekine, H., and Kawaguchi, T. (1983). J.Electroc.hem. Soc. 130, 1397. Ohmi, T. (1991). In Defects in Silicon I I , W. M. Bullis, U . Gosele, and F. Shimura (eds.), p. 351. The Electrochemical Society, Pennington, N.J. Osaka, J.. tnoue, N., and Wada, K. (1980). Appl. Phys. Lett. 36, 288. Ourmazd. A.. and Schroter, W. (1984). Appl. Phys. Lett. 30, 781. Pearce, C. W . , and McMahon, R. G. (1977). 1. Vac. Sci. Techno/. 14,40. Peibt, H.,and Raidt, H. (1981). Phys. Stat. Sol. A68, 253. Ponce. F. A.. Yarnashita, T., and Hahn, S. (1983). Appl. Phys. Lett. 43, 1051. Rath, H. J . , Reffle, J., Huber, D., and Eichinger, P. (1985). In Impurity Diffusion and Gefferingin Silicon, R. B. Fair, C. W. Pearce, and J. Washburn (eds.), p. 193. Materials Research Society, Pittsburgh. Read, W. T., Jr. (1954). Philos. Mag. 45, 775. Robinson, P. H., and Heirnan, F. P. (1971). J . Electrochem. Soc. 118, 141. Rozgonyi, G. A. (1981). In Semiconductor Silicon 1981, H . R. Huff, R. J. Kriegler, and Y. Takeishi (eds.), p. 477. The Electrochemical Society, Pennington, N.J. Rozgonyi, G. A., Deysher, R. P., and Pearce, C. W. (1976). J . Electrochem. Soc. 123, 1910. Rozgonyi, G. A., and Kola, R . R. (1990). In Defect Control in Silicon, K. Sumino (ed.), p. 579. North-Holland, Amsterdam. Rozgonyi, G. A., Salih, A. S. M., Radzirnski, Z., Kola, R. R., Honeycutt, J . , Bean, K. E . , and Lindberg, K. (1987). J . Crystal Growth 85, 300. Ruitz. H. J . , and Pollack, G . P. (1978). J . Electrochem. Soc. 125, 128. Salih, A. S. M., Kim, H . J., Davis, R. F., and Rozgonyi, G. A. (1984). In Semiconductor Processing, D. C . Gupta (ed.), p. 272. Am. SOC.Test. Mater., Philadelphia. Shimura, F. (1981a). Appl. Phys. Lett. 39, 987. Shimura, F. (1981b). J . Crystal Growth 54, 588. Shimura, F.(1982). In VLSIScience and Technologyil982, C . J. Dell’Ocaand W. M. Bullis (eds.), p. 17. The Electrochemical Society, Pennington, N.J. Shimura, F. 11986). J . Appl. Phys. 59, 3251.

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Shirnura. F. (1989). ,Sc.mic.orzduct o r Silicon Cr\.,tcrl Technologv. Academic Press. San Diego. Shiniura. F. ( I991 ). Solid Siore Plit,nomtwti 19-20, I , Shiniura. F.. Baiardo. J . P.. and Fraiindorf. P. (1985). Appl. Phvs. Lerr. 46,941. Shirnura. F. and Craven. K. A. 119x4). In The Plrv5ic.s of' VLSI. J . C. Knight (ed.). p. 205. American Institute of Physics. New York. Shiniura. F.. Higuchi. T.. and Hochett. K. S. (1988). Appl. P h v s . Lert. 53, 69. Shimura. F.. and Tsuya. H. (1982a).J . Elcc./roc.lrem. Sex. 129, 1062. Shimura. F.. and Tsuya, H. (1982h). J . E l t ~ c ~ r r c x h e r nSoc. . 129, 2089. Shimura. F.. Tsuya. H.. and Kawmiura. T. (198Oa).J . Appl. Plivs. 51, 269. Shiniura. F.. Tsuya. H.. and Kaw;iniui-a. 7 .( IYXOb). Appl. Phys. Lett. 37, 483. Shiniura. F . . Tsuya. H . . and Kawaniurii. T. (1981). J . Electrochem. Soc. 128. 1579. Shirai. H . . Yamaguchi, A . . and Shiniui-a, I-' (1989). Appl. Ph?s. Lett. 54, 1748. Stacy. W . IT. Allison. 0. F., and W u . I' C . (1981). In Scmic,onduclor Silicwn l Y 8 l . H . R. Huff, R. J . Kriegler, and Y. I;ikei\hi ( e d \ . ) . p. 344. The Electrochemical Society. Penninpton. N . J . Takano. Y.. Koruka. H.. Ogirima. M.. and Maki. M. (1981). In Srrniconduc.tor .Silicon I Y X I . H . K . Huff, R . J . Kriegler. and Y. Takeishi (eds.). p. 743. The Electrochemical Society. Pennington. N.J. 'lamura. M.. Isomae. S . . Ando. T . . Ohvu, K . . Yamagishi. H . . and Hashimoto. A. (1991). In Dc~fc~.r.r in ,Sili(,on I / . W . M. Bullis. U . Gosele. and F. Shimura (eds.). p. 3. The Electrochemical Society. Pennington. N .J. Tan. T. Y. (1991). In fIqf&.is in .Silt[ o r i / I . W . M . Bullis. U . GZisele. and F. Shimura (eds.). p. 613. 'The Electrochemical Societv. Pennington. N . J . 'Tan. 7 . Y.. Gardner. E. E . . and 'Iice, W . K. (1977). Appl. Phv.5. Lrri. 30, 175. Tan. T. Y .. and G6cele. C . ( 1981) A p p l . Phv.r Letr. 39, 86. Tan. T-.Y.. and Tice. W . K. (1976) / ' / i ~ / o s . Mtrp. 34, 615. 'rice. W . K.. and Tan. T . Y. 11981 ) . In / k ~ c r . in s Srrnicondrrcrors. J . Narayan and T. Y. Tan (eds.). p. 367. North-Hollmd. Amsterdam. l s u y a . H . . Ogawa. K.. and Shimui-a. f:. (1981). Jupari. J . Appl. Phys. 20, L31. Tsuva. H . . and Shiniura. F. (19x3) P/rv,$.S k i r . Sol ((1) 79, 199. Tsuva. H.. Shimura. F.. Ogawa. K . . ond Kawamura. T. (1982). J . Eleelrochem. S o c . 129, 374. t!eJa. 0 . .Nauka. K.. Lagowshi. J . . and (Jato\,. H . C. (1986). J . Appl. Phys. 60. 6 2 . I J w m i . T.. Matsushita. Y.. and Opino. M . (19x4). J . Crvsrul GroM.tli 70, 319. Wada. K.. Inoue. N.. and Kohra. K . (1980). J . Cnjstcil GroM.tli 49, 749. Weher. E. K..and Gilles, I). (1990). I n Srnrr~.ondirrrf)rSilicon lY90. H. R. Huff. K . G . Barraclough. and J . Chikawa (ed\ ). p. 5 8 5 . The Electrochemical Society. Pennington. N.J. Yasutake. K.. IJmeno. M.. and Kamahe. H. (1984). Phys. Slut. Sol. ( ( I ) 83, 207. Zhong. I,.. and Shimura. F. (1993) J . A p p l . P h \ . 73. 707.

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Oxygen Effect on Electronic Device Performance H. Tsuyu RESEARCH A N D D F V E l O P M E N I CZROLIP N E C CORPORATION S A G A M I H A R A , JAPAh.

I. 11.

INTRODUCTION

. . . . . . . . . . . . . . . . . . .

619

DEFECTS . . . . . .

62 I 622 623 625 625 628 630 633

D E V I C E CHARACTERIS.II('S A N D C R Y S T A L

I . Device

Structure

L ~ J C'rvstcrllinr .

Defec./.s . . . . . . .

2 . Failure Modes in 1.SI Devic,es . . . . . . . . . . . 111.

DEFECT GENERATION . . . . . . . . . . . . . . . . I . O.rvgen Precipitctre Rcltited Fuilure Modes . . . . . .

2 . Residuul Stress of' S i 0 2 Film . . . . . . . . 3 . O.rygen Related 1kfi.c.t.s by I o n lmpluntarion . 4. O.ride Film Degrudution . . . . . . . . . 5 . Lattice Defect Gc,nercrtion Due t o Heuvv Mettrl Con tamination . . . . . . . . . . . . I V . IMPROVEMENT OF D E V I CYIEL.D E . . . . . . . . I . Intrinsic Gettering App/ic.ct/ion t o VLSI . . . 2 . Homogenization (it Prcc.ipituted Oxygen . . .

. . . .

. . . . . . . . . . . . . . . .

. . . .

. . . . Epitaxial Wcifers t o

3 . Intrinsic. G'e'tteritiX App/ic.ci/icm0.f VLSl . . . . . . . . . . . . . . . . 4. Gettrruhi1itvf;ir t l e c r ~ ~Meter1 v lrnpurities . . 5 . Control of Mec~htinii~~il .StrcnXth . . . . . 6 . Advonced Intrinsic- Gcrtcring . . . . . . . V. S U M M A R Y . .. . . . . . . . . . . . . . . A ~ ~ k n o ~ ~ ~ l e d ~ m.e n. r s. . . . . . . . . References

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634 635 636 640 647 65 I 652 660 663 663 664

I . Introduction ULSI, as seen symbolically in the development of D R A M size reduction and higher-degree integration. has made great progress. For example, D R A M is now commercially going into the era of 16 Mbit passing through 4 M . I n parallel with the development of high-performance devices, it is not too much to say that silicon device industry is characterized by constant struggles with chip yield. Factors affecting chip yield are grown-in crystal defects. particulate, residual ions and so on as well as process-induced failure modes. Furthermore. the unwanted heavy metal impurities in619 Copyright 9 1994 hy Academic Press. Inc All right\ of reproduction In any form reserved. ISBN 0-1?-75?14?-9

620

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duced by the chip fabrication process degrade the electrical characteristics resulting in the decrease of chip yield. Oxygen atoms are closely related to electronic device performance. If crystalline defects induced by oxygen precipitation exist near device active regions, they degrade device characteristics. On the other hand, as described in Chapter 13, inner defects due to oxygen precipitation play a role of gettering sinks for heavy metal impurities, resulting in good device yield. Furthermore, as discussed in Chapter 1 1 , oxygen atoms prevent the dislocation movement, giving rise to good mechanical strength, however, excessive oxygen precipitates have the possibility of degrading the mechanical strength of a wafer. For this reason it is said that oxygen atoms are “two-edged swords” for device performance. Historically, in order to achieve a high-performance device, new process technologies and new device structures have been developed and introduced into mass production. For example, ion implantation and dry etching technologies have been utilized from the era of 4K DRAM and 16K DRAM, respectively. As for device structures, LOCOS isolation has been adopted since the era of 1-4 K DRAM, and trench capacitor and LDD structures have been practically introduced into 1M DRAM production. Figure 1 illustrates the trend of new technologies and DRAM high integration (Tsuya, 1991a). Though these new technologies realized high10

3 1.20.5

0.1

Process __

DRY ETCHING ) w

1960

,

,

,

1970

1980

1990

2’ I0

YEARS

Fic. I . Trend of DRAM high integration and related technologies (Tsuya, 1991a).

14.

OXYGEN EFFFC 1 O N I-I F C r R O N l C DEVICE PERFORMANCE

621

100 1G 256M64M 16M

0.01

0.1

4M

1M

1

10

DEFECT DENSITY (cm-’) k i ~ 2 Calculated curve of LSI chip vield v \ the equivalent detect density tor each generation of DRAM ( r s u y d . 1991t r )

performance devices, at the same time they introduced t h e unwanted heavy metal impurities and increasing local stress in the device region. Heavy metal impurities easily gather around these local stresses, resulting in the increase of leakage current. In order to fabricate VLSl devices with high yield, it is fundamentally important to suppress crystallographic microdefects and completely eliminate heavy metal contaminants in device active regions. These microdefects originate from bulk defects such as oxygen precipitates and dislocation or heavy metal contamination during device processing. In this chapter the oxygen effect on electronic device performance will he discussed from the standpoint of device characteristics and yield improvement. 11. Device Characteristics and Crystal Defects

Figure 2 shows the curve of LSI chip yield versus the equivalent defect density due to crystalline defects. particulate. residue of resist and so on for each generation of DRAM calculated (Tsuya, 1991b), using the forand u are yield, the mean defect mula of Y = exp( -Dou), where Y. D,, density and the susceptible area of a device, respectively (Murphy, 1964). I n order to obtain good chip yield, the equivalent defect density must he dramatically suppressed with increased packing density, because 61 increases with increased packing density. One of the severe criteria of DRAM is leakage current. Acceptable leakage current roughly estimated using the formula of I , = 0 . where I , , Q, and 1, are leakage current. capacitance and refresh time. respectively, must be drastically re-

622

n.

I

I

4M

16M

TSUYA

64M

I

I

256M

1G

PACKING DENSITY OF D R A M

FIG.3 . Acceptable leakage current per unit cell at 25°C vs. packing density of DRAM (Tsuya. 1992).

duced with increasing packing density as shown in Fig. 3 (Tsuya, 1992). For example, the leakage current per unit cell of 256M DRAM must be less than A at 25°C. It has been pointed out that heavy metal impurities and crystalline defects are related to leakage current. I . DEVICE STRUCTURE vs. CRYSTALLINE DEFECTS

Basically, there are two kinds of device structures, MOS (metal oxide semiconductor) and bipolar types. In the case of the MOS transistor, majority carriers from a source are controlled by the electric field on the silicon surface applied by gate electrodes. Majority carriers passing through channel are drift currents, and they are proportional to the voltage of gate electrode; that is, the action of the MOS transistor is influenced by its crystal surface. On the other hand, for the bipolar transistor, minority carriers injected into base region from the emitter are collected into a collector region by the concentration gradient of carriers through the base region. Minority carriers are diffusion currents, and they move into the interior of a crystal unlike the MOS transistor. The amplification potential of a bipolar transistor is strongly influenced by the injection efficiency of minority carriers from emitter to base and their lifetime in the base region. These phenomena are strongly related to bulk crystallinity. The CCD (charge coupled device) is fundamentally MOS type. CCD

14.

OXYGEN FFFEC T O N f I ICTKONIC DEVICF PFKFOKMANCF

623

ln r; 10,000,000 3

8

1,000,000

L

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100,000

.-

10,000

U

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1

0

Normal chip

u-

.-g

1,000

E’

100

L

-m

5

u

10 1

-.ooi

.or

.i

-i

io

100

Data retention time (sec.)

F I G .4 . Commulative failed bit count\ of data retention time for normal and failed chips (Ohni\hi el al.. IWOb).

-

a particle

l-ic,

5

Various modes of minuritv c‘arriei injection to DRAM cell node (courte3v of S.

0h v 1

is an analog device unlike memory or logic. The sensitivity of CCD to

individual defects is one to two orders of magnitude higher than in DRAM (Jastrzebski, 1982). 2 . FAILURE MODESI N LSI D1-vic-i~~

The holding-retention time failure mode is the most serious problem for DRAM devices. The holding time must increase with increasing packing density of DRAM for saving power consumption to refresh the stored information. Figure 4 shows commulative failed bit counts of data retention time for normal and failed chips (Ohnishi et al., 1990b). Several bits with shorter retention time, on the order of 0.1-0.01 sec, are seen in the failed chip and device yield is evaluated only by these failed bits, whereas the retention time of normal chip i s above 1 sec. The holding time failure mode is caused by the diminution of stored charges in a capacitor due to the injection of minority carriers. As shown in Fig. 5 . there are various modes of minority carrier injection to cell

624

n.

TSUYA

FIG.6. Leakage current pattern of a processed CCD wafer.

node such as (A) generation current in depletion region, (B) diffusion current from the bulk, (C) forward current from I/O, (D) carriers injected from peripheral circuits and (E) carriers generated by a-particles with high energy. The standby leakage current of SRAM by flipflop circuits must be absolutely reduced because of no periodic refresh operation unlike DRAM. The junction leakage current between the source-drain and substrate is a main cause behind this. For bipolar devices, the emitter-collector (E-C) short circuits crossing base region are a well-known problem, which was first termed pipes by Miller (1960)and are still a matter of concern with decreasing base width. This failure mode is induced by oxide-nitride-edge dislocations and stacking faults formed during LOCOS process (Franz et al., 1981). The pipes are also caused by enhanced diffusion of the emitter dopant atoms along such dislocations (Franz et al., 1981).

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O X Y G E N EFFECT ON ~ I . E , C T R O N I CDEVICE PERFORMANCE

625

The CCD image device has a variety of failure modes, such as white spot defects, smear and blooming. Figure 6 shows an example of leakage current patterns, which almost correspond to white spot defect modes, of an entire wafer. The lattice defects corresponding to the swirl are dislocation half-loops (DHLs) distributed at random. These DHLs are considered to be generated by the interaction of field oxide edge stress, suggested by Hu et al. (19761, with microdefects that are caused by the interstitial oxygen distributed in a swirl pattern. 111. Defect Generation

Oxygen atoms that are incorporated in Si during crystal growth and are knocked on by ion implantation, and the residual stress of SiO? film generate crystalline defects. resulting in the device failure modes such as leakage current and oxide film degradation. Furthermore, lattice defects are generated by heavy metal contamination.

I . OXYGEN PRECIPITATE RELATED FAILURE MODES Residual oxygen concentration is closely related to device performance. Figure 7 shows the relationship between residual oxygen concen-

a a

A 10

14

15

16

17

RESIDUAL OXYGEN CONCENTRATION (x10”/cm31

Fic, 7 Holding lime failure rate v 5 iesidudl oxvgen concentrdtion after processing for vdriou\ DRAM devices (Tsuya. 1992)

626

H . TSUYA

FIG.8. X-ray topographic picture (upper) and optical cross (lower left) and plane (lower right) pictures of SRAM (Tsuya, 1992).

14.

627

OXYGEN EFFECT ON ELECTRONIC DEVICE PERFORMANCE

tration after processing and holding time failure rate obtained for various DRAM devices (Tsuya, 1992). The holding time failure rate increases with increasing residual oxygen concentration, in which oxygen precipitates were hardly observed. On the other hand, holding time failure rate decreases for low residual oxygen concentration. In this region a moderate amount of inner defects due to oxygen precipitation were observed. However, in the case of overprecipitates, holding time failure rate likewise increased, because lattice defects due to oxygen precipitation were generated near the surface region. This situation for SRAM is now discussed. Figure 8 shows an X-ray topographic picture and optical cross and plane pictures of SRAM (Tsuya, 1992). A lot of defects are observed near the wafer periphery compared to the central portion, which shows good denuded Lone from the cross-sectional picture of Fig. 8(a), resulting in good device yield. On the other hand, in the peripheral region, crystalline defects due to oxygen precipitates locate on the device surface region from the plane picture of Fig. 8(b) and increase the leakage current of SRAM. The spatial distribution of residual oxygen concentration meawred by p-FTIR for the previous SRAM wafer is shown in Fig. 9 a ) . The low density of residual oxygen concentration near the periphery is observed. Figure 9(b) shows the uniform distribution obtained from another improved wafer of processed SRAM. The retention failed bit of a Mbit DRAM with a trench cell capacitor was found to be related to oxygen precipitation. The FIB (focused ion beam) marking method was successfully applied to correlate retention failure electrically identified with crystalline defects one by one (Nishio et al.. 1990). Figure 10 shows cross-sectional TEM images of a failing I

Y ';i

12OEt17-

60Etl7-

44Etl7 4Ottl7 16Et17 -

3DEtI7-

-29 !' 0

K

(a)

85Et17BOEtl775Et1770Et170

(ax

3.2Et17 -

,

10

20

30

40

-L--

50

2OEt17

0

10

20

30

40

50

X-position

X-position

(b)

FIG.9. Spatial dihtribution of residual oxygen concentration measured by p-FTIR for the SRAM wafer shown in Fig. 8(a) and for another improved SRAM wafer (courtesy of M. Kit akata) ,

628

n. TSUYA

memory cell, where defects are recognized below the bottom of trench capacitor. EDX analysis and TEM observation showed that these defects were the SiO, amorphouslike octahedral structure that is peculiar to oxygen precipitation (Shimura, Tsuya and Kawamura, 1980a), and this is grown in a high-temperature p-well drive-in diffusion process. From these observations, it was confirmed that oxygen precipitation near the memory cell caused the retention failure of DRAM. This result indicates the importance of optimizing initial oxygen concentration and the necessity of perfect denuded zone (DZ) formation in the active surface layer. Another example of oxygen precipitate defects, which are sometimes called BMDs (bulk micro defects), existing in the N-MOS and C-MOS devices is described (Matsushita, 1989). Figure 11 shows the dislocation density induced at the LOCOS edge as a function of BMD density in N-MOS. Dislocation density increases with increasing BMD density. On the other hand, the dislocation generation relating to the BMD density in C-MOS is quite contrary to that in N-MOS. This is because the C-MOS process includes a well diffusion at a high temperature, which gives rise to oxygen out-diffusion, resulting in the BMD-free zone near the wafer surface. Therefore, BMD distribution must be designed into the device manufacturing process (Matsushita, 1989).

2. RESIDUAL STRESS OF SIO, FILM The residual stress present in thermal SiO, film is relevant to dislocation generation in the Si substrate and induces mechanical damage effects in devices. The mechanical properties of SiO, film depend on growth

FIG.10. Cross-sectional TEM image of the bottom of trench capacitor of failing memory cells (Nishio et al., 1990).

14. OXYGEN EFFFC'I

O N F.LEClRONIC DEVICE PERFORMANCE

629

NTl000 -

-.-E

0

r 100In C

f

10-

.-0

L

.... .

m

0

0

1-

v)

6 0 11 102

103

104

105

106

BMD Density (cm-2)

Fic, I1 Dislocation density induced N-MOS (MdtsuShita. 1989)

dt

pattern edge as a function of B M D density in

FL. I ? . X-ray topography of bipolar memory device wafers after LOCOS process for (a) and 1000°C (b).

two different growth temperatures of SiO? under 5 atom oxygen pressure at 950°C

temperature (EerNisse, 1979). During growth at 950°C and below, compressive stress is generated in the SiO,. On the other hand, during growth at 975 and IOOO'C, the SiOzfilm gi-ows in a stress-free environment, which is explained by the viscous flow around 965°C (EerNisse and Derbenwick. 1976). In Fig. 12 X-ray topographic pictures of bipolar memory device wafers after LOCOS process for different growth temperatures of SiO, under 5 atom oxygen pressure are shown. In the case of oxidation at 950"C, a high density of defects due to the stress of S O , is generated, as shown

630

n.

TSUYA

FIG. 13. The concentration profiles of phosphorus, arsenic and recoiled oxygen in Si for 150 keV 10" Pc/cm2 and 315 keV lot6Ast/cm2 through SiO, of 950 A (Hirao et al., 1979).

in Fig. 12(a). However, at the 1000°C oxidation, as shown in Fig. 12(b), defects are drastically reduced due to the release of intrinsic oxide stress. Device failure rate was reduced in accordance with the SiO, growth temperature.

3 . OXYGEN RELATED DEFECTS BY ION IMPLANTATION The ion implantation process induces defects related to oxygen. In practice, ion implantation is carried out through SiO, film in order to avoid the channeling phenomenon and contamination. In this case, however, oxygen atoms are knocked on or recoiled, and oxygen related lattice defects are generated. Figure 13 shows the concentration profiles of P, As and knocked-on oxygen after ion implantation through SiO, of 950 A (Hirao et al., 1979). More oxygen atoms are knocked on by the implantation of larger mass ions. It has been reported that the presence of oxygen atoms can produce an applicable retardation in the growth rate of SPE (solid phase epitaxy) (Kennedy et al., 1977), which is substantially necessary for the annealing process after ion implantation, and also interact with high-dose As atoms during annealing process (Sadana et al., 1983),resulting in lattice defects. From the detailed experiment of lattice defects in high-dose As implantation in a through-oxide layer, it was concluded that the survival or elimination of As-precipitate induced defects was strongly affected by recoiled

14.

O X Y G E N EFFECI ON t i ECTRONIC DEVICE PERFORMANCE

631

oxygen atoms (Tamura and Horiuchi, 1988). The knocked-on oxygen atoms at about 2 x 10” atonis/cm’ had a strong pinning effect on Asprecipitate induced defects after high-temperature annealing. However, oxygen above 2 x IO”/cm’ had the reverse effect, i.e., dissolution on these defects. The influence of defects induced by recoiled oxygens and unsaturated As atoms on retention failure of DRAM was investigated (Ohnishi et al.. 1990a). Using a method to directly observe the failure bit by TEM, it was found that the leakage of Mbit DRAM was introduced by t h e dislocation line from the sidewall edge across the memory cell, as shown schematically in Fig. 14. The dislocation lines are considered to be generated in connection with the small dislocation loops during the cooling period. From the through-oxide thickness dependence of the dislocation loop density after annealing at 950°C for 30 min and SIMS analysis, it was found that the recoiled oxygens were gettered at the position of the defect generation, and the concentration of the recoiled oxygen had a good correspondence to the defect density. In order to improve the failure of charge leakage in the n +-implanted region, it is important to avoid knocked-on oxygen atoms using the thick through-oxide layer. The failure of n+-substrate leakage was greatly decreased by increasing the through-oxide thickness above SO nm (Ohnishi et al., 1990a). The application of high-energy or high-dose ion implantation for retrograde well formation and a SIMOX (separation by implanted oxygen) substrate has been actively investigated. Especially, SIMOX is a promising substrate for future advanced VLSI. The insulating layer of SIMOX is fabricated by implanting high-dose oxygen atoms with high energy, resulting in defect generation and the surface roughness of the top Si layer. For practical use, it is important to control and suppress crystalline defects generated by implanted oxygen in the device active region. In order Transfer gate LOCOS

I

1

Side wall

I

Disloc\ation Dislocation line

FIG.14. Schematic drawing of the DRAM failed bit (Ohnishi et al.. 1950a).

632

H . TSUYA

to reduce defect density, a combination of implantation and subsequent high-temperature annealing procedures has been carried out. Figure 15 shows a cross-sectional TEM image of SIMOX structures formed by high-dose (1.2 x 10'8/cm2 O+/cm2)oxygen implantation at 150 keV after annealing at different temperatures (Yoshino, Kasama and Sakamoto, 1989). Several characteristics layers, marked A , B , C (the buried oxide layer) and D , are observed in the as-implanted stage. In the region A-B, a high density of oxide precipitates, which are identified SO., (0 < x < 2) by XPS, are observed. After annealing at 1280°C for 12 hr, these oxide precipitates disappear by dissolution, and the surface of the top Si and SiO, layers become flat. By a multiple procedure of the implantation of relatively low-dose oxygen and high-temperature annealing, the crystalline quality of SIMOX was dramatically improved (Jaussand et a]., 1985). The evolution of SIMOX defect density is shown in Fig. 16 (Colinge, 1992). It was also reported that the dislocation density decreased to the order of 102/cm2as the dose decreased (Nakashima and Izumi, 1990). Recently, the dislocation-free SIMOX substrate with a dislocation density of less than 7 x 1O-'/cm2 was first reported (Yoshino, 1992). The key process consists of a low-dose single implant (Nakashima and Izumi, 1990) less than 1 x 10'*/cm2and the exclusion of heavy metal contamination during SIMOX

FIG. 15. Cross-sectional TEM images of the SIMOX structure annealed for 5 min at different temperatures: (a) As-implanted, (b) 1 15OoC, (c) 1230°C and (d) 1280°C (Yoshino et al., 1989).

14.

O X Y G E N EFFFC I O N t I t C T R O N I C DEVICE PERFORMANCE

633

breakdown field (MVkm)

FIG 17 Typical dielectric bredkdoun histoprdm of thermally grown SiOZ(Yamabe et rd

. 1983)

formation. The thinner SiO layer fabricated by low-dose ion implantation is more attractive for sub-quarter-micron CMOS devices (Omura et al., 1991).

4. OXIDE FILMDEGRADATION

Much attention has been paid to the quality of thin oxide film, because the thickness of gate oxide film for VLSl is becoming thinner to reduce the propagation delay time. Thermal SiO, film characteristics are greatly influenced by oxygen precipitates near the crystal surface, heavy metal impurities and the surface micro-roughness of a wafer. The dielectric breakdown (DB) histograms of thermal SiOz films are typically separated into three peaks, A , B and C modes as shown in Fig. 17 (Yamabe, Taniguchi and Matsushita, 1983). Among them, B mode failure is closely related to time-dependent dielectric breakdown (TDDB). The experiment of preoxidation high-temperature annealing on the B

634

H . TSUYA

mode failure fraction suggested that surface contamination prior to gate oxidation and microdefects in the Si near the surface were two main origins of B mode defects (Matsushita, 1989; Yamabe et al., 1983). Microdefects are considered to be related to oxygen precipitates from a comparison result of CZ Si with FZ Si wafers, which showed the increase of oxide BD failure with increasing oxygen concentration. However, the oxide BD failure was different from wafer to wafer with the same oxygen concentration, in the range of from about 10I8 to 1.8 X 1018/cm3,suggesting that the contaminated nucleus of the bulk microdefects are related to the B mode (Matsushita, 1989). The influence of heavy metal impurities on gate oxide integrity has been quantitatively clarified (Honda et al., 1987; Hiramoto et al., 1989). Heavy metal impurities are incorporated into oxide film and grown metalsilicides degrade the BD characteristics. Recently, the strong effect of 11-group elements such as Ca, Mg and Zn on dielectric degradation of SiOz films has been discussed (Takiyama et al., 1992). It is also pointed out that atomic scale micro-roughness in the Si wafer surface degrades surface channel mobility (Ohmi, 1991) and the BD characteristics of thin oxide film (Miyashita et al., 1992). The micro-roughness formation is discussed in terms of Si wafer cleaning method (Ohmi, 1990), the nonuniform distribution of the Si vacancy clusters based on the comparison between bulk and epitaxial wafers (Miyashita et al., 1992), oxidation procedures (Carin and Bhattacharyya, 1985) and Si crystal growth condition (Tachimori, Sakon and Kaneko, 1990). The investigation of the BD failure versus growth rate of Si crystals showed that crystals grown at faster pulling rates ( > 1 mm/min) had an increasing BD failure mode, whereas the BD failure mode was much improved for crystals grown at lower pulling rates (<0.4 mm/min). This result was explained by the difference of point defect formation and outdiffusion giving rise to oxygen precipitation in these crystals (Tachimori et al., 1990). However, the reason why the crystal growth rate affects the gate oxide integrity is not satisfactorily clarified. Recently, it was reported by TEM observation that the size and morphology of microdefects depended considerably on crystal pulling rate (Takeo, Ushio and Takenaka, 1992). In order to discuss the effect of crystal pulling rate on the size and morphology of defects, the difference in thermal history during crystal growth also must be considered. 5. LATTICE DEFECTGENERATION DUETO HEAVY METALCONTAMINATION

Heavy metal contamination generates haze defects (Stacy, Allison and Wu, 1981), which are termed S(saucer)-pits and surface microdefects

14.

OXYGEN EFFECT O N t.1 ECTRONIC DEVICE PERFORMANCE

635

4

OF loio l o i i

(

1

loi2 1013 loi4

Surface Metal Conc. (atoms/cm2)

FIG. 18 Density of S p i t s induced by N i . Cu and Fe as a function of surface metal concentration (Hourai et al., 1989)

(Shimura, Tsuya and Kawamura, 1980a), and OSFs (Hourai et al., 1989) in some cases. The density of S-pits strongly depends on annealing temperatures. S-pits with the density of 106-107/cm2are observed on a usual wafer surface by preferential etching after heat treatment above 1100°C in wet 0, (Tsuya and Shimura. 1983). In the case of heavily contaminated wafer and repeated heat-treatment procedures, extrinsic stacking faults are generated, and they are decorated with Cu (Shimura, Tsuya and Kawamura, I980a) and Ni (Stacy el at., 1981). The formation and growth of surface microdefects are discussed (Shimura and Craven, 1984). Recently, the behavior of S-pits and OSFs has been clarified by quantitative experiments (Hourai et al., 1989). Figure 18 shows the relationship between the density of S-pits after the 1150°C annealing and the concentration of metallic impurities, Cu. Ni and Fe, introduced by a spin-coating method. A high density of S-pits are observed for Ni and Cu, but low density for Fe. This means that S-pits are strongly related to the Ni and Cu contamination, but not so to the Fe contamination. Futhermore, after the subsequent oxidation at 1000°C. OSFs were observed at high densities for Cu and Ni. In the case of Fe contamination, OSFs were generated under the second heat treatment below 850°C. Figure 19 shows the densities of S-pits and OSFs induced by Fe as a function of the surface concentration. They are drastically increased for densities over 3 x IO”/crn’. IV. Improvement of Device Yield The intrinsic gettering (IG) technique using bulk microdefects generated from precipitated oxygen is an attractive method to achieve high

636

H . TSUYA

device yield. The fundamental behavior of IG and its related phenomena are described in the previous chapter. In this section the improvement of device yield using IG procedures and the mechanical strength will be discussed. 1 . INTRINSIC GETTERINC APPLICATION TO VLSI

Since the intrinsic gettering (IG) effect was first reported (Tan, Gardner and Tice, 1977), the investigations on IG effect have been extensively carried out; and the dominant effectiveness on device performance, for example, latch-up suppression in CMOS circuits (Anagnostopoulos et al., 19841, the improvement of CCD failure mode such as crosstalk and white spots-lines (Anagnostopoulos et al., 1984; Ogino et al., 1983; Jastrzebski et al., 1987), the reduction of emitter-collector leakage current in bipolar devices (Tsuya, 1983; Jastrzebski et al., 1984; Hirao and Maegawa, 1988) and the improvement of holding time failure in DRAM (Huff et al., 1983; Ohtsuka et al., 1982) have been reported. The improvement of device yield by the IG technique is achieved by the elimination of heavy metal impurities from the device’s active region, the reduction of surface microdefects originating from metal impurities described in Section 111.5, the capture of excess minority carriers and so on. Ikuta, Nakajima and Inoue (1984) first demonstrated successful IG application for eliminating heavy metal impurities and surface point defects introduced by reactive ion etching (RIE), resulting in an improvement in electrical characteristics such as minority carrier lifetime and

Fe

Surface Metal Conc. (atoms/cm2)

FIG.19. Density of S-pit and OSFs induced by Fe as a function of the surface concentration. Second annealing was done at 850°C for 2 hr in N2 for S-pit formation (Hourai et al.. 1989).

14.

OXYGEN EFFtC I O N t l hC rRONlC DEVICE PERFORMANCE

r--

'

I

"

"

I

637

'

a

Without IG annealing

0

500

1000

Ion Accel. Voltage (V)

FIG.20. Intrinsic gettering effect on KIE damage at various ion acceleration voltages for several bulk defect densities (Ikuta et id.. 1984)

[

~~

0

CONVENTIONAL

DEFECT FREE YIELD

FUNCTION YIELD

YIELD (Arbitrary Units)

FIG.21. Histograms of I Kbit ECL R A M function yield and defect-free chip yield with and without HCI IG (Hirao and Maegawa, IY88).

leakage current of oxide film. Figure 20 shows lifetime in the RIE wafers with and without IG as a function of ion acceleration voltages. The IG procedure using HCI oxidation completely eliminated epitaxial stacking faults and suppressed the junction leakage current of high-speed bipolar device (Hirao and Maegawa, 1988). A s shown in Fig. 21. the functional yield of 1 Kbit RAM was five times higher than one without IG-HCI. The holding time degradation of DRAM cells due to excess minority carriers emitted from adjacent MOS transistors was discussed for various substrates (Ohtsuka et al., 1982). The IG wafer is less susceptible to holding time degradation than other pip substrate and bulk wafers, as shown in +

638

H. TSUYA

I I

!

4

5

6

7

Drain Voltage (volts)

FIG. 22. Holding time vs. drain voltage of adjacent transistors at a distance of 150 bm for three kinds of substrate materials: bulk silicon, P I P + epitaxial silicon (Epi), and intrinsic gettering silicon (IG) (Ohtsuka et al., 1982).

1 0-2

-Y

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6

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i

wlthoul generlng slnk

lod, t

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E HEAT PROCESS

ABCD

-

F

FIG. 23. The change of gettering effects of IG(O), BD(A) and PG(O) during the heat treatment of CMOS. The lifetimes at the point A are the initial values without Cu contarnination. Symbol * at the point B shows the lifetimes of contaminated wafers without gettering sinks (Sano et al., 1988).

Fig. 22. This showed that bulk microdefects acted effectively as sinks for migrating excess minority carriers. The IG technique utilizing the precipitation of supersaturated oxygen is substantially a heat-treatment procedure, so it is highly matchable to the IC process. Furthermore, extra treatments are not necessary, unlike EG. Generally, gettering ability does not disappear and is persistent because oxygen precipitation occurs with every heat treatment process. Figure 23 compares the gettering ability for IG and EG after intentional

14.

O X Y G E N EFFLC7 O N I I E( 1 RONIC DEVICE PERFORMANCE

639

quantitative Cu contamination (Sano et al., 1988). The generation lifetimes were measured at some typical CMOS equivalent heat processes. It is seen that 1G keeps its effect until the end of the heat process, compared to other polysilicon geltering and backside damage (BD). 1G has a strong correlation with the initial oxygen content of a wafer. It was first shown that the wafers taken from the top-side of an ingot, having higher oxygen content, had a strong 1G effect, but the wafers from the tail had a weak effect (Kozgonyi, Deysher and Pearce, 1976). Also, due to radial and longitudinal inhomogeneities of oxygen in the crystal only a portion of the material was effective to IG (Steinbeck et al., 1980), although today’s Si crystals have the radial and longitudinal uniformity of oxygen content. Figure 24 is an example of the relationship between initial oxygen content and the yield of CMOS type devices fabricated on BD wafers (Tsuya, 1983). High yield is seen within a narrow range of high oxygen content. I t was also pointed out that the efficiency of intrinsic gettering was a strong function of the amount of precipitated oxygen and precipitate’s morphology from the investigation of I’L and linear logic bipolar circuits fabricated on different wafers with and without preannealings (Jastrzebski et al., 1984). Figure 25 shows the gettering efficiency for analog circuits as a function of the amount of precipitated oxygen present after processing. This result shows that the most efficient gettering takes place around 10 ppm of precipitated oxygen. Hitherto, in order to utilize IG effect, the range of initial oxygen content has been specified for each device, expecting the generation of oxygen precipitates during device processing. This is called process-indrrced IG (Tsuya. 1989) or NIG (natural IG). However, as shown in Fig. 26, symbolically. the specified range of initial oxygen content has been becoming narrower with the increasing packing density of VLSI, because IG procedures need the more skillful control of oxygen precipitation and

non IG

-----10

12

14

16

18

20

22

24x10”

OXYGEN CONTENT (cW3)

l-ic, 24 Initial oxygen content v \ the yield of CMOS type devices fabricated on BD wafer\ (Tsuyd. 198.3)

n.

640

TSUYA

I

I

I

I

5

10

15

20

PRECIPITATED OXYGEN (ppm)

FIG. 25. Normalized yield loss as a function of amount of precipitated oxygen after completion of the analog process (wafers without preannealing): 0 , Group I ; x , Group 2; A,Group 3: W, Group 4; A,Group 5 (Jastrzebski et al., 1984).

INITIAL [Oil (Arb)

FIG.26. Trend of initial oxygen content for the packing density of DRAM (Tsuya, 1989).

the quantity of oxygen precipitates for highly dense VLSI is more restricted. If this tendency continues, no solution for process-induced IG will be found. Furthermore, it is well known that oxygen precipitation differs from wafer to wafer, even if each wafer contains the same initial oxygen content (Chiou and Shive, 1985). This is well understood by the difference in thermal history during crystal growth (Nakanishi et al., 1980; Tsuya et al., 1982). 2 . HOMOGENIZATION OF PRECIPITATED OXYGEN

In practice, it is important to expand the range of initial oxygen content and homogenize oxygen precipitation independent of thermal history. A multistep heat treatment for IG ( M E , hereafter) enhances the effectiveness of 1G compared to an isothermal preannealing (Tsuya, Tanno and

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OXYGEN EFFECT O N k:I.ECTRONIC DEVICE PERFORMANCE

641

Shimura, 1980) and homogenized oxygen precipitation after hightemperature annealing (Tsuya, Ogawa and Shimura, I98 I ) . This improved heat treatment procedure can produce IG ability even in a low-oxygen wafer of 11-12 x 10"/cm3 by the old ASTM procedure (ASTM, 1979). The typical MIG heat treatment procedure consists of a three-step sequence at 520°C. 620°C and 720°C successively, each for 16 h r in dry O2 followed by a 1140°C annealing for 2 hr in wet 02.Prior to MIG annealing, the high-temperature heat treatment at 1230°C for 3 hr in dry N, (25% 02)for the DZ formation was carried out. The heat treatment procedure is shown in Fig. 27, in which a cross-sectional picture of an MIG-treated wafer is inserted. Figure 28 shows Sirtl-etched patterns of inner defects observed on the cleaved surfaces for low-oxygen-content wafers ( I 1 x 10'7/cm3)and high-oxygen-content ones (18 x 10'7/cm3)after a two-step annealing ( 1230"C, 3 hr + 720"C, 64 hr + I 140"C12 hr) and MIG annealing ( 1230°C + MIG + 1140°C). A two-step annealing generated only a low density of inner defects, 103/cm2.On the other hand, after MIG annealing, a high density of inner defects, 5 x 10'/cm2, was observed even in low-oxygen wafers as well as high oxygen ones. This is called DZlC wafer (Tsuya, 1989). It is desirable that the behavior of the IG effect does not depend on the intrinsic material properties of different vendors (Kishino et al., 1979), different ingot positions (Chiou et al., 1985; Tsuya et al., 1982) or growth conditions. For the IC; application, it is important to homogenize oxygen precipitates by heat treatment.

'c

200 1

w

5

800-

I-

Q

5

600-

a

5 400

+ I

DENUDED

ZONE 1 FORMATION 1

9-

-

jrGROWTH.

L-2 NUCLEATION

200 ~

AENEALING TIME (a.u )

FIG 37 Typical MIG heat treatment procedure and the cross-bection picture of MIG wdter after Sirtl etching (Tsuya, 1992)

642

ti. TSUYA

FIG.28. Sirtl-etched patterns of inner defects for each process: (a) 720"C, 64 hr + I140"C. 2 hr; (b) 1230"C, 3 hr + 720"C, 64 hr + 114O"C, 2 hr; (c) 1230°C. 3 hr + 520°C. 16 hr + 620°C. 16 hr + 720°C, 16 hr 114O"C, 2 hr. Right: low-oxygen-content wafers of 11-12 X 10"/cm3. Left and center: high-oxygen-content wafers of 18 x 10"/cm3 (Tsuya et al., 1981).

+

14.

OXYGEN EFFECl O N ELECTRONIC DEVICE PERFORMANCE

643

za 8 + MIG, 16H ( 0 ) --t

114O'C, 2H ( 0 )

15

I-

Z

W

I2

0

i P

0 2 W

?x

i

i

I

CL.*.''

0 t

I J -1-1 top bottom top

bottom

POSITION

POSITION

(a)

(b)

Fiti. 29. The oxygen content of' wafers obtained from the top to the bottom of a crystal after each annealing process: (a) '3. as-grown; 0 , 820°C. 64 hr; 0. 820°C. 64 hr + 1140°C. 2 hr. ( b ) €3. as-grown; 0 . MIG: 0.MlG + 1 140GC,2 hr.

In order to examine the homogenization of precipitated oxygen by heat treatment, two kinds of heat treatment procedures, two-step and MIG annealings, were compared for wafers obtained from the top to the bottom of a crystal ingot (Tsuya. 1982). Two-step annealings consist of a first annealing (620"C-l050"C, for I6 hr) followed by a second annealing at 1140°C for 2 hr. In the case of MIG annealing, the high-temperature heat treatment prior to the MIG step was carried out. Figure 29(a) shows the ( 0 , )of different wafers at each stage of the two-step annealing, 820°C + 1140°C. It was found that after the two-step annealing the (0;)increased from the top to the bottom, although asgrown crystal shows a nearly uniform oxygen content distribution. A similar tendency was found after annealing at 720°C + 1140°C. This is because the density of the precipitate nuclei, grown-in nucleus (Shimura, Tsuya and Kawamura, 1980b) or latent microdefects (Kishino et al., 1982) may decrease from the top to the bottom due to the difference in thermal history during crystal growth (Nakanishi et al., 1980; Tsuya et al., 1982). On the other hand, as shown in Fig. 29(b), after the MIG annealing fol-

644

H. TSUYA

1017(c,,i3)

I

(Oil I

I

600

I

I

I

I

I

,,

I

700 800 900 loo0 IlOO" MIG 1 st anneal temp. ("C1

I

1230

+

MIG

FIG.30. The range of oxygen content for a variety of wafers after 1140°C for various + 1140°C. 2 hr (Tsuya, 1982).

first annealing temperatures including MIG

lowed by the 1140°C annealing, the uniform distribution of (Oi) was observed. These results suggest that, in the case of a two-step annealing, the interstitial oxygens that do not precipitate completely after the first heat treatment proceed to precipitate by the second heat treatment, whereas almost all of interstitial oxygens precipitate completely after MIG annealing, and then oxygen precipitates are partially redissolved by the final annealing at 1140°C. Figure 30 shows the range of (Oi) for a variety of wafers after the 1 140°C heat treatment for various first annealing temperatures including MIG. In the case of two-step annealing, the values of (Oi) after the 1140°C heat treatment distribute extending over the wide range. On the other hand, after the MIG + 1140°C annealing, the nearly constant value of (00,(9.4 t 0.4) x IO"/cm3, which is close to the solubility limit at 1140°C (Takano and Maki, 1973), was obtained for all wafers examined.

14.

OXYGEN EFFECT O N E I FCTKONIC DEVICE PERFORMANCE

645

Therefore, it will be possible that the density of inner defects as well as (0,) is homogenized in spite of the thermal history of crystal ingot, if the (0,)of a crystal is controlled to be constant extending over the whole length . Recently, the effects of two preheatings on the homogenization of precipitated oxygen was reported (Chiou. 1992). A high-temperature rapid thermal process (RTP) preheating, at 1200°C for 2 min in Ar can influence the thermal history effect by reducing the oxygen precipitation at the seed end of the crystal in comparison to the tang end. On the other hand, a low-temperature preheat treatment can increase the oxygen precipitation of the tang-end wafers much more than that of the seed end. These procedures can achieve the homogenization of precipitated oxygen from the top to the bottom likewise. Next. the application of MIG to LSI devices will be described. I n a CMOS device, the high temperature of p-well drive-in seems to play a role of redissolution described previously. Wafers were n-type ( 5 1 1 ) orientation with the ( O i )of 12-18 x 101’/cm7.The holding time failure rate of CMOS fabricated on BD and MIG heat-treated wafers with different oxygen content is shown in Fig. 31 (Tsuya, 1983). In the BD wafers. a low failure rate was obtained with a narrow range of oxygen content. because the process-induced IG effect occurred in these limited wafers.

q I-

z

(3

n

/

10

,MIG

12

14

OXYGEN

16

I8

20

Z2XlO”

CONTENT ( c r n - ’ )

FIG 3 1 Initial oxygen content v \ holding lime failure rale of CMOS fabricated on BD nnd MIG wafers (Tsuya. 1987)

646

H. TSUYA

Holding time (sec)

FIG. 32. An example of 4M DRAM holding time characteristics for DZIG and NIG wafers. HOLDING TIME FAILURE RATE

-

0

N

W

(Arb.)

*

**

NIG

:::*: * ***** **** e

DZIG-A

FIG.33. Holding time failure rate of DRAM for DZlG and NIG wafers.

On the contrary, in MIG wafers, improvement of the failure rate was apparently observed across a wide range of oxygen contents, and it was especially dominant in low-oxygen wafers such as 12 x 10'7/cm3.In the CMOS devices with high yield, no slip dislocations were observed. For practical use, DZIG is considered to be a promising technique, because DZlG has many advantages: (i) uniform oxygen precipitation, (ii) a wide range of usable initial oxygen contents, (iii) resistivity to the fluctuations of a mass production line. Figure 32 shows 4M DRAM holding time characteristics for both DZIG and NIG. The DZIG wafer shows the holding time more than 2 sec; however, the holding time of the NIG wafer is much shorter than DZIG wafer. Figure 33 shows the holding time failure rate of DRAM for DZlG and NIG wafers. DZIG wafers have the lower average value of failures and also a narrower scattering than NIG wafers. Ramping pre-heat treatment for IG (RIG) (Kishino et al., 1984) is an efficient procedure for shortening total IG-annealing time in practical use

14.

O X Y G F N EFFEC I ON k LECTRONIC DEVICE PFKFORMANCE

647

and for low (0,) wafers (Kitakata et al.. 1988). After the high-temperature annealing at 1200"C, 3 hr in N , for the annihilation of grown-in nuclei of precipitation and for the DZ formation. the 550°C to 850°C ramping annealing with the rates of 0.2"Cirnin and 0.7"C/min was carried out in dry 0,. as shown in Fig. 34 (Kitakata el al., 1988). To evaluate the gettering ability of low (0,)wafers, 11-12 x 1017icrn3,the leakage fails in the CMOSSRAM TEG circuits were surveyed over the MIG wafers. the RIG wafers and the reference wafers. which were of higher oxygen concentration and were not 1G preannealed. The 1G annealed wafers, MIG and RIG wafers, have achieved excellent results compared to the reference wafers. This is due to the effective gettering of contaminants in the CMOS process and also due to the good uniformity of precipitation measured by F-FTIR. It was also found that the precipitation and the DZ formation depended highly on the final high-temperature annealing. The I140"C-2 hr annealing in N, gave t h e good results i n the control of the bulk microdefects. The RIG annealing created the sufficient microdefects, mostly stacking fdLdts, even at one-third of total annealing time of the MIG (Kitakata et al., 1988).

3 . INTRINSIC GETTERING APPI.ICAl'lON

OF

EPITAXIAL WAFERS TO VLSI

Besides bipolar devices, epitaxial wafers grown on lightly or heavily doped substrates, nln, pip' and nln' , which are called M O S e p i t a i u l Mufer.7, are widely used for advanced VLSI. The application of 1G technique to the CCD image sensor using epitax-

9001

Annealing Time

(H)

I-ic 3.1 The modulated ramping sequences adopted for the investigation of nucleation (Kltakatd el dl . 1988) kinetic5 in

648

H . TSUYA

Epi

zn

s=

o

103

o

-j- Sub

Before Annealing After Annealing

10

20

DEPTH (pn)

FIG. 35. Spreading resistance in the n/n epitaxial wafer before and after annealing at 1200°C for 6 hr (Hiroshima et al., 1984).

ial wafers is described. The fixed pattern noise (FPN) due to the fluctuation of resistivity can be suppressed by making use of epitaxial wafers. However, oxygen atoms that are out-diffused from the substrate to the epitaxial layer during the high-temperature process for p-well formation generate oxygen related defects in the epitaxial layer, resulting in the yield degradation (Hiroshima et al., 1984). Figure 35 shows the spreading resistance in the n/n epitaxial wafers before and after annealing at 1200°C for 6 hr, which indicates the outdiffusion of oxygen atoms after hightemperature annealing. By using IG procedures before and after epitaxial growth, oxygen atoms were well confined in the substrate as precipitates, resulting in extremely low-noise CCD image sensors. The n/n+ and p/p+ wafers are immune from soft error and latch-up characteristics. Furthermore, p+ substrate has a strong gettering ability for Fe due to the formation of a B-Fe pair (Weber and Roitte, 1980). The oxygen precipitation of nf and pf substrates has been actively investigated. The dependence of oxygen precipitation on dopant concentration drastically differs between p- and n-type wafers (Pearce and Rozgonyi, 1982). Figures 36 and 37 show the densities of thermally induced microdefects observed in Sb-doped and B-doped wafers as a function of dopant concentration, respectively (Tsuya, Kondo and Kanamori, 1983). N- and p-type Si crystals were grown by the Czochralski method under the same growth conditions. Wafers were subjected to the heat treatment at 620°C + 720"C, each for 16 hr, followed by annealing at 1140°C for 2 hr. In the range of resistivities of 1-0.01 ohm * cm, the generation of thermally induced microdefects is strongly affected by the type and dopant concentration. A high density of microdefects over 106/cm2were likely to generate in B-doped wafers, whereas the microdefects necessary for IG were not easily generated in heavily Sb-doped wafers. For other n-type wafers (P-doped), a similar tendency was observed.

14.

O X Y G E N EFFECT ON F I ECTRONIC DEVICE PERFORMANCE

649

7 106-

5

Y

>

s lo5w

n c

0

fw

104-

n

P0 5

103-

10-2 10-1 1 SPECIFIC RESISTIVITY (Q. cm)

F I G . 36. Microdefect density as a function o f dopant concentration of n-type (Sb-doped) wafers (Tsuya et a l . , 1983)

1 SPECIFIC RESISTIVITY ( Q . cm)

FIG. 37. Microdefect density a\ a function of dopant concentration of p-type (B-doped) wafers (Tsuya, 1986).

650

n.

TSUYA

By raising the doping level by about an order of magnitude higher than those studied previously in B-doped wafers (Pearce, Kock and Jaccodine, 1985; Tsuya, 1986), Pearce et al. found that the generation of stacking fault and thermally induced microdefects were significantly suppressed in the ultra-heavily B-doped with resistivities of 0.003-0.001 ohm . cm (Pearce et al., 1985). Observed results in the range of 0.007-0.0015 ohm . em are added to Fig. 37 (Tsuya, 1986). These phenomena have been discussed mainly in terms of oxygen incorporation (Abe, 1985; Tsuya et al., 1985; Liu and Carlberg, 1991) and nucleation mechanism based on charged vacancy model as nucleus centers (Pearce and Rozgonyi, 1982; Tsuya et al., 1983; de Kock et al., 1980; Shimura et al., 1985). From the measurement of the interstitial oxygen content of heavily doped Si wafers by infrared absorption after electron irradiation, it was found that the (0;)of heavily Sb-doped wafer was of the order of 60% of that in lightly doped ones, which is not so small for oxygen precipitation (Tsuya et al., 1985). Recently, Hahn et al. (1990) found that the difference in oxygen precipitation between p- and n-type wafers is due to the difference in point defect density using positron annihilation and X-ray techniques. In order to promote oxygen precipitation, the supersaturation ratio of interstitial oxygen must be increased. Improved MIG is an effective method. Figure 38 shows the microdefect density in heavily P-doped wafers as a function of the final annealing temperature (Tsuya et al., 1983). Dense microdefects of around I05/cm2 were generated around 950°C. A ramping preannealing from low temperature to high is also a useful procedure. A high density of microdefects were successively generated in heavily Sb-doped wafers using a ramping preannealing of 0. l"C/ min from 550°C to 850°C followed by the 1140°C heat treatment. Similar results using ramping nucleation annealing for the improvement of oxygen precipitation in a Sb-doped n / n + epi wafer has been reported (Comeau, 1992). As described previously, oxygen precipitation in p+ substrate occurs easily. If such a p + substrate is used for epi growth, unwanted crystalline defects generate on the epi wafer. For example, pairs of etch pits or "viper pits" appear on p/p+ epi wafer surface (Lin, 1990). In order to apply p/p+ epi wafer to VLSI, it is proposed to tailor the p+ substrate so that (a) there is little or no precipitation as a result of pre-epi thermal treatment, (b) during epi deposition, some preparation occurs to provide intrinsic gettering and (c) full precipitation occurs early in the device fabrication (Lin, 1990). This situation, of course, must be considered to what devices pip+ epi wafers are applied.

14.

O X Y G E N EFFECI O N I.I.ECTKONIC DEVICE PERFORMANCE

I 1 800

I

900

1

I

65 1

1

1000 1100 120(

TEMPERATURE ("C)

FIG. 38. Microdefect density as a function of the final annealing temperature after MIG annealing for heavily P-doped wafer ( ' l w y a et id., 1983).

4. GETTERABILITY FOR HEAVY M E T A LIMPURITIES

Among the heavy metal impurities, Cu, Ni and Fe are easily introduced by the fabrication process and harmful to device characteristics. Due to a larger diffusion constant and t h e large affinity of Cu with Si, Cuprecipitates have been often observed in failed devices of which the failure mode is leakage current. Figure 39 shows the TEM image of Cuprecipitates observed at the hottom o f leaky bipolar trench isolation due to contamination and EDX spectra (Mikoshiba et al., 1992). It is well known that heavy metal impurities respond differently to gettering procedures due to their different physical and chemical properties. For practical use. it is important to clarify which metals are easily gettered. Cu and Ni atoms are easily gettered at oxygen precipitates (Hourai et al.. 1989; Falester and Bergholz, 1990)due to their large diffusion coefficient and large solubility in the bulk, which are very important factors for 1G (Weber and Gilles. 1990).On the other hand, Fe atoms are difficult to getter compared to Cu and Ni (Hourai et al., 1989; Abe et al.. 1990) because of a low diffusion constant and solubility. Furthermore, it has been reported the Fe atoms were gettered by the oxide larger than oxygen precipitates and again dissolved in Si crystal at high temperature (Abe et al., 1990).

652

I

I

n. TSUYA

Precipitate

S;

i

cu

I

I ,

I I

FIG. 39. The TEM image of Cu-precipitates observed at the bottom of bipolar trench isolation and EDX spectra (Mikoshiba et al.. 1992).

5. CONTROL OF MECHANICAL STRENGTH The gettering sinks of DZIG are intentionally created by oxygen precipitation, so excessive oxygen precipitates have a possibility of degrading the mechanical strength of a wafer. Figure 40 shows the relationship between microdefect density and induced warpage for different ingots after CMOS process simulation (Shimizu, Watanabe and Kasui, 1985). Induced warpage increases drastically for the microdefect densities over 5 x 10V/cm3.Induced warpage depends critically on the initial oxygen concentration and is also influenced by heat treatment procedures. Figure 41 shows wafer warpage versus heat-treatment step number observed in the n-well CMOS process (Lee and Tobin, 1986). Thermally induced warpage occurred for wafers having an initial oxygen concentration greater than 32 ppm during a 900°C push-pull in the implant annealing step.

14.

O X Y G E N EFFEC I O N k L ECTKONIC DEVICE PERFORMANCE

653

70 60 50 40 -

30 20 10 -

0-

Microdefect Density

(cm-’l

F I G . 40. Warpage behavior of precipitation-treated wafers in warpage experiments as a function of microdefect density. Prior to the warpage experiment. samples were heat treated at IOOO’C for I 6 hr in a wet oxygen ambient. ‘The letters A to F present the crystal ingots u\ed in the investigation rShimizu et i d . , 19x5)

CONCENTRATION

‘0

1

2

3 4

5

6 7

8 9 10111213

STEP NUMBER

I-K, 41 Wafer warpage

v\

he,it-tre;itment step number (Lee and Tobin. 1986)

Induced warpage is also caused by the poor matchability to device processes such as wafer spacing and withdrawal velocity of a wafer in the furnace. In order to make wafers resistive to induced warpage. the optimization of (0,)after heat treatments utilizing the redissolution phenomenon of precipitated oxygen is important as well as heat treatment procedures. It was found that the excesx oxygen precipitates generated by MIG annealing were redissolved partially at 1230°C (Tsuya, 1982). Figure 42 shows the correlation of induced warpage with annealing time at 1230°C. Warpage was not induced in the wafers that were subjected to the heat treatment at 1230°C for 2 hr at least. Furthermore, in these wafers, a high

654

n. TSUYA

density of inner defects of 5 x 105/cm2,which is less than the density of inner defects generated by MIG annealing but sufficient for the effective IG, remain. The (Oi) after the redissolution process was 11 x lOI7/cm3,which is comparable to the solubility limit at 1230°C whereas the (Oi) of the asgrown wafer was 16 x 1017/cm3.In the MIG heat-treated wafer, 11 x 10'7/cm3of oxygen was observed to precipitate. Then after the 1230°C annealing, 7 x 10'7/cm3of precipitated oxygen was redissolved. Consequently, 4 x 10'7/cm3of precipitated oxygen did not redissolve and contributed to IG effect, because 1 x l'017/cm3of oxygen out-diffused. It was also confirmed that even MIG wafers that were subjected to the annealing at 1230°C for 8 hr showed the JG ability. The redissolution process was examined by TEM. Dense precipitatedislocation complexes (PDCs) were observed in the specimen that was annealed at 1230°C for 0.5 hr, as shown in Fig. 43(a). After the 1 hr annealing, dislocation were observed to pinch off around SiO, precipitates, which are identified as amorphous SiO, (Shimura et al., 1980a), as shown in Fig. 43(b). Furthermore, after the 8 hr annealing, the specimen results in dense dislocations and stacking faults, which play a role of gettering sinks after redissolution. The precipitation-redissolution is well reproducible (Shimura and Tsuya, 1982)for the optimization of interstitial oxygen content. Two examples of controlling the mechanical strength of LSI devices, CCD and bipolar, are discussed. Generally, CCD image devices are highly sensitive to material problems and susceptible to induced warpage. CCD devices were fabricated on a MIG wafer with the (Oi) of 15-18 x

ANNEALING

TIME ( h )

FIG.42. Induced warpage as a function of annealing time at 1230°C.

14

OXYGEN FFFEC 1 O N t L t ( 7 H O N I C DEVICE PFRFORMANCt

655

F I G . 43. TEM micrographs of inner detect\ after redissolution: ( A ) after 0.5 h r at 1230°C. ( B ) after I hr at ll3o"C.

l0"/cm3. Induced warpage was measured in some typical processes. Figure 44 shows an example of warpage for two lots, A and B. Device fabrication was completely finished after process 1V. Wafers on which devices had been fabricated were stripped to bare silicon in process V . Therefore, the difference in warpage between 1V and V corresponds to elastic deformation. It was found that warpage was not induced in lot B , whereas induced warpage was drarnatically observed in the central and peripheral regions of lot A . Device characteristics corresponded t o induced warpage. White spot defects were not observed in devices fabricated from lot B . On the other hand, white spot defects were seen in ones made from lot A , in which dislocation arrays from LOCOS edges as shown in Fig. 45 and a high density of inner defects were observed by Wright etching, on a cleavage plane. whereas no dislocation arrays but only many inner defects in lot B . Almost all of the dislocation arrays are observed along ( 1 I ) and ( 1 1 1 ) planes from the pattern edge of field oxide. as schematically shown in Fig. 46(a).It is interpreted that dislocations generated at the pattern edges penetrate into inner parts along the Clli) and ( 1 1 1 ) planes. Therefore, these dislocation pits. which correspond to white spot defects in the device region, are concluded to the dislocation-half loops due to induced stress by field oxide, as shown in Fig. 46(b). In the case of CCD, the

n.

656

TSUYA

I5Ot

R

o lot A 0 lo1

I \

0

\\

I

\\

I

\

I I

100-

\

b

I I I I I

-

I

I

E

W

I I I

50-

0 U

a

n

2

0-

-5OI

I

I

- n - m - IV - v I

I

I

I

PROCESS

FIG.44. Induced warpage of CCD after some typical processes for lot A and lot B (Tsuya, 1992).

film-edge induced stress (Franz et al., 1981) is one of the main causes to induce white spot defects. So, it is important to suppress the film-edge induced stress in the application of IG to CCD devices. In the application of IG technique to a bipolar device, it is important that the IG wafers are matchable to the epitaxial growth process. In order to evaluate the matchability to the epitaxial growth process, two kinds of epi-reactor were used. Substrates were p-type (1 11) or (100) orientation and 10-15 ohm. cm. Three kinds of (O;), 18, 15 and 12 x 10"/cm3, were examined. When the epitaxial layer was grown by the induction heating, MIG wafers were susceptible to warpage, which degraded device yield. Figure 47 shows the correlation of induced warpage with yield (Tsuya, 1983). The yield criterion is a leakage current between the collector and emitter of less than 1 FA. Device leakage limited yield degraded with increasing

14.

of

OXYGEN EFFEC

r

O N t.l.tCTKONIC DEVICE PERFORMANCE

657

FIG.45. ( a ) X-ray topographic picture oTCCD processed wafer; ( b )cross sectional picture chip as shown by arrow in ( a ) .

FIELD OXIDE AKEA

coiii

. DISLOCATION

(b) iii)

FIG.46. (a) Schematic picture of dislocation rnatic dislocation-half loops.

pit3

observed on a cleavage plane; ( h ) cche-

n.

658

TSUYA

1-<

^xv M

c-

-9 ? m

z!

0.5

-

M

w> 0

YIELD

DEFECT

FIG.48. An example of bipolar device yield and defect distribution in a wafer. In the case of yield distribution, hatched and open regions show bad and good chips, respectively. For defect distribution, slip dislocations and dislocation pits are observed mainly in hatched and dotted regions, as shown in photos. Crystallographic defects are not observed in unmarked regions.

14.

OXYGEN EFFEC I O N t.l.I:CTRONIC DEVICE PERFORMANCE

659

induced warpage. In this case, a nonuniform temperature profile in a wafer due to the induction heating causes induced warpage. In Fig. 48, an example of device yield and defect distribution in a wafer is shown. Crystallographic defects such as slip dislocations and dislocation pits were observed in failed chips, resulting in the good correspondence between defects and yield distribution. On the other hand, when the epitaxial layer was grown by radiant heating, warpage was not induced and significant yield improvement was obtained. Figure 49 shows an example of collector-emitter leakage current histogram of bipolar devices fabricated on backside-damaged and MIG heat-treated wafers with the (0,)of 15 x 101’/cm3(Tsuya, 1983). It was found that MIG heat-treated wafers were far superior to backsidedamaged ones extending over the wide range of oxygen content from 12 x 10”/cm3 to 18 x IO”/cm’ examined. During the epitaxial growth process using SiHzClzgas under reduced pressure, the backside-damaged thin layer is considered to be easily etched by HCI gas from SiHzClz source gas and lose gettering ability.

Ice0

10-100

I

,? .

I

1

10mA ”

0

I G

bockside domogc

i

10-100

0 FREOUENCY

(%)

F I G . 49. An example of the collector-ernltter leakage current histogram of bipolar devices on B D and MIG wafers (Tsuya. 19x3)

660

H. TSUYA

d

I

!

B

12

10

0

- *’

8 O

#*STARTING , WAFERS

.. . 2.e.

.

AFTER 5h.1050’C +BIPOLAR PROCESS

115 ’ ’ ;9 I 21 INITIAL WAFER [ Oi ] PPMA

1;

FIG.50. Graphic relationship between initial (O,), amount of enhanced precipitation and remaining ( 0 , )in a bipolar process (Lin and Moerschel, 1986).

From the standpoint of oxygen precipitation to maintain the wafer’s yield strength for a bipolar device, an optimization of initial oxygen content and remaining oxygen content after bipolar device processing was proposed (Lin and Moerschel, 1986). Figure 50 shows the graphic relationship between initial (Oi), amount of enhanced precipitation and remaining (0,)in a bipolar process. This suggests that at least 10 ppma of initial oxygen should be retained to prevent the onset of slip dislocations during processing of a bipolar device. The gettering ability and mechanical strength are not easily compatible with each other. This is the reason why IG is also called a “two-edged sword,” like oxygen. It is of practical importance to improve heat treatment procedures and epitaxial growth processes in order to decrease thermal stress by maintaining residual oxygen content reasonably by a proper heat treatment. In recent ULSI processes these are well controlled. 6. ADVANCED INTRINSIC GETTERING

In order to apply the IG technique more effectively to VLSI, DZIG must be upgraded. The thorough understanding and control of point defects affecting the oxygen precipitation are required. Among others, the perfection of the denuded zone must be thoroughly investigated using advanced analytical tools and advanced heat treatment procedures. The width of the denuded zone has been conventionally measured by optical microscopy after preferential etching. However, as shown in Fig. 51, the width of the denuded zone evaluated by infrared tomography is found to be considerably narrower than one measured by optical microscopy after preferential etching.

14. O X Y G F N EFFECT O N

€ I ECrRONIC DEVICE PtRFORMANCE

66 1

On the other hand, the surface photovoltage (SPV) method, which measures minority carrier diffusion length, is useful for the nondestructive measurement of the denuded zone width and the density of oxygen precipitates in 1G wafers (Jastrzebski. 1990). The correlation between diffusion length and device yield for CCD imagers (Jastrzebski et al., 1988) and bipolar devices (Jastrrebski et al., 1984) have been reported. Figure 52 shows the correlation between yield of bipolar circuits as a function of diffusion length measured in processed wafer (Fung. 1988). Leakage-limited yield increases with increasing diffusion length. At present, it is not feasible to measure the denuded zone width more precisely and more reproducibly. For advanced lC, more advanced analytical tools must be developed. Very recently, it was reported that the H2annealing at high temperature improves the quality of denuded zone (Kurihara et al., 1992; Shirai et al.. 1992). Figure 53 shows the radial distribution of surface BMD densities below 10 km for the annealing at 1200°C and without H, annealing. The surface BMD density measured by infrared tomography for the H2 annealing at 1200°C was drastically decreased compared to the annealing without H,. This is tentatively interpreted by the diminution of precipitated nuclei and the acceleration mechanism of oxygen out-diffusion in the H, atmosphere. The oxygen concentration in the Hz annealed sample measured by SIMS was an order of magnitude lower than one without H,. The Hz annealing procedure at high temperatures suppresses the OSF density and improves oxide film breakdown characteristics.

FIG. 51. ( a ) Optical microscopic picture of a cleavage plane after Wright etching: ( b ) infrared tomographic picture (l'suya. I Y Y 2 ) .

662

H . TSUYA

L

-

Bipolar Logic 7 Repeated Experiments

/

$ El00 .2 ;g,

u)

al .P

80

-

96 Y

60-

-I 0

40-

IX B

I-

measured in the

FIG.52. The yield processed wafers (Fung, 1988).

108 I 1o7

s

?

106

Y

lo5 .-c2. In C

8 lo4 0 al

f

102

m

t

0 Center

H2 anneal

".,./" ^

^

-

^

Edge

FIG.53. The radial distribution of surface BMD densities below 10 pm for the H, annealing at 1200°C and without H2 annealing (Kurihara et al., 1992).

It has been considered that p/p+ epitaxial substrate is an ideal wafer (Electronics, 1981), because p/p+ wafer has a lot of advantages, such as a nearly perfect denuded zone, a strong getterability for Fe, lower diffusion current at elevated temperatures (Slotboom, Theunissen and de Kock, 1983), and also applicabilities to latch-up free (Borland and Deacon, 1984) and advanced devices fabricating substrate plate trench capacitor cell (Sakamoto et al., 1985) and vertical transistor (Richardson et al., 1985), for example. Figure 54 shows a typical cross-sectional picture of p/p+ epitaxial wafer.

14.

Fic,

O X Y G E N E F F E C l O N FI EC IRONIC DEVICE PERFORMANCE

663

54 A typicdl crw,\-scction,il picture of a pip' epitaxial wafer

V. Summary As the dimension of ULSI is decreased into half-micron level and a high density of 30 million elements are integrated in a small chip area, it has become difficult to clarify the origins of device failure modes, which is indispensable for the achievement of high-yield devices. Especially, the oxygen effect on device performance is complicated and important. As described earlier, a small amount of oxygen related defects in a denuded zone drastically affect the device performance (Nishio et al., 1990). Oxygen precipitates couple with heavy metal impurities and generate plastic deformation, resulting in the degradation of device characteristics. On the other hand, defect control technologies are more and more important to obtain high reliability and high yield. Among them, intrinsic gettering, which is inevitably related to oxygen, is sure to continuously support the ULSI Si industry with ultraclean technology. It should be emphasized that the development and utilization of advanced analysis technologies. new heat treatment procedures and possibly new crystal growth methods are more effective to the development of more advanced defect control technology and deeper understanding of oxygen behavior.

ACKNOWLEDGMENTS The author would like to thank M . Mikarni. H . Kikuchi. M . Kitakata, S . Ohya and S. Teranishi of NEC Corp. for their discussions and valuable data.

664

n.

TSUYA

REFERENCES Abe, T. (1985). In VLSI Electronics 12, N . G . Einsruch and H . Huff (eds.), p. 3. Academic Press Inc., London. Abe, T., Itoh. T., Hayamizu, Y., Sunagawa, K., Yokota, S., and Yamagishi, H. (1990). In Defect Control in Semiconductors, K. Sumino (ed.), Vol. 1, p. 89. North-Holland, Amsterdam. Anagnostopoulos, C. N., Nelson, E. T., Lavine, J. P., Wong, K. Y., and Nichols, D. N. (1984). IEEE Trans. Electron Devices ED-31, 225. ASTM. (1979). Method F121-79, 1979 Annual Book of ASTM Standards, Part 43. Borland, J. O., and Deacon, T . (1984). Solid Stare Tech. (Aug.), 123. Carin, A. H . , and Bhattacharyya. A. (1985). Appl. Phys. L e t t . 46, 872. Chiou, H.-D. (1992). J . Electrochem. Soc. 139, 1680. Chiou, H.-D., and Shive, L. W. (1985). In VLSI Srience and Technologyif985, W. M. Bullis and S. Broydo (eds.), p. 429. Electrochem. SOC., Pennington, N.J. Colinge. J . P. (1992). Paper presented at NTU Satellite Network-SO1 Tech. in VLSI Processing. Comeau, A. R. (1992). J. Electrochem. S o c . 139, 1455. d e Kock. A. J . R., and van de Wijgert, W. M. (1980). J. Cryst. Growth 49, 718. EerNisse, E. P. (1979). Appl. Phys. L e t t . 35(1), 8. EerNisse, E. P., and Derbenwick, G. F. (1976). IEEE Trans. Nucl. Sci. NS-23, 153. Electronics. (1981). (Feb. 10). Falester, R., and Bergholz, W. (1990). J. Electrochem. SOC. 137, 1548. Franz, G.;Kolbessen, B. O., Lemme, R., and Strunk, H. (1981). In Semiconductor Silicon/ 1981, H. R. Huff, R. J. Krieger, and Y. Takeishi (eds.), p. 821. Electrochem. SOC., Pennington, N.J. Fung, M. S. (1988). Ext. Abst. ECS Spring Meeting, 88-1, p. 269. Hahn, S., Ponce, F. A., Dannefear, S., Mascher, P., Kerr, D., Puff, W., Stojanoff, V . , Ishigami, S., and Tiller, W. A. (1990). Ext. Abst. ECS Spring Meeting, 90-1, p. 650. Hiramoto, K., Sano, M., Sadamitsu, S., and Fujino, N. (1989). J p n . J. Appl. Phys. 28, L2109. Hirao, T., Inoue, K., Yaegashi, Y., and Takayanagi, S. (1979). Jpn. J. Appl. Phys. 18,647. Hirao, T.. and Maegawa, S. (1988). J . Electrochem. Soc. 135, 2361. Hiroshima, Y.,Matsumoto, S., Senda, K., Kuriyama, T., Horii, K., Kuroda, T., Kunii, T., and Mizuno, H. (1984). I E D M 8 4 Tech. D i g . , 32. Honda, K., Nakanishi, T., Osawa, A., and Toyokura, N. (1987). In Microsc. Semicond. Muter. Conf., p. 463. Hourai, M., Murakami, K., Shigematsu, T., Fujino, N , , and Shiraiwa, T. (1989). Jpn. J . Appl. Phys. 28, 2413. Hu, S. M., Kepner, S. P., Schwenker, P. 0.. and Seto, D. K. (1976). J . Appl. Phys. 47, 4098. Huff, H. R.. Schaake, H . F., Robinson, J. T., Baber, S. C., and Wong, D. (1983). J. Electrochem. SOC. 130, 1551. Ikuta. K.. Nakajima, S., and Inoue, N. (1984). Ext. Abst. 16th ICSSDM, p. 483. Jastrzebski, L. (1982). IEEE Trans. Electron Devices ED-29, 475. Jastrzebski. L. (1990). In Defect Control in Semiconductors, K. Surnino (ed.), Vol. 1, p. 593. North-Holland, Amsterdam. Jastrzebski, L., Saydan, R., Goldsmith, B., and McGinn, J . T. (1984).J . Electrochem. Soc. 131. 2944.

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This Page Intentionally Left Blank

Index

B

A A-center, 217

B mode failure. 633

uh rnirio theory. 327 Absorption band. 255, 267f; 282

Back-surface condition. 125 Back-surface effect. 123, 125 Backside roughness. 57 Baffle, 49 Barrier. nucleation. 524 Baseline. infrared spectroscopy. 113. 114. 115, 123 Beer's law, 99. 117 Berg-Barrett topography. 64 Binding energy, thermal donor. 256 Bipolar device. 656. 658. 659. 660 Bipolar proces\. 514, 542 Bipolar transistor. 622 Bond center. 169 Bond length. 330. 334 Boundary layer. hydrodynamic. 20 Boundary layer. melt-crucible, 34 ( ' ? I Bourgoin-Corhett mechanism, 171. 182 BPS equation. 19 Brag spacing comparator. 54 Hragg reflection, 63 Brewster-angle method. 112. 120. 123 Butterfly-shaped complex, 614

Abwrption coefficient. 57 Acceptor. closely spaced. 613 Activation analysis technique. 74 Activation energy. 2 diffusion, 161 oxygen diffusion. 293 thermal donor. 280 thermal donor annihilation. 266 Activation reaction. 75 Ambient pressure. 25 Annealing. 590 CMOS-type. 426. 427 tII-L.O-HI, 416 H1-LO-HI. 542 hydrogen. 661 L,O-HI, 416 multistep. 424 new donor. 282 nucleation. 421 o v . 220 O V %, 241 .iubstitutional. 428 thermal donor. 252-257 three-step, 416 Annealing temperature. 431 Annealing time. 43 I Annihilation. thermal donor. 256.

266 Aspect ratio. 42. 5 0 Auger microprohe, 61 Auger recombination. 79 Axial profile dopant. 47 nxygen. 38. 40

C Calibration factor. 57 ASTM. 124. 144 Kaiser-Keck. 137 oxygen. 101. 125. 136. 137. 138. 141 Certified reference material. 145. 146 Calibration method. load factor. 143 Calibration method. load-line, 130. 143 Capture radius. oxygen dimer, 300. 306. 346

669

670

INDEX

Car-Pamnello theory, 331, 335 Carbon, 5, 269, 282, 375 irradiation defect, 222, 224 pairing with oxygen, 214, 222 substitutional, 224 Carbon incorporation, 18 Carrier removal, 58 Cassette-to-cassette operation, 596 CCD. 598, 622, 625, 656, 657 Characterization technique, 53, 58 chemical, 69 electrical, 77 physical, 55 Charge size, 46 Charge state OVA,, 239, 241 point defect, 173, 174, 182 Charged particle activation (CPA), 61, 54, 76 Charged particle activation analysis (CPAA), 139 Chemical defect etch, 54, 69, 72 Chemical etching, 69, 77, 85 Chemical technique, 54, 69 Chip yield, 621 Chlorine-containing ambient, 594 CMOS, 598, 639 CMOS process, 514, 542 CNDO, 328 Coesite, 527 Concentration carbon, 545 critical oxygen, 604, 605, 607 dopant, 649 equilibrium, 61 1 initial oxygen, 545, 652 interstitial oxygen, 420, 440, 597, 601 oxygen, 136, 251, 266 precipitated oxygen, 414, 417, 420 residual oxygen, 625 self-interstitial, 176, 177 thermal donor, 252 threshold. 604 Conduction band, 257, 264, 268, 2748, 281 Configuration acceptor-hydrogen complex, 230 CiOi complex, 223 donor-hydrogen complex, 232 interstitial hydrogen, 229, 230, 232 interstitial oxygen, 201,204,208, 234,237

OV, 217 OVA,in GaAs, 241 oxygen-vacancy (OV), 220 self-interstitial, 167, 169, 170, 181, 182 thermal donor, 276 Constant melt volume, 46 Contamination, 577, 583, 590 Contamination heavy metal, 634 metal, 546 metallic, 578, 596 Contamination source, 596 Continuous CZ growth, 5, 17, 604 Continuous feed mechanism, 46, 49 Convection forced, 21, 25 thermal, 20, 25 Cooling, crystal growth, 418,419, 433. 434, 435 Corrugated crucible surface, 40 Cottrell atmosphere, 464 Cottrell effect, 613 CPA. See Charged particle activation CPAA. See Charged particle activation analysis Critical radius, 541 Critical radius, oxygen precipitate, 415, 424 Crucible quartz, 1 vitreous silica, 1 Crucible dissolution, 25 Crucible ramping, 38 Cryogenic temperature, 135 Crystal defect, 621 Crystal rotation rate, 44 Crystal-crucible rotation, 28 Crystal-melt interface, I Curve-fit method, 117 CZ. See Czochralski Czochralski (CZ) method, 1 Czochralski growth, 13 dislocation-free, 14

D Dangling bond, 613 Dash etch, 70, 72 Dash’s technique, 14

INDEX

Decoration copper. 560 crystal defect. 549 nickel. 560 Deep level. 578 Deep level transient spectroscopy (D1.7'S). 54.77.78, 257. 272. 276,283 Defect engineering. 579 Defect etch. 54. 69, 72 Defect A swirl. 553 B swirl. 553 bulk. 5%. 599 D. 553. 557 dark spot. 519 flow pattern. 568 grown-in, 513, 551, 567. 579 interior. 4. S79. 583, 590. 596, 598. 614 internal. 6, 593. 612 point, 514 process-generated, 579 process-induced. 513. 579 ribbon-like. 527 secondary, 5 I 3 stacking fault-like loop. 527 Surface, 579, 5% Defect-free surface region. 579. 594 Defect-free zone. 606 Dens it y microdefect. 649 oxygen precipitate, 398. 414. 419. 423. 427. 430. 435 packing. 622. 640 precipitate. 544 Denuded zone (DZ), 64.66. 69. 77. 84. 252. 416. 420. 597. 599, 604, 606. 61 I . 615. 628. 660. 661 Denuded zone depth. 608 Device characteristics. 621 Device yield. 578. 635 Device zone. 615 Dichroism. localized vibrational i ~ i ~ t f t . . 197. 210. 236 Ilielectric break down. 633 [)iffraction limit. 58 I>iffraction technique. 62 Diffusion. 577 hydrogen. 318 interstitial oxygen. 367 self-. Ihl

67 1

Diffusion boundary layer, 19 Diffusion constant. 331 Diffusion current, 622 Diffusion length, 77, 80. 661 minority carrier, 77. 80 Diffusion mechanism dissociative. 178 dual. I55 Frank-Turnbull. I78 interstitialcy. 155 kick-out, 178 vacancy. 155 Diffusion-limited process, 604 Diffusivity oxygen. 266. 267, 271 self-interstitial, 177 Diode leakage current, 83, 84 Dislocation. 61. 546, 579. 603 60" degree, 519 Burger's vector of, 451 dipole. 519. 529 dynamical behavior of. 3 extrinsic. 585 Frank partial, 582 glide. 45 I , 452 HREM image of, 453 misfit. 594 oxygen segregation on, 463. 486, 504 prismatic punching. 379 punched-out. 491. 498, 588 release stress of. 463, 468, 473, 500 shape of. 453, 460 Shockley partial. 452. 455 slip. 5, 659 unlocking stress of, 463 Dislocation array, 655 Dislocation dipole, 587 Dislocation generation by thermal stress, 474, 488 critical stress for. 472. 490 from amorphized region, 469 from damaged structure. 469 oxygen effect on. 472 suppression of, 474 Dislocation half loop. 625, 655, 657 Dislocation immobilization. 454. 460. 463, 473. 481, 490. 500, 504 Dislocation interaction, 461 Dislocation line. 631

672

INDEX

Dislocation locking, 455, 481, 499 in carbon-doped silicon, 504 in CZ silicon, 463, 467, 472, 481 in nitrogen-doped silicon, 501 Dislocation loop, prismatic, 519, 537 Dislocation motion, 458, 500 Dislocation multiplication, 474, 481 Dislocation velocity, 454, 500, 504 i n carbon-doped silicon, 504 in CZ silicon, 457 in FZ silicon, 455 i n nitrogen-doped silicon, 500 Dissolution rate, 409, 410 oxygen, 603 Distribution function, oxygen precipitate size, 396, 401, 403, 408, 412, 428, 433 DLTS. See Deep level transient spectroscopy donor, 251 annihilation. 3 new, 2 old, 2 oxygen, 6 , 599 thermal. 2. 2 5 1 8 Dopant axial uniformity, 47 Dopant striation random, 23 rotational, 23 Doping, nitrogen, 559 Double crucible, 17, 49, 42 Double crystal method, 64 DRAM, 620, 622, 627, 631 Drift current. 622 Dynamical theory, 63

E EDX. See Energy dispersive X-ray spectroscopy EELS. See Electron energy loss spectroscopy effective charge, 196, 208, 224, 237 Effective mass, thermal donor, 255 Effective-thickness method, 120, 125 EL2 center, 2 3 9 8 EL3 center, 241 Elastic strain, 590 Electrical activity, OV, 217, 219 Electrical technique, 54, 77 Electron beam induced current (EBIC), 85

Electron diffraction, 60 Electron energy loss spectroscopy (EELS), 60 Electron nuclear double resonance (ENDOR), 260, 262, 279 Electron paramagnetic resonance (EPR), 257, 260, 268, 272, 284 Electron paramagnetic resonance, OV, 217 Electron spin resonance (ESR), 86 Electron, unpaired, 613 Electronic device performance, 619 Emitter-collector short circuit, 624 ENDOR. See Electron nuclear double resonance energy chemical, 522 elastic, 522 surface, 522 total, 523 Energy barrier, point defect, 157 Energy dispersive X-ray spectroscopy (EDX). 651 Entropy barrier, point defect, 157 Epitaxial wafer, 647 Epitaxy, 546 Equilibrium concentration, oxygen, 434, 435 Error function, 607 Etch pit linear, 581, 583 saucer, 580 Etching dry, 578, 620 ion-beam, 578 plasma, 578 preferential chemical, 581 reactive ion (RIE), 578, 637 wet, 578 Etching reagent, 578

F Fast neutron irradiation. 58 Fast-diffusing, 610 Fe-B pair, 648 Feed-and-pull, 48 Film-edge induced stress, 656 Float zone growth, 12 Float zone (FZ) method, 1 Fluorescence yield, 60

673

INDEX

Fokker-Planck equation. 404. 405. 406. 408, 409 Formation new donor, 282, 284 thermal donor, 252-257. 266. 269 Formation energy. point defect. I 7 5 Fourier transform infrared spectroxopy (FTIR). 54, 58, 73 Fraction. precipitated oxygen. 422 Free carrier absorption. 58. 81 Free energy, oxygen precipitation, 3x6 Free-carrier trapping. 133 FTIR. See Fourier transform infrared spectroscopy F'I'IR. micro. 627 FZ. ScJe Float zone FZ silicon. 614

G GaAs. 236.t'f

Ciamma photon activation (GPA). 54. 75 Gamma-ray diffraction. 66 Gate oxide. breakdown. 564 Generation lifetime, 77. 79, 81, 82 Gettering. 32. 466, 473. 490. 579, W I chemical (CG). 593 external (EG). 593 extrinsic (EG). 4. 593 extrinsic!external, 594 extrinsic/internal. 594 in situ. 4, 593 internal (IG). 4, 548, 593 intrinriciinternal. 577. 594, 596 Gettenng effect. 6. 591. 611 Gettering sink. 579. 612. 614 internal, 591 Gettering technique. 593 Gibbs energy, 394. 402. 406. 410, 436. 437, 590 GPA. See Gamma photon activation (jrdphite fusion, 76 Grashof number. 20 Ground state, thermal donor, 255. 26X. 272. 275 Growth. oxygen precipitate. 362. 767. 371. 372. 375 Growth law, oxygen precipitate. 397. 407

Growth rate, 409. 410 Growth striation. 58

H Hall effect, 2548. 275 Hartree-Fock theory. 327 Haze, 560, 634 Heat treatment homogenizing. 605 multistep. 601. 610 multistep 1G (MIG). 641 Heavily doped wafer. 648 Heavy metal, 634, 635, 651 Heterogeneous factor, 5 , 603, 605 Hexagonal site. 167, 181, 182 HF-HNOI etch. 70, 72 High-resolution electron microscope (HREM). 61 High-temperature processing, 5 Holding time, 623, 638 Holding time characteristics. 646 Holding time failure. 625 Homogenization. precipitated oxygen. 640. 643, 645 Hot zone, 15 HREM. See High-resolution electron microscope hydrogen, 213. 267. 269. 271. 281 antibonded. 232 bond centered. 229 hidden. 320 oxygen interaction. 335-339 plasma, 319 Hydrogen gas. 319 Hydrogen passivation. 277 Hydrogen site. 337

I I-atom. 346 IC See Integrated circuit Ideal strength of silicon, 469 IG. process-induced, 639 IG effect. 599 IGFA See Inert gas fusion analysis IG technique. dibadvantage of, 610

674 Impurity distribution, Fermi-Dirac statistics for, 464 Impurity striations, 42 Impurity acceptor, 603 diffusivity of, 595 donor, 604 heavy metal, 634, 635, 651 metallic, 578, 596, 61 1 solubility of, 595 subsidiary, 5, 590, 603 Induction heating, 656 Inert gas fusion, 72 Inert gas fusion analysis (IGFA), 53, 54, 72, 137. 142 Infrared absorption, 2, 96 air reference, 99, 121 double beam difference, 99 free camer, 96, 98, 121 impurity, 96 interstitial oxygen, 96, 200ff OV, 218 OVA,, 238 silicon lattice, 96 single beam difference, 99 thermal donor, 254ff, 268, 272, 276 Infrared spectrometer dispersive, 102 Fourier-transform (FTIR), 107 Infrared spectroscopy, 53, 55 Brewster angle incident, 57 Infrared tomography, 660 Initial oxygen content, 431 Integrated circuit (IC), 251 Integrated-area method, I15 Intensity, localized vibrational mode, 196 Interface states, 78 Interface, Si0,-Si, 534 Interference, 76 Interference fringe, 11 I , 118, 120 International oxygen coefficient (IOC-88), 101, 137, 141, 145 Interstitial, 552 Interstitial friction, 293 Interstitial oxygen, 207, 233, 237 diffusivity of, 609 Interstitial site, 2 Intrinsic point defect, 579, 603, 604 Ion implantation, 620, 630, 631

INDEX

Ionization energy, thermal donor, 255, 257, 258, 264 IR. See infrared absorption Irradiation defect carbon, 222,ff interstitial silicon, 222 oxygen, 222ff, 236 vacancy, 220 Irradiation point defect, 172 Isosceles triangle, 2 Isotope shift, 195, 200, 205, 215, 224, 234, 237, 243 localized vibrational mode, 195

J Jump energy, 335

K Kinematical theory, 63 Kirkendall effect, 168 KOH etch, 71, 72

L Lambert-Beer law, 57 Lang topography, 64 Latch-up, 32 Lattice absorption, silicon, 102, 106, 121 Lattice expansion, 192 Lattice imaging, 60 Lattice site, 333 oxygen, 292, 340 Leakage current, 621, 624 collector-emitter, 659 Level, donor, 257 Lifetime, 638 Lifetime measurement, 265 Lifetime profiling, 81, 83 Light point defect (LPD), 567 Lithium, 211 Lithium diffusion method, 139 Local density function, 327 Localized defect, 194ff

675

INDEX

Localized vibrational mode. 194tf LOCOS, 620, 624. 628. h29. 655 Low-dose single implant. 632 LPD. See Light point defect Luders band. 469. 477, 491. 494. $02.

M Magnetic field applied CZ growth (MC'Z). 4. 42, 44 horizontal. 42 vertical. 44. 45 Majority carrier. 622 Master equation, 404 MCZ. See Magnetic field applied C'Z growth Mechanical strength. 3. 5. 6, 12. 591, 599 wafer. 651 Melt flow pattern, 29 Melt stagnation. 22 Melt transfer. 48 Melt turbulence. 20 Melt-crucible contact. 39 MEMC etch, 71, 72 Metal-silicide. 634 Micro-FTIK. 627 Microdefect. 32. 43. 156, 577 interior, 577 latent, 643 process-induced. 590 surface. 579. 580. 582. 634 Microprecipitate, 587 Microroughness. 634 Microscopic structure, thermal donor, 27 I Microsegregation. 58 Microstructure. 69 Migration. self-interstitial, 166, 170. 171, I82 MINDO. 328 Minority carrier, 598, 622, 623 Modern CLochralski crystal grower. I I Molten zone, 12 Monte Carlo model. 402. 403 Morphology, precipitate. 515 MOS capacitor. 83, 84 MOS transistor. 622 Multiple reflection correction. 100. I I8 Multiple reflection effect, I20

N n + growth. 32

n + substrate, 648 nin, 647 nln', 647, 648 Natural IG, 639 Necking. 14 Negative U OV,,, 241 Anderson's, 173, 182 thermal donor. 275 Neutron transmutation doping (NTD). 1 I New donor, 25 I . 2 8 2 f l DLTS, 283 Nitrogen, 5. 226 NLIO, 257Jf NL8. 257jf, 268 NTD. See Neutron transmutation doping Non-oxygen containing crucible, 42 Nonlinear Si-0-Si bridge, 2 Normal freezing. 16 Nucleation heterogeneous, 4, 600, 604, 61 1 homogeneous. 4, 359, 605 metal precipitate. 550 new donor. 283 oxygen, 33. 359 precipitate, 252, 256, 267 strain relief. 362 Nucleation active center. 601, 603 Nucleation rate, 393. 395, 534 Nucleus, grown-in, 643

0

0. 0' line. 264 0-C complex, 609 0, dimer. 339 0:-1defect. 342 OED. See Oxidation-enhanced diffusion OH, 242 01atom, 332 (Oi)?-Vdefect, 310-312 01-H interaction, 335 01-1 complex. 341 01-1 defect, 312. 341 0 1 - V complex 341

676

INDEX

OI-V defect, 309-312, 341 One-pass zone leveling, 47 Optical microscopy, 54, 69, 660 Optical tomography, 85 ORD. See Oxidation-retarded diffusion Orientation dependence, 71 OSF. See Oxidation induced stacking fault OSF-ring, 564 Out-diffusion. 542 carbon, 609 oxygen, 599. 606, 607, 609, 610, 661 OVA,, 237,ff Oxidation induced stacking fault (OSF), 162, 163. 165, 635, 636 Oxidation, thermal, 577, 580 Oxidation-enhanced diffusion (OED), 155, 164 Oxidation-retarded diffusion (ORD), 166 Oxide breakdown failure mode, 623 Oxide film degradation, 633 Oxide platelet, 56 Oxygen axial profile. 40 beneficial effect of, 4 depth profile, 608 detrimental effect of, 3 incorporation modeling, 25 interstitial, 66, 77 knocked-on, 630, 63 1 molecular, 610 precipitated, 66, 640 precipitation of, 3 quasi-substitutional, 217 recoiled, 63 I solid solubility of, 607 source. 39 supersaturated, 3 uniformity degradation, 45 Oxygen aggregation, 267, 2 6 9 , 2 8 0 8 Oxygen atom, 6 Oxygen concentration, FZ silicon, 12 macroinhomogeneity, 34 microinhomogeneity , 34 Oxygen content, 643 Oxygen diffusion A-center, 3 1 I carbon interaction, 316 dimer, 314, 339 electron irradiation, 317 enhanced, 309-326

hydrogen interaction, 318-324, 335-339 metal interaction, 317, 326 normal, 292-308 self-interstitial interaction, 3 12 SIMS profile, 297 single jump, 293 stress-induced dichroism, 233, 294 X-ray measurement, 290, 297 Oxygen dimer, 314-316, 339-341, 346 Oxygen evaporation, 25 Oxygen loss, 416, 418, 419, 420, 427, 429, 433, 434, 441 Oxygen precipitation, computer-aided design of, 428 Oxygen precipitation model, 393-439 Oxygen precipitation simulation, 391 Oxygen reduction, 134 Oxygen transport, 25 Oxygen-lean region, 606

P p f growth, 32 p + substrate, 648,650 plp'. 647,648, 650,662 PAA. See Photon activation analysis Pairing, interstitial oxygen, 208 Passivation of dopant, by hydrogen, 230 PCD. See Photoconductive decay PDC. See Precipitate-dislocation complex Peak-height method, 115 Pendellosung, 63 Perturbed C(3) center, 609 Phase contrast, 60 Phonon spectroscopy, 206, 234 Photoconductive decay (PCD), 54 Photoluminescence (PL), 2 6 3 8 Photon activation analysis (PAA), 140 Photovoltaic device, 598 Physical sputtering, 578 Physical technique, 54, 55 Piezo-spectroscopic coefficient, 197, 198, 210, 218 Piezospectroscopy, 274 Pipe, 624 PL. S e e Photoluminescence Planar etch, 70, 72 Plastic temperature, 14 Point defect energetics, 178, 179, 182, 183

677

INDEX

Point defect. intrinsic. 153 Polarization energy. self-interstitial. I67 Polysilicon. high-purity, I Pohitron annihilation, 85 vacancy. 175 PRDDO. 330 Pre-heat treatment. ramping, 646 Preannealing. 541 isothermal. 640 Precipitate. 60, 64. 69. 78 arsenic (As). 630 grown-in. 604 metal. 548 octahedral. 537, 588 oxide. l 3 S , 632 oxygen. 4. 54. 77. 78, 1.54. 176, 513 plate-like. 530. S87 polyhedral. 540 SiO,. 6 spherical. 540 Precipitate-dislocation complex (PDC), 5x7 Precipitate morphology. 60 Precipitation. 59 100%. 604

oxygen. 33. 134. 252. 283. 299-305. 467. 490. 515. 526. 551, 578, 5x3. 5 8 5 , 591. 599. 601. 627 partial. 604 x r o . 604 Precipitation condition. 603 Precipitation equation. 441 Precipitation rate, oxygen. 603 Precipitation retardation, 439 Precursor. oxygen precipitate, 552 Prismatic loop. 61 Prismatic punching. 587 Pseudopotential. 328 Pulling rate. 634 Pulling speed. 563. S66

R Radial uniformity. dopant, 2 I. 22 Radiant heating, 659 Radiative recombination. 79 Radioactivation, 74 Radiochemical feparation, 76 Radius. oxygen precipitate. 414, 430 Rapid thermal annealing (RTA). 441

Rapid thermal process (RTP), 645 Rate equation chemical. 404 Fokker-Planck. 408 Real defect-free zone, 615 Recombination lifetime. 77. 79. 80, 81. 79 Redissolution, 654 oxygen. 599. 601 Reduced-temperature device processing, s9s Reference silicon. 68 Reference specimen float-zone ( F Z ) silicon, 121 infrared spectrometry. 121. 122 Reflectivity. 57 Refresh time, 621 Reorientation interstitial oxygen, 210, 236, 238 localized defect. 197. 210. 236, 238

ov, 219

Residual gas limitation. 68 Residual oxygen, 121, 625 Residual stress. SiOzfilm, 628 Resistivity. S46 Resistivity change. I , 2 Retention time, 623 Reynolds number. 21 Ribbon-like defect. 305 RIE. See Etching. reactive ion etching Rocking curve. 65, 66 RTA. See Rapid thermal annealing RTP. See Rapid thermal process

S

S-curve. 416. 432 s-pit, 580. 634. 635, 636 Saddle point. 331 Schimmel etch, 70. 72 Secco etch, 70. 72 Secondary ion mass spectroscopy (SIMS), 54. 66. 78, 130, 141, 143. 145 Section topography. 64, 77, 84. 85 Seeding, 14 Segregation. 604. 61 I oxygen. 34 Segregation coefficient effective, 19 equilibrium, 34

678

INDEX

Self-interstitial, 379, 523, 558, 583, 603, 613 Self-interstitial energetics, 178, 179, 182, 183 Shallow-junction bipolar transistor, 598 Shockley-Read-Hall (SRH) recombination, 79 S i - 0 bond, 55 S i - 0 phase diagram, 36 Sidewall edge, 631 Silicide, 613 Silicon monoxide, 1 Silicon Czochralski (CZ), 563 float zone (FZ), 553 hexagonal, 527 low resistivity, 130, 142 single crystal, 1 SIMOX, 631 SIMS. See Secondary ion mass spectroscopy SIMS profile, oxygen diffusion, 297 SiO, beads, 42 SiO, amorphous, 584 crystalline. 584 SiO,, 284 Sirtl etch, 70, 72, 580 Site hydrogen. 337 oxygen precipitate, 544 Slip generation, 14 Slow-diffusing, 610 Sn-V defect, 309 Softening, 490 Solid phase epitaxy (SPE), 630 Solubility limit, 644, 654 Solubility hydrogen, 318, 321 interstitial oxygen, 192, 233, 236 oxygen, 303 SPE. See Solid phase epitaxy Spreading resistance, 648 Sputtering, 67 SPV. See Surface photovoltage SRAM, 624, 626, 627 SRH. See Shockley-Read-Hall recombination, stacking fault, 61, 452, 491, 579, 582, 603 bulk, 547

extrinsic, 491, 519, 583, 585 intrinsic, 452 oxidation induced (OSF), 582 STEM-EDX, 582 Strain, 267, 523 Strain relief carrier capture, 199, 218, 241 I-emission, 362, 371 prismatic punching, 362 V-absorption, 362, 372 Stress effect dichroism, 197, 210, 218, 239 mode splitting, 1968, 208, 218, 237, 241 piezo-DLTS, 219 piezo-EPR, 193, 223 Stress-induced splitting, 196 Stress-strain curve, 452, 474, 477, 490 carbon-doped silicon, 504 CZ silicon, 476, 493 dislocated silicon, 477, 502 FZ silicon, 474 nitrogen-doped silicon, 501 theoretical derivation of, 481 Striation, oxygen, 35 Super clean technology, 596 Supercooling, 14 Supersaturation, oxygen, 600 Surface oxide, 73 Surface photo voltage (SPV), 54, 661 Surface tension, 578 Swirl, 156 A, 553 B, 553 c, 553

T Teal-Little method, 1 TEM. See Transmission electron microscopy TEM, oxygen precipitate, 299, 304 Temperature fluctuation, 43 Tetrahedral site, 167, 181, 182 Thermal cycle, 416, 424, 428, 431 Thermal defect, 159 Thermal desorption spectroscopy, 73 Thermal donor, 77, 78, 86, 193, 228, 234, 297, 315, 342-345 alignment, 268, 272

679

INDEX

bistability. 252. 275 core, 263, 278jT DLTS, 257, 272. 276 ENDOR, 260. 262, 279 EPR. 257. 260, 268. 212 formation. 252-257, 266, 269 metastability, 277 piezospectroscopy, 214 species. 255. 257 Thermal donor model. 278 Thermal gradient. 51 I Thermal history. 5, 15, 418. 431, 432. 5 5 1 604. 640 Thermal process. 3 . 5, 583 Thermal stability, 48 Thermal stress, 5, 14 Thermogravirnetnc analysis. 73 Through-oxide layer. 630 Transition metal, 577, 578, 580. 581. 590 diffusivity, of. 578 solubility of. 578 Transmission electron microscopy ( T E M ) 3, 54, 58. 77, 84, 628. 655 Transmittance, 56. S7 Trap. 7X Trap profiling. 79 Trench, 578. 620. 628. 651 Tridymite, 534

Vacuum fusion analysis (VFA). 73. 137 Variable crucible-crystal rotation rate. 38 VFA. See Vacuum fusion analysis Viscoelastic flow. 585 Volume expansion, 522

W Wafer flatness. 5 Wafer strengthening, 488 Warp, 548 Warpage. 3, 5, 64, 591, 652, 653, 654. 656. 658 Wavefunction. thermal donor. 2 6 1 , 272, 280 Whisker. 582 Wright-Jenkins etch. 70, 72

X X-ray X-ray X-ray XRT.

diffraction, 62 microanalysis, 60 topography (XRT). S4, 62. 63. 65 See X-ray topography

Y

Uniaxial stress, thermal donor. 272. 274

V

Vacancy. 5 5 2 , 603 Vacancy energetics. 175, 178. 181. 183

Yield stress, 452. 474. 477. 480. 491. 502 carbon-doped silicon, 504 CZ silicon, 476, 493 dislocated silicon, 477. 502 dislocation-free silicon. 476, 502 effect of oxygen precipitation. 490 FZ silicon, 474 nitrogen-doped silicon. 502 theoretical derivation. 481

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Contents of Volumes in this Series Volume 1

Physics of 111-V Compounds

C . Hilsum, Some Key Features of Ill-V Compounds Franco Bunani. Methods o f Band Calculations Applicable to 111-V Compounds E. 0. Kane, The k - p Method V . L. Bonch-Bruevich, Effect o f Heavy Doping on the Semiconductor Band Structure Donald Long, Energy Band Structures of Mixed Crystals of HI-V Compounds Laura M . Rorh and Perros N. Argyre.7, Magnetic Quantum Effects S. M . Puri and 7.H . Geballe, Thermomagnetic Effects in the Quantum Region W. M . Becker. Band Characteristics near Principal Minima from Magnetoresistance E. H . Purley, Freeze-Out Effects, Hot Electron Effects, and Submillimeter Photoconductivity in InSb H . W e m . Magnetoresistance Bersv Ancker-Johnson, Plasma in Semiconductors and Semimetals

Volume 2

Physics of 111-V Compounds

M . G. Holland. Thermal Conductivity S. 1. Novkoua. Thermal Expansion U . Piesbergen, Heat Capacity and Debye Temperatures G . Giesecke. Lattice Constants J . R. Drahhle, Elastic Properties A . U . Mac Rae and G. W .Gobeli, Low Energy Electron Diffraction Studies Rohtw Lee Mieher, Nuclear Magnetic Resonance Bernard Goldstein. Electron Paramagnetic Resonance T . S. Moss. Photoconduction in 111-V Compounds E . AnronCik and J . Tauc, Quantum Efficiency of the Internal Photoelectric Effect in lnSb G W . Gobeli and F. C. Allen. Photoelectric Threshold and Work Function P. S. Pershan. Nonlinear Optics in Ill-V Compounds M . Gershenzon, Radiative Recombination in the Ill-V Compounds Frank Srern. Stimulated Emission in Semiconductors

Volume 3

Optical of Properties 111-V Compounds

Marvin H a s . Lattice Reflection William G. Spirzer, Multiphonon Lattice Absorption D. L. Srierwalr and R. F. Porrer. Emittance Studies H . R. Philipp nnd H . Ehrenveich. Ultraviolet Opticai Properties Manuel Cardona, Optical Absorption above the Fundamental Edge Earnest J . Johnson, Absorption near the Fundamental Edge John 0. Dimmock. Introduction to the Theory of Exciton States in Semiconductors B. Lax and 1. G. Movroides, Interband Magnetooptical Effects

CONTENTS OF VOLUMES I N THISSERIES H. Y . Fan, Effects o f Free Carries on Optical Properties Edward D. Pulik and George B. Wright, Free-Carrier Magnetooptical Effects Richard H. Bube. Photoelectronic Analysis B. 0. Seraphin and H . E. Bennett, Optical Constants

Volume 4

Physics of 111-V Compounds

N. A . Goryunova, A . S. Borschevskii. and D. N. Treriakov. Hardness N. N. Sirofa. Heats o f Formation and Temperatures and Heats of Fusion of Compounds *lllBV

Don L. Kendall. Diffusion A . G. Chynoweth, Charge Multiplication Phenomena

Roberr W . Keyes, The Effects o f Hydrostatic Pressure on the Properties of ill-V Semiconductors L . W. Aukerman. Radiation Effects N. A . Goryunova, F. P. Kesamanly. and D. N . Nasledov. Phenomena in Solid Solutions R. T. Bare, Electrical Properties of Nonuniform Crystals

Volume 5 Infrared Detectors Henry Levinsfein. Characterization of Infrared Detectors Paul W. Kruce. Indium Antimonide Photoconductive and Photoelectromagnetic Detectors M . B. Prince. Narrowband Self-Filtering Detectors / v a n Melngalis and T. C. Harman. Single-Crystal Lead-Tin Chalcogenides Donald Long and Joseph L. Schmidf, Mercury-Cadmium Telluride and Closely Related Alloys E. H . Purley. The Pyroelectric Detector Norman B. S!evem. Radiation Thermopiles R. J . Keyes and T. M. Quisf, Low Level Coherent and incoherent Detection in the Infrared M . C . Teich. Coherent Detection in the Infrared F. R. A r a m , E. W. Sard, B. J . Peyfon. and F. P. Pace. Infrared Heterodyne Detection with Gigahertz IF Response H. S. Sommers. Jr., Macrowave-Based Photoconductive Detector Roberr Sehr and Rainer Zuleeg, imaging and Display

Volume 6 Injection Phenomena Murray A . Lamperf and Ronald B. Schilling, Current Injection in Solids: The Regional Approximation Method Richard Willliam, Injection by Internal Photoemission Allen M . Earner!. Current Filament Formation R. Baron and J . W . Mayer, Double Injection in Semiconductors W. Ruppel, The Photoconductor-Metal Contact

CONTENTSOF VOLUMES I N THIS SERIES

Volume 7 Application and Devices PART A John A Copeland and Stephen Knighr, Applications Utilizing Bulk Negative Resistance F A Padouani. The Voltage-Current Characteristics of Metal-Semiconductor Contacts P L Hower. W W Hooper. B R Cairns, R D Fairman. and D A Tremere, The GaAs Field-Effect Transistor Marvin H White, MOS Transistors G R Anrefl. Gallium Arsenide Transistors T L Tansfey, Heterojunction Properties

PART B T Mrsawa. lMPATT Diodes H C Okean. Tunnel Diodes Rohcrr B Campbell and Hung-Chi Chang, Silicon Carbide Junction Devices R E Ensrrom. H Kressel. and L Krassner, High-Temperature Power Rectifiers of GaAs, .P,

Volume 8 Transport and Optical Phenomena Richard J Srim. Band Structure and Galvanomagnetic Effects in 111-V Compounds with Indirect Band Gaps Roland W Ure, Jr , Thermoelectric Eflects in Ill-V Compounds Herherr Pifler. Faraday Rotation H Barrv Behh and E W Wiffiamy. Photoluminescence 1 Theory E W William and H Barry Behh Photoluminescence I I Gallium Arsenide

Volume Y

Modulation Techniques

B 0 Seraphin, Electroreflectance R L Aggarwal. Modulated lnterband Magnetooptics Daniel F Blossev and Paul Handler, Electroabsorption Bruno Barz. Thermal and Wavelength Modulation Spectroscopy /Liar Balsfev, Piezopptical Effects D E Aspnes and N Botrka, Electric-Field Effects on the Dielectric Function of Semiconductors and Insulatorc

Volume 10 Transport Phenomena R L Rode, Low-Field Electron ‘Transport J D. Wiley, Mobility o f Holes i n Ill-V Compounds C M Wove and G E Stillman, Apparent Mobility Enhancement in Inhomogeneous Crystals Roberr L Perenen, The Magnetophonon Effect

CONTENTS OF VOLUMES IN THIS SERIES

Volume 11 Solar Cells Harold J . H o d , Introduction; Carrier Collection, Spectral Response, and Photocurrent; Solar Cell Electrical Characteristics; Efficiency; Thickness; Other Solar Cell Devices; Radiation Effects; Temperature and Intensity; Solar Cell Technology

Volume 12 Infrared Detectors (11) W. L. Ekeman. J . D. Merriam. and R . F. Potter, Operational Characteristics of Infrared Photodetectors Peter R. Bratt. Impurity Germanium and Silicon Infrared Detectors E. H . Putley, lnSb Submillimeter Photoconductive Detectors G. E. Stillman, C. M . Wove, and J . 0. Dimmock, Far-Infrared Photoconductivity in High Purity GaAs G. E. Stillman and C. M . Woffe, Avalanche Photodiodes P. L. Richards, The Josephson Junction as a Detector of Microwave and Far-Infrared Radiation E. H. Putley, The Pyroelectric Detector-An Update

Volume 13 Cadmium Telluride Kenneth Zanio, Materials Preparation; Physics; Defects; Applications

Volume 14 Lasers, Junctions, Transport N . Holonyak, Jr. and M . H . Lee, Photopumped 111-V Semiconductor Lasers Henry Kressel und Jerome K. Butler, Heterojunction Laser Diodes A . Vun der Ziel, Space-Charge-Limited Solid-state Diodes Peter 1. Price. Monte Carlo Calculation of Electron Transport in Solids

Volume 15 Contacts, Junctions, Emitters B. L. Sharma, Ohmic Contacts to 111-V Compound Semiconductors Allen Nussbourn. The Theory of Semiconducting Junctions John S. Escher, NEA Semiconductor Photoemitters

Volume 16 Defects, (HgCd)Se, (HgCd)Te Henry Kressel, The Effect of Crystal Defects on Optoelectronic Devices C. R. Whits%. 1. G. Broermun, and C. J . Summers, Crystal Growth and Properties of Hg,-,Cd,Se alloys M . H. Weiler. Magnetooptical Properties of Hg,-,Cd,Te Alloys Paul W , Kruse and John G. Ready, Nonlinear Optical Effects in Hg,-,Cd,Te

CONTENTS OF VOLUMES IN THISSERIES

Volume 17 CW Processing of Silicon and Other Semiconductors James F. Gibbons, Beam Processing of Silicon Arlo Lietoila, Richard B. Gold, James F. Gibbons, and Lee A . Chrisrel, Temperature Distributions and Solid Phase Reaction Rates Produced by Scanning CW Beams Arlo Leitoila and James F. Gibbons. Applications o f CW Beam Processing to Ion Implanted Crystalline Silicon N. M. Johnson. Electronic Defects i n CW Transient Thermal Processed Silicon K. F. Lee, T. J. Sfultz, and James F. Gibbons, Beam Recrystallized Polycrystalline Silicon: Properties, Applications, and Techniques T. Shibata. A . Wakita, T. W.Sigmon, and James F. Gibbons. Metal-Silicon Reactions and Silicide Yues 1. Nirsim and James F. Gibbons. CW Beam Processing of Gallium Arsenide

Volume 18 Mercury Cadmium Telluride Paul W . Krure, The Emergence o f ( H g , ~,Cd,)Te as a Modern Infrared Sensitive Material H. E. Hirsch, S. C. Liang. and A . G. White, Preparation of High-Purity Cadmium, Mercury, and Tellurium W. F. H . Micklerhwaite. The Crystal Growth of Cadmium Mercury Telluride Paul E. Petersen, Auger Recombination in Mercury Cadmium Telluride R. M. Broudy and V . J . Mazurczyck. (HgCd)Te Photoconductive Detectors M. B. Reine. A . K. Soad. and T. J . Tredwell. Photovoltaic Infrared Detectors M. A . Kinch. Metal-Insulator-Semiconductor infrared Detectors

Volume 19 Deep Levels, GaAs, Alloys, Photochemistry G F Neumark and K Kosal, Deep Levels in Wide Band-Gap 111-V Semiconductors David C Look, The Electncal and Photoelectronic Properties of Semi-Insulating GdAs R F Brebrick, Ching-Hua Su. and Pok-Kal Liao. Associated Solution Model for Ga-In-Sb and Hg-Cd-Te Yu Ya Gurevich and Yu. V Pleskon. Photoelectrochemistry of Semiconductors

Volume 20 Semi-lnsulating GaAs R. N . Thomas, H . M . Hobgood. G W. Eldridge, D. L. Barren, T. T. Braggins, L. B. Ta, and S. K. Wang. High-Purity LEC Growth and Direct Implantation of GaAs for Monolithic Microwave Circuits

C. A. Stolte. Ion Implantation and Materials for GaAs Integrated Circuits C. G. Kirkpatrick. R. T. Chen. D E . Holmes, P. M. Asbeck, K. R. Elliotr, R. D. Fairman, and 1. R. Oliver. LEC GaAs for Integrated Circuit Applications J . S. Blakemore and S. Rahimi. Models for Mid-Gap Centers in Gallium Arsenide

Volume 21 Hydrogenated Amorphous Silicon Part A Jacques I. Pankooe Introduction Masataka Hirose, Glow Discharge; Chemical Vapor Deposition

CONTENTS OF VOLUMES IN THISSERIES Yoshiyuki Uchida, dc Glow Discharge T. D. Moustakas, Sputtering lsao Yamada, Ionized-Cluster Beam Deposition Bruce A . Scott. Homogeneous Chemical Vapor Deposition Frank J . Kampas. Chemical Reactions in Plasma Deposition Paul A . Longeway, Plasma Kinetics Herbert A . Weakliem, Diagnostics of Silane Glow Discharges Using Probes and Mass Spectroscopy Lester Guttman. Relation between the Atomic and the Electronic Structures A . Cheneuas-Paule. Experiment Determination of Structure S. Minomura. Pressure Effects on the Local Atomic Structure David Adler, Defects and Density of Localized States

Part B Jacques 1. Pankoue, Introduction G . D . Cody, The Optical Absorption Edge of a-Si: H Nabil M. Amer and Warren B. Jackson, Optical Properties of Defect States in a-Si: H P . J . Zanzucchl, The Vibrational Spectra of a-Si: H Yoshihiro Hamakawa, Electroreflectance and Electroabsorption Jefrey S. Lannin, Raman Scattering of Amorphous Si, Ge. and Their Alloys R. A . Street. Luminescence in a-Si: H Richard S. Crandall, Photoconductivity 1. Tauc, Time-Resolved Spectroscopy of Electronic Relaxation Processes P. E. Vanier. IR-Induced Quenching and Enhancement of Photoconductivity and Photoluminescence H. Schade. Irradiation-Induced Metastable Effects L. Ley. Photoelectron Emission Studies

Part C Jacques 1. Pankoue. Introduction 1. David Cohen, Density of States from Junction Measurements in Hydrogenated Amorphous Silicon P . C. Taylor, Magnetic Resonance Measurements in a-Si: H K . Morigakr. Optically Detected Magnetic Resonance J . Dresner. Carrier Mobility in a-Si: H T. Tiedje, information about band-Tail States from Time-of-Flight Experiments Arnold R. Moore, Diffusion Length in Undoped a-Si: H W . Beyer and J . Ouerhof, Doping Effects in a-Si: H H . Fritzche. Electronic Properties of Surfaces in a-Si : H C. R. Wromkr. The Staebler-Wronski Effect R. J Nemanich. Schottky Barriers on a%: H B. Abeles and T. Tiedje, Amorphous Semiconductor Superlattices

Part D Jacques 1. Pankoue, Introduction D. E . Carlson, Solar Cells

CONTENTS OF VOLUMESI N THISSERIES G. A . Swartz, Closed-Form Solution of I-V Characteristic for a-Si: H Solar Cells lsamu Shirnizu. Electrophotography Sachio Ishiok'u, Image Pickup Tubes P. G . LeComber and W . E. Spear. The Development o f the a-Si: H Field-Effect Transistor and Its Possible Applications D. G. Ast, a-Si: H FET-Addressed LCD Panel S. Kaneko. Solid-state Image Sensor Masakiyo Mafiumura. Charge-Coupled Devices M . A . Bosch. Optical Recording A . D'Amico and G . Fortunato, Ambient Sensors Hiroshi Kukimofo. Amorphous Light-Emitting Devices Robert J . Phelan. J r . , Fast Detectors and Modulators Jacques 1. Pankoue. Hybrid Structures P. G , LeComber. A . E. Owen. W . E. Spear, J . Hajfo. and W . K . Choi, Electronic Switching in Amorphous Siliocn Junction Devices

Volume 22

Lightwave Communications Technology Part A

Kazuo Nakajrma. The Liquid-Phase Epitaxial Growth of IngaAsp W T Tsang, Molecular Beam Epitaxy for Ill-V Compound Semiconductors G B Sfnngfellow, Organometdllic Vapor-Phase Epitaxial Growth of Ill-V Semiconductors G Beuchet, Halide and Chloride rrdnsport Vapor-Phase Deposition of InCaAsP and GaAs Munileh Razeghi. Low-Pressure Metallo-Organic Chemical Vapor Deposition of Ga,In, ,ASP, , Alloys P M Pefrofl, Defect\ i n Ill-V Compound Semiconductors

Part B I P uan der Ztel, Mode Locking of Semiconductor Lasers

Kam Y Lau and Ammon Yariv. High-Frequency Current Modulation of Semiconductor Injection Lasers Charley H Henry, Spectral Properties o f Semiconductor Lasers Yasuharu Suemafsu. Kaaumr Krrhino Shrgehlsa Arar. and Fumio Koyama Dynamic Single-Mode Semiconductor Lasers with a Distributed Reflector W T Tsang, The Cleaved-Coupled Cavity (C') Laser

Part C R J Nelson and N K Duna. Review o f InGaAsP InP laser Structures and Comparison of Their Performance N Chinone and M Nakamura, Mode Stabilized Semiconductor Lasers for 0 7-0 8- and 1 1-1 6-ym Regions Yoshilr Horikorht, Semiconductor Lasers with Wavelengths Exceeding 2 pm B A Dean and M Dixon, The Functional Reliability of Semiconductor Lasers as Optical Transmitters

CONTENTS OF VOLUMES IN THISSERIES R. H . Saul, T. P. Lee, and C. A. Burus, Light-Emitting Device Design C. L. Zipfel, Light-Emitting Diode-Reliability Tien Pei Lee and Tingye Li, LED-Based Multimode Lightwave Systems Kinichiro Ogawa, Semiconductor Noise-Mode Partition Noise

Part D Federico Capasso, The Physics of Avalanche Photodiodes T. P. Pearsall and M. A. Pollack, Compound Semiconductor Photodiodes Takao Kaneda, Silicon and Germanium Avalanche Photodiodes S. R. Forrest, Sensitivity of Avalanche Photodetector Receivers for High-Bit-Rate Long-Wavelength Optical Communication Systems J . C. Campbell, Phototransistors for Lightwave Communications

Part E Shyh Wang, Principles and Characteristics of Integratable Active and Passive Optical Devices Shlomo Margalit and Amnon Yariu, Integrated Electronic and Photonic Devices Takaoki Mukai. Yoshihisa Yamamoto, and Tarruyo Kimura, Optical Amplification by Semi-conductor Lasers

Volume 23 Pulsed Laser Processing of Semiconductors R. F. Wood, C. W . White, and R. T. Young, Laser Processing of Semiconductors: An Overview C . W. White, Segregation, Solute Trapping, and Supersaturated Alloys G. E. Jellison, J r . , Optical and Electrical Properties of Pulsed Laser-Annealed Silicon R. F. Wood and G. E. Jellison, Jr., Melting Model of Pulsed Laser Processing R. F. Wood and F. W . Young, Jr., Nonequilibriurn Solidification Following Pulsed Laser Melting D. H . Lowndes and G . E. Jellison, Jr., Time-Resolved Measurements During Pulsed Laser Irradiation of Silicon D. M . Zebner, Surface Studies of Pulsed Laser Irradiated Semiconductors D.H. Lowndes, Pulsed Beam Processing of Gallium Arsenide R. 8.James. Pulsed CO, Laser Annealing of Semiconductors R. T. Young and R. F. Wood, Applications of Pulsed Laser Processing

Volume 24 Applications of Multiquantum Wells, Selective Doping, and Superlattices C. Weisbuch, Fundamental Properties of 111-V Semiconductor Two-Dimensional Quantized Structures: The Basis for Optical and Electronic Device Applications H. Morkoc and H. Unlu, Factors Affecting the Performance of (Al,Ga)As/GaAs and (Al, Ga)As/InGaAs Modulation-Doped Field-Effect Transistors: Microwave and Digital Applications

CONTENTS OF VOLUMES IN THISSERIES N . T. Linh, Two-Dimensional Electron Gas FETs: Microwave Applications M . Abe ef 01, Ultra-High-speed HEMT Integrated Circuits D . S. Chemla, D. A. E . Miller, and P. W . Smith, Nonlinear Optical Properties of Multiple Quantum Well Structures for Optical Signal Processing

F. Capusso. Graded-Gap and Superlattice Devices by Band-Gap Engineering W. T. Tsang, Quantum Confinement Heterostmcture Semiconductor Lasers G. C. Osbourn er al., Principles and Applications of Semiconductor Strained-Layer Superlattices

Volume 25

Diluted Magnetic Semiconductors

W. Giriar and 1. K . Furdyna, Crystal Structure, Composition, and Materials Preparation of Diluted Magnetic Semiconductors W. M . Eecker. Band Structure and Optical Properties of Wide-Gap A~!,Mn,BVi Alloys at Zero Magnetic Field Saul Oserof and Piefer H . Keesom. Magnetic Properties: Macroscopic Studies T. Giebulrowicz and T. M. Holden. Neutron Scattering Studies of the Magnetic Structure and Dynamics of Diluted Magnetic Semiconductors 1. Kossur, Band Structure and Quantum Transport Phenomena in Narrow-Gap Diluted Magnetic Semiconductors C. Riquaux. Magnetooptical Properties of Large-Gap Diluted Magnetic Semiconductors J , A . Caj, Magnetooptical Properties of Large-Gap Diluted Magnetic Semiconductors J . Mycielrki. Shallow Acceptors in Diluted Magnetic Semiconductors: Splitting, Boil-off, Giant Negative Magnetoressitance A . K. Ramdus and R. Rodriquez. Raman Scattering in Diluted Magnetic Semiconductors P. A . W o l f . Theory of Bound Magnetic Polarons in Semimagnetic Semiconductors

Volume 26 Ill-V Compound Semiconductors and Semiconductor Properties of Superionic Materials Zou Yuanrr. Ill-V Compounds H . V. Winston, A . T. Hunter, H . Kimura, and R . E . Lee, InAs-Alloyed GaAs Substrates for Direct Implantation P. K . Eharrachary and S . Dhar. Deep Levels in Ill-V Compound Semiconductors Grown by MBE Yu. Yu. Gureuich and A . K . fuunou-Shi6, Semiconductor Properties of Superionic Materials

Volume 27 High Conducting Quasi-One-Dimensional Organic Crystals E

M Conwell, Introduction to Highly Conducting Quasi-One-Dimensional Organic Crystals f A Howard, A Reference Guide to the Conducting Quasi-One-Dimensional Organic Molecular Crystals J P fouquer, Structural Instabilities E M Conwell, Transport Properties

CONTENTS OF VOLUMES IN THISSERIES C. S.Jacobsen, Optical Properties J . C. Scorr. Magnetic Properties L. Zuppiroli, Irradiation Effects: Perfect Crystals and Real Crystals

Volume 28 Measurement of High-speed Signals in Solid State Devices J . Frey and D. loannou, Materials and Devices for High-speed and Optoelectronic Applications H. Schumacher and E. Strid, Electronic Wafer Probing Techniques D. H . Ausron. Picosecond Photoconductivity: High-speed Measurements of Devices and Materials 1. A . Valdmanis. Electro-Optic Measurement Techniques for Picosecond Materials, Devices. and Integrated Circuits 1. M . Wiesenfeld and R. K. lain, Direct Optical Probing of Integrated Circuits and High-speed Devices G . flows. Electron-Beam Probing A . M . Weiner and R. 8. Marcus. Photoemissive Probing

Volume 29 Very High Speed Integrated Circuits: Gallium Arsenide LSI M . Kuzuhara and T. Nazaki, Active Layer Formation by Ion Implantation H. Hasimoro. Focused Ion Beam Implantation Technology T. Nozaki and A . Higashisaka, Device Fabrication Process Technology M. Ino and T. Takada, GaAs LSI Circuit Design M. Hirayama. M. Ohmori. and K. Yamawki, GaAs LSI Fabrication and Performance

Volume 30 Very High Speed Integrated Circuits: Heterostructure H. Waranabe. T. Mizurani, and A . Usui, Fundamentals of Epitaxial Growth and Atomic Layer Epitaxy S. Hiyamizu. Characteristics of Two-Dimensional Electron Gas in Ill-V Compound Heterostructures Grown by MBE T. Nokanisi. Metalorganic Vapor Phase Epitaxy for High-Quality Active Layers T. Nimura. High Electron Mobility Transistor and LSI Applications T. Sugera and T. Ishibarhi, Hetero-Bipolar Transistor and Its LSI Application H . Malsueda. T. Tanaka, and M. Nakamura, Optoelectronic Integrated Circuits

Volume 3 1 Indium Phosphide: Crystal Growth and Characterization J . P. Forges. Growth of Discoloration-free InP M. 1, McCollum and C. E. Srillman, High Purity InP Grown by Hydride Vapor Phase Epitaxy T. Inada and T. Fukuda, Direct Synthesis and Growth of Indium Phosphide by the Liquid Phosphorous Encapsulated Czochralski Method 0. Oda. K. Katagiri, K. Shinohara, S. Kauura, Y. Takahashi. K. Kainosho, K. Kohiro, and R. Hirano, InP Crystal Growth, Substrate Preparation and Evaluation

CONTENTs OF VOLUMES IN

THISSERIES

K Tada. M Talsumr. M Morroka, T Araki, and T Kawase, InP Substrates. Production

and Quality Control M Razeghr. LP-MOCVD Growth, Charactenzation. and Application of InP Matenal T A Kennedy and P J Lin-Chung. Stoichiometric Defects in InP

Volume 32 Strained-Layer Superlattices: Physics T P Pearsall. Strained-Layer Superlattices Fred H Pollack. Effects of Homogeneous Strain on the Electronic and Vibrational Levels in

Semiconductors

J Y Marzin. J M Gerard. P V o w n . und J A Brurn. Optical Studies of Strained Ill-V

Heteroldyers

R

People and S A Jackson, Structurally Induced States from Strain and Confinement M Jaros. Microscopic Phenomena in Ordered Superlattices

Volume 33 Strained-Layer Superlattices: Materials Science and Technology R. H u l l and 1. C. Bean. Principles and Concepts of Strained-Layer Epitaxy William J . Schaff, Paul J . Tusker, Mark C . Foisy. and Lester F. Eastman. Device Applications of Strained-Layer Epitaxy S . T. Picraux. B. L. Doyle. and J Y. Two. Structure and Characterization of Strained-Layer Superlattices E. Kusper and F. Schafler. Group IV Compounds Dale L. Marlin. Molecular Beam Epitaxy of IV-VI Compound Heterojunction Roherr L. Gunrhor. Lesslie A . Kolodziejski, A r l o V . Nurmrkko. and N o h 0 Olsuka. Molecular Beam Epitaxy of 11-VI Semiconductor Microstructures

Volume 34 Hydrogen in Semiconductors J . 1. Pankoue and N. M. Johnson, Introduction to Hydrogen in Semiconductors C. H. Seager, Hydrogenation Methods 1. / Pankoue. Hydrogenation of Defects in Crystalline Silicon J . W. Corheir. P Deak. I/. V . Desnica. and S. 1. Pearron. Hydrogen Passivation of

Damage Centers in Semiconductors S. 1. Pearron. Neutralization of Deep Levels in Silicon J 1. Pankove. Neutralization of Shallow Acceptors in Silicon N . ,V. Johnson. Neutralization of Donor Dopants and Formation of Hydrogen-Induced

Defects in n-Type Silicon M . Srauola and S. J . Pearron. Vibrational Spectroscopy of Hydrogen-Related Defects in

Silicon A.

D .Marwick. Hydrogen in Semiconductors: Ion Beam Techniques

C. Herring and N. M . Johnson. Hydrogen Migration and Solubility in Silicon E . E . Hailer. Hydrogen-Related Phenomena in Crystalline Germanium J . Kakalios. Hydrogen Diffusion i n Amorphous Silicon J , Chevalier. B. C'lerpud, and B . Papr. Neutralization of Defects and Dopants in Ill-V Semiconductors

CONTENTSOF VOLUMES IN THISSERIES G. G. DeLeo and W . B. Fowler, Computational Studies of Hydrogen-Containing Complexes in Semiconductors R. F. Ki@ and T. L. Estle, Muonium in Semiconductors C. G. Van de Walle, Theory of Isolated Interstitial Hydrogen and Muonium in Crystalline Semiconductors

Volume 35 Nanostructured Systems Mark Reed, Introduction H . van Houten, C. W. J. Beenakker, and B. J . van Wees, Quantum Point Contacts G. Timp, When Does a Wire Become an Electron Waveguide? M. Biittiker, The Quantum Hall Effect in Open Conductors W. Hansen, J . P. Kotthaus, and U. Merkt, Electrons in Laterally Periodic Nanostructures

Volume 36 The Spectroscopy of Semiconductors D. Heiman, Laser Spectroscopy of Semiconductors at Low Temperatures and High Magnetic Fields Art0 V . Nurmikko, Transient Spectroscopy by Ultrashort Laser Pulse Techniques A . K. Ramdas and S. Rodriguez, Piezospectroscopy of Semiconductors Orest J . Glembocki and Benjamin V . Shanabrook, Photoreflectance Spectroscopy of Microstructures David G . Seiler, Christopher L. Littler, and Margaret H. Weiler, One- and Two-Photon Magneto-Optical Spectroscopy of lnSb and Hg, -,CD,Te

Volume 37 The Mechanical Properties of Semiconductors A,-B. Chen, Arden Sher and W . T. Yost, Elastic Constants and Related Properties of Semiconductor Compounds and Their Alloys David R. Clarke, Fracture of Silicon and Other Semiconductors Huns Siethofl, The Plasticity of Elemental and Compound Semiconductors Sivaraman Guruswamy, Katherine T . Faber and John P. Hirth, Mechanical Behavior of Compound Semiconductors Subhanh Mahajan, Deformation Behavior of Compound Semiconductors John P. Hirth, Injection of Dislocations into Strained Multilayer Structures Don Kendall, Charles B. Fleddermann, and Kevin J . Malloy, Critical Technologies for the Micromachining of Silicon Ikuo Mafsuba and Kinji Mokuya. Processing and Semiconductor Thermoelastic Behavior

Volume 38 Imperfections in III/V Materials Udo Scherz and Matthias Schefler, Density-Functional Theory of sp-Bonded Defects in III/V Semiconductors Maria Kaminska and Eicke R. Weber, EL2 Defect in GaAs David C. L o o k , Defects Relevant for Compensation in Semi-Insulating GaAs

CONTENTS OF VOLUMES I N THISSERIES R. C. Newman, Local Vibrational Mode Spectroscopy of Defects in III/V Compounds Andrzej M . Hennel, Transition Metals in I W V Compounds Kevin 1. Malloy and Ken Khocharuryon. DX and Related Defects in Semiconductors V. Swaminothan and Andrew S . Jordan. Dislocations in III/V Compounds Krzyszrof W. Nauka. Deep Level Defects in the Epitaxial III/V Materials

Volume 39 Minority Camen in 111-V Semiconductors: Physics and Applications Niloy K . Durra. Radiative Transitions in GaAs and Other 111-V Compounds Richard K. Ahrenkiel. Minority-Carrier Lifetime in 111-V Semiconductors Tomofumi Furufu, High Field Minority Electron Transport in p-GaAs Mark S . Lundsrrom, Minority-Carrier Transport in 111-V Semiconductors Richard A . Abram, Effects of Heavy Doping and High Excitation on the Band Structure of GaAs David Yevick ond Witold Bordyszewski. An Introduction to Non-Equilibrium Many-Body Analyses of Optical Processes in Ill-V Semiconductors

Volume 40 Epitaxial Microstructures E . F. Sdiuhert, Delta-Doping of Semiconductors: Electronic. Optical, and Structural Properties of Materials and Devices A . Gossurd. M . Sundururn. und P . I f o p k i n s , Wide Graded Potential Wells P. Petri& Direct Growth of Nanometer-Size Quantum Wire Superlattices E . K u p o n , Lateral Patterning of Quantum Well Heterostructures by Growth of Nonplanar Substrates H . Ternkin, D . Gershoni. und M P u n i s h . Optical Properties of Gal-,In,As/InP Quantum Wells

Volume 41 High Speed Heterostructure Devices F. c'upu.r.~.o.F'. Beltrum. S. Sen. A . Puhlrvi. rind A , Y . Cho. Quantum Electron Devices: Physics and Applications P. Solomon, D . J . Frunk. S . 1.. WrigIir. tirid F. Cunoru. GaAs-Gate SemiconductorInsulator-Semiconductor FF.7 M. H . Hushemi und U . K . Mishru, Unipolar InP-Based Transistors R . Kiehl, Complementary Heterostructure FET Integrated Circuits 7 . /shihu.shi. GaAs-Based and InP-Based Heterostructure Bipolar Transistors If. C. Lirr und T . C . L . G . Sollnrr. High-Frequency-Tunneling Devices H . Ohnishi,7.More, M . Tukut.su. K . Imaniuru. und N . Yokoyamu, Resonant-Tunneling Hot-Electron Transistors and Circuits

CONTENTS OF VOLUMES IN

THISSERIES

Volume 42 Oxygen in Silicon F. Shirnuru, Introduction to Oxygen in Silicon W. Lin, The Incorporation of Oxygen into Silicon Crystals T. J. Shuflner and D. K. Schroder, Characterization Techniques for Oxygen in Silicon W. M . Bullis. Oxygen Concentration Measurement S . M . Hu, lntrinsic Point Defects in Silicon B. Pujor, Some Atomic Configurations of Oxygen J . Michel und L . C . Kirnerling, Electrical Properties of Oxygen in Silicon R. C. Newman and R. Jones, Diffusion of Oxygen in Silicon T . Y. Tun und W. J. Taylor, Mechanisms of Oxygen Precipitation: Some Quantitative Aspects M . Schrerns, Simulation of Oxygen Precipitation K. Surnino and I. Yonenuga, Oxygen Effect on Mechanical Properties W. Berpholz, Grown-in and Process-Induced Effects F. Shirnuru, Intrinsic/Internal Gettering H. Tsuyu, Oxygen Effect on Electronic Device Performance