Semiconductors and Semimetals: Semi-Insulating GaAs (Vol. 20)

SEMICONDUCTORS AND SEMIMETALS VOLUME 20 Semi-Insulating GaAs

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SEMICONDUCTORS AND SEMIMETALS Edited by R. K. WILLARDSON WILLARDSON CONSULTING SPOKANE, WASHINGTON

ALBERT C. BEER BATTELLE COLUMBUS LABORATORIES COLUMBUS, OHIO

VOLUME 20 Semi-Insulating GaAs

1984

ACADEMIC PRESS, INC. (Harcourt Brace Jovanovich, Publishers)

Orlando San Diego San Francisco New York London Toronto Montreal Sydney Tokyo SZo Paul0

COPYRIGHT @ 1984, 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 ANY INFORMATION STORAQE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER.

ACADEMIC PRESS, INC.

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United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD.

24/28 Oval Road. London W 1

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Library of Congress Cataloging in Publication Data Main entry under title: Semiconductors and semimetals. Includes bibliographical references and indexes. Contents: v. 1-2 Physics of 111-Vcompounds v. 3. Optical properties of 111-Vcompounds - [etc.] v. 18. Mercury cadmium teIIuride. 1. Semiconductors-Collected works. 2. Semimetals Collected works. I. Willardson, Robert K. 11. Beer, Albert C. QC610.9.S47 537.6'22 65-20648 ISBN 0-12-752120-8 (V. 20)

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PRINTED IN THE UNITED STATES OF AMERICA 84858687

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Contents LISTOF CONTRIBUTORS . . PREFACE .

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Chapter 1 High-Purity LEC Growth and Direct Implantation of GaAs for Monolithic Microwave Circuits R. N. Thomas, H. M, Hobgood, G. W. Eldridge, D. L. Barrett, T. T. Braggins, L. B. Ta, and S. K. Wang List ofSymbols

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1. Introduction . . . 11. Large-Diameter GaAs Crystal Growth

111. Compositional Purity . IV. Electrical Properties . V. Direct Ion Implantation VI. GaAs Materials Processing References . . .

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Chapter 2 Ion Implantation and Materials for GaAs Integrated Circuits C. A. Stolte List of Acronyms

I. Introduction

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11. Materials Preparation

111. Ion Implantation IV. Device Results V. Summary . References .

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89 90 93 109 143 151 154

Chapter 3 LEC G aAs for Integrated Circuit Applications C,G. Kirkpatrick, R. T. Chen, D. E. Holmes, P. M. Asbeck, K. R. Elliott, R. D. Fairman, and J. R. Oliver List ofSymbols I. Introduction

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159 161

vi 11. LEC-Growth Technique 111. Crystalline Quality

CONTENTS

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IV. Impurity and Defect Analysis V. LEC GaAs in Device Fabrication VI. Conclusions . References . , .

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163 167 192 212 226 230

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Chapter 4 Models for Mid-Gap Centers in Gallium Arsenide J. S. Blakemore and S. Rahimi List of Symbols . . . . I. Introduction . . . 11. Quantum-Mechanical View of Flaw States . . . Ill. Effective Mass Formalism: Its Limitations for Deep-Level Centers . IV. Delta-Function Potential and Quantum-Defect Models . . . V. Electronic Transition Phenomena Involving Flaws, and the Square-Well Potential and Billiard-Ball Models . . . VI. Techniques Based on Molecular Orbitals . VII. Pseudopotential Representations . . . . . VIII. Green’s Function Method . . . . . IX. Brief Notes on Other Approaches . . . . References . . . . . .

INDEX . CONTENTS OF PREVIOUS VOLUMES.

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234 235 242 245 25 1 267 309 320 328 349 353

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363 376

List of Contributors Numbers in parentheses indicate the pages on which the authors’ contributionsbegin.

P. M. ASBECK,Defense Electronics Operations, Microelectronics Research and Development Center, Rockwell International Corporation, Thousand Oaks, California 91360 (1 59) D. L. BARRETT, Westinghouse Research and Development Center, Pittsburgh, Pennsylvania 15235 (1) J. S. BLAKEMoRE, Oregon Graduate Center, Beaverton, Oregon 97006 (233) T. T. BRAGGINS, Westinghouse Research and Development Center, Pittsburgh, Pennsylvania 15235 (1) R. T. CHEN,Defense Electronics Operations,MicroelectronicsResearch and Development Center, Rockwell International Corporation, Thousand Oaks, California 91360 (159) G. W. ELDRIDGE,WestinghouseResearch and Development Center, Pittsburgh, Pennsylvania 15235 (1) K. R. ELLIOTT,Defense Electronics Operations, Microelectronics Research and Development Center, Rockwell International Corporation, Thousand Oaks, California 91360 ( 1 59) R. D. FAIRMAN,? Defense Electronics Operations, Microelectronics Research and Development Center, Rockwell International Corporation, Thousand Oaks, California 91360 (1 59) H. M. HOBGOOD,WestinghouseResearch and Development Center, Pittsburgh, Pennsylvania 15235 ( 1) D. E. HOLMES, Defense Electronics Operations, Microelectronics Research and Development Center, Rockwell International Corporation, Thousand Oaks, California 91360 (1 59) C. G. KIRKPATRICK, Defense Electronics Operations, MicroelectronicsResearch and Development Center, Rockwell International Corporation, Thousand Oaks, California 91360 (159) 7 Present address:Microwave Product Department, TRW, Inc., Redondo Beach, California 90278.

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LIST OF CONTRIBUTORS

J. R. OLIVER, Defense Electronics Operations, Microelectronics Research

and Development Center, Rockwell International Corporation, Thousand Oaks, California 91360 (1 59) S . RAHIMI,~ Oregon Graduate Center, Beaverton, Oregon 97006 (233) C. A. STOLTE,Hewlett-Packard Laboratories, Palo Alto, California 94304 (89) L. B. TA,$ Westinghouse Research and Development Center, Pittsburgh, Pennsylvania 15235 (1) R. N. THOMAS,Westinghouse Research and Development Center, Pittsburgh, Pennsylvania 15235 (1) S . K. W A N G ,Westinghouse ~ Research and Development Center,Pittsburgh, Pennsylvania 15235 (1)

t Present address: Sonoma State University, Rohnert Park, California 94928. -$ Present address: Microelectronics Center, McDonnell Douglas Corporation, Huntington Beach, California 92641. 8 Present address: Torrence Research Center, Hughes Airc& Company, Torrence, California.

Preface The advent of monolithic GaAs integrated circuits is having a broad impact on microwave signal processing and power amplification. Impressive improvements are being made in the performance and cost effectiveness of advanced systems for military radar and telecommunication as well as in digital integrated circuits for ultra-high-speed or fifth generation computers. A multibillion dollar market for GaAs analog, digital, and optoelectronic integrated circuits is predicted for the 1990s, with estimates as high as eight billion dollars in 1993 being made. In the 1950s, semi-insulatingGaAs was made by float-zone refining and by bombardment with electrons, neutrons, and protons. In the 1960s, the standard preparation technique involved the addition of chromium or the use of native defects (the EL2 center) and Fe, Zn, or Cd impurities-either natural or preferentially added. High-purity aluminum oxide, aluminum nitride, or boron nitride crucibles were used. The purity of the gallium and the arsenic was comparable with that available today, as was the GaAs produced. In the 1970s, the group at the Naval Research Laboratory, as well as others, revived much of the dormant technology of the 1960s and added further improvements. High-purity undoped semi-insulating GaAs was prepared. High-pressure liquid-encapsulated Czochralski (LEC) pullers, developed at the Royal Radar and Signals Establishment and manufactured by Cambridge Instruments, provided an in situ method of reacting gallium and arsenic plus a technique for growing low-cost, large-diameter, stable, high-resistivity GaAs single crystals. A low-pressure technique for meeting the same objectiveswas developed at Hewlett-Packard.In this volume, these methods of crystal growth, including means for determiningcrystal quality, electrical and optical properties related to impurities and point defects, as well as use of direct ion implantation for the preparation of integrated circuits, are explained by experts working in this field. The group at the Westinghouse Research and Development Center used the Melbourn (Cambridge Instruments) puller to grow highquality GaAs crystals, with diameters ranging from 2 to 4 in. In Chapter 1, details of this process are described, including dislocation distributions and the effect of water in the boric oxide on twinning. Thermal gradients, asymmetries, and

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fluctuations can be influenced by pressure and boric oxide thickness, and these are related to dislocation densities and impurity stria. Advances are proceeding very rapidly in this area and after these chapters were set in type a procedure was reported, involving the use of indium, which gave a reduction in dislocation densities by as much as a factor of 25. Also, Terashima and co-workers at the Optoelectronics Joint Research Laboratory in Kawasaki have shown that the application of a magnetic field can reduce both the number of EL2 defects and the dislocation density in crystals grown with a Melbourn puller. In Chapter 2, materials and ion implantation procedures, which are used at Hewlett-Packard for the fabrication of GaAs integrated circuits, are discused. Emphasis is given to a low-pressure LEC technique, which has been used for in situ synthesis of the GaAs to produce high-quality 65-mmdiameter single crystals, having dislocation densities as low as 200/cm2. Interestingly, similar results have been reported by Zou and co-workers in China. Spectrographic analyses and Hall mobilities of electrons in implanted semi-insulating GaAs produced by high- and low-pressure LEC, Bridgman, and liquid-phase-epitaxial growth are used to evaluate these growth methods and their suitability for producing device quality substrates. Extensive studies of Melbourn LEC growth of GaAs,including dislocations, twins, surface gallium inclusions, microdefects, and stoichiometry by the group at Rockwell Microelectronics Research and Development Center are presented in Chapter 3. The key to reproducible growth of undoped semi-insulating GaAs is control over melt stoichiometry and impurity content -the balance between EL2 deep donors and shallow acceptors. The incorporation of EL2 centers increases as the atom fraction of arsenic increases. An acceptor lattice defect, which increasesin concentration as the gallium atom fraction is increased above the stoichiometric proportion, is also described. Fine structure in dislocation distributions shows both cellular structure and lineages, with relatively high densities being measured along ( 100) compared to ( 1 10) directions. More recently, it has been reported that similar distributionsor inhomogeneitiesin the EL2 center are revealed by infrared imaging. Chapter 4 focuses on models for deep levels in semiconductors such as semi-insulating GaAs. It extends the discussions of deep levels in 111-V compounds which were treated in Volume 19 of our treatise and provides a guide for experimentalists to extensive and detailed theoretical treatments of localized states in the central part of the intrinsic gap. A classification scheme for the principal varieties of localized flaws in semiconductors is presented. Approaches that have been made theoretically to describe deeplying states derived from nonextended flaw situations are explained. The features responsible for a flaw’s signature are examined, including the form

PREFACE

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of the potential, site symmetry, and any distortion or relaxation of the lattice. The editors are indebted to the many contributors and their employers who made this treatise possible. They wish to express their appreciation to Willardson Consulting and Battelle Memorial Institute for providing the facilities and the environment necessary for such an endeavor. Special thanks are also due to the editors’ wives for their patience and understanding.

R. K. WILLARDSON ALBERTC. BEER

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SEMICONDUCTORS AND SEMIMETALS.

VOL.

20

CHAPTER 1

High-Purity LEC Growth and Direct Implantation of GaAs for Monolithic Microwave Circuits? R. N. Thomas, H. M. Hobgood, G. W. Eldridge, D. L. Barrett, T. T. Braggins, L. B. Ta,$ and S. K. Wangj’ WESTINGHOUSE RESEARCH AND DEVELOPMENT CENTER PITTSBURGH, PENNSYLVANIA

LISTOF SYMBOLS. . . . . . . . . . . . . . . . . . . I. INTRODUCTION .................... 11. LARGE-DIAMETER GaAs CRYSTAL GROWTH.. . . . . . . I. High-pressure LEC Technology. . . . . . . . . . . . 2. Growthfrom Large GaAs Melts. . . . . . . . . . . . 3. Crystalline Imperfections. . . . . . . . . . . . . . . 111. COMPOSITIONAL PURITY. . . . . . . . . . . . . . . . 4. Mass Spectrometry . . . . . . . . . . . . . . . . . 5 . Boron and Silicon. . . . . . . . . . . . . . . . . . IV. ELECTRICAL PROPERTIES. . . . . . . . . . . . . . . . 6. Crucible/Encapsulant Efects . . . . . . . . . . . . . I . Melt Composition Efects . . . . . . . . . . . . . . 8 . Residual Impurities . . . . . . . . . . . . . . . . . 9. Thermal Stability. . . . . . . . . . . . . . . . . . 10. Uniformity Considerations . . . . . . . . . . . . . . V. DIRECTIONIMPLANTATION ............... 1 1 . Si-Implanted GaAs . . . . . . . . . . . . . . . . . 12. Experimental Procedures. . . . . . . . . . . . . . . 13. Measured Implant Profiles and Electrical Activation . . . 14. Hall Mobility of Implanted Layers. . . . . . . . . . . 15. Implications to FET Device Processing. . . . . . . . . VI. GaAs MATERIALS PROCESSING. ............. REFERENCES. . . . . . . . . . . . . . . . . . . . .

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7 Work supported in part by the Defense Advanced Research Projects Agency and monitored by Office of Naval Research on Contract NOOO14-80-C-0445. Present address: MicroelectronicsCenter, McDonnell Douglas Corporation, Huntington Beach, California. 0 Present address: Torrance Research Center, Hughes Aircraft Company, Torrance, California.

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CopyriBht 63 1984 by Academic Pms,Inc. All rights of reproduction in any form reserved. ISBN0-12-752120-8

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List of Symbols ASES

c- v D

DLTS EL2 DWS

f FET

2 g

K kl

LEC LPE LVM MESFET NA N$a Ni K

O

ni Nsc NSM NSMH NSMO

PHI PBN PR PSG V RU RP RPA

sccm SIMS SSMS {Si) T. Tang end VP

VPE VB

vast

Arc source emission spectroscopy Capacitance- voltage Diffusion constant (cm2sec-l) Deeplevel transient spectroscopy Main deepdonor level in undoped GaAs Differential weight gain signal Fraction melt solidified Field effect transistor Ground-state degeneracy factor Full channel current (A cm-I) Effective segregation coefficient Mass action constant governing the donor/acceptor role of implanted silicon via interaction with n(T,) Mass action constant describing the contribution of arsenic vacancies V,, on the electron density measured at Ta Liquid-encapsulatedCzochralski Liquid-phase epitaxy Localized vibrational mode far-infrared spectroscopy Metal-semiconductor field effect transistor Ionized donor concentration (crn-9 Residual ionized donor concentration ( ~ m - ~ ) Ionized acceptor concentration ( c m 9 Residual ionized acceptor concentration (cm-’) Intrinsic free-electron concentration ( c m 3 Net donor concentration in the implanted layer (cm-2) Free-electron concentration in the implanted layer including surface depletion effects (cm+) Free-electron concentration in the implanted layer as determined by surface Hall-effect measurement (cm-*) Concentration that can be depleted at breakdown in an idealized parallel plate geometry (ern+) Water content in the encapsulant Pyrolytic boron nitride Photoresist Phosphosilicateglass Electronic charge Depth of maximum implanted concentration Projected range of the implanted ion concentration Projected range of the ionized net donor concentration Standard cubic centimeter per minute Secondary ion mass spectrometry Spark source mass spectrometry Implanted silicon concentration (cm-7 Annealing temperature Tail section of an ingot Pinch-off voltage Vapor-phase epitaxy Breakdown voltage Electron saturation velocity

1. HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION A €

AJ PD PSH

tl tlA

tlr P Os,d

e I:

3

Net donor concentration (N&- NJ Permittivity of GaAs Surface-depletion depth Effective channel thickness (RM * ud) Electron drift mobility Average electron mobility as determined by surface Hall-effect measurement Differential net donor activation efficiency determined with respect to the implanted-ion concentration Differential net donor activation efficiency determined with respect to 5 Differential total ionized center activation efficiency determined with respect to implanted-ion concentration Resistivity Standard deviations of a single energy implant based on joined half-gaussian modeling for the surface and deep sides of R,, respectively Compensation ratio defined as the concentration of implanted ions acting as acceptors divided by the concentration of implanted ions acting as donors [e.g., (Si-)/(Si+)] Total equivalent ionized center concentration (N; N i )

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+

I. Introduction

GaAs metal - semiconductor field effect transistors (MESFETs) have received increasingattention over the past decade for applicationsbeyond the 1 - 2-GHz operating range of silicon devices because of the higher electron mobility and saturated velocity in GaAs, and because of its availability as a semi-insulating substrate. This technology has now progressed to where monolithic integration in GaAs of many high-frequency circuit functions is being pursued vigorously in several laboratories throughout the world. The advent of monolithic GaAs integrated circuits (ICs) is expected to have a broad impact on the way in which microwave detection, signal processing, and power amplification will be carried out in the future. Military radar and microwave telecommunication systems, in particular, are expected to reap dramatic benefits of improved performance and availability at significantly reduced costs from this emerging technology. Significant advances have already been demonstrated in the fabrication of monolithic GaAs amplifiers for low-noise/high-gain or high rf power outputs at X-band frequencies and beyond, as well as in very high-speed GaAs digital logic ICs for “front-end” data processing. Historically, GaAs MESFET technology has been strongly influenced by the quality of the underlying semi-insulating substrate and, over the years, an epitaxial processing technology has been developed to circumvent the unpredictable and often undesirable effects of the substrate. High-purity, epitaxial buffer layers are often utilized to decouple the active device region from the substrate, and the commercial availability of high-performance, epitaxial field effect transistors (FETs) capable of very low-noise figures (as

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low as 2.8 dB at 18 GHz) or with high output powers (exceeding 5 W at 12 GHz) attests to the effectiveness of these techniques. In contrast to discrete FETs, the present trend in monolithic GaAs circuit fabrication strongly favors the use of direct-into-substrate implantation techniques. This follows from the much greater flexibility of direct ion implantation over epitaxial techniques for device processing. In particular, selective implantation enables active device regions to be confined to selected areas on a semi-insulating substrate without resorting to the mesaetch isolation techniques of epitaxial structures. Relatively simple planar processing can therefore be used to combine diode and FET structures with passive circuit elements on the same semi-insulating substrate. This planar and selective nature of implantation is a significant advantage and holds considerablepromise of evolving as a high-yield manufacturingtechnology. Significant progress (Welch et al., 1974; Thomas et al., 1980)is currently being made toward developinga viable planar ion-implantationtechnology, but it is widely recognized that direct implantation imposes severe demands on the quality of the semi-insulatingGaAs substrate. In the past, the inferior properties of commercially available semi-insulating substrates, usually prepared by horizontal Bridgman or gradient freeze techniques, have been major limitations to attaining uniform and predictable device characteristics by implantation. These problems of substrate reproducibility are now well recognized in a symptomatic sense and are probably associated with excessive and variable concentrations of impurities- particularly, silicon, chromium, oxygen, and carbon -present in typical Cr-doped semi-insulating GaAs substrates, which contribute to the difficulties in achieving uniform implant profiles. A common manifestation of the problem is the formation of a conductive ptype surface layer following a thermal annealing process. These anomalous conversion and compensation phenomena, which have been observed followingpost-implantation annealing, adversely affect the implant profile and activation and can result in poor control of full-channel current and pinch-off voltage in directly implanted FET structures. Chromium redistribution has been graphically demonstrated in the case of directly implanted Crdoped substrates by Huber et al. (1979a) and Evans et al. (1979). In addition, typical Cr-doped GaAs substrates contain at least I X 10'' cm-3 ionized impurities that severely reduce the electron mobility in directly implanted FET channels and degrade the FET performance and frequency limitations. Monolithic GaAscircuits require substrates that (a) exhibit stable, high resistivities after thermal processing to maintain both good electrical isolation and low parasitic capacitances associated with active elements;

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HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION

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(b) contain very low total concentrations of ionized impurities so that the implanted FET channel mobility is not degraded; and (c) permit fabrication of devices of predictable characteristics so that active and passive elements can be matched in monolithic circuit designs. Another important consideration is the need for uniformly round, largearea substrates. Broad acceptance of GaAs ICs by the user and systems communities will occur only if a reliable GaAs IC manufacturing technology capable of yielding high-performance monolithic circuits at reasonable costs is realized. Unfortunately, the characteristic D-shaped slices of boatgrown GaAs material have been a serious deterrent to the achievement of this goal, since much of the standard semiconductor processing equipment developed for the silicon IC industry relies on uniformly round substrate slices. To address these needs for a reliable “siliconlike” technology base in semi-insulatingGaAs materials processing, liquid-encapsulatedCzochralski (LEC) growth was selected over other growth technologies because of its current capability for producing large-diameter, ( 100) and ( 1 11) crystals of semi-insulating GaAs. The 50- and 100-mm-diam wafers cut from (100)oriented LEC GaAs crystals are shown in Fig. 1 to illustrate the significant economic benefits of large-area processing. The monolithic power amplifiers shown on the 50-mm slice are approximately 5 X 2 mm. Device

FIG. 1. Comparison of available wafer area for monolithic power amplifier fabrication on 50- and 100-mm-diam GaAs slices cut from (100) crystals grown in high-pressure Melbourn LEC puller.

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processing on 100-mm wafers would increase the die count from 75 to 300 per wafer, although the handling and processing costs in manufacturing are approximately independent of wafer size. In the following sections, we report on the growth of high-purity, large-diameter (100) GaAs crystals; on assessments of the structural perfection, compositional purity, and electrical properties of these crystals; and upon evaluation of their suitability and compatibility for direct ion-implantation device processing. Finally, the application of many of the wafer fabrication techniques now confined to the silicon industry to produce uniform, largearea substrates in GaAs is discussed briefly. The underlying aim is to establish a reproducible GaAs materials base in order to realize the full potential of direct ion implantation as a reliable, cost-effective fabrication technology of high-performance GaAs MESFET devices and integrated circuits. 11. Large-Diameter GaAs Crystal Growth

1. HIGH-PRESSURE LEC TECHNOLOGY

Liquid encapsulation was first demonstrated experimentally by Metz et al. ( 1962)for the growth of volatile PbTe crystals and has since been applied to the Czochralskiprocess by Mullin et al. ( I 968) and others (Swiggard et al., 1977; Henry and Swiggard, 1977; AuCoin et al., 1979; Ware and Rumsby, 1979) for the growth of several 111-V crystals. In liquid-encapsulated Czochralski, the dissociation of the volatile As from the GaAs melt is avoided by encapsulating the melt in an inert molten layer of boric oxide and pressurizing the chamber with a nonreactive gas, such as nitrogen or argon, to counterbalance the As dissociation pressure. The LEC technique has been developed intensively in recent years, and high-pressure pullers are now available commercially. One is the “Melbourn” high-pressure LEC puller (manufactured by Cambridge Instruments, Ltd., in Cambridge, England, and is the outcome of developmental efforts at the Royal Radar and Signals Establishment, Malvern, England), which is currently being introduced by many laboratories for the growth of large bulk GaAs as well as GaP and InP crystals. With high-pressure capability,in situ compound synthesis can be carried out from the elemental Ga and As components, since the boric oxide melts before excessive As sublimation starts to take place (5460°C). Compound synthesis occurs rapidly and exothermally at about 820°C under a sufficient inert gas pressure (- 60 atm) to minimize significant sublimation of the arsenic component. To maintain a nearly stoichiometric or slightly arsenic-rich melt, a slight excess of As is utilized to compensate for inadvertent loss of As during the heat-up cycle. After compound synthesis, the chamber pressure can be

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HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION

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FIG.2. Melbourn high-pressure,liquid-encapsulated Czochralski puller. (Courtesy of Cambridge Instruments Ltd., England.)

decreased to -20 atm and crystal growth initiated from the 1238°C GaAs melt by seeding and slowly pulling the crystal through the transparent boric oxide layer. Large-diameter GaAs crystals are typically pulled at speeds less than 10 mm hr-', and counter- and corotation of seed and crucible at rates between 6 and 18 rpm have been investigated. The Melbourn LEC puller shown in Fig. 2 consists of a resistance-heated 150-mm-diam crucible system capable of charges up to about 10 kg and can be operated at pressures up to 150 atm. The GaAs melt within the pressure vessel can be viewed by means of a closed-circuit TV system. A high-sensitivity weight cell continuously weighs the crystal during growth and provides a differential weight signal for manual diameter control. In addition, a unique diameter control

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technique, which involves growing the crystal through a diameter-defining aperture, has been developed for ( 11 1)-oriented growth (Ware, 1977). In this “coracle” technique, the defining aperture is fabricated from pressed silicon nitride, which conveniently floats at the GaAs melt -B,O, encapsulant interface. 2. GROWTH FROM LARGEGaAs MELTS

a. Manual Diameter Control At our laboratories, the high-pressure Melbourn LEC puller has been employed to develop a reproducible growth technology for preparing largediameter (up to nominally 100 mm), (100)-oriented GaAs crystals. Techniques for producing crystals which are free of major structural defects (such as twin planes, lineage, inclusions, and precipitates), and which yield stable, semi-insulating properties without resorting to conventional Cr doping, have been successfully developed over the course of about 70 experimental growths. The work expands upon earlier LEC studies of Swiggard et al. (1977) and AuCoin et al. (1979), who showed independently that improved purity, semi-insulating GaAs crystals could be grown from undoped LEC melts when contained in high-purity, pyrolytic boron nitride (PBN) crucibles. The present effort is directed at the growth of much larger crystals required for commercial GaAs IC processing, and exploits the recent availability of 150-mm-diam PBN crucibles in conjunction with an advanced high-pressure LEC technology as embodied in the Melbourn puller. For comparison purposes, GaAs crystals grown from Cr-doped melts and using conventional fused silica crucibles have also been investigated. Two semiinsulating ( 100)GaAs crystalspulled from pyrolyticboron nitride crucibles and grown using the differential weight signal for diameter control are shown in Fig. 3. The crystal in Fig. 3a is nominally 50 mm in diameter and weighs 3 kg; Fig. 3b shows a nominally 100-mm-diamcrystal weighing 6 kg. Such a crystal will yield approximately 200 semi-insulating substrates. The growth of crystals in the ( 100) orientation has relied upon the ability to control the crystal diameter by continuously monitoring the crystal weight and the instantaneousderivative of the weight gain signal (DWS). On the basis of these measured quantities and visual monitoring through the TV system, adjustments to the power level are made to correct for undesirable changes in crystal diameter. However, owing to reliance upon operator judgment and the inability to see clearly at all times the growth meniscus through the boric oxide layer, as well as systematic errors in the differential weight gain signal due to capillaryforces (Jordan, 198l), this growth method results in crystalswith diameterswhich vary (usually within k 5 mm) along the boule length, as demonstrated by the crystals in Figs. 3a and 3b and the

1. HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

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H 20 mm

(a)

(bl

FIG.3. Nominally 50- and 100-mm diam ( 100)-orientedGaAscrystals pulled from 3- and 6-kg undoped melts, respectively.

trace of the differential weight signal of Fig. 4b. Much attention in several laboratories has recently been focused on the development of automatic diameter control systems for LEC crystals of I11-V compounds. Investigations of automatic computer-controlled LEC growth techniques for GaP single crystals by Fukuda et al. (1981) have shown that largediameter ( 11 1)- and ( 100)-oriented single crystals of up to 62 k 1.5 mm could be successfully grown by a closed-loop control using crystal weighing. Jordan (1 98 I ) has formulated and analyzed a realistic, tractable model for the

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f a ) Diameter Variation: <1M)> LEC GaAs Coracle Control

.-m

I

Diameter Variation: <100> LEC GaAs Manual Control

( b)

I

I,

0

I

40

,

I

80

I

1

I

I

A

I

I

160 200 Time (min)

120

I

I

240

,41280

FIG.4. Examples of differentialweight gain signals for (a) “coracle” and (b) manual coracle diameter control in growth of large-diameterGaAs crystals.

closed-loop LEC growth of axisymmetric 111-V crystals based on the use of an on-line computer for comparison of the measured derivative weight gain signal with a theoretical differential weight signal correspondingto a crystal with the desired diameter uniformity. These studies show that the continuous monitoring of the crystal weight and the instantaneous determination of the derivative weight gain signal with attendant adjustment to the power level is a viable approach to diameter control. However, unlike the case of important oxide crystals, the method is complicated in the LEC pulling of 111-V compounds by the B203 liquid encapsulant and the significant capillary forces (Jordan, 198la).

b. “Coracle” Technology An alterriativetechnique for diameter control of I11 - V LEC crystals is the so-called coracle technique, in which the crystal is pulled through a diameter-defining flotation ring or coracle. 1 he coracle is made of pressed Si3N,, which floats at the interface of the GaAs melt and the B203encapsulant and retains the growth meniscus with a convex shape. The coracle technique is well developed for growths of large-diameter ( 1 1 1) GaP and GaAs crystals and diameter control to within f 2 mm is achievable (Fig. 4a), but its use for (100) GaAs growths has in the past been frustrated by the tendency for (100)-oriented crystals to twin at the early stages of growth. The result of preliminary attempts at using the coracle technique for 50-mm-diam ( 100) growths is shown in Fig. 5b and indicates that the onset oftwinning has been delayed to approximately halfway along the boule length, demonstrating that the (100) twinning problem associated with a diameter-defining

1. HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION

11

\loo>

T <110>Flat

Scale In l Inches

0

1

FIG. 5. Uniform 50-mm diam (100) LEC GaAs crystals prepared by (a) conventional grinding and (b) utilizing the coracle diameter control during growth.

growth technique can perhaps be resolved in the future, provided proper meniscus shape and stable attendant growth conditions can be maintained. An alternative approach to achieving uniform, cylindrical, ( 100)-oriented GaAs crystals is illustrated in Fig. 5a, where a ( 100) ingot has been ground accuratelyto a 50-mm diameter with ( 1 10)-orientationflatsby conventional grinding techniques. Surface work damage is removed by etching. Approximately 150 polished wafers of uniform diameter with a thickness of 0.5 mm can be typically obtained from a 3-kg, (loo), 50-mm-diam crystal. Improved diameter control is nevertheless highly desirable, since the changes in growth conditions that give rise to diameter variations are probably reflected by modifications to the materials properties.

12

R. N. THOMAS et

al.

3. CRYSTALLINE IMPERFECTIONS Large-diameter GaAs crystals are usually characterized by high densities of dislocations ( 104- 1O5 cm-2), which arise as a result of the large thermal stressesassociated with the LEC growth of this material. Although at present there is scant evidence that these relatively high-dislocation densities give rise to harmful effects in majority carrier devices such as MESFETs [in contrast to minority-camer devices such as LEDs and laser structureswhere dislocations are known (Petroff and Hartman, 1973) to play a deleterious role in device performance], the general consensus is that GaAs of significantly lower dislocation densities will eventually be required for advanced monolithic circuit functions and possibly from improved processing and reliability considerations. For LEC GaAs crystal growths at diameters I 1 5 mm, the attendant thermal stressesare diminished and the crystalscan be grown entirely free of dislocations (Steinemann and Zimmerli, 1963). In these small crystals, successful dislocation-free growth depends primarily upon a Dash-type seeding (Dash, 1957) in which dislocations in the seed are removed by growing a thin neck before increasingthe diameter to form the crystal cone. Additional factors which have been found to influence dislocation generation in these small crystals include melt stoichiometry (Steinemann and Zimmerli, 1963), temperature gradients at the growth interface (Brice, 1970) and the resulting shape of the growth front (Grabmaier and Grabmaier 1972), and the angle of the crystal cone as it emerges from the encapsulant (Roksnoer et al., 1977). Although large-diameterGaAs crystals can be grown free of twins and inclusions, a preponderance of experimental evidence indicates that dislocation generation (and clustering) in large LEC crystals always occurs and is almost exclusively controlled by local thermal stresses. Successful growth of large dislocation-freeGaAs crystals has been observed only in highly doped crystals, where dislocation generation is impeded by impurity-hardening effects (Seki et al., 1978). Factors governing twin formation and dislocation generation in large-diameter GaAs crystals are now discussed.

a. Twinning in Large-Diameter ( 100) Crystals The tendency toward twinning in ( 100)-orientedGaAs crystals has often frustrated large-diameter (100) growth efforts in the past. Although the exact cause of twinning is rarely known, it has been empirically observed that the frequency of twinning is affected by deviations from stoichiometry (Steinemann and Zimmerli, 1963), excessive thermal stresses due to variations in crystal diameter (Kotake el al., 1980),or instabilities in the shape of the crystal growth front associated with the emergence of the crystal through

1. HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION

13

the boric oxide layer. Our early experiences indicated that twinning commonly caused a change in the crystal growth direction from the ( 100)to the (22 1) direction in large-diameter GaAs crystals. Frequent twinning was associated with abrupt shouldering of the crystal in the growth of flat-topped crystals, and the initiation of a twin plane was found to be usually coincident with the As facet when the crystal diameter was changed rapidly. In this regard, a gradual increase to the desired crystal diameter has proven to be highly effective in avoidingtwinning in the early stages of growth, as has also been demonstrated in the case of LEC InP crystals (Bonner, 1981). To achieve reproducible growths of twin-free crystals, a growth procedure was adopted, which included the use of vacuum baking of the boric oxide encapsulant to remove residual moisture. This was found empirically to be an important factor in reducing twinning in large ( 100) crystal growths and in maintaining high visibility of the melt-crystal interface during growth (Hobgood et af.,1981b). Similar findings have been reported by other workers (Aucoin et af.,1979), who found that twinning in ( 100)-oriented crystals was associated with the use of unbaked, high [OH]-content B20, in the growth of LEC GaAs crystals. More recently, Cockayne et af. (1981) have definitively related the water content of the Bz03encapsulant to the generation of defect clusters in LEC InP crystals. Statistics relating the incidence of twinning for growths with “dry” (<500 ppm wt [OH]) and “wet” (> 1000 ppm wt [OH]) B203are given in Fig. 6 for growths from fused Si02 and PBN crucibles. For both types of crucibles, the incidence of twinning within the first 75% of growth is substantially lower when using vacuum-baked B203([OH] < 500 ppm). A growth methodology of gradual increase to crystal diameter, coupled with loo

-Q v1

P

V

- Fused Si02 Crucible 27 Crystals

&I-

60-

3 c

-

-2

-

5 40-

LL

80-

- -

.-z

P

-

looPymlytic Boron Nitride Crucible 26 Crystals

20-

-,,f I W l > B2°3

/-B2°3

’

60-

I OH1 > 1wO ppm

1WOppm

40B2°3

20-

IOH1 < 500 ppm

14

R. N. THOMAS et

al.

use of B203of low-moisturecontent, has proven to be effective in achieving consistent, reproducible growth of large twin-free, ( 100) GaAs crystals.

6. Dislocation Generation in Large-Diameter GaAs Crystals Expanding upon Penning’s (1958a,b) early work on thermally induced stresses in crucible-grown germanium and silicon, Jordan et al. ( 1981) has analyzed the thermal stresses associated with the LEC growth of GaAs.The dislocation generation mechanism in large-diameter crystals (>20 mm) is believed to be due primarily to thermally induced stresses that accompany large axial and radial temperature gradients, owing to the large convective heat-transfer coefficient of the B20! encapsulatinglayer and the temperature differencebetween the crystal intenor and the B203ambient near the growth interface. A comparison of the thermal stresses associated with LEC growth of GaAs and InP relative to Czochralski silicon pulled in a gaseous ambient is illustrated in Fig. 7. In contrast to Czochralski-grown silicon crystals, which can withstand a factor of three higher stresses (Jordan et al., 1981) and still be grown dislocation-free even at diameters of 100 mm and larger, the resulting thermal stressesassociated with LEC growth of GaAs can easily

FIG.7. Comparison of calculated excess shear stress or dislocation density distribution in Czochralski-pulled (100) crystals of GaAs, InP, and Si when ambient temperature is 200°K below the respective melting points. Shaded areas depict dislocation-free regions. (From Jordan ef al., 1981.)

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HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

15

exceed the critical resolved shear stress for dislocation motion at temperatures near the melting point. Dislocation-free growth has been achieved only for small-diameter (< 15 mm) GaAs crystals where the thermal stresses are reduced (Steinemann and Zimmerli, 1963). Figure 8 shows a photograph of a 75-mm-diam, (100) GaAs slice etched in molten KOH to 300°C to reveal the distribution of dislocations. The dislocation densities are highest at the center and near the periphery of the wafer, in qualitativeagreement with the thermal stress distribution predicted by Penning’s and Jordan’s models. Repeated attempts to grow large dislocation-freeGaAs crystals by initiating dislocation-free seeding using the Dash technique of melting back the seed crystal and then growing a thin seed at a relatively high-growth rate as shown in Fig. 3a, a standard practice in the growth of dislocation-free

’

100rnm

’

FIG.8. Dislocation distribution in 75-mm-diam (100) GaAs slice as revealed by KOH etching.

R. N. THOMAS et

16

al.

silicon, have proven unsuccessful and confirm that effects other than dislocation multiplication from the seed dominate the dislocation generation. To illustrate this point, Figs. 9a and 9b show x-ray reflection topographs of longitudinal sections of seed-end cones for two ( 100) GaAs crystals corresponding to two different cone angles: a relatively shallow cone approaching a flat top (Fig. 9a) and a steeper cone of 27 deg to the crystal axis (Fig. 9b). Although in both cases dislocation-free growth was initiated by the Dashtype seeding, the dislocation-free seeding alone was insufficient to prevent the subsequent generation of dislocations as the crystal diameters were increased. In agreement with the thermal stress model, the regions of highest dislocation density ( 105-cm-2range) are confined to the center of the crystal and a layer near the crystal periphery correspondingto regions of maximum thermal stress; however, severe glide plane activation in the early stages of crystal growth, which is typically observed in flat-topped growths (Fig. 9a), has been reduced by the use of steeper cone angles (Fig. 9b) (Thomas et al., 1981). At their full diameters, large 50- and 75-mm-diam GaAs crystals exhibit radially nonuniform dislocation distributions with maximum dislocation densitiesin the lo4- 105-cm-2range at the center and periphery of the crystal with minima at about one-half of the radius, as shown in Fig. 10. The systematic variation in dislocation density across the wafer diameter replicates the thermal stress distribution in the crystal in excellent agreement

(a)

Ibl

FIG.9. Reflection x-ray topographs of longitudinal (01 1) sections showing influence of crystal cone-angle on dislocation generation.

1. HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

75 - mm Diam

I I I

5

I

.n

1

50- mm Diam \

loo -

17

'

/'

1

1.00.80.60.40.2 00.20.40.60.8 Edge Normalized Radius

1.0 Edge

FIG. 10. Radial dislocation density distribution along ( 100) direction in 50- and 75-mrndiarn LEC (100) GaAs slices.

with the Jordan model. The axial dislocation distribution for a 50-mm-diam crystal is observed to be relatively constant along the crystal length, which again suggests that the dislocation generation is driven by local thermal stress rather than by dislocation multiplication (which would produce an increase in dislocation density with length). The current status of crystalline quality in large LEC GaAs crystals relative to horizontal Bridgman-grown crystals of comparable dimensions (50-mm maximum or diameter) is illustrated in Fig. 11, where Lang reflection x-ray topographs of the central wafer areas are shown. In spite of the commercial availability of small Bridgman wafers With very low dislocation densities (0- 500 cm-2), Fig. 11 suggests that in large-area semi-insulating GaAs wafers somewhat similar dislocation densities ( 104-cm-2 range) are observed in both Bridgman and LEC substrates. c. Thermal Distributions in LEC Melts

Since the magnitudes of the axial and radial temperature gradients existing at the melt - B203interface and across the boric oxide layer itself help to drive the thermal stresses in the GaAs solid, they play an important role in determining whether the crystal will dislocate at the growth interface and during the time required for the crystal to transit the boric oxide layer thickness. Reduction of thermal gradients should lead to a corresponding decrease in thermal stress levels and a reduction in defect density. Thus, a

FIG.1 1 . X-ray reflection topographs comparing dislocation densities in large-area (100) wafers prepared from (a) semi-insulatinghorizontal Bridgman-grown GaAs and (b) semi-insulatingLEC/PBN-grown Gas. Wafers are approximately 50 mm in maximum dimension or diameter. For both (a) and (b), g = (3 15), and the area is 0.41 cm2.

1.

HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

19

knowledge of the thermal distributions existing in the melt/encapsulant/ high-pressure ambient system is instructive in establishing which growth parameters should be optimized to reduce dislocations. The influence of crucible position in the 150-mm hot zone of the highpressure Melbourn furnace on the thermal profile along the geometric axis of the system is illustrated in Fig. 12. The profiles were measured using a Pt- 1090Rh thermocouple attached to the movable pull rod. The data were measured with reference to the crucible bottom and extend through the GaAs melt, the B203encapsulatinglayer (- 20 mm thick), and 5 cm into the inert argon ambient above the encapsulant. Even though the measurements were made in the absence of a crystal growing (where effects due to latent heat dissipation and heat conduction up the growing crystal can significantly modify the thermal gradient at the growth interface), the relative change in temperature across the system of melt/B,O, /ambient under these conditions should approximate those corresponding to the early stages of LEC growth when the crystal is totally submerged in the B203 encapsulant. An axial thermal gradient of 140°C/cm [Fig. 12, curve (b)] was measured across the B203layer for normal operating conditions (Le., PBN crucible low in heat zone, ambient pressure 20 atm). When the crucible is moved up 25 mm in the heat zone, the gradient increases to 18O"C/cm The sensitivity owing to the 200°Cgreater cooling at the surface of the B203. of the B203surface to changes in ambient pressure is also reflected in the

-

-

-

-

, m0 10 Crucible

20

3

4) 50 60 Distance [ mm )

70

8l

90

100

Bottom

FIG.12. Thermal profiles alonggeometric axis of LEC GaAs melt system. Crucible position and Ar ambient pressure are (a) 14.4 mm, 5 atm; (b) 14.4 mm, 20 atm; and (c) 40 mm, 20 atm. Nominally 3-kg GaAs melt contained in a 6-in.diam PBN crucible.

20

R. N. THOMAS et

al.

thermal profile of Fig. 12 [curve (a)], which corresponds to a factor of four reduction in pressure. The surface temperature of the B203increases by - 100°Cwhen the ambient pressure is dropped from 20 to 5 atm. However, the thermal gradient near the GaAs melt surface is relatively unaffected. Moreover, growths carried out under 5-atm pressure yield crystal surfaces with severe decomposition (due to As loss), owing to the higher ambient temperature. The insensitivity of the gradient across the B203 layer to variations in crucible position and ambient pressure indicates that varying the B203thickness itself may offer the best possibility of reducing the axial temperature gradient at the melt - B203interface. This observation is supported by a similar recent finding of Shinoyama et al. (1980) on the growth of dislocation-free LEC crystals of InP. In addition to crystal rotation rate and pull speed, the radial uniformity of the melt thermal distribution is known to play an important part in determining the shape of the growth interface and the radial variations in impurity incorporation, as well as having a significant effect on crystal diameter control. Measurements of the radial temperature profile at the melt interface region of the GaAs melt-B203 encapsulant in the 150-mm hot zone of the Melbourn puller indicate very shallow gradients of less than 0.5 "C/mm over the central 60-mm diameter of the melt surface which tend to promote relatively flat growth interfaces. Beyond this central region, the radial gradient increases steeply (2"C/mm at 125-mm diameter) and is consistent with observations that the diameter control is significantly improved by these steeper radial gradients in the growths of 75-mm-diam crystals in the Melbourn LEC system. Fluctuationsin the microscopic growth rate in Czochralski crystal growth arise because of thermal asymmetries at the crystal-growth interface. Symmetrical or rotational impurity striations are almost always observed for impurities, with effective segregation coefficientsdiffering significantlyfrom unity because of the seed- crucible rotation, which is conventionally employed. Nonrotational striations, which are caused mainly by turbulent thermal convection flows in the melt, become increasingly important in large-volume melts (Carruthers et al., 1977). Inhomogeneities such as these are of grave concern for device processing, particularly for submicron geometries over large-area substrates, because of the deleterious effects on device performance and yields. The convective flows in a large-volume GaAs melt (viscosity 0.1 P) covered by a relatively viscous (30-P) BzO3 encapsulant and situated in a turbulent high-pressure (20-atm) gas ambient are probably characterized by large Rayleigh numbers. Temperature fluctuationsdue to convective turbulence in the melt can therefore be expected to be quite severe. Measurements of the temperature fluctuations observed in a 150-mm-diam,3-kg, B,O,-en-

1. HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION

21

capsulated GaAs melt in the high-pressure Melbourn system are shown in Fig. 13. The melt was contained in a PBN crucible that was rotated at 15 rpm. The inert argon ambient was held constant at 20 atm. The measurements correspond to positions along the geometric axis of the system. Temperature fluctuations at the B,O,-GaAs interface (Fig. 13a) display a AT, > 3°C with individual temperature excursions >2°C. Over the total 1Zmin time interval shown, a somewhat systematic variation is observed with a large period of about 1 min. Superimposed on this coarse periodicity is a more rapid fluctuation with a frequency of approximately 10 temperature excursions per minute. No obvious cause (such as variations in heater power or mechanical vibrations) for the periodic nature of these fluctuations was detected. Figure 13b shows the thermal fluctuations observed under the same conditions for a position of about 1 cm below the surface of the GaAs melt. Here, the amplitude of the fluctuations is much larger than at the B,O,-GaAs interface. AT, is 9"C, with individual excursions as large as 6°C. The fluctuation frequency is also higher than at the interface, -20 6

10

8

- 6 u

(b) f

a 4

2

Time (min)

FIG. 13. Axial temperature fluctuations measured (a) at B,O,/GaAs melt interface AT,,, 1 3°C and (b) within encapsulated GaAs melt AT,,,, 1 9 ° C . Crucible is 150 mm in diameter and contains 3-kg melt and 0.6-kg B203encapsulant.

R. N. THOMAS et

22

al.

excursions/min. Temperature fluctuations associated with crystal and/or crucible rotation were also explored by probing the melt with the thermocouple probe displaced to different positions from the center of the melt. Temperature fluctuations with the exact periodicity of the relative rotation rate were observed. The rotational temperature fluctuationswere, however, quite small and were often difficult to observe because of the larger, more random nonrotational fluctuations. The much larger magnitude of these temperature variations indicates a much higher degree of convectiveturbulence for the encapsulated GaAs melt relative to large-volume (unencapsulated) silicon melts, where axial temperature fluctuations of about 1 "C are typical (Suzuki et al., 1981). Preliminary investigations of impurity striation behavior in large-diameter LEC GaAs crystals pulled from 3-kg melts are illustrated in Fig. 14. For this study, (1 1 1) axial cross sections sliced from 50-mm diam, ( 100)-oriented LEC GaAs crystals were polished to a mirror finish in Br-methanol and then etched in an A-B solution to reveal longitudinal striations under a

FIG.14. Striations observed in ( I 1 1 ) longitudinal sections cut from ( 100) LEC-grownGaAs crystals. (a) Undoped, semi-insulatingGaAs/PBN ( p 10' C2 cm) and (b) Si-doped GaAs/ fused SiOz( p 0.04 R cm) samples.

-

-

1.

HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

23

Nomarski contrast interferometer. These studies revealed longitudinal striations (presumably due to microscopic variations in resistivity) for undoped semi-insulating GaAs grown from PBN crucibles (Fig. 14a) and low-resistivity n-type crystals pulled from fused Si02crucibles (Fig. 14b). In the case of the semi-insulating GaAs/PBN crystal, the impurity content is low, suggesting that the observed striations correspond to microscopic variations in compensation and may arise from local fluctuations in stoichiometry. The closely spaced striations in the low-resistivity, n-type material (Fig. 14b) result from variations in dopant incorporation (in this case, Si, k,,- 0.1, introduced from the SiO, crucible) due to fluctuations in microscopic growth rate. An even greater axially striated impurity distribution and greater microscopic inhomogeneity is expected in Cr-doped GaAs because of the very low segregation coefficient of chromium (k, 6 X lo4). These investigations suggest that further optimization of the thermal distributions in large-volume LEC melts is crucial to the development of large-diameter GaAs crystals with highly uniform properties on a microscopic as well as macroscopic scale. It is speculated, based on recent experiments with Czochralski-grown silicon (Suzuki et al., 1981; Braggins, 1982), that the application of magnetic fields across large-volumeLEC GaAs melts can have important beneficial effects on the suppression of thermal fluctuations, with corresponding improvements in microhomogeneity.

-

111. Compositional Purity

It is now well established that melt interactions with the container, and in the case of LEC growth with the encapsulant, are the principal sources of residual chemical impurities in melt-grown GaAs. Silicon contamination of bulk and epitaxial GaAs grown in fused silica containers is a well-known example of inadvertent contamination. There is some evidence, however, that GaAs, when grown epitaxially in sufficiently high purity, is a defectdominated semiconductorin which the electrical properties are significantly influenced by stoichiometry-related defect centers as well as residual chemical impurities. In general, however, particularly with melt-grown bulk crystals, the observed properties have almost always been related to the presence of residual chemical impurities that are inadvertently introduced into the melt or possibly are present in the starting Ga or As components. 4. MASSSPECTROMETRY Analytical assessment of the chemical purity of bulk GaAs has relied mainly upon secondary ion mass spectrometry (SIMS) and spark source mass spectrometry (SSMS)techniques, and a wide range of impurity species have been examined. In the SIMS technique, quantitative estimates of

24 90

80

T -

70

60 vi "0 I

1

'i

R. N. THOMAS

0 LEClQuartz LEC/ PBN ( Avg of 10 Crystals) [3 Boat GrowthlQuartz

et al.

50 E

.s L (0

c OI c

U

V

4

2

FIG. 15. Bulk SIMS analysis of semi-insulating GaAs prepared by LEC and horizontal Bridgman growth. (Data supplied courtesy of Charles Evans and Associates, San Mateo, California.)

impurity concentrationscan be obtained by calibration against GaAs samples that have been implanted with known doses of specific impurities. Comparative results? for the most important residual impurities in LEC GaAs material pulled from both fused silica and PBN crucibles, as well as large-area, boat-grown substrates purchased from outside suppliers, are shown in Fig. 15. The markers on each bar represent data for different crystals. In the case of the GaAs grown from PBN crucibles, the markers on each bar correspond to the maximum impurity concentration observed for ten representative crystals. The detailed SIMS data for crystals pulled from PBN crucibles are shown in Table I. Residual silicon concentrations typically below 1 X loL5 cmm3are observed in GaAs/PBN samples compared to levels that range up to 10l6cm-3 in crystals grown in quartz containers. The residual chromium content in undoped LEC GaAs crystals pulled from either PBN or fused silica crucibles is below the detection limit of the SIMS ~. of LEC-grown instrument, estimated to be in the low loL4~ m - Analyses crystals pulled from Cr-doped melts contained in quartz crucibles reveal - ~the seed end and approaching that the Cr content (typically 2 X 1OI6~ r n at loL7 at the tang end) is close to the anticipated doping level based on the amount of Cr dopant added to the melt and its reported segregation behavior (Willardson and Allred, 1967). Cr-dopant levels of (2-9) X 10I6

t The SIMS analyses were performed at Charles Evans and Associates, San Mateo, California, using a Cameca IMSJF ion microanalyzer.

1. HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

25

TABLE I HIGHSENSITIVITY SECONDARY ION MASSSPECTROSCOPY ANALYSIS~ OF LEC SEMI-INSULATING GdS CRYSTALS PULLED FROM HIGH-PURITY PYROLYTIC BORONNITRIDE CRUCIBLES

SIMS analysis, courtesy of Charles Evans & Associates, San Mateo, California. (s) Seed-end sample and (t) Tang-end sample. Detection limits for C. 0. Fe (<mid ern-') not well defined.

~ r n were - ~ typically observed in material grown by horizontal Bridgman or gradient-freeze methods. The reduced concentration of shallow donor impurities in growths from PBN crucibles permits undoped or, alternatively, lower Crdoping levels to be utilized as shown in Table I, where typical Cr-dopant concentrations range from 3 X lOI5 cm-3 at the crystal seed end to 6 X 1015cm-3 near the crystal tang end. The SIMS studies also indicate that LEC growths, particularly from PBN - ~ of boron. crucibles, generally result in high concentrations(10’’ ~ r n range) Carbon and oxygen cannot be measured directly below about 10I6cm-3 by mass spectrometric techniques and are estimated to be in the low 10I6 range or lower in GaAs. (See Kirkpatrick et al., Chapter 3, Section 6, this

26

R. N. THOMAS

et al.

volume, for a discussion of localized vibrational mode far-infrared spectroscopy (LVM) determination of total carbon concentration in GaAs and this chapter, Section 8,for Hall-effect measurements of electrically active carbon content.) Other impurities, such as Groups 11, IV, and VI, and iron and other transition elements are typically below the 1015-cm-3range. Agreement between analyses performed by SIMS and SSMS by different investigators is generally excellent. (For other SSMS and Arc Source Emission Spectroscopic(ASES) analyses, see Stolte, Chapter 2, Section 1,this volume. A key feature in the SIMS investigation of Cr-doped substrates has been numerous observations of the movement of Cr under implantation annealing conditions for Si and Se implants into GaAs substrates (Huber et al., 1979a; Evans et al., 1979). The uncontrollable out-diffusion and redistribution of Cr in implanted layers in Cr-doped substrates has been correlated with surface conversion and poor uniformity of implant profiles (Thomas et al., 1981). 5. BORONAND SILICON

Boric oxide is now commercially available in six 9s (0,999999) purity through high-purity recrystallization and vacuum-bakingprocedures. Typical mass spectrometry measurements for highest grade B203 reveal the presence of a few transition metals (principally, Cu and Fe) at 1-ppm wt levels, with all other detectable elements being below the detection limit of the mass spectrometry. Infrared absorption measurements show [OH] contents ranging from 150 ppm wt to 1000 ppm wt, depending upon the degree of vacuum baking to which the B203has been subjected (data supplied by Johnson-Mathey Chemical, Ltd.) The influence of the water content [OH] in the B203encapsulant on the incorporation of Si and B impurities for growths from fused SiO, and PBN crucibles has been investigated (Hobgood et al., 1981b). The results are shown in Figs. 16a and 16b, respectively. In these measurements, low [OH] content was assured by vacuum baking the oxide at 1O0O0C/8hr immediately before use for crystal growth. For growths from fused SOz crucibles (Fig. 16a), the Si and B content of the GaAs (as measured by SIMS) is a strong function of the [OH] content of the B2O3 encapsulant, with B20? having high [OH]content (> 1000 ppm [OH]) yielding lower contents of Si and Bywhile concentrationsof Si nd B in the mid-10'6-cm-3range have been observed for growths utilizing vacuum-baked B203(<500 ppm OH). The results indicate that B203 with a high-moisture content can be used to suppress silicon contamination of the melt and to yield high-purity, undoped GaAs from fused SiO, crucibles (Fairman et al., 1981; Oliver et al., 1981). Semi-insulating GaAs crystals pulled from undoped melts contained in fused SiO, crucibles have been achieved (Section 6) but, as shown earlier

-

1.

HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

l0lS

27

10l6 Bomn (cm-3)

(al

_

I

L

l

-

.

lot6

10l6 Boron (cm-3)

(b)

.,

FIG. 16. Effect of [OH] content of boric-oxideencapsulanton silicon and boron incorporation in undoped LEC GaAs crystals pulled from (a) fused silica and (b) pyrolytic boron nitride crucibles. (a) 0, [OH] < 500ppm; 0, [OH]> lo00 ppm. (b) 0, [OH] <500ppm; [OH] > 1000 ppm; A,N, ambient (30 atm).

in Fig. 6, considerations of twinning associated with growths using high [OH]-content B203make this technique less desirable for the reproducible growth of large, twin-free crystals of GaAs. For growths of undoped GaAs crystals from PBN crucibles (Fig. 16b), the silicon content nearly always borders on the detection limit of the SIMS

28

R. N. THOMAS

et al.

instrument (-4 X loL4 cm-9, while boron can range from low cm-3 up to lo1*~ m - ~ . The chemical kinetics controlling the apparently linear relationship between silicon and boron in growths from fused SiO, crucibles is not yet completely clear, Oliver et al. ( 198 1) suggest that the introduction of silicon and boron into the melt derives from the chemical reduction of the Si02 crucible and B,03 encapsulant in the presence of metallic Ga to give Ga,O, according to

-

SiO,

+ 4Ga

B,O,

+ 6Ga

and

+

(1)

+

(2)

2Ga20 Si

-

3Ga20 2B.

However, the presence of moisture in high [OH]-content B,O, provides an alternative mechanism by which the reaction proceeds by the chemical reduction of the water at the expense of the Si02 and B 2 O 3 , thereby inhibiting the silicon and boron contamination. This mechanism is supported by the earlier demonstration of Lightowlers(1972), that the addition of Ga203to LEC Gap melts drives the reaction shown in Eq. (2) to the left, suppressing the incorporation of boron by about two orders of magnitude relative to oxygen-deficient melts. It was also shown in this work that nitrogen is effective in reducing the boron concentration in LEC GaP crystals, and it was speculated that this occurs by the precipitation of boron nitride: 2B

-

+ N2

2BN.

(3)

Similar observations have recently been made for the growth of LEC GaAs crystals pulled from a PBN crucible in a high-pressure nitrogen ambient, as shown in Fig. 16b. These observations support the view that silicon and boron contamination of LEC melts derives primarily from the interaction of the melt with the encapsulant and crucible, and confirm that some control over the degree of contamination can be achieved by effective manipulation of the chemical kinetics in the melt. It is clear, however, that the availability of silicon-free PBN crucibles offers the crystal grower significant advantages for reliably producing GaAs crystals containing low concentrations of electrically active, residual impurities. Even though boron is generally incorporated at high concentrations in these GaAs/PBN crystals, no evidence exists at present of any electrical activity attributable directly to boron in semi-insulating GaAs grown from stoichiometric or As-rich melts. The effect of boron in ptype GaAs grown from Ga-rich melts will be discussed in Section 8.

1,

HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

29

IV. Electrical Properties Traditionally, the preparation of semi-insulatingGaAs crystals has relied upon the addition of chromium doping, usually at high concentrations, to compensate residual silicon contamination of the melt as well as other shallow donors such as sulfur, which can be a major contaminant in high-purity elemental As. Semi-insulatingbehavior is therefore believed to be the result of compensation of these shallow donor impurities by the deep-level chromium acceptors (Ev 0.86 eV) in a wide-band-gap semiconductor (EG= 1.43 eV). In the horizontal Bridgman or gradient-freeze techniques, oxygen derived from small quantities of Ga203added to the melt inhibits the reaction of Ga with the fused silica boat and thereby reduces silicon contamination (Woodall, 1967). Experimental evidence suggests that melt-grown GaAs crystalscontain significant concentrationsof oxygen, and these observations have led to considerable speculation that oxygen plays an important role in determining the observed semi-insulating properties of “oxygen-doped” and “0-0 doped” GaAs prepared by boat growth. For example, Zucca (1977) has proposed a model that includes both a deep acceptor (Cr) and a deep donor (oxygen) to interpret experimental resistivity data in lightly Cr-doped GaAs (5 X loi5 Cr). The assignment of the measured deepdonor level at between 0.64 and 0.76 eV below the conduction band edge (which is usually designated as the EL2 level) is, however, quite controversial (Huber et al., 1979b), and recent observations by these researchers in fact clearly indicate no dependence of the concentration of the EL2 deep donor upon the oxygen content in Bridgman-grown crystals. Resistivity studies (Thomas et a/., 1981) of semi-insulating GaAs prepared by liquid-encapsulated Czochralski in our laboratories also demonstrate the dominant role of the deep EL2 level. Log resistivity versus reciprocal temperature plots yielded an activation of 0.76 eV independent of whether the GaAs is undoped or intentionally doped with chromium up to 1 X 10’’ cm-3 concentrations(Thomas et al., 1981).Recent independent investigations (Foose et al., 1981; Holmes et al., 1982a,b; Hobgood et al., 1982) of the compensation mechanisms in undoped, semi-insulating GaAs crystals pulled from silicon-free PBN crucibles support earlier suggestions (Martin et al., 1980a) that the EL2 level is specifically related to Ga and/or As point defects in the crystal. No obvious role of oxygen in determining the semi-insulating properties of GaAs is suggested by these studies. The concentration of the EL2 deep donor is found to depend strongly upon the stoichiometry of the GaAs solid and is influenced by thermal annealing, as expected qualitatively from theoretical predictions (Hurle, 1979) of the solid-phase extent of GaAs in melt growth.

+

30

R. N. THOMAS et

al.

Electrical and optical assessments of LEC-grown GaAs substrates which reveal the principal factors controllingthe purity, semi-insulatingproperties and thermal stability are discussed in Sections 6 - 9, which follow. 6. CRUCIBLE/ENCAPSULANT EFFECTS

Undoped GaAs/PBN crystalspulled from stoichiometricor As-rich GaAs melts are found to exhibit reproducible, uniform, semi-insulating behavior, with resistivities ranging from mid-10' to lo8 R cm over the full crystal length, as shown in Fig. 17. Additions of small amounts of chromium (<5 X lOI5 ~ m - result ~ ) in a slight increase of resistivity (> lo8 R cm range) and a corresponding reduction in mobility. These results suggest that high Cr concentrations in GaAs/PBN substrates serve no useful purpose and contribute to excessive ionized impurity scattering, as well as other detrimental effects related to chromium impurity redistribution. In contrast, the LEC growth of undoped semi-insulating crystals pulled from conventional fused silica crucibles has met with very limited success, owing primarily to the deleterious silicon contamination arising from crucible - melt interaction. The variable and unpredictable nature of this growth technique for the production of semi-insulating material is illustrated by the data of Fig. 18. Resistivities show large variations over the full crystal length, and semi-insulating behavior, when it occurs, is usually confined to only a small section of crystal. Attempts to achieve uniform high resistivities in GaAs/Si02 crystals by intentionally increasing the [OH] content of the B203to inhibit

0

20

40 60 m Fraction Melt Solidified 1%)

1Oa

FIG. 17. Axial resistivity of undoped semi-insulating GaAs crystals pulled from pyrolytic boron nitride crucibles. The different symbols are representative of eight crystals grown from stoichiometric or slightly As-rich melts and using vacuum-baked B,O, encapsulant.p = 48006800 cm2 V-' sec-I.

1. HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

M

0

40

60

80

31

100

Fraction Melt Solidified (%)

FIG.18. Axial resistivity variation of undoped GaAscrystals grown from natural (solid lines) and synthetic (dashed lines) fused silica crucibles by high-pressure LEC. p = 300 6500cm2V-'sec-I. WetB,O,:O, W-lS;O, W-l8;A, W-23;V, W-60;0,W-61.DryB203:0, w-50. w-30; m,w-31; A,w-48;

v,

crucible and encapsulant contamination of the melt has not given rise to a dramatic improvement in semi-insulatingbehavior, as indicated by the dry and wet B,03 results of Fig. 18. Effects of different types of fused silica containers on the semi-insulating behavior of undoped LEC GaAs crystals have also been investigated.In Fig. 18, most of the crystals were pulled from conventional fused silica crucibles (type HV-2 14 fused silica), while crystals W-48and W-50 were pulled from high-purity synthetic fused silica containers of differing [OH] contents (Suprasil-W, 5 - 10-ppm wt [OH], and Spectrasil, 1500-ppm wt [OH], respectively). In contrast to other work (Fairman et al., 1980), all of these crystals exhibited low-resistivity, n-type behavior regardless of the water content of the fused silica crucible. We conclude that semi-insulating GaAs can be produced reliably from undoped melts using in situ compounding and growth under high-pressure liquid encapsulation, only when high-purity PBN crucibles are utilized. In contrast, other workers (Ford et al., 1980;Stolte, Chapter 2,Section 1, this volume), using separate or in situ compounding and low-pressure LEC

32

R . N . THOMAS

et al.

conditions, report that the semi-insulatingproperties of undoped GaAs are not adversely affected by the use of fused silica containers. 7. MELTCOMPOSITION EFFECTS Recent studies of the growth of GaAs using high-pressure LEC techniques indicate that reproducible, semi-insulating behavior in undoped GaAs/PBN crystals requires close control of the melt composition. Holmes et al. (1 982a,b; see also Kirkpatrick et al., Chapter 3, Section 7, this volume) have shown that n-type, high-resistivity material can be grown only from melts above a critical As composition. Ga-rich melts were found to yield ptype, low-resistivity crystals due to hole conduction from uncompensated residual acceptors, which were identified as predominantly carbon impurities. This study also indicated that semi-insulating behavior in undoped GaAs results from the compensation of these residual carbon acceptors by defectrelated EL2 deep donors. The concentration of the latter depends upon the crystal stoichiometry and increases with increasing As composition. The electrical transport and optical absorption measurements presented in this section provide independent evidence of the role of melt composition and confirm the findings of Holmes et al. (1982a,b). The data support the view that the deep-donor (EL2) level in GaAs is a point defect-related level, the concentration of which is a sensitive function of exact stoichiometry of the solid. Our results additionally indicate that the thermal stability of undoped semi-insulating GaAs is also strongly influenced by the crystal stoichiometry (Ta et al., 1982a). Thermal treatments commonly employed in implantation processing can reduce the surface concentrations of compensating deep-defect donors in undoped, semi-insulating GaAs and can lead to substrate conversion effects, a phenomenon which was previously attributed to the out-diffusion and pileup of residual acceptors, such as Mn (Klein et al., 1980), at the surface. The measured mobility of undoped, semi-insulating GaAs is found to be a sensitive indicator of substrate stoichiometry and quality, and it is suggested that this parameter can uniquely “qualify” substrates for direct ion-implantation device processing. To investigate the effects of crystal stoichiometry on the transport properties and thermal stability of undoped LEC GaAs, a series of large-diameter (575 mm) ( 100) crystals were grown from melts of varying compositions in the high-pressure Melbourn LEC puller. Nominally, 3-kg undoped melts contained in a PBN crucible were utilized, which were synthesized in situ from six 9s purity, elemental Ga and As charges. Because the deviations in stoichiometryof the solid are small and difficult to measure directly, electrical behavior of as-grown and thermally annealed samples was studied as a function of the correspondingly much larger variations in melt composition. Changes in the initial melt composition were made from one growth run

1.

HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

33

to the other by varying the proportions of starting Ga and As charges. The composition was determined accurately at the end of the run by accounting for the inadvertent vaporization loss of As during the compounding cycle from weight-inlweight-out measurements. Any measured mass loss was attributed to vaporization losses of the arsenic component during the heat-up portion of the synthesis cycle prior to total encapsulation by the liquid B,03. No incorporation of As, and less than 0.1% of the Ga charge, into the boric-oxide encapsulant layer was revealed by emission spectrometry studies of the oxide after crystal growth. From the starting composition, the melt composition at any point during crystal growth can then be computed as a function of the fraction of melt solidified. To verify the validity of the weight-in/weight-out technique for determiningmelt composition, the actual composition of the residual GaAs melt remaining in the crucible after each crystal growth was measured by a precise analytical titration procedure (Cheng, 1961). Based on this analysis, the measured and computed compositions were found to agree within a few percent. Resistivity as a function of the normalized crystal length for five GaAs/ PBN crystals pulled from undoped melts of different compositions is shown in Fig. 19. Uniform, n-type high resistivity over the full crystal length is observed only for growth from a slightly As-rich melt ([Ga]/[As] = 0.98). In contrast, low-resistivity, ptype conduction is observed when growth prolo1

lo8

-G

106

c -

.c 104 .c .VI

E

lo2

100 1

1

x,

1

!

40

,

I

1

60

!

80

L

J

loo

Fraction Melt Solidified ( 61

FIG.19. Effect of starting melt composition on axial resistivity of undoped LEC GaAs/PBN crystals. The number adjacent to each curve indicates the starting melt composition. Open points indicate n-type; closed points indicate ptype conduction.

34

R. N. THOMAS

et al.

ceeds from a highly Ga-rich starting composition ([Ga]/[As] = 1.2) or from near-stoichiometric Ga-rich melts once the composition becomes enriched beyond a critical Ga composition with the progressive depletion of the melt during growth. Figure 20 illustrates that this transition from n-type, high-resistivity behavior occurs at a Ga-melt composition of about 0.53 atom fraction Ga ([Ga]/[As] 2 1.13), in excellent agreement with other recent observations (Holmes et al., 1982a,b). Electrical transport data show that solid GaAs grown from slightly Garich compositions can exhibit high-resistivity n-type behavior. However, mobility and thermal stability begin to degrade for solid crystallizing from melts containing more than 0.495 atom fraction Ga( [Ga]/[As] 2 0.98), i.e., the composition for exact stoichiometryin the solid. Mobility, also shown in Fig. 20, is observed to be highly sensitive to excess Ga in the melt, and the measured 6500 cm2V-' sec-' electron mobility of semi-insulating GaAs grown from a slightly As-rich melt ([Ga]/[As] = 0.98) decreases to about 300 cm2V-I sec-I , corresponding to low-resistivity hole conduction for melt compositions with [Ga]/[As] ratio 1 1.1. This ptype behavior observed in GaAs/PBN crystals pulled from Ga-rich melts is derived from the presence of residual electrically active impurities such as carbon (Ev+0.025 eV) and other unidentified impurity or defect levels (E, 0.073 eV) (Section 8). It has already been established that the deep-donor EL2 level plays an important role in controlling the semi-insulating behavior of LEC GaAs

+

Melt Composition, ICa l/IAs 1 FIG.20. Effect of stoichiometry on resistivity and measured carrier mobility of undoped LEC GaAs/PBN (at 300°K). Open points indicate n-type; closed points indicate ptype conduction.

1. HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION

35

(Martin et al., 1980a,b).The variation in the deep-donor EL2 concentration with melt composition has also been investigated. Figure 21 shows the optical absorption coefficient at 1-10pm (corresponding to electron excitation of the EL2 donor level) for GaAs samples pulled from melts with compositions on the As and Ga sides of the liquidus. The measurements were made at room temperature using 500-pm-thick polished samples in a Perkin-Elmer (Model 330) absorption spectrometer. In agreement with previous observations (Holmes et al., 1982a,b), the EL2 absorption drops abruptly when the solid composition moves from the As-to the Ga-rich side, and is presumably due to a corresponding reduction in the concentration of the EL2 deep-donor level. These observations are consistent with the fact that the EL2 level is not observed in GaAs layers grown by liquid-phase epitaxy from Ga-rich solutions, and suggest that the formation of the EL2 level involves native point defects such as A h a or VGa.Recent electron paramagnetic resonance measurements and shallow donor-doping experiments (Lagowski et al., 1982) in GaAs grown by the Bridgman technique also suggest that the EL2 deep donor is associated with As,. The EL2 donor concentration in GaAs is therefore intimately related to the exact stoichiometry of the solid and is estimated (Martin et a!., 1980a) from Fig. 2 1 to be about 1 X loL5 in Ga-rich material, and greater than 1OI6 cmd3in the As-rich solid. These observations have important implications for the growth of undoped GaAs/PBN crystals with reproducible semi-insulating properties. Since the semi-insulatingbehavior is controlled predominantly by the EL2 deep-donor level, only growths from GaAs melt compositions

1.26 1.22 1.18 1.14 1.10 1.06 1.02 0.98O.W Melt Composition. I Gal/[ As1

0.90 0.86

FIG.2 I . Measured optical absorption at 1.10pm due to EL2 level excitation as a function of melt composition. Undoped GaAs/PBN at 300°K. 1 = 1.1 pm.

36

R. N. THOMAS et

al.

with [Ga]/[As] < 0.98 yield crystals with uniformly high semi-insulating resistivities and high measured mobilities throughout the grown crystal. 8. RESIDUAL IMPURITIES

Rigorous analysis and interpretation of mobility measurements in semiinsulating GaAs have been shown to be formidable problems (Look, 1978, 1983) because of the need to separate electron and hole contributions to the conduction process at the low carrier concentrations. However, simplified theoretical treatments such as the Brooks- Herring relationship (Brooks, 1955; Rode, 1975) do provide a valuable, if approximate, assessment of the total ionized impurity content in the n-type semi-insulatingGAS.Figure 22 shows mobility measurements for a number of undoped GaAs/PBN and Crdoped GaAs/PBN crystals using a high-impedance Van der Pauw technique (Hemenger, 1973). High measured mobilities, ranging from 5000- 7000 cm2 V' sec-', are typical of undoped, semi-insulating Gas/ PBN substrates. Electron conduction with carrier densities in the lo6- lo7 cm-3 are measured at 300°Kand, when analyzed in accordance with the Brooks-Herring relationship, the data yield a total ionized impurity content of approximately 1 X 10l6 ~ m - A ~ ,similar analysis of the measured mobilities of Cr-doped GaAs strongly suggests the doubly ionized state of

-

c (

'u 7000

%

-

I

> N

mBmks-Herring Theory

2 3

5-

ZsoooE e

z m-

H

g2oOo-

I

loao 0:

I

I

I

I

I

I

J

1.

HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

37

the Cr impurities. For lightly Cr-doped samples (<5 X 1015cmV3Cr), the measured mobilities fall in the 3000-4500-cm2 V-l sec-' range. At the higher Cr-dopinglevels normally employed in conventionalsemi-insulating ) , mobility falls into the 2000-cm2V-' sec-' range GaAs (>5 X 10l6~ r n - ~the corresponding to a total ionized-impurity concentration in the low cm-3 range. These measurements suggest that high-purity, undoped GaAs/PBN material contains residual, electrically active impurities in the 1 X 1016-cm-3 range and, in view of the low concentration of common shallow donors and shallow acceptors detected by the SIMS analysis of this material (low 1015-cm-3range or less), this observation poses a question as to the origin of the 1 X 10l6cm-3 residual ionized impurity concentration derived from the mobility analysis. Residual carbon impurity, a shallow acceptor in GaAs, has been suggested as the source of this residual electrical activity. Both secondary-ion and spark source mass spectrometry indicate that the presence of carbon in both Bridgman- and LEC-grown GaAs crystals, and recent local vibration mode far-infrared spectroscopy studies (Holmes et al., 1982a,b; Kirkpatrick et al., Chapter 3, Section 8, this volume) identify carbon as the predominant shallow acceptor impurity in undoped G a s / PBN substrates. Independent identification and an assessment of the electrically active carbon concentrationare obtained from the variable temperature Hall-effect measurements shown in Fig. 23 of two undoped, ptype, low-resistivityGaAs/PBN crystals pulled from Ga-rich melts. The data are fitted (Blakemore, 1962; Thomas et al., 1978) by using a least-squares-fit computer program to the charge neutrality relation for the case of compensated monovalent multiple acceptor levels:

where NAi, E A i , and gi are the concentration, ionization energy, and ground-state degeneracy of the ith acceptor level, respectively. ND is the net donor compensation density. A number of samples from different crystals, which show ptype behavior, have been analyzed. The parameters used in the analyses are gi = 4 and effective mass* = 0.493m0(Mears and Stradling, 197l), which accounts for the effect of both heavy- and light-hole valence bands. A best fit indicates an ionization energy of about 0.025 eV for the shallow-acceptorlevel, which is predominant in the seed-end substrate. This measured value for EAis relatively close to the effective mass ionization energy of 0.026 eV (Baldereschiand Lipari, 1974)and the value of 0.026 eV determined from photoluminescence (Ashen et al., 1975; Sze and Irvin, 1966) for carbon acceptor in GaAs, suggesting that the ptype behavior in this material results from uncompensated carbon residual impurities with

38

R. N. THOMAS

5

10

20 30 lRUl/T

et al.

40

50

J

FIG.23. Carrier concentrationas a function of reciprocal temperature of two low-resistivity ptype GaAs crystals pulled from undoped, Ga-rich melts. Data are fitted to theoretical curves using g = 4 and m* = 0.493 m,.

concentration in the low 101s-cm-3range. The ionization energy obtained for the deeper acceptor level in the tang-end substrate is about 0.073 eV, which is about 5 meV lower than the values of 0.077 eV (Yu et al., 1981) and 0.078 eV (Elliott el al., 1982)determined from photoluminescence and infrared absorption, respectively. The occurrence of this level in the tang section suggests that the carbon concentration in this crystal is extremely low and thus compensated by residual donors. Our studies indicate that the 0.073-eV acceptor level is associated with excess Ga (Ta et al., 1982c),as illustrated by the photoluminescence spectra in Fig. 24. The emission peak (1.442 eV) associated with the free-to-bound transition (Yu et al., 1981)at the 0.073-eV acceptor level is clearly identified in Ga-rich samples (Fig. 24b) but is conspicuously absent in all semi-insulating crystals pulled from stoichiometricor slightly As-rich melts (Fig. 24a). Elliott et al. (1982) have recently shown that this acceptor concentration increases with increasing Ga atom fraction in the melts. This observation

39

1. HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION 1

1

1

1

1

1

1

1

Carbon 1.4% eV

1

,

,

Exciton 1.514 eV

Q c

c M

Exciton

Defect-Boron Complex 1.442 eV

FIG.24. Photoluminescence spectra at 4.2"K of (a) semi-insulating GaAs grown from slightly As-rich melt, showing carbon as the dominant residual acceptor impurity (Ga/As < I), and (b) b-type GaAs grown from Ga-rich melt showing the defect-boron complex as the predominant acceptor. (Courtesy of Dr. G. W. Wicks, Cornell University, 1982.)

I

E

(b)

Carbon

Wavelength

and their excited-state IR absorption studies have led to the suggestion that the new acceptor level is attributable to the anti-site GaAs defect (Elliott et al., 1982). However, detailed Hall analyses show that the 0.073-eV acceptor is probably not a simple intrinsic defect. Typically, both carbon and the 0.073-eV acceptor levels are observed in crystals pulled from Ga-rich melts. The axial variation of the carbon and 0.073-eV acceptor levels is clearly indicated in Fig. 25, which shows the temperature-dependent Hall measurements of a ptype GaAs crystal pulled from a Ga-rich melt at two positions along its length. The curve at the position corresponding to fraction of the melt solidified off= 38% shows a saturation at room temperature, indicating that carbon is the predominant acceptor in this material. However, the 0.073-eV acceptor becomes predominant as the crystal becomes heavily Ga-rich toward the tang end, as shown by the curve atf= 79%. Furthermore, thef= 79% curve is shifted down in concentration compared to the curve atf= 3896, indicating an increase in the net residual donors, due to impurity segregation effects. Our analysis at various positions in this crystal, as shown in Fig. 26, indicate a combined effective segregation coefficient for residual donors of keE- 0.4, and an effective segregation coefficient for carbon of k,, 0.9, close to the value of

-

Seed End, f =38%

I

I

10

20

I

30 lOOOlT (

I

40

50

60

FIG.25. Carrier concentrationas a function of reciprocaltemperature for an undoped GaAs crystal grown from Ga-rich melt. Theoretical curves are fitted to the data using g = 4 and m* = 0.493 m,.

Defect-Boron CornDlex

1014

M 2 0 4 0 6 0 8 0 1 0 0

0

Fraction Melt Solidified I%)

FIG.26. Axial distribution of residual impurity and defect densities in an undoped, Ga-rich ptype GaAs crystal, determined from Hall analyses, yielding effective segregationcoefficientof k, - 0.9 for carbon and kH 0.4 for residual donors.

-

1.

HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

41

0.8 obtained for ( 1 1 1 ) GaAs crystals (Willardson and Allred, 1967). However, the axial variation of the deeper acceptor concentration does not show normal impurity segregation behavior, suggesting that it is probably associated with intrinsic defects. The dependence of the defect-related 0.073-eV acceptor density on the melt composition for GaAs crystals grown from Ga-rich melts is shown in Fig. 27. For GaAs crystals containing boron concentrations in the range of about (0.9-2)X lOI7 cm-3 (open points), the density of the 0.073-eV acceptor level increases with increasingGa richness, in good agreement with recent observations (Elliott et al., 1982). However, our data also indicate a strong influence of boron on the 0.073-eV acceptor concentration (Fig. 27, closed points). An increase of about two orders of magnitude in the acceptor concentration is observed when the boron concentration increases from about 9 X 10l6to 1 X lo1*~ m - ~ . The explicit dependence of the 0.073-eV acceptor level on boron [measured by high-sensitivity (SIMS) analysis] is shown more clearly in Fig. 28 for Ga-rich samples corresponding to nearly equal melt compositions (0.54 atom fraction Ga), so that any dependence on stoichiometry has been removed. For these samples having nearly the same stoichiometric composition, the concentration of the 0.073-eV acceptor level increases dramatically with increasing boron concentration over the range (1 - 10) X cm-3 boron and exhibits an approximate square law dependence on the boron content. These results, therefore, suggest that the 0.073-eV acceptor is not a simple anti-site defect but rather a complex of an intrinsic defect involving boron, 1018, 0

m -

m

6 O'

1

10i4L 0.50

,

,

,

,

,

0.54 0.58 0.60 0.64 0.68 Ga Melt Composition (atom fraction)

FIG.27. Effect of melt composition and boron concentrationon the 0.073-eV defect-complexacceptorconcentrationfGa-richptypef.0,[B] =(0.9-2) X lO"~rn-~;O,[B]= ( 5 - 10) X 10''

~ 3 1 1 ~ ~ .

R. N. THOMAS et al.

42 1ol8

4

6 8 10’’

I

1

I l l

I

I

2

4

6 8

2

4

1018

Boron Concentration (crn-3)

FIG.28. Concentration of 0.073-eV acceptor level as a function of boron concentration for Ga-rich samples corresponding to nearly equal melt compositions (0.54-Ga atom fraction).

although the exact structure of the complex is not clearly identifiable at this time. A simple form of such complex would be (VAs- B), (Gai - B), or (Ga,, - B), with boron occupying the isovalent Ga site. However, the roughly quadratic increase in the concentration of the defect acceptor, observed in these preliminary experiments, with increasing boron concentration suggeststhat the complex may involve a boron pair. Figure 29 shows the measured resistivity of unintentionallydoped GaAs pulled from Ga-rich melts as a function of the boron content. In contrast to the low-resistivity, ptype behavior observed in samples containing 2 5 X loi6 boron, n-type conduction and resistivities between lo3and 104 R cm and mobilities in the 7600-cm2V-I sec-’ range are measured in low boron content, Ga-rich substrates (- loL5 ~ m - ~We ) . conclude, therefore, that the 0.073-eV defect - complex acceptor is not formed in any significant concentration in GaAs crystals pulled from Ga-rich melts when the boron content is low. The observed n-type conduction is suggested to be the result of intrinsic Gai or V,, defects, since Ga, should be an acceptor. Variable temperature Hall-effect measurements of these samplesreveal a deep-donor activation energy of about 0.45 eV, as shown in Fig. 30, in good agreement with recent theoretical calculations (Bachelet et al., 1981) of about 0.46 eV from the bottom of the conduction band for an ideal V,, in GaAs.However, since Ga, is also expected to be a donor, and probably a deep donor, this defect cannot be ruled out. In summary, our results have shown a strong dependence of electrical properties of undoped LEC GaAs/PBN on stoichiometry and residual

lo3

1

n -Type

E =0.45eV D

:I .-x

\

L\

101

\

a

PI

loo

10-1

1

p-Type EA=0.073eV

\

O0\

1 1

0

/ O\

1

I

\ I

1018 Boron Concentration ( ~ r n - ~ )

FIG. 29. Resistivity of undoped GaAs grown from Ga-rich melts as a function of boron concentration determined from SIMS. Open points indicate p-type; closed points indicate n-type conduction.

10

3.0

3.5

40

4. 5

1W/T (

FIG.30. Camer concentrationas a function of reciprocaltemperaturefor two GaAs crystals ~ m - ~[B] ) . loLsern-). 0,WBNl ; pulled from Ga-rich melts having low boron content (- loL5 W, WBN35.

-

44

R. N. THOMAS

et al.

impurities. GaAs crystals grown from stoichiometric or As-rich melts exhibit high-resistivity, n-type behavior, resulting from the compensation of residual carbon impurities by the deep-donor defect EL2, which increasesin concentration with increasingAs richness in the melts. GaAs crystals pulled from Ga-rich melts and containing high boron concentrations (Z 5 X 1OI6 ~ m - exhibit ~) low-resistivity, p-type behavior. The hole conduction is predominantly controlled by an acceptor level having an energy of about 0.073 eV (determined from Hall analysis) associated with defect - boron complex, such as (VAs- B) or (Gai - B). However, GaAs crystals pulled from Ga-rich melts and containing low boron concentrations(- lOI5 crn-’) are n-type, with resistivities of about lo3- lo4 Q cm. The electron conduction is due to a deep-donor level of about 0.45 eV, associated with intrinsic defects such as V,, or Ga,.

STABILITY 9. THERMAL A significant extent of the GaAs solid field at or just below the melting point is predicted theoretically (Hurle, 1979)in the phase diagram shown in Fig. 3 1 , High concentrationsof Ga or As point defects, depending upon the melt composition, can therefore be incorporated into the lattice during growth from the melt. In contrast, nearly exact stoichiometric solid compositions are expected in liquid-phase epitaxial layers because of the much lower temperatures (- 75OOC) that are employed. Figure 3 1 also indicates that the defect content in melt-grown GaAs crystals can be significantly modified and reduced by thermal annealing at lower temperatures. Changes in the concentration of the EL2 level and hence in the semi-insulating I

I

Ciquidus

I

I

Congruent Point 1

I

49.9

50.0

50.1

[Asl I (%)

FIG.3 1. Predicted GaAs solidus curve. (After Hurle, 1979.)

1. HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

45

behavior of undoped GaAs can therefore be expected to occur during post-implantation annealing. Conventional thermal conversion measurements of sheet resistance and surface conductivity type have been carried out on undoped, semi-insulating GaAs prepared from melts of different compositions. The samples were first encapsulated by a 900-A-thick, low-temperature plasma silicon nitride (Section 1 1) and subjected to annealing at 860°C for 15 min in forming gas. Other samples were annealed for up to 16 hr. The results for as-grown and annealed samples shown in Fig. 32 indicate that high thermal stability is achieved only for substrates with stoichiometric or As-rich compositions. Sheet resistance is observed to decrease dramatically, and conduction becomes p-type with increasing Ga composition, annealing time, and probably annealing temperature. Interestingly, all GaAs substrates with Ga compositions up to 5 1.5% atom fraction Ga would “qualify” for implantation device processing (i.e., yield 2 lo7 sZ/sq, n-conduction after a standard 860°C/15-min encapsulated anneal), although it is clear that further reduction in sheet resistance occurs with prolonged annealing. Deep levels of defect origin have been strongly implicated (Martin et al., 1980a)in the semi-insulatingbehavior of undoped epitaxial and melt-grown GaAs, and recent infrared absorption studies (Holmes et aL, 1982a,b) conclude that high resistivity results from compensation of residual carbon acceptors by deep EL2 donors. The effect of thermal annealing on deep levels has been investigated by deep-level transient spectroscopy (DLTS) using capacitive measurements of GaAs substrates with near-stoichiometric

ri

I

I

I

I

I

I

I

I

I

I

Melt Composition, I Gal/[ As1 FIG.32. Effect of heat treatment and stoichiometryon semi-insulatingbehavior of undoped LEC GaAs/PBN at 300°K.

46

R. N. THOMAS

et al.

composition and made conductive by either silicon doping of the melt or by silicon implantation. Typical DLTS spectra obtained using deposited A1 Schottky structures before and after the sample has been exposed to an encapsulated anneal are shown in Fig. 33. High concentrations of deep levels are observed in the as-grown Si-doped GaAs sample, which are significantly reduced by annealing. The dominant EL2 level at E, - 0.82 eV (uncorrected) is reduced by a factor of 5 in the approximately 1-pm-deep surface-depletion region sampled by these capacitive DLTS measurements. These results, therefore, suggest that the type of thermal conversion observed in undoped GaAs of near-stoichiometriccompositions is predominantly a surface phenomenon. Conversion occurs when the EL2 concentration at the surface falls below the residual acceptor concentration. It was verified that 86O0C/16-hr annealing caused no change in the l.lO-,um absorption band in these 500-pm-thick, near-stoichiometric substrates. In contrast, absorption by EL2 centers was substantially lower in Ga-rich substrates that showed hole conduction either before or after annealing.

r-

7 1 el5

R d I

"

Y

L

-55

0

50

I

95

I

I

I

I

176

Temperature ("C)

(b)

FIG.33. DLTS measurements of effects of thermal annealing at 750°C for 16 hr on deep levels in silicon-dopedGaAs samples. (a) After 75OnC/16-hr anneal; (b) as-grownGaAswith no anneal.

1. HIGH-PURITY

LEC GROWTH A N D DIRECT IMPLANTATION

47

(n-Type)

As - Grown

f

0 1

2

3

4

5

6

7

8

9 10 11 12

Depth From Surface (pm)

FIG.34. Sheet resistance profile as a function of depth from surface for a semi-insulating undoped GaAs substrate exhibitingp-type surface conversion after 860°C/16 hr anneal.

Incremental etching experiments demonstrate even more clearly that a p-type surface layer is formed following annealing. The results shown in Fig. 34 indicate that the low ptype sheet resistance at the surface increasesto the original (as-grown) high value, and conduction changes from p to n-type as successive layers are removed. Hall-effect analysis of this annealed seed-end sample again shows a thermal ionization energy of 0.025 eV, close to that of carbon, and a net acceptor concentration of 3 X 10*5-cm-3range. These results are supported by the photoluminescence spectrum of the 860°C/ 16-hr annealed GaAs sample shown in Fig. 35, which indicates carbon acceptor ( I .49-eV peak) as the predominant impurity, and the SIMS depth profile of the same sample, shown in Fig. 36, in which no out-diffusion of common impurities such as B, Fe, or Mn is detected. We therefore conclude that thermal conversion effectsin undoped LEC GaAs are governed mainly by out-diffusion of Ga and/or As defects to the surfaces, a phenomenon first observed by DLTS in vapor-phase epitaxy (VPE) GaAs layers (Mircea et al., 1976)and more recently reported for Se-doped LEC GaAs pulled from fused

I

9036

I

I

8707

8319

Wavelength

I 150

th

FIG. 35. Photoluminescence spectrum at 4.2 K of a semi-insulatingGaAs substrate after 86OoC/16-hr thermal anneal showing carbon acceptor as the dominant residual impurity. (Courtesy of Dr. G . W. Wicks, Cornell University, 1982.)

10l6

Boron

-

Manganese

I 0

4

8

12

16

20

Depth from Surface ( p m )

FIG.36. SIMS depth profile of a GaAs substrate after 86OaC/16-hrthermal anneal showing no surface pile-up of B, Fe, or Mn residual impurities.

1.

HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

49

SiO, crucibles (Makram-Ebeid et al., 1982). Thermal conversion effects in undoped, semi-insulating LEC GaAs are therefore controlled by the diffusion kinetics of stoichiometric defects, which are presumably responsible for the EL2 defect level. Conversion occurs readily and over large depths in high-resistivity GaAs samples of high Ga composition and is limited to the surface region in near-stoichiometric substrates. Only in slightly As-rich GaAs substrates can conversion be avoided under normal implantation annealing. Substrates of high As composition are, however, subject to As precipitation effects (Hobgood et a/., 1981b). Figure 37 shows a (100) surface of an As-rich GaAs sample that was etched in A-B etchant. Small As precipitates with dimensions of several micrometers are observed to decorate the dislocations. Similar observations have been made by Cullis et al. (1980),who postulate that the segregation of As precipitates along dislocations occurs by condensation of As interstitials from the surrounding lattice. The behavior of the electrical properties in as-grown bulk material as well as annealed samples as a function of melt composition suggests a model in which the semi-insulatingbehavior in undoped GaAs/PBN material results primarily from the compensation of shallow acceptors (e.g., carbon) by the deep-donor EL2 level, as illustrated in Fig. 38. The concentration of the EL2 level in bulk material depends upon the crystal. stoichiometry achieved during crystal growth, while in the near surface region, the EL2 concentration is influenced additionally by any alteration in stoichiometry as a result of thermal treatment of the wafers. For undoped GaAs pulled from Ga-rich melts with [Ga]/[As] 2 1.13, the material is low-resistivity, ptype, and independent of any post-growth thermal treatments, since the EL2 deepdonor concentration is already below the residual acceptor concentration (Fig. 38). For GaAs substrates pulled from near-stoichiometricmelts ([Gal/ [As] 1 1) and exhibiting as-grown, semi-insulating behavior, the thermal anneal studies show that the thermal treatments commonly employed in implantation processing can reduce the concentration of defect-relateddeep donors in the near-surface region and lead to substrateconversion effects for sufficiently long annealing times (Fig. 38). Under standard implantation annealing conditions (860°C/15 min), undoped semi-insulating su6strates pulled from stoichiometric or As-rich melts ([Ga]/[As] 5 1) exhibit surface sheet resistances that consistently maintain the high lateral isolation required for IC fabrication (typically > 10' Q/sq). As illustrated in Fig. 38, for these substrates the deep-donor concentrations after 15-min ( t J implant anneal are still sufficiently high to provide complete compensation of residual shallow acceptor levels. However, increasing the annealing time (tz >> t , , as indicated by the dashed curve) will further reduce the deepdonor concentration, and ptype conversion can eventually occur. In our laboratories, the growth of a large number of undoped, semi-insu-

50

R. N. THOMAS

et al.

FIG.37. Decoration of dislocationslying in (100) surface by As precipitates in As-rich LEC GaAs wafer. (a) Dislocations lying in (100) surface of LEC GaAs/PBN wafer (with A-B etchant); (b) dislocation line showing decoration due to As precipitates.

1. HIGH-PURITYLEC GROWTH AND DIRECT IMPLANTATION

I a)

(b)

51

I cl

FIG.38. Schematic representation of influence of stoichiometry and out-diffusion on thermal stability of undoped, semi-insulating GaAs by compensation of residual shallow acceptors (SA) by deep-donor level (EL2). (a)p-type bulk with Ga/As > 1; (b)ptype skin with Ga/As 2 I ;(c) n-type semi-insulating with Ga/As 5 1.

lating GaAs crystals from PBN crucibles has been achieved reproducibly through very close control of the time and temperature during the critical compounding cycle and the addition of about 1 -2-mol excess As to compensate for losses in this process. Figure 39 shows the Hall mobility measured on as-grown, polished substrates as a function of the fraction of melt solidified for several undoped, semi-insulating GaAs/PBN crystals. These crystals are characterized by high resistivities > 5 X lo7 Sl cm (Fig. 19)and measured mobilities ranging from 4500 - 7000 cm2 V-' sec-l over 90% of the crystal length. The greatest variation usually occurs in the last-to-freeze portion of the crystal, where ionized impurity scattering resulting from impurity segregation effects and/or deviations of the solid from the stoichiometric composition may begin to dominate the transport behavior. loo00 r 8

-

6 4

I

0

3

2 n

FIG.39. Measured Hall mobility as a function of the fraction of melt solidified for a number of undoped semi-insulating GaAs/PBN crystals pulled from stoichiometric or As-rich melts. Different crystals are indicated by the different data symbols.

R. N. THOMAS et

52

af.

It is empirically observed that these substrates exhibit excellent thermal stability and uniform, high-quality implantation characteristics (Hobgood el af., 198la). Conversely, high-resistivity substrates with low measured mobility are found to yield implants with low near-surface activation and suggest that the “qualification” of undoped GaAs substrates for direct implantation can be based uniquely upon measurement of these two important parameters. In particular, it is suggested that the cumbersome, time-consumingqualification procedures which have been evolved to select substrates for implantation device processing can perhaps be avoided in the future by specification of the measured mobility in addition to resistivity and conductivity type. 10. UNIFORMITY CONSIDERATIONS

It has been found empirically that factors such as seed-crucible rotation and pull speed in the LEC growth of undoped semi-insulatingGaAs crystals from stoichiometric melts affect the radial and slice-to-slice uniformity. These effects were first observed during investigationsof directly implanted GaAs substrates, which indicated that the implanted doping density can vary radially across the uniformly implanted wafer (Ta et af.,1982b). The capacitance- voltage (C -V) profile measurements of activated 29Siimplants shown in Fig. 40 are representative of substrates cut from crystals grown with corotation of the seed and crucible. Significant reductions of the peak and undepleted donor concentrationsin the implanted layer are apparent at

M

I

E, 1.0 0.8

V 0

b 0.2

v0

0.1

? 0.1

0.2

0. 3

Depth

lwl

0.4

0.5

FIG.40. Radial variations of net donor profiles across a 50-mm-diam undoped GaAs/PBN substrate after uniform 29Si implantation and 860°C/15-min encapsulated annealing. 1.4 X lo1*cm-1 at 125 keV; 4.2 X lo’*cm-l at 275 keV.

1. HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION

53

the center of the wafer. More detailed investigations of corotated crystals reveal only small radial resistivity variations in the as-grown state, corresponding to the characteristic M-shaped resistivity distribution observed by others (Grand et al., 1982)for LEC-grown GaAs substrates. However, after encapsulated annealing at 860°C/15 min, significant radial variations ofthe measured sheet resistance and mobility are typically observed. The results for four substrates selected from various positions along the length of an undoped GaAs crystal pulled at 6 mm/hr from a stoichiometric melt and employingcorotation of the seed and crucible at 6 and 15 rpm, respectively, are shown in Fig. 4 1. Although this crystal displayed high as-grown resistivities (2lo7 R cm) and mobilities (- 5000 cm2 V-' sec-l) over the full crystal length, annealing results in sheet resistances (Fig. 41a) and mobilities (Fig. 4 1b), which decrease radially toward the center of the wafers. In particular, as the tang end of the crystal is approached (wafer No. 63 corresponding to about 55% of melt solidified), the development of distinct low-mobility, p-type cores becomes apparent. In contrast to these results, highly uniform GaAs crystals are produced when counter rotation and/or reduced growth rates are employed during growth. This is illustrated in Fig. 42, where high annealed sheet resistances (- lo9 R/sq) and mobilities (3000-6000 cm2V-I sec-I), which show little variation across the full wafer area or from slice to slice, are observed for both crystals grown under counter-rotation conditions as well as corotated crystals pulled at a reduced pull rate of 3 mm hr-'. Under uniform 29Si implantation, these substrates enable uniform donor activation (+5%)to be achieved over the wafers (Section 13). These results (and more recent studies using capless As overpressure annealing techniques) indicate conclusively that the coring phenomenon observed in undoped GaAs cannot be ascribed to faulty encapsulation or to inhomogeneous implantation. Neither faceted growth (common in ( 1 1 1) Czochralskigrowth but unknown in ( 100) growths) nor possible considerations related to constitutionalsupercooling provide an adequate description of this coring effect at present. We suggest that these effects are associated with localized stoichiometric defects that result from the preferential segregation of excess Ga at the center of the growing crystal. During subsequent crystal or substrate annealing, these effects are also possibly enhanced by point defect gettering to regions of frozen-in thermal stress in LEC-grown GaAs. Since these stoichiometric defects can exert a strong influence on the observed electrical activity (through, for example, modifying the EL2 concentration), local increases in point-defect density can therefore affect the local resistivity, thermal stability, and, probably, site selection in the implantation of amphoteric silicon. Growth conditions of counter rotation and reduced growth rates are conducive to maintaining a uniform diffusion

R. N. THOMAS et

54

al.

lo9

M

25

0

Slice Radius ( m m l (a)

6

>

A

n

I

I

0

I

25 Slice Radius Imm) (

I 50

b)

FIG.41. Radial variation of (a) sheet resistance R, and (b) Hall mobility across undoped GaAs/PBN substrates after 860°C/15-min encapsulated annealing (with Si,N,). The slice

numbers indicated give relative position from seed end of crystal.

boundary layer across the melt interface in Czochralski crystal growth and thereby aid in the uniform incorporation of impurities and stoichiometric point defects into the crystal (Burton et al,, 1953). These conditions are found empirically to be beneficial in the growth of uniform, undoped GaAs

1. HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION 1o1O

-

Slice #81

1

. U

c:

-

Slice X7

lo9

~

Slice #24

YI

z

lo8

55

-

--

-

-

4

lo4

6

-

#l

-I i!

-

>

N

E,

-

lo3

-

v

2 lo2

I

I

I

I

I

I

I

I

I

I

I

crystals exhibiting high-resistivity, thermal stability, and predictable implantation characteristics (Ta et a/., 1982b).

V. Direct Ion Implantation A direct ion-implantation technology yielding uniform and reproducible doping characteristics across each substrate and from substrate to substrate is highly desired for GaAs IC processing. Our approach implicitly assumes that higher-purity, semi-insulating GaAs substrates will eliminate many of the difficulties encountered in the empirical “qualification” procedures which have evolved over the past few years for assessing substrate suitability for direct implantation processing, and to provide a better understanding of problems such as spurious activation of residual impurities, redistribution phenomena, and interactions with the implanted species. With this objective in mind, silicon implantation of undoped LEC GaAs/PBN has therefore been emphasized with data from Cr-doped LEC GaAs included for comparison. The characterization of implanted substrates involvesdiagnostic techniques that are modified to meet the particular requirements of monolithic power FET amplifier development. It is shown that directly implanted n-layers of superior and predictable characteristicsare indeed achieved in undoped, semi-insulatingGaAs/PBN substrates. The observed electrical activity can be attributed to the im-

56

R. N. THOMAS

et al.

planted ions without measurable activation of residual impurities or defects in the semi-insulating substrate. This conclusion is based on a particular model of how GaAs should respond ideally to implantation, and the activation and mobility data are analyzed from a somewhat unconventional perspective throughout this discussion to demonstrate that undoped GaAs/ PBN exhibits this response. This model, methods of data analysis, and relevance to device design are presented in Section 1 1. Experimental details of the particular implantation technology employed are presented in Section 12; of necessity, the bulk of the work discussed here employs this technology, but sensitivity to the basic conclusions to the detailed technology is noted wherever possible. Measurements of implant profiles and electrical donor activation in undoped and Cr-doped GaAs substrates are presented in Section 13, and the channel mobility is discussed in detail in Section 14. Finally, in Section 15 the basic characteristics required of the GaAs substrate to ensure a reproducible ion-implantation technology are summarized. 1 1.

%IMPLANTED

GAS

a. Ideal Activation of Implanted GaAs

Modem implantation techniques result in the chemical doping of a semiconductor surface to depths on the order of 0.1-2.0 pm with an estimated concentration uniformity of about k3% over 75-mm-diam wafers. Dose precision is excellent, although its accuracy may be as bad as Ifi 20%. Statistical models (Gibbons et al., 1975) of the ion-stopping process in amorphoustargets yield reasonable first approximationsto the implanted atomic distribution in misaligned, single-crystalwafers. The electrical activation of implanted atoms in GaAs is typically achieved by thermal annealing at 700-950°C using either an encapsulant (Welch et aL, 1974;Harris et al., 1972;Gyulai et al., 1970; Sealy and Sunidy, 1975)or an As overpressure (Malbon ef al., 1976)to prevent substrate decomposition. Although chemical profiling techniques (Huber et al., 1979a; Evans ef al., 1979) have been utilized to correlate the atomic distributionsof implanted speciesto theoretical profiles and the measured electrical activity at high concentrations (>loi8 cm-’1, these techniques generally lack the sensitivity to measure concentrations of interest for FET channels (5 X 10”-3 X lO”-~m-~ range). Association of the measured electrical activity with the distribution of implanted atoms in FETs must therefore be inferred. This measured activity can be modified by partial or amphoteric doping, redistribution during annealing, gettering and/or precipitation of residual impuritiesin the semi-insulatingsubstrate, interactions with the encapsulating medium, and generation or precipitation of native defects. Absence of measurable activity

1. I‘IJH-PURITY

LEC GROWTH AND DIRECT IMPLANTATION

57

in wafers annealed after receiving inert gas implants (Bozler et al., 1976) suggests that secondary activation phenomena are not important, but such tests do not rule out the possibility that these secondary phenomena can be associated with the implanted species or be masked by surface depletion effects. A one-to-one correspondence between implanted dose and net donor activity per cubic centimeter has been employed to qualify stable semi-insulating substrates and to infer an optimized implantation process in the past. Even this interpretation is, however, in sharp conflict with abundant crystal growth (Kuznetsov et al., 1973), vapor-phase epitaxy (Wolfe and Stillman, 1975), and liquid-phase epitaxy (Casey et al., 1971) data showing that all of the shallow n-dopants exhibit similar and significant amphoteric character in GaAs.If the activation of implanted ions is also amphoteric, any qualification and optimization routine that seeks 100% net donor activation necessarily requires spurious activation to compensate for the net activity “lost” through amphoteric doping by the implanted species. Figure 43 illustrates the present model of “ideal” activation of ion-implanted n-layers in semi-insulating GaAs.The implanted silicon profile is representative of channel implants employed for power FET fabrication. It includes the effects of gaussian implant profiles, dual-energy implants used to approximate a flat-channel profile, and redistribution of the implanted species as a result of annealing. The implanted Si can act as donors, I

I

I

I

FIG.43. Construction of net donor concentrationprofile n ( z )resulting from 29Siimplantation of GaAs with Nz,, - N& residual acceptor impurity concentration. Calculated channel mobility &z) is also shown.

58

et al.

R. N. THOMAS

acceptors, or neutral centers by processes such as

+ + e+

Si -+ (SiL) e-,

+ e+,

(5)

(6) (7) as well as formation of more complex states. Under ideal conditions, it is reasonable to assume that all of the implantation defects are annealed out, that annealing does not result in the formation of active defects, and that at low implanted densitiesthe formation of nearest-neighbor, donor -acceptor pairs is negligible. It is not reasonable to assume that the obvious amphoteric doping possibilities of a Group TV dopant in a 111- V compound semiconductor can be ignored. This does not imply that Si is a poor choice for implantation, since there is abundant evidence that the group VI dopants also exhibit amphoteric behavior as noted previously. The electrical activity profile of an implanted GaAs sample can be generated by the ad hoc assumption that, independent of the depth and implanted Si concentration, after annealing a fraction of the implanted silicon occupies singly ionized donor sites N & in the host lattice while the remainder act as singly ionized acceptors N,. In particular, it is assumed that none of the implanted silicon remains electrically neutral or behaves as a multiply-ionized impurity. Under these conditions, the differential activation efficiency can then be defined as Si -+ {SiJ Si Six

-

or

(Sic. V0J

(S& SiJ,

or

q = S(N&- Nz)/S(Si)

(8)

rt = [W+, - NA)/W+o+ N,)I[W;f + NA)/4Si)1,

(9)

or where (Si) is the implanted silicon concentration. The differential activation efficiency can then be written rt=tlArtZ,

(10)

where the internal net donor activation efficiency q,, is given by VA

= S(N&

- N,)/d(N&+ N i )

(1 1)

and reflects the amphoteric doping nature, while the total activation efficiency q z is given by

+

(12) qZ = S(N& NA)/S{Si) and reflects both completeness of the implanted ion activation and the absence of spurious activity. The net donor activity profile shown in Fig. 43 is generated using the values of qz = 1 and qa = 0.75, which are derived from experimental data in subsequent sections. Construction of the net

1. HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

59

donor profile in Fig. 43 is completed by subtraction of the implanted net donor concentration required to compensate any residual electrically active acceptor impurities in the GaAs substrate. This residual acceptor concen~ ) adversely affect the compensation tration ( N i O- N&, = 1 X 10l6~ m - can ratio near the channel-substrate interface while making the net donor profile more abrupt than the chemical profile. The drift mobility as a function of depth shown in Fig. 43 is calculated assuming N i O >> N+, and using the tabulated theoretical values of Walukiewicz et al. (1 979). This calculation assumes that the mobility is dominated by ionized impurity scattering or, conversely, that effects associated with surface stress, microscopic inhomogeneities,neutral point defects, and dislocations, etc., are negligible in properly performed n-implants of good quality substrates. The validity of this assumption is confirmed by these studies and provides a rational basis for analyzing ion implantation and crystal selection techniques. Plots of 300" K drift mobility, as tabulated by Walukiewicz et al. as a function of net donor density for various acceptor and total ionized impurity densities, are shown in Fig. 44. They are included here for future reference and to indicate that a measurement of net donor concentration and mobility at ambient temperature can be employed to deduce the total ionized impurity density. In practice, a series of concentration and mobility measurements performed on wafers implanted to differ-

1

2

5

10

20

MX l0l6

Electron Concentration, n

FIG.44. Theoretical drifi mobility p,, versus electron concentration n = ( N ; - N i ) at 300°K as a function of ionized acceptor density ( N J and total ionized impurity density ( N , NA), -, N , X 1OI6 ~ r n - ---, ~ ; N& N i X 10I6cm-? (From Walukiewicz ef al.. 1979.)

+

+

60

R . N. THOMAS et

al.

ent concentrationsshould therefore yield the total ionized impurity concentration X, where

2 = qx{Si) + ( N i 0 + N&).

(13) The scatter in the data is a measure of process reproducibility or substrate uniformity; q x < 1 and q x > 1 indicate incomplete and uncontrolled activation, respectively, and the magnitude of Nz0 N&, is an indication of crystal purity or spurious activation during processing. Equation (13) is essential to an understanding of substrate and implantation quality, even though the net donor concentration n, given by

+

n = qAqS (si) - (NzO - N&O)

(14) is more readily accessible. Optimization and control of qa and Nz0 - N&O are required for reproducible, high-quality implanted n-channels, but this process must be subject to the more fundamental constraints of Eq. (13). If interest is confined to only the net donor density produced as a result of implantation, quite misleading conclusions as to substrate selection and process development can be drawn. For example, the achievement of 100% implant activation (as deduced from a measured net donor concentration of 1 X lo1' cm-3 when implanted with 1 X lo1' cm-3 silicon) and a measured channel mobility of, say, 4200 cm2 V-l sec-', is not necessarily a good result. The measured mobility when referenced to Fig. 44 would indicate a highly compensated implanted layer with a total ionized impurity content Z of 2 X 1017 composed of N& = 1.5 X 1017cm-3 and N i = 0.5 X 1017 ~ m - It ~ .would therefore be difficult to believe that substrate selection and implantation technology have been properly optimized or that a reproduo ible crystal-to-crystal implantation technology could be achieved when the spurious or residual ionized impurities are of the same order as the implanted ion density.

b. Power FET Requirements Selective, direct ion implantation of GaAs for power FET applications requires the ability to predict the undepleted net donor concentration (NSM) in the implanted FET channel. NSMis given by

N&

=

6

( N &- N z ) dz,

(15)

where dd is the surface depletion depth. NsMdefines to a first approximation the output power triangle. This follows from the full-channel current of the gate-recessed FET,which can be written as

1, HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

61

Ifc = qvsatNSM

(16) where u,, is the saturated velocity. The breakdown voltage V, can be approximated by

- (NSM/NS&)2nl,

(17) where Ns& (n) is the depleted-surface concentration per square centimeter at breakdown for an ideal parallel plate geometry, n is the volume concentration and VB(n) is the corresponding breakdown voltage. y is a numerical constant on the order of three. Equation (16) is intuitively reasonable, while Eq. ( 17) is a more heuristic expression, which agrees with experimental data and incorporatesthe correct asymptotic dependence on NSM (Wemple et al., 1980; Wisseman et al., 1979). These equations suggest control may be more important for matching the maximum power that NSM load line to the fixed, passive output impedance-tuning circuits. Control of NSMmust be followed by control of the peak implant depth R, and the half-height depth A,, in order to control input impedance, gain, and pinch-off voltage and to match the active device to the passive input circuits in multistage amplifiers. Surface Hall mobility and concentration measurements yield a precise evaluation of undepleted concentration per unit area. The variation of mobility with depth implies that the measurements represent vB

kiH

=

= YVB(n)[l

2(z)n(z)dz/ /&P(z)n(z)dz,

(19)

where theoretical estimates (Debney and Jay, 1980) of the Hall factor in systematically underestimates NSM by about Cr-free GaAs suggest that NsMH 7% for channel concentrations of greatest interest (see Fig. 43). The depth average introduces an additional 2%error applied to the particular example instead of shown in Fig. 43. Evaluation of v,, [Eq. (16)] employing NsMH NSMyields a value of (1.18 k 0.05) X lo7 cm sec-' independent of maximum concentration, profile width, low field mobility, and Cr doping of the substrate. This value of u, is somewhat higher than the (1 .O- 1.1) X lo7 cm sec-' usually assumed, and may compensate for a systematicunderestimate of NSM. Association of the surface Hall mobility with the drift mobility at maximum-channel concentration involves an error of the same magnitude. This association is nevertheless made and applied with Fig. 44 to infer ionized impurity densities.

62

R. N. THOMAS et

al.

12. EXPERIMENTAL PROCEDURES Direct ion implantation of undoped and Cr-doped GaAs substrates was performed at ambient temperature using 29Si+ions in a 400-kV Varian/Extrion ion implanter. The Si beam was generated from a SiF, source so that the Si isotope ratios could be measured and 29Si+beam purity assured. The choice of Si as the primary implant species was made on the basis of achievable range, integrity of the implanted profile through annealing, and ability to activate ambient temperature implants. The implants were performed through a front-surface Si3N4encapsulation layer. Experimental details of this encapsulation technology, the selectivearea implantation, and the techniques used to evaluate implanted GaAs samples are described here, a. Plasma Nitride Encapsulation

The wafers utilized are normally 50-mm-diam GaAs, cut on the (100) crystal growth axis (+0.5"),lapped and front-surface polished in brominemethanol to a thickness of 0.5 mm. Spin scrubbing is employed to remove :H,O) is particulates, and an 0.5 pm etch back in 50 : 1 :2 (H,S04: H202 employed to remove residual Br and hydrocarbon contamination immediately prior to nitride deposition. An LFE Corporation PND-30 1 experimental plasma deposition system is employed to deposit the front-surface Si3N4 encapsulant. The system itself has been substantially modified to eliminate vacuum leaks. Silicon nitride is deposited at 100-W rfpower and at a rate of 70 A/min on the 340°C substrate by reaction at nominal flows of 40 sccrnT of 1.5% SiH, in Ar with 3 sccm of N2containing 1% H,. A 2-min preburn at the same power and using only the N2:H, gas flow is employed to reduce native oxides on the GaAs surface prior to actual deposition. The thickness of the nitride layers is typically uniform to within about & 5% across the 50-mm diameter of the GaAs slices. Nonuniform thickness of the nitride translates directly into a radial variation in the implanted dose actually deposited into the GaAs substrate; the extent of this variation is estimated to be about 3~2% for 50-mm-diam wafers and nominally 3000-Adeep-power FET channels. Refractive index is not clearly related to Si,N, quality nor to its ability to encapsulate GaAs. Good encapsulation is achieved for refractive indices lying between 1.9 1 and 1.96, where the index increases with increases in the SiH4/N2reactant gas ratio. Infrared absorption measurements of these films indicate no detectable oxygen contamination of the Si3N, (<2%) but significant N-H and Si-H bonding, where N - H bonding dominates in low index films and Si - H bonding dominates in the higher index layers. Etch rate in buffered HF decreases with increasing

t Cubic centimeter per minute at standard temperature and pressure.

1.

HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

63

refractive index, but this effect appears to be associated with excess Si in the layer rather than denser or more complete Si-N bonding. No systematic variation of activation efficiency or mobility of implanted layers associated with these effects has been observed. Auger profiling performed through Si3N4layers after high-temperature annealing indicates no Ga or As loss when the refractive index lies in the 1.80- 2.00 range, but losses are observed at both limits. The morphology is disturbed at these limits, and the appearance suggeststhat the mechanisms are migration through the encapsulant at low refractive indices and formation of pinholes at high indices. Our experience indicates that the characteristicsof implanted channels in GaAs depend critically upon the reproducibility of this encapsulation technology and demand stringent control of surface stoichiometry and the absence of contamination and residual damage at the GaAs- Si3N4interface. Nitride encapsulation is therefore performed prior to implantation (which is subsequently carried out through the nitride layer) in order to protect and preserve the wafer surface through selective implantation processing. Recoil implantation of Si and N from the Si,N4 encapsulant does not affect net donor surface activity, and no modification in the total ionized impurity density is observed due to surface depletion. During device fabrication, an improvement in source-drain contact resistance upon 500-A selective recessing suggests that the latter effect, however, may be present.

b. Selected-AreaImplantation Uniform area and selected-area implantation is carried out at ambient temperature and 7 off-normal incidence using the cassette-load end station of the Varian/Extrion implanter. The 29Si+beam from a SiF,-fed plasma source is utilized to avoid the N2+ and CO+ contamination which can accompany the 2sSi+ion beam. Both the 29Si+and the 29Si2+ beams are well resolved from neighboring isotopes and possible contaminants, but the Si3+ is not well resolved from I9F2+. Typical power FET channel implants require only 29Si+at 250-275 keV to achieve the required channel depth and concentration, with an added 125-kV 29Si+implant to adjust the net donor density at the GaAs-Si,N4 interface and to approximate a flat doping profile. However, experimental profiles required to assess activation as a function of implanted Si concentration may utilize the full 800-keV potential and three intermediate energy implants to approximate flat doping profiles. Selective-area implants employ 2500-A-thick layers of 7% weight phosphosilicate glass (PSG) to define the implant areas and to encapsulate the back surface. Back-surface encapsulation is used solely to avoid the hazards of As evolution and has no measurable effect on the front-surface behavior. Phosphorus doping is employed to yield a dielectric encapsulant that is O

64

R. N. THOMAS

et al.

plastic at the anneal temperature so that stresses associated with densification do not cause mechanical distortion of the GaAs wafer. The 2500-Athick PSG layer applied over the primary front-surface nitride encapsulant prior to annealing is also used for the purpose of covering any pinholes in the Si3N4 that might result from particulates on the GaAs surface during deposition. Although this PSG layer has no measurable effect on front-surface activation, failure to provide some form of auxiliary encapsulation can lead to localized eruptions at any pinholes, which renders a wafer unsuitable for contact photolithography. Figure 45 outlines the selective implantation procedure schematically. Photoresist (PR)is employed to define the channel window on the PSG. Ion milling followedby a light buffered HF etch yields a well-defined window without affecting the Si3N4.The PR/PSG/Si3N4composite acts as the beam stop for the selective-channel implant; a slight PR overhang prevents adhesion of carbonized resist to the PSG at the window edges, while the Si3N4encapsulant prevents recoil implantation of carbon and oxygen from the photoresist (Fig. 45a). A second front-surface PSG layer provides secondary encapsulation at the implanted channels. If n implants are required, windows are again opened in the second PSG using the first PSG windows for registration.The n+ implants are again performed +

PhOlOreSiSt

Ohmics

( c)

FIG.45. Selective implantation fabrication sequence. (a) Channel implant through nitride; (b) self-aligned ohmic contact formation; (c) selective implantation fabrication sequence.

1.

HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

65

through the Si,N4 and can incorporate both 29Si+and 34S+implants (Fig. 45b). Annealing of the composite n-n+ implants does not require secondary encapsulation of the n+ areas, so that subsequent plasma etching can be used to achieve self-aligned ohmic metallization (Fig. 45c). Annealing is performed in an atmosphere of flowing forming gas by heating the samples up to 860°C at a rate of lS"C/min to prevent disrup tion of the front-surface PSG pattern, followed by annealing at 860°C for 15 min. The cooling cycle rate 2"C/min is a compromise between the observed effect of quench cooling in reducing mobility and the effect of slow cooling in reducing n+ activation efficiency. Annealing is performed with the wafers laid on flat horizontal pallets of high thermal conductivity to provide mechanical support and uniform annealing temperatures. Since GaAs implantation anneals are routinely performed at temperatures well above the plastic deformationtemperature of GaAs,special care is needed to ensure that wafer flatness is not adversely affected during annealing.

c. Evaluation Techniques The activated net donor profile for an implanted layer is obtained from C- V measurements using deposited A1 Schottky barrier contacts, while the total activation can be derived indirectly from surface Hall-effect mobility measurements. The C- V data provide information on profile shape and concentration but are somewhat unreliable for detailed analysis because of difficulties in determining the contact area accurately and difficulties associated with perimeter effects. Measurements of pinch-off voltage are useful, since

V- = (V,d

l m z(N&- N ; ) dz 0

= ( V/W,,NSc

Y

(20)

where (21) and R,, has a direct analog in the implanted-ion projected range R,, and Nsc can be correlated with surface Hall-effect data [(Eq. 18)]. Hall data are obtained using a Van der Pauw configuration defined by selective implantation or by mesa isolation of uniformly implanted samples. The data are typically taken at 300"K, although 77°K analysis has been performed in low-concentration wafers. All the available symmetry operations are exercized during measurement to cancel extraneoussignals. In order to achieve a high yield of symmetrical specimens, it is found necessary to perform both

66

R. N. THOMAS

et al.

the alloying of ohmic contacts and the measurements with the encapsulant in place over the active area. 13. MEASUREDIMPLANTPROFILES AND ELECTRICAL ACTIVATION a. Implant Profiles

Figure 46 illustrates the flat net donor electrical activity profiles achieved by 29Si+ion implantation of undoped GaAs/PBN substrates. Each profile represents the result of multiple energy implants such as 800,400,200, and 100 keV at the deepest, lowest concentration profile to a single 150-keV implant for the shallowest, highest concentration profile. The data are drawn from six different substrate crystals to ensure that the data represent the behavior of undoped GaAs/PBN material rather than anomalies of a particular crystal. The lowest concentration profile represents the current lower limit of ion-implanted layer concentration exhibiting crystal-to-crystal reproducibility. In part, this may be associated with the difficulty in avoiding contamination of the 800-keV 29Si2+beam by 375-keV 29Si+ions in the implanter, which can result from Sit dissociation prior to mass analysis. A more basic limitation appears in the net donor density versus implanted dose relationship, showing that the measured concentration can be ascribed to a fixed net donor activation efficiencyand a concentration of approximately 1 X loL6 net acceptors in the semi-insulating GaAs, 5-

0

1

1

0.1

I

I

0.2

0.3

I

I

0.4 0.5 Depth (pin)

I

I

0.6

0.7

0.11

FIG.46. Net donor implant profiles obtained by multiple energy 29Siimplants in undoped semi-insulating GaAs illustrating effect of surface depletion. n = ~ ( * ~ s-i (N, ) - NL),

1. HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

67

which must be populated prior to observation of extrinsic conduction. This residual acceptor density or threshold varies from crystal to crystal within Ifr0.5 X 10l6cm3, and the seed-to-tang variation suggests that it may be associated with a near-unity, effective segregationcoefficient impurity in the as-grown crystal. All of the wafers used to generate Fig. 46 were drawn from the seed half of the various undoped semi-insulatingGaAs crystals. The energies and doses required to achieve flat net donor profiles are derived from a series of single energy implants employed to determine the implanted net donor profile parameters. These profiles can be represented by joined-half gaussian distribution for net donor concentrations between 3 X 1OI6 and 3 X 10’’ ~ m - ~ Inspection . of these profiles yields the range of maximum concentration (&), the deep standard deviation (odd), and for energies greater than 200 keV the shallow standard deviation (q). Profile measurement as a function of dose indicates that these parameters are not a function of dose and that the peak net donor concentration n(R,) can be written as

+ c d ) - (NiO - N&l h

(22) where (Si) is the implanted dose and q = 0.75, independent of the implant energy. The profiles are summarized in Fig. 47. These values exhibit reasonable agreement, with tabulated calculations for the implanted Si distribution only if the standard deviations are modified by simple diffusion broadening, i.e., a2 a2 2Dt, (23) fl(RM) = (2/n)”2q(si>/(cs

-

+

where 2Dt = 2.5 X lo-’’ cm-2 for 86Oo/15-minannealing. Diffusion broadening is reduced at lower annealing temperatures. Steeper implant profiles are observed following brief 750°C capless annealing in an As overpressure, and the magnitude of 2Dt is reduced to about 0.5 X lo-” cm2. Surface depletion effects make it necessary to employ extrapolated profiles for the lowest energy implants (100 keV). Within the limits of this extrapolation, the activation efficiency is constant to the GaAs interface. There is no indication of a surface “dead” layer or an anomalous n-layer associated with recoil implantation from the Si,N, encapsulant or an interface interaction. This is indicated in Fig. 42 by the dashed line, which is the calculated zero-bias depletion depth assuming an 0.8-eV A1-GaAs bamer and constant net donor concentration to the surface. Agreement with the experimental result indicates that the behavior in the inaccessible surface layer can be assumed to be identical to that of the bulk insofar as determining the surface depletion depth and the undepleted net donor concentration per unit area. Figure 47 compares wafer-to-wafer profile reproducibility in several

68

R. N. THOMAS et

al.

doped LEC GaAs/PBN and Cr-doped GaAs (>5 X 10l6cm-3 Cr) crystals. The undoped material (Fig. 47a) exhibits excellent reproducibility (*1 X 10l6 cm-j) and a consistent, relatively broad transition into the semi-insulatingsubstrate. Implantation of the Crdoped material to achieve the same net donor density and effective profile width requires higher doses at slightly higher energies. Reproducibility of the profile depth is poor, although the profile abruptness can be excellent (Fig. 47b). A detailed analysis of both electrical activation and the channel mobility in Cr-doped GaAs shows that implanted 29Si concentrations below 9 X 10l6 cm-I3 exhibit no measurable n-type activity, whereas implantation to (0.9- 1.2) X 10’’ane3results in poorly controlled n-activity in which the chromium appears absent as either compensating acceptors or ionized impurity-scattering centers. This transition from an apparent “Cr-free” implanted layer to a Cr-doped substrate results in an abrupt interface between the channel and the semi-insulating substrate. Unfortunately, the depth of this interface is difficultto control.

,

,

‘,

d L S S Theoretical Profiles

I

Al-GaAs

,\

Interface

1

\

\

\*

‘I I

1000

2000 Depth

3000

(A)

I

I \ ,

4000

I

5000

.

I

6000

FIG.47a. Uniformity of implant profiles in undoped GaAs/PBN substrates measured by C- Vprofiling. 29Siimplant through 900-A BIN, cap. 2 X lo1*cm-*at 125 k e y 5 X 10l2cm-l at 325 keV. Theoretical profiles in this figure and in Fig.47b are based on Lindhart, ScharEand Schiott’s theory as tabulated by Gibbons et 01. (1975).

1.

HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

69

C

c

Measured Profiles

.c

e

c a l

5

lo1'

L

6 \

Y L S S Theoretical Profiles

,

.Al-GaAs Interface

10161

0

'1,

\ \,

,

1 '

\ 1

1000

"

2000

'

I

3000

'

1

4000

'

I

5000

'

I 6000

Depth (A) FIG.47b. Implant profiles in heavily Cr-doped GaAs/fused silica substrates measured by C - Vprofiling. 29Siimplantthrough 900-ASi,N,cap. 3 X lo1* at 125 k e y 7 X 10'2cm-2 at 325 keV.

b. Electrical Activation The characterization of different GaAs crystals for selective direct implantation was determined by surface Hall-effect measurements, which yield directly the total undepleted net donor density NSMin implanted wafers. In these studies, a series of wafers was implanted at a fixed pair of energies and fixed surface-to-channel dose ratio to yield approximately flat-channel profiles (as illustrated in Fig. 47) at different concentrations. Measurements of NSMas a function of the implanted 29Sidose for 2850-Adeep, flat channel profiles into undoped semi-insulating GaAs/PBN substrates are shown in Fig. 48. Current practice for implanting 2850-Adeep channels utilizes 250- and 125-keV implants at a three- or four-to-one dose ratio, depending upon the exact profile shape desired. The total dose required to achieve a specified undepleted concentration can be interpolated directly from the NsMversus dose data shown in Fig. 48. Corrections are required to obtain q and N;;o - N&, ,however. An a priori correction for surface depletion can be achieved by assuming that the net

70

R. N. THOMAS

1

2

3

4

5

et al.

6

7

8

9

-1 10

Z9Si-Implanted Dose ( lo1’ an-’) FIG.48. Activation efficiency by Hall measurements of 29Si implants in undoped GaAs/

PBN substrates. The data as measured (NSM) and after correction for surface depletion and implant deposition in nitride cap ( N T )are shown. 250 kV/125 kV 29Si+(4: I).

donor concentration profile is flat between the Si3N4-GaAs interface and of the channel implant and that the range of maximum concentration (RM) od) the equivalent, uniform concentration implant depth (Ao = R M is known. The vertical arrows in Fig. 48 indicate the calculated correction of NSMto NK assuming a 0.6-eV surface-depletion potential. The horizontal arrows correct the total implanted Si concentration for 40% deposition of the surface-fill implant into the Si3N4rather than the GaAs. The slope of the corrected data is the net donor activation efficiency q = qpqA, and the intercept on the vertical axis divided by the effective depth A. yields the net residual acceptor density NzO- N&, = NAo.In Fig. 48, q = 0.72 and NAo= 0.9 X loL6cm+. Direct C- V measurements of these samples yield volume concentrations which agree within k5% of those derived from the corrected Hall data. The effective depth agreement is k3%. The values of q and N;, - N&, can be employed in an inverse process to predict undepleted charge and net volume carrier concentration at other channel implant energies down to volume concentrationsas low as 1 X 10l6~ m - At ~ . high concentrations (>2 X 10’’ ~ m - ~however, ), this is complicated by sublinear activation. In the concentration range shown in Fig. 48, 29Siimplantation of undoped GaAs/PBN consistentlyyields q = 0.75 k 0.03 and NAO = (1.O f 0.3) X 10l6~ m - with ~, little or no suggestion of wafer-to-wafer variation within these limits. Comparable measurements have been carried out for lightly Cr-doped GaAs/PBN substrates (<5 X 1015cm-3Cr) and heavily Cr-doped GaAs [(5 - 12) X 10l6cm-3 Cr] pulled from fused silica and from PBN crucibles.

+

1.

HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

71

I

X

FIG.49. Comparison ofelectrical activation of 29Siimplants in undoped, lightly, and heavily Cr-doped GaAs substrates.

The results are shown in Fig. 49. Lightly Cr-doped GaAs yields q = 0.82 k 0.06 and NAo= (1 -2) X 10l6 ~ m - ~and , is similar to undoped GaAs. Analysis of the high Cr material is complicated by a depth-dependent activation efficiency which is presumably related to Cr pileup near the Si,N,-GaAs interface and by thickness variations in the conducting layer owing to compensating Cr in the substrate. For net donor concentrations less than 2 X 1017crnp3,the channel implant activation efficiencyis found to be q = 0.90 f 0.05 and NAo= (4-8) X 10I6 ~ r n - ~At. low-implanted Si concentrations [(0.2-6) X 1016cm-3)],the observed behavior is neither linear nor reproducible.

14. HALLMOBILITY OF IMPLANTED LAYERS a. Undoped GaAsfPBNSubstrates

Low-field Hall-effect mobilities as a function of the net donor concentration have been measured at room temperature in implanted 29Sichannels formed in undoped and Cr-doped GaAs substrates. The results, shown in Fig. 50, represent measurements on randomly selected slices from five undoped, three lightly Cr-doped GaAsfPBN crystals, and five heavily Crdoped GaAsffused Si02crystals. Inspection of the measured carrier mobility over a broad range of net donor densities reveals complex differences in the behavior of undoped and Cr-doped GaAs material, which is fairly

72

R. N. THOMAS

et al.

Bulk Mobility (Theory) 7000

1

NA

Undoped GaAs-PEN

~

6000

5000 >

-5 4ow

N

m 2wo 1wO

0

1 1016

I

1

2

5

I

I

1

2

5

I

I

lo1*

Net Donor Concentration (cm-')

FIG.50. Measured direct %i implant mobility at 300°Kin (a) semi-insulating undoped GaAs,(b) lightly Crdoped, and (c) heavily Cr-doped GaAs.Theoretical bulk mobility is also shown for comparison.

systematic with respect to the Cr-doping content, but is not specific to a particular GaAs crystal. The experimental data shown in Fig. 50 are overlaid by theoretical bulk drift mobility data from Fig. 44. Although comparison of depth-averaged Hall mobility data with this theory may not be strictly valid, this approach is believed to provide a valuable engineering perspective. Figure 50 shows that the observed mobilities in undoped GaAs/PBN substrates at low net donor concentrations can be attributed to coulombic scattering by a residual , agreement with the ionized acceptor density N i Oof about 1 X 10l6~ m ' ~in value derived from electrical activation measurements (Fig. 48). Curve fitting of the low-concentration data for implanted undoped GaAs in Fig. 50, while ignoring the distinction between surface Hall mobility and local drift mobility, yields the relationship

N, = 0.8 X 1OI6 + 0.12 N&.

(24) The differential compensation ratio 8 = N J N & in turn indicates a differential net donor activation efficiency q,, = 0.78. This use of the two mobilities is expected to underestimate 8 and overestimate q,, . Figure 5 1 shows the change in carrier mobility achieved by reducing the

1. HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION

-.‘z

’i >

40.000

-5

20,wo

t1

73

,Theory

N

Y 0

15.W

I-

c

c .--

-

f

10,000 8.000

6.000

Directly Implanted Data

4.000 1

I

I

I

I

0. 6 0. 8 1

2

4

6

8 10

I

I

15X 10l6

Carrier Concentration N~ (cm-3)

FIG.5 1. Comparison of measured mobility at 77°K for n-layersformed by direct implantation and by vapor phase epitaxy using undoped GaAs/PBN substratcs.

measurement temperature from 300-77°K. At the upper end of the concentration range, the 77°K mobility values are comparable to quoted values for epitaxial layers, while the values are somewhat lower at low concentrations. The significant result, however, is that Hall-mobility analysis of the ionized impurity density at 77°K yields

iV, = 0.9 X 1OI6 + 0.12 (N&- N , )

(25) using the formalism of Wolfe et al. (1970). This result is in excellent agreement with analysis of the 300°K data. The use of mobility data to evaluate the ionized impurity density assumes that other scattering processes have no role in limiting mobility in ion-implanted layers. This assumption appears to be fully justified by the self-consistent analysis presented here.

b. Amphoteric Behavior At net donor concentrations greater than 1.7 X loL7~ m - the ~ , carrier mobility in implanted GaAs/PBN substrates is observed to decrease rapidly (Fig. 50) and strongly suggests that an increasing fraction of the implanted 29Siresides on acceptor sites, such as Si,, and S&V& in the lattice. Similar “amphoteric” behavior has been documented for both Groups IV and VI impurities when used for doping high-purity vapor-phase epitaxy (VPE) (Wolfe and Stillman, 1975) and liquid-phase epitaxy (LPE) (Casey et al., 1971) GaAs layers. Figure 52 shows the total ionized impurity content Z,

74

et al.

R. N. THOMAS

2r

/-

10161/ 1016

I

I

2

5

I

I

I

1017

5

2

1018

1

2

Implanted Si Concentration ) FIG.52, Total ionized impurity density as a function of implanted 29Sidensity for undoped LEC GaAs/PBN substrates. [Cr] < 5 X I O l 4 ~ m - ~ .

derived from mobility measurements (Fig. 50), as a function of the implanted 29Siconcentration in implanted GaAs/PBN substrates. The total ionized impurity concentration C is given by Eq. (13), which can be approximated by

where the background center concentration associated with the substrate N&, is about 1 X 1OI6 ~ m - Figure ~. 52 indicates that the activation of the implanted silicon as singly ionized donors and acceptors is always loo%, suggesting the absence of inactive 29Sidue to processes such as interstitials, pair formation, spurious activation of other impurities, or the generation of active native defects. Finally, the similarity of ( N , - N&), determined from activation analysis (Fig. 48), and Nz0 N&,, derived from mobility analysis [Eqs. (25) and (26)], leads to an estimated residual ionized donor density of less than about 1 X 10” cm-3 in undoped GaAs/PBN substrates in good agreement with Hall analyses in Section 4. A more detailed description of the amphoteric doping character of Si-implanted GaAs can be derived from considerations of the thermodynamic equilibrium (Hurle, 1979)which can exist at the annealing temperature T,. For a reaction of the form

+

+

Si-

F’

Si+

+ 2e-

the compensation ratio 8 can be written as

(27)

1. HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION

8 = Si-/Si+ = ( N , - N i o ) / N &= Kn2(T,), where n( T,) is the free-electron density at T,, which is given by n( T,) = [n:( T,)

75

(28)

+ k, V,,]/n( T,) + (Si+- Si-),

(29) where the first term corresponds to the intrinsic and As vacancy contributions [n:(T,) k, VAs=r 2.5 X 10'' cm-3 at Ta= 860"Cl (Nichols et al., 1980), and the second term represents the implanted doping assumed to equal the net silicon doping measured at 300°K. Figure 53 indicates that Eqs. (28) and (29) provide an excellent representation of the measured mobility as a function of the net donor concentration measurements for undoped GaAs/PBN, using K (860°C) = 1 . 1 X cm*. Additional data as a function of anneal temperature are required to confirm this model, and preliminary data in the annealing temperature range 750 - 950°C indicate that the low-concentration amphoteric doping ratio increases with anneal temperature and that the threshold concentration for sublinear net donor activation also increases with increasing annealing temperature. These results are qualitatively consistent with this thermodynamic model. A better understanding of the activation of ion-implantedSi would be achieved if Eq. (29) could be written in chemically complete form; this analysis, however, is sensitive only to the number of free electrons emitted when a Si acceptor is changed to a Si donor.

+

.

6000r

4000 -

\

\

3000 2000

-

1000 01

10l6

I

I

I

5

1017

I

I

2

5

I

1018 2

Net Donor Concentration ( c ~ n - ~ ) FIG.53. Comparison of measured and calculated mobility of 29Si-implantedchannels in undoped GaAs/PBN substrates (at anneal temperature). 0, 860°C nitride encapsulated; 0, 750°C unencapsulated.

76

R. N. THOMAS

et al.

c. Cr-Doped GaAs

The Hall mobility of implanted layers formed in heavily Cr-doped GaAs substrates (>5 X 10l6 Cr) exhibits strikingly different behavior to implanted undoped GaAs, as was shown in Fig. 50. At low net donor concentrations, anomalously low carrier mobilities are observed in implanted Cr-doped GaAs,while at high concentrations, doping saturation is displaced to higher levels as the Cr content is increased. Measurements of implanted channels formed in lightly Cr-doped GaAs/PBN substrates (- 5 X loL5 cmF3Cr content) indicate mobilities that lie midway between the undoped GaAs/PBN and the Cr-doped GaAs curves shown in Fig. 50. The role of Cr impurities in implanted GaAs substratescan be analyzed from the perspectiveof the total equivalent concentration of ionized centers, as derived from mobility measurements, as a function of the implanted silicon concentration. By analogy with Eq. (26), the total ionized impurity content Z in implanted Cr-doped GaAs can be represented by

where Ncris the Cr impurity concentration which is assumed to be a doubly ionized deep acceptor. Plots of the total ionized impurity content Z, as a function of the implanted silicon concentration for lightly doped (<5 X loL5cm-3 Cr) and heavily doped (>5 X 10l6 ~ m Cr) - ~GaAs substrates are shown in Figs. 54 and 55, respectively. Implantation of lightly Cr-doped GaAs (Fig. 54) indicates two distinct regions: one above and one below implanted concentrations of 9 X loL6 ~ m - ~At. implanted silicon concentrations greater than 9 X 10l6 ~ r n - ~ , complete (100%)activation of the implanted silicon as donors or acceptors within the lattice is observed. The total ionized impurity content of the implanted layer is well represented by simply I:= N ; N&, and the expected influence of the doubly ionized chromium acceptors (4Ncr= 2 X 10l6cmW3)and the residual impurity concentration (KO1 X 1OI6 ~ r n - ~ ) are noticeably absent. At silicon implant concentrationsbelow the 9 X cm-3 threshold concentration, however, Fig. 54 illustrates clearly that the observed total impurity concentration reflects the effects of the Cr doping and residual acceptor density in accordance with Eq. (30). The observed is distinct and abrupt and is not well threshold dose at 0.9 X loL7 understood at present. We speculate that the apparent presence or absence of electrically active chromium in the implanted layer may reflect possible Cr interactions and complex formation and/or out-diffusion to either the surface or deeper regions of residual implant damage. Figure 55 shows the total ionized impurity content as a function of the

+

-

1, HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

77

Implanted Si Concentration (cm')

FIG. 54. Ionized density as a function of implanted 29Sidensity for lightly Cr-doped cm-]. Substrates from different crystals are represented GaAs/PBN substrates [Cr] 5 5 X by the various data symbols shown.

Implanted Si Concentration (cm')

FIG. 55. Ionized impurity density as a function of implanted 29Si density for heavily Crdoped LEC GaAs/SiO, substrates [Cr] 2 5 X 10l6crn-].

78

R. N. THOMAS et al.

implanted silicon concentration in heavily Cr-doped GaAs (>5 X 10l6 cm-3 Cr) pulled from fused silica crucibles. At silicon concentrations greater complete , activation of the implanted silicon is again than 1 X 1017~ m - ~ silicon. observed, except that saturation occurs at about 3 X 10l8 Saturation is believed to be common to all three types of GaAs crystals, but only the heavily Cr-doped GaAs substrates were implanted to the 5 X lo1*cm-3 level. Again, a threshold silicon dose of approximately 9 X 10l6cm-3 is observed. In this case, the net donor density is not sufficient to overcome the effects of Cr doping, and measurable n-type activity cannot be readily achieved in the implanted layer. At implanted silicon concentrations below the threshold dose, the total ionized impurity content therefore becomes poorly defined and presumably very large (mid-10I7~ m - from ~ ) the simultaneous formation of donors and their neutralization of the chromium acceptor impurities. All ofthe mobility data at net donor densities below 8 X 10l6 cm-3 in heavily Cr-doped GaAs (Fig. 50) represent samples implanted at the same nominal silicon concentration. We therefore conclude from these studiesofthe effects ofCr doping on the quality of silicon-implanted layers that undoped, semi-insulating GaAs offers some important advantages in terms of achieving uniform, reproducible implant profiles, high electrical activation, and high near-theoretical channel mobilities. In contrast, implantation of heavily Cr-doped GaAs substrates appears generally unsuitable for normal FET doping levels because of poor wafer-to-wafer reproducibility. Variations in Cr concentrations in wafers (due to Cr segregation effects during growth), Cr out-diffusion characteristics, and possible Cr-implanted ion interactions probably contribute to this poor reproducibility. It is especially unsuitable if lightly doped n-layers are desired. ~) Our studies also indicate that low Cr-doping levels (55 X 1015~ m - in the GaAs substrate have no serious adverse effects on the electrical activation of directly implanted FET layers and, in some instances, can be utilized to some advantage. For example, the implanted layers are noticeably more abrupt in lightly Cr-doped GaAs than in undoped substrates. Unfortunately, evidence (Magee, 1982) exists which suggests that subsequent low-temperature processing, such as ohmic contact formation, or prolonged device operation can lead to the reappearance of electrically active Cr in the implanted channel and to high concentrations at the drain contact region. TO FET DEVICE PROCESSING 15. IMPLICATIONS

Direct implantation of undoped, semi-insulating GaAs/PBN substrates prepared by large-diameter liquid-encapsulated Czochralskiyields excellent quality n-layers for high-frequency FET circuit applications. The results support the view that substrate selection for implantation device technology can be based simply and uniquely upon measurement of the resistivity and

1.

HIGH-PURITY LEC GROWTH A N D DIRECT IMPLANTATION

79

mobility of undoped GaAs substrates. Crystal selection requirements for undoped, semi-insulating GaAs include

(1) use of crystals grown from stoichiometric or slightly As-rich melts, [Gal/[Asl 5 1, (2) substrate resistivity 2 lo7 R cm or sheet resistance k lo9 R/sq, (3) measured mobility k 4500 cmz V-' sec-' with n-type conduction, and (4) sheet resistance 2 lo7 R/sq and an n-Hall coefficient following nitride encapsulation and 860°C/15 min annealing in forming gas. At present, however, more exhaustive crystal selection or qualification procedures continue to be used and rely upon evaluation of representative slices cut from different locations along each crystal. Control of selectiveimplantation processing is performed through the use of 29Sitest implants, Hall-effect measurements, and C- Vprofiling of the implanted layers. These evaluations amount to establishing the magnitude and reproducibility of parameters such as the profile shape, the activation efficiency (for net donor and total ionized impurities), and the residual electrical activity associated with the substrate. In practice, those parameters which can be directly related to probable FET performance are also monitored and include (1) profile concentration, depth, and shape, (2) zero-bias depletion width, (3) undepleted net donor concentration, (4) channel mobility, ( 5 ) current per unit periphery after source and drain processing, and (6) pinch-off voltage.

Independent investigations have shown that the dominant electrically active residual impurity in the seed half of undoped GaAs/PBN crystals is carbon, while toward the tang end of crystals at least one other shallow acceptor defect level has been identified by Hall-effect and photoluminescence studies. Residual acceptor activity at concentrations of 1 X 1OI6 or less is clearly indicated in implanted layers in undoped GaAs/PBN substrates. Its presence is not an artifact of the implant process and is not affected by, for example, annealing at temperatures between 750 and 950' C, implanting bare unencapsulated surfaces, or under capless annealing conditions instead of the encapsulated technology described here. The axial variation of the residual electrical activity appears to match that of a near-unity segregation coefficient impurity in GaAs. Our investigations indicate that wafers from at least the initial two-thirds length of each crystal are suitable for providing tight control ofthe net channel doping obtained by direct implantation without dose or energy trimming. The background donor activity in undoped GaAs/PBN substrates is

R. N. THOMAS et

80

al,

estimated to be below the 101S-cm-3range and is significantly lower than in implanted layers formed in Bridgman or LEC GaAs prepared in fused silica containers. Mass spectrometric analyses confirm directly the generally highbackground concentrations of silicon in GaAs compounded and grown in fused silica crucibles using high-pressure LEC technology. Complete (100%)activation of silicon implants as either singly ionized donors or acceptors is obtained in undoped GaAs at silicon concentrations up to 1.5 X 10l8cm-3 with 860°Cannealing. Decreasing the anneal temperature to 750°C lowers this limit to 6 X 10’’ ~ m - while ~ , raising it to 950°C causes an increase to 5 X 10l8~ m - The ~ . influence of the annealing temperature on the compensation ratio and the net donor activation efficiency is of more practical importance, and preliminary measurements of the effects of annealing temperature are shown in Fig. 56. These experiments were camed out on unencapsulated substrates which were annealed in an As overpressure at different temperatures after implantation. The donor activation efficiency is seen to increase to almost 90%for 750°Canneals, reflecting the reduced free electron concentration availableat the lower annealing temperature to create silicon acceptors. 12t8

”$.

Anneal Temperature (“C) 97

20

0.05 6

7

a

9

‘Xl 10

1 h T (“K)

FIG.56. Effect of annealing temperature on compensation ratio and net donor activation efficiency of Si-implanted undoped GaAs.

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HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

81

The amphoteric nature of silicon implants is not a significant problem with this technology in the sense that implantation of Group VI species also exhibits amphoteric doping characteristics and poses other disadvantages. The relatively deep implant profiles required for power FETs make Se implants unattractive, while the high diffusivity of S results in broad, difficult-to-control profiles. Co-implantation (Eldridge, 1980; Stolte, Chapter 2, Section 8, this volume) of low concentrations of S with Si can, however, be employed to achieve higher donor concentrations in n+ device structures. It is now clear that the technology described here was developed originally to cope with the particular problems of Cr-doped GaAs substrates. For example, 860°C annealing was chosen because it was the lowest temperature at which high mobility could be achieved in implanted channels doped range required for FET device structures. It is now to the 1 X 1017-~m-3 known that 860°C is the lowest temperature at which electrically active Cr can be effectively removed from the implanted layers by out-diffusion. The annealing temperature was not raised beyond 860°Cbecause of the resulting reduction in activation efficiency; it is now known that this is the result of increased amphoteric doping at the higher temperature. The challenge for GaAs implantation development in the near future will be to redesign processes to take advantage of undoped semi-insulating GaAs and, hopefully, eliminate much of the laboratory black art that exists today.

VI. GaAs Materials Processing The considerable efforts directed at improving basic GaAs materials and processes result from the strong interdependence of high-frequency GaAs circuit performance upon substrate quality. Significant progress is being achieved, and GaAs IC processing using selective implantation is being successfully applied to both linear and digital circuit designs in several laboratories throughout the world at the present time. The successful transition of this technology from the laboratory to full-scale manufacturingwill, however, be influenced by many considerations. One factor of overriding importance is the need for highquality, large-area GaAs substrates produced to close mechanical specifications, so that the successful “multiple chip-per-wafer” process philosophy of the silicon IC industry can be applied to drive down the costs of monolithic GaAs circuits to reasonable levels. Many of the conventional wafer preparation techniques used today in silicon (including crystal grinding, sawing, lapping, edge-rounding, and polishing) have been applied on a laboratory scale to large LEC-grown GaAs crystals. Figure 57 illustrates high-purity, semi-insulating GaAs wafers of (100) orientation, which have been fabricated to tight dimensional toler-

82

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al.

FIG. 57. Batch of high-purity, semi-insulatingGaAs wafers fabricated to tight dimensional tolerances. Wafers are 50 mm in diameter and are fabricated with ( 110) orientationflats and rounded edges.

ances (50 k 0.5-mm diameter and 0.5 rl: 0.02-mm thickness). The polished slices contain ( 110) orientation flats and are edge rounded. Recent experiencein wafer fabrication and device processing on a laboratory scale, however, reveals several areas where further improvements in wafer preparation will be required. One is the need for improved surface flatness of GaAs wafers, especially when intended for large-area processing of submicron gate-length FETs. The relatively unsophisticated rotary-polishing techniques that are commonly used today in GaAs typically yield surfaces that are flat to within only 5 - 10 pm across 50-mm-diam wafers and offer poor control of wafer parallelism, bow, taper, and so forth. Such wafers are clearly unsuitable for modem high-throughput optical lithographic techniques that will be applied increasingly to GaAs IC processing in the future. For example, today’s direct-step-on-wafer photoaligners require a tntal surface flatness of better than 0.5 pm/cm to achieve micron and submicron gate lengths in sparse geometry FET structures over large-area

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HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION

83

slices. GaAs wafer fabrication to these tight flatness tolerances has been demonstrated on an experimental basis by adopting the precision singleand double-sided waxless methods currently being used in silicon (Barrett et al., 1982). Nevertheless, the achievement of ultraflat and ultraparallel polishing of 75-mm-diam GaAs slices on a routine basis will require a considerable development effort. Another concern relates to the fragile nature of large-area GaAs wafers. This is illustrated in Fig. 58, where the results of simple impact tests are shown for GaAs and Si wafers. These measurements were performed by striking the center of the wafer with a small steel ball until breakage occurred. The fracture strength of (100) GaAs wafers is found to be about one-third that of silicon wafers of the same diameter and thickness. Tests conducted for edge breakage by striking the wafer edge showed similar differencesbetween GaAs and silicon. Edge-rounding appeared to have little or no effect on the fracture strength of GaAs to edge impact. The factors influencing fracture strength in GaAs are currently being investigated in more detail, and it has been found, for example, that no significant differences exist between wafers prepared from PBN (with high B content) or fused silica crystals (with low B concentrations), as shown in Fig. 58. It is clear, however, that low-breakage processing of GaAs will demand the development of special handling techniques based probably on the automated cassette and wafer transport methods now being utilized in silicon IC manufacturing. lo

r

8

3 L

e"6

Y

Ln

a l "-

c

= 4

f z

I b) Silicon ( 9 Wafers)

2

0

loo0

2000 3000 Fracture Impact, g force

4000

FIG.58. Measured surface fracture strength of Czochralski-grownGaAs and Si (100)wafers of same dimensions. Diameter = 50 mm;thickness = 0.5 mm;(100) orientation. Data suggest that boron content of GaAs has no significant effect on breakage.

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al.

ACKNOWLEDGMENTS The authors wish to thank many of our colleagues at the Solid State Division of the Westinghouse Research and Development Center, and at the Advanced Technology Division of the Defense and Electronic Systems Center in Baltimore, for their valuable contributions to this work. We are particularlygrateful to Dr. W. J. Takei for the x-ray topographic studies, Dr. A. Rohatgi for the DLTS studies, and Mr. R. C. Clarke for assistancein implantation annealing studies. We gratefully acknowledge valuable consultations on power FETs and monolithic circuits provided by Drs. J. G. Oakes and M. C. Driver (Solid State Division) and Mr. H. W. Cooper and Drs. M. Cohn, and J. Degenford (Advanced Technology Division). The work was made possible by the excellent technical assistance of Messrs. W. E. Bing, L. L. Wesoloski, and T. A. Brandis in crystal growth, Mrs. E. A. Halgas and Mrs.J. C. Henke in substrate preparation and evaluation, and Messrs. P. Kost and R. L. Galley and Mrs. D. J. Hellett in ion implantation. We also gratefully acknowledge the valuable contributions of other colleaguesto this work, including Dr. G. W. Wicks of Cornell University for providing the photoluminescence data, Dr. C. Evans of Charles Evans and Associates for the SIMS data, and Dr. R. M. Ware of Cambridge Instruments for his assistance in the LEC growth of GaAs crystals. The authors also especially wish to thank Dr. H. C. Nathanson for his moral support, technical advice, and guidance, and Dr. R. A. Reynolds, Mr. S. Roosild (Materials Sciences Office,DARPA), and Mr. M. Yoder (Office of Naval Research) for their continued encouragement and support. Finally, we thank Mr. D. K. Fox, Manager of the Solid State Division, for his continued interest and permission to publish this chapter.

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Elliot, K. R., Holmes, D. E., Chen, R. T., and Kirkpatrick, C . G. (1982). Appl. Phys. Lett. 40 (lo), 898. Evans, L. S., Deline, V. R., Sigmon, T. W., and Lidow, A. ( 1979). Appl. Phys. Lett. 35,291. Fairman, R. D., and Oliver, J. R. (1980).In “Semi-Insulating 111-V Materials” (G. J. Rees, ed.), Vol. 1, p. 83. Shiva, Orpington, England. Fairman, R. D., Chen, R. T., Oliver, J. R., and Chen, D. R. (1981). IEEE Trans. Electron Devices ED-28, 135. Foose, C. N., Moysenko, A. E., Linares, R., and Walline, R. E. (1981). Bienn. Conj Act. Microwave Semicond. Devices Circuits, 8th, Ithaca, New York. Ford, W., Elliot, G., and Puttbach, R. C. (1980). IEEE GaAs Integr. Circuit Symp., 2nd. Las Vegas, Nev. Fukuda, T., Washizuka, S., Kodubun, Y., Ushizawa, J., and Wantanabe, M. (1 98 1). Int. Symp. Gallium Arsenide Relat. Compd., Oiso. Jpn. Gibbons, J. F., Johnson, W. S., and Mylroie, S. W. (1975). “Projected Range Statistics-Semiconductors and Related Materials,” 2nd Ed. Wiley, New York. Grabmaier, B. C., and Grabmaier, J. C. ( 1 972). J. Cryst. Growth 13,635. Grant, I., Rumsby, D., Ware, R. M., Brozel, M. R., and Tuck, B. (1982). In “Semi-Insulating 111-V Materials” (S. Makram-Ebeid and B. Tuck, eds.), p. 98. Shiva, Nantwich, England. Gyulai, J., Mayer, J. W., Mitchell, I. V., and Rodriguez, V. (1970). Radiat. E x 17, 352. Hams, J. B., Eisen, F. H., Welch, B., Haskell, J. D., Pashley, R. D., and Meyer, J. W. (1972). Radiat. Eff 21, 601. Hemenger, P. M. (1973). Rev.Sci. Instrum. 44,698. Henry, R. L., and Swiggard, E. M. (1977). Con$ Ser.-Inst. Phys. No. 33b, p. 28. Hobgood, H. M., Eldridge, G. W., Barrett, D. L., and Thomas, R. N. (l981a). IEEE Trans. Electron Devices ED-28, 140. Hobgood, H. M., Braggins, T. T., Barrett, D. L., Eldridge, G. W., and Thomas, R. N. (1 98 1b). Int. Conj Vapor Growth Epitaxy, SthJAm. ConJ Cryst. Growth, Sth, Sun Diego, Calif: Hobgood, H. M., Ta, L. B., Rohatgi, A., and Thomas, R. N. (1982). In “Semi-Insulating 111-V Materials” (S. Makram-Ebeid and B. Tuck, eds.), Vol. 2. Shiva, Nantwich, Holmes, D. E. Chen, R. T., Elliott, K. R., and Kirkpatrick, C. G. (1982a).Appl. Phys. Lett. 40, 46. Holmes, D. E., Chen, R. T., Elliott, K. R., Kirkpatrick, C. G., and Yu,P. W. (1982b). IEEE Trans. Microwave Theory Tech. MTT-30,949. Huber, A. M., Merillot, G., and Linh, N. T. (1979a). Appl. Phys. Lett. 34,358. Huber, A. M., Linh, N. T., Valladon, M., Debrun, J. L., Martin, G. M., Mittonneau, A., and Mircea, A. (1979b). J. Appl. Phys. 50,4022. Hurle, D. T. J. (1979). J. Phys. Chem. Solids 40,6 13,627. Jordan, A. S. (198 I). Int. Con6 Vapor Growth Epitaxy, SthfAm. Conf: Cryst. Growth, Sth, San Diego, Calif: Jordan, A. S., Caruso, R., Von Neida, A. R., and Nielsen, J. W. (I98 I). J. Appl. Phys. 52,3331. Klein, P. B., Nordquist, P. E. R., and Siebernman, P. G. (1980). J. Appl. Phys. 51,4861. Kotake, H., Hirahara, K., and Wantanabe, M. ( 1 980). J. Cryst. Growth 50, 743. Kuznetsov, G. M., Pelevin, 0. V., Barsukov, A. D., Olenin, V. V., and Saul’eva, I. A. (1973). Izv. Akad. Nauk SSSR, Neorg. Mater. 9, 847. Lagowski, J., Gatos, H. C., Parsey, J. M., Wada, K., Kaminska, M., and Walukiewicz, W. (1982). Appl. Phys. Lett. 40, 342. Lightowlers, E. C. (1972). J. Electron. Mater. 1, 39. Look, D. C. (1978). J. Electron. Marer. 7, 147. Look, D. C. (1983). In “Semiconductors and Semimetals” (R. K. Willardson and A. C. Beer, eds.), Vol. 19, Chap. 2. Academic Press, New York.

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SEMICONDUCTORS AND SEMIMETAU, VOL. 20

CHAPTER 2

Ion Implantation and Materials for GaAs Integrated Circuits C.A . Stolte NEWLETT-PACKARD LABORATORIES P A L 0 ALTO, CALIFORNIA

LISTOF ACRONYMS.. . . . . . . . . . . . . . . . I. INTRODUCTION .................... 11. MATERIALS PREPARATION. ............. 1. Semi-Insulating GaAs Ingot Growth . . . . . . . .

..

.. .. 2. Epitaxial BufferLayer Growth . . . . . . . . . . . . 3. Thermal Stability. . . . . . . . . . . . . . . . . .

111. ION IMPLANTATION ........ 4. Introduction . . . . . . . . . . .

.......... ......... 5 . Ion-Implant Conditions . . . . . . . . . . . . . . . 6 . Anneal Conditions . . . . . . . . . . . . . . . . . I . Substrate Influence . . . . . . . . . . . . . . . . .

8. High-Dose Implants. . . . . . . IV. DEVICE RESULTS.. . . . . . . . . 9. IC Fabrication . . . . . . . . . 10. IC Performance. . . . . . . . . I I . Backgating . . . . . . . . . . . V. SUMMARY.. . . . . . . . . . . . . REFERENCES. . . . . . . . . . . .

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

89 90 93 93 103 106 109 109 111 119

125 134 143 143 146 148 151 154

List of Acronyms AES ASES BFL

c- v CVD DLTS ECL FET IC

JFET LEC

Auger emission spectroscopy Arc source emission spectroscopy Buffered FET logic Capacitance- voltage Chemical vapor deposition Deep-level transient spectroscopy Emitter coupled logic Field effect transistor Integrated circuit

LPE LSI MBE MESFET MSI OMVPE

89

Junction field effect transistor Liquid-encapsulated Czochralski Liquid-phase epitaxy Large-scale integration Molecular beam epitaxy Metal-semiconductor field effect transistor Medium-scale integration Organo-metallic vapor-phase epitaxy

Copyright 0 1984 by Academic Press. Inc. All rights of reproduction in any form reserved. ISBN 0- 12-752 120-8

90 PBN PRBS

RBS SDFL

C. A. STOLTE

Pyrolytic boron nitride Pseudorandom-bit-sequence generator Rutherford backscattering Schottky diode FET logic

SIMS

SSMS VLSI VPE

Secondary ion mass spectroscopy Spark source mass spectroscopy Very large-scale integration Vapor-phase epitaxy

I. Introduction The materials and implantation procedures used to produce high-quality regions for the fabrication of GaAsintegrated circuits (ICs) will be discussed in this chapter. The present state of the art in the preparation of materials, the ion implantation technology, the device processing procedures, the circuit design, and the evaluation of GaAs ICs has yielded circuits of the complexity of that shown in Fig. 1 (Liechti el al., 1982a).This circuit, which was designed, fabricated, and tested at the Hewlett-Packard Laboratories, is a 5-Gbit/sec data rate word generator that contains 400 transistors and 230 diodes on a 1.1 - by 1A-mm chip. The topics covered in this chapter are many-faceted. Therefore, specific topics considered important by some may not be addressed. The main experimental results included here are representative of the work of the author and his colleagues at Hewlett-Packard since 1975. Appropriate references are made to the literature to complement the information presented here with the results obtained in other laboratories. The intent of this chapter is to cover ( I ) the important aspects of the selection and characterization of the substrate materials that serve as the basis for all the work, including the investigation of ion implantation and the fabrication of ICs, and (2) the procedures used to produce the doped, active regions in the substrate material required to form the channel regions of MESFETs, the ohmic contact areas, and other active regions necessary for the production of ICS.

In Part 11, the important aspects of the growth, properties, characterization, and thermal stability of substrate materials are' presented. The basic requirement for the substrate material is that it provide electrical isolation between devices while at the same time allowing the formation of high-mobility controlled-doping regions in the areas where devices are to be fabricated. This requirement is met in most applications by selective region ion implantation into bulk substrate material of sufficientquality or by selective region ion implantation into high-purity epitaxial layers produced by liquid-phase epitaxy (LPE) or vapor-phase epitaxy (VPE). These active regions

FIG. 1. Photomicrograph of the 5-Gbit/sec GaAs MSI word generator. The chip measures 1.1 X 1.6 mm and contains over 600 active components and 32 contact pads.

92

C. A. STOLTE

can also be formed by the production of n-type layers by epitaxy combined with an alternative isolation technique such as mesa etching, proton bombardment, or oxygen ion implants. The use of epitaxial techniques for the active regions is, in general, limited to the production of discrete devices due to the nonuniformity of the layer thickness. The techniques used to produce Cr-doped and undoped semi-insulating GaAs ingots will be discussed, with emphasis on the 2-atm liquid-encapsulated Czochralski (LEC) technique used at Hewlett-Packard.The properties of substrate materials and the compensation mechanisms responsible for the high resistivity are presented. The thermal stability of these materials and the generally accepted model for the thermal conversion are reviewed. The growth and properties of high-purity epitaxial layers grown on semi-insulating substrates are discussed. The formation of electrically active regions by ion implantation is discussed in Part 111. Recent review articles by Donnelly (1977) and Eisen (1980) present background material on ion implantation, including numerous references to the literature. In this chapter, only the procedures used for the formation of n-Iayers, for the active regions of MESFETs and diodes, and for the formation of n+ regions for the ohmic contact regions of the circuits will be discussed. The discussion will be limited to the conditions necessary to produce normally on depletion mode MESFETs and will not address the production of normally off enhancement mode FETs. For a discussion of the relative merits of depletion mode versus enhancement mode devices and extensive references to the literature, see Liechti ( 1976), Bosch ( 1979), and Lehovec and Zuleeg ( 1980). Descriptions of the fabrication and characteristics of ion-implanted, normally OR,junction FET ICs are given in Zuleeg et al. (1 978), Kasahara et al. (198 l), and Troeger et al. (1979). Recent developments in MBE growth of GaAs-AlGaAs heterojunctions have led to the development of advanced devices with higher speed capabilities. The high mobility, modulation-doped FET (Mimura et al., 1980; Tsui et al., 1981; Judaprawira et al., 1981; Tung et at., 1982; DiLorenzo et al., 1982; Drummond et al., 1982) has been developed and is being integrated (Abe et al., 1982) for high-speed applications. The heterojunction bipolar GaAs-AlGaAs transistor (Asbeck et al., 1982; Su et al., 1983) is another candidate for high-speed integrated circuits. These devices are now being incorporated in integrated circuits in many laboratories and will have an impact on future GaAs integrated circuits. A discussion of these devices and their fabrication is beyond the scope of this chapter. The discussions of the material characteristics and requirements presented below do, however, apply to these devices.

2.

ION IMPLANTATION AND MATERIALS

93

The conditions of ion implantation discussed include the choice of the ion species, the temperature during implantation, the orientation of the substrate during implantation, and the use of through-dielectric-layerimplantation. The effect of these conditions on the resulting properties of the layers is presented in a systematic way to indicate the importance of each. The conditions required to anneal the damage produced by implantation and to electrically activate the implanted species are discussed. The anneal conditions include the techniques used to protect the surface of the substrate during the high-temperature anneal by the use of dielectric caps as well as by capless anneal techniques. The influence of the time and temperature of the anneal on the electrical properties of the implanted layers are presented. The application of transient annealing, using electron beams or laser beams, for the production of n+ regions with sufficiently high-doping concentration to produce ohmic contacts with nonalloyed metals is presented and its use for ICs is discussed. The influence of the substrate materials on the electrical properties of the implanted and annealed regions, as well as the characteristics of the devices fabricated in these layers, will be discussed. In Part IV of this chapter, the production of medium-scale integration (MSI) GaAs ICs is discussed, with emphasis on the influence of the implantation conditions, the anneal conditions, and most importantly, the influence of the starting substrate material on the properties of the devices and circuits. In particular, the phenomenon of backgating is discussed, and the influence of the substrate material on the magnitude of this effect is documented. Finally, in Part V, the state of the art is summarized and the necessary improvements in materials, ion implantation, and processing to advance GaAs IC technology are discussed.

11. Materials Preparation

1. SEMI-INSULATING GAASINGOTGROWTH

The material used as the substrate for the fabrication of GaAs ICs falls into two general classes. The first is bulk semi-insulating material grown by the LEC, gradient-freeze, or Bridgman techniques. The review article by Lindquist and Ford (1982) contains an extensive list of references as well as a summary of the growth and characterization of semi-insulating GaAs. The compensation mechanisms responsible for the semi-insulating behavior of

94

C . A. STOLTE

GaAs are discussed by Martin et al. (1980) and Johnson et al. (1983). The second class is a high-purity epitaxial buffer layer grown on the bulk substrate material by LPE, VPE, or molecular beam epitaxy (MBE). Both types of material produce satisfactory results, as will be discussed below. The production of semi-insulatingGaAs by the horizontal Bridgman and gradient-freeze techniques is well documented in the literature (Mullin, 1975). In the horizontal techniques, GaAs is synthesized in an evacuated tube by the vapor transport of As from an elemental source to Ga contained in a quartz boat. The As is held at a temperature of 607°C to produce a 1-atm As pressure, and the Ga is held at 1238°C. The stoichiometry of the resulting GaAs melt is controlled by the relative amounts of As and Ga loaded into the tube and by the temperature of the components in the system. The crystal growth is initiated by producing a temperature gradient to cool the GaAs melt such that the freezing interface travels along the length of the boat. With the Bridgman technique, the moving interface is produced by moving the boat with respect to the furnace. In the gradient-freeze technique, the freezing interface is produced by lowering the temperature profile. The main advantage of these techniques is that the ingots produced have appropriately a factor of 10 lower dislocation density as compared to those grown by the LEC technique. The main disadvantage is that the ingots are the shape of the boat and are smaller than the cylindrical, large-diameter ingots pulled using the LEC technique. Recent work (Lagowski et al., 1982; Kaminska et al., 1982) has produced material with improved electrical properties using the Bridgman technique. The production of GaAs ingots by the LEC technique was developed by Mullin et al. (1968) using the techniques demonstrated by Metz et al. ( 1962). The use of the LEC technique to produce high-quality material has received increased emphasis in many laboratoriesin the last few years. Most laboratories use a high-pressure LEC puller (AuCoin et al., 1979); results obtained using this material are reported in other chapters of this book (Kirkpatrick et al., Chapter 3 ; Thomas et al., Chapter 1). The commercial high-pressure (30 atm) LEC technique was developed by the Royal Radar and Signals Establishment and put into commercial use by Metals Research Ltd., Cambridge, England, which supplies bulk-grown LEC material as well as marketing the high-pressure pullers-the Malvern puller for 2-in.-diam ingots and the Melbourn puller for 3-in.-diam ingots. Several companies, including Rockwell International, Westinghouse, Hughes, and Microwave Associates, have purchased the Melbourn puller for their in-house production of semi-insulating GaAs. The characteristics of this material and the results obtained using it as substrate material will be presented below as part of a comparison of the different materials available for use in ICs. Recent investigations at Laboratoires d’Electronique et de Physique Appliqu6e in

2.

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95

France (Jacob et al., 1980)have compared the gradient-freeze grown material with the high-pressure LEC-grown material. The technique we have used (Ford and Larsen, 1975) for the production of semi-insulating GaAs ingots since 1974 is the low-pressure, 2-atm LEC procedure. This technique has been used to produce standard Cr-doped (Cronin and Haisty, 1964),semi-insulating substrates. This material is used as the substrate material for epitaxial growth of the n-type layers used to fabricate discrete FETs as well as for the substrate material used for the growth of high-purity buffer layers, which is the starting material for the formation of n-type layers by ion implantation. Since 1978, this technique has also been used to produce nonintentionally doped, high-purity, semi-insulatingGaAs ingots suitable for use as substratesfor epitaxial growth as well as for the production of n-type regions by direct ion implantation into the bulk substrate material. A cutaway view of the LEC puller employed for the 2-atm technique is shown in Fig. 2. The apparatus consists of a resistively heated crucible, either quartz or pyrolytic boron nitride (PBN), which holds the GaAs melt. The GaAs starting material is either compounded externally to the puller in a standard quartz ampoule by a standard As vapor transport technique (Mullin, 1975) or by the injection of As into the Ga melt (Pekarek, 1970),as will be discussed below. These methods for the synthesis of GaAs eliminate the need for the high-pressure LEC pullers. The appropriate dopants, if any, are added and the melt is covered with a layer of boric +SEED

GATE VALVE

ROD

GaAs SEED

CRUCIBLE

Bzo3 (L) GsAr (L) PEDESTAL

FIG.2. Schematic diagram ofthe 2-atm LEC puller. The gate valve is used to isolate the melt while the seed crystal or the injection cell is attached to the seed rod.

96

C. A. STOLTE

oxide (B203)which acts.as a protective encapsulant to eliminate the loss of the volatile constituentsat the growth temperature of 1238°Cand to isolate the melt from the crucible. The GaAs crystal is pulled by inserting a seed of the proper orientation to the surface of the melt, which is held at 1238"C, and extracting it at a controlled rate while the seed and the melt are rotated in opposite directions. By careful and judicious control of the rotation rates and the pull rate, ingots with good crystallographic properties and reasonably controlled diameters are produced using this technique. The melt charge is typically 2 kg, which produces ingots of approximately 65 mm in diameter and 100 mm in length. The ingot can be pulled in either the [ 11 11 or the [ 1001direction; in the past, the majority of the ingots were grown in the [ 1 1 11 direction. In the case of the [ 1 1 11ingots, the (100)oriented wafers used for device fabrication are cut from the ingot and the typical D-shaped wafer is produced. The control of background impurities in the crystals is of utmost importance, independent of the type of crystal being pulled. In the case of undoped high-purity ingots, this need is obvious. In the production of Cr-doped ingots, it is just as important since the Cr added to compensate the background shallow donor diffuses during the required anneal procedures following implantation (Evans et d., 1979). This diffusion can lead to inconsistencies since the decrease in the Cr concentration reduces the degree of compensation, and layers with inferior electrical properties are obtained, as discussed below. A novel and proven technique for in situ synthesis of the GaAs in the 2-atm LEC puller has been refined and is used to produce substrate material for our use (Puttbach et al., 1981).The apparatus used for this technique is shown in Fig. 3. In this procedure, the Ga and dopant species are loaded in the crucible, which can be either quartz or PBN, and the B203encapsulantis placed over the melt. The furnace is heated and the Ga melt brought to the growth temperature, during which time the B203encapsulatesthe melt. The injection cell, either quartz or PBN, is lowered to position the injection stem through the B,03 into the Ga melt. Arsenic is injected into the melt by a vapor-transport process driven by the controlled temperature of the As injection cell. After the As has been incorporated in the melt, the injection cell is extracted through an air lock and the seed crystal, mounted on the control rod, inserted into the melt in the usual manner. The advantage of this system is that the melt is compounded in situ, eliminating the need for external synthesis and the potential of impurity incorporationin the melt. In addition, if all the parts, including the injection cell and the crucible, are fabricated from PBN, the contamination by Si from the quartz parts is eliminated. In practice, the use of PBN is not necessary; high-purity crystals have been grown in all quartz systems, as documented

97

HE!

HIELO

! .L

FIG. 3. Schematic diagram of the LEC puller showing the A injector cell used fa the synthesis of GaAs.

below. The crucial conditions required to produce high-quality semi-insulating GaAs by these techniques include the use of very high-purity starting material, at least six 9s. A recent investigation by Oliver et al. ( 198 1 ) ha\ demonstrated the role of H,O in the BZO3encapsulant, which acts as a gettel for Si. For their growth conditions, in a quartz crucible, an HzO content ot approximately 1000 ppm was necessary to reduce the Si concentration and obtain semi-insulating GaAs. The importance of the control of the As/Ch ratio during the growth of non-Cr-doped semi-insulating ingots has been demonstrated by Holmes ( 1982). The LEC technique has historically produced ingots with higher disloca tion densities than the Blidgman or gradient-freeze technique. The densit ICY are in the 1 X lo4- 1 X lo5cm-2 range, depending on the dopant concc'n tration and manufacturer. The paper by Holmes et al. (1983) presentj experimental distributions of the dislocation densities, and the EL2 l e (4~

98

C. A. STOLTE

concentration, observed in a high-purity semi-insulatingwafer grown using the high-pressure LEC technique. Early results by Grabmaier and Grabmaier ( 1972)indicated that low dislocation material could be pulled by the LEC techniques by a necking-in procedure. The ingots pulled, however, were small in diameter (< 15 mm). Recent work in our laboratories (Hiskes et al., 1982) has produced large-diameter, 65-mm, LEC material with dislocation densities under 200 cm-2 over 80% of a wafer cut from the tail region of the ingot for Si-doped material. The typical dislocation density for semi-insulatingmaterial is in the low 1 X 104-cm-2range with regions in the 1 X 103-cm-2range near the axis of the ingot. The importance of dislocation density on the quality or yield of high-density GaAs ICs has not been demonstrated but could be expected to become important as the area of critical regions of the circuit, e.g., the gate regions, occupy a significant fraction of the chip area. The 2-atm LEC technique has routinely produced high-quality Cr-doped semi-insulating GaAs since 1974. The necessary conditions for the production of high resistivity material is that the dopants satisfy the following relations: if ND> NA,then NDA - NDD > (ND- NA) (Lindquist, 1977)

(four-level model)

or (three-level model) if NA > ND, then NDD > ( N A - ND) (Swiggard et al., 1979), where NsDand NSAare the concentration of shallow donors and acceptors, respectively, and NDDand NDA are the concentration of deep donors and acceptors, respectively. The energy levels of these dopants, shown in Fig. 4, have been measured by many laboratories. See the recent paper by Martin (1 980) for an overview of these results. The shallow donors are believed to be due to S and Si as unintentional dopants or to Te as an intentional dopant used to prevent ptype conversion of the Cr-doped material when it is used as a substrate for epitaxial growth (Swiggard et al., 1979). The addition of Te for this purpose is no longer necessary with the improved purity of the growth conditions possible today. The shallow acceptors are believed to be due to C, Mn, or other impurities in the melt. The deep acceptors are due to the Cr intentionally added to the melt to compensate the shallow donors in order to assure semi-insulating material with resistivitiesgreater than 1 X lo* R cm. The deep donor, the EL2 level, was originally ascribed to oxygen (Milnes, 1973); however, Huber et al. (1979) demonstrated that the EL2 level is not due to oxygen. It is believed

2.

ION IMPLANTATION A N D MATERIALS

99

Cr" ? A'

1.43 eV

C.B.

ND

o,9 eV

Cr" ? A '

E,,

N m 0 . 7 eV 0.62 eV 0.45 eV

0.15 eV

CrZf

EL (')

A-

&

0.7 eV N,

EF

Cr3* A'

cr4+

D+ NA

-

= 0.825

V.B.

FIG.4. Electron energy diagram of semi-insulating GaAs showing the shallow ND and NA levels and the deep traps, Crz+and EL2, along with the charge state of Cr in GaAs.

that the EL2 level is due to a native defect, As on a Ga site, formed during the post-growth cooling of the crystals (Lagowski et al., 1982a). Recent results by Holmes et al. (1982) demonstrated that the EL2 concentration is related to the stoichiometry of the LEC melt and therefore can be controlled to some degree. The growth of nonintentionally doped ingots which are semi-insulating and thermally stable has been a production process since 1978. Because there is no Cr added to the melt, the semi-insulatingproperty of this material is described by the three-level model. It is essential to minimize the concentration of the shallow donors and to control the concentration of the shallow acceptors relative to the concentration of the deep donor level EL2. This control can be maintained, as was demonstrated by our consistent results obtained over a three-year period. An indication of the practicality of the production of this high-purity bulk material is the routine operation of a second facility of Hewlett-Packard (the Santa Rosa Technology Center), which has successfully constructed a 2-atm LEC puller and is pulling high-purity semi-insulating GaAs ingots. In addition, as indicated above, several companies have installed the Melbourn puller manufactured by Metals Research, and they are successfully growing high-purity semi-insulating material. The quantitative determination of impurities in GaAs substrate material is a difficult problem and it is not difficult to obtain erroneous results. The techniques used for impurity analysis include secondary ion mass spectros-

100

C . A. STOLTE

copy (SIMS) (Clegg, 1982), Auger emission spectroscopy (AES) (Holloway, 1980),spark source mass spectroscopy (SSMS)(Brown el al., 1962), and arc source emission spectroscopy (ASES) (Wang, 1968). The use of AES is limited due to the lack of sensitivity. ASES has been successfully used in these investigations for the determination of impurities such as Cr, with a ~ ;with a detection limit of 1 X 1015~ m - ~ ; detection limit of 1 X 1015~ m - Si, and Mg, with a detection limit of 4 X loL5~ m - ~ SIMS . analysis has been used by many laboratories to evaluate the redistribution of Cr and to measure the background impurity concentration. In this application, extreme care must be taken in the interpretation of results due to matrix and background effects. The most sensitive technique for the analysis of impurities is SSMS. This technique requires precise preparation and use of calibration sources and careful operation of the apparatus to avoid instrumental background levels which can lead to erroneous results. The data presented in Table I were obtained by SSMS at three different facilities from samples taken from the same regions of two different high-purity semi-insulating ingots grown in our facilities. For comparison purposes, results obtained using ASES in these laboratories are included. There are large discrepancies in the magnitudes of the impurities measured by the three different SSMS facilities for important species such as Cr, Si, S, and 0.The most consistent and reliable results, and those which are in agreement with the measured electrical behavior, thermal stability, and implant and anneal resuIts, are those obtained by facility A. It is interesting to note that although emission spectroscopy lacks sensitivity, it is in agreement with the SSMS analysis of facility A. The data in Table I1 were obtained by SSMS in facility A for a number of different samples from different ingots produced by the 2-atm LEC technique at Hewlett-Packard, F402 and F450, and by the high-pressure Melbourn puller at Metals Research using in situ synthesis. Using the three-level model described above, and assuming that C is the dominant shallow acceptor (Brozel et al., 1978) and that Si and S are the dominant shallow donors, the concentration of the EL2 level to produce semi-insulating material can be calculated. From the impurity analysis given in Table 11, it is seen that these materials will be semi-insulating if an EL2 level concentration of about 4 X 10l6cm-3 is assumed for the LEC materials. This is the concentration of the EL2 level that is quoted in the literature for materials grown by this technique (Martin, 1980). The properties of these bulk materials, both the Cr-doped and the nonintentionally doped, high-purity semi-insulating materials, are discussed in detail in the sections that follow and are compared with the properties of bulk material from other sources and grown by other techniques. In addition, the properties of these bulk materials will be compared with the properties obtained using very high-purity buffer layers.

TABLE I SPECTROGRAPHIC ANALYSIS OF HIGH-PURITY BULKG a s

Ingot HP F402 Element

B C N 0 Na Mg A1

Si S Ca Cr Mn Fe cu Zn Te

ASES hp labs (cm-%)

SSMS facility A (~rn-~) 6.6 X

=

<8.0 x 10'5 a . 2 x 1014

< 1.7 x 1015 1.5 x 1014 ~3.x 8 1017

1.1 x 1016 <2.2 x 1015 <3.5 x 1014 3.1 x 1014 8.9 x 1014 a . 7 x 1014 2.2 x 1015 <3.5 x 1014 a . 7 x 1014 <3.i x 1014 <4.4 x 1014 <6.6 X IOl4

a . 9x

SSMS facility B (~rn-~)

1014

SSMS facility C (cm-3) 1.3x

IOl5

18.9 x 1015 53.1 X 10l6 4.0 x 1014 < 1.2 x 1015 < i . i x 1015

Ingot HP F450

1015

4.0 X lo1* 1.3 x 1017 4.0 X 10l8 1.3 X 10l6 2.7 x 1015

1.3 X lot6 1.3 X 10I6 4.4 X loL5 8.9 x 1015 8.9 x 10'4 1.3 x 1015 <4.4 x 1014

<8.9 X < 1.3 x

IOI4

1015

SSMS facility A (~rn-~) 4.4 x 1015 51.5 X loi6

a . 1 x <4.4 x 1015 1.3 X <4.4 X 10l6 < 1.3 X lot6

1.3 x 1015 <4.4 x 1014 <4.4 x 1015

< 1.8 x 1015

1015

10l6 1014

5 1.5 X ~ 4 .x 4 7.9 x 2.6 x 1.3 X

1014

~3.x 1

1014

1014 loB5 8.8 X loi4 1 . 1 x 1015 a . 6 x 1014 <2.2 x 1014 <2.2 x 10'4 <4.4 x a.2x

1014 1014

SSMS facility B (~rn-~) 4.4 x 4.0 x 4.0 X 1.3 x 2.2 x

1015

1017 loL6 10'8 10'6

1.8 x 1015 8.9 x 1015

1.3 X 10l6 4.4 x 1015 4.4 x 1015 2.2 x 1015 2.2 x 1015 4.4 x 1015

8.9 x

1014

TABLE I1

SSMS ANALYSIS OF HIGH-PURITY G A SINWTS HP F450 Element

B C N 0 Na Mg

Al Si

S ca Cr Mn Fe cu Zn

Te

MR-A (SiO, cruc.) (cm-)) 6.6 X lOI5

54.4 x 10’6 53.1 X 10”

59.7 x 10”

c 1.3 x 1015 4.4 x

1014

1.3 x 1014 4.4 x 1015 4.4 x 1015 4.4 x 10’6 < 1.3 x 1014 ~ 8 . x9 1013 1.3 x 1014 < 1.8 x 1014 <4.4 x 1014 <3.5 x 1014

MR-B (PBN cruc.)

MRC

(Cm-))

(m-?

x 1015 x 10’6 x 10’6 x 10” ~ 8 .x 9 1014 3.5 x 1014 < 1.8 x 1014

1.3 x 1015 1.1 x 1015 55.5 x 1015 53.1 x 1017 <6.6 X lof4 1.3 x 1015 1.8 x 1014 4.4 x 1014 2.2 x 1015 3.1 x 1015 <2.2 x 1014 < 1.8 X IOl4 <2.2 x 1014 ~ 2 .x 7 1014 <4.4 x 1014 <4.4 x 1014

4.4 54.4 54.4 54.4

3.1 X lo1‘ 6.6 X 10l5 1.3 X lot6 ~ 2 .x 2 1014 < 1.8 x 1014 ~ 2 .x 2 1014 a . 7 x 1014 6.6 X 1014 <4.4 x 1014

5

HP F402 (m-’)

Head

Tail

(m-’)

(cm-’)

1015 4.4 x 1015 1015 5 1.5 X 10I6 1016 53.1 x 1015 10’6 5 1.5 X 10I6 10” <4.4 x 1014 1014 7.9 x 1014 a . 1 x 1014 2.6 x 1014 8.9 x 1014 1.3 x 1015 e . 7 x 1014 8.8 X 1014 2.2 x 1015 1.1 x 1015 <3.5 x 1014 ~ 2 . x 6 1014 a . 7 x 1014 <2.2 x 1014 a . 1 x 10’4 ~ 2 . x 2 1014 ~ 4 .x 4 1014 a . 1 x 1014 <6.6 X lot4 ~ 4 . x 4 1014 a . 9 x 1014 a . 2 x 1014 6.6 X 58.9 x 53.1 X 5 1.1 x <2.2 x <3.5 x

2.2 x 1015 1.5 X 10l6 53.1 x 1015 54.4 x 10’6 ~ 4 .x 4 1014 6.2 x 1014 <2.2 x 1014 3.5 x 1014 2.2 x 1015 6.6 X lOI4 ~ 2 .x 6 1014 <2.2 x 1014 3.5 x 1014 ~ 3 .x 5 1014 3.1 x 1015 <6.6 X loL4 5

2.

103

ION IMPLANTATION A N D MATERIALS

2. EPITAXIAL BUFFERLAYERGROWTH The growth of high-purity epitaxial layers has been accomplished by VPE [using the AsCl, system, the ASH, system, and the organometallic vaporphase epitaxy (OMVPE)] by LPE, and by molecular beam epitaxy (MBE). These growth techniquesare discussed,with emphasison the LPE technique used in our investigations. A recent paper by Abrokwah d al. (1981) lists numerous references to literature describing techniques used to grow LPE layers. In that paper, procedures are described to obtain high-purity buffer layers by LPE. The technique requires prolonged (24 - 96 hr), high-temperature(775 "C)baking of the melt and substrate prior to the growth at 700°C. The results of Morkoc and Eastman ( 1 976) indicate that a prebake of the graphite boat at a high temperature, greater than the 700°Cgrowth temperature, in H, before growth is necessary for the growth of low camer concentration layers, These high-temperaturetreatments are not used in the procedures described below for the production of high-purity buffer layers. The growth of high-purity GaAs buffer layers by the LPE technique in these laboratories has provided consistently high-quality substrates for the investigation of ion implantation and for the production of GaAs ICs. This LPE material has been the standard against which the properties ofimplants into other materials have been compared. The growth of these materials has been routine since 1974 using the techniques of sample preparation determined by Vilms and Garrett (1972). Layers with consistent properties have been available for our investigationssince 1975 (Stolte, 1975). The layers are produced using the system illustrated schematically in Fig. 5, which shows the horizontal graphite slider system. The Ga, six 9s (0.999999) purity, is loaded in the slidinggraphitebin to a depth of about 5 mm. The source of As HIGH-PURITY GaAs WAFER

PUSH ROO

/

M A I N BLOCK

I

(1UARTZ THERMOCOUPLE SHIELD

FIG.5 . Schematic diagram of the horizontal graphite slider system used to grow high-purity liquid-phase epitaxial GaAs buffer layers.

104

C. A. STOLTE

is a 500-pm-thick,high-purity GaAs wafer placed on top of the Ga melt, as shown. The source wafer is the high-purity material pulled by the LEC process described earlier. The Ga melt, with the source wafer in place, is inserted into the reactor and baked for four to five days at a temperature of 700°C under a hydrogen flow of 4 liter/sec. The substrate used for the growth is prepared using a chemical-mechanical polish with bromine-methanol to produce a mirrorlike finish, free from any surface irregularities. The final thickness of the substrateis controlled to produce the appropriate wiping clearance between the slider bin and the substrate surface. This control is necessary to eliminate Ga carryover on the surface of the epitaxial layer at the termination of the epitaxial layer growth. The polished wafer is loaded into the LPE reactor under a N, purge. The system is then baked under an H, atmosphere for 4 hr at 7OO0C,with the substrate wafer exposed, to saturate the melt. Prior to the growth, the melt temperature is reduced by 2°C to supersaturate the melt. The growth is initiated by sliding the melt over the substrate and continuing the temperature drop rate of l"C/min for the time required to grow the desired thickness. The melt and source wafer are changed after approximately 30 epitaxial layers have been grown. These 30 layers include approximately 26 thin, 3-pm layers used for implant substratesand four thick, 20-pm layers used for electrical characterization of the epitaxial layers. It has been observed that after approximately 30 layers have been grown, the layers begin to show an increased pit density, greater than 10 cm-2, and that the uniformity of the layer thickness decreases. The pits are believed to be due to a buildup of Ga,O, with time or to an accumulation of graphite particles from the graphite slider. The thickness nonuniformity is due to a depletion of the GaAs source wafer. The thick layers are used to measure the electrical properties of the layersby Hall measurements using the van der Pauw ( I 958) geometry. The criteria used for the acceptance of the buffer layers for use in implant or device investigations are that the Hall mobility measured at sec-' and that the room temperature must be approximately 8000 cm2V 1 Hall mobility measured at 77°K must be greater than 120,000 em2 V-I sec-l. The epitaxial layers are always n-type, with a net carrier concentration less than 1 X lOI4 The analysis of Wolfe el a/. (1 970), using the Hall mobility measured at 77"K, indicates that ND NA is in the range of 1 - 4 X loL4 cmb3and that the material is very closely compensated with ND in the same low I X 1014-cm-3range. The thickness uniformity of the 3-pm layers is adequate for the production of ICs with a 1-0 standard deviation of the thickness of about 20% over a single wafer, and a wafer-to-wafer uniformity of the average thickness of 10%. The surface morphology is of utmost importance in the fabrication of ICs,

+

2.

ION IMPLANTATION A N D MATERIALS

105

especially in contact printing lithography, and extreme care is taken to minimize the typical surface imperfections such as meniscus lines, terraces, pits, and Ga carryover. The best surface conditions are obtained using substratesoriented to within 0.2" ofthe (100) surface to minimize terracing. High-purity buffer layers have been grown by VPE using the AsCl, system (Cox and DiLorenzo, 1980);by the ASH, hydride system (Stringfellow and Horn, 1977); and by the OMVPE (Dapkus et al., 1981). These systems consist of a reactor, either horizontal or vertical, which contains a substrate heater and internal components that can serve as sources of Ga and/or dopants and also as getters for impurities. The reaction gases are introduced via a gas manifold. The systems are operated either at 1 atm or at a reduced pressure, depending on the particular technique used. The epitaxial layers are grown by the reaction of the appropriate vapors at the substrate which is held at a growth temperature of 600-700°C. The advantage of this technique over the LPE technique is the capability to grow large-area layers with very uniform thickness. The OMVPE system has produced layers with total impurity concentrations of 5 X loL4cm-, and mobility, measured at 77"K, of 125,000 cm2V-l set+ (Dapkus et al., 1981). The layers grown by the AsC1, system have net camer concentrations in the mid- 1014-cm-2range and show evidence of Cr diffusion from the substrate into the epitaxial layer when grown on Crdoped substrates (Cox and Dihrenzo, 1980). The hydride system buffer layers have been evaluated as part of our material investigation. The properties of the implanted and annealed layers are comparable to those obtained using the LPE buffer layers. The layers grown in the hydride system are high purity for the first 2 - 3 pm of growth, but for thicker layers the camer concentration increases (Stringfellow and Horn, 1977). This limits the usefulness of these layers in applications where thicker buffer layers are desired, e.g., to reduce backgating (see Part IV). The inability to grow thick layers also precludes the determination of the purity of these layers by a Hall measurement. These limitations of the VPE buffer layer material reduce the value of this material in an investigation of ion implantation or device studies. The growth of high-purity buffer layers by MBE has been demonstrated (Morkoc and Cho, 1979; Calawa, 1981). In this technique the layers are grown at 500 - 640°Cby the impingement of molecular beams of Ga and As on the substrate in ultrahigh vacuum (< Tom). Buffer layers have been grown using this technique with net camer concentrations in the mid1014-cm-3range, with mobilities, measured at liquid nitrogen temperature, greater than 100,000 cm2 V-I sec-'. These buffer layers are expected to be important when used in conjunction with the unique properties of MBE layers.

106

C. A. STOLTE

3. THERMAL STABILITY The use of bulk material as the substrate for ion implantation or as the substrate for epitaxial growth requires that the properties of the substrate material remain unchanged during the required thermal cycles. When the material is used as a substrate for epitaxial growth, it must remain semi-insulating during the growth cycle. In the case of the LPE growth described, this includes a 4-hr period at 700°C under a flowing H, atmosphere. The semi-insulating material produced by the 2-atm LEC technique using controlled doping with Cr-Te, as described, always meets the criterion that the sheet resistance after this heat treatment is greater than 1 X lo8 Q/sq. The high-purity, undoped, substrate material produced by the 2-atm LEC process meets this same criterion. It should be noted, however, that some material, both Cr-doped and high-purity, purchased from outside vendors has failed to satisfy this criterion. The ability of both the Cr-doped and the undoped semi-insulatingsubstrates to meet this thermal stability criterion, required for epitaxial growth, provides greater flexibility in the choice of the materials systems. This has aided in the investigation of backgating, as described later. Since the preferred technique used to produce the active layers used for the production of GaAs ICs is ion implantation, it is crucial that the substrate material be stable under the anneal conditions used to activate the implanted species. The condition used for the anneal, described in Part I11 of this chapter, is a heat treatment at temperatures up to 900°Cfor periods up to 30 min in an Ar atmosphere with the GaAs surface protected by a Si3N., cap. The second stability condition imposed on any material to be used for ion implantation is, therefore, that it retains its high resistivity under these conditions of anneal. In the case of the epitaxial layers, this means that they retain their high mobility and low carrier concentration during the anneal cycle. The LPE buffer layers, produced as described above, are stable and show no decrease in quality under these anneal conditions. The bulk material must meet these same criteria if it is to be used as a substrate material for direct ion implantation. A large percentage of the Cr-doped material produced a few years ago and a significant percentage of recent high-purity, as well as Cr-doped, materials exhibit a thermal conversion during the anneal cycle which in extreme cases reduces the sheet resistance from lo8 Q/sq to less than 300 Q/sq. The magnitude of the decrease in resistivity is determined by the impurity concentration in the substrate material. This conversion process, due to the out-diffusion of Cr during the anneal cycle, has recently been examined by many investigatorsusing direct measurement techniques such as SIMS analysis (Evans et al., 1979) and

2.

ION IMPLANTATION A N D MATERIALS

107

SU BSTAATE 1-1 0 1-2 * 1-3 x 1-4 3-1 0

3-2

NSi (cm-?

FIG.6. Sheet carrier concentration N, versus Si impurity concentration, Nsifor unimplanted semi-insulating GaAs substrates that have been annealed at 900°C for 15 min with a Si,N4 anneal cap.

radiotracer analysis (Tuck et al., 1979), as well as by inferring the mechanisms of the conversion from electrical measurements (Asbeck et al., 1979). Early work at Hewlett-Packard (Stolte, 1975) demonstrated the effect of Cr diffusion in a fairly crude but definitive experiment. The results of this experiment, with additional, more recent data, are shown in Fig. 6. The sheet carrier concentration of unimplanted Cr-doped material, which had been subjected to a 900°C anneal temperature for 30 min with a Si,N, cap, is plotted as a function of the background concentration of Si, measured by ASES on material from the same area of the ingot. These data represent material from several different suppliers; each sample was semi-insulating prior to the anneal cycle. This material was typical of the Cr-doped material available at the time of these experiments (Stolte, 1975). The Cr concentration in these materials, measured by emission spectroscopy, is greater than the Si concentration by a factor of at least 2. The carrier concentration profiles, measured by the capacitance- voltage (C- V ) technique, for these converted samples are shown in Fig. 7. The background Si concentration of the samples and the mobilities measured after the anneal are indicated on the figure. Based on these measurements, a simple model of Cr out-diffusionwas postulated to describe the conversion process. The decrease of the Cr concentration reduces the degree of compensation of the background donors, and this produces the thermal conver-

108

C. A. STOLTE 1017

-

86-

-

-I

?

&..,,(

1

-3

4-

4 2

'

2-

z 10'6 8-

64-

:

2-

1015~

0.2

0.4

0.6

lLm (OK)

Substrate

(cm2V-I sec-I)

0.8

1.0

1.2

Nsi

(~rn-~)

1-4 3580 2.4 X 1016 2.3 x 1015 3-1 5840 1-2 4350 3.5 x 10'6 3.0 X loL6 1-3 4120 5 160 8.0 X lof5 3-2 FIG.7. Camer concentration profiles for different unimplanted semi-insulatingGaAs substrates that have been annealed at 900°C for 15 min with a Si,N, anneal cap.

sion seen in these substrates. The diffusion constant inferred from the data of Fig. 7, based on a simple diffusion model of Cr, is approximately 1 X lo-" cmz sec-l at 900°C. This value is in good agreement with the more recent value determined by Asbeck et al. (1979). The early work of Sat0 (1973) proposed a similar model; in that investigation, the conversion was dependent on the cap material used during the anneal cycle. The high-purity semi-insulating material is compensated by an excess of the EL2 electron trap, as described earlier. In this case, the decrease in resistivity can occur via a change in the surface stoichiometry.The loss of As by evaporation would produce donors while the loss of Ga via diffusion into the cap material, if used, would produce acceptors (Stolte, 1977)in addition to changing the relative donor to acceptor ratio of amphoteric species such

2.

ION IMPLANTATION A N D MATERIALS

109

as C, Si, and Sn. The degree of conversion will depend on the relative concentration of the EL2 level and the shallow-donor and -acceptor concentration in the surface region following the anneal. Recent investigations (Makram-Ebeid et a!., 1982; Lagowski et al., 1982b) have demonstrated a decrease in the concentration of the EL2 level at the surface during thermal treatments. This can produce a surface-conduction layer by reducing the degree of compensation of the background acceptors. In addition to these basic materials-related mechanisms of conversion, there is the possibility of incorporating impurities during the anneal cycle. These impurities can be introduced by the cap material or in the ambient used during the anneal and can lead to surface conduction for improperly annealed samples. An additional technique used to evaluate the stability of substrate material under implant and anneal conditions is Kr ion implantation (Higgins et al., 1978)to the same dose and depth as that of the dopant ion implant. This Kr implant produces the equivalent damage profile to simulate the diffusion and/or other effects which may be damage-dependent. This technique was used for a period in these investigations; the results obtained using the Kr-implanted samples always agreed with the unimplanted samples in the investigation of the thermal stability of the samples. As described below, a part of our substrate evaluation includes the use of a standard Se implant, and the effects of the implantation damage are evaluated as part of that procedure. The experiments prior to 1976 indicated a serious problem in the interpretation of results obtained from the implant and anneal experiments using standard Cr-doped substrates. This included greater than 100% doping efficiency in an implant experiment and carrier concentration profiles dependent on the particular substrate used. The decision was made to avoid the use of Cr-doped substrates for direct implantation and to concentrate on the use of the LPE buffer layers as the standard implant substrate. Because this was viewed as a necessary, but not a practical, solution in the long term, sources of high-quality bulk material were evaluated to lay the basis for the use of this material when it became available in reliable quantities. As demonstrated below, it is now possible to produce bulk material that has sufficient purity and stability under the required process temperatures to produce high-quality layers by direct ion implantation. 111. Ion Implantation

4. INTRODUCTION

The topic of ion implantation is broad and diverse, with many interdependent parameters. In this part, the importance of the implant and anneal

110

C. A. STOLTE

parameters on the electrical properties of the implanted and annealed regions is presented. In addition, the conditions necessary for the production of regions with optimal electrical characteristicsare given. The implant and anneal conditions were investigated using high-purity buffer material, described earlier. This material is ideal for this purpose since it is of very high purity and does not convert during the anneal process. Using this starting material, the properties of the implanted and annealed layers are evaluated independent of inconsistenciesof the material properties. The influence of the starting implant material on the properties of implanted and annealed layers, produced using standard implant and anneal conditions, will be presented. As a result of the investigation to be described, a set of standard implant and anneal conditions has been established for the production of active layers for the fabrication of GaAs ICs as well as for the evaluation of materials. In the discussion to follow, it will be assumed that these standard conditions are used in the investigation. If one or more of the implant and/or anneal parameters are varied, it will be specifically noted. The standard conditions are as follows: (1) Implant conditions. The substrate is oriented at a tilt angle of 10" between the beam and the normal to the ( 100)substrate surface and rotated 30 deg with respect ot the (1 10)cleavage plane to eliminate axial and planar channeling. The substrate is held at a temperature of 350°Cduring the implantation. The wafers are implanted bare, with no dielectric coatings, and are cleaned in a sulfuric acid/hydrogen peroxide etch prior to loading into the implant machine. (2) Anneal conditions. The implanted layers are annealed for 15 min at 850°C under flowing Ar. The surface of the wafer is protected with 1500 A of silicon nitride, which is deposited by a pyrolytic reaction of silane and ammonia at 650°C.The Si,N., deposition rate is 100A/min; the heat-up time prior to the deposition is 3 min with the wafer under flowing hydrogen. The wafer is given a very light surface etch in a sulfuric acid/hydrogen peroxide etch prior to loading into the chemical vapor deposition (CVD) reactor. A discussion of the implant and anneal conditions and the experiments which led to the adoption of the standard conditions is presented below. The electrical characterization of the implanted and annealed layers includes the determination of the sheet resistance p8, the effective mobility pe, the sheet camer concentration N,, and the carrier concentration and mobility profiles. The values of ps and p e are measured using Hall-effect measurements employing the van der Pauw geometry (van der Pauw, 1958) with the sample at room temperaure or liquid nitrogen temperature. The ohmic contacts are formed by alloying a standard NiCr-Au-Ge-Au

2.

ION IMPLANTATION AND MATERIALS

111

metallization system. The majority of the mobility measurements were made with a magnetic field of 1 150 G, and good agreement was obtained with measurements at 5000 G. The measurement of ps and ,uein conjunction with a layer-removal technique allows the determination of the carrier concentration and mobility profiles of the implanted and annealed layers (Mayer et al., 1967). The samples are thinned using a dilute etch,l00: 1 : 1 (H20:H202:H2S0,), which removes approximately 400 A/min. The sample geometry is designed to permit Taly Step measurements of the layer removed at each step. The carrier concentration profile is more conveniently measured using the standard Schottky barrier C- V technique. The ohmic contact used for this technique is the NiCr- Au-Ge - Au alloyed contact, which is coplanar with the evaporated A1 Schottky barrier contacts. The measurements are performed using an automatic LCR meter in conjunction with a calculator to measure the C- V and plot the carrier concentration as a function of depth. The depth range of the measurements is increased by etching a series of steps in the sample before the A1 Schottky barriers are deposited. With this technique, the series of concentration profiles obtained on the different etch steps are plotted together using horizontal, depth, displacements corresponding to the etch step heights. 5. ION-IMPLANT CONDITIONS The species used for ion implantation depends on the desired properties of the resulting layer. This discussion is limited to n-type implants since the GaAs ICs discussed in this chapter use MESFETs; the topic of normally off FETs, which are fabricated by p-type implants or very low-dose n-type implants, will not be discussed. The most crucial implantation procedure for GaAs ICs is that used to form the active channel region for the metalsemiconductor field effect transistors (MESFETs). The requirements for the channel region are a shallow-doping profile, approximately 0.1 -0.2 pm, a peak concentration of approximately 1 X 10'' ~ m - and ~ , the highest mobility consistent with this doping concentration (approximately 4500 cm2V-' sec- ). The discussion to follow will first concentrateon the production of n-type layers suitable for channel regions; the topic of the formation of n+ regions to produce low resistivity regions and n2+ regions to form nonalloyed contacts is discussed later. The choice of the implant species for a particular application is dependent on many factors, including the availability of the ion species in the implantation machine available for use. The majority of the studies of n-type implants into GaAs have used Se, Si, S, Te, Sn, and Ge. Gibbons et al. ( 1975) have published implant range data in tabular form, which allows the

112

C. A. STOLTE

TABLE 111 RANGE AND STANDARD DEVIATION FOR

IONS IMPLANTED INTO GAAV

Energy

200 keV Ion species

Se Si

S Te

Sn Ge

R, (pm) 0.0695 0.174 0.151 0.0498 0.051 1 0.0735

400 keV

A R, ( p m )

-~

0.0313 0.0753 0.0667 0.0207 0.0216 0.0334

800 keV

R, (pm) A R, (pm) R, ( ~ m )AR, (pm) ~

0.137 0.351 0.307 0.0917 0.0950 0.1463

~

~~

0.0557 0.121 0.1 10 0.0364 0.0381 0.0594

0.280 0.675 0.600 0.179 0.186 0.300

0.0982 0.178 0.166 0.0654 0.0684 0.104

From Gibbons ef al. (1975).

calculation of the predicted carrier concentration profile for a large number of species in different substrate materials. The data shown in Table 111 give the range and standard deviation for some of the more useful implant species into GaAs at the maximum energies readily available in commercial machines. It should be noted that a 200-keV machine can produce an ion beam with an equivalent 400-keV ion energy by using the doubly ionized species, and a implanter can produce an 800-keV equivalent ion energy. The early investigations of n-type implantation into GaAs employed Te since it is the only useful n-type species that is heavier than the GaAs substrate. This allows the use of Rutherford backscattering (RBS)analysis (Chu et ul., 1978; Gamo et al., 1975; Eisen, 1975) to investigate the crystallineproperties of the implanted regions. These measurements include a determination of the implant-induced damage and the efficiency with which the dopant species is located on lattice sites. The use of Te as an implant species for the formation of channel regions is limited since the projected range of Te at 400 keV, the maximum energy available using singly ionized Te in a 400-keV machine or doubly ionized Te in a 200-keV machine, is just 0.092 pm and for doubly ionized Te in a 400-keV machine it is 0.179 pm. An example of the electrical properties obtained for results of Te implants into GaAs under the standard conditions, annealed at 900°C for 15 min, is shown in Fig. 8. Here, the carrier concentration profiles measured by the C- I/ technique are shown and compared with the predicted results using the published range and deviation data.This theoretical curve is adjusted in magnitude to determine the doping efficiency q and in the width of the profile to determine the diffusion coefficient. This fit to the experimental profile is discussed in more detail below. The difference

2.

113

ION IMPLANTATION A N D MATERIALS

Te + GaAs 4-

2-

101786-

J

4-

za I

L"

2-

10'6 8 -

64-

I

I

1

I

I

I

I

0.1

0.2

0.3

0.4

0.5

0.6

0.7

d (rm) FIG.8. Carrier concentrationprofiles for Te-implanted Cr-doped and LPE buffer substrates to a dose of 6 X 10l2cm-' at 500 keV and 350"C, annealed at 900'C for 15 min with a Si,N4 cap. Theoretical profile: 0 = 50%; R, = 0.1 13 pm; A R, = 0.044pm; and D = 1.1 X cm2 sec-'.

between the two experimental profiles is due to thermal conversion of the Cr-doped substrate. The species most often used for the channel-region implants are Se, Si, and S. These species have sufficient range to produce the necessary carrier concentration depth for the channel regions for MESFETs. The choice of the implant species in a particular application is determined by the electrical properties obtained with that species and on the preference of the organization established during the development of their implant and anneal technology. Sulfur produces high-mobility layers with good doping efficiencies, but during the anneal cycle can exhibit undesirable fast diffusion rates as illustrated in Fig. 9. The profile for S implanted into LPE buffer substratesis anomalous at the surface, and the implant into the Cr-doped substrate does not resemble the predicted gaussian profile. The best fit that can be made to the theoretical profile is that which uses a low q and ignores the surface

114

C. A. STOLTE

Cr -Doped Substrats

0

2

l"

f

Buffar LPE Theoretical Profile

1015L---i-

0

0.1

I

I

0.2

0.3

-A,

Substrate

I

0.4

0.5

0.7

0.6

d (pm)

FIG.9. Carrier concentration profiles for S-implantedCr and LPE buffer substrates to a dose of 5 X lo'* cm-2 at 250 keV and 350"C,annealed at 900°C for 15 min with a Si,N, cap. cm2sec-I. Theoretical profile: q = 1394; R, = 0.190 prn; A R , = 0.078 pm; D 2.2 X =i

region. The inconsistent profile shape limits the usefulness of S as an implant species. The camer concentration profile for Si implanted into a buffer layer, shown in Fig. 10,illustrates the good fit to the theoretical profile with an activation efficiency of 80%.Data for a Se implant into a buffer layer substrate are shown in Fig. 11. The predicted profile is shown and agrees with the experimental data assuming the diffusion coefficient and doping efficiency indicated on the figure. The influence of the anneal conditions on the doping efficiency and on the carrier concentration profiles is discussed below. The conditions used during the implantation of the dopant species into the substrate influence the properties obtained after the anneal process. The important parametersare the implant energy; implant dose; substrate material; orientation of the substratewith respect to the beam; temperature of the substrate; and the purity, uniformity, and the dose accuracy of the implant beam. This discussion will assume that the implant machine is capable of a

2.

115

ION IMPLANTATION A N D MATERIALS

2 -

Si -+ CaAr

10”-

-

8 6 -

I

5

7 -

a

THEORETICAL PROFILE

2

I

s

BUFFER LPE 2 -

1ol6-

0

0.1

0.2

0.3

0.4

0.5 d

0.6

0.7

0.8

0.9

(m)

FIG. 10. Camer concentration profiles for a Si-implanted LPE buffer substrate to a dose of 1 X 10” cm-2 at 400 keV and 350°C, annealed at 850°C for 15 min with a SiO, cap. Theoretical profile: 4 = 80% R , = 0.351 pm; A R, = 0.121 pm; D = 3.3 X cm2 sec-*.

high-quality ion beam with good uniformity and dose accuracy. This is the case for properly maintained implant machines now available. The orientation of the implanted substrate with respect to the ion beam during the implantation influences the carrier concentration profile of the implanted species. This is illustrated in Fig. 12 for Se implants into GaAs at different substrate orientations, as indicated in the figure. The standard implant and anneal conditions are used, with the exception of the substrate orientation. The angles indicated on the figure are the tilt angle and the rotation angle. The orientations listed are accurate to k 1 deg and therefore the (0 deg, 0 deg) orientation is not precise enough to be a true channeling direction in the lattice. With the tilt angle at 0 deg there is significant axial channeling (Wilson, 1976) to produce an abnormally deep profile. The narrowing of the profile as the rotation angle is increased, with the tilt angle held at lo”,is shown in Fig. 12. A substrate rotation of 30-45 deg from the ( 1 10)direction is necessary to eliminate planar channeling. These results are in agreement with those of Wilson and Deline ( 1980), where an extensive investigation of these effects is reported for Se, Si, S, and Te implants into GaAs. Through-dielectric-layerimplantations have been investigated to evaluate the effect of these layers on the channeling phenomenon and to evaluate the electrical‘properties of this implant technique. Results of this investiga-

116

C. A. STOLTE

10" 8 6

sa + GlA¶ 4

2

10': 8

-B "I

6 4

4

z

I D

*

2

10" 8

6 4

2

10" 0

0.1

0.2

0.3

0.4

d

0.5

0.6

0.7

(won)

FIG. 1 1. Camer concentration profiles for a Se-implantedLPE buffer substrate to a dose of 6 X loi2 cm-2 at 500 keV and 350'C, annealed at 850°C for 15 min with a Si,N, cap. Theoretical profile: q = 67%;R , = 0.172 pm; ARp = 0.067 pm;D = I. I X lo-" cm2 sec-I.

tion are shown in Fig. 13, where camer concentration profiles produced by Se implants through Si,N, are shown. One effect of the nitride film is to randomize the ion beam direction before it enters the GaAs substrate. This produces a profile corresponding to the random orientation implant direction even for the nominal (0 deg, 0 deg) direction. The decrease in the range of the implanted ion with increasing film thickness is due to the loss of ion energy as the beam travels through the nitride film. The doping efficiency of

2. 8

117

ION IMPLANTATION A N D MATERIALS

-

6 -

Sa-+GsAr

4 -

ROTATION)

(0.0)

/

1015 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

d (pd

FIG.12. Camer concentrationprofiles for Se implanted into LPE buffer substratesoriented as indicated on the illustration. The Se implant was to a dose of 6 X 10I2cm-2 at 500 keV and 350"C,annealed at 850°C for I5 min with a Si,N, cap.

the implant decreases for nitride thicknesses of 300 and 500 A as a result of Se implanted in the nitride film. There is a slight increase in the doping efficiency at the 800-A film thickness. This is believed to be due to the knock-on of the Si atoms from the nitride into the GaAs substrate, as predicted by the calculations of Christel et al. ( 1980). Through-dielectric implants are used in the fabrication of GaAs ICs by Rockwell International (Welch et al., 1980) with good results, and there seems to be no significant evidence of knock-on dopants in the implanted layers. The temperature of the substrate during implantation has an effect on the

118

C. A. STOLTE 10'8

8 6

Se +GaAn

4

2

1017 8 -

m

5

c

6

4

4: E

I 0

=

2

10l6 8

6 800 A 4

\ \

2

10''

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

d (wnun)

FIG. 13. Camer concentration profiles for Se-implanted through Si,N, layers, with the thicknessesindicated on the illustrationwith the substratesoriented in the nominal channeling cm-* at 500 keV and 350°C,annealed at direction. The Se implant was to a dose of 6 X 850°C for 15 min with a SIN, cap.

properties of the layers, which is dependent on the implanted species and the dose. For high-dose implants, > 1 X loL4cm-2, the combination of the incident ion flux and the substrate temperature determine the degree of implant-induced damage and, in extreme cases, whether or not the implanted region is driven amorphous. It is generally agreed that the subsequent activation of the layer is less if the sample is driven amorphous during the implant (Harris et al., 1972). At moderate implant doses, in the range 1 X loL2-1 X lOI3 cm-2, the effect of the implant temperature on the

2.

119

ION IMPLANTATION AND MATERIALS

characteristics of the implanted and annealed samples is dependent on the species implanted. This is illustrated in Fig. 14, where the doping efficiency and mobility are plotted as functions of the implant temperature for S and Se implants. In the case of the S, there is a significant effect above an implant temperature of 300°C; in the case of Se, the effect of the implant temperature is minimal. The majority of the Se implants reported in these investigations were performed at an implant temperature of 350°C. This is our standard condition. It should be emphasized, however, that for the implant dose required for formation of the channel regions by Se and Si implants, the properties of the annealed layer following a room-temperature implant are essentially the same as those produced by an elevated temperature implant. This is of practical significance due to the complexity of the apparatus required to heat the substrate during implantation.

6. ANNEALCONDITIONS It is necessary to anneal the implanted regions to remove the damage produced during the implant process to obtain layers with useful electrical properties. This requires anneal temperatures in excess of 800°C for n-type implants into GaAs. At these temperatures, it is necessary to control the loss

- 5000

-

r

n

- 4000

5 N

-6

-

3000

c

::I U

W

20

1'"O '0W

100

200

300

IMPLANT TEMPERATURE

400

500

O

("C)

FIG. 14. The influence of the substrate temperature during implantation on the doping efficiency r] and the effective Hall mobility p for Se and Si implants into LPE buffer substrates. The Se implants were to a dose of 3 X 10l2cm-2 at 500 keV, and the Si implantswere to a dose of 1 X lOI3 cm+ at 250 keV, annealed at 900°C for 15 min with a Si,N, cap.

120

C. A. STOLTE

of As from the surface during the anneal and at the same time avoid the in-diffusion of contaminates or the out-diffusion of the dopant species. There are numerous techniques reported in the literature to minimize the loss of As during the anneal, including the use of dielectric layers, capless and/or proximity anneal and transient anneal techniques. The technique used by a given organization is determined by the specific technology which each has developed. In the work reported in this chapter, the standard cap is the chemical vapor deposition (CVD) Si,Ni, dielectric layer described earlier. Other cap materials have been evaluated during this investigation including reactively sputtered AlN and Si3N, and CVD Si02. The A1N films had a very low oxygen concentration (lessthan 2%) as compared to the high oxygen content films reported in the literature (Pashley and Welch, 1975). It is believed that poor adhesion observed is due to the lack of oxygen. Reactively sputtered Si3N, films yielded good adherence but produced inferior electrical properties. This is due to a high ( 15%)oxygen concentration in these films. Thick, 7000-A CVD SiOz films grown in a Silox reactor at 450°C give better results for Si implants than the standard CVD Si3N, cap. The influence of the anneal cap for Si implants is illustrated in Fig. 15. The increased doping efficiency for Si implants using Si02 caps is due to the out-diffusion of Ga through the cap (Vaidyanathan et al., 1977), which produces Ga vacancies near the surface. These vacancies yield a higher Si on a Ga-site concentration compared to the Si on an As-site concentration, which results in a net increase in the n-type concentration for the amphoteric Si dopant (Bhattacharya et al., 1983).Although the doping efficiencyis higher using the oxide cap, as compared to the nitride cap, there can be a problem with the reproducibility of results if the Ga out-diffusion is not consistent from run to run. In the case of the nitride cap, there is no Ga out-diffusion; therefore, more consistent results can be expected. The opposite effect of the cap material is observed in the case of Se implants, as is illustrated in Fig. 16. In this case, the nitride cap gives better doping efficiencyas compared to the efficiency obtained with the oxide cap. The nitride cap used in these investigations has been very reproducible and has produced reliable results since the initiation of the work in 1975. The thermal expansion mismatch between the nitride film and GaAs produces cracks in the nitride for films thicker than approximately 2000 A. The surface quality of the samplesis unchanged during the anneal cycle using the standard 1500-A-thick cap. The nitride films produced are pinhole free; there is rarely evidence of a thermal etch pit due to a pinhole in the nitride film. An indication of the integrity of the nitride films is the successful annealing of samples with nitride films as thin as 300A with excellent surface properties and electrical characteristics. The through-nitride-im-

2.

121

ION IMPLANTATION AND MATERIALS

4t

Si + GaAs

2 -

1017 8 I

? I

-

6 -

e 4 -

ic

I D 2

2 -

10'8

-

0

I

1

I

I

I

1

I

I

I

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

d

Anneal cap

tlw

(mum)

p (cm2 V-l sec-l)

1500-A Si3N, 64 4250 7000-A Si02 95 4300 FIG. 15. Carrier concentration profiles for Si implants into LPE buffer substrates. The Si implants were to a dose of 1 X 10" cm-, at 400 keV and 350"C,annealed at 850°C for 15 min with 1500-A Si,N, or 7000-A SiO, cap, as indicated on figure.

planted layers represented by the data of Fig. 13 were annealed with the thin nitride films. The standard nitride films are deposited in a small research-type CVD reactor. Recent experiments using a commercial Si CVD reactor have produced nitride films with properties comparable to those produced in the small reactor. In the commercial reactor, the cap and anneal are done in one load by first depositingthe nitride film at 650"C, using silane and ammonia, and then ramping the temperature up to 850°C under H, and holding that temperature for 15 min to anneal the sample. This cap and anneal technique, capable of batch-annealing of large-diameterwafers, is a production process as opposed to the limited throughput of the small research CVD nitride reactor. The Santa Rosa Technology Center of Hewlett-Packard uses a Si02 anneal cap to anneal Si-implanted GaAs layers in a high-yield integrated circuit fabrication process (Van Tuyl et al., 1982).

122

C. A. STOLTE

8

-

6

-

4

-

Ss + GaAs

2 -

1017

-

8 -

-6

6

-

0

I

4

-

4

z I

2210'6

-

8 -

6 -

4 -

2 -

10'51 0

I

I

I

I

I

I

0.1

0.2

0.3

0.4

0.5

0.6

1 0.7

d (mn)

Anneal cap

r](W

,u (cm2V-1 sec-I)

1500-A Si,N4 67 4590 7000-A SiO, 57 4270 FIG.16. Carrier concentrationprofiles for Se implants into LPE buffer substrates. The Se implants were to a dose of 4.5 X lo1, cm-* at 500 keV and 35OoC,annealed at 850°C for 15 min with a 1500-A Si,N4 or 7000-A SiOz cap as indicated on the figure.

The use of capless (Kasahara et al., 1979; Kasahara and Watanabe, 1980), proximity (Immorlica and Eisen, 1976; Molnar, 1980), and/or controlled As pressure (Malbon et al., 1976) anneal procedures has proven useful in producing good results in many laboratories. These anneal procedures are similar to those used to protect the GaAs surface during the diffusion of

2.

123

ION IMPLANTATION A N D MATERIALS

dopants in a sealed ampoule or flowing gas technique. With these anneal techniques, it is necessary to eliminate the loss of As from the surface by an As overpressure. These techniques can yield better results since the stoichiometry of the sample can be controlled during the anneal. This flexibility can, however, lead to potential problems with the uniformity and consistency of the results if the process is not under complete control. One of the most significant parameters in the production of high-quality layers is the anneal temperature. This is illustrated for the case of Se in Fig. 17, where the doping efficiency and mobility are plotted as functions of the anneal temperature. The standard anneal temperature, 85OoC,used in these investigations is more than adequate to anneal the moderate-dose-implant layers used for the channel region of MESFETs. The situation is much 100-

-c

P

<

Se + GaAs

80 -

V

9u

60-

U U W

0

2

40-

0

,

20-

0

dl 9

1000

/'

.d

700

I

I

I

I

750

800

850

900

ANNEAL TEMPERATURE

,

(%I

(b) FIG. 17. Influence of the anneal temperature on the (a) doping efficiency q and (b) effective mobility ,n for Se implants into LPE buffer substrates to the dose indicated on the figure at 500 keV and 350"C,annealed at the indicated temperatures for 15 min with a Si,N, cap.

1 24

C. A. STOLTE

different when higher-dose implants are used, for example, for ohmic contact formation, as discussed below. An additional consideration in the selection of the anneal time and temperature cycle is the diffusion of the implanted species, and the diffusion of Cr, if Cr-doped substrates are employed, during the anneal process. The effect of diffusion of the implanted dopant is illustrated in Fig. 18, for the case of Se implants in GaAs. The carrier concentration profiles are calculated using the range and deviation data of Gibbons et al. (1975) and the diffusion of implanted ions. The starting condition is the assumed gaussian lo’* 8 6

Se -t GaAs 4

2

10”

8 6

F 4

-I c

2

10’6 8

6 4

2

1015 ._

0.00

0.10

0.20

0.30

0.40

0.60

0.60

0.70

d (CM)

FIG.18. Calculated atomic profiles for Se implanted into GaAs. The calculation assumes a gaussian profile with a projected range R, of 0.172 pm and projected deviation A R , of 0.067 pm, corresponding to an energy of 500 keV; and a dose of 3 X lot2cm-*. The values of Dt, the diffusion coefficient times the time, are given in the figure.

2.

125

ION IMPLANTATION AND MATERIALS

profile; a diffusion bamer at the interface between the GaAs and the anneal cap layer is assumed in the calculations. The anneal cycle has the effect of = (A Rz 21)t)1/2, where increasingthe A R, of the implant profile to A RpeW A R, is the profile standard deviation without diffusion, D is the diffusion coefficient at the anneal temperature, and t is the time duration of the anneal. Analysis of the experimental carrier concentration profiles, shown in Figs. cm2 sec-l 8- 11, yields diffusion coefficients of approximately 2.2 X for S and 1.1 X cm2 sec-I for Te at 900°C. The value for Si is 3.3 X cm2sec-', and for Se the value is 1.l X cm2sec-' at 850°C. The value of the diffusion coefficient for S is derived for S implanted into buffer material; S implanted in other types of material yields larger values. In order to minimize diffusion, the anneal time must be held as short as possible, consistent with good electrical characteristics. There is minimal improvement in the electrical properties for anneal times greater than 10 min under our anneal conditions; therefore, 15 min is the standard anneal time used in these investigations. In addition to these techniques, the use of transient annealing (Sealy, 1982)has been demonstratedin the laboratory for implants of Se (Chapman et al., 1982), Si (Kuzuhara et al., 1982; Arai, 1981), and for Zn and Si (Davieset al., 1982).This technique, in which the temperature ofthe sample is raised as high as 900°C in a matter of seconds and in which the entire temperature cycle is less than a minute, produces good activation and mobilities for concentrations up to the mid-1018range. The use of pulsed e-beam and laser annealing for higher-dose implants will be discussed in Section 8. In summary, the standard conditionsof implant and anneal were selected on the basis of the experiments described here. These conditions have been used in our implant investigations and in the preparation of materials for the investigation of GaAs ICs since 1975. This provides a consistent set of experimental procedures and allows meaningful comparisons of other parameters which influence the properties of the implanted and annealed regions and the performance of GaAs ICs.

+

7. SUBSTRATE INFLUENCE The formation of the channel region for the fabrication of GaAs MESFETs is a crucial step in the production of integrated circuits. The emphasis of the work described in this section will be on the comparison of various substrate materials used for the formation of active channel regions by ion implantation. The influence of the substrate material has been investigated using Se as the implant species and the standard implant and anneal conditions to allow meaningful comparisons of the different substrate mate-

126

C. A. STOLTE

rials. The influence of the starting material on the performance of circuits is discussed in Part IV. The standard material used in the majority of these investigations is the high-purity buffer layers grown on Cr-doped semi-insulating substrates. This starting material is the standard of comparison for the implant investigation as well as for the production of ICs. During the several years of this investigation,a large number ofdifferent substratesfrom a variety of sources have been evaluated, including material from outside vendors as well as materials synthesized at Hewlett-Packard. The electrical characteristics of the implanted and annealed layers to be considered are the doping efficiency, mobility, doping profile control, uniformity, and consistency of these characteristics as a function of the properties of the starting materials. The substrate material used for implantation can have a large influence on the profiles obtained. Substrate material that shows a significantthermal conversion during the anneal produces an abnormally high-concentration profile with a long tail region on the profile (see Fig. 8). This is the result of background donor impurities in the substrate material which become electrically active as a result of the Cr out-diffusion during the anneal cycle, as discussed in Part 11. An additional diffusion effect which also produces an abnormal profile is shown in Fig. 9. The long diffusion tail observed for S implanted into Cr-doped substrates is believed to be due to a vacancy-enhanced diffusion. In the case of S implants, the profile characteristics are very dependent on the substrate material. Another deviation from the predicted carrier concentration profile shape is observed using material grown under high-purity conditions, described in Part 11, with a small amount of Cr added to the otherwise high-purity melt to evaluate the influence of Cr. The profiles shown in Fig. 19 illustrate the changes produced by the addition of the amount of Cr indicated on the figure, The profiles for Se implants into the buffer layer and into high-purity, undoped materials are as expected; the implants into the Cr-doped substrates show anomalous behavior. The excess Cr incorporated in the substrate compensates the implanted donor, and the net effect is to decrease the magnitude of the profile in the tail regions. There is also a large decrease in the magnitude at the peak of the profile, which is larger than can be explained by the background concentration of Cr in the material. This discrepancy is due to the pileup of Cr in the damage region created during the implant, as observed using SIMS analysis (Evans et al., 1979). The profile data for the different substrate materials demonstrates that the choice of the substrate material is very important for the production of high-quality devices. The properties of the substrate material have a dramatic effect on the doping efficiency and on the camer concentration profile shape, as illus-

2.

ION IMPLANTATION A N D MATERIALS

127

Sa + GaAs

10151

0

I

I

1 0.4

0.2 d

I

0.6

(rd

FIG. 19. Carrier concentration profiles for Se implanted into the types of substrates indicated in the figure to a dose of 6 X 10l2cm-2 at 500 keV and 350"C,annealed at 850°C for 15 min with a Si,N, cap.

trated earlier. The properties of the substrate material also affect the mobility ofthe implanted and annealed layers, as reported in the literature (Stolte, 1975). The results of that experiment are summarized in Figs. 20 and 21. In Fig. 20, the experimental results used to obtain meaningful mobility measurements on implanted and annealed layers are shown. In this case, S was implanted into bulk GaAs, and the differentialvan der Pauw technique was used to measure the carrier concentration and Hall mobility profiles. This technique was used on a number of different substrate materials and provided the data to investigate the dependence of the mobility on the carrier concentration for different substrate types. The data from Fig. 20 are replotted in Fig. 21, where the mobility as a function of carrier concentration is plotted for this sample and for data obtained from other samplesin the same way. In Fig. 2 1, the results obtained for two implanted samples using the standard buffer material and four direct

128

C . A. STOLTE

10": 10";

P

-fi C

1017:

- 6000 7 -4000

i L N

i,,,, -2000 2000

10160

O.'l

0:2

OI3

014

015

0:s

5 a

0.71000 0.7

d (rm)

FIG.20. Carrier concentration and mobility profiles measured by the differential Hall technique for S implanted into a LPE buffer substrate to a dose of 2 X loL3cm-* at 250 keV and 350"C,annealed at 850°C for 15 min with a Si,N, cap.

implanted samples with different Cr concentrations are plotted; the Cr concentrations are indicated on the figure. Theoretical mobility versus carrier concentration curves (Rode and Knight, 1971) for the indicated compensation levels are plotted on the figure for comparison purposes. There is a large substrate influence on the mobility in the carrier concentration range of 1 X 10'' cm-3 due to the Cr concentration. This is the doping concentration used for MESFET channel implants. Thus, the excess Cr decreases the mobility and, therefore, will have a deleterious effect on the devices fabricated using this substrate material. These mobility results are in agreement with the calculations of Debney and Jay (1980). The influence of the substrate material on the mobility of implanted and annealed layers can be more conveniently measured using the surface van der Pauw technique to measure the Hall mobility on implanted and annealed samples. The mobility measured in this way is an effective mobility since it is measured on a nonconstant doping concentration. If the profile characteristicsfor the different substrates are reasonably consistent in shape and magnitude, the measured effective mobility is a meaningful indicator of

2.

129

ION IMPLANTATION A N D MATERIALS

1

S + GaAs

6000

c

I-

.?

4000

>

-

N

E

t

2000

0

0

0.8

1.6

2.4

3.2

4.0

n ( x 10’~crn-J)

FIG. 21. Hall mobility as a function of camer concentration for S implanted into the indicated GaAs substrates. The data are taken from Fig. 20 and from similar data obtained using the different substrates. The implant and anneal conditions in all cases are the same as indicated in Fig. 20. The dashed lines represent the theory of Rode and Knight (197 1).

material quality. Additional information is obtained when the Hall mobility measurements are extended to liquid nitrogen temperature. The results of an extensive investigation, spanning a time period of about three years (Stolte, 1980), of the properties of implanted and annealed layers in a large number of different substrate materials is summarized in Fig. 22. In this figure, the effective Hall mobility measured at room temperature and at 77°K for a large number of different substrate materials is plotted. In all cases, the standard implant and anneal conditions were used so that a meaningful interpretation of the results is possible. In this figure, the results are separated into regions representingthe different type substrates. The first three samples represent results obtained using high-purity LPE buffer material grown on Cr-doped material. These samples illustrate the desired mobility properties, namely, a high-room-temperature mobility, >4200 cm2V-I sec-I, and a significant increase in the mobility measured at 77°K. The next series of samples represent 17 ingots grown at the Optoelectronic Division of Hewlett-Packard using the 2-atm LEC technique described earlier. For each ingot, there are two data points: One represents the head of the ingot, the other the tail of the ingot. With the exception ofone sample, all the results show the desired mobility behavior. The sampleslabeled 9 and 10 were pulled using the in situ injection cell technique described in Part 11; the other ingots were compounded in a quartz ampoule and pulled from a quartz crucible. These 17 ingots were grown and processed over a 3-yr

I, , ,

, ,

,

1

,

,

I

,

,

, I L ,,I.,

I

,

'

L

2.

ION IMPLANTATION A N D MATERIALS

131

period and therefore demonstrate the consistencyof the growth technique as well as the consistency of the implant and anneal procedures. The next five samples of Fig. 22 represent ingots pulled by the same low-pressure LEC technique in a different facility of Hewlett-Packard, the Technology Center at Santa Rosa (SRTC). These samples show the desired mobility properties, with the exception of one sample. This demonstrates that the low-pressure technique is transferable and not unique to one reactor at one site. High-purity, undoped material from outside sources has also been evaluated using these standard implant and anneal techniques. The next three samples are from ingots grown in a Metals Research high-pressure LEC reactor using in situ synthesis. The next three samples represent ingots grown at the Naval Research Laboratory (Swiggard et al., 1979). These six samples have the desired mobility behavior and demonstrate that this semi-insulating material, produced without Cr doping, is of consistently high quality and is not restricted to one organization or to one technique. As noted in Part 11, other organizations have purchased the high-pressure LEC reactors and have pulled material of high quality, as has been reported in the literature (Fairman et al., 1981;Thomas et al., 1981;Hobgood et al., 1981). The effect of adding Cr to high-purity material is shown in the next series of 9 points in Fig. 22. In each case, the material wasgrown under high-purity conditions, except for the intentional addition of small, controlled amounts of Cr. The effect of the added Cr is to decrease the room-temperature mobility and also to produce a much lower 77°K mobility as compared to the high-purity material. The final six samples of Fig. 22 represent data obtained using Bridgman material from two different sources. These materials contain a small amount of Cryand this is reflected in the measured mobility for the implanted and annealed samples. The effect on the mobility of adding Cr to high-purity material is shown in Fig. 23, where the data of Fig. 22 are replotted as a function of the Cr concentration as measured by ASES. The sensitivityof this technique is 1 X lOI5~ m - those ~ ; samples with Cr below the detection limit are plotted to the left of the figure with no horizontal scale. From these data, it is seen that the addition of Cr, even in small amounts, degrades the mobility of the material in addition to influencing the carrier concentration profiles, as shown in Fig. 19. All the materials represented in Fig. 22 were thermally stable under the cap and anneal test conditions, with the exception of three of the commercial samples with low Cr concentrations. These showed a slight thermal conversion under the cap and anneal conditions. The consistency of the implanted and annealed layers produced in the high-purity ingots grown by the 2-atm LEC technique is very good. The data in Fig. 24 illustrate the consistency of the carrier concentration profiles for

132

C. A. STOLTE 5500 0

5000 -

r

b

4000-

oo O

Lo

'

0

O

S,.* GaAn

0

08,

0

o o o o o

..

a

-6

.

A A

0

n o 3500-

3000 -

UNDOPED c-

I

2500

A'

. 0

Cr DOPED

A

.,

1

17

FIG.23. Hall mobility measured at 300°K (0,HP; other) and at 77°K(0,H P A, other) as a function ofthe Cr concentration measured in the substrate material by ASES. The samples represented on this figure are those of Fig. 22.

I

?

-

I

RANGE OF PROFILES FROM41 WAFERS

a

L

I

a

L

d (rm)

FIG.24. Carrier concentration profile uniformity for Se implanted and annealed under the standard conditions for 2 1 ingots grown using the 2-atm LEC technique. These samples are the HP high-purity LEC and the HP SRTC samples indicated in Fig. 22.

2.

ION IMPLANTATION AND MATERIALS

133

4 1 wafers taken from 2 1 high-purity LEC ingots. The carrier concentration profiles are very reproducible with a very small range of variation. These data, taken over a period of three years, also illustrate the consistency of the implant and anneal procedures. Another indication of the uniformity and consistency of the implant and anneal procedures in different materials is that provided by a measurement of the sheet resistance. The results presented in Table IV were obtained by a noncontact microwave absorption measurement of the sheet resistance. These data represent four samples implanted into four different substrate materials, including one buffer layer and wafers from three different highpurity ingots. The uniformity over a single wafer is very good, Q less than 3.1 %, and the wafer-to-wafer consistency is also very good, Q less than 3%. A more practical measurement of the uniformity and consistency of the implanted and annealed properties of layers produced for MESFETs is a measurement of the saturated source-drain current prior to the gate step in the circuit fabrication process. Data for 16 buffer layer implants and for 12 direct implants into high-purity material are given in Table V. There is good uniformity, Q less than 4%, on each wafer as well as good wafer-to-wafer consistency, Q less than 6.1%. In addition, there is good agreement in the values of the saturated source-drain current for the two different material types. This uniformity and consistency are also experienced in the integrated circuits fabricated using these materials and implant procedures, as described in Part IV. The preceding paragraphs have demonstrated the quality and consistency of implanted and annealed layers that are suitable for the formation of channel regions of MESFETs. The techniques used are compatible with a TABLE IV UNIFORMITY OF IMPLANTED WAFERS'

p-wave n1.q measurements Sample No.

Substrate

p, (Q/sq)

Se 320 Se319 Se318 Se 317

LPE Buffer F402No. 13 F403No.70 F405 No. 59

24 1 252 257 256 ~~

Ave

252

0

(96)

1.8 1.5 2.8 3.1 ~

2.9

a Implant: Se, 500 keV, 6 X 1OI2 cm-*; anneal: Si,N,, 850°C, 15 min.

134

C. A. STOLTE TABLE V UNIFORMITY OF MESFET IMPLANTS (Im,MEASUREMENTS)

Number of 1 X 1 in. wafers

Substrate ~

High-purity LPE buffer High-purity bulk

Average uniformity on wafer (%)

Wafer to wafer uniformity IDss(mA)

.(%)

~~

16 12

3.2

85.8

4.0

83.9

5.0 6.1

selective implant procedure as is needed, and used, for the production of complex integrated circuits. An example of the application of these techniques is the production of integrated circuits fabricated in both the high-purity buffer materials as well as in high-purity, undoped LEC material using the te.chniques described. The performance and properties of these circuits are described below in the device results section. 8. HIGH-DOSE IMPLANTS

High-dose implants can be classified into two types, depending on the intended application. The first includes those used to produce regions with low sheet resistance, less than 150 fJ/sq. The low sheet resistance regions are used to decrease the source -drain resistance of MESFETs and to produce low resistance passive components. The technology for the formation of these regions includes the use of high-temperature (greater than 9OO0C) anneal temperatures and special cap or capless techniques to preserve the surface at the higher anneal temperatures. Dual-speciesimplants (Ambridge et al., 1975; Stolte, 1977; Woodcock, 1976; Stoneham et al., 1980)designed to increase the doping efficiency of high-dose implants by stoichiometry control have been used to decrease the sheet resistance. Multienergy, singlespecies implants yield a reduction of the sheet resistance by producing an increased carrier concentration profile depth. In contrast to the requirements for channel-region implants, the profile control, mobility, and consistency of the implanted and annealed regions are of secondary importance to the requirement for low sheet resistance. The second application of high-dose implants is the formation of ohmic contacts by an implant and anneal procedure without the use of alloyed contacts. This application of ion implantation has been investigated, and good progress has been made using laser beam and e-beam annealing. The major improvement to be gained by nonalloyed contacts is that the same metal used for the MESFET gate can be used for the ohmic contacts. This simplifiesthe process and would improve the performance and reliability of

2.

135

ION IMPLANTATION A N D MATERIALS

the integrated circuits. The formation of these high carrier concentration regions is discussed below. Increasing the dose of the implant species to obtain lower sheet resistance decreases the doping efficiency, as indicated in the compilation of data shown in Fig. 25a. In this figure, the sheet carrier concentration, measured by the van der Pauw technique, is plotted as a function of the implant dose for three different species. The general trend in all the data is the same, i.e.,

4" 100

Sn

'

10 10'2

I

1013

1 I I I

1014

,N

I

1 1 1 1

1015

I

I l l 1

10'6

I

I

Ill 10"

bm-2)

(bl FIG.25. Total sheet camer concentration N, (a) and sheet resistivitypa(b) as a function of the implant dose for Si (50 keV), Se (100 keV), and Sn (250 keV) implanted into LPE buffer substrates at 35OoC,annealed at 850°C for 15 min with a SipN, cap.

136

C. A. STOLTE

the doping efficiency decreases to less than 1% at the high end of the dose range. Investigations of this effect have demonstrated (Lidow et al., 1978a) that the decrease in doping efficiencywith increasing dose is due to saturation solubility of the dopant in GaAs.The maximum camer concentration is limited to the solubility limit at the anneal temperature. The effect of increasing the implant dose on the sheet resistance of the implanted and annealed layers is demonstrated for the same set of samples in Fig. 25b. The decrease of the sheet resistance as the peak concentration approaches saturation is due to a broadening of the profile of the electrically active dopant, as demonstrated in Fig. 26. Here the camer concentration profiles for Si implants are plotted for differentimplant doses. These data were taken using the differential van der Pauw technique. The mobility for these implanted and annealed layers was very low at the surface, indicating a heavily damaged region, which results in a very low-doping efficiency in the near surface region. The maximum carrier concentration obtained at the ~, anneal temperature used in these experiments, 85OoC,is 4 X lo1*~ m - and the decrease in the sheet resistance with increasingdose is due mainly to the deeper carrier concentration profile at the higher dose. The atomic concentration profile, measured by Auger spectroscopy, for a dose of 2 X 10l6cm-2 is shown in the figure. The implanted dopant in excess of the saturation solubility is not electrically active. The more extensive experimental data and theory reported by Lidow et al. (1980) are in agreement with this simple model. The effect of increasing the anneal temperature on the sheet carrier concentration and sheet resistance is shown in Fig. 27 for Se implants. In these experiments,the dual dielectriccap developed by Lidow et al. (1978b) was used to prevent the deterioration of the GaAs surface at the elevated temperatures. The increase of N, with temperature agrees with the saturation solubility model proposed by Lidow et al. (1978a). The highest temperature used, 1 lOO"C, resulted in a peak carrier concentration of 1 X loL9 cm-) and a sheet resistance of 30 n/sq.The technological problems at these extreme temperatures preclude the technique as a practical solution for the production of high concentration regions. The doping efficiency at high-implant doses can be increased by controlling the stoichiometry of the substrate by dual-species implants. The data of Fig. 28, obtained in the investigation by Stoneham et al. ( 1980), illustrate the use of a dual-species implant, Se plus Ga, to increase the peak carrier concentration and therefore decrease the sheet resistance of the implanted and annealed layers. In the investigation of Stoneham, a sheet resistance of 9 Q/sq was obtained using a Si plus P dual-species implant annealed at 1000°Cfor 15 min. The most reproducible technique for the production of low sheet resist-

2.

137

ION IMPLANTATION A N D MATERIALS

r

2 -

1019

-

8 r 7 6 -

-ga r

4 -

I 0

z

2 -

10’8-

8 6 -

4 -

p

DOSE = 2 x

\

\ \

\ \

t

DOSE =q2=x3.2% 1014 cm-*\ \\

p*=3B5s2lSs

I

1

\

I

2 -

0

DOSE = 2 x 1015 Cm-f

A

L

q-1.2% p,=115~llx1 I

I

I

I

I

1

0.1

0.2

0.3

0.4

0.5

0.6

d (mm)

FIG.26. Camer concentrationprofiles and atomic concentration profile for Si implanted into LPE buffer substratesat 100 keV to the doses indicated on the figure, annealed at 850°C for 15 min with a Si,N, cap. The doping efficiency q and the sheet resistance p, measured for each dose are indicated on the figure.

ance regions is by implantation of a light species, e.g., Si, in multienergy steps to produce a high carrier concentration, near the solubility limit, which extends over a deep region. An example of this type of implant is shown in Fig. 29, where the results of triple-energy Si implants into buffer LPE and high-purity bulk substrates are shown. The sheet resistances for these im-

138

C. A. STOLTE

t

Se +GaAr

850

I

I

I

I

900

950

1000

1050

1100

ANNEAL TEMPERATURE ("C)

FIG.27. Sheet carrier concentrationN, and sheet resistance p,, as a function of the anneal temperature for Se implants into LPE buffer substratesto a dose of 1 X 10" cm-* at I50 keV and 350°C for 15-min anneal times with the dual dielectricSi,N,/SiO, anneal cap.

plants were less than 65 Q/sq. The integrated circuits produced for the MSI circuits described by Liechti et al. (1 98 1) employ a source-drain implant of 500-keV Si at dose of 1 X lOI3 cm-2 in the source and drain region in addition to the standard Se channel implant, 500 keV, 6 X loL2cm-2, to yield the doping profile shown in Fig. 30. The sheet resistance of this layer is 120 Q/sq. These results demonstrate that it is possible to routinely produce layers with sheet resistances less than 150 Q/sq using multienergy Si and/or multispecies implants and standard 850°C anneal procedures. The second application of high-dose implants, nonalloyed ohmic contact formation, has received increased attention over the last few years. The majority of this work has used transient annealing techniques, either e beam or laser beam, to activatethe high-dose regions. The bibliography by Stevens (1978) contains references on the general topic of laser processing of semiconductorsprior to 1979. The investigationsat Lincoln Laboratories(Fan et al., 1979) and Hughes (Anderson et al., 1980) using cw irradiation indicated that the use of cw laser annealing of the implanted region was not promising.

2.

139

ION IMPLANTATION A N D MATERIALS

a z I 0

z

1017

I

I

10'6

I

1

I

1.o

0.5

0

d (pm)

FIG.28. Camer concentration profiles measured by the differential Hall technique for Se and Se Ga implants into high-purity bulk substrates to a dose of 1 X 10l6cm-2 for each species at an energy of 200 keV, annealed at 1000°Cfor 15 min using a SiO, anneal cap. (Data supplied courtesy of Stoneham ef al., 1980.)

+

10'88 6 -

-7

4 -

2

10'78 -

-f 1

1

I

I

1

I

____-------

I

I

2 -

BUFFER LPE

2 6 4 Si -+ GaAr

2 10'6-

I

I

I

I

1

I

HIGH-PURITY BULK

-

-

140

C. A. STOLTE

So + Si --t GaAs

10'6' 0

I

I

I

I

I

0.1

0.2

0.3

0.4

0.5

I

I

I

0.6

0.7

0.8

I 0.9

1.0

d (run)

FIG.30. Camer concentration profile for dual species Se, 6 X lo1*cm-* at 500 keV, and Si, I X loi3cm-2 at 500 keV, implants, annealed at 850°C for I5 min using a Si,N, cap.

This is due to the narrow range of parameters over which reasonable dopant activation occurs without severe surface damage. Transient anneal techniques that result in good activation of the highdose implants employ Q-switched lasers (Barnes et af.,1978; Pianetta et af., 1980a; Sealy et af.,1978)or a pulsed e beam (Mozzi et af.,1979;Pianetta et af.,1980b) to produce short bursts of energy in the 0.5 - 1.O-J-cm-* range. The short burst of radiation melts a thin layer, less than 0.4 pm at the GaAs surface. This melt duration of less than 300 nsec is followed by a rapid regrowth of the GaAs. During the rapid regrowth, 85% of the implanted species is incorporated into the lattice, as demonstrated by RBS measurements using Te as the implant species (Amano et af., 1980); electrical measurements indicate that 20% of the implanted Te is activated. This low activation is accompanied by a mobility that is low by a factor of aproximately 2 compared to the value expected at the measured dopant concentration. It is possible to activate high-dose implants of Te, Se, Si, and Sn using either a pulsed e beam or a Q-switched ruby laser anneal technique. Typical results obtained using a pulsed e beam are shown in Table VI (Pianetta et al., 1980a), where the results for high-dose Se implants are shown. As indicated, the sheet resistance is less than 50 n/sqand, more importantly, the surface carrier concentration, measured using the differential van der Pauw ; samples have had surface method, is greater than 1 X 1019~ m - ~other ~ . high values of surface carrier concentrations as high as 6 X loL9~ m - The concentration have been verified by measuring the contact resistance of unalloyed metal contacts on the laser annealed layers that were formed by

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ION IMPLANTATION A N D MATERIALS

TABLE VI ELECTRICAL AND ALUMINUM CONTACT PROPERTIES OF GAASTRANSIENT ANNEALED LAYERS ~

van der Pauw Implant conditions

TLM

(Qlsq)

n, (cm-2)

n at surface (~m-~)

Pattern number

(Q/sq)

(Qcm2)

35

9.1 X 1014

> 2 X lOI9

1

39.6

5.8 X 10”

2

48.6

2.3 X lod

3

30.8

5.5 X 104

4

42.1

5.4 X lo4

PS

p,

rc

~

5 X lOI5 cm-2

250-keV Se

5

x loi5cm-2

43

5.3 X loi4

> I X 1019

50-keV Se

the evaporation of metal contacts at room temperature. The values in Table VI are in agreement with those predicted by the theory of Chang et al. ( 1971) assuming a bamer height of 0.6 eV and the measured surface concentration. Layers with contact resistances as low as 2 X 1O-’ IR cm2have been obtained using nonalloyed CrAu contacts to high-dose laser annealed GaAs. The sheet camer concentrationdecreases rapidly during post-laser anneal heat treatments, as illustrated in Fig. 3 1 for the case of high-dose Te implants

FIG. 3 1. The change in the sheet camer concentration as a function of the post-laser anneal isochronal heat treatment for a Te implant into an LPE buffer layer to a dose of 5 X IOl5 cm-2 at 250 keV.

142

C. A. STOLTE

into GaAs (Pianetta et al., 1980a). The stability of the carrier concentration of these layers has been investigated (Amano et al., 1980; Pianetta et al., 1981) to aid in the understanding of the anneal process. There is a two-step decrease in carrier concentration during the isochronal anneal following laser annealing. The first rapid drop is not accompanied by a major change in the lattice site occupancy of the implanted species in spite of the large decrease in the carrier concentration. The activation energy of the first step is 1.3 eV, suggesting a vacancy diffusion mechanism. The second decrease beyond 500°Cis accompanied by a decrease in the Te occupancy on lattice sites and the formation of dislocation loops and Ga,Te3 precipitates (Pianetta et al., 1981). The practical implications of this lack of thermal stability of the carrier concentration have been investigated in the laboratory by Pianetta. Results of that investigation are presented in Fig. 32, where the sheet carrier concentration N,, the sheet resistance ps, and the contact resistance R, are plotted as a function of time during a 250°C stability test. The contact

2x10" 10-6 G-

I

5" a

10-7

t

101 0

I

200

I

400

I

600

I

800

I

1000

I

1200

11 30

TIME Ihr I FIG.32. The change in the sheet camer concentrationN,, the contact resistanceR,, and the sheet resistance p,, as a function of time at 250°C for a ruby laser annealed sample implanted with Se in LPE buffer material to a dose of 5 X lOI5 cm-* at 250 keV.

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143

resistance changes rapidly for short times and then increases with a time constant of about 5000 hr. This stability is better than that reported for e-beam annealed AuGe-Pt ohmic contacts (Lee et al., 1981). The values of contact resistance, maintained during the heat treatment, taken with the lOO-Q/sq value for the sheet resistance, indicate that these contacts would be acceptable for MESFET applications. To apply the laser mneal technique to the fabrication of circuits, it is necessary to laser anneal the contact regions selectively while protecting the channel regions. The laser annealing of channel region implants produces very high-resistivity regions due to a large defect density produced during the rapid regrowth during the laser anneal process. The techniques for selective laser annealing have been investigated in these laboratories. The procedure developed to provide this selective anneal uses an A1 mask to reflect the incident laser radiation to protect the quality of the channel regions. MESFETs employing selectively laser annealed source-drain nonalloyed contacts have been fabricated. The dc characteristicsof these devices are comparable to devices fabricated using standard alloyed ohmic contacts. The long-term stability of these devices is under investigation.

IV. Device Results 9. IC FABRICATION The materials and implantation technology described have been used to produce GaAs ICs of true MSI complexity. Examples of these circuits are the pseudorandom-bit-sequence generator (PRBS) (Fig. 33) operating at 2.5-Gbit/sec (Liechti et al., 1982b) and the MSI word generator (Fig. I), which operates at data rates as high as 5 Gbit/sec (Liechti et at., 1982a). These circuits employ selective ion implantation into high-purity LPE buffer layers, grown on Cr-doped substrates or grown on high-purity substrates, or implants directly into high-purity substrates. Figure 34 shows cross sections of a transistor, a diode, and interconnectionsas implemented in these circuits. Figure 35 illustrates schematically the process steps used in the fabrication of the ICs. The MESFET channel is formed by selective ion implantation of 500-keV Se ions into the substrate (heated to 350OC) to a dose of 6 X 10l2 cm-2 using an 0.8-pm-thick A1 mask to define the implanted regions. The substrates are implanted bare; no through-dielectric implants are used. A second selective Si ion implant is used in addition to the Se implant in the active area of diodes and under the ohmic contact regions of the transistors to lower the sheet resistance. For this purpose, Si is implanted at 500 keV to a dose of 1 X lOI3 cm-2 using an A1 mask with the substrate at room

144

C. A. STOLTE

FIG. 33. Photomicrograph of the 2.5-GHz PRBS generator. The chip measures 1 . 1 X 1 . 1 mrn and contains 400 MESFETS and 150 Schottky diodes.

S

0

,,

A

C

2.

ION IMPLANTATION AND MATERIALS

145

GaAs f UNDOPED SUBSTRATE

I

r

N-

Cr-Pt-Au-Ni

@

r-l

GATE CONTACT

I

T ,

,

SiO2 LAYER

I

y Ti-Pt-Au

FIG.35. Process steps used for the fabrication of the GaAs circuits shown in Figs. 1 and 33. The details of the fabrication process are discussed in the text.

temperature. After removal of the A1 mask, both implants are simultaneously annealed at 850°C for 15 min using the Si3N4cap. The resultant doping profile under the gate is shown in Fig. 11; this region has sheet resistance of 325 O / q . The dual species, Se plus Si, implant region profile is shown in Fig. 30. This region has a sheet resistance of 120 O/sq. The ohmic contacts used are processed in a conventional way by a multilayer evaporation of NiCr, Au, Ge, and Au, lifting of the excess metal outside the contact patterns, surface capping, and alloying. The resulting specific contact resistance is typically 2 X 10” $2cm2, and the sheet resist-

146

C. A. STOLTE

ance of the alloyed Au-Ge metal film is 1.3 n/sq.As indicated, ohmic and Schottky contacts have been produced during the same fabrication step by use of the very high doping concentration layers produced by laser annealing of high-dose implants. Laser-annealed contacts have not been used in the fabrication of the ICs described here. The gate processing step is by far the most crucial part of the processing sequence used to produce the integrated circuits. Here, high resolution is required in the lithography of thousands of l-pm gate lines printed on the wafer. This is a very complex procedure which, in summary, is as follows: The gate lines are fabricated by lifting evaporated metal with a combination of two positive resist layers. Prior to the gate-metal evaporation, the channel region is precisely etched to a depth of 0.12 pm,leaving a gate trench above the FET channel. This trench lowers the level of the Schottky contact below the unpassivated GaAs surface. This gate geometry yields a lower series resistance of the source and drain compared to a planar structure with the same gate-cutoff voltage. It also reduces the modulation of the drain current due to changing depletion layer widths at the free surface during switching transients. Finally, it allows adjustment of the gate-cutoff voltage during processing. The circuits are completed by an intermetal dielectric deposition, via patterning, and the deposition and patterning of the second metal. The circuits processed as described above, e.g., the PRBS circuit shown in Fig. 33, have a 30% functional yield. This process technology differs in some fundamental ways from that used at Rockwell International (Welch et al., 1980). In the Rockwell process they implant through a Si,N, dielectric layer and maintain that passivation throughout the process, except for metallization regions. They do not use the recessed gate process and therefore rely on a well-defined materials characterization and implant control to provide the needed control of the device parameters. This has produced a high-performance 8 X 8 multiplexer circuit that contains over 1000gates on a 2.7 X 2.25-mm chip (Lee et a/., 1980). 10. IC PERFORMANCE The 5-Gbit/sec GaAs word generator IC shown in Fig. 1 consistsofan 8 : 1 parallel-to-serial converter, timing generator, control logic, and emitter coupled logic (ECL) interface networks. The circuit generates multiple 8-bit words whose number can be dynamically controlled. In the circuit, data from eight parallel input channels are amplified and applied to a tree of 2 : 1 multiplexers that connects the eight inputs to a single output in a time-multiplexed sequence. The key featuresof the 2 : 1 GaAs multiplexer used in the circuit are its speed and its capability of generating clean waveforms with fast transition times. Even at a 5-Gbit/sec data rate, the circuit is perfectly

2.

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ION IMPLANTATION A N D MATERIALS

stable; the waveforms are very clean, with no glitches and with negligible overshoot, ringing, and time jitter. The voltage rises and falls with 100-psec transition times. By changing the clock frequency, the output data can be varied from 1 kbitlsec up to 5 Gbitlsec while maintaining perfect stability at all frequencies. This circuit is described in detail by Liechti et al. (1982a). The PRBS generator (Fig. 33) is based on a 10-stage shift register whose seventh- and tenth-stage outputs are fed back to the first-stage input via an exclusive OR gate. The circuit generates the maximum-length sequence of 1023bits. The shift register stages are complementary-clockedmaster - slave flip-flops. The 10-stage PRBS generator operates in a stable and reliable mode for clock frequencies ranging from several kHz out to 2.5 GHz. Transition times of the pulses generated are 1 10 psec, and the output voltage swing into 50 R is 1 V. The waveforms generated by this circuit are shown in Fig. 36. For a detailed discussion of this circuit, see Liechti et al. (1982b). These circuits all use buffered FET logic (BFL),which allows the maximum speed of operation for a given geometry, e.g., a propagation delay, measured with a 5-stage ring oscillator, of 56 psec for a fan out of one with a power dissipation of 15 mW/stage, power - speed product equal to 850 f J/gate. Additional information on the design, fabrication, and operation of these and other digital IC circuits is contained in the report by Liechti et al. (1982~). The 8 X 8 multiplier circuit fabricated at Rockwell International (Lee et al., 1982b) has a multiplier speed of 5.3 nsec. The gate circuits used in this

c: 0 Ul

PRBS (2,5 Gbit /sec)

SYNC. PULSE

TIME (2 nseddiv) FIG.36. Output waveforms of the synchronization pulse (bottom) and PRBS at 2.5-Gbit/sec data rate (top).

148

C. A. STOLTE

circuit have a propagation delay of 150 psec and a speed- power product of 3 10 fJ/gate. This circuit employs Schottky-diodeFET logic (SDFL), which operates a lower-power dissipation and requires less total gate area than BFL (Eden et al., 1979). This decrease in power dissipation is offset by the increase in the propagation delay for this type logic, as presented in Lehovec and Zuleeg (1980). Analog monolithic GaAs ICs have been fabricated, which operate in the gigahertz frequency range, including a 4-GHz amplifier (Van Tuyl, 1978), a 4-GHz frequency divider (Van Tuyl et al., 1977), and a 1.5-GHz signal generator (Van Tuyl, 1980). The review article by Bosch (1 979) contains a review of GaAs microwave devices and an extensive list of references on this topic. 1 1. BACKGATING

One of the problems encountered in the design, fabrication, and successful reduction to practice of complex circuits has been the phenomenon of backgating (Itoh and Yanai, 1980; Kitahara et al., 1980; Immorlica et al., 1980). This effect can be described as a change in the drain current of a MESFET caused by the application of a negative potential on a pad in the vicinity of the transistor (Bimttella et al., 1982). The effect is caused by a change in the depletion width of the channel, which is not controlled by the gate on the surface of the channel region but by a space-chargelayer (Hower et al., 1969)present at the interface between the active layer (the implanted channel region) and the substrate material. The degree of backgating typically varies with location on a single wafer and changes from wafer to wafer. This variation results in major problems in circuit design due to the uncertainty of the source-drain current under different circuit bias conditions. It has been demonstrated by Kocot and Stolte (1982) that backgating is caused by an excess negative charge on the substrate side of the interface between the active layer and the semi-insulating substrate and a corresponding net positive charge on the active layer side. The origin of these charges is illustrated in Fig. 37, where the band diagram for Cr-doped and for high-purity substrates is shown. In the case of high-purity material, the deep level is the EL2 electron trap. In the bulk region remote from the interface, the EL2 level is partially ionized since the Fermi level is near mid-gap and slightly above the trap level, as required for the material to be semi-insulating. In the region of the interface, the EL2 level traps electrons from the shallow donors in the active layer and therefore produces a negative charge region in the substrate, which induces a positive charge layer in the active region as shown in Fig. 37. It is this space-chargeregion that is modulated to reduce the drain current when a negative voltage is applied to the back side of the channel. The case for the Cr-doped material is similar; in this case, the Cr level, a

2.

ION IMPLANTATION A N D MATERIALS

149

SPACE CHARGEREGION

--

SUBSTRATE

I

-

I+ 1

I

I 1

II

I

I

I

IMPLANTED ACTIVE LAYER

CrZ+ -&-*-&*&-&-A&-

F.L. -&I--L-*.L--cI-A EL 2

V.B.

I

I 1I

I

t

1

FIG.37. Band diagram for the backchannel region of a MESFET illustratingthe origin ofthe space charge region responsible for the phenomenon of backgating.

deep hole trap, is only partially occupied in the bulk; therefore, in the interface region, electrons are captured by the Cr2+level to form a negative space-charge region in the substrate and the positive region in the active layer. In the case of buffer layers on either kind of substrate material, the same model holds except that the electrons that fill the traps originate in the buffer layer and produce a much wider depletion width. The use of buffer layers will reduce the magnitude of backgating, but if the depletion layer in the buffer reaches the active layer under the biased condition, the devices will still show backgating. The conductance deep-level transient spectroscopy (DLTS) technique (Borsuk and Swanson, 1980; Alderstein, 1976) has been used in our investigations to analyze the long-time constant change of the source-drain current following the application of a negative backgate bias. The levels detected in these experiments are consistent with the activation energiesand capture cross sections reported in the literature for these levels (Martin, 1980). This technique is being used in the continuing investigation of the phenomenon of backgating. Measurements of the spectral response of the source-drain current with a backgate bias also support the model and, in addition, explain the light sensitivity observed. The type of substrate material used and the concentration of deep traps will determine the magnitude and the spectral dependence of backgating. The data of Fig. 38, obtained by Diesel et al. (1980), show the dependence of the back-side channel-depletion width on the Cr concentration. These experimental data were obtained by measuringthe change in the width, A W, of the space-charge region, using the standard C- V profile technique, as a

150

C. A. STOLTE

25 x

0

0.5

1.0

1.5

2.0

2.5

3 . 0 10” ~

CHROMIUMCONCENTRETION (cm-3)

FIG.38. The change of the depletion width of the backchannel space charge region per volt of applied potential to the back side of the semi-insulatingsubstrate as a function of the Cr concentration in the substrate. (Data supplied courtesy of Diesel et al., 1980.)

function of a change of the back-side voltage A I/ on samples of different Cr concentration. A survey of the results obtained in different substrate material types is summarized in Fig. 39, where the average and standard deviation of the magnitude of backgating are presented. As predicted by the model, the buffer layer devices produced the least backgating, with the exception of the Cr-doped sample, which was chosen to be closely compensated to test the validity of the backgating model. The model predicts that if the substrate material is very closely compensated, the number of excess negative charges in the interface region between the active area and the substrate will be very small. In this case, no appreciable space-charge region will be present at the interface, and hence the backgating effect will be small. This has been experimentally verified (Kocot and Stolte, 1982), and additional experiments are in progress to further evaluate the effect of closely compensated material. The magnitude of backgating has been reduced by DAvanzo (1982) through the use of proton-bombardment isolation in the insulating regions of the circuits. The proton bombardment improved the isolation between components of circuits produced by direct implantation into high-purity material and, as an additional effect, decreased the magnitude of backgating. This reduction of backgating is interpreted to be the result of decreasing the

2.

151

ION IMPLANTATION AND MATERIALS

I ISD 2 mA @Vs=OV 1.2

1.0

-

0.8

-

0.6

-

> ? "

HIGH PURITY

BUFFER ON CR

CR

-

It

e,

-2 a

I

0.4 -

0.2

0

f I

1

1 ~

1

1

1

1

1

1

1

1

1

1

1 I I I 1 1 1 l 1

UFFEP ON HIGH 'URITY

I

I I

SAMPLE NUMBER

FIG. 39. The change of the source-drain current as a result of the application of -4V potential applied 15 pm from a MESFET for the different substrate types indicated in the figure. The average value of the change measured for about 30 devices on each wafer is indicated by the point on the figure; the standard deviation of the measured values is indicated by the bars.

potential which appears at the back side of the channel for a given sidegate potential by changing the trap-fill-limit voltage (Lee et al., 1982a). The degree of backgating has been linked to the light sensitivity of the drain current by Diesel (1980). He showed that the light sensitivity was dependent on the Cr concentration in the same way as the magnitude of backgating. In addition, it is reasonable to expect that the effect of gain compression seen in high-power devices is related to the charging and slow emission from the deep traps in the substrate material. Other effects are observed in the performance of GaAs ICs. For example, lag effect and premature power saturation are dependent on the deep trap density in the substrate material (Immorlica et al., 1980)as well as by the effects of surface charging. These observations indicate that it is necessary, in addition to producing stable semi-insulating material, to control the presence and relative concentration of the deep traps in the substrate material. V. Summary

The work reported here has demonstrated the current state of the art in materials preparation and ion implantation technology required for the

152

C . A. STOLTE

production of MSI GaAs ICs. The materials technology has made great strides during the last four years; there is now available an ample supply of high-quality materials to provide the necessary starting materials for the further advancement of IC technology. In the area of ion implantation, the necessary techniques and procedures are available to allow the production of selectively implanted regions, with adequate quality and reproducibility to satisfy the needs of today’s ICs. The growing degree of complexity and the increased degree of integration, beyond the several hundred transistor level that is now being integrated on a chip, will require further improvementsin the materials and implantation technology. In the area of materials, the question of the importance of the dislocation density has not been resolved. Dislocations in the channel region could, for example, result in increased gate current leakage, a decrease in the gate breakdown voltage, and produce diffusion spikes of the implanted species during the anneal cycle. These effects will become increasingly important as the relative area of the channel region increases. It is expected that, as the density of the devices increases, it will be necessary to reduce the dislocation density from the 1 X lo4to 1 X 10s-cm-2range, which is now available by at least an order of magnitude in order to provide reasonable yields at higher integration levels. At the present time, it appears that the dislocation density is not the limiting factor on yield, but that can be expected to change in the future. Another requirement for the realization of large-scale integration (LSI) will be the availability of large, at least 76-mm diameter, wafers grown in the [ 1001direction, with an orientation flat, to allow the use of modem processing equipment. Wafers with these characteristics have been successfully pulled by several laboratories with the desired high purity (Thomas et al., Chapter 1, this volume; Kirkpatrick et al., Chapter 3, this volume). Additional concerns now being formulated are rapidly becoming firstorder effects rather than second-order effects. These problems include the influence of the starting material and the implant and processing procedures on the phenomena of backgating, noise, gain compression, light sensitivity, and the reliability of GaAs ICs. As the technology matures, these and other as yet unidentified problems will occupy the efforts of the research laboratories. In the past two years, great strides have been taken to increase the technology of GaAs ICs in all phases of its development: The production of improved quality material in quantities that will support the development efforts; the maturing of the implant and anneal technology to the point where it is more than a laboratory technology; and sophisticated IC design, where true MSI complexity circuits have been demonstrated with practical yields. Finally, the process technology necessary to produce these circuits has been demonstrated.

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153

The MSI, < 1 X lo3 gate/chip, circuits described in this chapter were fabricated using depletion-mode MESFETs in BFL and in SDFL circuit configurations. The device structures and circuit types that can be used to extend the level of integration are described in detail in the articles by Eden et al. (1979), Eden (1 982), Lehovec and Zuleeg (1980), and Bosch (1980). It is generally agreed that the next step to LSI, 1 X lo3 to 1 X lo4gates/chip, can be accomplished using depletion mode MESFETs and SDFL when improvements in materials and active layer uniformity, which are well within the realm of possibility, are implemented. These circuits should operate in the 2 - 3-GHz/sec clock frequency range, lower than those demonstrated with BFL but with increased complexity. The use of enhancement mode MESFETs could increase the gate count into the very large-scale integration (VLSI)range, > 1 X lo4gates/chip, with clock frequencies greater than 1 GHz/sec. These devices will require a very stringent control of the doping profile in the active channel region in order to produce a totally depleted channel region for zero gate bias and still provide a good device transconductance for gate voltages less than about 0.5 V, the maximum gate voltage which can be applied without drawing excessivegate current. Another candidate for use in the VLSI regime is the enhancement mode junction field effect transistor (JFET). In this device, the channel-region doping is somewhat less stringent than the e-MESFET since the p - n junction characteristic allows a larger gate voltage swing. However, the investigations to date on this device have indicated problems with the control of the geometry of the device due to the lateral diffusion of the p-type dopant during the anneal cycle, in the case of implanted devices, or during the diffusion of the dopant for diffused junction devices (Dohsen et al., 1981). In order to penetrate the regime of VLSI complexity, there are several improvements which must be made. First, the materials used as substrates will have to have improved uniformity of electrical characteristics and improved dislocation densities. Second, the production of the n-type regions for enhancement mode MESFET devices or the p-type regions for JFET devices will require improved control of the doping profiles produced by ion implantation. In this area, alternate techniques such as organo-metallic vapor-phase epitaxy (OMVPE) and molecular beam epitaxy (MBE), with appropriate isolation techniques, will be evaluated as an alternative to ion implantation. Finally, the process techniques used to produce these complex circuits will have to be compatible with the materials and active-region - formation techniques in order to produce practical yields of functional circuits. It is the author’s judgment that the decade of the 1980s will see the practical production of GaAs circuits of LSI complexity operating with

154

C. A. STOLTE

clock frequencies in the 2 - 3-GHz/sec range. The competition from smallgeometry Si devices (Lepselter, 1980, 1981)will be a factor in the high-speed LSI devices. However, the inherent advantagesofGaAs over Si, namely, the higher electron mobility and electron velocity at low fields and the availability of semi-insulating substrates, makes possible much higher switching speeds for GaAS ICs as compared to Si. The future for GaAs indeed looks bright, and we can look forward to the time when GaAs is no longer the material of the future but the material of the present. ACKNOWLEDGMENTS The author extends his thanks to his colleagues at Hewlett-Packard who contributed to the work reported in this chapter. In particular, to Grant Elliot, Bill Ford, and Dick Putback, who grew most of the substrate material used; to Simone Malcolm and Mane Amistoso, who grew and characterized the LPE buffer layers; to Jim Hansen, for his expertise in ion implantation; and to Vibeke Bitsch and Jessie Kafia for the processing of samples. The inclusion of results supplied by Ed Stoneham, Chris Kocot, Piero Pianetta, and Joe Diesel added to the breadth of the chapter content and is acknowledged. The excellentcooperation of Charles Liechti and his IC group, including Elmer Gowen, Ruth Noll, Ruth Devereaux, Rod Lanick, and Falke Hennig has aided in all phases of the work reported. The substrate materials supplied by Ed Swiggard of Naval Research Laboratory, Roland Ware of Metals Research, and Ian Sanders of Plessey Research (Caswell) Ltd. increased the scope of the materials evaluation. The enthusiastic support during the course of these investigations,the useful and stimulating discussions, and the constructive comments regarding the content of this chapter by Bob Archer, Charles Bittmann, and Charles Liechti are appreciated and acknowledged. Finally, the assistance by Soyla Ybarra and JoAnn Hill in the preparation of the illustrations and the manuscript is appreciated.

REFERENCES Abe, M., Mirura, T., Yokoyama, N., and Ishikawa, H., (1982). IEEE Trans. Microwave Theory Tech. Mn-30,992. Abrokwah, J. K., Hitchell, M. L., Borell, J. E., and Schulze, D. R. (1981). J. Electron. Muter. 10, 723. Adlerstein, M. G. (1976). Electron. Lett. 12,297. Amano, J., Pianetta, P. A., and Stoke, C. A. (1980). Appl. Phys. Lett. 37,948. Ambridge, T., Heckingbottom, R., Bell, E. C., Sealy,B. J., Stephens,K. G., and Surridge,R. K. (1975). Electron. Lett. 11, 314. Anderson, C. L., Dunlap, H. L., Hess, L. D., Olson, G.L., and Vaidyanathan, K. V. (1980). I n “Laser and Electron Beam Processing of Materials” (C. W. White and P. S. Peercy, eds.), p. 334. Academic Press, New York. Arai, M., Nishiyama, K., and Watanabe, N. (1981). Jpn. J. Appl. Phys. 20, L124. Asbeck, P., Tandon, J., Babcock, E., Welch, B., Evans, C. A., Jr., and Deline, V. R. (1979). IEEE Trans. Electron Devices ED-26, 1853. (Abstr.) Asbeck, P. M., Miller, D. L., Petersen, W. C., and Kirkpatrick, C. G. (1982). IEEE Electron. Devices Lett. EDL-3, 366. AuCoin, T. R., Ross, R. L., Wade, M. J., and Savage, R. 0. ( 1979). Solid State Techno/. Jan., p. 59.

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SEMICONDUCTORS AND SEMIMETALS,

VOL. 20

CHAPTER 3

LEC GaAs for Integrated Circuit Applications C. G. Kirkpatrick, R. T. Chen, D. E. Holmes, P. M. Asbeck, K. R. Elliott, R. D. Fairman, f and J. R. Oliver DEFENSE ELECTRONICS OPERATIONS MICROELECTRONICS RESEARCH A N D DEVELOPMENT CENTER ROCKWELL INTERNATIONAL CORPORATION THOUSAND OAKS, CALIFORNIA

LISTOF SYMBOLS. . . . . . . . . . . . . . . . . . . I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . 11. LEC-GROWTH TECHNIQUE . . . . . . . . . . . . . . . 111. CRYSTALLINE QUALITY. . . . . . . . . . . . . . . . . I. Dislocation Studies . . . . . . . . . . . . . . . . . 2. Single-Crystal Yield (Twinning) . . . . . . . . . . . . 3. Surface Ga Inclusions . . . . . . . . . . . . . . . . 4. TEM Observed Microdejects . . . . . . . . . . . . . 5 . Conclusionson Crystalline Quality . . . . . . . . . . Iv. IMPURITY A N D DEFECT ANALYSIS . . . . . . . . . . . . 6. Chemical Purity . . . . . . . . . . . . . . . . . . 7. Electrical and Optical Characterization. . . . . . . . . 8. Compensation Mechanism . . . . . . . . . . . . . . 9. Residual Impurities . . . . . . . . . . . . . . . . . V. LEC GaAs IN DEVICE FABRICATION. . . . . . . . . . . 10. Approach . . . . . . . . . . . . . . . . . . . . . 1 1. Substrate Influence . . . . . . . . . . . . . . . . . 12. Impact of LEC GaAs . . . . . . . . . . . . . . . . VI. CONCLUSIONS ..................... 13. Electrical Properties and Compensation Mechanism . . . 14. Structural Perfection. . . . . . . . . . . . . . . . . 15. Crystal Growth Technology. . . . . . . . . . . . . . 16. Application to ICs. . . . . . . . . . . . . . . . . . REFERENCES. . . . . . . . . . . . . . . . . . . . .

159 161 163 167 168 182 187 187 190 192 192 195 206 208 212 212 216 222 226 227 228 229 229 230

List of Symbols$ LEC IC

Liquid-encapsulated Czochralski Integrated circuit

MMIC CCD

Monolithic microwave integrated circuit Charge-coupleddevice

t Present address:Microwave Product Department, TRW,Inc., Redondo Beach, California. $ Listed in order of occurrence. 159 Copyright Q 1984 by Academic Press, lac. All rights of reproduction in any form reserved. ISBN 0-12-752120-8

160 FET

111- v

six 9s PBN (111) (100)

TEM EPD g

b

cE S SADP BF B/W STEM 9

SIMS LVM p,,2

I J r7

r* UOPl

AE

TD s,2

C3" BAI

GaAs

v*, P

6 A

c. G. KIRKPATRICK et al. Field effect transistor Three-five (columns of periodic table) Six nines (0.999999) Pyrolytic boron nitride 11 1 crystal axis orientation 100 crystal plane orientation Transmission electron microscopy Etch pit density Burger vector Burger vector Extinction distance Extinction coefficient Bragg absorption Selected-area diffraction patterns Bright field Black and white Scanning transmission electron microscopy Cone angle Secondary ion mass spectrosCOPY Local vibrational mode angular momentum state with I= I,J=j Orbital angular momentum Total angular momentum Symmetry label or electronic state Symmetry label or electronic state Optical cross section Full-width-at-half-maximum energy of spectral feature Tetrahedral group Angular momentum state with I = 0, J = 4 Point group of threefold symmetry about an axis Boron substitutional on arsenic site Gallium substitutional on arsenic site Arsenic vacancy Spherical spin- orbit splitting parameter Cubic spin -orbit splitting parameter Effective spin-orbit splitting

Screening parameters Screening parameters Gallium substitutional on Ga, antimony site Electron paramagnetic EPR resonance Arsenic substitutional on A%. gallium site Electron trap label EL2 Gallium site vacancy vo. Density of ionized centers Ni Electron density n Density of neutral centers Nu Equilibrium constant K Shallow acceptor concentraNASA tion Shallow donor concentration NDSD NA- N p , concentration of Nf: residual acceptors Net concentration of carbon N p acceptors Concentration of EL2 deep NEL2 donors PITS Photoinduced transient spectroscopy R-PITS PITS using rise in photocurrent PITS using decay D-PITS Change in current Al Current at time t , I(4) Current at time t2 Emission rate of trap el l/(t2 - t,), sampling rate Ar-I Time t2 Type unknown U? Vapor-phase epitaxy WE Hole trap label HLlO U Cross section Semi-insulating SI Electron trap label EL3 Electron trap label EM Electron trap label EL7 MESFETs Schottky barrier field effect transistor Junction field effect transistor JFETs MISFETs Metal insulator semiconductor field effect transistor Buffer field effect transistor BFL logic Schottky diode field effect SDFL transistor logic Very large-scale integration VLSI

A,

4

mz) 4

9

3. DCFL

LEC GAS FOR INTEGRATED CIRCUIT APPLICATIONS

Direct coupled field effect transistor logic Capacitance-voltage Pinch-off voltage Elementary charge Dielectric constant Profile depth Donor profile Distance Built-in potential of Schottky bamer

Nimpht NS.4

NDA NSD

NDD JCS HB

161

Millivolts Mean pinch-off voltage Standard deviation of pinch-off voltage Implanted donor density Shallow acceptors in substrate Deep acceptors in substrate Shallow donors in substrate Deep donors in substrate Integrated circuits Horizontal Bridgman

I. Introduction Recent developments in liquid-encapsulated Czochralski (LEC) techniques for the growth of semi-insulating GaAs for integrated circuit (IC) applications have resulted in significant improvements in the quality and quantity of GaAs material suitable for device processing. The emergence of high-performance GaAs IC technologies has accelerated the demand for high-quality, large-diameter semi-insulating GaAs substrates. The new device technologies, including digital ICs, monolithic microwave integrated circuits (MMICs), and charge-coupled devices (CCDs), have largely adopted direct ion implantation as the key fabrication technique for the formation of doped layers. Ion implantation lends itself to good uniformity and reproducibility, high yield, and low cost; however, this technique also places stringent demands on the quality of the semi-insulating GaAs substrates. Although significant progress has been made in developinga viable planar ion-implantation technology, the variability and poor quality of GaAs substrates, particularly the commercially available Bridgman and gradientfreeze GaAs materials, have hindered progress in process development. Among the most prevalent problems have been the formation of a conductive layer at the surface following encapsulation and annealing processes, and the lack of reproducibilityin implanted profiles. These effects are the result of impurity redistribution in the substrates during the thermal processing. These impurities include background levels of donors and acceptors, particularly silicon (Si) and chromium (Cr), which may be present in high concentrations. Due to the incorporation of silicon from the quartz boat in the gallium arsenide melt, large amounts of Cr are added to compensate these donors and produce semi-insulating materials. The Cr can redistribute during annealing, resulting in a Cr-depleted region near the surface which can be conductive and “tails” in the profiles of shallow n-type implanted layers. The semi-insulating property of the material is the basis for dzvice isolation in direct implant technology and is necessary for the

162

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minimization of parasitic capacitances.Variability in implant profile results in poor control in the pinch-off (threshold) voltage and current through the channel of field effect transistors (FETs). It is therefore essential to utilize thermally stable, electrically uniform, and reproducible materials in GaAs device processing. High purity in these materials is desirable since substrates containing high total impurity concentrations exhibit reduced channel mobility and degraded frequency response. The physical characteristics of GaAs substrates are equally important, with the implementation of uniform, round, large-area substrates essential for the device technology to reach manufacturing. Commercial GaAs substrates grown by Bridgman or gradient-freeze methods are typically limited to a maximum of 2-in.-diam D-shaped wafers. Thermal gradients tend to preclude the extension of these techniques to larger substrate sizes without the formation of twins or polycrystalline regions. With the startup of production of GaAs ICs, it is essential that the standard semiconductor processing equipment, configured for large round wafers for the silicon IC industry, be utilized for cost effectiveness and yield. The critical need for improved size, quality, and quantity of GaAs materials for integrated circuit fabrication has been the driving force for the development of LEC techniques to produce high-yield, low-cost materials. In summary, these GaAs materials must exhibit (1) large, uniform, and round wafers; (2) reproducible and high resistivity with thermal stability;(3) low background impurity levels; and (4) high degrees of crystalline perfection. To meet the demands of GaAs device applications, a program in the growth of GaAs crystals using the LEC technique has been initiated at this laboratory to produce GaAs meeting the criteria described above, with high yields of single-crystal, undoped semi-insulating materials. Exceptional properties for these crystals have been observed through material characterization and device processing. In this chapter, major findings of this research effort are described which have significantly affected the GaAs materials applied to the fabrication of high-performance GaAs integrated circuits. Part I1 describes the basics of LEC growth and how this method differs from other growth techniques. In Part 111, an analysis of the defects present in LEC materials is presented, together with a description of techniques to reduce the incidence of twins and dislocations in GaAs crystals. The results of detailed investigations of impurity and trapping levels are described in Part IV. A compensation model for undoped semi-insulatingmaterial based on these studies is presented, and the implications of the model for highyield growth of semi-insulatingmaterial are discussed. In Part V, the use of LEC GaAs in integrated circuit fabrication is addressed, including data on the qualification of GaAs crystals for device processing, the results of ion

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163

implantation, and the performance of digital ICs on LEC substrates. Conclusions and implications resulting from these advances in LEC GaAs technology are outlined in Part VI. 11. LEC-Growth Technique

The LEC technique was first applied to the growth of PbTe by Metz et al. (1962), applied to 111-V materials by Mullin et al. (1968) and adapted for use with pyrolytic boron nitride (PBN) crucibles by Swiggard et al. (1977) and AuCoin et al. (1979). The LEC-crystal-growthfacility at this laboratory has a Melbourn puller developed by Metals Research, Ltd., Cambridge, England (see Thomas et al., Chapter 1, this volume, Fig. 2). The resistanceheated puller holds a 6-in. crucible with charge capacities up to 10 kg. The growth process is monitored through a closed-circuit vidicom TV camera. The puller features in situ synthesis of the compound GaAs from elemental Ga and As. The technique eliminates the need for a separate high-temperature synthesis step before crystal growth, reducing the potential for contamination. A schematic of the LEC crucible configuration is shown in Fig, 1. The Ga and As components [six 9s (0.999999) purity] are weighed and loaded into either a high-purity quartz or pyrolytic boron nitride crucible, and topped by a preformed disc of boric oxide (B,O,) with known moisture content. Except where noted otherwise, 500-g disks of B203were used, with the moisture content of hermetically sealed packages accepted as specificed by the manufacturer. No additional heat treatment is used prior to growth. Charges with a total weight of 3 kg were used in these studies. The crystals were typically 3 in. in diameter and weighed 2.5 kg. Both quartz and PBN crucibles have been successfully utilized in the growth of semi-insulating

-

-

PBN CRUCIBLE BORIC OXIDE

FIG.1. Cross section of the LEC crucible before growth showing the charge of elemental Ga and As and the preformed B,O, disk.

164

c. G . KIRKPATRICK et al.

GaAs. Although the initial cost of PBN crucibles is high (generally $4000$6000, depending on quantity and manufacturer), the crucibles can be cleaned and reused about a dozen times. The use of PBN crucibles is favored due to the higher yield of high-resistivity single crystals, as will be discussed later. The stoichiometry of the GaAs melt can be changed by varying the composition of the charge. To make an accurate determination of the initial melt composition, it is necessary to take into account the loss of As from the charge during the heat-up cycle resulting from incomplete wetting of the B203 to the crucible (particularly PBN crucibles) before synthesis. The weight loss is determined by comparing the weight of the initial charge with the weight of the crystal and the charge remaining in the crucible after the growth process. The As concentration of melts has effectively been vaned from 0.46-0.51 atom fraction. When samples for characterization were obtained along the length of the crystal, the melt composition for each sample was determined by adjusting the initial melt composition for the crystal weight at the time of growth. The crystal weight and length are recorded during growth as a function of time. The Ga, which is solid to just above room temperature, is loaded on top of the As so that the liquid Ga serves to encapsulate the As. Starting with a chamber pressure of 600 psi, the crucible is heated to between 450 and 5OO0C,at which point the B203softens, flows over the charge of Ga and As, and seals at the crucible wall. The boric oxide flows at relatively low temperatures (450"C) before significant arsenic sublimation occurs. The Bz03floats on top of the melt and wets the surface of the crucible and the = GaAsmUJoccurs growing crystal. The synthesis reaction (Ga%~d As, at about 800°C. The presence of the B 2 0 3 and the use of high argon overpressures (- 1000 psi) prevent significant loss of As due to sublimination and evaporation during and subsequent to the exothermic synthesis. The GaAs melt is effectively sealed by the boric oxide, suppressing not only As loss but also shielding the melt against contamination from the crucible and growth ambient. The melt reaction is then allowed to equilibrate and the growth procedure begins. Growth is initiated by dipping the seed, which is held on the pull shaft, through the transparent B203 and into the melt. The seeds are generally sliced from low dislocation material. The crystal is grown by gradually withdrawing the seed from the melt. The system configuration during growth is shown in Fig. 2. The crystal diameter is gradually and controllably increased to full dimension. The seed and the crucible are rotated in the same direction at 6 and 15 rpm,respectively. The pull rate for this work was 7.0 mm hr-', and crucible lift rate was 1.4 mm h r l . When the growth process was terminated, the crystal was positioned above the B203 encapsu-

+

3.

LEC GaAs FOR INTEGRATED CIRCUIT APPLICATIONS

165

INERT GAS

*

.:.

GaAs MELT

FIG.2. Cross section of the crucible for the LEC growth system showing the location of the B203during growth.

BORIC OXIDE

\

FIG.3. Cross section of the LEC system during growth with a Si,N, coracle.

166

c. G . KIRKPATRICK et al.

FIG.4. Photograph showing the neck, cone, and fulldiameter sections of a LEC crystal.

lating layer, and the system was cooled at a constant rate of between 30 and 80°C hr-'. The diameter of the crystal can be controlled either by manual operation or through the use of the coracle shaper. The coracle, shown in Fig. 3, is a Si3N, die with a round hole in the center. The coracle floats on top of the GaAs melt. A crystal pulled from the melt through the die has exceedingly good diameter control. However, the use of the coracle seems to be limited

3.

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GaAs FOR INTEGRATED CIRCUIT APPLICATIONS

167

to growth in the ( 11 1) direction because other low index planes, such as (loo), show a high susceptibility to twinning. In these studies, the crystal diameter was monitored manually through the differential weight signal. This signal was obtained from the “load cell,” a special weighing device on which the crystal and pull shaft are mounted in the LEC system. An increase or decrease in the differential weight indicates a corresponding increase or decrease in diameter. The crystal diameter is controlled by varying the heater temperature and the cooling rate in response to changes in the differential weight signal. The growth process is viewed continuously on the TV monitor as well to ensure stable control. The crystals were grown in three different sections with respect to diameter: the neck, the cone, and the body, as illustrated in Fig. 4. After the seed is dipped into the melt and pulling has begun, the “neck” is formed by reducing the diameter of the crystal below the seed diameter (- 4 mm) to 1 to 3 mm. Then the diameter is gradually and controllably increased, forming the “cone.” When the diameter of the cone reaches the desired dimension, the diameter of the crystal is kept constant for the remainder of the growth run. In the following sections, the results of studies on the impact of growth parameters on the crystalline and electrical characteristics of the resulting GaAs ingots are detailed. The tests included studies of seed quality, melt stoichiometry, B,O, wetness, seed necking, cone angle, and diameter control.

111. Crystalline Quality

The primary defects observed in LEC materials include dislocations, twins, surface Ga inclusions, and microdefects. Preferential etching x-ray reflection topography, and optical, infrared, and transmission electron microscopy (TEM) have been used to characterize these defects. Significant progress in improving crystalline quality through reduction of the defect concentrations in large-diameter LEC GaAs has resulted from a matrix of growth experiments. Dislocation densities below 10,000 cm-* and a singlecrystal yield >80% have been observed under the appropriate growth conditions. In the following discussion, results are presented on the dislocation density and distribution, reduction of dislocation density by various growth techniques, reduction of twin formation by control over the melt stoichiometry, surface Ga inclusions, and microdefects observed by TEM. Substantial reductions in the dislocation densities of LEC materials and in twinning incidence have resulted from studiet investigating dislocation formation

168

c. G. KIP.KPATRICK et al.

and distribution, cone angle, and the effects of B203 height, ambient pressure, seed quality and necking, diameter control, and stoichiometry. 1. DISLOCATION STUDIES

Current interest in large-diameter GaAs crystals grown by the LEC technique (Fairman et at., 1981; Thomas et al., 1981) stems from the need for substrate material for digital and monolithic integrated circuit fabrication. As these circuits become larger and more complex, possible adverse effects from dislocations on device performance and reliability may appear. However, at this stage of development, there have been virtually no systematic studies reporting the possible role of dislocations. As a first step, the density and distribution of dislocations across large-diameter substrates have been characterized and the means by which these are controlled by the crystal growth process is determined. This understanding is also important for the application of large-diameter LEC material to minority-carrier devices such as solar cells, where low dislocation densities are required to achieve high minority-camer lifetimes and diffusion lengths. A principal cause of dislocationsin bulk GaAs crystals is stress induced by thermal gradients (Penning, 1958;Mil’vidskii and Bochkarev, 1978;Jordan et al., 1980; Jordan, 1980) during crystal growth. Radial gradients are of particular concern in Czochralski-type growth configurations (LEC, Gremmelmaire). Most of the published dislocation studies on GaAs concern small-diameter (<0.5-in. diam) crystals grown by the LEC (Grabmaier and Grabmaier, 1972;Brice, 1970;Seki et al., 1978), Bridgman (Brice and King, 1966; Parsey et al., 1981), and modified Gremmelmaire (Steinemann and Zimerli, 1963) techniques. Since gradients generally decrease as the crystal diameter decreases, “effectively” dislocation-free, small-diameter GaAs crystals have been grown (Grabmaier and Grabmaier, 1972; Seki et al., 1978; Parsey et al., 1981; Steinemann and Zimmerli, 1966).Growth parameters reported to reduce radial gradients in small-diameter LEC crystals include the height of the B203encapsulating layer (Grabmaier and Grabmaier, 1972; Shinoyama et al., 1980) and the cone angle (Roksnoer et al., 1977). Material properties which have been identified with the suppression of dislocations include the concentration of impurities (Seki et al., 1978; Suzuki et al., 1979; Mil’vidskii el al., 1981) and melt stoichiometry (Brice, 1970; Brice and King, 1966; Parsey et al., 1981). Other dislocation studies for large-diameter LEC GaAs have ben made by Thomas et al. (Chapter 1, this volume, Section 3) and by Hiskes et al. (1982; see also Stolte, Chapter 2, this volume, Section 1). Eighteen undoped crystals were grown and analyzed in this study. The crystals were sliced according to the diagram shown in Fig. 5. The samples were lapped and polished on both sides. Dislocation densities and distribu-

170

c. G. KIRKPATRICK et al.

tions were evaluated by preferential etching (KOH for 25 min at 400°C). This etch preferentially attacks dislocations intersecting the surface of the sample, forming hexagonal etch pits! The etch pit density (EPD) corresponds directly to the dislocation density, as confirmed by x-ray topography at this laboratory and elsewhere (Angilello et al., 1975). The EPD measurements were typically made from low-magnification(70 X) micrographs by counting the pits over 1.3 X 10-mm regions. Higher magnification (either 140X or 280 X) was required to resolve the pits when the EPD exceeded approximately 1 X lo5 cm-2. The estimated error in counting the pits on each micrograph was less than f5%. Investigations concentrated on studying the effects of seven growth parameters on the dislocation density and distribution. These include (1) cone angle, (2) seed quality, (3) seed necking, (4) diameter control, ( 5 ) melt stoichiometry, ( 6 ) height of the B203encapsulating layer, and (7) ambient pressure. The cone angle, defined as the angle between the wall of the cone and the horizontal,was varied from 0 to 65 deg. Crystals with a cone angle of 10 deg or less than 20 deg are referred to as “flat-top” crystals. The EPD of the seed crystals ranged from about 1.5 X lo3to 5 X lo5cm-2. Crystals were grown with high and low EPD seeds, with and without Dash-type necking (Dash, 1957). The neck diameter varied from 1.2 to 3.0 mm. Diameter control refers to the deviation of the diameter from the average value. The lowest diameter deviations (k 1.1 mm) were achieved by controlling the diameter with the cooling rate with minimal direct adjustments of the melt temperature. The initial melt stoichiometry varied from 0.462 to 0.506 As atom fraction. Procedures necessary for making an accurate determination of the melt composition have already been discussed. The height of the B203 encapsulant above the melt was approximately 17 mm in the majority of the growth experiments, corresponding to 500 g of material. One experiment each was made with 170 and 390 g of B203,corresponding to 9- and 13-mm heights, respectively. The ambient pressure during growth was typically 300 psi. One experiment was conducted at a lower pressure of 50 psi. (See Stolte, Chapter 2, this volume, Section 1, for a discussion of low pressure growth.) a.

Radial Dislocation Distribution

The distribution of dislocations across wafers exhibits fourfold symmetry indicative ofthe ( 100) crystallographicorientation, as shown in Fig. 6. The main features of the distribution are that (1) minimum EPD occurs over a large annulus between the center and edge (region 1, or ring region); (2) intermediate EPD occurs in the center (region 2, or center region); (3) maximum EPD occurs at the edge (region 3, or edge region). A microscopic view of the dislocation distribution across wafers, as shown in Fig. 7, clearly shows the large variations of EPD. In addition, the EPD in the ring and edge

3.

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LEC GaAs FOR INTEGRATED CIRCUIT APPLICATIONS

171

\Region 3

FIG.6. Photograph of KOH-etched 3-in. (100) LEC GaAs wafer showing fourfoldsymmetry and (1) ring, (2) center, and (3) edge regions. [From Holmes ef al. (1983).]

regions is greater along the (100) than the ( 110) direction (see Fig. 7). Measured EPD distributions across the full diameter of wafers typically display a W-shaped profile, as shown in Fig. 8. Experimentally determined radial EPD distributions are consistent with theoretical thermoelastic analyses of Czochralski crystals of Penning ( 1958) and Jordan et al. (1980; Jordan, 1980). Jordan calculated the total stress in the crystal in terms of 12 ( 1 1 1) ( 1 10) slip systems. The dislocation density is assumed to be proportional to the total stress within an additive constant. Since the periphery of the crystal is cooler than the center as the crystal is pulled from the melt, the periphery and center are under tension and compression, respectively. The calculated stress is highest at the periphery, consistent with the experimental finding that the maximum EPD occurs in the edge region of the crystals. The calculatedstressis lowest in the transition between regions of tension and compression, consistent with the fact that the lowest measured EPDs occur in the “ring” region. The relatively high EPD measured along ( 100) compared to along ( 110) is explained in terms

172

c. G . KIRKPATRICK et al.

U

200 p n I

FIG.7. Photomicrographsof regions on a KOH-etched (100) LEC GaAs wafer cut from the front of ingot No. 18/Mshowing radial distribution of dislocations on 3-in.-diam wafer and (1) ring, (2) center, and (3) edge regions. [From Chen and Holmes (1983).]

of the theory by the fact that more slip systems contribute to the total stress along ( 100). The agreement between theory and experiment indicates that radial gradient-induced stress is the principal cause of dislocations in these crystals. These results agree with other experimental studies (Jordan et al., 1980) of (100) GaAs. Variations in the nature of the radial distribution from the front of the tail of the crystal are discussed in Section Ic.

3.

(31

EDGE

300

173

LEC GdS FOR INTEGRATED CIRCUIT APPLICATIONS

(11 RING

(21

-

CENTER

-

-

1 I

L

I-

I'

I-

I-

'1

TAIL

I I

!-

FRONT

0

2

4

6

a

DISTANCE ALONG SLICE IN C 110 > DIRECTION (cm)

FIG.8. Radial and longitudinal dislocation density for 3-in. LEC GaAs crystal. [From Chen and Holmes (1983).]

b. Dislocation Net works An important morphological feature of the microscopic dislocation distribution is the formation of etch pit networks. Two types of morphologies are observed.The first is a cellular network, seen in Figs. 6 and 7, where the dislocations form an interconnected network of cells with few dislocations

174

c. G . KIRKPATRICK et al.

within each cell. The approximate diameter of the cells is 500 pm, correspondingto an EPD of 2 X lo4cm-2. The cell diameter decreases as the EPD increases ( 100 pm, correspondingto an EPD of about 1 X lo5cm-2). When the EPD is less than about 2 X lo4 cm", the morphology of the network takes on a lineage structure, where the etch pits form visible wavy lines. These lines extend from a few millimeters to more than 1 cm and are oriented along ( 1lo), as shown in Fig. 6. These dislocation networks may form as a result of the polygonization process (Reed-Hill, 1973), where the dislocations realign themselves after solidification to reduce the strain energy of the crystal. The realignment probably occurs by both climb and glide processes. In general, dislocations in zincblend materials can undergo alignment into walls defined by (1 10) planes perpendicular to (1 1 1) slip planes. These walls would intersect (100) planes along ( 1 10) directions, consistent with the observations.The cellular network, in effect, constitutes a high packing density of lineage structures, where one dislocation may interact with several dislocation lines, forming interconnected networks. c. Longitudinal Dislocation Distribution

The longitudinal variation (along the growth direction) of the dislocation density was examined by comparing radial distributions of wafers obtained from the front, middle, and tail of the crystals, as shown in Fig. 8. Except for the edge in ingots 9, 1 1, 12, and 15 as well as the center of ingot 15, the EPD invariably increased from front to tail in each of the three regions, as shown in Table I, while the radial profiles remained W-shaped, as shown in Fig. 8. This behavior could indicate that the overall level of stress increased along the crystal or that the dislocations multiplied after growth, or both. The average EPD increased from front to tail (see Table I) by factors of 8,7, and 1.5 in the ring, center, and edge regions, respectively. Further, the ratio of the EPD in the center to that in the ring region decreased from front to tail in the majority of the crystals, as shown in the table. These results show that the radial EPD distribution becomes more uniform toward the tail of the crystals, even though the W-shaped profile persists.

d. Parameters Afecting Dislocation Density In this section, results are presented concerning the quantitative dependence of the dislocation density on cone angle, B203 thickness, ambient pressure, seed quality and necking, diameter control, and melt stoichiometry. The effect of each growth parameter was evaluated by determining the change in the EPD across each substrate as that parameter was independently vaned. Since the EPD density in the ring, center, and edge regions represents local limits of the entire EPD distribution, the entire distribution

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175

TABLE I

SUMMARY

OF EPD MEASUREMENTS ON

LEC INGOTS"

EPD (cm-*)

Ingot number 1 2 3 4b 5

6 7 8 9 10 11

Wafer locationC F T F M F T F M F T F T F M F T F T F T F T

12

F

13

T F

Td 14 15b 16 17 18

F T F T F T F T

F T

(1) Ring

(2) Center

(3) Edge

EPD ratio (center to ring)

7.6 x 104 6.1 X los 2.2 x 104 3.2 x 104 4.0 x 104

4.6 X 104 6.1 X lo5 5.ox 104 7.3 x 104 8.0 x 104

3.0 x 105 1.1 x 106 2.3 x 105 2.5 x 105 2.9 X lo5

0.6 1.o 2.3 2.3 2.0

N/Ae 4.0 x 104 3.0 x 104 1.5 x 104 1.2 x 105 1.8 x 104 8.6 X lo4 1.0 x 104 2.5 X 104 1.4 x 104

N/A

x 104 1.0 x 105 1.0 x 104 1.4

N/A

7.5 x 103 8.1 X lo4 1.2 x 104 9.0 x 104 3.5 x 104 8.0 x 104 6.0 x 103

N/A

1.1 x 105 1.3 x 105 1.3 x 104 1.4 x 105 1.1 x 104 1.5 x 105 8.5 x 103 9.7 x 104

High-EPD seed used. Flat-top growth. F = front, M = middle, T = tail. ingot length area. N/A: Not available.

-

N/A

1.4 x 105 1.0 x 105 3.4 x 104 1.4 x 105 2.6 X 104 7.7 x 104 2.5 x 104 3.9 x 104 3.7 x 104

N/A

2.0 x 104 1.0 x 105 2.1 x 104

N/A 104

1.3 x 1.8 x 1.7 x 1.0 x

1.0 x 1.1 x 1.8

x

105 104 105 105 105 104

N/A

2.4 x 105 2.3 x 105 2.8 x 104 2.2 x 105 2.0 x 104 2.5 x 105 1.6 x 104 1.3 x 105

N/A 4.0

x 105

N/A

1.7 x 105 2.1 x 105 8.0 xi04 2.0 x 105 5.6 X 104 7.8 x 104 1.0 x 105

N/A

2.5 X lo5 2.4 x 105 1.1 x 105

N/A

1.9 x 105 1.8 x 105 2.5 x 105 2.2 x 105 1.5 X lo5 2.0 x 105 9.6 x 104

N/A

2.7 X lo5 1.6 x 105 1.7 x 105 2.4 x 105 1.1 x 105 1.7 x 105 1.2 x 105 2.4 x 105

-

3.5 3.3 2.3 1.2 1.4

0.9 2.5 1.6 2.6

-

1.4 1.o 1.9

-

1.7 2.2 1.4 1.1 2.9 1.1 3.0

-

2.2 1.8 2.2 1.6 1.8 1.7 1.9 1.3

176

c. G . KIRKPATRICK et al.

can be characterized with these three EPDs. Only when all three of these EPD values changed in the same direction, were conclusions drawn concerning the effect of that particular growth parameter. The spatial resolution of these measurements in the center and ring regions (averaging over 1.3 X 1.O-mm areas) is sufficientto reflect true variationsin the average dislocation density across wafers while minimizing contributions due to microscopic fluctuations in density associated with polygonization. However, since higher magnificationswere used to determine the EPD near the edge of the crystals, these measurements probably represent the true average EPD to within k259/0.Therefore, measurements obtained from the center and ring regions were more sensitive indicators of actual EPD variations from crystal to crystal than measurements from the edge. In effect, the center and ring regions weigh more heavily. (Since the center and ring measurements encompass approximately 80% of the area of a substrate, the heavier weighting of the center and ring measurementsis justifiable from a practical standpoint.) The EPD values reported in the tables are an average of at least two measurements. (1) Cone angle. The effect of the cone angle on the dislocation density can be evaluated by comparing the EPD of fulldiameter wafers cut from the front of each crystal. The results, shown in Table 11, show no correlation between cone angle and EPD for cone angles greater than about 25 deg. For example, crystals Nos. 9 and 10were grown under very similar conditions in terms of the other six parameters reported in this paper. The only difference is the cone angle, which is 30 and 62 deg for crystals Nos. 10 and 9, respectively. The data show virtually no difference between the EPD values in the center and ring regions. On the other hand, the EPD in the front of the flat-top crystal (No. 15)is in the low- 105-cm-2range. In addition, the longitudinal distribution is inverted along approximately the first half of the crystal, first decreasing from the front toward the tail before increasing again as in all the other crystals. The crystal began to expand rapidly when the top of the crystal emerged from the B203encapsulating layer, leaving a bulge at a distance from the front of the crystal equal to the height ofthe B203layer. This behavior showsthat the crystal experienced significant additional cooling when emerging from the B20?, indicating that the convective heat transfer from the crystal to the ambient was large compared to the heat transfer to the liquid-encapsulating layer. The increased cooling presumably raised the level of stress near the top of the crystal, leading to the unusually high dislocation density. Dislocation maps of longitudinal cross sections of cones (see Fig. 9) were analyzed to follow the dislocation density distribution along the growth direction for various cone angles. The W-shaped radial distribution ob-

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177

TABLE I1 EFFECTOF CONEANGLEON DISLOCATION DENSITY

EPD (cm-2)

Ingot number

Cone angld (deg)

15

0

4

10

Front 1

2 3 1 2

3 1 2 3 1

17

25

10

30

2 3 1

6

50

9

62

2 3 1 2 3

8

65

1

2 3

1.1 x 105

2.4x 105 2.7 x 105 4.0x 104 1.4x 105 4.0 X los 1.1 x 104 2.0 x 104 1.1 x 10’ 1.1 x 104 2.1 x 104 1.1 x 105 1.8 X l(r 2.6 X 104 8.0 x 104

1.4X 104 2.0 x 104 2.5 x 105 1.4x 104 3.7 x 104 1.0 x 105

Other growth parameters are similar. 1, ring; 2, center; 3, edge (see Fig. 8).

served across wafers was clearly visible in these samples, as shown in Fig. 9. However, the longitudinal EPD increased after the neck, reached a maximum value, and then decreased before the crystal reached full diameter. (A continuous increase in EPD was expected in the cone region because the diameter expands continuously, and radial gradients typically increase as the diameter increases.) The maximum value of the EPD decreases as the cone angle increases, as indicated in Fig. 9. A high concentration of slip traces was also observed in the cone region in crystals grown with shallow cones. In addition, the maximum of the longitudinal EPD distribution was located directly below the neck in shallow cones and closer to the center of the high-angle cones, as is evident in Fig. 9. The variation with cone angle of both the EPD at the maximum and the position of the maximum within the cone as the cone angle decreased from 65 to 30 deg is consistent with the behavior of the flat-top crystal; i.e., the

9.OE3 (SEED)

9.7E4-1

3.3E3 (SEED) .8 E.4

1.3E4-

1.1

l.l'E5

i . i ~ 42 . 1 ~ 4

(a 1

5.5E3 (SEED)

3.2 ! E4

2.5E5

.OE5

1.4E4 2.OE4 (C)

8.0E4

1.8E4 2.6E4 (b)

FIG.9. Dislocation maps of longitudinal cross sections of ingot cones grown with varying cone angles: (a) No. 10 (30 deg cone), (b) No. 6 (50 deg cone), (c) No. 9 (62 deg cone). [From Chen and Holmes (1983).]

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LEC GaAs FOR INTEGRATED CIRCUIT APPLICATIONS

179

maximum EPD occurred at the top of the flat-top crystal, and the EPD at the maximum was the highest of all the crystals. Evidently the same mechanism controls the dislocation density and distribution at the top of all of the crystals, with the flat-top crystal representing the limiting case of a 0-deg cone angle. In view of the discussion earlier in this section concerning the flat-topcrystal, the dislocation maximum forming as the cone emerged from the B203encapsulating layer is likely a result of increased convective heat transfer to the ambient. The dislocations associated with the maximum represent a “secondary” distribution added to the primary (“grown-in”) distribution which formed at the solidification front. Study of the secondary dislocation distribution suggests the following model for the heat flow in the crystal at a position corresponding to the top surface of the encapsulating layer. The isotherm shape is determined by the relative vertical and radial components of heat flow. The vertical heat flow is relatively strong when the crystal is thin (as the neck emerges from the B203),and the isotherm shape is relatively flat. When the cone begins to emerge from the B203, radial heat flow becomes more important; the isotherm shape becomes more concave with respect to the solid as the radial gradient increases. The radial gradient increases as the cone angle decreases, leading to more pronounced EPD maximums for shallower cone angles. As the vertical wall of the crystal begins to emerge from the encapsulating layer, the curvature of the isotherm decreases, leading to reduced gradients. ( 2 ) Bz03 height. By varying the height from 9 to 17 mm, the effect of the height of the B203 encapsulating layer on the EPD was evaluated. The results in Table I11 show that the EPD decreases in regions 1 and 2 as the height of the layer increases. The effect is more pronounced at the front of the crystals. In addition, the nature of the secondary dislocation distribution in the cone region was independent of B203height. This behavior indicates that the radial gradients near the crystal - melt interface decrease as a direct result of the presence of a thicker Bz03 layer. In view of the results of the previous section, which showed that the heat transfer from the crystal to the ambient (above the B203)is greater than the heat transfer to the B203liquid, apparently the reduction of the radial gradient in the crystal attributed to thicker Bz03layers results from more effectivethermal isolation between the region of the crystal near the melt interface and the Ar ambient. This finding disagrees with the theory of Jordan et al. (1980), which predicts that the radial gradient would decrease as the B2O3 height decreases.

( 3 ) Ambient pressure. One crystal (No. 14) was grown at low pressure (50 psi). EPD measurements from the front of the crystal are shown in Table IV. Excessive thermal degradation took place at the surface of the crystal due to the low ambient pressure. As a result, Ga droplets, which formed at the

c. G . KIRKPATRICK et al.

180

TABLE 111 EFFECTOF B203 HEIGHTON DISLOCATION DENSITY EPD (cm-2) Ingot number

Weight OP B203(g)

13

270

*

Front

Tail

1

3.5 x 104 1.0 x 105

8.0 x 1 0 4 ~

2 3 1

16

390

2

3 1

500

12

2

3 a

1.5 x 105 1.3 x 104 2.8 x 104 1.7 x 105 1.2 x 104 1.7 X 104 2.5 X lo5

1.1

x 105~

2.0 x 105~ 1.4 x 105 2.2 x 105 2.4 x 105 9.0 x 104 1.0 x 105 2.2 x 105

Other growth parameters are similar.

* 1, ring; 2, center; 3, edge (seeFig. 8).

-

ingot length area.

cone, thermally migrated through the crystal to the tail. The presence of the Ga in the crystal prevented the measurement of the EPD in the tail. The degradation, and subsequent loss of As from the crystal during growth, also prevented making an accurate determination of the melt stoichiometry. However, the electrical characteristicsof the material indicated that both the initial and final melt compositions were within the As-rich range similar to crystal No. 16. A comparison of the EPDs of the crystal grown at low pressure and crystal No. 16 shows that the EPD of crystal No. 14 was lower TABLE IV EFFECTOF AMBIENTPRESSURE ON DISLOCATION DENSITY ~

~~

~~

~

~

EPD (crn-3 Ingot number

Ambient pressurea (psi Ar)

14

50

I 2 3

16

300

2

Front

1

3 ~~

~~~

~

Other growth parameters are similar. Not available (see text). 1, ring; 2, center; 3, edge (see Fig. 8).

6.ox 1.8 x

103 104 9 . 6 104 ~

1.3 x 104 2.8 x 104 1.7 X 10’

Tail NIA~ 1.4 x 105

2.2 x 105 2.4 X lo5

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LEC GdS FOR INTEGRATED CIRCUIT APPLICATIONS

181

throughout, as shown in Table IV, indicating that the use of lower ambient pressures is effective in reducing the EPD. In fact, the EPD of 6000 cm-2 in the ring region was the lowest value achieved in this study. The results reported in Section Id of this chapter indicate the importance of convective heat transfer via the ambient in controlling the dislocation density. The heat-transfer coefficient of the crystal-ambient surface is expected to increase as the square root of the pressure, according to Jordan et a/. (1 980; Jordan, 1980). Therefore, a reduction in heat transfer by no more than a factor of 2.5 would be expected for reducing the pressure from 300 to 50 psi. The experimental finding of a 50Yo reduction in EPD is consistent with the theoretical prediction. (4) Seed quality and necking. A series of experiments determined the effectiveness of the seed quality and the Dash-type necking procedure in reducing the EPD by growing crystals from high-and-low EPD seeds with and without thin necks. The crystals were evaluated by comparingthe EPDs in the front of each crystal at full diameter. The results, given in Table V, show that low-EPD crystals (EPD < 2.5 X lo4 cm-2) can be grown by employinglow-EPD seedswith and without necking as well as by employing high-EPD seeds with necking. To understand the effect of seed necking, longitudinal cross sections of TABLE V EFFECTOF SEEDQUALITY AND NECKING ON DISLOCATION DENSITY

EPD (cm-2)

Ingotnumber

Necking

Seed

Tail ~~

1 1

No

High (5 x 104)

5

Yes

High (5 x 105)

9

Yes

16

No

LOW

(3.3 x 103) LOW

(4.5 x 103)

2 3 1 2 3 1 2 3 1 2 3

7.6X lo4 4 . 6 104 ~ 3.ox 105 1.5 X lo4 3.ox 104 1.7 x 105 1.4X lo4 2.0 x 104 2.5 X 10” 1.3X lo4 2.8 X lo4 1 . 7 105 ~

a All cone angles > 25’ and other growth parameters are similar. 1, ring; 2, center; 3, edge (see Fig. 8).

182

c. G . KIRKPATRICK et a/.

crystals in the neck region were examined. Grown-in EPD in this region could not be directly observed for neck diameters of less than about 2.5 mm because the neck region apparently deformed under the weight of the crystal, as shown in Fig. 10. However, dramatic reductions in EPD were observed for necks between about 2.5 and 3.5 mm in diameter, as shown in Fig. 10. These results indicate that the Dash-type necking procedure indeed works to reduce the dislocation density independent of the EPD of the seed. Yet, the effect was registered in the first full-diameter wafer only for highEPD seed. This behavior can be interpreted to mean that dislocationscan be transmitted from the seed to the crystal, and the transmission is reduced by necking. However, the effect of necking is limited since dislocations will be generated in the crystal even if the seed is perfectly dislocation-free. ( 5 ) Diameter control. It is known that good diameter control favors lower dislocation densities. Some of the data on the 3-in. GaAs crystals support this view, although a more definitive statement cannot be made because of the limited data. Crystals Nos. 6 and 9 in Table VI were grown under very similar conditions, except that the diameter deviation was smaller in No. 6. Note that the EPDs in the front of No. 6 are higher than in the front of No. 9, whereas the EPDs in the tail are lower. The lower EPD in the tail of No. 6 is attributed to the improved diameter control. Note, however, that the effect of diameter control is much less pronounced compared to that of cone angle, seed quality, and seed necking. Apparently, crystals with more unstable diameter control were subjected to greater transient gradient-induced stress, which resulted in higher EPDs.

(6) Melt stoichiometry. The effect of melt stoichiometry on the dislocation density was studied by growing crystals from stoichiometricand nonstoichiometric melts. No correlation between EPD and melt stoichiometry was evident for Ga- or As-rich melts with compositions less than 0.503 As atom fraction, as shown in Table VI. However, the growth conditions and physical parameters of crystals Nos. 11 and 12 are nearly identical, except for the melt composition. Yet the EPD values in the front of crystal No. 1 1 are significantly lower compared to crystal No. 12. The reduced EPD values in the front of the crystal would indicate that the As-rich melt favors reduced dislocation densities for melt compositions greater than about 0.505 As atom fraction. No significant improvement is apparent in the tail of No. 11, possibly suggesting that a small range of melt compositions between 0.505 and 0.535 provides for optimal EPD reductions. 2. SINGLE-CRYSTAL YIELD(TWINNING) A major problem that can affect the yield of GaAs material suitable for device processing is the incidence of twin formation. Twinning causes

4.8 104-

-1.6 mm

1

e 3

mm

103-

1.4x 1044.8 104-(a ) Ibl F~G. 10. Dislocation maps of longitudinal cross sections of seeds,necks,and tops of cones with varying neck diameters: (a) No. 10: 1.6-mm neck diameter showing severe deformation in the neck region and (b) No. 12: 3-mm neck diameter showing dramatic dislocation density reduction. [From Chen and Holmes (1983).]

c. G . KIRKPATRICK et al.

184

TABLE VI

EFFECTSOF MELTSTOICHIOMETRY AND DIAMETER CONTROL ON DISLOCATION DENSITY EPD (cm-2)

Ingot number

Initial melt‘ composition

Diameter variation (mm)

Frontc 1

8

53.0% Cia

f 4.0

6

51.5%Ga

f 3.0

9

51.5%Ga

f7.1

10

50.7% Ga

f4.5

Stoichiometric

f 8.5

12

50.1% As

f 1.6

16

50.3% As

f 1.5

5

2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2

3 50.6%As

11 ~~

a

f 1.5

1 2 3

1.4 x 104 3.7 x 104 1.0 x 105 1.8 x 104 2.6 X 104 8.0 X 104 1.4 x 104 2.0 x 104 2.5 x 105 1.1 x 104 2.1 x 104 1.1x 105 1.5 X 10’ 3.0 X 10‘ 1.7x 105 1.2 x 104 1.7 x 104 2.5 x 105 1.3 X 104 2.8 x 104 1.7 X 10’ 7.5 x 103

1.3 x 104 1.9 x 10’

Tail N/A

8.6 X 104 7.7 x 104 2.2 x 10’ 1.0 x 105 1.0 x 105 2.4x 105 N/A

1.2 x 105 1.4 X 10’ 2.1 x 105 9.0 x 104 1.0 x 105 2.2 x 105 1.4 X los 2.2 x 105 2.4 x 105 8.1 x 104 1.8 x 105 1.8 x 105

_____

All cone angles > 25 deg and other growth parameters are similar. 1 ring; 2 center; 3 edge (see Fig. 8). Diameter control should have no effect on front EPD.

changes in the crystallographic orientation of the material and can also lead to polycrystallinity and the formation of grain boundaries. Therefore, twinning must be prevented in the crystal growth process to achieve a high yield of 100%single-crystal wafers for device processing. Control over the melt stoichiometry was found to be important to prevent twin formation in large-diameter, undoped, ( 100) GaAs crystals grown by the liquid-encapsulated Czochralski technique. Twenty GaAs crystals were grown from stoichiometnc and nonstoichiometric melts to study this phenomena. The results of this study, summarized in Table VII, show that the incidence of twinning is significantly reduced

TABLE VII INCIDENCE OF TWINNINGIN LARGE-DIAMETER (100) LEC GaAS CRYSTALS~ ~~

Crystal number

~~~

Melt stoichiometry

Melt composition, initial

1 2 3 4 5 6 7 8

PBN PBN PBN PBN PBN PBN PBN Quartz

0.462 0.477 0.486 0.488 0.489 0.492

9

Quartz

Ga rich Ga rich Ga rich Ga rich Ga rich Ga rich Ga rich Ga rich Ga rich Ga rich Ga rich Ga rich As rich As rich As rich As rich As rich As rich As rich As rich

10 11 12 13 14 15 16 17 18 19 20

Q-

Quartz

Q-

PBN PBN PBN PBN PBN PBN PBN PBN

~~~~~

a

~~

Crucible material

As

Atom fractionb final 0.445 0.459 0.439 0.434 0.439 0.457

-

-

e c e e e

0.500 0.500

0.500 0.500 0.500 0.501 0.502 0.502 0.504 0.506 ~

0.501 0.508 0.512 0.509 0.534 0.536

Result Twin Twin Twin Single Single Twin Twin Twin Single Twin Twin Single Single Single Single Single Single Single Twin Single

~~~

160- 500 ppm H20in B,O, . Calculated melt composition corresponding to the growth of the front (initial) and tail (final) of the crystal. The angle between the wall of the cone and the horizontal, e.g., a 0 deg cone refers to a “flat-top’’ cone. M, multiple twins; lL, one longitudinal twin. See the text.

Cone angle (deg)

Twin morphology‘

65 30 60 60 50 30

M M M

40 20 70 10 50 60 30 25 30 30 30 0 35 30

1L M

M M M

1L

186

c. C . KIRKPATRICK et al.

when crystals are grown from As-rich melts. Only 4 of 12 (33%) crystals grown from Ga-rich melts were single. On the other hand, 7 of 8 (88%) crystalsgrown from As-rich melts were single. Furthermore, the incidence of twinning could not be correlated with other growth parameters, such as the wetness of the B2O3(AuCoin et al., 1979),the cone angle (see Table VI), or the fluctuations in the diameter of the crystal, The results indicate a sharp increase in twinning probability on the Ga-rich side of the stoichiometric composition. Previous studies (Steineman and Zimmerli, 1963; Bonner, 1980) have shown that the incidence oftwinning in small-diameterGaAs crystals can be reduced by growing with gradual cones: i.e., large cone angles. No correlation was evident in this work between the incidence of twinning and cone angle in large-diameter crystals. Moreover, the significantly reduced incidence of twin formation experienced using As-rich melts in the present study was achieved with small cone angles ranging from 0 to 35 deg. Growth experiments employing quartz crucibleswere not conducted with As-rich, undoped melts to compare with the results obtained with the Ga-rich melts. However, recently several crystals were grown with Se, Si, and Zn doping from As-rich melts using quartz crucibles. The incidence of twin formation was very low in this series of experiments (8 out of 9 crystals were single), indicating that twin formation is independent of the type of crucible material used. The twinned crystals were categorized according to the twin morphology. One group was characterized as having only one longitudinal twin, which nucleated at the surface of the crystal and cut the crystal obliquely on a (1 11) plane. The twinned region of one such crystal was found by x-ray analysis (Lind, 1981) to be oriented with the { 122) direction parallel to the growth direction. The second group of crystals contained multiple twins. Twins in all crystals invariably nucleated at one of the four peripheral facets that run axially along the crystals. [The peripheral facets result from the intersection of ( 11 1) As and ( 1 1 1) Ga facet planes with the edge of the crystal along { 1 10) directions that are perpendicular to the { 100) growth axis.] No preference was observed for either As or Ga peripheral facets as nucleation sites for twins. The reduced incidence of twin formation in As-rich melts has been reported for GaAs grown by the Bridgman (Weisberg et al., 1962) and modified Gremmelmaier (Steinemann and Zimmerli, 1963) techniques. The consistent effect of melt stoichiometry on twin formation in GaAs grown by three different techniques would therefore seem to reflect a fundamental behavior of the material. The dramatic variation in the incidence of twinning over a relatively small range of melt compositions observed in the present study suggests that the stoichiometry of the solid at

3.

LEC GaAS FOR INTEGRATED CIRCUIT APPLICATIONS

187

the growth interface could play an important role. Thus, the variable resistance of the crystal to twin formation could be related to different solidification kinetics, depending on whether vacancies, interstitials, or anti-site defects are incorporated into the solid.

3. SURFACE Ga INCLUSIONS Small (0. I - 1-mm-diam) Ga droplets, observed around the edges of a depth of up to about 2 mm, form as a result of the preferential evaporation of As from surface of the crystal during growth. The penetration is due to the thermal migration of the droplets from the cooler surface to the hotter interior. The direction of motion was downward, rather than horizontal, which has been confirmed by infrared microscopy. In general, dislocation clusters are formed around surface Ga inclusions; small fissures, developing from very large Ga inclusions, could eventually cause cracking of a wafer. Significant penetration of Ga droplets is observed to occur only when the diameter of the crystal increased markedly. Therefore, good diameter control precludes the penetration of Ga inclusions and also prevents wafer damage. However, the centerless grinding technique appears to be the best way to remove all surface Ga inclusions, as well as the edge region with the highest dislocation density. 4. TEM OBSERVED MICRODEFECTS

Transmission electron microscopy was used to examine the microstructure of undoped and Cr-doped LEC GaAs grown under different stoichiometric conditions. A chemical jet etching technique using 1OHCl :1H202 :1H,O etching solution was applied to produce thin foils less than 4000 A thick. Figure 11 shows bright-field (BF) TEM micrographs obtained from these wafers, indicating material free of stacking faults, low-angle grain boundaries, and dislocation loops. However, a few dislocations, as well as some black-and-white microstructures with diameters of 80 A,are observed.

-

a. Dislocations

Figure 12 shows the bright field contrast micrographs of the dislocations observed by TEM in typical LEC GaAs samples. The dislocation densitiesin these samples are in the range of lo4- los cm2. These values are consistent with etch pit density values measured by preferential etching techniques. Preliminary TEM analyses using g b = 0 criteria have shown that the Burger vectors for these dislocations are f [ 1lo], which are typical for the dislocations observed in crystals with the face-centered cubic structure. Further, as shown in Fig. 12b, a precipitate with a size 500 A,which is entangled with dislocations, can be observed in a sample grown from the

-

c. G . KIRKPATRICK et al.

I88

FIG. 1 1 . Bright field micrograph for (a) an As-rich sample (No. 1 IT) = (022) s = 0, foil thickness 750 A, 73,000 X;(b) LEC GaAs sample (No. 8T) g = (022), s = 0, foil thickness -750 A, 120,000~.

-

3.

LEC

GaAs FOR INTEGRATED CIRCUIT APPLICATIONS

i-

189

FIG. 12. Bright field micrograph for (a) typical LEC GaAs sample (022), s>O, 38,OOOX; (b) BF micrograph for an As-rich sample (No. 11T) (032), s > 0, 13,OOOX.

i=

c. G. KIRKPATRICK et al.

190

As-rich melt (No. 11T, 53.6% As). The nature of the precipitate is still unknown. However, a similar defect has been reported in LEC or Bridgman-grown GaAs materials and confirmed to be an As precipitate (Cullis et al., 1980). b. Black-and-White Contrast Microstructures

-

Black-and-white (B/W) contrast microstructures with sizes 80 A have been observed in 3-in.-diam, Cr-doped LEC material. Similar B/Wmicrostructures with sizes 80 A as in Figs. 1 la and b are observed in all undoped LEC crystals grown from Ga-rich, near-stoichiometric, or As-rich melts in quartz or PBN crucibles. The estimated density for these B/W 1la and 1 lb show two special microstructures is about 10l6~ m - Figures ~. features: (1) The B/W microstructures exhibit good contrast only in thin regions of the foil (thickness < 1500 A 3 &,where is the extinction distance), and (2) the image depends sensitively on foil thickness under anomalous absorption conditions (i.e., s = 0, no deviation from the Bragg reflection condition). Optimum contrast is obtained in a narrow region at the front of the first or second dark thickness fringe. The microstructuresare bright (white) at the front of the dark contour (thinner region) and dark (black) at the front of the bright contour (thicker region). Since no fine structure was observed in selected-area diffraction patterns (SADP), which would have indicated the presence of precipitates, these B/W microstructures are probably due to cavities. However, additional TEM analysis and further microanalysis using scanning transmission electron microscopy (STEM) are required to confirm such predictions.

-

-

5. CONCLUSIONS ON CRYSTALLINE QUALITY The density and distribution of dislocations have been characterized in 3411. diam LEC GaAs crystals. The radial distribution across wafers is W-shaped, indicating excessive thermal gradient-induced stress as the primary cause of dislocations, as predicted on the basis of the models of Penning (1958) and Jordan et al. (1980; Jordan, 1980). The dislocation density along the crystals increases from front to tail at full diameter, indicating that the level of stress in these crystals increases as the crystal is pulled from the melt, or that the dislocations multiply after growth. The radial EPD distribution becomes more uniform toward the tail of the crystals, even though the W-shaped distribution prevails. Jordan et al. (1980) noted that a more “diffuse” radial dislocation distribution could result from the movement of 60-deg dislocations out of their slip planes into the next-to-grow layer of the crystal, adding to the glide dislocations at the solidification front. This explanation would seem to be a reasonablebasis for modelling the observed behavior.

3.

LEC GdS FOR INTEGRATED CIRCUIT APPLICATIONS

191

The dependence of the dislocationdensity on seven crystal growth parameters was determined, with the following findings.The EPD of the full-diameter crystal is virtually independent of the cone angle 8 for 20 deg < 8 < 70 deg. However, the EPD increases significantly for 0 deg< 8 < 20 deg. Analysis of the longitudinal dislocation distribution within the cone region further shows that the EPD inverts for 20 deg < 8 < 70 deg, first increasing and then decreasing from front to tail before the crystal expands to full diameter. These findings can be explained in terms of the dominant role played by convectiveheat transfer from the crystal to the ambient gas as the crystal emerges from the B203. In practical terms, these results show that crystals can be grown with a minimum dislocation density using a cone angle of about 30 deg. The use of 30-deg cone angle maximizes the number of low-dislocation wafers that can be obtained from crystals while minimizing the time required to grow the cone. The dislocation density in the front of the crystals is found to be a relatively strong function of the height of the encapsulatinglayer, decreasing as the layer height increases. This effect is a direct result of a reduction in the radial gradients in the crystal near the solidification front. One possible explanation for this effect is that thicker B203layers more effectivelyinsulate the growth interface from the ambient gas, reducing the radial gradient. Studies reveal that Dash-type seed necking procedure is effective in reducing the dislocation density only when the EPD of the seed is high (25000 cm-2); low-dislocation crystals were grown with poor quality seeds with necking, and with high-quality seeds with and without necking. These results indicate that dislocations indeed transmit from the seed to the crystal, and necking greatly reduces this effect. However, the mechanism can have only a limited effect, since dislocations are generated in the crystal even if the seeds were perfectly dislocation-free.Additional reductionsin the dislocation density in LEC crystals (achieved by altering the present thermal configuration) will require higher-quality seeds if the necking procedure were to be eliminated from the growth process. The elimination of necking through careful selection of seeds would be advantageous from the practical standpoint of minimizing the time required to grow a crystal. Good diameter control and the use of slightly As-rich melts favor reduced dislocation densities. However, these effects are small compared to those of the cone angle, B 2 0 3 height, seed quality, and necking. Further work is needed to understand the effect of the melt stoichiometry. The experimental results presented concerning the effect of cone angle B,03 height, and ambient pressure indicate the influence of relatively high convective heat transfer at the crystal - ambient surface compared to the crystal - B203surface. These findings disagreewith theoretical predictions of the relative heat-transfer coefficients. Reconciliation of this discrepancy

c. G. KIRKPATRICK er al.

192

between theory and results is needed for a better understanding of the LEC crystal growth process and further reductions of the dislocation density. The incidence of twin formation in large-diameter, undoped, ( 100) LEC GaAs is reduced when the melt composition is slightly As rich. In view of the potential for the loss of As from the charge when using in situ synthesis, the yield of single, (100) crystals will depend on close control of the melt composition. Finally, the results suggest that the barrier to twin formation is related to the stoichiometry of the solid at the solidification front. IV. Impurity and Defect Analysis

To evaluate purity of LEC GaAs, and to establish a model for the compensation mechanism in the undoped semi-insulating material, the principal impurities and electrically active centers were characterized and correlated with the crystal-growth conditions.

6. CHEMICAL PURITY The chemical impurities were determined by secondary ion mass spectrometry (SIMS) and localized vibrational mode (LVM) far-infrared spectroscopy. SIMS, a chemically specific microanalytical technique, is particularly well suited to determining the concentration of transition metals and shallow donors in GaAs. The SIMS measurements for these crystals were made by Charles Evans and Associates, San Mateo, California. LVM, an optical absorption technique, is useful for identiEying low-atomic-number impurities in GaAs, e.g., carbon. Carbon ( W ) induces a local mode absorption at 582 cm-l at 77°K; the integrated intensity of the absorption is proportional to the carbon concentration. The LVM measurements were made at 77°K. Average impurity concentrations for LEC material grown from quartz and PBN crucibles are shown in Table VIII. Results obtained from Crdoped, semi-insulating GaAs grown by the Bridgman method, which had passed material qualification procedures for GaAs integrated circuit processing, are shown for comparison. The principal impurities found in LEC GaAs are carbon, silicon, and boron. The carbon concentration is lowest (on average) in LEC GaAs grown from quartz crucibles, ranging from nondetectable limits (<2 X lOIs ~ m - ~ ) to about 9 X lOI5 ~ m - ~LEC . GaAs grown from PBN crucibles always contains carbon, with concentrations between 2.0 X l0ls and 1.5 X 10l6 ~ m - High ~ . carbon levels (- 2 X 1OI6 ~ r n - ~are ) detected when the coracle shaper is used, indicating contamination directly from the coracle. Carbon has not been detected in the Bridgman material studied for comparison. - ~quartz-grown LEC Si is present in the range of 5 X 1014- 3 X 10l6~ r n in

TABLE VIII ANALYSIS OF CHEMICAL IMPURITIES IN LEC GaAs Number of Growth technique LEC

LEC

crystals

Crucible

averaged

S

!3e

Te

Mg

Cr

Mn

Fe

C

Si

B

-3E15 ND-9E15 1-3E16

5E14-3E16

1E14-2E17

5E14-3E16

lE14-2E17

2E15-1E16 2E16

<2E15 2E15

1E 14-2E 17 1E 14-2E 17

2E16

<2E14

Quartz

Manual

6

2E15

<1E14 <1E14 <5E14

Coracle PBN

7

2E15

<1E14

Manual

7 1

1.5E15 5E14 5E13 2E14 2E15 1.5E14 <1E14 4.4E14

<5E14 1E15 3E15 8.5E15 1.5E15 <5E15

4

3E15

3.1E16 4.7E14 4.7E15 ND

Coracle Bridgman Quartz (Cr doped)

3E14

<5E14 <1E15 <9E15

<1E14 2-10E15

4E13

4.5E14

194

c. G. KIRKPATRICK et al.

material, On the other hand, the Si concentration of PBN-grown material is consistently at the 1 X 1015-cm-3level or lower. No Si contamination from the coracle, which is made from Si3N4,seems to occur. In comparison, the Si concentration in Bridgman material is consistently in the low 1016-cm-3 range, about one order of magnitude higher than LEC PBN-grown material. The boron concentration in LEC GaAs varies from 1 X loL4 to 2 X 10'' ~ m - This ~ . result is independent of the crucible material, indicating that the source of boron is the Bz03encapsulating material. Although boron is the predominant chemical impurity, boron is isoelectronic with Ga, and no evidence has been found in these investigations to indicate that boron is electrically active. The boron concentration in Bridgman material is very low (I 2 X 1014cm-3). The large variations in the concentrations of both silicon and boron in LEC material are explained in terms of the effect of the wetness of the BzOJ encapsulant: The Si and B concentrationsboth decrease as the water content of the B,03 increases, as shown in Fig. 13. The Si concentration decreases

3.

LEC

GaAs FOR INTEGRATED

CIRCUIT APPLICATIONS

195

from the low 1016-cm-3range to below 1 X 1015cm-3 as the water concentration in the B203 increases from about 200 to 1000 ppm. The boron concentration decreases from the low lO”-~m-~ range to below 1 X lOI5 cm-3 with the same change in water level. The dependence of the Si concentration on B203 wetness is critical for the growth of semi-insulatingmaterial from quartz crucibles. The Si concentration is suppressed by the use of wet B203,producing semi-insulating material; otherwise, with dry boric oxide, the material becomes n-type. These studies indicate that the critical water content of the B z 0 3 , above which semi-insulatingGaAs is produced, is about 700 - 800 ppm. The specification of 700 - 800-ppm water in the B203 can be met by commercial suppliers. However, at this and other laboratories, it has been observed that the incidence of twinning increases as the water content of the BZ03increases. This behavior is illustrated in Fig. 13. Therefore, it is difficult to meet the two basic requirements for device-quality GaAs crystals using quartz crucibles -single crystallinity,which requires dry B203,and semi-insulatingelectrical properties, which require wet B2O3. The use of PBN crucibles virtually eliminates Si contamination. Single-crystal,twin-free semi-insulatingmaterial can be grown by using dry B203 (also see Thomas et aZ., Chapter 1,this volume, Section 5). AND OPTICAL CHARACTERIZATION 7. ELECTRICAL

An important question surrounding semi-insulating LEC GaAs has concerned the compensation mechanism by which the undoped material is semi-insulating. The understanding of the compensation mechanism has two important practical consequences. First, knowledge of the cause -effect relationships between crystal growth and electrical characteristics of the material can greatly improve the yield of semi-insulating crystals in the growth process, as well as the crystal-to-crystaland wafer-to-wafer reproducibility. Second, this understanding can lead to improved device performance. For example, backgating effects may possibly be diminished by adjusting (Kocot and Stolte, 1981) trap levels in material intended for integrated circuit processing (see Stolte, Chapter 2, this volume, Section 1 1). Studies have shown that high-resistivity material could be obtained when unintentionally doped material was exposed to oxygen (Haisty et a!., 1962; Gooch et al., 1961). One explanation for this behavior was that a deepdonor level associated with oxygen was responsible for the semi-insulating behavior. A deep level has been observed by photoconductivity (Lin et aZ., 1976), by optical absorption (Lin et al., 1976) and in transient capacitance experiments (Hasegawa and Majerfeld, 1975; Sakai and Ikoma, 1974).The result shows approximately 0.78 eV from the conduction-band minimum, and has been labeled EL2 or “0.”

c. G. KIRKPATRICK et al.

196

Transient capacitance (Kaminska et al., 1981), optical absorption (Lin et al., 1976), and photoconductivity (Lin et al., 1976)measurements indicate that the concentration of EL2 deep donors is not affected by the amount of Gaz03added to the melt or by the amount of oxygen in the material as determined by secondary ion mass spectrometry. However, other studies indicate a different role for oxygen. There is evidence that oxygen can act as a getter for other impurities, such as silicon. In this study, the effects of melt stoichiometry on the concentration of the deep-donor EL2 and the effects of such changes on the electrical properties of the material have been studied. The results show that the stoichiometry of the melt controls the electrical compensation of the crystal through incorporation of EL2, a defect that has been implicated (Martin et al., 1980a)as the compensation-controllingcenter. These results indicate that ( 1) EL2 is the center responsible for the observed semi-insulatingbehavior and (2) EL2 is either an intrinsic defect or intrinsic defect complex. Investigationsin this study have included a number of techniques in an effort to determine which defects are important in affecting the cornpensation and the growth conditionsunder which these defects are produced. The LEC material was characterized through variable temperature Hall mea109

-

108

-

107

-

-E

106-

5

105-

> t 2 I-

I

*I

' -

I

p-TYPE

104-

E a

I I -

SEMI-INSULATING

I#

;103-

I

102

-

CRITICAL AS COMPOSITION

101

-

*

100

-

I

.*

W 0

.

0

.

t

STOlCHlOMETRlC COMPOSITION

3.

LEC GaAs FOR INTEGRATED CIRCUIT APPLICATIONS

197

surements, near infrared absorption, far infrared optical absorption, photoluminescence, photoinduced transient spectroscopy (PITS), and capacitance transient spectroscopy. The electrical characteristics of LEC GaAs crystals were evaluated by Hall-effectmeasurements using samples obtained from the fronts and tails of the 12 crystals, and from detailed resistivity profilesof 5 crystals. The resistivity was found to be a strong function of the melt stoichiometry, as shown in Fig. 14. Figure 14 shows that the material is semi-insulating (n-type) above, and p-type (low resistivity)below, a critical As concentration in the melt ofabout 0.475 As atom fraction. The resistivity peaks at the critical composition at a value of about 1.5 X lo8 Q cm and decreases approximately eight orders of magnitude below the critical composition. The resistivity also decreases very gradually as the As fraction increases from the critical composition. The variation in resistivity across the melt composition range is explained in terms of the corresponding free-carrier concentration and Hall mobility, as shown in Figs. 15 and 16. The semi-insulating material grown at the critical composition is n-type, with a camer concentration and mobility of 1-2 X lo7 cm-3 and (1 -2) X lo3 cm2 V-I sec-', respectively. These Hall

.* p-TYPE

SEMI-INSULATING

-1-

I I CR ITICALAS COMPOSITION

$

109 108 107

1

0.42

I

,

I

0.44

I

0.46

.. *.

. t o

: : T R l ;

0.48

0.50

0.52

;,

0.54

ARSENIC ATOM FRACTION IN M E L T

FIG.15. Dependence of free carrier concentration of LEC GaAs on melt stoichiometry. The semi-insulating material is n-type, and the free-electron concentration increases gradually as the As concentration in the melt increases from the critical composition. The free-carrier concentration rises approximately nine orders of magnitude following a 1% reduction in As fraction from the critical composition. [From Holmes ef al. (1982b).]

c. G. KIRKPATRICK et al.

198

1 .

C R I T I ~ A AS L COMPOSITION

*

.

. ./I

..=*

p-TYPE

-I-

'

SEMI-INSULATING

1. STOlCHlOMETRlC COMPOSITION

. 1001 0.42

I

I

I

0.44

I

0.46

I

I

0.48

I

1 : 0.60

I

I

0.52

I

I 0.54

ARSENIC ATOM FRACTION IN M E L T

FIG.16. Dependence of Hall mobility of LEC GaAs on melt stoichiometry. The mobility of the semi-insulatingmaterial varies from 1-2 X lo3to 4- 5 X lo3cm2V-' sec-' as the As atom fraction increases from the critical composition to about 0.535. The mobility of the ptype material grown in the transition region, within about 1% of the critical composition, is low, between 1-30 cm2 V-I sec-'. The mobility of the ptype material grown outside of the transition region ranges from 215 -330 cm2 V-' sec-'. [From Holmes et al. (1982b).]

mobilities are low for n-type GaAs. As the As atom fraction increases from the critical composition to about 0.5 1, the mobility gradually increases .to 4-5 X lo3 cm2 V-' sec-l, which is more typical of n-type material. The corresponding electron concentration gradually increases to 6 - 8 X 1O7 ~ m - The ~ . combined increase of both the mobility and camer concentration leads to a reduction in resistivity of about one order of magnitude. The relatively low resistivity of the sample at 0.54 As fraction is due to an exceptionally low concentration of carbon. The material becomes p-type below the critical composition. The free hole concentration rises approximately nine orders of magnitude following a 1% reduction in As fraction in the melt from the critical composition. The hole concentration and Hall mobility of this material are in the range of (1 - 3) X loL6cm-3 and 2 15 - 330 cm2 V-' sec-l, respectively. Some of the mobilities obtained from the p-type material grown in the transition region, correspondingto melt compositions within about 1% of the critical composition, were very low, between 1 and 30 cm2V-' sec-l. The measured hole These . carrier conconcentrations were about 1 X lo1*and 2 X lOI4~ m - ~ centrations are too high to explain the low mobilities in terms of mixed conduction. The low mobilities of material grown in the transition region could reflect inhomogeneities in the material. For instance, a striated pattern of regions of high and low resistivity could cause such behavior.

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Detailed resistivity profiles of crystals grown from initially As- and Garich melts further emphasize the role of the melt stoichiometry in controlling the electrical compensation, as shown in Fig. 17. It is important to note that unless the initial melt is precisely stoichiometric (small differences between the stoichiometric and congruent melting compositions are neglected), As-rich (Ga-rich) melts become progressively more As-rich (Garich) as the crystal is pulled from the melt. Crystalsgrown from As-rich melts were invariably semi-insulating from front to tail. Crystals grown from Ga-rich melts initially below the critical composition were p-type throughout. On the other hand, crystals grown from Ga-rich melts initially above the critical composition underwent a transition from semi-insulating to p-type at the point along the crystal where the corresponding melt composition reached the critical value. This behavior clearly indicates that the resistivity is controlled by the melt stoichiometry and that the semi-insulating to p-type transition is not related to the normal segregation of some common background impurity toward the tail of the crystal. Otherwise, the tail of As-rich-grown crystals would have become p-type as well. Evaluation of the electrical and optical properties of the semi-insulating material indicates that the deep donor, commonly referred to as EL2, is the predominant deep center. An optical absorption band shown in Fig. 18

108

-

107

-

..

I-' -.

-A As-RICH

A --- ---

- - - - -SEMI-INSULATING

(As INITIALLY BELOW CRITICAL COMPOSITION)

*0.1

0.4 0.5 0.6 0.7 FRACTION SOLIDIFIED

0.2 0.3

0.8 0.9 1.0

FIG.17. Resistivity profiles for LEC GaAs crystals grown from Ga-rich and As-rich melts. [From Holmes et al. (1982a).]

200

c. G. KIRKPATRICK et al. I

I

I

I 6

WAVELENGTH lpn)

FIG. 18. Optical absorption of the deepdonor EL2 in semi-insulating LEC GaAs.T = 300°K:NEL,= 1.8 X 10l6ern-'; n = 7.4 X lo7 ~ r n - ~ .

between 1 and 1.4 pm previously identified With the EL2 center (Martin, 1981) was observed in all of the semi-insulating material. In addition, the activation energy of the electron concentration, obtained from plots of the temperature-corrected free-electron concentration as a function of the reciprocal of temperature, was 0.75 f0.02 eV. This energy is consistent with published values (Martin et al., 1980b)for the activation energy of EL2. The behavior of the photoconductivity thresholds (Lin et al., 1976) above and below 120°K was also found to be consistent with the presence of EL2. The concentration of EL2 in LEC GaAs samples was determined by optical absorption using the cross section reported by Martin et al. (1980b). Absorption due to unoccupied EL2 centers was not observed, and variabletemperature Hall measurements (300-420°K) indicated that the centers were more than 90% occupied. Consequently, the absorption was taken to be proportional to the total EL2 concentration. The concentration of EL2 was found to depend on the melt stoichiometry, as shown in Fig. 19, as the As atom fraction increasing from about 5.0 X I O l 5 to 1.7 X 10l6cmW3 increased from about 0.48 to 0.5 1. The concentration remained constant as the As fraction increased further to about 0.535.

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STClCHlOMETRlC COMPOSITION

t 0

0

. 0

0

0

01 0.47

I

I

I

I

I

I

0.48

0.49

0.50

0.51

0.52

0.53

J 0.54

ARSENIC ATOM FRACTION I N MELT

FIG.19. Dependence of EL2 concentration as determined by optical absorption on the melt stoichiometry. The concentration of EL2 increases from 5 X lOI5 cm-' to 1.7 X lot6cm-3 as the As atom fraction increases from about 0.48 to 0.5 1, and appears to saturate as the As concentration increases further to 0.53. [From Holmes et ul. (1982a).]

The results of photoluminescence (PL) studies of the semi-insulating material are consistent with the measured dependence of EL2 on melt stoichiometry. Typical PL spectra at 4.2 "K of semi-insulating material grown from As- and Ga-rich melts, shown in Fig. 20 (curves a and b, respectively),exhibit bands peaking at 0.68 and 0.77 eV. The 0.68-eV band has been attributed (Yu et al., 1981) to radiative recombination between EL2 electron traps and the valence band, and the 0.77-eV band to recombination possibly associated (Yu et al., 1981) with a hole trap. The intensity of the 0.68-eV band in the semi-insulating GaAs grown from Ga-rich melts (curve b) is substantially reduced by comparison with As-rich grown material (curve a). This behavior is consistent with the decrease of the EL2 concentration with decreasing As fraction (Fig. 19)as determined by optical absorption. Neither band was observed in the p-type material. Photoluminescence spectra from p-type conducting material (Ga-rich), indicate the presence of an additional acceptor 77 meV above the top of the valence band (Yu et al., 1981). Hall measurements show that this defect is the primary defect in the ptype undoped material. The 77-meV acceptor was studied through infrared absorption.In Fig. 2 1, the room-temperature( T = 300°K) and low-temperature ( T - 20°K) infrared absorbance spectra of unintentionally doped ptype GaAs are shown. Absorption at room temperature is due to two-phonon lattice mode absorption (Cochran et at., 1961) and local vibrational mode absorption. In the low-temperature spectra, three additional peaks are observed at energies

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c. G. KIRKPATRICK et al.

202

FIG.20. Typical photoluminescence spectra of undoped semi-insulating GaAs grown from (a) an As-rich melt (As atom fraction - 0.507, p = I .8 X lo7f2 cm) and (b) aGa-rich melt (As atom fraction = 0.488, p = 1.4 X lo8 CI cm). ( T = 4.2"K.) The intensity ofthe 0.68-eV band decreases as the As atom fraction decreases toward the critical composition consistent with

E

I

W

(b)

1 t

.

"5/2

(r8)

2p5/2( r7)

(b) l

*

l

r

l

r

l

-

l

,

0

FIG.2 1. Far infrared absorption spectra of 78-meV acceptor in Gas. At room temperature, only phonon absorption is observed. At lower temperatures the spectrum associated with the acceptor is observed. (a) T - 300°K; (b) T = 20°K. [From Elliott er al.(1982).]

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LEC G d S FOR INTEGRATED CIRCUIT APPLICATIONS

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70.95, 72.94, and 74.5 meV. These peaks are only observed below 50°K in p-type material, indicating that the absorption is between different electronic states associated with an acceptor level. A comparison of spectra in these studies with previously published absorption and photoconductivity (Jones and Fisher, 1965; Kirkman et a/., 1978) results for Ge and GaAs leads to the identification of these lines as transitions from the ground state to the 2P,,2(T8) state (70.92 meV), the 2P5,2(T7) state (72.95 meV), and a higherenergy state (74.5 meV), which has previously been tentatively identified as the 3P,!, (Kirkman et al., 1978) state. Excellent agreement is obtained for the excited-state splittings with this identification compared to those measured for other defects. Results for C, Zn, Si, and Mg (Kirkman et al., 1978) have given a value for the 2P,,,(T,)-2P,,,(T8) splitting of 16 cm-I k 1 cm-I compared to the value 16 k 0.5 cm-' obtained here. The splitting between the 2P,/,(T8) and higher-energy state has been reported as 28.8 cm-I compared to 28 cm-' k 1 cm-l observed here. As a result, the excited-state structure can be accurately described by effective mass theory for simple acceptors. The ground-state energy can be estimated by settingthe energy of the 2P5/,(r8)state relative to the valence band at 7 meV. The value obtained, 78 meV, is consistent with theoretical values (>6 meV) and experimental estimates (76 meV) of this energy (Kirkman et al., 1978; Hunter and McGill, 1982), and is in good agreement with the value obtained from the luminescence measurements (77 meV). By combining the results of Hall measurements with absorption measurements, the optical cross section of the transition to the 2P5,2(T,) state was estimated to be aOpt A E = 1.9 X 1 O-I4 cm, where ow is the cross section and AE is the full width at half maximum of the peak. The concentration of the 77-meV center in the crystals was determined from optical absorption using this cross section. The concentration of the center depends strongly on the melt stoichiometry, as shown in Fig. 22, for melt compositions above 0.47 As atom fraction, increasing from less than 1 X lo1, ~ m to- a~level 3 X 10l6 ~ r n -as~ the melt composition decreases from 0.47 to 0.43 As atom fraction. Local vibrational mode measurements and variable-temperature Hall measurements indicate a background hole concentration of 3 X lo',- 12 X 10l6 ~ r n -from ~ residual carbon acceptors. These acceptors prevent compensation of the 78-meV level in most cases. There is also some evidence that growth kinetics influencesthe incorporation of the defect. For example, capacitance- voltage profiles for implanted wafers along the length of a crystal indicate fluctuations in the trap concentration. These fluctuations affect the net carrier concentration near the crossover point from p-type material to semi-insulating material and contribute to the scatter in the data. It is possible to rule out intrinsic defects which have symmetry lower than

-

c. G. KIRKPATRICK et al.

204

1 x 1016

\+ \

t

01 0.42

+\

\ ++-+

I

I

I

,

*\]

0.43 0.44 0.45 0.46 0.47 ARSENIC ATOM FRACTION IN MELT

0.48

FIG. 22. Stoichiometry dependence of the 78-meV acceptor. The concentration of the 78-meV acceptor increases rapidly from 0.47 As atom fraction to approximately 3 = 10I6cm-) at 0.43 As atom fraction. [From Elliott et ul. (1982).]

tetrahedral (TD).Such defects would have a split 1S3,2(rn) ground state associated with the local strain field and short range impurity potential of the defect. In addition, the P states of the acceptor are mixed by such a field so that the 2P5,,(T8)state would be split and the 2P,,,(T,) state would be shifted in energy. The excellent agreement between these results and those obtained for substitutional impurities and the absence of additional splittings in these spectra indicates that such effects are small. The linewidth of the 2P5,2(T8)state puts a limit on the magnitude of such a splitting at < 5 cm-* (0.62 meV). Since the deformation potential associated with the ground state should be on the order of 1 eV, and because the acceptor wave function should be well localized on the defect, a much larger splittingwould be expected for an axial or lower symmetry defect. For instance, the 150-meV Cu acceptor level is observed to have axial C3,symmetry and has a different far-infrared spectra than the substitutional simple acceptor levels (Willman et al., 1973). The defect responsible for the 78-meV level is most likely to be intrinsic in origin as opposed to an impurity-related defect. The only impurity, as determined by SIMS and LVM, occurring in these samples in sufficient concentration to be involved in this defect is boron. Although a Bh defect

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would produce a double acceptor, no correlation was found between the boron content in the crystals and the concentration of the defect. The 78-meV center is most likely associated with the anti-site Ga, or the arsenic vacancy. The levels associated with V, are thought to lie somewhere near midgap (Bachelet el al., 1981). On the other hand, the first ionization energy of the Ga, acceptor is estimated to be very close to the value measured for this defect, 78 meV, by using simple scaling arguments. Such an estimate is based on the point defect model for isocoric acceptors (Pantelides, 1978; Lipari and Baldereschi, 1978). Inspection of the Hamiltonian used by Baldereschi and Lipari for single acceptors shows that the energy is a function of the valence band parameters p and S, the effective spin -orbit splitting3,and the screening parameters Ai and B,. The form of the Hamiltonian for the double acceptor levels of isocoric defects is similar and also depends only on these parameters. Values of these parameters are very similar in Ge and GaAs, so an estimate of the Ga, levels can be made simply by scaling known values of the isocoric double acceptor Zn in Ge by the ratio of effective Rydbergs for the two materials. Using 32 meV for the first ionization of Zn in Ge, an energy of 84 meV is obtained for GaAs using Baldereschi and Lipari’s estimates for the effective Rydbergs of the two materials. This defect can also be compared to the well-known native double acceptor in GaSb (gallium antimonide), which is believed to be Ga, (van der Mulen, 1967). The theoretical basis for such a comparison is much weaker than in the previous case because Gasbis not isocoric and the band parameters are considerably different in this case. Even so, good agreement is obtained with the Ge and GaAs values. Using an energy 34.5 meV for the native defect in GaSb (Noack et al., 1978), an energy of 83 meV is obtained for in GaAs. If the 78-meV level is identified with the anti-site Ga,, it is possible to model the stoichiometric dependence of EL2 and the 78-meV level. Although speculative, it is appealing to consider the identification of EL2 with the As anti-site (A&) and the 78-meV level with the Ga anti-site defects (Ga,). Such an identification is supported by recent electron paramagnetic resonance (EPR) measurements (Wagner el al., 1980), which indicate the presence of As, in relatively large concentrations, lOI5- 10l6 cm-3 in melt-grown material. In addition, Van Vechten has predicted that such defects are potentially more stable than vacancy-related defects and can be introduced by deviations from stoichiometry during growth (Van Vechten, 1975). Such an ,interpretation is consistent with these results. When the stoichiometry dependence of the 78-meV defect is compared to that of EL2, the concentrations of both defects extrapolate to 0 at a melt composition near 0.47 As atom fraction. Such behavior can be explained by assuming

206

c. G.

KIRKPATRICK et

al.

that the A s , (EL2?)and Ga, (78-meV)defects annihilate each other during the cool-down process by forming neutral antistructure As,- Ga, defects. Since As,-Ga, defects should have a relatively low enthalpy of formation (Van Vechten, 1975), these defects would presumably anneal out at relatively low temperatures. Thus, after cool-down, only excess A s , or Ga, defects remain, depending on whether the material was grown As- or Ga-rich. In such a case, the dominant defects in unintentionally dopedmelt-grown GaAs would be either A s , or Ga,, depending on the stoichiometry of the melt. Recent results in gallium phosphide (GaP) support the anti-site model (Kaufmann and Kennedy, 1981). Po, anti-site defects in GaP have been found to occur in as-grown material. On the othe hand, V, defects have only been observed in electron-irradiated material.

8. COMPENSATION MECHANISM To develop a model for the electrical compensation in terms of the concentration of predominant electricallyactive centers in the semi-insulating material, the concentration of shallow and deep centers was related using simple theoretical considerations. The ionization of EL2 produces an ionized center plus an electron in the conduction band: un-ionized EL2 Ft ionized EL2

+ e-.

(1)

According to the principle of detailed balance, the concentration of ionized centers N,, the concentraton of electrons n, and the concentration of unionized centers Nu, are related by the following equation:

Nin/Nu= K, (2) where K is a constant determinedby the thermodynamicsof the system. Niis equal to the net acceptor concentration, given as the difference in concentration between shallow acceptors NsA and shallow donors NsD: Ni = N u - N S D .

(3) The concentration of acceptors is given as the sum of the concentrations of carbon and other residual acceptors, N f ;

+

NA = [ N p ] N i .

(4)

The concentration of un-ionized centers is equal to the EL2 concentration as determined by optical absorption. That is, only EL2 centers that are occupied by electrons contribute to the optical absorption process:

Nu = NEu. (5) By substituting Eqs. (3)-(5) into Eq. (2), the following expression for the

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207

free-electron concentration is obtained in terms of the predominant centers in the material: NEL2 ( [ N p ] NZ

+

n=K

(6)

- ND)'

This expression can be rewritten in the following form:

Therefore, the carbon concentration is proportional to the ratio of the EL2 concentration to the electron concentration. The material was evaluated according to Eq. (7), measuring the carbon concentration (by LVM), the EL2 concentration (by optical absorption), and the electron concentration (by Hall-effect measurements) for each sample. A plot of the carbon concentration as a function of the ratio of the EL2 concentration to the electron concentration, shown in Fig. 23, follows

. z

J

a / <

Y

/'

0

z

0

a K

.4 /

5 x 1015

8

/

0

I

I

I

1x10'

2x108

3x108

I

4x10'

I

5x108

I 6x10'

RATIO OF EL2 CONCENTRATION

TO ELECTRON CONCENTRATION

FIG.23. Dependence of the carbon concentration on the ratio of the EL2 concentration to the electron concentration. [Carbon] = K([EL2]/n) N D - N,R. The concentration of carbon, EL2, and electrons was determined for each sample. The dashed line is a least-squares fit to the data. The linearity of the data indicates the dominant roles played by EL2 deep donors and carbon acceptors in controlling the compensation (see text). The small value of the intercept (ND- N:) also indicates the predominance of carbon acceptor. [From Holmes et al. (1982b).]

+

208

c. G. KIRKPATRICK et al.

linear behavior, indicating that the electron concentration is indeed controlled by the balance between EL2 and carbon. This result is independent of possible errors in the published values of the optical cross sections for carbon and EL2. It is important to note that if some other impurity were the predominant acceptor, such as Mn, Fe, Cu, Zn, or the 78-meV acceptor level, the linearity predicted on the basis of Eq. (7) would still necessarily hold. However, the linearity would not be distinguishable because the carbon term would be small compared to N i ; the figure would be a scatter plot. In fact, the scatter in these data probably reflects actual fluctuations in the concentration of other background impurities rather than random error in the experimental measures. The small value of the intercept (N,-N;) of the least-squares fit to the data also indicates the predominance of carbon acceptors. Thus, EL2 deep donors and carbon acceptors control the electrical compensation. The variation of the electrical characteristicsof the semi-insulatingmaterial (Figs. 14- 16) with melt stoichiometry can now be explained on the basis of the preceding analysis. The EL2 concentration must either exactly match or exceed the carbon concentration to produce semi-insulating properties. The EL2 concentration in material grown from Ga-rich melts below the critical composition is insufficient to compensate the carbon, while in addition, the 78-meV acceptor appears to lead to p-type conductivity. Semi-insulating material grown at the critical composition is closely compensated, leading to a maximum of the resistivity. As the As atom fraction in the melt increases from the critical composition to about 0.5 1, the EL2 concentration becomes progressively higher than the carbon concentration. As a result, thermal ionization of (un-ionized)EL2 centers [see Eq. (1 )] gives rise to a gradual increase in the electron concentration and a corresponding decrease in the resistivity (Figs. 14 and 15). In practical terms, these results show that semi-insulating GaAs can be grown by the LEC technique reproducibly and with high yield, provided that the melt is As-rich. This condition ensures that the melt will not become Ga-rich during the growth process. The nine crystals grown during the course of this investigation from near-stoichiometric As-rich melts were semi-insulating from front to tail.

9. RESIDUAL IMPURITIES As discussed in the preceding section, the major electrically active centers in these LEC GaAs materials are deep-donor EL2, the 78-meV acceptor (tentativelyidentified as Ga,), and the carbon acceptors. Using a technique known as photoinduced transient spectroscopy (PITS), the presence of other defect levels has also been detected. Although quantitative information

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209

regarding trap concentrationsis not yet obtainablewith PITS, the technique is useful in determining the presence of traps. Photoinduced transient spectroscopy is a transport technique which detects the transient rise or decay of the sample photocurrent during chopped illumination. A typical PITS spectrum is obtained by sampling either the photocurrent rise (R-PITS)or decay (D-PITS)at two points in time, with the differenceA I = [I(tl)- I@?)]recorded continuously as a function oftemperature. Any peaks observed in the spectrum will correspond to a trap emission rate e,, which is directly proportional to the sampling rate A1-l = (t2 - tl)-’. Successive temperature scans at different sampling rates can therefore determine both the trap energy and capture cross section, assuming a single-exponential rise or decay. In Table IX, a table of traps which have been observed using PITS is presented. Some of the more important of these are discussed below. Figure 24 shows a typical PITS spectra (note the logarithmic scale) comparing Cr and unintentionally doped LEC material. TABLE 1X

TRAPS OBSERVED INLEC GaAs FROM PITS ETWU 0.15

~ ( c m ~ ) ~

Identity‘

-

0.18 0.14 0.26 0.28 0.30 0.34 0.26

8E14 (n) 8E 13 (u?) 1E16 (n) 2E12 (u?) 2E12 (n?) 4E14 (P) 5E14 (n) 1El6 (n)

0.5 1 0.57 0.52 0.65

9E13 (u) 6El3 (n) IE15 (P) 8E14 (n)

EL4 EL3 HL8

0.83 0.89 (0.74)

2E13 (P) 3E14 (P) 8E 14 (n)

HLlO HL 1 EL2

Commentsd c

ELI 1

-

c

HL6 EL6

-

-

c c

Si-0 acceptor complex; 0.22 eV from dark conductivity e e

Fee; prominent within Cr doping [O]-related; also from dark conduct Cre acceptor From dark conductivityC

a Energy referred to 0°K band gap, including energy (if any) associated with the cross section; (n)= donor level, (p) = acceptor level, (u?)-unknown. Cross section uncorrected for temperature dependence of the band gap. From Martin et a!. (1977). All levels except 0.89-eV Cr acceptor apear in undoped material. Refers to Cr-doped material.

ol/lV '1VNDIS a3ZllVWtlON

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A major difference in the two spectra (outside of the Cr level) is the 0.52-eV

hole trap. The 0.52-eV hole trap (HL8) is due to Fe and is particularly prevalent in Cr-doped samples, probably as a result of Fe contamination of the Cr. A second acceptor level at E, 0.35 eV has also been associated with Fe (Nakai et al., 1977) but only appears under conditions of light doping (<5E15 ~ m - ~A ) .hole trap was observed at 0.34 eV, 0 = 8E14, but only in Bridgman and VPE material. The fact that this second level does not appear in the PITS spectra for undoped LEC material possibly indicates a lower degree of contamination in the LEC material. The trap at 0.65 eV appears to be related to the pressure of oxygen in both Cr-doped and undoped material. It is particularly prevalent in LEC material grown from melts encapsulated by wet B203(Fairman et al., 1981), and its concentration is an effective end-point indicator for the suppression of Si incorporation from Si02 crucibles. This 0-related deep-donor level was observed in both LEC and Bridgman material (Oliver et al., 1981) in concentrationsestimated to be on the order of lOI5 or less. A hole trap at 0.83 eV, 0 = 2E13 (HL10) has also been observed by PITS measurements, but curiously not simultaneously with the 0.65-eV level. This suggests that HLlO may be due to the 0-related level acting as a hole trap, but the large-hole capture cross section would identify it as an acceptor level, inconsistent with the analysis of dark conductivity results. Furthermore, HLlO has prominently appeared in PITS spectra for LEC material grown with a dry B20, encapsulant, in contrast with results for the 0.65-eV level. Therefore, HLlO is tentatively assigned to a defect different from the 0-related level. The electron trap at 0.57 eV (EL3) has appeared infrequently in LEC material, being far more prevalent in Bridgman growths. This level has been associated with point defects or point defect/impurity complexes (Itoh and Yani, 1980). The electron trap at 0.34 eV (EL6/EL7) occurs frequently in semi-insulating (SI) GaAs, including LEC material. It is prevalent in samples containing Fe or Cr, but not exclusively so. A comparison of the defect levels occurring in Cr-doped LEC, undoped LEC, and undoped Bridgman GaAs indicates a number of advantages for undoped LEC GaAs grown from PBN crucibles. By eliminating residual iron and silicon levels in the material, it is possible to reduce the number of defects in the material to a minimum. As a result, only the deep-donor EL2, the 78-meV acceptor, and the carbon acceptor are electrically significant in these LEC materials. The 78-meV acceptor concentration can be reduced by growing with the appropriate melt composition. In this way, semi-insulating material can be grown with high yield in a consistent fashion.

+

c. G . KIRKPATRICK et al.

212

V. LEC GaAs in Device Fabrication

Improvements in the quality of LEC semi-insulating GaAs dramatically affect the fabrication and performance of discrete microwave transistors and diodes, monolithic microwave integrated circuits, and digital integrated circuits. This discussion focuses on digital integrated circuits. The GaAs digital IC technology is presently undergoing rapid development, with the aim of providing circuits that operate at higher switching speeds than is possible with silicon-based ICs (Eden et al., 1979; Van Tuyl et al., 1977; Mizutani et al., 1980). Most attention will be given to the technology developed at Rockwell International as a representative example. 10. APPROACH

Digital integrated circuits currently being developed are based on field effect transistors. Most have Schottky barrier field effect transistors (MESFETs), although structureswith p- n junction field effect transistors (JETS) or metal gates with intervening insulating layers (MISFETs) have also been reported (Zuleeg et al., 1978; Yokoyama et al., 1980). Additional circuit elements commonly include Schottky diodes and resistors of n-type GaAs (which may or may not be “saturated resistors” i.e., two terminal devices which make use of the velocity - field characteristicsof electrons in GaAs to achieve a desirable current - voltage nonlinearity). Typical circuit designs for digital gates are illustrated in Fig. 25. The circuits differ in the power consumed, the levels of integration, and the requirements placed on the switching FETs. Figure 25a illustrates buffered field effect logic (BF’L), which was the first type of circuit design used with GaAs (Van Tuyl et al., 1977). Depletion-mode (normally on) FETs are used. Relatively high-power supply voltages, high-pinch-off (threshold) voltages (>- 2 V), and high-power consumptions have typically been employed to achieve gate propagation

&

OUT

OUTPUT IN

7 -”ss (a)

(b)

(C)

FIG. 25. Circuit diagrams for three GaAs logic approaches: (a) buffered FET logic, (b) Schottky diode FET logic, (c) direct coupled FET logic.

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delay times below 100 psec. Figure 25b corresponds to Schottky diode field effect transitor logic (SDFL). This design also makes use of depletion mode FETs but allows a reduction in the power consumption at no cost in switching speed. Pinch-off voltages - 1 V are typically used. The reduced power consumption permits a larger number of gates to be placed on the same chip. Operating circuits (as shown in Fig. 26) containing more than 1000 gates have been reported with SDFL (Lee et al., 1980), and very large-scale integration (VLSI) levels of integration appear feasible (>10,000 gates). The circuit of Fig. 25c is direct-coupled FET logic (DCFL), which employs enhancement-mode (normally off) FETs, and typically has the lowest power consumption requirements (Mizutani et al., 1980; Zuleeg et al., 1978). The logic voltage swings are lowest with this approach; they are limited by the Schottky bamer turn-on voltage to avoid conduction of substantial current from the gate to the source. The allowable variations in pinch-off voltage, processing, and substrate characteristics are also the smallest. Fabrication yield is currently a significant problem with this approach. In addition to these three types of circuits, a variety of other circuit approaches and FET approaches have been demonstrated (Nuzillat, 1980). For all cases, however, at the high switching speeds achievable with GaAs,it is of major concern to maintain low-energy dissipation per switching operation so that a high level of circuit integration can be obtained without excessive power dissipation per chip. The high level of integration is particularly advantageous because it reduces the system burden of long-delay-time chip-to-chip interconnection, which might negate the system advantage obtained by using high-speed gates. On the other hand, for low switching energy, logic swings and voltage noise margins are reduced, placing stringent demands on the control over pinch-off voltage in the FETs.This requirement is further emphasized by the need for very high yield of FETs in order to produce circuits with large numbers of gates. The high degree of device reproducibility required for high system performance places stringent demands on the fabrication processes and substrate material characteristics. Active regions for the FETs, diodes, and resistors have been produced by epitaxial growth, by ion implantation, and by combinations of both (growth of an epitaxial “buffer” layer, followed by ion implantation). The most cost-effective approach is that of ion implantation directly into semi-insulating substrates, which will be emphasized here. A typical fabrication sequence (Welch et al., 1980) is illustrated in Fig. 27. Polished wafers of ( 100) semi-insulating GaAs are coated with a thin ( 1000 A) layer of Si3N4, which protects the surface from mechanical and chemical damage during the process and serves as an annealing cap, as described here. Donor ions are implanted in the desired device areas, with the remaining regions of the

-

FIG.26. Photograph of 8 X 8 multiplier fabricated on LEC GaAs. The Circuit contains 1008 gates.

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INSULATOR DEPOSITION AND M A S K I N G FOR N - IMPLANT 1. Si3N4 DEPOSITION

2.

N- IMPLANT (PHOTORESIST MASK)

3.

Nt IMPLANT (PHOTORESIST M A S K )

4.

DEPOSIT REST OF CAP INSULATOR

5.

ANNEAL IMPLANTS

6.

OHMIC METAL

7.

ALLOY OHMIC CONTACTS

8.

SCHOTTKY METAL

9.

2ND INSULATOR

10.

CUT WINDOWS

N+ IMPLANT

ENCAPSULATION AND ANNEAL

OHMIC CONTACT METALLIZATION

SCHOTTKY-BARRIER AND INTERCONNECT METALLIZATION

SECOND-LAY ER METALLI ZATl ON

I

SECOND-LEVEL INTERCONNECT

/INSULATOR 11. LND-LEVEL METAL <WAFER COMPLETE>

FIG.27. Fabrication steps for planar fabrication process using localized implantation into semi-insulatingGaAs. Note that the bare surface of the GaAs is never exposed, except for the areas where the encapsulating dielectric is briefly open for metal depositions.

sample protected by photoresist. The implanted ions are activated, and the lattice damage from the implant is removed by a post-implant anneal. Subsequently,metallizations are deposited on the GaAssurface, in windows etched in the Si3N4cap. The metallizations include, first, an ohmic contact layer typically of Au -Ge -Ni (which requires a subsequent alloy cycle) and, second, a layer of Ti-Pt- Au, which serves both as Schottky gates and as first level of interconnectsbetween devices. The metallizations are typically defined by a lift-off process; metal linewidthsin the Schottky gate region are typically 1 pm or less. To complete the circuits, a second level of interconnects is produced (in this case using Au) after appropriate deposition of an insulating layer of silicon nitride and via hole opening (Lee et al., 1980).

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The multiple, localized ion implant approach described earlier has a significant number of advantages over alternative techniques for producing the doped areas of the devices. The implantation technique is very flexible. A number of separate implants may be used, allowing independent optimization of the doping profile in different device regions. This capability is employed to obtain, for example, relatively heavily doped regions near the source and drain contacts to minimize series resistance in the switching FETs as well as to produce a low carrier density (8 X 10l6 ~ m - ~thick ) (>3000 A) active region for the Schottky diodes, to minimize diode capacitance. Isolation between devices is automatically obtained in the unimplanted areas through the semi-insulating substrate. The technique is cost effective since the throughput can be very high. Finally, the degree of control attainable in the doping concentration and thickness of the device areas is superior to most epitaxial techniques. A drawback of direct implantation is that the device characteristicsare relatively sensitive to the substrate properties-a relationship which has motivated much of the recent research in LEC growth. 1 1 . SUBSTRATE INFLUENCE

The GaAs substrates can affect device performance in several ways. First, the doping concentration and distribution obtained for the donor-implantation process can vary from ingot to ingot and also from region to region of the same ingot. Variations in electron mobilities in the doped regions may also occur. Second, the resistivity of unimplanted material has been found to decrease near the surface of wafers from a number of ingots during the post-implant anneal, which can cause a loss of isolation between devices. Third, the polished wafers typically must display good mechanical properties (size, flatness, parallelism, smoothness) in order to permit high-quality optical lithography (needed for 1-pm-long Schottky gates). Additional influences of the substrates on device performance have been suggested, but their existence has not been verified experimentally. These include effects of dislocations on current-voltage characteristics of devices and effects of impurities or lattice imperfections on circuit reliability. A typical implanted doping density profile for the FET channel region is shown in Fig. 28. These results were obtained from capacitance versus voltage measurements using Schottky barrier diodes produced on the sample surface. The peak camer density is of the order of 10’’ ~ r n - ~and , the depth is near 0.2-pm, achieved with 400 keV, Se ions implanted into the GaAs with a fluence of typically 2.2 X 10l2cm-2. The ion energy is sufficient to penetrate the Si3N, cap layer that is deposited prior to the implantation. The doping density profile is approximately gaussian in shape, although it has somewhat deeper tails than expected from a gaussian dependence. The measured doping density in the tail region is affected by

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2

0

t

2t z

w

0 2

0

0

a

wa a

a

0

10’6

FIG. 28. Carrier concentration profiles for ion-implanted FET channel-type regions in semi-insulating GAS,showing the difference in profile shape between substrates which are thermally stable and those which undergo surface conversion.

(1) a slight amount of channeling of the implanted ions (despite the fact that the ions are directed at the crystal 8 deg off the (100) orientation in order to minimize the channeling); (2) a slight amount of diffusion of the implanted Se during the 850°C post-implant anneal; and (3) the fact that the C- V technique used to get the doping profile exhibits artifacts due to the proximity of the semi-insulating substrate. From the circuit standpoint, one of the principal parameters of the implanted region is the pinch-off (threshold) voltage V,, measured in FETs or in Schottky diodes. The value of Vp corresponds to

where Nd is the net donor concentration in the implanted region (as

c. G.KIRKPATRICK et al.

218

discussed here), xis the distance from the surface, w, is the effective depth of the profile, V, is the built-in potential of the Schottky bamer, q is the electronic charge, and e is the static dielectric constant of GaAs. Variations in V, occur principally as a result of changes in the doping distributionNd(x) induced by variations in the substrate or in the implantation process. As discussed earlier, it is of interest for the fabrication of digital ICs to control Vp to within a relatively narrow range. For circuits of the SDFL type, control of (V,) to within C200 mV is desirable for high-yield fabrication of integrated circuits, where ( V,) is the average pinch-off voltage of FETs in an area corresponding to an entire circuit. The (V,) is affected by ingot-to-ingot and run-to-run reproducibility, as well as by long-range uniformity of the processed wafers. Too high a value of ( V,) will result in FETs that will not turn off, while too low a value will lead to excessively slow circuit operation. An additional constraint is that of short-range uniformity of V,; i.e., the deviations of V, from ( V p )among the FETs of the same circuit must be small. This is necessary to ensure that the input drive requirements of each gate will be met by the output capabilities of the preceding gates (after allowing for their fanout). The maximum tolerable standard deviation a, of V, within a circuit is dependent on the circuit size; values of a, of 50 mV appear to be needed for LSI circuits (> 1000 gates). To maintain the average pinch-off voltage V, within the required k 200mV range, the maximum tolerable deviations in Nd are of the order of 8 X loL5~ r n - ~assuming , a uniform deviation over the 2000-&thick channel. The maximum tolerable deviations in channel thickness are of the order of 80 A. These tolerances are significantly more stringent than what is routinely achieved with epitaxial growth techniques. The influence of the substrate on the measured V, is principally through the net donor distribution& ,as already mentioned. Here, Nd is given by the expression

- NSA - NDA + NSD

(9) where Nimpmt is the doping density introduced due to the implanted donors, and NsA,NDA,and NsDrepresent the substrate contributions of shallow acceptors, deep acceptors, and shallow donors, respectively, in the region of the implant. The deep donors N D D do not influence the FET behavior since they are neutral in the n-type channel region. There is, however, an effect of the deep donors in producing slow shifts in FET characteristicswhen the channelsare nearly pinched off. As detailed earlier, it is typical of semi-insulating undoped LEC GaAs grown in PBN crucibles that there is a net excess of shallow acceptors over shallow donors. There are, in addition, more than Nd

= Nimpht

3

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enough deep donors to compensate out the net p-type shallow doping concentration. The deep acceptor concentration is typically small. Under these circumstances, it is expected that the net channel doping will be somewhat lower than the doping from the implant alone, in a variable amount depending on NsA- NsD. This general behavior may be observed experimentallyby making a series of donor implants into neighboring test wafers from the same ingot. Figure 29a shows, for example, the carrier density profiles obtained by implanting Si at 390 keV with a series of fluences into a representativeingot. The camer distributions scale approximately with fluence; however, if one plots the camer density at a fixed depth (2500 A in this example) versus fluence, one

FIG.29. (a) Carrier concentration profiles for various fluences of Si implants into semi-insulating GaAs. (b) Plot of carrier concentration (at 0.25-pm depth) versus Si influence for implants into three different substrates: 0, G17-271; 0, R5; A, R7. The intercept at zero fluence is an indication of the substrate contribution to the doping. Ingot G17-27 1 was grown by the Bridgman method; the other two ingots were grown by the LEC method.

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obtains a linear relation that extrapolates back to a nonzero carrier density at zero fluence, as shown in Fig. 29b. For undoped LEC substrates grown from PBN crucibles, this extrapolated value is typically negative (acceptorlike) with a value in the range (1 - 5 ) X lOI5 ~ r n - ~in, reasonably good agreement with the expected range of NsA-Ns, on the basis of chemical analysis. In contrast, Cr-doped Bridgman semi-insulating substrates display an extrapolated carrier density with a value in the range (5 - 15) X lOI5 ~ m - ~ .

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This result corresponds to the fact that at the surface of the substrate there is an excess of shallow donors over shallow and deep acceptors while the substrate remains semi-insulating,In fact, this results from the phenomenon of Cr redistribution during the post-implant anneal. In the horizontal Bridgman technique, typically, considerableamounts of Si contaminate the ingots due to decomposition of the quartz-crystal-growth apparatus at the growth temperature. With the silicon donors, the predominant shallow impurity, it is possible to obtain semi-insulating GaAs only by the intentional incorporation of deep acceptors (Cr) to pin the Fermi level near midgap. As part of the ion implantation process, however, a post-implant anneal (typically at 850°C)is needed to ensure proper dopant activation. It has been shown by SIMS measurements that during this heat treatment, considerable motion of the Cr typically occurs near the substrate surface. Figure 30 shows, for example, the Cr profile obtained before and after an 85O0C/30-minanneal. The Cr is depleted over several microns from the surface. As a result, the silicon donor concentration may become undercompensated, yielding an n-type surface layer. If, however, the net donor ~ ) extends only over a thin layer, concentration is small (<5 X 1015~ m - and it is possible that the doped region will be completely depleted due to Fermi-level pinning at the surface and in the bulk. In such a case, there will

0 a

-- ___---_

---CR CONCENTRATION MEASURED IN "PURE" GaAs -

10

10140

1

2

3

4

5

DEPTH (pm)

FIG.30. SIMS data indicating the Cr concentration profile in annealed and unannealed Cr-doped Gas. Si3N4cap at 950 A.

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be no surface conductivity developed in the unimplanted material; only a slight donorlike contribution to the implanted channel will result. The phenomenon described earlier is known as “thermal conversion” of horizontal Bridgman (HB) substrates- the formation of a conducting surface region on a previously high-resistivity wafer as a result of heat treatment. Thermal conversion of wafers during IC fabrication gives rise to a loss of electrical isolation between devices and consequent circuit failure. A second type of thermal conversion has been identified, in which the surface of the wafer becomes ptype. This type of conversion is common when wafers are heated in a non-As-containingambient without an encapsulation layer, and is thought to be related to the pileup of Mn acceptors in the surface region. The incidence of p-type conversion, as well as of the n-type conversion described, depends on both the substrate material and the detailed processing. Possible processing variables include substrate cleaning techniques, chemical nature of the encapsulant, the deposition technique for the encapsulant, and anneal temperature and ambient. Ingot-selection techniques have been introduced at laboratories involved in fabricating integrated circuits, as a result of the variable incidence of thermal conversion among horizontal Bridgman ingots, as well as of the variable substrate donor contribution developed near the surface of the wafers. Sample slices from the front and tail of candidate ingots are submitted to qualification tests typically involving a test implant (to monitor the extra doping component contributed by the ingot, as well as to observe the mobility obtained) and a thermal treatment similar to the post-implant anneal (to see if any thermal conversion occurs). Experience at this laboratory showed that the fraction of ingots qualified from commercial suppliers of horizontal Bridgman ingots was -30% or less. A dramatic change in qualification yield occurred with the introduction of LEC substrates. Virtually all the undoped ingots grown from PBN crucibles at Rockwell have passed the electrical qualification tests. 12. IMPACT

OF LEC GaAs

Introduction of the LEC material has also led to improved ingot-to-ingot reproducibility of pinch-off voltages in ion-implanted FET channel layers. The magnitude of the improvement in reproducibility is evident in the data of Fig. 3 1. Test chips were obtained from a variety of (qualified)horizontal Bridgman substrates and in-house-grown undoped LEC substrates; the test chips were processed together, capped with Si3N,, implanted with Se, and annealed; the resultant effective pinch-off voltage Vp was determined with the C- V technique. In this fashion, variations in the results due to processinduced effects were minimized. A standard deviation of 304 mV is displayed among the horizontal Bridgman samples, even after excluding 2 of the 12 ingots which, in fact, displayed unqualified behavior (due, presum-

3. 6

LEC I

GaAs FOR INTEGRATED CIRCUIT APPLICATIONS I

I

I

I

I

I

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n v)

g

4

t 0.

0

a Y

m 4

2

2

I

Vd (V)

(b)

FIG.3 1. Histogramscomparing the variations in pinch-off voltage among different ingots of undoped LEC and Bridgman GaAs.(a) Rockwell LEC undoped; a, = 95 mV.(b) Bridgman; a, = 304 mV 16%excluded).

ably, to nonuniformity within the previously tested ingot). The distribution of V,, among the 9 undoped LEC ingots grown from PBN crucibles is significantly tighter; the corresponding standard deviation was 95 mV. The radial and longitudinal uniformity of the ingots has been another important advantage of the LEC-grown substrates over the horizontal Bridgman material for digital ICs. The growth size and geometry, and the absence of Cry decrease the effects of impurity segregation in the LEC material. As a result, pinch-off voltages of FETs tend to display smaller variations across fabricated wafers when LEC substrates are used. The uniformity of FET characteristics has been studied at Rockwell for a number of years. To facilitate the study, an array of 1-pm gate length test

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transistors is included on each processed wafer, and, after completion, an automated test setup is used to probe the devices and accumulate the corresponding statistics and wafer maps (Zucca et a/., 1980). Figure 32 indicates the degree of uniformity in threshold voltage distribution possible with undoped LEC GaAs; a standard deviation of 25 mV is measured for these transistors, distributed across the IC wafer, which measures 25 X 25 mm on a side (and is thus smaller than a typical slice from an ingot). To compare the uniformity of HB and LEC substrates, it is of interest to compare the V, statistics for a number of wafers. Over a six-month period, for example, in which more than 50 wafers (including both HB and LEC material) were processed, the median standard deviation of V, across the wafer was 85 mV for the Bridgman material and 55 mV for the LEC material. It should be noted that the pinch-off voltages of FETs close to one another on a wafer are correlated so that the standard deviation of V, within a relatively small neighborhood (with dimensions on the order of millimeters) is smaller than that obtained over the entire wafer. No significant differences have been noted between the short-range statistics for horizontal

1.0 IN.

DEPLETION VOLTAGE 1.2

- 1.3 V

1.3 - 1.4 V 1.4

- 1.5 V

FIG.32. Histogram showing the variation in pinch-off voltage across a 1-in. processedwafer of undoped LEC GaAs, showing minimal variations.

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Bridgman and LEC material. The low amount of variation obtained in both cases is favorable for the high-yield fabrication of LSI circuits. To further probe the uniformity of LEC substrates, Se implants have been carried out on wafer sections larger than the IC wafers used to date at this facility. Figure 33 shows, for example, a map of effective pinch-off voltage as obtained from C- V measurements on a quarter of a 3-in. LEC wafer. The standard deviation of V, is only 39 mV (2.8% of the mean). Additional data are shown in Fig. 34, which indicates the high degree of uniformity of V, obtained among test chips selected along the length of a LEC ingot. The size and shape of LEC substrate material should have a major long-term impact on the fabrication procedures for GaAs ICs. At this laboratory, a fabrication line is in place employing 3-in.-diam round (100) GaAs wafers. Considerable economy results from using photolithography, plasma etching, metal deposition, and other equipment designed and optimized for silicon wafer processing. At the same time, the expanded area per wafer should contribute to the reduction of processed GaAs chip costs.

1

H 0.02 V FIG. 33, Map of a quarter of a 3-in. LEC undoped LEC wafer showing variations in the depletion voltage across the length of an undoped LEC ingot. Vp = 0.9441 V; ( V,) = 2.491E2

(2.6%).

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et al.

VARIATION OF Vp ALONG INGOT LENGTH

P 2.0

t

1

WAFER NUMBER

FIG.34. Variation of depletion voltage along the length of an undoped LEC ingot.

There has been concern regarding the effect of dislocations in LEC GaAs on device performance and reliability. Preliminary studies indicate that the performance of ICs is not affected by substrate dislocations. For example, some of the larger integrated circuits fabricated at in this facility have been produced on substrates with a 2 X 10S-cm-2 dislocation density. These circuits contain sufficient FETs and diodes that the probability is close to unity that at least one FET channel region or Schottky diode active region is traversed by a dislocation. The successful operation of the circuits with reasonable yield indicates that a single dislocation is not a fatal flaw. In summary, undoped LEC GaAs substrates have had a positive impact on the fabrication of digital ICs. The uniformity and ingot-to-ingot reproducibility of implanted FET channel characteristics have been markedly improved, and the problem of thermal conversion has been eliminated, making the ingot qualification procedures formerly employed no longer critical. The availability of material has improved considerably, and the size and shape of the wafers are conducive to batch fabrication with available semiconductor processing equipment. At the same time, there appear to be no detrimental effects from the higher dislocation density generally associated with LEC material.

VI. Conclusions These investigations of undoped, semi-insulating LEC GaAs have focused on four principal issues: (1) the crystal growth technology, (2) structural perfection, (3) electrical properties, and (4) behavior of the material

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during device processing. The results have brought about a considerable improvement in the understanding of the cause- effect relationships between properties of the material and crystal-growth parameters. Through these results, undoped, semi-insulating material can be grown reproducibly with good yield primarily through proper control of the stoichiometry. Furthermore, the undoped LEC material has demonstrated the uniform, thermally stable properties required for GaAs device fabrication. The LEC GaAs material offers superior properties for device fabrication and control of device parameters, particularly depletion-mode digital integrated circuits. 13. ELECTRICAL PROPERTIES AND COMPENSATION MECHANISM

The key to the reproducible growth of undoped semi-insulatingGaAs by the liquid-encapsulated Czochralski technique is the control over the melt stoichiometry. Evidence presented indicates that the free-carrier concentration is controlled by the balance between EL2 deep donors and carbon acceptors; furthermore, the incorporation of EL2 is controlled by the melt stoichiometry, increasing as the As atom fraction in the melt increases. As a result, semi-insulating material can be grown only from melts above a critical As composition. Using the in situ synthesis, As can escape from the charge during the heat-up cycle through sublimination with the loss of significant quantities of As. Ga-rich melts and p-type (low resistivity) crystals can result from this loss, which depends on at least two parameters- the crucible material and the initial heating rate of the charge. The empirically determined dependence of the concentration of EL2 (and the 77-meV acceptor) on melt stoichiometry provides strong evidence for the existence of electrically active native defects in GaAs. Although it is generally acknowledged that native defects could play an important role in controlling the properties of GaAs, no consistent picture has yet emerged concerning the nature and properties of the defects. However, results from these studies show that native defects can have profound effects on the electrical characteristics of bulk material. The connection between EL2 and a native defect in bulk LEC GaAs is consistent with published work on GaAs grown by vapor-phase epitaxy and organometallic chemical vapor deposition. These previous reports showed that the EL2 concentration increasesas the As/Ga ratio in the vapor increases. Isolated native defects which would follow the observed stoichiometry dependence of EL2 include the gallium vacancy V, ,the arsenic interstitial As, and the arsenic-on-galliumanti-site As,. Since V, would be expected to be an acceptor, EL2 would more likely be related to one of the latter two defects. A second stoichiometry-related defect, an acceptor, found in material grown from Ga-rich melts was also identified. Interpretation of the optical absorption spectra and variable-temperature Hall measurements suggests

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that the center is a gallium-on-arsenic antisite ( G a d double acceptor. The defect is complementary to EL2: The concentration of both defects is about 5 X 1015 cm-' in material grown from melts with a concentration of 0.47-0.48 As atom fraction; the EL2 concentration in the material increases above this As composition in the melt, while the acceptor concentration increases below this melt composition. The complementary nature of these defects would suggest that EL2 is an arsenic-on-galliumanti-site As,. An issue yet to be resolved concerns the thermal annealing behavior of native defects, during both crystal growth and device processing. The solidification process takes place at the melting point of GaAs (1238°C)or a few degrees below this temperature, depending on the degree of nonstoichiometry in the melt. The material remains at elevated temperatures for several hours after solidification, cooling slowly as the crystal is pulled from the melt, and the growth chamber is slowly brought to room temperature. It is highly likely that the grown-in defect density undergoes some change in concentration during this cooling process.

14. STRUCTURAL PERFECTION The density and distribution of dislocationsin 3-in.-diam, undoped GaAs crystals grown by the liquid-encapsulatedCzochralski technique have been characterized. The radial distribution across wafers exhibits a W-shaped profile, indicating excessive thermal gradient-induced stress as the primary cause of dislocations. The density along the body of each crystal increases continuously from front to tail. In contrast, the longitudinal distribution in the cone region is inverted, first increasing and then decreasing as the crystal expands from the neck to full diameter. Growth parameters favoring reduced dislocation densities include good diameter control and the use of thick B203encapsulating layers, slightly As-rich melts, and low ambient pressures. The dislocation density in the body of the crystal is practically independent of cone angle 8 for 20 deg < 8 < 70 deg. However, high densities result for flat-top (0 deg < 8 < 20 deg) crystals. Dash-type seed necking reduces the dislocation density only when high-density seeds (>5000 cm-2) are used. Further, studies revealed that convective heat transfer from the crystal to the high-pressure ambient plays a dominant role in controlling the dislocation density. Low-dislocation, 3-in.-diam GaAs can be grown by the LEC technique. Material has been produced at this laboratory with EPDs as low as 6000 cm-2 in selected regions of the crystal. The average EPD over approximately 80%of the area of 3-in.-diam wafers has been less than 5 X lo4cm'2. Further reductions in dislocation density are expected through proper control of the crystal growth parameters, including, for example, the use of thick B203 encapsulating layers to reduce the radial gradients and reduction of the

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growth pressure to decrease the heat transfer at the crystal ambient surface (provided that the thermal degradation of the crystal can be controlled). Modification of the crystal growth configuration to reduce convective heat transport in the ambient would also be beneficial. 15. CRYSTAL GROWTH TECHNOLOGY

Advances made in diameter control and in reducing the incidence of twinning are important recent accomplishments in the LEC crystal growth technology. Since single crystalline wafers with the (100) orientation are required for integrated circuit application, twin formation during crystal growth (leading to changes in crystallographic orientation) and polycrystallinity must be avoided. Studies indicate that one of the most important growth parameters for the control of twinning is the melt stoichiometrythe incidence of twinning is significantly reduced when crystals are grown from As-rich melts. A yield of single crystalline material of over 90% has been achieved by growing from As-rich melts, with further improvements expected with tighter control over the stoichiometry. The success and cost effectiveness of GaAs device technology will ultimately depend on the availability of round, uniform-diameter wafers for automated device fabrication. The first step in achievingthis is the growth of crystals with a uniform diameter (also shown to be important in maintaining a low-dislocation density). Through proper control of the growth parameters (i.e., cooling rate, crystal rotation and pull rate, and crucible rotation and lift rate), the diameter can be controlled manually to a tolerance as low as f 1.1 mm and with a routine tolerance of better than +-3 mms. This degree of diameter control, together with centerless grinding, results in the maximum yield of usable material. Although further reductions in the dislocation density will accompany reductions in the radial temperaure gradients in the growth system, the lower gradients will likely lead to increased difficultiesin maintaining diameter control. Therefore, automatic diameter control will eventually become necessary for the production of large-diameter material for integrated circuit applications. 16. APPLICATION TO ICs

The progress achieved through these studies of the LEC growth technique for undoped semi-insulatingGaAs has resulted in substantialimprovements in the uniformity and reproducibility of critical parameters of integrated circuits. The electrical and crystalline parameters exhibited by these materials are superior to those observed from materials grown by other techniques and meet the requirements for use in the fabrication of LSI devices.

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c. G . KIRKPATRICK er al. ACKNOWLEDGMENTS

The authors wish to thank the National Aeronautics and Space Administration/Army for partially supporting this work under Contract No. NAS3-22224. We also acknowledge the support of the Air Force in making the photoluminescencemeasurementsunder Contract No. F336 15-8I-C-1406.

REFERENCES Angilello, J., Potenski, R. M., and Woolhouse, G. R. (1975). J. Appl. Phys. 46,2315. AuCoin, T. R., Ross,R. L., Wade, M. J., and Savage, R. 0.(1979).Solid State Technol. 22,59. Bachelet, G. B., Baraff, G. A., and Schliiter, M. (1 98 I). Phys. Rev. B 24, 9 15. Bonner, W. A. (1980). Muter, Res. Bull. 16,63. Brice, J. C. (1970). J. Cryst. Growth 7,9. Brice, J. C., and King, G. D. (1 966). Nature (London) 209, 1346. Chen, R. T., and Holmes, D. E. (1983). J. Cryst. Growth 61, 1 1 1. Cochran, W., Fray, S. J., Johnson, F. A., Quarrington, J. E., and Williams, N. (196 1). J. Appl. Phys. 32,2102. Cullis, A. G., Augustus, P. D., and Slirland, D. J. (1980). J. Appl. Phys. 51,2556. Dash, W. D. (1957). J. Appl. Phys. 28, 882. Eden, R. C., Welch, B. M., Zucca, R., and Long, S. I. (1979). IEEE Trans. Electron Dev. ED-26,299. Elliott, K. E., Holmes, D. E., Chen, R. T., and Kirkpatrick, C. G. (1982). Appl. Phys. Lett. 40, 898. Fairman, R. D., Chen, R. T., Oliver, J. R., and Ch'en, D. R. (198 I). IEEE Trans. Electron Devices ED-28, 135. Gooch, C . H., Hilsum, C., and Holeman, B. R. (1961). J. Appl. Phys. 32,2069. Grabmaier, B. C., and Grabmaier, J. G. (1972). J. Cryst. Growth 13/14,635. Haisty, R. W., Mehal, E. W., and Stratton, R. (1962). J Phys. Chem. Solids 23,829. Hasegawa, F., and Majerfeld, A. (1975). Electron. Lett. 11,286. Hiskes, R. et 01. (1982). Proc. Con! Amer. Assoc. Crystal Growth- West, Fallen Leaf Lake, May 1982. Holmes, D. E., Chen, R. T., Elliott, K. R., and Kirkpatrick, C. G. (1982a). Appl. Phys. Lett. 40, 1. Holmes, D. E., Chen, R. T., Elliott, K. R., Kirkpatrick, C. G., and Yu,P.W. (1982b). IEEE Trans. Microwave Theory Tech. M'IT-30,7. Hunter, A. T., and McGill, T. C. ( 1 982). App/. Phys. Lett. 40, 169. Itoh, T., and Yani, H. (1980). Int. GaAs Symp., Vienna. Jones, R. L., and Fisher, P. (1965). J. Phys. Chem. Solids 26, 1 125. Jordon, A. S . (1 980). J. Cryst. Growth 49,63 1. Jordan, A. S., Caruso, R., and Van Neida, A. R. (1980). Bell Syst. Tech. J. 59,593. Kaminska, M., Lagowski, L., Parsly, J., and Gatos, H. C. (198 1). Lund Con! Deep Levels, 3rd, Southbury, Conn. Kaufmann, U., and Kennedy, T. A. (1981). J. Electron. Muter. 10, 347. Kirkman, R. F., Stradling, R. A., and Lin-Cheung, P. J. (1978). J. Phys. C 11,419. Kocot, C., and Stoke, C. (198 I). GaAs IC Symp., San Diego, Calg Lee, F. S., Shen, E., Kaelin, G., Welch, B., Eden, R. C., and Long, S . I. (1980). High Speed LSI GaAs Digital Integr. Circuits, GaAs IC Symp., Las Vegas, Nev. Lin, A. L., Omelianouski,E., and Bube, R. (1976). J. Appl. Phys. 47, 1852. Lind, M. D. (198I). Personal communication.

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Lipari, N. O., and Baldereschi, A. (1978). Solid State Commun. 25,665. Martin, G. M. (198 1). Appl. Phys. Lett. 39, 747. Martin, G. M., Honneau, A. M., and Mircea, A. (1977). Electron. Lett. 13(7), 191; 13(22),666. Martin, G. M., Farges, J. P., Jacob, G., and Hallais, J. P. (1980a). J. Appl. Phys. 51,2840. Martin, G. M., Jacobs, G., Goltzene, A., and Schwab, C. (1980b). Proc. Int. Con! De$ects Radiat. Efl Semicond., I Ith, Oisa, Jpn Metz, E. P. A., Miller, R. C., and Mazelsky, R. ( 1962). J. Appl. Phys. 33,20 16. Mil’vidskii, M. G., and Bochkarev, E. P. (1978). J. Cryst. Growth 44,61. Mil’vidskii, M. G., Osvensky, V. B., and Shifrin, S. S. (1981). J. Cryst. Growth 52,396. Mizutani, T., Kato, N., Ishida, S., Osafune, K.,and Ohmori, M. (1980). Electron. Lett. 16,3 15. Mullin, J. B., Royle, A., and Benn, S. (1980). J. Cryst. Growth SO, 625. Nakai, N., et al. (1977). J. Electrochem. SOC.124, 1635. Noack, R. A., Ruhle, W., and Morgan, T. N. (1978). Phys. Rev.B 18,6944. Nuzillat, G., Bert, G., Ngu, T. P., and Gloanec, M. (1980). IEEE Trans. Electron Devices ED-27, 1102. Oliver, J. R., Fairman, R. D., and Chen, R. T. (1981). Electron. Lett. 17, 839. Pantelides, S. T. (1978). Rev. Mod. Phys. 50,797. Parsey, J., Namiski, Y., Lagowski, J., and Gatos, H. C. (1981). J. Electrochem. Soc. 128,936. Penning, P. (1958). Philips Res. Rep. 13,79. Reed-Hill, R. E. (1973) “Physical Metallurgy Principles,” 2nd Ed., p. 174. Van Nostrand, Princeton, New Jersey. Roksnoer, P. J., Huijbregts, J. M. P. L., Van De Wijgert, W. N., and DeKock, A. J. R. ( 1977).J. Cryst. Growth 40,6. Sakai, K., and Ikoma, T. (1974). Appl. Phys. 5, 165. Seki, U., Watanabe, H., and Matsui, J. (1978). J. Appl. Phys. 49,822. Shinoyama, S., Uemura, C., Yarnarnoto, A., and Tokno, S.4. (1980). Jpn. J. Appl. Phys. 19, L331. Steinemann, A., and Zirnrnerli, V. (1963). Solid-state Electron. 6, 597. Steinernann, A., and Zirnrnerli, V. (1966). Proc. Int. Con$ Cryst. Growth, Boston, MA p. 8 1. Swiggard, E. M., Lee, S. H., and Von Batchelder, F. W. (1977). Conf:Ser. --Inst. Phys. No. 336, p. 23. [Seealso Henry, R. L., and Swiggard, E. M. (1977). Conf:Ser.-Znst. Phys. No. 336, p. 28.1 Thomas, R. N., Hobgood, H. M., Eldridge, G. W., Barrett, D., and Braggins, T. T. (1981). Solid-State Electron. 24, 387. van der Mulen, Y. J. (1967). J. Phys. Chem. Solids 28,25. Van Tuyl, R. L., Liechti, C. A., Lee, R. E., and Gower, E. (1977). IEEE J. SolidState Circuits SC-12,485. Van Vechten, J. A. (1975). J. Electrochem. Soc. 112,423. Wagner, R. J., Krebs, J. J., and Straw, G. H. (1980). Solid State Commun. 36, 15. Weisberg, L. R., Blanc, J., and Stofko, E. J. (1962). J. Electrochem. SOC.109,642. Welch, B. M., Shen, Y.-D., Zucca, R., Eden, R. C., and Long, S. I. (1980). IEEE Trans. Electron Devices ED-27, 1116. Willman, F., Bliitte, M., Queisser, H. J., and Treusch, J. (1973). SolidState Commun. 9,2281. Yokoyama, N., Minura, T., and Fukuta, M. (1980). IEEE Trans. Electron Devices ED-27, 1124. Yu,P. W., Holmes, D. E., and Chen, R. T. (198 1). Int. Symp. GaAsRelat. Compd., Oisa, Jpn. Zucca, R., Welch, B. M., Lee, C. P., Eden, R. C., and Long, S. I. (1980). IEEE Trans. Electron Devices ED-27,2292. Zuleeg, R., Notthof, J. K., and Lehovec, K. (1978). IEEE Trans. Electron DevicesED-25,628. Zuzuki, T., Akai, S., Kohe, K., Nishida, Y., Fujita, F., and Kito, N. (1979). Sumitomo Electr. Tech. Rev. 18, 105.

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SEMICONDUCTORS AND SEMIMETALS,

VOL. 20

CHAPTER 4

Models for Mid-Gap Centers in Gallium Arsenide -f J. S. Blakemore and S. RahimiS OREGON GRADUATE CENTER BEAVERTON, OREGON

LISTOF SYMBOLS.. . . . . . . . . . . . . . . . . , I. INTRODUCTION. . .. .. . . . . .. . .. ... .. 1. Phenomena Affected by the Presence of Mid-Gap States . 2. A ClassiJcationSchemefor Deep-Level Centers . . . . 11. QUANTUM-MECHANICAL VIEW OF FLAW STATES . . . . . 111. EFFECTIVE MASSFORMALISM: ITSLIMITATIONS FOR DEEP-LEVEL CENTERS.. . . . . . . . . . . . . . . . 3. Effective Mass Theory . . . . . . . . . . , . . . . 4. A First Look at Radiative Transitions . . . . . , . . IV. DELTA-FUNCTION POTENTIAL AND QUANTUM-DEFECT MODELS. . . . . . . . . . . . . . . . . . . . . . . 5. LucovskyS Delta-FunctionPotentiat Model . . . . . . 6. The Quantum-Defect Model. . . . . . . , . . . . . 1. Flaw Wave-FunctionSpatial and Spectral Properties . . V. ELECTRONIC TRANSITION PHENOMENA INVOLVING FLAWS, AND THE SQUARE-WELL POTENTIAL AND BILLIARD-BALL MODELS. . . . . . . , . . . . . . , . . . . . , . . 8. The Spherically Symmetric Square-Well Potential Model 9. Photoionization and the Billiard-Ball Model. . . . . . 10. Phonon-Assisted Optical Transitions . . . . . . . . . 1 1. Notes on Carrier Capture and Emission Mechanisms . . VI. TECHNIQUES ORBITALS. . . . . . BASEDON MOLECULAR 12. The Defect Molecule Method . . . , . . . . . , . . 13. The Extended Hiickel Theory (EHT) Cluster Approach . 14. The Xa-Scatiered-Wave Method, . . , . . . . . . . 15. The Cluster- Bethe-Lattice Method . . . . . . . . . VII. PSEUDOPOTENTIAL REPRESENTATIONS. .. . . . .,, . VIII. GREEN'SFUNCTION METHOD . . . . . . . . . . . . . 16. General Formulation. . , . . . . . , . , . . . . . 17. Green's Function Method Results . . . . . . . . . . IX. BRIEFNOTESON OTHER APPROACHES.. . . . . . . . . REFERENCES .....................

234 235 235 238 242 245 245 249 25 1 252 260 264 261 268 27 1 282 293 309 309 31 I 313 319 320 328 328 331 349 353

t Supported by the National Science Foundation, through DMR Grants 1916454 and 8305731. $ Present address: Sonoma State University, Rohnert Park, California. 233 Copyright 0 1984 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-752120-8

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List of Symbols UA

a, ad

BBM C3"

cc

CBL Cr+ Cr2+ Cr3+ cr, C

cu,

cw det 4-c

DLTS DMM E. E A

ECH

ECI

Ed ED

E Ello,

EHT

Ei Eimp

Ek

EMA EMT E",k

JP ESR Es

Characteristic Bohr radius of deep acceptor Characteristic Bohr radius of deep donor Scaled Bohr radius of shallow donors Billiard-ball model Trigonal point group Configurational coordinate Cluster-Bethe -lattice Doubly ionized chromium Singly ionized chromium Neutral chromium Chromium substituting for gallium Speed of light Copper substituting for gallium Coulomb wave function Determinant Franck-Condon shift Deep-level transient (capacitance) spectroscopy Defect molecule model Ground-state binding energy of shallow acceptors Ground-state binding energy of deep acceptors Core eigenstate of host atoms Core eigenstates of impurity atoms Ground-state binding energy of shallow donors Ground-state binding energy of deep donors Energy level of the imperfect crystal Host energy Extended Huckel theory Intrinsic gap Impurity energy Kinetic energy Effective mass approximation Effective mass theory Energy level of the perfect crystal p-orbital energy Electron spin resonance s-orbital energy

Iron impurity substituting for gallium Spectral function Manganese impurity in GaAs Copper impurity in GaAs Mercury impurity in germanium Green's function Matrix elements of Go Nonrelativistic crystal Hamiltonian Long-range potential Imperfect crystal Hamiltonian Perfect host-crystal Hamiltonian Potential energy introduced by the flaw Short-range potential Matrix elements of h Imaginary Modified Bessel function of the first kind Bessel function Komnga, Kohn, and Rostoker Linear combination of atomic orbitals Conduction-band effective mass Mass of electron Molecule orbital Multiphonon emission Multiple scattering approach Valence-band effective mass Bose- Einstein occupancy number Oxygen substituting for phosphorous Orthogonalized plane wave method Phosphorous substituting for arsenic Photoluminescence Photoluminescence excitation Photoluminescence quenching Plane wave Quantum-defect model Rydberg constant Radius of square-well potential

4. MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE Spherical-well model Antimony substituting for arsenic Selenium substituting for arsenic Huang-Rhys factor Boron impurity in silicon Indium impurity in silicon Silicon substituting for gallium Tin substituting for arsenic Effective phonon temperature Point group of tetrahedral molecules Kinetic energy of electrons Kinetic energy of nuclei Trace Vacancy at arsenic site Vacancy at gallium site Depth of square-well potential Perfect host-crystal potential energy Potential energy Host pseudopotential Impurity pseudopotential

235

Vacancy at antimony site

Xa scattered wave Effective valence number Zinc substituting for galium Nominal valence number Number of valence electrons Shallow-acceptorenergy level Shallow-donor energy level Electron wave function Wave function of the perfect crystal Dielectric constant Total atomic wave function Wave function of the imperfect crystal Kronecker delta function Laplacian operator Photoionization cross section Effective field ratio Spin-orbit splitting Dirac delta function Enthalpy change Entropy change

I. Introduction This chapter concerns models for centers (in a semiconductor such as GaAs) that provide localized states in the central part of the intrinsic gap. It is offered as a guide for experimentalistsrather than as a rigorous theoretical exposition. Thus, our purpose and mode of presentation differ from those found in some detailed deep-level theory reviews prepared by theoretical writers. The latter include extensive accounts by Roitsin (1974), Stoneham (1973, Pantelides (1978), Jaros (1980, 1982), and Lannoo and Bourgoin (1981) among others. Frequent literature notations in the text can direct the interested reader to these theoretical writers and to the voluminous primary literature on deep-level theory. Concern with the semiconductor gallium arsenide motivated the study reported herein. Many of the principles are clearly relevant also to other semiconductors, however, especially those of Td symmetry- with zincblende or diamond structures. 1. PHENOMENA AFFECTEDBY THE PRESENCE OF

MID-GAPSTATES The presence of large concentrations of mid-gap states in GaAs became apparent when semi-insulating crystals were first inadvertently grown

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J. S. BLAKEMORE A N D S. RAHIMI

(Whelan and Wheatley, 1958; Bube, 1960). Hilsum (1965) summarized the experiments and speculations of those early years, including the effects of copper doping (Blanc et al., 1961) and the apparent influence of oxygen (Allen, 1960). The role of chromium doping (Cronin and Haisty, 1964; Martin et al., 1980), and ofthe EL2 center (Lang and Logan, 1975; Martin et al., 1 977) in creating semi-insulating GaAs without deliberate deep-level doping, have motivated numerous studies. Both native defect states and impurity states near mid-gap exert a variety of influence on GaAs, which is not necessarily semi-insulating. Thus, shallow donors (such as Si or Se) in n-type GaAs are obliged to provide electrons to any mid-gap acceptor impurities, such as Cr,, or Fe,. The effective activity of a shallow-donor dopant in providing conduction band electrons is thus reduced by this compensation. Similarly, a deep donor such as EL2 reduces the effectiveness of zinc or carbon shallow acceptors in providing free holes for ptype GaAs. Ionized impurity scattering (Chattopadhyay and Queisser, 1981), at both the ionized shallow centers and the charged deep compensating centers, also results in a lowered carrier mobility for a given camer density (Thomas et al., 1980; Bhattacharya et al., 1981). The phenomena of the preceding paragraph show themselves especially for mid-gap state concentrations of 1015cm-j or more. However, the influences of such states on generation-recombination phenomena in GaAs can be dramatic even with a much smaller concentration. The carrier lifetime and minority carrier diffusionlength in this direct gap semiconductor can be dominated by band-to-band transitions [a situation achieved more readily if either n, or po is large (Casey and Stem, 1976)l; but, more typically, the excess carrier regime of GaAs is indicative of recombination dominantly through mid-gap states (Casey et al., 1973; Jastrebski et al., 1979). The capture and emission coefficients of a mid-gap center, and the mobile camer densities n and p , determine whether the center will behave under a given set of conditions as a recombination center or as a carrier trap (Rose, 1963; Blakemore, 1962). The magnitudes and temperature dependencies of the emission coefficients are, of course, strongly affected by the large energy separations of the level from both conduction and valence bands; but, they depend also on the efficiencies of charge and energy transfer mechanisms. The efficiencies of these mechanisms are indicated more directly by the magnitudes of the capture coefficientsc, and cp,and trapping is given more of an advantage compared with recombination when cJcP is far removed from unity. Accordingly, our knowledge and understanding of a mid-gap center is incomplete if we know (and can even model) its energy spectrum, yet cannot model the characteristics and numerics of its most significant

4. MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

237

electron and hole capture processes. The competition between capture and emission coefficients in determining whether a center near mid-gap will behave as an electron trap, hole trap, recombination center, or generation center- for a given combination of T, n, and p-is apt to be further complicated if the center in question is in a depletion region, in a high electric field. Some enhancement of the emission probabilitiescan be expected from the Poole - Frenkel mechanism (Frenkel, 1938) of barrier lowering. However, an emission coefficient field enhancement much larger than this is often seen experimentally, for centers such as Cr in GaAs (Vorobevet al., 1977;Makram-Ebeid et al., 1980),EL2 in GaAs (Makram-Ebeid, 1980,1981;Printsand Bobylev, 1980),and Zn-Oin GaP (Makram-Ebeid, 1980). It was shown by Pons and Makram-Ebeid (1979) that phonon-assisted tunneling, in a high electric field environment for the center, gives this much larger enhancement, particularly for en. Among the various energy transformation processes that are possible for a deep-level center, those involving photon absorption or emission attract considerable attention, both for experimental study, and for theoretical speculation and modeling. In a straightforward-yet very useful -application of the optical properties of EL2 in GaAs, Martin (1981) described measurement of the concentration of this center from the near-infrared transmittance of semi-insulatingwafers. Several of the better known models for localized states have included predictions of the spectral dependence for the photoionization cross section (Lucovsky, 1965; Bebb and Chapman, 1967, 1971; Burt, 1980; Ridley and Amato, 1981), as discussed in more detail in Parts IV and V of this chapter. The photoionization spectrum provides information, in the form of a Fourier transform, concerning the spatial distribution of the bound carrier (Rynne et al., 1976). That is so whether the bound state is shallow or deep. Extrinsic photoconductivity involves photoionization and other complicating phenomena, but the convenience oEthis kind of measurement has led to much experimental work involving mid-gap centers. Such work for chromium in GaAs has extended over a long period of time (see, e.g., Broom, 1967; Look, 1977; Eaves et al., 1981; Blakemore et al., 1982). It is less easy to classify the experimental photoconductivity literature for EL2 in GaAs, since much work of the period 1960- 1980 is described as involving oxygen-related levels (see, e.g., Lin et al., 1976; Tyler et al., 1977; Arikan et al., 1980). It now appears likely that not all of these reports dealt with the same deep-level center. Luminescencewith hv substantiallysmallerthan the band gap manifests a finite efficiency for radiative relaxation at mid-gap centers and is also a popular experimental technique. The literature for “chromium-related” luminescence in GaAs has been a puzzle for some years and has perhaps

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J. S. BLAKEMORE AND S. RAHIMI

been finally resolved. That resolution requires a distinction between the luminescent components caused by electron or hole capture at isolated substitutional Cr, (Leyral et al., 1981; Picoli et a/., 1981) and those arising from transitions at impurity complexes including Cr. The latter could well be a two-atomic site nearest-neighbor complex, with a Cr, in a trigonally strained environment (White, 1979, 1980; Picoli et al., 1981; Voillot et al., 1981). The 0.839-eV luminescence line that has been studied for so long (Turner and Pettit, 1964; Lightowlers et al., 1979) then exemplifies the second category. This points up the importance of being able to deal with deep-level complexes, as well as with those “flaws” (a useful term encompassing both impurities and native defects)that derive from the presence (or absence) of a single atom. 2. A CLASSIFICATION SCHEME FOR DEEP-LEVEL CENTERS What does the term deep-level center imply? Pantelides ( 1978)makes the distinction between shallow and deep centersthat ed(or e,) < ei for shallow centers. Three remarks made by Jaros (1980) are worthy of repetition and thought: (i) “The localized states with energies lying further in the forbidden gap, the deep states, are understood to be different from the shallow ones and not amenable to treatment within the hydrogenic theory.” (ii) “The link between the depth of the level in the gap and the localization is by no means obvious.” (iii) “Clearly, both the longer-range and short-range interactions must be equally well represented in the impurity potential and accounted for in the numerical solution of the Schrodinger equation.” Two other statements, made by Vogl(198 I), also merit some reflection: (iv) “ . . ., we define an impurity to be a deep trap theoretically, if its central-cell potential alone, without any long-range Coulombic or elastic potential, is sufficiently strong to bind a state within the band gap of the host.” (v) “Thus we experimentally define a trap to be deep if it does not follow a nearby band edge when that edge is perturbed by alloying or pressure.” The importance of the short-range part of the potential for a deep-level center was singled out by both Jaros (1980) and Vogl(198 1) in quotations (iii) and (iv). Furthermore, the relationship of the center to its semiconductor host cannot be ignored. This has led to a wide variety of proposed models, some of which are discussed in this chapter.

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

239

In one of his earlier papers, Jaros (1979) provided another thoughtful comment on the attributes of a deep-level center, as contrasted with a shallow one: In the presence of a strong, short range potential, the matrix elements involving Bloch states from different bands can no longer be neglected and the procedures based on the approximate nature of the effective mass theory are inadequate. In contrast with the “hydrogenic” impurities, the defects bound by short range interaction may (1) bind deeply several carriers; (2) exhibit strong dynamic coupling to the lattice due to the high degree of localization of the bound particles; (3) exhibit static reconstruction in the vicinity of the defect demanded by minimum energy requirements; (4) act as non-radiative recombination centers with large probability of multiphonon emission; ( 5 ) give rise to “excited” states located, perhaps, several tenths of an eV from the ground state and often degenerate with the host crystal bands. A graphic description indeed, of the range of attributes to be borne in mind! Figure 1 illustrates one simple method for indicating the gross classifications of localized flaws, whether these lead only to shallow states or to deep ones. Of the classes indicated at the right in Fig. 1, most modeling has concerned isolated foreign impurities and the simpler forms of native point defect. The reader may wish to compare the classification of Fig. 1 with that shown by Pantelides (1978) just for substitutional and interstitial single impurities. Pantelides emphasized the appropriateness of the word isovalent for a substitutionalimpurity from the same column of the Periodic Table as the host atom, e.g., PASor Sb, in GaAs. An isovalent impurity is not necessarily electrically inactive or innocuous- as exemplifiedby the bound states of nitrogen in GaAs,-Zx alloys (Wolford et al., 1979). That type of substitutional impurity is referred to as “isoelectronic” in much of the literature, (see, e.g., Faulkner, 1968; Hsu et al., 1977), a use of that word which Pantelides considers misleading. (The semiconductor hosts Ge and GaAs are truly isoelectronicin having the same number of cure electrons as well as of valence electrons per primitive basis.) A monovalent substitution, by an impurity with valence differing by f 1 from that of the host atom, can usually be expected to yield a shallow donor or acceptor. Donor examples include arsenic in silicon, and SeAsor Si,, in GaAs,while acceptor examples include boron in silicon, and Zn,or Sn, in GaAs. One can often hope to describe such relatively shalow monovalent impurities by an effective mass (EMA) approach (Pantelides, 1978),with a central cell correction (chemical shift) determined by the difference (if any) of the cores of the host and substituent. Thus this approach can be expected

240

J. S. BLAKEMORE A N D S. RAHIMI POINT DEFECT

-

VACANCY

INTERSTITIAL LINE DEFECT [Dlslocalionl

ANTISITE DISORDER

PLANAR DEFECT

NATIVE COMPLEX

(Sleckinp Fault1

[ V a c a n c y palr. Frenkel

disorder. otc.1

LOCALIZED FLAW -SUBSTITUTIONAL

- - ISOVALENT

- INTERSTITIAL FOREIGN -IMPURITY

- MONOVALENT - ISOCORIC

- IMPURITY-IMPURITY COMPLEX

- TRANSITION ELEMENT

- IMPURITY-DEFECT COMPLEX

-OTHER

ELEMENTS

FIG. 1. A classification scheme for the principal varieties of localized flaw in a semiconductor.

to be particularly straightforwardfor an impurity which is isocoric as well as isovalent; e.g., Se, (donor) or Z n , (acceptor) in GaAs. Wolfe et al. (1977) review the experimental evidence concerning chemical shifts for shallow monovalent donors in GaAs. The isocoric impurity category extends beyond monovalent substitutions. However, much deeper bound states are more likely With multivalent substitutions, whether the core shell configuration is different or not. The published literature on Cu in GaAs [ascritically reviewed by Milnes (1983)] is complex and confusing, but does seem to indicate isocoric double acceptor status for C u , (reasonable for valency shift A 2 = -2). One, however, with e, 150 meV and ea = 450 meV. For that matter, the Ga,, anti-site in GaAs is also an isocoric A 2 = -2 perturbation, and Yu et al. (1982) identify this double acceptor with states 77 meV and 230 meV above the valence-band edge. By the same token, the A s , anti-site in GaAs should be a double donor ( A 2 = +2). This center has been studied by electron spin resonance (ESR) and photo-ESR (see, e.g., Wagner et at., 1980; Schneider, 1982), and evidence was thus seen of quite deep-lying bound states. Lagowski et al.

-

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

241

(1982a) proposed that an A s , anti-site is the EL2 center in GaAs. Other hypotheses concerning EL2 were all competing vigorously when this chapter went to press. We shall have more to say about EL2 later. By virtue of their partially filled d subshells, transition elements provide opportunitiesfor deep-lyinglocalized states in GaAs and other semiconductor hosts. Such atoms are active when isolated, substitutionally or interstitially, and are also recognized as participants in complexes. There has been a great deal of experimental study of the Cr, impurity in GaAs since the first measurements (Cronin and Haisty, 1964)showed chromium to be responsible for a mid-gap level. [The electron trapped at this level convertsCr, from Cr3+ (3d3) into C9 + (3d4).] Theoretical attempts at the description of transition group impurities such as chromium (Jaros, 197lb, 1982; Fazzio and Leite, 1980; Hemstreet and Dimmock, 1979a,b) are discussed later in this chapter. Because of the partially filled d subshell for a transition element impurity in the lattice neutral condition, it is plausible that a change in the relative supplies of electrons and holes might add to or subtract from the charge of the center- a change not necessarily limited to a single electronic charge. In short, such an impurity may be amphoteric, and may also be multivalent as either an acceptor (electron trap) or donor (hole trap). Thus, Cr, was at one time interpreted as a trap for one or two electrons in GaAs (Krebs and Stauss, 1977b), although it has since been demonstrated that the Cr+ (3d5) state is resonant with the conduction band (Hennel et al., 1981). This substitutional impurity is amphoteric (Kaufmann and Schneider, 1980a,b; Blakemore et al., 1982),and comparable activity is to be expected with other transition elements in semiconductor hosts with reasonably wide band gaps (Kaufmann and Schneider, 1982). Impurity atoms -including those of transition elements-have opportunities to become incorporated into complexes: both those involving one or more other foreign atoms, and those involving a native defect. The simplest type to contemplatein GaAs might involve an acceptor (such as Cr) on a Ga site, with a Group VI donor on one of the four nearest-neighborAs sites. That geometry for a complex would tend to create a trigonal distortion (C,, symmetry) of the local environment. Picoli et al. (198 1)suggested that a Cr-donor complex of this kind could be the often studied 839-meV photoluminescence center in GaAs.Skolnick et al. (1982) suggested instead a Cr,, -V,, complex for that luminescent entity. Many as-yet unidentified deep-level centers have been detected in GaAs by the deep-level transient (capacitance) spectroscopy (DLTS) method (Lang, 1974) and other versions of capacitance or current transient analysis (Lang and Logan, 1975;Martin et al., 1977;Mitonneau et al., 1977;Milnes, 1983). Some of these appear to depend on the manner of crystal growth, and

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some show up as consequences of processing (including those arising from radiation damage). One can reasonably expect that a major proportion of these elusive deep-lying states arise from complexes of various kinds. The comment above concerning an anticipated trigonal distortion for a Cr-donor two-atom complex in GaAs is relevant to the distorted lattice environment expected around most complexes, and is also possible around many single-atom interstitial or substitutional impurities. Jahn- Teller distortions have been deduced for two of the three charge states of Cr, at low temperatures, from the ESR spectrum (Kaufmann and Schneider, 1980b; Stauss and Krebs, 1980),and from the fine structure of optical absorption at 0.82 eV (Clerjaud et al., 1980; Abhvani et al., 1982). A change in the magnitude of and symmetry of the lattice distortion around a deep-level impurity is entirely likely when an electron is added or removed from the site. More extended defects-dislocations, stacking faults, etc. -all appear inherently capable of holding electrons at mid-gap energies, and this is a subject of great technological importance. However, these more extended defects lie outside the scope we can hope to cover adequately in the present chapter. Throughout, this chapter attempts to report -and hopefully explainsome of the approaches that have been taken theoretically to describe deep-lying states derived from nonextended flaw situations. The terms “deep-level” and “mid-gap” remind us that the energy for a localized electron is of major importance. Thus, the eigenvalues of a quantummechanical treatment provide the make-or-break criterion for many approaches. However, a model based on unsound starting assumptions or invalid approximations occasionally appears to provide “the right binding energy” for spurious reasons. Jaros (1980) has cautioned that it is the “signature” of the impurity which is important, of which the energy spectrum emerges as one consequence. Accordingly, we shall attempt to examine those features that are responsible for a flaw’s signature. These include the form of the potential, the site symmetry, and any distortion or relaxation of the lattice. Consequences then include the symmetry and localization of the wave function (i.e., the spatial distribution of bound charge around the flaw site). This, in turn, affects the energy and charge transformation properties of the center, including (in principle) the physics underlying capture of electrons, and the photoexcitation and photoionization properties. 11. Quantum-MechanicalView of Flaw States

For reasons of space and appropriateness, it is not intended that this account should exhaust all available theoretical approaches and models for

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243

mid-gap centers in any semiconductor. Rather, we attempt here a brief outline ofjust some of the methods that have been proposed for dealing with deep-level impurities. It is our hope that this might serve as a starting point for a proper comparison between theoretical predictions and experimental results -with the direct gap semiconductor GaAs as the prototype host. That may, in turn, lead to extraction of some information concerning the characteristic signature(s) of the deep-level center type(s) under study. A crystal consistingof a system of nuclei and electrons may be specifiedby its nonrelativistic Hamiltonian H, ,

H, = T,

+ To+ V.

Here, T, and To represent the kinetic energies of electrons and nuclei, respectively, and V is the total (electron-electron and electron- nuclei) coulomb interaction. (See the List of Symbols for the symbols used in this chapter.) The internal magnetic interactionsamong the particles have been neglected in writing Eq. (1). The solution of the corresponding time-independent Schrodinger equation HcVri Rn)= E'Vri R n ) 9

(2)

looks like an impossibility, unless some simplifying conditions are imposed on this many-body problem. Born and Huang ( 1954) treated T, in Eq. (1) as a perturbation to T, V in terms of the perturbation parameter K. Here, K4 is of the order of the ratio of the electronic mass to the mean ionic mass. They showed that, for a degenerate system, the total wave function Y(ri, R,) may be expressed as a product of an electronic wave function c#J(ri)and a nuclear wave function X(Rn),provided the wave function is evaluated to the second order in K. The above approximation, by which the motion of electrons can be treated independently from the motion of nuclei, is called the Born -Oppenheimer approximation. In this approximation, the positions of electrons are referred to the equilibrium position of the nuclei. In contrast, in the adiabatic approximation, the Hamiltonian contains a potential which is measured from the actual position of the ions (Colson and Bernstein, 1965). [See Ridley (1978b) for a nonadiabatic approach.] In principle, a system of electrons is adiabatic when, during the course of evolution of the system, a change in some external parameter such as position of the nuclei will not induce any electronic transitions. The many-body electronic Hamiltonian can thus be reduced to an effective one-electron Hamiltonian. [For details, see Stoneham (1975, p. 15).] A perfect crystal may then be described by a one-electron Hamiltonian H = T, V. In order to distinguish between a perfect and an imperfect crystal, we refer to their one-electron Hamiltonians as

+

+

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J. S. BLAKEMORE AND S. RAHIMI

H"=T+V"

(3)

H=Ho+h,

(4)

and respectively. Here, h represents the potential (from now on we take the liberty of using potential for potential energy) introduced by the defect into the host crystal. The problem of obtaining a solution to the Schrodinger equation for the perfect crystal has long been dealt with. Methods of approach to this particular problem may be found in standard solid-state physics textbooks (see, e.g., Ziman, 1972; Callaway, 1976; Harrison, 1980). Major papers dealing with the pseudopotential approach (Chelikowsky and Cohen, 1976; Ihm and Joannopoulos, 198 1), the orthogonalizedplane wave (OPW) method (Herman et al., 1968), the linear combination of atomic orbitals (LCAO)calculations (Stocker, 1962), the band-orbital tight-binding approach (Harrison, 1973; Harrison and Ciraci, 1974), and the linear combination of Gaussian orbitals method (Wang and Klein, 198 1) may be noted. The energy-band structure and density of states of many semiconductors are thereby obtained. Information relative to the bands of GaAs in particular has recently been reviewed by one of us (Blakemore, 1982b). In some of the models to be discussed later, the solution of the Schrodinger equation Ho@,(r)= En,k@n,k(r)

(5)

is assumed to be known. In some other cases, the solution of Eq. ( 5 ) is directly obtained and is employed to obtain a solution to the Schriidinger equation of the host crystal plus the defect Hyn,k(r)

= Evn,k(r)*

(6)

Here, E, and @n,k, y , , k are the electronic energy levels and wave functions of the perfect host crystal and the imperfect crystal, respectively. Attempts to find a suitable solution to Eq. (6) for defect states in semiconductors are nothing new, and are as old as the work of Mott and Gurney (1 940). Several comprehensivereviews of the subject during the past decade have been published (Roitsin, 1974; Masterov and Samorukov, 1978; Pantelides, 1978; Jaros, 1980). In the light of such articles, we have made an attempt to review the earlier models briefly and critically, and to devote the remainder of this chapter to the more recently proposed models. As a preliminary to mentioning some of the model approaches, it is legitimate to ask, What things would one like an impurity model to describe? The hasty answer is that one would like to be able to describe all properties. However, that is not practicable for any impurity model of

4. MODELS FOR MID-GAP

CENTERS IN GALLIUM ARSENIDE

245

manageable proportions, any more than it is possible for any band model of manageable scope. For some who have worked with impurity models, the touchstone of success has often been regarded as the ability to yield an apparently correct value for the ground-state energy. That is certainly a desirable attribute, although some model makers have been willing to forego this as the price for obtaining different insights, once an empirical value for the binding energy has been inserted into the model. Ofcourse, the same price is paid cheerfully in some band models-such as pseudopotential models (Chelikowsky and Cohen, 1976), where known energy gaps are used to set the pseudopotential coefficients. The hydrogenic and effective mass models mentioned briefly in Section 3 are arranged to provide the eigenenergies of the ground state and excited states as output quantities. In contrast, the delta-function potential model of Lucovsky ( 1965), reported in Section 5, uses a known impurity ionization energy as an input parameter in order to determine the scale of the bound configuration wave function and, thereby, model properties such as the photoionization response spectrum. Best of all, one would like to have both the kinetic and potential parts of the Hamiltonian so well chosen that the eigenenergy and the wave function truly represent an electron at the deep-level impurity site-that is to say, a wave function that correctly provides the electron’s various abilities to interact with both the valence and conduction-band systems.

111. Effective Mass Formalism: Its Limitations for Deep-Level Centers

Since the work of Mott and Gurney (1 940) until today, there has been a steady stream of work trying to treat problems of impuritiesin semiconductors through the mechanism of effective mass or hydrogenic theories. The success of this theory in explaining the properties of shallow impurities in germanium and silicon (Luttinger and Kohn, 1955;Kohn, 1957)has been a source of temptation to extend effective mass theory (EMT),for application to deeper level impurities. In spite of all the efforts, and some interesting successes in the extension of EMT to predict some properties of “moderately” deep centers (Pantelides, 1978),this approach has not been successful with truly deep centers-such as mid-gap states in GaAs.

3. EFFECTIVEMASSTHEORY The basic assumption of EMT (Luttingerand Kohn, 1955;Kohn, 1957)is that the bound-state wave function Y(r) consists of two parts:

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J. S. BLAKEMORE AND S. RAHIMI

Here, Q(r) is a slowly varying envelope function that spreads over a large region of real space (therefore, a very small region of k space), with a range of several nanometers from the impurity core; and Oj(k,r) is the Bloch function of the host crystal at thejth extremum of the band under consideration, defined by

aj(k, r) = q(r)erUsr. (8) Uj(r) is the periodic function belonging to the perfect crystal. Once 4 ( r ) is known, Y(r) may be obtained easily. Another assumption of EMT is that the effect of the periodic potential of the perfect host crystal can be represented by an effective mass tensor. The well-known effective mass equations may then be written as a system of coupled differential equations such as

z, G

(D$(id/dxa)(id/dxfl)

+ [u(r) - E]dfl)4.(r) = 0.

(9)

j

Equation (9) has been written for an acceptor impurity in a host crystal with “G” valence bands sharing a common (degenerate)maximum. A comparable equation may be written for donors, in relation to conduction band properties. The parameters DFf, in Eq. (9) are directly related to the effective mass tensor. In the simple case of a single scalar (and energy-independent) efective mass m*, the relation is (Bebb and Chapman, 1967) DTj? = (h2/2m*)d,,djj, , and Eq. (9) reduces to the simple effective mass equation

[(-h2/2m*)v*

+ u(r)]F(r) = EF(r).

(10) (1 1)

The choice of the impurity potential u(r) is obviously a crucial matter in determination of the impurity energy level and wave function. In the simplest case (the hydrogenic model), this potential is represented by the potential of a point charge as if it was embedded in a material of dielectric constant K,i.e., u(r) = -e2/Kr. The choice of this coulomb potential further restricts the applicability of the effective mass equations, to the case of shallow impurities with long-range nonlocalized potentials. The solutionsof Eq. (1 1) may be obtained using a variational method, by minimizing the energy E in order to find the function F(r).For details of calculations, and treatment of more general cases of EMT, the interested reader is referred to Pantelides (1978) and references therein.

4.

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247

There seems to be a consensus that, while the hydrogenic model is able to explain the general characteristicsof shallowimpurities (such as Ge, or Se, shallow donors in GaAs, for example), it does have some shortcomings. There is a significant discrepancy in some cases between experimental and theoretical results for the ground-state energies(Roitsin, 1974). Thus, Wolfe et al. (1977) indicate that the central cell “chemical shift” is larger for the Ge, isocoric donor in GaAs than for the nonisocoric Group IV donors (Si, Sn, Pb). Most seriously of all, the hydrogenic model cannot predict, even qualitatively, the nature of the impurity when dealing with localized potentials and wave functions. However, these failures of the hydrogenic model do not necessarily imply the failure of EMT. Effective mass theory has been elaborated in order to overcome many of the initial discrepancies. The improvementswere mostly based on changing the form of h(r) from a simple coulombic potential to some more appropriate model potentials, replacing the H-like Hamiltonian with a He-like Hamiltonian, or taking both the conduction and the valence bands into consideration (Roitsin, 1974; Pantelides, 1978). Pantelides and Sah ( 1972, 1974a,b) co@-ucted different potentials for isocoric and nonisocoric impurities. They showed in their “point-charge model” that if one discards the idea of a uniform dielectricconstant K and considers a dielectric screening function K(q) (properly obtained for the perfect host crystal), then the chemical shifts of the binding energies of Group V donors in silicon could be accounted for. Bernholc and Pantelides ( 1977) subsequently applied this point-charge model to the case of acceptors in Ge and Si. The impurity potential was defined as

U,

=

1

-

[4meZ/qzlc(q)]exp (iq r) d3q.

(12)

Two extremes, of zero, and infinite, spin - orbit splitting were considered. Alternatively, one could use a model potential (Abarenkov and Heine, 1965) such as a square-well potential with a coulombic tail, defined by = - Ze2/Kr, r > r,. (13) Here, the subscript M denotes the model potential, A, is a general function of electron energy (indicative of well depth), PI is the projection operator associated with the angular momentum quantum number, and 2 is the ion valency. This kind of approach has been used for shallow impurities in Group IV elements (Jaros and Kostecky, 1969;Jaros, 197la) and has led in turn to the model potential of Ning and Sah (197 1a), which is described in Section 8.

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J. S. BLAKEMORE AND S. RAHIMI

While such improvementsin EMT modeling may help with shallow (and even some fairly deep) flaws in covalent semiconductors, the partly ionic nature of a compound semiconductor makes the adoption of a model potential approach less straightforward. Nonetheless, several model potential proposals are noted in the following sections- some self-consistent, others not. Let us return for the moment to the homopolar situation of silicon. It is interesting to see a comparison of several approaches to the neutral silicon vacancy Vsi, one ofwhich (Pantelides et al., 1980)incorporated the acceptor EMT scheme developed by Lipari and Baldereschi (1978). This deep-lying defect had previously been analyzed by Baraff and Schluter (1978), and by Bernholc et al., 1978), using different forms of the self-consistent Green’s function method discussed later in this chapter. Those had yielded defect state energies of (E, 0.7 eV) and (E, 0.8 eV), respectively. When Pantelides et al. (1980) simplified the potential to spherical symmetry in order to accommodate the EMT scheme, they deduced that Vsiwould be at (E, 0.9 eV), in apparently good agreement. Moreover, the k-space behavior of their wave function was of EMT form: The envelope fupctions FJk) [which are in fact the Fourier transform of F,(r)] peaked near the valence and conduction-band extrema, and most of the contribution to the Vsi state came from the three highest valence bands. It is advisable to recognize, however, that this interesting result was obtained with conduction-band terms and Umklapp terms (Pantelides, 1978) omitted, and with the impurity potential simplified to spherical symmetry. Jaros et al. (1979) have argued that the nonspherical nature of the potential around a vacancy has a nontrivial contribution to the solution. Naturally, there have been other studies-which we can expect to see continue-toward examination of the relevance of extended EMT to specified deep-level impurity situations and properties. For example, it is reasonable to expect EMT to be entirely appropriate in describing the quite shallow excited states of much deeper centers. That could be relevant to the consideration of electron capture mechanisms that involve initial capture into a shallow excited state. The cascade model of Lax (1960) described this classically, and there have been a number of successor models (Smith and Landsberg, 1966; Ralph and Hughes, 197I; see also the review in Abakumov et al., 1978). Cascade capture is further noted in Section 1 lc. The two preceding sentences reemphasize the significanceof the remarks made earlier, that the signature of an impurity involves much more than just the ground-state eigenvalue. The energy values- and wave functions- for both ground and excited states are of importance, as are the matrix elements for electron transitions.

+

+

+

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249

4. A FIRSTLOOKAT RADIATIVE TRANSITIONS

It is often desired to model radiative transition probabilities involving flawstates- whether they are shallow or deep. A few remarks are made here concerning photoionization and photoneutralization for shallow (effective mass) flaws. This subject occurs again in Sections 5, 6, 7, 9, and 10. The mathematical framework is treated most fully in Section 9, and the effects of phonon assistance are discussed in Section 10. That framework requires a description of the lower and upper states involved in a process of photoexcitation, photoionization, or luminescence. The upper state involved is excited (but still localized) for processes of photoexcitation, and of “internal transition” bound-to-bound luminescence. Photoionization and “noncharacteristic” (free-to-bound) luminescence both involve a band state. A photoionization treatment for hv not far above threshold ought to take into account the coulombic interaction between the ejected electron and the resulting localized flaw charge. That involves coulomb wave functions (Gottfried, 1966). Photoionization is often treated simply in practice with a plane wave final state assumed. That amounts to the Born approximation (Schiff, 1968), a procedure that is properly appropriate only when hv is much larger than the ionization energy. It is normal practice, in any event, to use the electric dipole approximation in working out the radiative transition probability. For, conveniently, the electric quadrupole and magnetic dipole contributions are both much smaller than the electric dipole term. For the simple supposition of a shallow donor that can be represented by a scaling of the hydrogen atom, the normalized ground-state wave function has the radial form

Y(r)= exp (- r/ad). (14) parametrized by the dielecHere the scaled Bohr radius is a d = (xh2/e2mc), tric constant IC and by the effective mass m,. The ground-state binding energy is Ed = (rn,e4/2xZh2)for a genuinely hydrogenic donor, which does not require a central cell “chemical shift” correction. And so a d and Edare interrelated by E d = (e2/2xUd) = (h2/2m&). (15) Part IV of this chapter will go on to discuss the quantum defect and delta-function potential models intended for rather deeper-lying flaws, with binding energy ED > Ed, and of characteristic radius U, < a d . It Will be noted there that (ED&) = (Ed&) = (h2/2rnc)for those more strongly bound situations, when the effective mass m, for just one band is used in parametrizing the bound state.

250

J. S. BLAKEMORE A N D S. RAHIMI

The photoionization cross section oI(hv)has a magnitude and form dependent on the assumption made about the nonlocalized state occupied after photon absorption. When the Born approximation (plane wave final state) is assumed for a hydrogenic donor, then

o](hv)OC (hv - Ed)3/2(hv)-5,

(16) This falls off as ( h v r 7 l 2 for hv > Ed, the energy range for which this approximation should be a reasonable one. Equation (16) also purports to show a maximum of q(hv) when hv c1.4Ed. However, the plane wave final state is much less appropriate for photon energies that small, when the wave vector k is small compared with ad1. The photoionization spectrum for a hydrogenic shallow impurity has also been examined with a coulomb wave function adopted for the final state. In the electric dipole approximation, this gives

q ( h v ) a exp(- 4y cot-' y ) / [ 1 - exp(- 2 ~ y ) ] + ~ ,

(17) where c$ = (hv/Ed)and y = (4 - 1)-'l2. In order to gain a little more insight into the significance of these dimensionlessparameters, it may be noted that photoionization to a conduction band state of wave-vector k requires a photon for which y (kad)-'. As with Eq. (16), the cross section of Eq. (17) has an ( h ~ ) - behavior ~/~ when hv > E d . However, the low energy range of Eq. (17) is the more significant one to study. This has a maximum of oI for the threshold condition, hv = Ed,with a step function total collapse of oIimmediately below that energy. (The absorption cross section will, in practice, show discrete excitation lines for various hv < Ed.) Burstein et al. (1956) used Eq. ( 17) for comparison with the continuum part of the optical absorption for the shallower members of the Group 111acceptor family in silicon. A more sophisticated EMT model (Lipari and Baldereschi, 1978) is required for a description of the excitation line spectra (Onton et al., 1967; Skolnick et al., 1974) associated with these shallow impurities. Although the transitionsjust described between the conduction band and transitions between the a shallow donor involve a photon energy hv -=szEi, conduction band and a fairly shallow acceptor have a threshold energy hv,, = (Ei- Ea),only slightly below band gap. The transfer of an electron from acceptor to conduction band is then a process of photoneutralization, while transitions in the downward direction give luminescencea little below the band edge energy. Such photoluminescence is widely used in GaAs for the detection of residual shallow impurities (Covington et al., 1979), for investigation of suspected impurity complexes (Rao and Duhamel, 1978), -5

4.

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251

and for finding slightly deeper impurities such as the 0.1 -eV manganese acceptor (Yu and Park, 1979; Xin et al., 1982). Radiative transitions across most of the intrinsic gap width are not necessarily much more efficient than their radiative brethren of much smaller hv. However, their relative importance is heightened by the fact that nonradiative competition is often much weaker for near-gap (conduction band to acceptor, or donor to valence band) transitions. For transitions between a fairly shallow center and its parent (nearest) band, nonradiative processes may be efficient enough to keep the radiative fraction below 1 04. Yet, transactions between that center and the opposite band may add up to a total transition probability several orders of magnitude smaller, with the modest radiative opportunity now quite prominent (Blakemore, 1967). Models have been developed by Eagles (1 960) and by Dumke ( 1963) for the photoneutralization cross section adhv) of a hydrogenic acceptor (ionization energy En)in providing an electron to the conduction band. Their results amount to a proportionality G N ( ~ V )a

(hv + E, - ~ ~ ) q (+hE,v - EJ + ~ ~ ( m ~ m ~ 3( 1- 8)4 .

While the initial rise of this expression is determined by the numerator, a maximum is soon reached, for a photon energy (19) hv,,, = Ei - En(1 - mv/7m,) and the subsequent decline eventually resembles aN.m (hv - Ei)-7/2 behavior. This hardly matters from a practical point of view, since that spectral region overlaps the intrinsic range and is undetectable. Indeed, with the band parameters of GaAs (Blakemore, 1982b), hv,,, is quite close to the band-gap energy. Thus photoneutralization for a shallow impurity is of interest mostly concerning the threshold energy hvmi, = (Ei - En) [or, (Ei- Ed) for a donor] and the rise of a , from threshold- that is, linear at first, soon becoming sublinear. The study of photoneutralization is more profitable for a deeper-lying impurity, so that the optical threshold energy is further removed from the intrinsic edge energy. Toward that end, we now move, via the delta-function potential and quantum-defectmodels, toward models better suited to some description of mid-gap centers. IV. Delta-Function Potential and Quantum-Defect Models

These models were proposed, respectively, by Lucovsky ( I 965) and by Bebb and Chapman ( 1967,197 1;see also Bebb, 1969). Both of these models were intended to be suitable for flaw states several times deeper than

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J. S. BLAKEMORE A N D S. RAHIMI

hydrogenic, for which an exclusively long-range coulombic potential appears to be improper. Lucovsky’s model actually took the opposite extreme, of a delta-function potential, with no long-range term at all. That constitutes the zero range limit of a square-well potential (Schiff, 1968). The quantum defect model of Bebb and Chapman (1967) provides a continuum of options for the radial dependence of wave function, with a scaled hydrogenic model as one limit and the delta-potential consequences as the other. For both of these models, an avowed objective was modeling of the magnitude and spectral form of the photoionization cross section. The working out of that objective requires, of course, an appropriate assumption about the continuum final state (Grimmeiss and Ledebo, 1975). 5.

LUCOVSKY’S

DELTA-FUNCTION POTENTIAL MODEL

We shall have more to say in Section 8 about the consequencesof a model potential in the form of a spherically symmetric square well (S3W)of finite radius r,. Lucovsky was interested in the solution of the Schrodinger equation for the short-range limit-that is, the combination of r, --* 0 while Vo+ CQ, in such a manner that the “strength,” gauged by ( Vorf), remains finite. That “strength” of the delta-function potential determines the ground-state binding energy, and no excited states are bound unless the strength is far too large to be useful in a semiconductor:flaw situation. Those featureswere explored by Bethe and Morrison (1956) in modeling the proton - neutron binding in a deuteron, and they showed that the solutions were relatively insensitive to the exactform of short-range potential. When the ionization energy (for a certain kind of flaw in a given host) is known, the strength of the impurity pseudopotential (represented in Lucovsky’s case by a delta-function potential) can be adjusted to be consistent with that ionization energy, which we shall call ED for a deep-donor flaw. This adjustment procedure reminds one of pseudopotential methods for band calculations (Chelikowsky and Cohen, 1976; Ihm and Joannopoulos, 1981). With the &potential strength set to produce a localized state of binding energy ED, the corresponding wave function has a radius a,, such that

aD = (h2/2m&p2. (20) Note thereby that ( a s D )= (h2/2mc)= (aiEd),where ad and Ed refer to the radius and ionization energy for a shallow hydrogenic donor. This scaling, with ED = Ed(ad/aD)’ (21) is an implicit consequence of using the conduction-band mass m, in the description of the bound state. One would similarly use the valence-band

4.

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253

mass rn, in describing a moderately deep acceptor by the delta-function potential model. We shall have more to say about this. The bound-state wave function Y(r) consequent upon a delta-function potential (of suitably adjusted strength) differs from Y(r) of Eq. (14) (the hydrogenic model) by a preexponential factor that makes quite a lot of difference. The Lucovsky model requires a radial wave function which, expressed in normalized form, can be written as Y(r) = ( 2 7 ~ ) - ' 'r-l ~ exp(- r/aD).

(22) Apart from the difference in the normalization constant, this differs significantly from Eq. (14) in having the factor r-' preceding the exponential. Figures 2 and 3 show that (for a given a,) this describes a bound electron distribution with a much more distinct outer limit. A bound-state radial wave function Y(r) has a radial charge density associated with it of p(r) = - 4 n e t - V . The two curves in Fig. 2 show p(r) plotted, versus normalized radius (r/ad)or (r/aD),for the hydrogenic wave function of Eq. (14) [curve (A)] and for the delta-function potential wave function of Eq. (22) [curve (B)]. Figure 2 uses ordinate units such that the integrated area under each curve is unity. It does not look quite like that, but only because of the logarithmic ordinate scale. Elementary texts on modern physics or physical chemistry often include artistic, airbrushed visualizationsof the hydrogenic 1s wave function. These

z

0 U l0 W

J W

NORMALIZED RADIUS

(r/a)

FIG.2. The radial dependence of the bound charge density associatedwith a flaw site. Curve (A) for a shallow hydrogenic donor ground state with Y(r), as described by Eq. (14). Curve (B) for the Lucovsky delta-functionpotential model so that Y ( r )is described by Eq. (22).

254

J. S. BLAKEMORE AND S. RAHIMI

..

0

I

2

3

NORMALIZED R A D I U S

4

(r/o)

FIG.3. The fraction of ground-state bound charge density remaining outside a sphere of radius r, centered on a flaw site, as a function of normalized radius (r/ud)or (rlu,,). (A) For a hydrogenic model Y(r),as in Eq. ( 1 4). (B) For the delta-functionpotential model Y(r),as given by Eq. (22).

are sometimes accompanied by a statement that p(r) is then a maximum for r = a d . However, those accounts usually do not go on to emphasize that p(r) for a hydrogenic wave function continues to be appreciable out to a radius three to four times larger than ad. In contrast, p(r) derived from the delta-function potential model falls monotonicaly and decisively as one moves from the flaw site, varying throughout as exp(- 2r/aD). The contrast between p(r) from Eqs. (14) and (22) is further emphasized by the curves in Fig. 3. That figure plots the fraction of the bound electronic charge lying outside a specified radius r. Once again, curve (A) shows the situation for a hydrogenic wave function. This curve shows that two-thirds of the bound charge lies (on a time-averaged basis) outside the sphere r = ad, and that nearly one-quarter lies in the region for which r > 2ad. Curve (B) illustrates the corresponding situation when Y(r)is given by Eq. (22); now only 2% of the bound charge density is associated with the region r > 2aD. Lucovsky assumed that the effective potential had entirely a zero range character. This could not be expected ever to be rigorously true. Yet his model did focus more attention on the importanceof a short-rangepotential term as a major component of the complete potential description. Since Lucovsky (1965) rescaled the electric dipole approximation result for deuteron photoionization (Bethe and Momson, 1956)into the language of a semiconductor :flaw problem, he was able to quote an expression for a&), and this has on many occasions been compared with experimental photoabsorption data. The expression for q(hv)that Lucovsky adapted was

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

255

based on the Born approximation and assumed that a liberated photoelectron would be describable by conduction-band plane waves (or, of course, valence band plane waves for an acceptar to valence-band transition). From remarks already made in connection with scaled hydrogenic models, we know that this approach is more nearly valid when hv > ED,to make ka,, >> 1. In making the scaling, Lucovsky assumed that the band effective mass (m,for donors, m, for acceptors)was valid for both the initial (bound) and final (free) states. The result for the donor situation is

s ( h v ) = [4(hv- ED)ED/(hv)2]3/2 omax,

(23)

where am,,= ( e 2 h / 3 C ~ ’ / 2 r n ~ ~ ) ( & , f f / E 0 ) 2 . (24) One of the features of Eq. (23) most often compared with experiment is that o, achieves omax for hv = 2ED. Just above threshold, a, should rise as (hv - ED)3/2, while for sufficiently large photon energy, oxis supposed, by this model, to vary as ( h ~ ) - ~ ” . Lucovsky chose to compare his photoionization expression [Eq. (23)J with some of the original photoabsorption data (Newman, 1955) for the moderately deep acceptor indium in silicon (EA= 0.15 eV). Figure 4 shows the Lucovsky expression compared with more recent experimental data for that same acceptor. The experimental curves are affected by the photoexcitation opportunities near the continuum threshold, but there is a considerable spectral range for which experiment and Eq. (23) appear to have similar trends.

0 Y

b ‘ i

256

J. S. BLAKEMORE AND S. RAHIMI

The maximum cross section of Lucovsky’s model, om,, of Eq. (24), can be seen to depend on the semiconductor-specific quantities K and m, and also on an “effective field ratio” (eew/&) (squared!). Dexter (1958) presented arguments as to the possible enhancement of a photon’s effective electric vector, when one visualizes a highly localized center as a sphericalcavity in a lattice of high dielectric constant. That viewpoint would allow eefl/kto be as large as (K 2)/3 in an extreme case-that is, as large as 4 for GaAs. One would expect the effective field ratio to depart much less seriously from unity for a flaw level that is only “moderately deep,” with a wave function radius a, or a, several times larger than the nearest-neighbor atomic spacing. One of us (J.S.B.) has found effective field ratios to be virtually indistinguishable from unity in analyzing experimental photoabsorption data for Mn in GaAs [ E A = 0.1 1 eV, a, = 0.8 nm; see Brown et al. (1973)l and for In in Si [EA= 0.15 eV, aA = 0.6 nm; see Messenger and Blakemore (197 l)]. As an experimental note-and thus outside the nominal scope of this chapter-it can be remarked that any underestimate of the neutral flaw density tends to boost one’s estimate of a ,, having an effect that resembles (~eff/&O)> 1. As with other analytic models, the elegant and simple approach that Lucovsky adopted cannot be adopted intact for any deeplying center, especially if this is a very deep one. Lucovsky recognized these limitations and remarked, for example, that a coulombic long-range potential would have to be used for excited states. Moreover, the model as indicated in Eqs. (20)- (24) uses the effective mass ofjust one (parabolic)band rn, for donors, rn, for acceptors. In addition, the simple choice of plane-wave-like band states for the expression of a,(hv) truncates a large part of the nature of the impurity, the perfect host crystal, and their relationship. Pantelides and Grimmeiss (1 980) have shown, both experimentally and theoretically, that deep-level optical spectra are often dominated by transitions to bound and quasibound final states induced by the strong shortrange potentials. Thus, the short-range potential which Lucovsky approximated by a delta-function potential affects both the initial and final states in an act of photoionization. Kravchenko et al. (198 1) discussed some variations on the delta-function potential approach in connection with the nature of the impurity potential, the size of the wave functions at the flaw site, the allowance for the charge state in photoionization, and the consequences of electron -phonon interaction. They applied one of these variations (on the nature of the potential) to the case of two deep centers often found in “undoped” GaAs and were able to arrange parameters for a fit between their model and experiment. However, it should not be assumed that an ad hoc arrangement of Lucovsky’s model, which appears to yield desired results for one deep-level center, will necessarily be a reliable guide to a variety of deeplying states.

+

-

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

257

It was argued by Grimmeiss and Ledebo (1975) that m,, rather than rn,, should be used in Eq. (20)for the deeper-lying kinds of flaw. When m,, > rn, (as is the case for GaAs, and for many other semiconductors), this has the effect of making U, smaller for a given E D . Their argument was based on the premise that a quite localized ground state should not be much influenced by the crystal periodic potential; and it is the crystal potential which produces Bloch functions and behavior which one simulates by an effective mass. Since the particular concern of Grimmeiss and Ledebo was the well-known 0.79-eV deep donor in GaAs (a state attributed by them at the time to “oxygen” and now more likely described as “EL2’7, then (h2/2mo&)1/2 = 0.2 nm, handsomely consistent with their argument in favor of the use of m0. With the plane wave final state (Born approximation) assumption for photoionization to a parabolic band, Grimmeiss and Ledebo thereby deduced that

+

CJI(hV)a (hv - ED)3/2/hV[hV ED(%/m,

-

(25) It is interesting to compare Eq. (25)with Eq. (23),the spectral dependence for Lucovsky’s version of the delta-function potential photoionization problem. Both equations rise initially from threshold in a ( h v - ED)3/2 fashion. Similarly, both equations eventually decline as ( h ~ ) - ~for ” sufficiently high photon energies. Yet the two equations have appreciably different spectral dependences for intermediate hv, and the maximum fdr Eq. (25) occurs right at hv = 2EDonly when rn, = m,,. Since this is germane to our consideration of mid-gap states in GaAs, Fig. 5 shows the photoionization data of Grimmeiss and Ledebo for the 0.79-eV “oxygen” level in GaAs, compared most favorably with Eq. (25), as displayed by curve (a). Curves (b) and (c) both show apparently less favorable comparisons with delta-function potential models using rn, for the boundstate wave function. Curve (b) is the conventional Lucovsky result [Eq. (23)],while curve (c) is the result of using a coulomb wave function for the final state. The superficial appearance of the curves and data of Fig. 5 is that the model [Eq. (25)]yielding curve (a) looks the best by far. However, it should be borne in mind that the spectral range for the comparison did not extend through and beyond the maximum (which would, of course, take it into the inaccessible hv > Ei region), and that the plane wave (Born approximation) simplification cannot be expected to be a true guide in the near-threshold region. Blow and Inkson (1980a), and Inkson (198 l), have pointed out that the choice of different effective masses for bound electrons or holes in a delta-potential model lacks clear justification. Those latter writers do not believe that this could be applied successfully to a variety of deep-level situations.

258

J. S. BLAKEMORE A N D S. RAHIMI

I

I

I .o

I

I

J

12

hU (eV)

FIG.5. Photoionization data, after Grimmeiss and Ledebo (1975), for the 0.79 eV deep donor in oxygen-influenced GaAs.(Most likely, this is the center otherwise known as EL2.) The data have been compared with curves based on three models: (a) Eq. (25), from the Grimmeiss-Ledebo model, using m, = 0.067m0;(b) an attempted fit to the Lucovsky model, Eq. (23); and (c) a result analogous to curve (a), except for use ofa coulombwave-functionfinal state.

Despite all these caveats, the simplicity of Lucovsky’s expression, [Eq. (13)] or of the Grimmeiss and Ledebo modification [Eq. (25)], automati-

cally appeals to many experimentalists who have data derived from optical absorption, photoconductivity, etc. As one illustration of this, Fig. 6 provides data and an analysis from the work of Vasudev and Bube (1 978), showing results for oxygen-dopedGaAs as investigated by photocapacitance measurements. These data points, covering a seven-decade range of amplitude, were fitted to the sum of three terms, each having the form of Eq. (25). With six parameters needed for fitting (three thresholds, as noted in the it is hard to imagine that the six figure caption, and three values for a,,), choices arrived at by Vasudev and Bube were all uniquely optimized. Yet the analysis of experimental data often calls for some kind of fitting to equations that are not too cumbersome, even when the available data cover much less than the ideally broad spectral range. The paper of Grimmeiss and Ledebo ( I 975) proceeded with a discussion of further ways that a delta-function potential model might be generalized. Here they were concerned with transitions from the ground state to a band that is warped and/or nonparabolic, having decided that the GaAs conduction-band nonparabolicity was insufficient to affect Fig. 5 . They also considered transitions to multiple bands, such as the heavy-hole, light-hole, and split-off band combination for the various Group IV and, I11 - V semiconductors.

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

I0’

FIG.6 . Photocapacitance data, after Vasudev and Bube (1 978), for bulk oxygen-doped GaAs. These authors fitted the swctrd response to the sum of three terms, each with

I

259

I

clo2

6

They illustrated the consequences of the latter specifically for the gold donor and acceptor states in silicon. Since Si has a small spin - orbit splitting (As-, = 0.045 eV), photoionization to the split-off valence band becomes possible shortly above the threshold for hole creation in either of the uppermost valence bands of that solid. The spin - orbit splitting $-, = 0.341 eV is nearly an order of magnitude larger in GaAs (Nishino et al., 1969;Aspnes and Studna, 1973).Yet a shoulder at (EA-I-$-,) is apparent in the photoabsorption spectral response for moderately deep acceptors in GaAs, such as Mn (Chapman and Hutchinson, 1967), or Co (Brown and Blakemore, 1972).The spectral behavior of Mn in GaAs will be illustrated a little later in Fig. 8. Banks et al. ( 1980)used Green’s function techniques (further discussed in Part VIII) to calculate optical cross sections for deep-level flaws, and in so doing commented on the weakness of the Lucovsky approach in describing the impurity wave function through concepts derived from just one band edge. They pointed out that a deep-donor wave function might well have nodal properties coinciding with those of the valence band, and showed that this would lead to a photoionization spectral dependence

+

q(hv) a (hv - E D ) ’ ” / ~ v ( ~ p)’. v

(26) For a “forbidden” donor- conduction-band transition, p = 0, and a, (modest in size, clearly) rises sublinearly from threshold, is maximized for hv = 1.2ED,and falls quite rapidly as hv increases further. This is illustrated

260

J. S. BLAKEMORE AND S. RAHIMI

by curve (B) of Fig. 7, contrasted with curve (A) of the Lucovsky model [Eq. (231.1 A family of curves could be drawn to represent Eq. (26) for various values of p, and curve (C) of Fig. 7 shows the limiting case ofp > E D . This shares in common with the Lucovsky model a maximum at photon energy hv = 2E,, but curves (A) and (C) look different in other respects, since one is the cube root of the other. Banks et al. deduce that

- (l + mc/mv)EDl (27) when the deep-donor wave function does have nodal properties coincident with the valence band nodes; and this value of p would be several times larger than the intrinsic gap Ei for any mid-gap donor in GaAs. Dzwig et al. ( 198la) have recently reported an interesting expansion of the Lucovsky model approach, in the form of an impurity super lattice. This approach is discussed in Part IX.

p = (mv/mc)[Ei

6. THEQUANTUM-DEFECT MODEL

In view of the recognized deficiencies of the effective mass models then available, and of the oversimplification in Lucovsky’s delta-function potential model, the “quantum-defect model” (QDM) was proposed by Bebb and Chapman ( 1967). This was an attempt to treat reasonably deep impuritiesin semiconductors in a fashion that was still analytic but, hopefully, more

I

I

I

2

3

4

hV/E,

FIG.7. Three possible forms for the spectral dependence of a, for a deep donor. Curve (A) follows Eq. (23) of Lucovsky’s delta-functionpotential model. Curve (B) is the limit /?= 0 in Eq. (26), from the approach of Banks et al. (1980). Curve (C) shows the opposite extreme of Eq. (26), for p > ED.

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

261

general. The model was based on that developed by Burgess and Seaton ( 1960) in connection with astrophysical spectroscopic problems. The aim of the model is to obtain an approximate solution for the impurity wave function outside the ion core site. Thus, a radius r, is defined (of the order of the nearest neighbor spacing) outside of which the QDM formulation is expected to be valid. As with the delta-function potential approach discussed in the preceding section, a knowledge of the observed binding energy is required to achieve the goal of the QDM. In conformity with the terminology already used, ED will be used to signifythe (empirical) binding energy of a deep donor. And so, instead of solvingthe effective mass equation, Eq. (1 l), for the energy eigenvaluesand eigenfunctions,the energy ED is inserted as a requirement. Assuming the validity of Eq. (1 1) used in this way for r > r,, one obtains the asymptotic form of the envelope function F(r)* Let us express radii in units of the “hydrogenic Bohr radius” ad, and energy in units of the hydrogenic donor Rydberg energy Ed [asrelated by Eq. (1 5)]. Then the radial part of Eq. (1 1) can be written as

+

[(d2/dr2) - /(I l)/r2 - u(r) + Elf‘@)= 0, r > I-,. (28) Substituting the coulombic potential for this large-radius part ofthe solution (which is just -2/r in this dimensionless system of units) in Eq. (28), the solution for F(r) was shown by Bebb and Chapman ( 1967) to be expressible in the form of a Whittaker function (Whittaker and Watson, 1964)-that is, as a linear combination of two confluent hypergeometric functions. For each of the specific quantum states, the correct form of the Whittaker function is determined by a quantum defect number p, defined by pun-v. (29) Here IE is the principal quantum number and Y = (Ed/ED)lI2. The reader may wish to note that Bebb and Chapman’s original terminology is retained here in writing the quantities p and v of Eq. (29). The dimensionlessquantity v here should be kept distinct in one’s mind from the use of v as an electromagneticwave frequency! A simplified form of the envelope wave function may then be written in the form (r/ad)‘l exp(-r/vad), r > rc, (30) and one sees that the wave function is scaled by the characteristic distance Fv(r)

CC

Vad = ad(Ed/ED)’”. (3 1) A comparison with Eq. (21) then shows at once that vad is the same as the quantity a , used in discussingthe delta-function potential model. As noted

262

J. S. BLAKEMORE A N D S. RAHIMI

by Bebb (1969), and by Bebb and Chapman (1971), the function Fv(r) provides a continuum of opportunities for the range 0 < v < 1, with the hydrogenic model as the v .--, 1 limit and Lucovsky's model as the v --c 1 extreme. A principal purpose of Bebb and Chapman in determining the approximate wave function form shown in Eq. (30) was calculation of a photoionization cross section nv(hv),for comparison with the Lucovsky expression of Eq. (23). That depends, in the manner ov(hv) a I(4dWYi ) I' (32) on three things: the initial bound state Yi, the final state +f in the relevant band, and the interaction W between the photon and the solid. The above matrix element has been calculated in QDM for two different forms of &. In one of these, as for the Lucovsky model, the Born approximation procedure of a plane wave envelope function for $+wasassumed (Bebb and Chapman, 197 1). If photon energy is written in dimensionless form, 4 = (hv/E,) [as an analogy to the use of 4 in Eq. (17)], then ovhas the spectral dependence 0" a

tL(+)IZ+-Y4- 1)-1/2,

(33)

where

f,(+)

+ 1) tan-'(+ - 1)'/*] + l)+-l/z cos[(v + 2) tan-'(+ - l)I/*].

=(+ - 1)-*Iz sin[(v

-(v

(34)

Photoionization in the QDM, but with a coulomb wave function used for the final state (+f), was formulated by Burgess and Seaton (1960) and described for the semiconductor situation by Bebb and Chapman (1967). That approach took the core and charge scattering into account. A simple analytical expression is not then possible, and Bebb and Chapman provided families of curves for n,(hv), for zero and small negative values of the continuum quantum defect number p. These families of curves were then used for comparison with moderately deep acceptors: Si: In (EA= 0.15 eV = 4E,),Ge: Hg (EA= 0.09 eV 8E,), and GaAs: Mn (EA -0.11 eV = 44). Mn in GaAs might be taken as a "middle-of-the-road" example of a center for which QDM could be considered appropriate. Here, v = 0.52. Figure 8 shows an example of GaAs:Mn photoionization spectral data, which are compared here with the Lucovsky model, and with the two kinds of final state choice in the QDM. Transitions to the split-off band affect the data and have been allowed for in the three calculated curves, for hv > (EA AB-o) = 0.45 eV. Rather surprisingly, the oversimplified Lucovsky model

-

+

4.

263

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

10 I

I

I

,.-

I

I

I

I

I

I

I

I

I

I

1

I

8

6 N

E

V

k

0

- 4

b" \.

COULOMBIC F I N A L STATE

2 0.I

I I I

I

0.2

I

I

0.3

I

I

0.4

I

I

0.5

I

'\

\.

\. 0.6

'\ '\

I

".'.0.7

hu ( e V ) FIG.8. Photoionization spectrum for Mn acceptors in GaAs (as measured at 20"K),after Brown et al. (1973), and compared with three models: the Lucovsky model, the QDM with plane wave final state (for v = 0.52), and the QDM with coulombic final state.

appears to match the data better than the QDM with coulomb wave function final state. Nature's perversity continues. The use of a delta-function potential, without any coulombic tail, makes the Lucovsky model a special case of QDM, valid only for a neutral center as v +0. On the other hand, the QDM itself may be considered applicable for both neutral and positively charged centers (Bebb and Chapman, 1971; Ridley, 1978a,b). It should be noted also that the Lucovsky and QDM approaches share some limitations, concerning in particular the influence of several bands on the ground state of the flaw, and thereby in observable processes such as photoionizaton. Bypassing the existence and form of the impurity potential for r < r, was obviously a drastic step in the formulation of the QDM, with clear parallels to the arbitrary choice of a zero range potential in Lucovsky's approach. Moreover, it should be noted that the full QDM wave function consists of an envelope function F(r) and a periodic function-taken to be the same as the periodic function in the relevant band. That certainly becomes less tenable as one considers flaw states nearer to mid-gap. However, QDM may be applied, under the right circumstances, to flaw levels of moderate depth. Ridley (1980), and Amato and Ridley (1980), have introduced a new model- the billiard-ball model (BBM)-

264

J. S. BLAKEMORE AND S. RAHIMI

which has its roots in QDM. They have pointed out the conditions under which more accurate results could be expected. The BBM is discussed in Section 9. For failures of the Lucovsky and QDM approaches with the deeper transition element impurity states, and specifically for Cr in GaAs, see Jaros (197 1b). In that paper, Jaros proposed a model in which both short- and long-range (screened Coulomb) potentials were taken into account and calculated a,(hv).Jaros assumed there that Cr could play both acceptor and donor roles, which has now been confirmed (Kaufmann and Schneider, 1980a,b) as being the case. 7. FLAWWAVE-FUNCTION SPATIAL AND SPECTRAL PROPERTIES Figures 4, 5 , 6 , and 8 show typical examples for experimental photoionization data, compared with one or more of the models outlined in this section. These figures exemplify a widely used procedure whereby a model (an existing one or a newly proposed one) is used to calculate a family of a,(hv)curves. The set of parameters which makes a calculated curve visually similar to experimental data is declared the “winner.” Some kind of model is certainly useful for determination of the “threshold energy” from data not far above threshold. Thus, if a model indicates versus hv should be that a, a (hv - E,)“/(hv)”, then a plot of [(hv)”~,]”“ linear, with EDas the intercept. However, data for a limited spectral range, and limited increase (or decrease) of a,, cannot be fitted with much confidence. The spectral dependence a,(hv)does incorporate information concerning the bound-state radial wave function Y(r),and it would be desirable if a measured curve for a, could be converted back into the equivalent Y(r), since the latter is much more informative about the character of the effective potential. That is straightforward only if (a) the wave function of the photoionized electron can also be described and (b) the form of the interaction can be described. For the latter of these provisions, the electric dipole approximation is recognized as adequate. However, point (a) is obviously far from simple for a truly deep center. For a center that is only moderately deep-the kind for which models such as 6 potential and QDM are reasonably appropriate-then the final state may be approximated by the Born approximation of plane waves for a single parabolic band. That simplified procedure was used by Rynne et al. (1976). Since their result, shown in Figs. 9 and 10, concerned several kinds of acceptors, an effective mass m, is used here in characterizingbound and unbound states. Wave-vector and photon energy are then related by k = [2m,(hv - E , ) / ~ I ~ ]Then, ’ / ~ . for an 1 = 0 bound state, q ( h v ) calculated in the electric dipole approximation has a spectral form controlled by

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

265

-I-

s 0 5 U

0

I

2

3

5

4

NORMALIZED RADIUS x = r / o A

FIG.9. Radial variation of bound charge density, as expected from hydrogenic and deltafunction potential wave functions [Eqs. (14) and (22)] and as calculated from experimental photoionization data for Si: B and Si: In. (After Rynne et al., 1976.)

I000 500

>-

200

U

a

LL

I00

m LL a

50

-+

20

t u

X

CL X W

3

10

A

x

FIG.10. Log- log plots ofF(x) for the shallow boron acceptor in silicon, and for four rather deeper kinds of acceptor in various semiconductor hosts. (Afier Rynne et al., 1976.)

5 2 I

0.2

0.5

1.0

2

5

NORMALIZED RADIUS x = r/aA

266

J. S. BLAKEMORE A N D S. RAHIMI

[r3Y(r)j,(kr)dr.

[q(h~)]'/~ Q

(35)

Here, j,(kr) is the n = 1 member of the family of spherical Bessel functions, given by

j,(kr)= (kr)-2[sin(kr) - (kr) cos(kr)].

(36)

Now, since

it is possible to invert the transformation of Eq. (35). This yields

Y(r)

Q

r-l

[

k3/2j,(kr)(a/v)1/2 dk.

(38)

Figure 9 is adapted from Rynne et al. (1 976), showing the radial dependence so deduced of the charge density-expressed as [xY(x)l2, where x = (r/aA)is the normalized radius. The data derived from photoionization measurements of boron and indium in silicon have been compared with theoretical curves using the hydrogenic wave function [Eq. (14)] and the Lucovsky model wave function [Eq. (22)]. Not surprisingly, boron displays a diffuse wave function, while indium is not far from the pattern generated by a delta-function potential. The various wave functions we have discussed [of Eqs. (14), (22), and the QDM wave function, Eq. (30)], can all be regarded as members of the class Y(x) = F(x) exp(-x)

(39)

in terms of the normalized radius x = r / f f A . Here, F(x) is constant for a shallow hydrogenic acceptor, vanes as xY-l for QDM,and as x-' for the delta-potential limit. Thus, the radial dependence of the quantity F(x) = Y(x) exp(+x) should be indicative of how effective a given kind of flaw is at keeping its bound charge within a defined radius (as discussed in connection with Fig. 3). Figure 10, after Rynne et al. (1 976), shows the form of F(x) for Si :B and Si :In, and for three additional moderately deep acceptors: Ge :Hg, GaAs :Mn, and GaAs :Cu. So far as the curves in Fig. 10 are concerned, that for Si:B has already been disposed of as irrelevant to deep-level impurities. For all four of the others, the slope of F(x) on this log- log plot is slightly steeper than - 1. The anomalous wiggles for x > 3 arise because of imperfections in the input optical data: This large-radius portion of the curve is especially affected by the part of the photoionization curve nearest to threshold, with ka, 1.

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

267

That defect of several curves in Fig. 10 is a reminder to the experimentalist that data as close as possible to threshold can have great value. At the opposite end of the abscissa scale for Fig. 10, it is optical information for hv >> EA or E D ,which has the greatest bearing on one’s ability to discern the bound charge density distribution nearest to the flaw site. We recognize, of course, that photoionization for a mid-gap center cannot be detected for hv > Ei = 2E,. That sets a limit on the kinds of information that can be extracted from photoionization data with a very deep level. Despite this limitation, the models to be discussed now, in Parts V-IX, often have to be scrutinized in terms of the optical properties they imply. V. Electronic Transition Phenomena Involving Flaws, and the Square-Well Potential and Billiard-Ball Models

As already remarked, the complete signature of a flaw in a given semiconductor host should include information about the following: (i) the eigen-energiesfor bound electrons and/or holes, (ii) the wave functions of the various charge states (in ground state form plus any excited states), (iii) the symmetry (or lack thereof) of the site for each state of charge and excitation, (iv) the multiplet fine structure resulting from crystal field asymmetry, (v) the strength of electron-lattice (vibronic) coupling, and (vi) the probabilities of any energy/charge transfer mechanisms. That is a tall order. The models discussed so far do little more than scratch the surface of that body of desired information, and the only transition phenomenon mentioned so far has been photoionization. More is said about this in Section 9, while Section 10 (also in this part) outlines phonon participation in optical transitions. Nonradiative multiphonon emission (MPE) relaxation and Auger-assisted capture are noted in Section 11. However, that still leaves many more detailed aspects of transition phenomena without an explicit treatment. Some of those topics can be handled only by elaborate numerical methods, since analytical approaches do not have enough generality. Despite this, analytical methods can sometimes relate experimentally measured quantities to various flaw attributes in a simpler (albeit inexact) way. This section briefly notes the localized states that are compatible with the Schrodinger equation for a spherically symmetric square-well (S3W)potential and goes on to discuss in some detail the so-called billiard-ball model (BBM) of Ridley (1980). This model sets out to put a severe limit on the bound charge density outside a certain radius, and so the occupied flaw state

268

J. S. BLAKEMORE AND S. RAHIMI

resembles a dense sphere, in real space. (Some readers may prefer to think of the occupied region as a baseball, or a golf ball, but the acronym BMM is used in what follows.) Figure 2 has already illustrated that the Lucovsky wave function of Eq. (22) is much more effective than the hydrogenic wavefunction, Eq. (14), in imposing such an outer limit for bound charge. An alternative-but equally radical -procedure is used in the BBM. Among the several criteria which might be suggested for classification of approachesto flaw state modeling, one is to draw a distinctionbetween those models which start with a declared form of model potential or pseudopotential, and accept the wave function(s) emerging as solution(s) of the Schrodinger equation (or some doctored form of that equation), and those models which start with a declared form of wave function description. The spherical-well (S3W) model, as with the Lucovsky model of Section 5, represents the first of those schools of thought. The BBM follows in the tradition of EMT and QDM in focusing principally on the eigenstate description. However, a “bridging model” version of BBM (Amato and Ridley, 1980)permits a numerically evaluated bridge between the S3Wand QDM approaches. 8. THESPHERICALLY SYMMETRIC SQUARE-WELL POTENTIAL MODEL

The delta-function potential model of Lucovsky (1965) and some of the ensuing modifications of that model were discussed in Section 5. That approach amounts to adoption of a spherically symmetric square-well potential of vanishingly small radius yet nonvanishing binding strength. It should now be noted that a square-well potential offinite radius, V(r) = - Vo, r < r,, V(r) = 0, r > r,, (40) can also bind a camer-potentially in a quite deep state. The terminology of Eq. (40) follows that of Eq. (1 3) in using r, to denote a critical radius at which the form of the model potential undergoes a stepfunction change. Part (a) of Fig. 1 1 illustrates the simple form of Eq. (40). The principal characteristicsof a quantum-mechanical system subject to the potential of Eq. (40) have been described in the standard quantum-mechanical textbook literature (see, e.g., SchiE, 1968). Those characteristics were rescaled by Walker and Sah (1973) for the S3Wversion of flaw statesin a semiconductor, and applied by them to deep-lying species of radiation-induced defects in silicon. The bridging model version of the BBM (Amato and Ridley, 1980)also amounts to an S3Wsituation, with [as in the model potential of Eq. (1 3)] the option of coulombic wings to the potential for r > r, . We shall return to that more complicated situation in Section 9.

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

269

vfrlO0

-

c

SYMBOLIC ACT uA L" BEHAVIOR

-V0

FIG,1 1. Some simplifiedforms for the radial dependence of potential around a flaw site. (a) The highly simplified spherically symmetric square-well (S3W) potential of Eq. (40). (b) The solid curve, after Ning and Sah ( 197 1a), symbolizesthe central-cell oscillations that one could expect with any "actual" potential, while the dashed curve shows the simplified monotonic trend provided by Eqs. (41) and (42).

The modeling of Walker and Sah appears to have been stimulated in part by a slightly earlier study (Ning and Sah, 197la,b) of a model potential EMT approach to Group V and Group VI donors in silicon. Ning and Sah had surmised that the effective potential seen by an electron bound to a donor might (apart from the rapid central-cell oscillations) resemble V(r) = (- ez/~r)Zeff(r),

(41)

with (42) Zeff(r)= Z,,,,[ 1 - (1 - Br)exp(- br)]. The nominal valence is Z,,, = 1 or 2, for a monovalent or divalent donor, respectively, while the parameters B and b (both with reciprocal length dimensions) describe the depth and effective radius of the potential well. The dashed curve in part (b) of Fig. 1 1 shows the monotonic course of V(r), from V,,, = [-$Z,,,(b B)/lc] in the central cell, to the usual screened coulombic form V(r) = (- $Z,,,/n) for large r. Z,, is maximized at radius r, = (&I B-'), and the curve of V(r)goes through its inflection point near that same radius. Ning and Sah (197 la) used the model potential of Eqs. (41) and (42) in calculating ground- and excited-state eigenfunctions and eigenvalues, for donors in silicon. That calculation used a multiband elaboration of EMTthe details of which are not pertinent here, except to remark that known spectroscopicexcitation energieswere used in deducing values for the model potential parameters b and B, for various donors. That modeling allowed, in turn, calculations of various other donor properties, such as the photoionization cross section a,(hv)and the Fermi contact hyperfine constants.

+

+

270

. I . S. BLAKEMORE AND S. RAHIMI

The much simpler model potential of Eq. (40), illustrated in part (a) of Fig. 1 I, was used by Walker and Sah (1973). That adoption allowed them to scale the standard quantum mechanical solutions (Schiff, 1968)for a potential of that radial step-function form. States that can be bound by the potential of Eq. (40) include some that are purely radial, 1=0. However, additional bound states of finite angular momentum (1 > 0) can also be included in the total picture, if the well depth V, is large enough. [As will be seen shortly, the actual criterion is controlled by the size of ( VorL).]Even so, the principal interest in an S3Wmodel for a deep-level flaw in a semiconductor is obliged to be concentrated on the simple wave function for the Is ground state: n = 1, 1 = 0. Following the terminology already used in previous sections, let ED denote the ground-state binding energy for a deep-donor type of flaw. We shall find it convenient, in what follows, to define quantities a and p (with dimensions of reciprocal length), as follows:

a = [2mc(VO - ED/h2]’/2,

p = (2m3D/h2)’”

(43) The 1 s ground state, for the potential of Eq. (40),then has a form that can be expressed as e

Yl(r) = (C/r)sin(ar), r < r,, (44) Y2(r)= (C/r)sin(ar) exp[-p(r - r,)], r > r,, where C is a normalization constant. Since it is necessary that (Y {/‘PI)= (Yi/Y2)for r = r,, then the three quantities r,, a,and p must be interrelated by the condition

p = -a tan(ar,).

(45) This condition requires, in turn, that the donor ionization energy ED, the well depth V, , and the well radius rM be connected by

ED = Vo C0S2(ar,)

Vo COS2[(r~/h)(2mc)1/2( VO- ED)"^].

(46) An S3Wpotential has no bound state at all, unless its depth V, exceedsthe minimum value =

That is equivalent to a requirement that (ar,) > @/2) radians. A second s-like bound state is not encountered until V, > 9 Vmin.Walker and Sah did point out that a first p-like excited state (n = 2,1= 1) becomes bound by the system when V, > 4 Vmin.However, solutions for V, not much larger than Vmin(and the Is state the only bound one) appear to be appropriate for any consideration of the S3W model in respect of mid-gap flaws in GaAs. In order to follow through with the implications of the above comment, let dimensionless variables x and y now be defined, such that

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

+

x = (2rM/~)z(~2p)= (32LVcr&Yo/h2)= (&/Ymin), J’=

(2r~/n)’P= (32mcr&/h2) = (E,/vmin).

271 (48)

Equation (46) can then be re-expressed in the form (2y/x) = 1

+ cos[n(x - y)l’*].

(49)

The angle in Eq. (49) exceeds n radians whenever x > 1, to permit y > 0. When y is small (because x is not much larger than unity), Eq. (49) can be reduced to a simple explicit form, for y as a function of x, viz., y = (x - 1)2/[2(x

+ 1)( 1 + 4/ZZX) - 41,

y < 1.

(50) Let us now consider the numerical specifics for gallium arsenide. The requirements for Vminare less severe if acceptorlike flaw states are considered, since rn, = 0.5m,-,, several times larger than m,. It would seem reasonable to suppose that Y, = 0.12 nm, half the nearest-neighbor interatomic spacing. Then Eq. (47) yields Vmin= 13 eV. Since this is nearly 20 times larger than the binding energy (- 0.7 eV) for a mid-gap center, one can see that the use of Eq. (50) will be quite justifiable. For the specific instance of a mid-gap acceptor in GaAs,with EA= 0.7 eV, Eqs. (49) and (50) have the solution x = 1.35, y = 0.06. The strong sensitivity of the ground-state binding energy to any modest change in potential well depth, under the y < 1 conditions of Eq. (50), should provide a warning that the S 3Wmodel needs to be approached with appropriate caution. With GaAs, as discussed above, a change in (Yo&) of & 10% is sufficient to move the acceptor ground state all the way from (E, EJ4) to (E, - EJ4). Perhaps because of that sensitivity to parameter choices, the study of Walker and Sah ( 1973) for radiation-induced flaws in silicon has not been followed up by many other applications of this “muffin-tin potential” approach to other semiconductor:flaw systems. As described in the latter part of Section 9, the “bridging” version of the BBM does revive the S3Was at least the major part of a model potential. In that case, a coulombic tail is added for Y > rMwith attractive or repulsive flaws [the procedure suggested in Eq. ( 1 3)].

+

9. PHOTOIONIZATION AND THE BILLIARD-BALL MODEL In order to develop the goals of the S3W model, it was necessary to prescribe an abrupt change in the effectivepotential at the critical radius r, . In contrast, the BBM makes its most important assumption concerning a change in the form of the electron wavefunction at a particular radius. That radius is here denoted r, for a deep donor (or r, when the flaw in question is known to be an acceptor). Of course, the S3W model also entails a change in the form of Y(r)at the

272

J. S. BLAKEMORE A N D S. RAHIMI

critical radius r,. This is described by Eq. (44). However, that comes as a consequencerather than as the starting premise. Ridley ( 1980)remarks that, for the BBM, the model is defined effectively not by the potential but by the choices of wave function for r < rD and r > rD.Ridley proposed that the flaw bound-state wave function be expressed as a product of a periodic part @(r) (constructed from Bloch functions) and an envelope function S(r). His expectation for S(r)was that this would be ‘Yl(r) of Eq. (44) for r < r,, and that it would behave like the quantum-defect wave function F,(r) of Eq.(30) for r > rD. Thus, for a deep-lying flaw (v +0), the envelope function would rapidly approach zero outside radius rD. That accounts for the “billiardball” name, epitomizing an abrupt exterior to the occupied region in space. The rather drastic assumptions that Ridley made in proposing the BBM view of a deep-level flaw do permit the modeling of several kinds of flaw property. It is thus prudent to think of this model as being a vehicle for describing the bound and free states of a flaw-derived electron by means of conveniently defined wave functions. The convenient forms of these wave functions simplify the calculation of matrix elements for transition phenomena. And, it is much to the point that one of Ridley’s major objectives was the derivation of analytic expressions for the photoionization cross section q(hv) for donors and acceptor flaws of attractive, neutral, and repulsive coulombic character. Thus, the concerns of Ridley and Amato (Ridley, 1980;Amato and Ridley, 1980;Ridley and Amato, 1981) included the processes of photoionization and photoneutralization. Expressions for q(hv)have been quoted at several points in this narrative, on the basis of various models: Eqs. (16)-(18) for a shallow hydrogenic donor, Eqs. (23)-(26)for delta-function potential models, and Eq. (33) for the QDM. The topic of Eqs. (35) and (38)also bears on this subject. This is, perhaps, a good point at which to comment on the general formalism of photoionization, of which the above-notedhave provided specific solutions. When light (i.e., a photon) interacts with a system containing an electron in a bound flaw state, the optical cross section for photoionization can be expressed in the form

o,(hv) = (8~22a~oloV/m,n,)(R,/hv)g(E~)la PI2 = (ha,,V/rn&v)g(E,)l[a PI2. (51) The terminology of Eq. ( 5 1) is as follows: a, = (h2/m&) = 0.0529 nm is the Bohr radius for a hydrogen atom; a,, = ($/hc) = Tfr is the fine structure = 13.6eV is the hydrogen atom Rydberg energy; constant;RH = (q,P‘/2h2) and Vis the volume of the cavity containingthe flaw site. [The final result for q ( h v ) does not depend on V.] Also, n,(= dI2)is the refractive index while g(&) is the conduction-band density of states, for kinetic energy & = (hv - ED)in the band and corresponding wave vector k. Of course, Ek=

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

273

(h2k2/2m,)for the simplest kind of parabolic band, characteristic of an effective mass m,, and g(Ek)= 4 ~ ( 2 m J h ~ ) ' / ~ Efor ~ ' / ~that situation. However, Eq. ( 5 1) is not itself restricted to the parabolic band assumption. Continuing with the terminology of Eq. (5 l), it should be noted that an effective field correction factor (eeff/eo)2, which might sometimes be necessary, has not been included. The effect of phonons on the transition probability has also been neglected for the present. (However, the effects of phonon emission and absorption upon optical transitions are discussed in Section 10.) The final quantities of Eq. (51) concern the matrix element for an optically induced transition. The vector a is a unit vector for the direction of the electric vector of the incoming light whereas

P = (Dlexp(- iq r)plC)

(52) is the matrix element for a transition from a donor state D to a conduction state C. Since the wavelength of the photon greatly exceeds the flaw diameter, the longwave limit q = 0 applies, and so P = (DlplC). (That becomes P = (A Ip I V) for an acceptor to valence-band transition.) The quantity p is the momentum operator. And so, for the dipole approximation, with electric dipole moment er, then p = 2zvrr4,r. The matrix element P can be evaluated when the envelope functions are specified. Thus, for a parabolic conduction band of mass m,, and with the longwave limit presumed, Eq.(52) reduces to

P = hk(m,/m,)(DIC).

(53)

Here, of course, the crystal momentum hk = [2m,(hv Equation ( 5 1) can be further simplified when the response to unpolarized light is considered. Then one can write q(hv) = aoG(hv), where the overall magnitude is scaled by

a, = 16~~4q,m~/3n,rn, = 1.08(rr4,/n,mc)X lo-'' cm2

(54) (55)

and the spectral function G(hv) is given by G(hV) = vEk(R,/hv)g(Ek)I (DlC) 1'.

(56) Ridley (1980) suggested that the wave function for an electron in the presence of the localized flaw potential should be capable of representation by the sum of a sufficient number of Bloch functions: Y(r) = P

I 2

ZB

nL

*(r) exp(& r).

(57)

214

I. S. BLAKEMORE AND S. RAHIMI

(Here, n signifies neither electron density nor refractive index, but rather the index identifyinga band.) Ridley remarked that theform of Eq. (57) should apply to both the bound state and the final conduction state of a photoionization process, although with different sets of coefficients, B:k and @k, respectively. The momentum matrix element P of Eq. (52) may then be written (in the longwave limit) as (58)

where

P,+,(k”, k ’ ) = I/-’

U$,Jr) exp(-ik”

r)pUnk,(r)exp(zlr’ r)dr (59)

This looks much more forbidding than it needs to, for the near vertical nature in k space of an optically induced transition eliminates all contributions except those for k ” = k’. And so,

For any band n, the diagonal terms of the momentum matrix P,,,,,(k’)are simply rn,vg, where vg = ( l/h)Vk& is the group velocity. Having gone through all of the above, which is applicable for any of the combinations of bound state and final state wave function that can be conjectured, let us now be specific for the billiard-ball model. This provides a very simple model for the and BFk coefficients (or BTkand B&, as the case may be) in Eqs. (57) and (58). As noted at the begining of this section, Ridley proposed that the wave function be constructed as the product of a periodic part Q(r) (using Bloch functions) and an envelope function S(r),

xk

Y(r) = @(r)S(r).

(61)

Such a construction, using functions with effective mass connotations, clearly cannot be rigorously correct for a deep-lying localized state. Thus, as usual, a price must be paid for the convenienceof being able to derive simple analytical forms for G(hv) and other flaw attributes. Ridley sought to minimize any errors by considering the most important volume of space ( r < rD) for S(r) of the bound state. The BBM assumes that a&) for the final state involved in photoionization of a donor can be approximated by the periodic part of a conduction band Bloch function, Qc(r) = U&). Ridley suggests that the periodic part of the bound-state wave function QD(r) might be approximatedby a suitable linear combination of conduction- and valence-band states, drawn from

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

275

around the extrema of those bands. Thus, in the two-band BBM case for photoionization of a deep donor,

@C(r) Ucdr), @D(r) bcUddr) + bvUdr)* (62) The participation of the conduction and valence bands in formation of the flaw wave function is thus determined through the coefficientsb, and bv. One would expect b, = 1, b, = 0 for a shallow donor, dominated by the conduction band; but that should not be the case for any mid-gap flaw in GaAs. As a further complication for GaAs,it may be remarked that b,U,(r) should probably be replaced by a sum of contributions from the first several conduction bands, with the large densities of states for the L6 and X , conduction minima having a powerful influence. The BBM is not complete until the envelope functions S,(r) and SD(r) have also been specified. In constructing ScL(r),Ridley was mindful of the scattering of an electron by a coulomb potential with a noncoulombic core. He deduced that an approximation envelope function for the final state (valid for kr << 1) would be of the form

+

Scdr) = (Co/V)l/z[cosSo (l/Cokr)sin So],

(63) where C, is the coulomb tunneling factor and So is the phase shift produced by the core for the zero angular momentum ( I = 0) wave. (Only the s-wave phase shift is of concern for a deep-lying flaw.) The quantity C, in Eq. (63) is such that C;1/2would be the enhancement of the plane wave at r = 0, caused by a purely coulombic attractive site, or the amplitude attenuation caused by a repulsive site. The coulomb factor is related to the photon energy involved in photoionization by

C, = 2xq/[ 1 - exp(-2aq)]. (64) Here q = z(&/Ek)1’2, where Ek= (hv - ED), and Ed signifies the hydrogenic donor energy of Eq. (19,as a parameter controlled by rn, and K. The phase-shift So used in Eq. (63) can be evaluated by requiring that the solutions match at I = rD. This yields tan So = (CohC)[tan(cucrD) - a!,rD] CokrD((k), (65) where, as with Eq. (43), the quantity acis used to express the maximum potential well depth (V,, for r = 0) through a,= [2rn,( V, &)/h2]1/2.The alternative of expressing the core scattering phase shift by means of the variable ((k) will be used in Eq. (68) for q(hv). The most interesting assumptions of BBM concern the forms to be selected for the bound-state envelope function SD(r).Ridley suggested that this might be approximated by a zero-order spherical Bessel function inside the critical radius:

+

276

J. S. BLAKEMORE A N D S. RAHIMI

SD1(r) a r-’ sin(cr,r), r < r,, (66) where the quantity 1(1, was left as a parameter (rather than as an expression in terms of an effective potential well depth) in the lack of any satisfactory basis for specification of an “effectivemass” to be associated with a deeplying state. Outside that radius, Ridley deduced that a QDM wave function, (67) ~d,cr)= ~l exp(- r/tud), r > rD should be appropriate. While we have previously used v = as the quantum-defect parameter, Eq. (67) uses the quantities x = V Z and = vl Z1. Thus, x = - for a center with 2 < 0, one that is repulsive toward recapture. The principal concern of this chapter is with deep-lying mid-gap centers, for which (Ea/ED)”2= v .Q: 1. The function SD2(r)of Eq. (67) falls off very rapidly outside radius rD under those circumstances.Moreover, sDl(r)of Eq. (66) is then nearly constant throughout 0 < r < r,. It is that deep-level limit of the BBM, with constant SDl(r)inside the billiard-ball sphere, and negligible &(r) outside that sphere, which-in turn-is consistent with the kr < 1 limiting form for S&) [i.e., Eq. (63)].For it is only inside radius r, that the bound state and final state wave functionsthen overlap to provide a nonvanishing contribution to the matrix element. The choices for the forms of the wave functionsas indicated above permit evaluation of the various BFk and & coefficientsof Eq. (57) and complete, normalized descriptions of the wave functions. These then allow a determination of the matrix element of Eqs. (52) or (53)and an expression for the photoionization cross section: o,(hv) = ( 8 a 2 ~ / m o n 3 ( R H / h v ) l p, b ~ (b,r&)//h)a’ vk&12

<

+

Here, V, = (4n&/3) is the volume of the billiard-ball core, P, may be obtained from Eq. (59), and the variable ((k) of Eq. (65) represents the strength of any core scattering on the transition probability. It is possible to further simplify Eq. (68) when the conduction band is parabolic, Ek= (h2k2/2mc),and when coulombic scattering by the core is weak, [(k)+ 0. For example, let us consider a flaw which is “donorlike,” in the sense that b, = I, b, = 0, in constructing a&). The forms for the photoionization spectral response [in terms of dimensionless 4 = (hv/ED)] are then (neutral, Z = O),

(69a)

(attractive, 2 > O),

(69b)

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

277

The quantum-defect parameter ( in Eq. (69c) is a positive quantity, even though 2 < 0. For, as defined in connectionwith Eq. (67), = (PE,j/ED)’”. The corresponding spectral forms for a flaw that is “acceptorlike” in having b, = 0, b, = 1, are as follow:

<

G(4) 4-’(4 - 1)’12 =;

= 4-1

= 4-l exp[-2a((+

- 1)-1/2]

(2= 01,

(70d

( Z > O), (2< 0 )

(70b) (704

in their dealings with the conduction band-i.e., for photoneutralization. A preliminary examination of Eqs. (69) and (70) shows right away that the G(4) of Eqs. (69a), (69b), and (70b) do not have maxima for any finite 4 = (hv/E,,) > 1. Thus, the functions of both (69a) and (69b) rise monotonically with hv, while G(4) of Eq. (70b) falls monotonically. G(4)of Eq. (70a) peaks for 4 = 2, which immediately reminds one of the Lucovsky model. That happens not to be the correct analogy, for Eq. (70a) actually has the same form as Eq. (26) under the limiting conditions of /3 > ED. That behavior was shown as curve (C) in Fig. 7. It is thus not immediately clear what new insights the BBM may have to offer concerning the photoionization response spectrum of a flaw. However, it is actually the region not very far above theshold (1 < 4 C 1.5)that should most properly be compared with the above-noted BBM spectral functions. When hv.exceedsthe threshold energy by more than a modest fraction of an electron volt, bands other than just the uppermost valence and lowest conduction bands assume a nontrivial significance. A simple two-band BBM is then no longer applicable. Despite the use of “effective-mass-like” assumptions-such as separation of Y(r) into a cell-periodicpart and an envelope factor -the effective mass m, itself did not appear explicitly in Eq. (68). This was so because the flaw wave function was expressedas a sum over Bloch functions from the various contributingbands. Otherwise, one would have had to use an effective mass from a k * p perturbation treatment (see, e.g., Kane, 1957; Herrmann and Weisbuch, 1977). The reader must be advised that the spectral functions G(4)of Eqs. (69) and (70) should be used with caution, in view ofthe simplifyingassumptions [including those of parabolic bands and ((k)= 01. However, the explicit dependence of q(hv) in the BBM approach upon the charge (Ze), the billiard-ball volume ( V J ,the coulomb scatteringfactor (C,,),and the character of the cell-periodic part of Y&) (using b, and/or b,) make this model quite distinct from those discussed earlier in this chapter. Amato and Ridley (1980) compared the BBM and QDM pictures of a deep-level flaw for centers which are neutral, attractive, and repulsive (when the electron is removed), and examined the ranges of applicability for each

278

J. S. BLAKEMORE A N D S. RAHIMI

approach, with respect to flaw depth E D . Their judgment of the validity or invalidity for each of these models under various conditions was facilitated by the introduction of a more complicated bridging model, treated numerically. The bridging model of Amato and Ridley amounts to an S3Wmodel for a neutral center, with coulombic wings added if the center is charged. In conformity with our previous terminology, the square-well potential depth is described as Vo, for r < r,. A step-function change to zero potential is assumed at radius r, for a neutral center. For comparison with the BBM key parameters, it was assumed by Amato and Ridley that rD= rM

+

vady

(71)

where a, = (~m,u,,/m,)is the shallow (hydrogenic) -donor radius. For the high dielectric constant, low conduction mass situation of a semiconductor such as GaAs, ad = 10 nm; and Amato and Ridley conjectured that rM = 0.05~ =~ 0.5 nm. And so the billiard-ball radius rD extends into the region outside the potential well to some extent, but withdraws towards rM as the flaw state binding energy increases, v -.+ 0. For a flaw that is (positively or negatively)charged when the bound state is vacated, the bridging model assumes an outer (dielectrically screened) coulombic tail:

r >rM, (72) as sketched in Fig. 12 for both charge sign options. One may assume that this tail will become essentially flat beyond a radius r, of the order of the Debye V(r) = (- ZeZ/l~r),

+

. quantity is very large for a screening length L D = [kT/4n$(n P ) ] " ~That semiconductor with small free carrier densities, as in semi-insulatingGaAs.

FIG.12. Form of the potential supposed for the bridging model version of the BBM, showing the coulombic wings assumed when the flaw is positively or negatively charged.

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

279

As with the regular BBM procedure described above, the bound-state envelope function for the bridging model is defined differently inside and outside the core. Inside the core, the envelope function for a spherically symmetric ground state is taken to be

&,PI

=~

l j o ( ~ l ~ rh< r ~ ,

(73)

where A, is the needed normalization constant and jo(z) = Z1sin@)is the zero order spherical Bessel function. The quantity a, in Eq. (73), with dimensions of reciprocal length, may be compared with the quantity a defined in Eq. (43), and with CU, of Eq. (66). One can write (Y, = [2rn*( Vo- ED)/h2]1/2in an attempt to relate a,to a potential well depth, but this is a rather empty exercise in the lack of any reliable perspective as to what effective mass m* is appropriate within the core radius. Amato and Ridley quite naturally chose to represent the envelope function SD,(r) for r > rM by the asymptotic form of a Whittaker function, as encountered in the QDM as Eq. (30),and as further mentioned earlier in this section by means of Eq. (67). They showed that the matching requirements at r = rM provide the normalization coefficients for SDl(r)and S&(r). In using their bridging model for describing photoionization processes, Amato and Ridley considered two possible forms of final state wave function. One of these, not surprisingly,was a simple plane wave (PW) function. This can be expected to be most reliable when hv > EDand for a weakly scattering (neutral) site. Their other choice was a type of coulomb wave function (CW), simplified to

Ydr) = (Co/Y ) l / zexp(zk r),

(74) where C, is the coulomb factor of Eq. (64). Substitution of the bound state and final state wave functions into Eq. (56) then permits a numerical evaluation of the photoionization spectral function G(hv).Amato and Ridley calculated familiesof these curves in order to assesshow adequate the BBM and/or QDM approaches could be. Table I reports the conclusions of Amato and Ridley concerning the applicability of PW and CW final states for photoionization modeling, in attractive, neutral, and repulsive types of situation. This table shows that they found either choice for the final state wave function admissable for a neutral center, with any value of the quantum-defect parameter v = (Ed ED)1/2. A coulomb wave function final state was deemed a requirement for any repulsive situation. The applicability limits are more complicated, however, for the important, attractive (2> 0) situations. In this regard, note that vku, = ku, = I, when hv = 2EDin the transition from a deep donor to a parabolic conduction band. For then, Ek= (hv - ED)= E D = (h2k2/2rn,).Thus, treatment of

280

J. S. BLAKEMORE A N D S. RAHIMI

TABLE I APPLICABILITY RANGESFOR DEEP-DONOR FLAW PHOTOIONIZATION: CHOICE OF PLANE WAVE OR COULOMB WAVE FINALSTATE‘

Flaw charge, with electron removed ~

~~

2-+1

Plane wave final state ~

~~

z=o 2--1

(Repulsive)

~

v>O.l,E,>E,

> 0.1,Ek < ED v < 0.1 for any Ek

Any v

Any v

Not applicable

Any v

(Attractive) (Neutral)

Coulomb wave final state _ _ _ _ _ ~

V

After Amato and Ridley (1980).

a positively charged (attractive) center by the coulomb wave treatment is apropriate only if the center is quite deep. That, of course, is the situation for a mid-gap center. So far, so good. Table 11, also from Amato and Ridley (1980), compares the ranges of applicability of the BBM and QDM approaches, for attractive, neutral, and repulsive flaws. This table suggests that the two models are complementary. (The bridging model is assumed to be applicable throughout 0 < v < 1.) It can be seen from Table I1 that the BBM is reported to be suitable for a repulsive center of any depth, and also for a neutral or attractivecenter if this is deep enough. Table I1 leads one to the conclusion that the QDM, inapplicable for a TABLE I1 RANGES OF APPLICABILITY FOR THE BILLIARD-BALL (BBM) AND QUANTUM-DEFECT (QDM) MODELSFOR A DEEP-LEVEL DONOR FLAW” Flaw charge, with electron removed

Billiard-ball model (BBM)

Quantum-defect model (QDM)

Z=+I (Attractive)

v < 0.1

v > 0.3

v
v > 0.5

Essentially any v

Not applicable

z=o (Neutral) 2--1

(Repulsive)

After Amato and Ridley (1980).

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

281

repulsive center regardless of depth, should not be used for a neutral or attractive center either, unless the ionization energy ED = (Ed/?) is a relatively small multiple of E d . That would appear to render the QDM approach inadvisable for any kind of mid-gap flaw level in GaAs. Figure 13 compares q(hv) curves calculated for a repulsive (negatively charged) deep donor in a semiconductor host, using the QDM, BBM, and bridging models. Part (a) is for a center of moderate depth, with v = 0.4. Part (b) is for a flaw 16 times deeper, with v = 0.1. Those two situations correspond to ED - 0.04 eV and -0.65 eV, respectively, if a d * 10 nm. Figure 13 confirms the listings in Table 11, which categorize the BBM approach as being suitable (as well as being simple and convenient) for a repulsive (2= - 1) flaw. In contrast, QDM tends to underestimate the strength of q(hv) for this class of flaw. It may be noted that the solid curve (bridging model) in part (b) of Fig. 13 has a spectral dependence not far from that provided by Eq. (23), the spectral form for a delta-function potential. Amato and Ridley went on to discuss q(hv) on the same comparative basis for neutral (2= 0) and attractive (2= 1) types of donor flaw. (The companion methodology for acceptor flaws is entirely analogous.) They examined the effect on oIof varying the radius rM supposed for the squarewell model potential. As expected, the choice for this parameter becomes more critical for a very deep-lying flaw -the problem for mid-gap centers that was remarked at the end of Section 8. It is clearly not desirable that the

+

I

I

r

I /

V=0.4 I

1.0

1.2

r

l

I

I

1.4

1.6

1.8

2.0

1.0

+ = hV/E,

1.2

I

I

I

1.4

1.6

1.8

I 2.0

is for a value (Ed/ED)1'2 = v = 0.4 of the quantum-defect parameter. Part (b) is for a flaw ground state 16 times deeper, with v = 0.1.

282

J. S. BLAKEMORE AND S. RAHIMI

wave function derived in an S3Wmodel should turn out to be more localized than the potential itself (Lindefelt and Pantelides, 1979). Avoidance of that difficultywith S3W types of model thus requires a realistic choice for r,, taken in conjunction with the quantum-defect parameter v = (EJED)”’, which is firmly tied to the flaw binding energy ED. Ridley and Amato (1 98 1) suggested that their BBM modeling of the Cr, center in GaAs provided a god fit to experimental data of Szawelska and Allen (1979) for the C P hv * Cr3+ e- photoneutralization reaction. [Szawelskaand Allen (1979) had obtained a threshold at 0.74 k 0.01 eV for this proces, from photocapacitance measurements.] Ridley and Amato also remarked that the BBM was compatible with results of Arikan for the spectral form of the C P -,Cr3+photoneutralization process. However, a much more complete compatibility could be demonstrated when the effects of phonon couplingand finite temperature on q(hv)[or, rather, adhv)]were taken into account. Arikan’s GaAs:Cr data are illustrated a little later, in Fig. 16, with those influences incorporated.

+

+

10. PHONON-ASSISTED OPTICAL TRANSITIONS

The complete photoionization cross section for a flaw must be expressed as a summation when concurrent processes of phonon emission and absorption are taken into account. For a “neutral donor” type of situation, which yields Eq. (69a) as the BBM spectral function before any phonon effects are allowed for, that summation for reduced photon energy 4 = (hv/ ED)can (with a simplified treatment) be expressed as

At the heart of that simplificationis an assumption that all participating phonons have the same energy, hw. In Eq. ( 7 9 , p denotes the number of such phonons emitted ( p > 0) or absorbed ( p < 0), as an adjunct to the photoionization (or photoneutralization)process, while 4p= (phu/E,). As in Eq. (64), the quantity C, is the coulomb scattering factor while Jp is the oscillator overlap factor, expressible as

J~ = z,{~s[N(N+1)]1/2} exp[(phw/kT) - ~ s ( N +$11. (76) Here Zp{z}denotes the modified Bessel function of the first kind, and

7? = [exp(ho/kT) - 11-1

(77)

is the Bose - Einstein phonon occupancy number. The extent of electron-phonon coupling is represented in Eq. (76) in terms of the dimensionlessHuang- Rhys factor S (Huang and Rhys, 1950). That, too, is obviously a simplification of how phonon emission and ab-

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

283

sorption can affect the near-threshold behavior of G(4).However, it is a highly convenient simplification. The exponential in Eq. (76) has so much influence that Jp is maximized for p = S at any finite temperature, even though Ip{z)itself is maximized for p = 0. And so, on a gross scale, electron-phonon coupling shifts the “apparent threshold” from E D to (ED Shu) = ( E D dF-,-).The quantity dF-c,with dimensions of energy, is the Franck -Condon shift (Condon, 1928; Lax, 1952). The total consequences are not limited, however, to that apparent shift. For while most of the photoionization activity is shifted upward in energy (that associated with p > 0), there is for any nonzero temperature a (smaller but nonzero) probability for phonon-absorbing processes ( p < 0). These provide a weak tail to the spectral function, and this extends below the energy E D . That feature will be illustrated in Figs. 16 and 17. The Franck-Condon shift dF-c= Sho, and the “Stokes shift” (which is twice as large), can be illustrated in a simple but useful way by means of a linear configurational coordinate (CC)diagram (Condon, 1928; Seitz, 1938; Huang and Rhys, 1950; Lax, 1952; Stoneham, 1975). Figure 14 shows a version of CC diagram useful for illustration of phonon effects on photoionization and radiative capture processes. The abscissa of Fig. 14 provides a one-dimensional equivalent-for the surroundingsof the flaw -of the normal lattice coordinate Q. That abscissa represents the extent of nuclear displacements from their equilibrium conditions. The ordinate of Fig. 14 conceptualizes the combination of electronic potential and vibronic (phonon) energy. The latter is expressed in

+

+

FLAW EMPTY

FLAW CONFIGURATION COORDINATE, Q

FIG. 14. A linear configurational coordinate model diagram, for the processes of photoionization and radiative relaxation (free-to-bound luminescence). The horizontal lines indicate vibrational levels, with interval hw.

284

J. S. BLAKEMORE A N D S. RAHIMI

terms of a single effective phonon energy hw. The lower curve in Fig. 14 represents the flaw in its unexcited, occupied condition, while the upper curve is for the sum of the empty flaw and its former (now nonlocalized) electron, as produced by photoionization. For a fairly low temperature, one can expect that the flaw is apt to be in its lowest state La, for which the equilibrium lattice coordinate is Q,. The Franck-Condon principle (Condon, 1928)is based on the supposition that absorption of a photon occurs too fast for concurrent nuclear readjustment. Thus, photoionization from state L, can be depicted as a vertical line to state U,,requiring photon energy hv,. (Note that this is also a vertical transition in k space, where k refers to the electron wave vector. However, all of Fig. 14 is for a given value of k.) Now the equilibrium condition Qbof the lattice configuration with the flaw ionized (state u b ) has been drawn in Fig. 14 to differ appreciably from Q,. Accordingly, U, is higher than u b , and an act of photoionization is followed by a nonradiative relaxation, causing (on average) S phonons to be emitted in this relaxation. For a transition at k = 0, to the lowest electronic states of the conduction band, the energy difference between u b and Lais just ED. For a transition at finite k, that difference is the sum of ED and the electron’s initial kinetic energy. Now consider an act of radiative relaxation, accompanied by free-tobound extrinsic luminescence. That will typically start from the lowest vibronic energy configuration of the ionized condition-in short, from u b . The radiative transition from u b to L b , without any concurrent nuclear readjustment, provides a photon of energy hvb. Subsequent lattice relaxation (from &,to La)causes S phonons (on average) to be emitted. And so the total Stokes shift (hv, - h v b ) = 2Shw = 2dF-C between the photon energies of ionization and relaxation for a given value of the electron wave vector k. Figure 18 will show an interesting (and complicated)example of luminescent emission, which has been predominantiy “Stokes-shifted” below the energies for zero-phonon transitions. First, however, there is more to be discussed here concerning the upward transitions of phonon-influenced photoionization. It is appropriate that we should start this by seeing how a nonzero Huang-Rhys factor results in an upward Franck-Condon shift for the major part of Gp(4).This is exemplified by the curves in Fig. 15. Curve a in that figure displays G ( 4 )for zero-phonon coupling (S = 0), using the spectral form of Eq. (69a). Curves b and c both accord with Eq. (75) as the phonon-assisted generalization of Eq. (69a), each with the supposition that ho = 0.05 ED and that S = 3 (i.e., that dF-c= 0.15ED). The slight

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

+=

285

hV,/ED

FIG.15. Phonon coupling effects illustrated for the photoionization spectral response of a deep flaw. (BBM, Z = 0; after Ridley, 1980.) G(4) shown from the zero-phonon threshold [q!~ = (hv/E,) = 11 upward, supposing phonon energy hw = 0.05ED. (a) For zero-phonon coupling, S = 0. (b) For finite phonon coupling (Huang-Rhys factor S = 3) and temperature such that 8* = (kT/hw)= 0.1. (c) Also for S = 3, but now with 8*= 0.4. (d) The zero-phonon curve, moved bodily to the right by 0.15ED(=3hw).

differences between curves b and c arise from differences in their assumed temperatures. Let temperature be expressed in dimensionless form as 8* = (kT/ho). Then curve b in Fig. 15 corresponds to O* = 0.1, and curve c to a temperature four times larger. It can be seen that the higher temperature curve extends slightly to the low energy side of its low-temperature counterpart when G(q5) is very small, but that it is slightly to the right of curve b for the upper part of the register. What temperatures would those situations correspond to for GaAs? In this semiconductor, the largest maximum in the phonon density of states occurs for o = 5 X 1013 rad/sec for ho = 33 meV. That means that 8*= 0.4 [the condition supposed for curve c in Fig. 151 when T '-. 150 K. One more curve in Fig. 15 remains to be mentioned. This is curve d, which is the zero-phonon curve bodily translated to the right by a FranckCondon shift dF-c= 0.154, (= 3ho). It can be seen that this agrees (rather

286

J. S. BLAKEMORE A N D S. RAHIMI

imperfectly) with the upper parts of curves b and c. And so, a&) experimental data, which have been affected by phonon emission-but which extend no lower than a few percent of ,a -tend to indicate an efective versus hv would appear threshold energy of (ED Sho). A plot of (hv~,)~” to extrapolate downward to an intercept at that energy. Ridley and Amato went on to analyze phonon coupling effects on G(4) for neutral (2= 0) and charged (Z = & 1) flaws, over the temperature range 0.1 < O* < 3. Some of their results for a fairly high temperature [8*= 1, corresponding to T = ( h o / k )= 400 K for GaAs] are exemplified by the curves in Fig. 16. This figure uses the spectral function from Eqs. (75) through (77) for three values of the Huang-Rhys factor. Since these curves all extend well down into the threshold region, to 0, less than 10dam,, ,the contributions of phonon-absorbing processes ( p < 0) are quite apparent, in providing a nonzero transition probability when hv < E D . In analyzing experimental data for an optical transition that has been

+

4

FIG. 16. Variation of the spectral dependence of a@) with lattice coupling strength, as represented by the Huang- Rhys factor S. These curves are for a neutral center ( Z = 0) and for a temperature such that kT equals the supposed phonon energy: 8+ = (kT/hw)= 1. (After Ridley and Amato, 198 1 .)

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

287

affected by phonon emission and absorption one would like to be able to deduce -at least -the threshold shift dF-c.If one had any confidence, moreover, concerning the predominant phonon energy hw, then the results of the analysis could be expressed in terms of a Huang-Rhys factor S = (dF-C/ho).Any of the above requires that the phonon influences be deconvolved from experimental optical data, as obtained in measurements of absorption, photoconductivity, or luminescence. Figure 17 provides a rather simple example of such an analysis. The data points in this figure trace out the room temperature spectral form of the photoneutralization cross section a,(hv) for the electron-producing reaction Cr2+ hv + Cr3++e- at a substitutional Cr, site in GaAs. (That constitutes photoneutralization, since Cr3+is the lattice neutral charge state of this mid-gap flaw.) The data in Fig. 17 are of extrinsic photoconductivity measured near room temperature, and were analyzed by Ridley and Amato (198l), assuming a transition from an s-like bound state to a (perceptibly nonparabolic) r, conduction band. The curve in Fig. 17 resulting from that modeling was based on a simplifying assumption that all phonon effects could be simulated by the use

+

Io4

- lo3 z

3

> a

a:

Em

102

a:

-a -' -

c 10

b'

I

06

07

08

09

10

I !

hv ( e V )

FIG.17. A fit of experimental photoconductivity spectral data to a transition model which allows for phonon participation. The data are those of Ankan (see Amato et a[., 1980) for the CrZ+ hv + Cr3+ e- photoneutralization reaction of Cr, in GaAs at 296 The analysis is that of Ridley and Amato (198 I), assuming the Cr3+state 0.76 eV above the valence band, for (E, - EA)= 0.66 eV as the zero-phonon photoneutralization threshold. Also assumed that ho = 0.03 eV and S = 3, for dF-c= Sho = 0.09 eV, and (El - E A dF-c)= 0.75 eV.

+

+

OK.

+

288

J. S. BLAKEMORE A N D S. RAHIMI

of a single phonon energy hw = 30 meV. That assumption can be Viewed as effecting a compromise with respect to the energy ranges of various LA and LO participating phonons in the GaAs normal mode spectrum (Waugh and Dolling, 1963). The caption in Fig. 17 indicates that the curve was fitted to the chromium data for a “zero-phonon” room-temperature threshold of Ei - E,, = 0.66 eV, and with the various phonon emission and absorption opportunities rendered by S = 3.0, dF-c = S h o = 90 meV. [This makes the room temperature effective photoneutralization threshold (Ei- EA dF-c)== 0.75 eV, in parametrizing the upper part of the curve.] That Franck-Condon shift for Cr, in GaAs,and its decomposition into effective values for S and ha,provide the first entry in Table 111. The second entry in Table I11 is the phonon shift deduced by Arikan et al. (1980) for the 0.4-eV oxygen-related (?)donor in GAS.[Look and Chaudhuri (1983) argue that this is a pure defect, which does not incorporate oxygen.] The result quoted by Arikin (1980) was obtained from an analysis of the temperature dependence of both the position and the shape of the extrinsic photoconductive edge. Table I11 does not list a much larger shill (dF-c= 240 meV), which was reported by Malinauskas et al. (1979), also based on the photoconductive threshold temperature dependence for (apparently) the same donor. The smaller value, that suggested by Arikan et al., is the one chosen for tabulation here, since those workers measured and commented on the large temperature dependence [(dEen/dT)= - 1.2 X lo4 eV/K] for the effective threshold energy. When the temperature dependences of the threshold energy and shape were jointly analyzed, it became clear that multiphonon effects account for slightly less than half of (dEeF/dT). The remainder arises from a true (&&it), as a consequence of lattice dilation. The next three entries in Table I11 are as reported by Makram-Ebeid ( 1980);based in part on analysis of his measurements of field-aided tunneling from flaw sites, supplemented by dF-cvalues from various experiments reported by others. One of the systems Makram-Ebeid measured was the E3 level in GaAs.This becomes evident near (E, - 0.6 eV) after MeV electron irradiation. Lang et al. (1977) concluded that E3 is V,, while Pons et al. (1980) were more conservative in assigning this simply to a Ga sublattice native defect. Another system that Makram-Ebeid examined was the well-known (even if not fully identified and explained) EL2 mid-gap flaw in GaAs.The third system was the so-called Zn -0 pair complex in GaP,an isovalent entity that is well known for its red luminescence properties. A more proper name for this (as indicated in Table 111) is O,-Zn,, signifying an oxygen donor on a phosphorus site with a zinc acceptor on a nearest-neighbor gallium site.

+

TABLE 111 FRANCKCONDON SHIFTS REPORTED FOR %ME FLAWS 1N

Semiconductor host lattice

Flaw

Franck-Condon dF-c(mev)

Apparent

hw (mev)

AND

Huang-Rhys S

Literature Source

3.0 3.5 9 6

Ridley and Amato (1981) Arikan et al. (1980) Makram-Ebeid(1980) Makram-Ebeid (1980) Makram-Ebeid (1 980) Monemar and Samuelson (1976)

~~~~~~~~~~~

GaAs GaAs GaAs

Substitutional Cr, 0.4-eV oxygen E3 EL2

GaP

4 - Z b

GaAS

GaP

Substitutional Op

90 110 100 120 200

85

30 31 11 20 19

[n

11

1.7 1.1

290

J. S. BLAKEMORE AND S. RAHIMI

A comparison of the first four entries in Table 111, all for flaws in GaAs, shows that a breakdown of dFF-c as the product of a Huang-Rhys factor S, and an eflective phonon energy, does not always yield the same value for ho. That ought not to be surprising,for one can expect “normal mode” phonons (Waugh and Dolling, 1963; see also Blakemore, 1982b), with energies essentially continuous from zero to some 35 meV, to have varying degrees of effectivenessin communicatingbetween the GaAs lattice and various kinds of flaw. Additionally, of course, there are local phonon modes (Dawber and Elliott, 1963),which arise specifically because the flaw differs in mass and/or charge from its neighbors. In writing Eq. (79, the ‘‘single flaw energy” ho was used together with a notation that this was a simplification of convenience. The various ho entries for GaAs in Table I11 demonstrate that the required phonon “mix” does differ from one flaw species to another. The fourth entry in Table 111, that for EL2, indicates a Franck-Condon shift only slightly larger than for the other three flaw species. Rather than let this pass without further comment, it should be remarked that the wealth of experimental reports concerning this flaw indicate more complexity than just a simple deep donor with a modest dF-c.In particular, EL2 behaves as though it has a metastable excited state (Vincent and Bois, 1978;Mitonneau and Mircea, 1979), with resulting properties including low-temperature persistent photoconductivity, photocapacitance quenching, luminescence quenching (Leyral et al., 1982), etc. Such phenomena are reminiscent of various low-temperature, long-persistence effects that have been noted in connection with flaws (many not fully identified) in a number of semiconductor hosts. These have been ascribed (Lang and Logan, 1977; Langer, 1980) to a large lattice relaxation around the flaw site. That amounts to extrinsic self-trappingof an electron. It can be described in terms of “small polaron” theory (Toyozawa, 1961, 1980; Emin, 1973),and a suitably drawn one-dimensional configurationalcoordinate diagram (Langer, 1980; Lang, 1980) can model some of the principles involved in a simplified form. The CC diagram view of nonradiathe transitions is discussed in Section 1 1c, with the large-lattice-relaxation situation illustrated there as Fig. 22. A major characteristicof a large-lattice-relaxationsituation is a very large Franck- Condon shift. Langer ( 1980)cites examples of this in I11- V, I1-VI, and I - VII types of host lattice. For example, the donor-related “DX” types of flaw in Ga,,Al,As alloys (Lang and Logan, 1977) have an apparent optical threshold exceding 0.6 eV, despite an apparent thermal depth of only 0.1 eV. The extent of lattice relaxation required to account for situations such as those noted above may be regarded as one extreme, dF-ca major fraction of

-

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

291

an eV. At the opposite extreme, some flaws do not appear to show any Franck - Condon shift at all. Reported values in I11- V compounds lie all the way in-between. Thus, dF-c= 120 meV for EL2, as listed in Table 111, is a middle-of-the-road value. That value gives no clue as to the metastable excited state. Perhaps EL2 in GaAs [and in related alloys (Matsumoto et al. (1982)] can be fully identified and understood by the time this book is in print. Such is not the case as this chapter goes to press, however. Early models for this mid-gap state presumed that this was oxygen -or at least oxygen-relatedand those ideas no longer hold. [However, Yu and Walters (1982) find a level they attribute to oxygen fairly near the energy of EL2, as a separate entity.] A proposal by Lagowski et al. (1 982a,b) was noted in Section 2 -that is, that EL2 is caused by an isolated A s , anti-site defect. This should be an isocoric double donor; and photo-ESR studies (Weber et al., 1982) of GaAs in which anti-sites have been generated by plastic deformation do show levels some 0.7 eV and 1 eV below the conduction band, with the mid-gap level displaying photoquenching characteristics reminiscent of those in EL2. However, ion implantation studies (Martin et al., 1982, 1983) show a differentiationbetween anti-site density and EL2 activity. Such information has encouraged other hypotheses. The metastable properties could indicate a two-site complex, such as a near-neighbor combination of A s , with an acceptor such as C, (Ledebo, 1983) or a vacancy (Lagowski et al., 1983; Kaminska et al., 1983). These and other hypotheses have fueled an interesting debate and active experimental research in the 1980- 1983 period, and one must assume that the puzzle will eventually be fully solved. A complete accounting for EL2 must include the status of lattice relaxation for each of the various states of charge and excitation. Before Table 111 is left too far behind, there is a sixth entry which merits some consideration. As with entry No. 5 , this concerns Gap, rather than GaAs, as the host solid. In contrast to the large Huang-Rhys factor that Makram-Ebeid ( 1980)deduced for the 0,- Z k anearest-neighbordonor acceptor pair complex, entry No. 6 deals with a situation of relatively small (but observably and interesting complicated) phonon coupling to optical transitions. The flaw in question is oxygen, substituted on a phosphorus site as a deep monovalent donor, 0, without an acceptor as a nearest neighbor. This donor has its ground state not far from mid-gap, with E D = 0.90 eV and (Ei- E D ) = 1.45 eV for low temperatures. The luminescence associated with the Gap: 0,system was analyzed in detail by Monemar and Samuelson (1976,1978; Samuelson and Monemar, 1978), using a variety of photoluminescence (PL) techniques, including

292

J. S. BLAKEMORE AND S. RAHIMI I

I

I

1 I

1

4

1.2

1.3

1.4

hv

1

I

Ic iiwp

I

5

(eV)

FIG.18. A two-stage deconvolution of phonon influences upon an optical transition involving a deeplevel flaw. Data here are those of Monemar and Samuelson (1976)for a donor-acceptor transition in Gap, observed by low-temperature photoluminescence( T = 4K).The deep donor is oxygen and the shallow acceptor is carbon, both on phosphorus sites. (a) The observed PL spectrum. (b) With the effects of CC phonons (ho2= 0.048eV) deconvoluted. (c) The electronic spectrum, with the effects of CC phonons ( h o , = 0.019 eV) also subtracted.

photoluminescenceexcitation (PLE) and quenching(PLQ) forms of experiment. The transitions analyzed for their electronic and vibronic (phonon) contributions included those from the conduction band to the Op donor, from that donor directly to the valence band, and from the donor to any reasonably nearby (but not nearest neighbor) shallow acceptors. As a fascinating example, Fig. 18 illustrates the effectsof phonon emission simultaneously with photon emission, for the PL spectrum of the specific Op---* Cpdonor +acceptor transition. That is to say, the receiving shallow acceptor was a carbon atom also substitutional on the phosphorus sublattice, with an ionization energy in isolation of E, = 46 meV. And so,in the absence of vibronic influences, one would expect a purely electronic PL spectrum representing members of the set That purely electronic spectrum is shown as curve (c) in Fig. 18, with a peak near 1.4 15 eV indicative of a most probable rDA = 7 nm. However, curve (c) as shown was the result of two stages of phonon influence deconvolution, since curve (a) was the measured low-temperature PL spectrum. In analyzing those data, Monemar and Samuelson ( 1976) deduced that the radiative transitions were accompanied by single or multiple emissions of

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

293

two kinds of phonon, of energies hw, = 19 meV and ho,= 48 meV, respectively. With reference to the normal vibrational mode spectrum of GaP (Yarnell et al., 1968), ho,approximates the maximum TA phonon energy, and is about two-thirds of the maximum LA phonon energy. However, the conclusion of Monemar and Samuelson was that h a , be interpreted in the light of a linear configurational coordinate model as being a CC phonon. That separates the concept of h a , from any direct connection with the normal vibrational mode spectrum of the 3D GaP lattice. It can be seen from Table I11 that Makram-Ebeid (1980) found the same phonon energy (19 meV) suitable for describing coupling to the Op-Zn, donor-acceptor pair system in Gap. The second phonon that Monemar and Samuelson had to invoke in order to deconvolute their data was much more energetic: ha, = 48 meV. This was also regarded as a CC phonon. Note, however, that 48 meV is the median of the narrow energy range (46-50 meV) for LO phonons in gallium phosphide. Curve (b) in Fig. 18 shows what happened when the effects attributed to these 48-meV phonons were deconvoluted. And as noted above, curve (c) shows the purely electronic part of the D A luminescent spectrum when the 19-meV phonon influences were similarly deconvoluted. In such a case, the Franck-Condon shift involves the energies and Huang-Rhys factors for both kinds of phonon. And so, for Gap: Op, Monemar and Samuelson concluded that --+

dF-== S,ho,

+ S,hw, = 85

meV, (79) as was noted in the last line of Table 111. Similar conclusions were reached concerning the influences of the ho,and hw, phonons upon transitions between Op and one or another of the bands of GaP (Monemar and Samuelson, 1978), using a modification of the Grimmeiss and Ledebo (1975) version of the Lucovsky (1965) delta-function potential model to describe the deep donor. 11. NOTESON CARRIER CAPTURE AND EMISSION MECHANISMS This chapter aims to provide a review of various model concepts for deep-level flaws, of the kinds that may be encountered in the middle part of the GaAs intrinsic gap. In order to keep the coveragewithin bounds, it is not feasible to account in detail for all the transition phenomena that such a mid-gap flaw may exhibit. Nevertheless, the reader may find it useful to include some brief notes here concerning various topics in electron capture and emission, including the nonradiative processes which so often dominate transition rates. As with the semiconductor :flaw systems exemplified in the preceding

294

J. S. BLAKEMORE A N D S. RAHIMI

section, in connection with vibronic influences on radiative transitions, the topics mentioned here are not restricted to flaws requiring a BBM or S3W type of treatment. Placement at this point in the narrative is made as a matter of convenience.

a. The Thermodynamic Relation of Capture and Emission Coefficients The optical cross section, for photoionization of a flaw, has been discussed at various points in the narrative to date. Downward radiative transitions of electronshave been acknowledged also, from the existence of luminescence. However, there has been no mention so far of thermal emission of an electron from a mid-gap flaw state. The thermal energy so involved is often most efficiently used as many phonons -the converse of multiphonon relaxation. The energy required for electron emission may alternatively be effective as excess electronic kinetic energy, in an impact ionization process, and then Auger recombination is the inverse process by which electron capture occurs. And, of course, a photon from the blackbody environment can induce photoionization (with or without phonon participation); the probability of this falls off with the required photon energy, as exp(- E , / k T ) . The probability of an energy/charge transformation process which elevates an electron from a flaw state to the conduction band, and of the converse electron capture process, can be related through the application of detailed balance arguments at thermodynamic equilibrium (Blakemore, 1962). (While this is discussed here in terms of electron emission and capture, the arguments concerning holes and the valence band are entirely analogous.)It is often convenient to express the probabilities for a converse pair of processes in terms of the electron emission coefficienten(dimensions sec-*) and the electron capture coefficient c, . If capture of an electron with speed v, by an empty flaw can be represented by a capture cross section an(vn),then c, = (unan) = i@,, averaged over the Maxwell-Boltzmann velocity distribution in the band, and for a mean speed ij, = (SkT/7cmc)1/2 of such a distribution. Note that En has an explicit T factor. Detailed balance provides a connection between c, and en for any given physical mechanism of energy/charge transformation, in the form

en = cn[(Nc&/gf)exp(-ED/kT)I cnn*(80) Here Nc = 2 ( 2 ~ r n , k T / h ~is) ~the / ~ effective density of conduction-band states for nondegenerateconditions, g, and g,are the statistical weights of the flaw electronic configurationswhen “empty” and “filled” with the electron in question, and E D is the Gibbs free energy of the transition. The quantity n* can be regarded as a mass-action density characteristic of the flaw depth. For most semiconductor :flaw systems, the quantity E D can be expected

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

295

to have some dependence on temperature (Elcock and Landsberg, 1957; Engstrom and Alm, 1978). This means that information relative to a transition may appear in terms of the enthalpy (AH,,) and entropy (AS,,)of the transition, rather than as an expression of E D directly. The three thermodynamic functions are related by AH,, = E D 4-TAS,,.

(81) This means that another way to arrange the expression for the emission coefficient in terms of c, is as

en = CnNc [(ge /gf)ex~(ASn/k)l ~xP(-m n IkT) = c,,N,X,, exp(-AH,,/kT).

(82)

Engstrom and Alm (1978)use the name “entropy factor” for the quantity X,, = [(ge/gf) exp(AS,,/k)]in Eq. (82). Note that c,, includes the TLI2 factor of the Maxwell- Boltzmann mean speed, over and above any temperature dependence that 5,may have in a given case, while N, contains a T312factor if the band is not far from parabolic. Because of those two explicit factors, one can think of Eq. (82) as being crudely equivalent to (83) T2/e,,= A exp(AH,,/kT). For this reason, emission data is often displayed as a plot of log(T2/e,,)versus l/T. [For examples with flaws in GaAs, see Martin et al. (1977) and Mitonneau et al. (1977).] When this is the display procedure, some caution is advisable as to the significance of the slope of the plotted data-a quantity one is tempted to regard as a thermal activation energy. As the simplest example of how this activation energy may relate to the thermodynamic quantities, suppose first that EDvaries linearly with T, for all temperatures: E D = (ED0 - CUT).In this case, AS,, = a,while the apparent thermal activation energy is AH,,= EDo, regardless of the range of measurement temperatures (and of the actual values of EDat those temperatures). Far more commonly, however, EDvaries with temperature in a nonlinear way. That nonlinearity may, of course, be small enough so that the emission probability can resemble

(84) en= CT2 exp(-AE,,/kT) over a reasonably broad temperature range of measurements. Under these circumstances, AEem indicates a value for AH,, for somewhere near the center of that measured range. When E D (typically)declines in a nonlinear way with rising temperature, any value deduced for AE,, will tend to exceed E D of any temperature. That behavior is exemplified by the curves in Fig. 19. Complications of this character beset comparisons of optical transition

296

J. S. BLAKEMORE AND S. RAHIMI

TI

T (KI-

FIG.19. The lower curve shows a hypothetical variation with temperature of the free energy of ionization ED for a deeplying donor flaw. At any temperature T,,the enthalpy of transition [givenby Eq. (8 I)] equals the quantity obtained by extrapolating the tangent to ED(T)from T, back to T = 0. Thus,the nonlinearity of ED(T)determinesthe courseof AHm(T).Note that for the behavior portrayed here, the apparent thermal activation energy AH, for any finite temperature exceeds ED for any temperature.

-

energies, “thermal activation energies,” and the like, in deducing Franck Condon shifts, actualground-state energies, etc., for mid-gap flaws in GaAs. In GaAs,as for other crystalline solids with zinc-blendeor diamond lattices, the lattice constant vanes with temperature in a complicated way, with two reversals in the sign of the expansion coefficient as temperature rises [information recently summarized by one of us (Blakemore, 1982b)I. Those complicateddilatationalcharacteristicsnaturally result in a nonlinear variation of Eiwith temperature (Thurmond, 1975), but they inevitably affect also the separation of deeplying donors and acceptors from one band or the other, in a way that is not conducive to a simple linear temperature dependence. This can be exemplified by analyses for Cr in GAS.The work of Martin et al. (1980) has provided extensive data, over the temperature range 300- 500 K, for the four processes of electron and hole emission and capture involved in Cr2+ Cr3+transitions. A comparison of the electron emission/capture data with Eq. (82) was found (Blakemore, 1982a) to yield an entropy factor X,, = 40. This provided a clear warning that the “thermal activation energy” would be an inflated one. Similarly, an entropy factor X, = 2 1 was found for the hole emission/capture processes. And so it was no surprise that the activation energies for electron and hole processes in the

*

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

297

Cr2+S Cr3+system added up to a little over 1.6 eV. This is more than 200 meV larger than Ei for the temperature range in which the data were acquired. Van Vechten and Thurmond (1 976) have also discussed the thermodynamic quantities relating to emission and capture from flaws, as has Lowther ( 1980). The discussion by Lowther is particularly interesting in that he considers an amphoteric deep flaw for which appreciable lattice reconstruction (Jahn-Teller distortion) occurs when the charge on the flaw changes. While the flaw that attracted his especial interest was gold in silicon, the principles involved are relevant to many situations we should expect for mid-gap flaws in GaAs.

b. Detailed Radiative Balance and the Radiative Capture Coeficient We have already discussed the physics which provides for a finite probability that a neutral donor should be photoionized in the presence of photons of adequate energy. The same physics also prescribes the probability that a conduction electron of kinetic energy EL can suffer a radiative capture process at an empty donor site. The relationship between the cross sections for “induced” upward processes and “spontaneous” (as well as “induced”) downward processes can be traced by arguments of detailed balance (Blakemore, 1967). A more sophisticatedargument follows Fermi’s “golden rule’ (Bebb and Williams, 1972). From either of these approaches, the radiative capture cross section is = [(hv/c)2~g,/2gfmcE,lq(hv)

(85)

from the conduction-band states of kinetic energy E L = (h2k2/2mc)= (hv - ED)down into one of the ground states of an empty donor. In order to express the radiative capture coefficient c, = (u,,a,)= En?&, an averaging process must be carried out with respect to the relative speeds and occupancy probabilities for the various Ek in the semiconductor conduction band. For a nondegenerate semiconductor (q, Nc), this results in

l-

C, = (2Kg,/gf~ckTCf)(2amckT)-”2 (hV)2 exp(-E,/kT)q(hv)

dEk (86)

as the thermally averaged radiative capture coefficient at temperature T. Despite the brisk fashion in which aI(hv)is apt to rise from threshold, the exp(- Ek/kT)factor in the integral of Eq.(86) ensures that c, will be heavily weighted by whatever contribution q(hv)is able to make in just the first few kTof the energy range. As a reasonably typical example, let us suppose that a,(hv)has a form just above threshold that resembles Eq.(69a), the spectral dependence that the BBM yields for a neutral donorlike flaw. The spectral

298

J . S. BLAKEMORE AND S. RAHIMI

dependence may change further above threshold, but that will not matter for the present intended purpose. And so, suppose that O ~ ( h v ) OM[2(hv - E D ) ~ / ~ / ~ V E # ~ ] (87) For the first 100 meV or so above threshold. Equation (88) is scaled by the quantity uM,which would be the apparent result of extrapolating Eq. (87) to a photon energy hv = 2& [i.e., much further than needed for Eq. (86).] In substituting Eq. (87) into Eq. (86), let a dimensionlessenergy terminology x = (E,/kT), z = (EDIkT) be incorporated in reexpression of the integral. The result then is

Now our principal interest here is with flaws that are deep enough to be in the central portion of the intrinsic gap for GaAs, and then z = (ED/ k T ) >> 1 even at room temperature. And so for all practical purposes, the e the - ~ integral , is just r(3)= 3Jsi/4. integrand can be regarded as ~ ~ / ~and This results in a thermally averaged radiative capture coefficient C, = (3kTKg,/g,c2)(E~/2m,3)‘/’U,.

(89) For those who prefer to think in terms of a radiative capture cross section, the corresponding expression for that quantity is -

a,= c,/v,, = (31cg,/4g,c2m,)(~kTE,)’/2~M. (90) Note, incidentally, that the particular supposed spectral form for a,(hv)just above threshold resulted in a thermally averaged capture cross section Zr a T*12,requiring c, 0: T. Had a supposition different from Eq. (87) been made about the spectral form of a,(hv), this would have resulted in a larger or smaller temperature dependence for Z, and hence for c,. However, most likely forms for the spectral shape near threshold would still result in a moderate power-law dependence on T. That contrasts with multiphonon nonradiative capture, for which any temperature dependence of the effective capture cross section is most usefully expressed as an activated barrier factor (Henry and Lang, 1977), as noted in Section 1 lc, which follows. Expressions to describe radiative capture of holes would obviously require the use of m, and EArather than rn, and ED, and would also necessitate inversion of the roles of g, and grin Eq. (85) and its successors. The Cr2+4 Cr3+transition of Cr, in GaAs can provide us with a useful numerical example involving hole capture. We assume here that the GaAs in question is not too far towards the p-type direction, so that a valence-band hole is much more likely to encounter an (electron) occupied acceptor,

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

+

299

h+ Cr2+-+ Cr3+ hv,

+

(91)

-

+ hv’,

(92)

than it is to find one already neutral,

+

h+ CrN

C F

in creating a hole-trap situation (Blakemore et af., 1982).For the radiative capture reaction of Eq. (9 I), most emitted photons will have an energy near EA 0.7 eV. We may assume a static dielectric constant K = 13 for GaAs and a hole mass m, 0.5 m,,providing a mean thermal hole speed Vp = lo6 cm sec-I. Kaufmann and Schneider (1980b) report g, = 4,gf= 5 for this flaw, and the extensive and varied literature concerning the strength of the optical transition could encourage us to suggest that 0, = 3 X cm2. These values yield 5 = 10-23 cm2, (93) c, = T cm3/sec, L-

=I

I

cm3 sec-I. and that means a room temperature value ~ ~ ( 3 0= 0 )3 X This value is not impressively large. It is several orders of magnitude smaller than that for nonradiative capture and so, as for most other flaw situations, the quantum efficiency of luminescence is low. We may select one physical mechanism (for example, light) to remove carriers from flaws, but the laws of physics will dictate the relative probabilities of the various processes by which these carriers may find their way back to flaw states.

c. Radiationless (Multiphonon) Transitions Having said so much about optical transition phenomena, it is only proper to comment about radiationfesstransitions that involve exclusively the absorption or emission of many phonons. This energy transformation mechanism provides by far the most efficient means of carrier capture in many cases and has been the subject ofa substantial literature- e.g., Huang and Rhys (1950), Kubo and Toyozawa (1 955), Kovarskii (1 962), Sinyavskii and Kovarskii (1967), Englman and Jortner (1970), Stoneham (1975,1977), Henry and Lang (1977), Passler (1978a,b), Ridley (1978a, 1982), Lang (1980), Langer (1980), Sumi (1980, 198I), and Burt (198l), among others. It was remarked in Section 3 that electron capture can start with (phonon-emission-aided)capture into a very shallow excited state of a flaw. Then the successive steps in a “phonon cascade” (Lax,1960; Smith and Landsberg, 1966; Abakumov et al., 1978) may make the eventual moves toward a ground state of the flaw an inevitable progression. Modeling of a sequential passage through excited states tends to predict a capture coefficient that increases with falling temperature, in a manner resembling c, a

300

J. S. BLAKEMORE A N D S. RAHIMI

T-”’, with the index rn somewhere in the range 2-4, depending on the details of the starting assumptions. This is all very well in accounting for the large capture coefficients of shallow, coulomb attractive, types of flaw. However, Lax noted in his 1960 paper that a phonon cascade cannot describe the transition from the (relatively shallow) excited states of a deep-level flaw into a ground state, with several hundred milli-electron-volts of energy to be disposed of. Gibb et al. (1977) pointed out that an initial phonon cascade may lower an electron’s energy enough so that thermal reexcitation to the band is unlikely, even if a direrent mechanism governs an ensuing transition to the ground state. The nature of that second stage of capture will most likely control the size and temperature dependence of the “two-stage” capture coefficient. Gibb et al. developed equations for two-stage capture and used them to model an active hole trap at (E, 0.75 eV) in GaP. [As further discussed in Part VII, this trap may be a vacancy, V, (see Jaros and Srivastava, 1977).] At any rate, Gibb er al. found behavior indicative of multiphonon emission (see below) as the second stage for this trap. One possible (if improbable) choice for the second stage with any flaw is radiative decay, and the two-stage process is then the inverse of two-stage “photothermal”ionization (Lifshitz and Ya, 1965).

+

IOOO/T ( K - ’ )

FIG.20. Variation with reciprocaltemperature of the (thermally averaged)electron and hole capture cross sections a, and a,,. For the Opdonor in Gap, and for four types of flaw in GaAs: EL2, EL3,and the A and B levels of Lang and Logan (1975). (After Lang, 1980, and with the curves fitted to the MPE capture model of Henry and Lang, 1977.)

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

301

In a different concept for a two-stage process, Ralph and Hughes (197 1) speculated that electron capture at positively charged (coulomb attractive) deep flaws in the partly ionic solid GaAs might occur with emission of an energetic polar phonon as the first step. This was conjectured as being followed by a cascade of less energetic phonons. Ralph and Hughes applied this concept to analysis of electron capture data at one species of flaw with an apparent 0.475-eV depth, and a room-temperature thermally averaged cm2. [Observethat this is lo7times capture cross section Z,(300) = 3 X larger than a, of Eq. (93).] Phonon cascades play no part, either as a first stage or as a subsequent stage, in a model that has been advanced (Lang and Henry, 1975; Henry and Lang, 1977; Lang, 1980) to account for carrier capture at a variety of deep-level flaws in GaAs and Gap. Lang and Henry concluded that these situations, with patterns of capture cross-section behavior as exemplified by the data of Fig. 20, could be accounted for by a multiphonon emission (MPE) process of radiationless lattice relaxation. Such a process is conceptualized as taking an electron directly from a band state to a flaw ground state, with no preliminaries. Lang and Henry ( 1975) remarked that their view of the transition process has analogies to a phonon-assisted radiative transition model (the CC diagram of Fig. 14), except that they evaluate the oscillator overlap factor Jp for the situation of vanishingly small emitted photon energy, hv, 0. Description of MPE capture by means of a CC diagram does give useful insights into the physics of the process, and Fig. 21 draws the kind of CC diagram necessary to account for a healthy MPE rate. By means of such a

-

Qa

Qb

Qc

FLAW CONFIGURATION COORDINATE, Q

FIG. 2 1 . A linear configurational coordinate model diagram (compare with Fig. 14) for a situation of stronger lattice coupling. Electron relaxation is now most likely to occur by MPE, with an activation energy EB.

302

J. S . BLAKEMORE AND S. RAHIMI

figure, the increase of MPE capture efficiency with rising temperature (seen for several of the data sets of Fig. 20) can be rationalized. Such behavior is in sharp contrast to the T-" temperature dependence of a cascade capture model. MPE relaxation processes were considered to be of vey low probability, from several of the earlier analysesof this topic (Godman et a/., 1947;Kubo, 1952;Haken, 1954).Sinyavskii and Kovarskii (1967)were among the first to suggest that MPE could form the basis for efficient capture at deep-level flaws in Si and Ge. Lang and Henry (1975) laid a similar emphasis on MPE for mid-gap flaws in GaAs and Gap, illustrating this with a figure that was the prototype for Fig. 20. How probable MPE capture can be, depends on the strength of the electron - phonon coupling. It could be said that the electron - phonon coupling is relatively mild for the situation illustrated in Fig. 14, in that there is no imminent sign of a crossing of the curves for the occupied and empty conditions of the flaw. Figure 2 1 shows a modification of the situation, so that the two curves now cross, for an abscissa coordinate value Q,.At this value for the configurational coordinate, the system energy exceeds that of the state u b by an amount EB. Consider what happens when an electron is in the vicinity of an empty flaw. If the lattice in that vicinity can, through the action of thermal and/or zero-point phonons, become perturbed to the condition Q,, there is a finite probability that MPE capture Will occur. As Lang and Henry (1975) put it, the (occupied flaw) level can cross into the conduction band and capture an electron. Imediately upon capture, the lattice equilibrium value of Q changes (from Qb to Q,).That leaves the captured electron in a highly excited vibrational state, which decays rapidly by MPE. Lang and Henry built on some of the reasoning of Englman and Jortner ( 1970)concerning the strong coupling limit of the electron - phonon interaction and the resulting spectrum over which integration must be performed. An S3W model was assumed for the potential, with radius modulated by the lattice. [From the remarks made in Section 8, it will be recalled that the binding energy for a situation resembling a mid-gap flaw in GaAs is highly sensitive to the value of ( V O r 9 . ]In this manner, they deduced an MPE capture cross section with a (thermally averaged) form ,, a = [A/2(akT*Shw)lJ2] exp(-E,IkT*]. (94) The factor S is, again, the Huang-Rhys factor, for a supposed single equivalent phonon energy hw. The variable T* is an efective phonon temperature for the combination of zero-point and thermal phonons, while cm2 eV. the parameter A was estimated to be A 4 The effective phonon temperature T* to be used in Eq. (94) is related to hw and to the actual temperature T by

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

303

2kT* = hw coth(hw/2kT), (95) from which T* = T when kT > hw. The capture cross section is thus thermally activated for reasonably high temperatures [in a manner first predicted by Mott (1938)], with EB as the effective height of the capture barrier. That kind of increase of 3 with decreasing T-’ can be seen for the five lower curves in Fig. 20. Thermal phonons rapidly become unavailable when kTis no longer large compared with the supposed ho.Also, Eq. (95) has the low-temperature solution T* = (hw/2k), indicative of the role played by the zero-point lattice vibrations. The resulting capture cross section should then be essentially temperature-independent, with a magnitude determined by the tunneling probabilities between vibronic states. The five lower curves in Fig. 20 were fitted by Lang ( 1980)to an activated MPE capture model of this type, assuming for GaAs that hw = 34 meV. He recognized that radiative capture will take over as the dominant low-temperature process if &,E is constrained by a rather large value of EB,and this appears to be the case for electron capture at the “B” center in GaAs (EB= 0.33 eV) and for hole capture at oxygen in Gap. Just as the extent of lattice relaxation indicated in Fig. 21 is larger than that of Fig. 14, the situation in Fig. 22 shows a much larger effect again. This is a CC diagram for describinga situation of “large-lattice-relaxation’’ (Lang and Logan, 1977; Lang, 1980; Langer, 1980), which is believed capable of causing the self-trapping of an electron at a flaw site. This concept of the possible conditions at a flaw site was commented on in Section 10, in

0 z a> K O

Lz 52 w w nJ zll Ui-

z z+

U W

g: m >

I

I

I

Q,

Qh

Qb

FLAW CONFIGURATION COORDINATE, Q FIG.22. A possible CC diagram for a large-lattice-relaxationtype of situation(compare with Figs. 14 and 2 1). Note that in the case illustrated here, the crossing occurs for Q = Q:, situated between the equilibrium values Q,and Qb for the occupied and empty states of the flaw.

304

J. S. BLAKEMORE AND S. RAHIMI

reference to the metastable state of EL2, and the various flaw species that exhibit persistent low-temperature photoconductivity, with a very large Franck-Condon shift. Figure 22 shows the curves for the occupied and empty conditions of the flaw, crossing for a lattice coordinate value QL.This occurs between the values Q, and Qb,which signify equilibrium for these two charge conditions. The photoionization threshold energy is now substantially larger than the differenceE D between equilibrium states. Moreover, even Sho is larger than E D ! The figure is drawn to show a slight barrier EBagainst capture, but in some cases this barrier may be negligibly small. The expression self-trapping is used for situations like this since, as remarked by Lang (1980), the unrelaxed flaw potential does not produce a bound state in the gap when the flaw is empty. However, the combination of the flaw potential and the electron-lattice coupling produce a bound state when MPE relaxation causes the flaw to become occupied. This means that the electron’s presence at the flaw site creates its own trap level-extrinsic self-trapping (Toyozawa, 1980). The entire theory of large-lattice relaxation is still a rather speculativeone at the time of writing, and it can be expected that fbrther contributions to this topic, subsequent to those listed at the beginning of this section, will provide a more rigorous and secure theoretical framework in the next few years.

d. Auger Recombination at a Flaw Site In the extrinsic form of the Auger effect, the energy given up by the captured carrier is acquired as kinetic energy by other carriers. This may thus be regarded as the inverse of an impact ionization process, and the rates of impact ionization and Auger-facilitated capture must match in toto and in detail under conditions of thermodynamic equilibrium (Blakemore, 1962). Since thermal equilibrium conditions at a normal temperature do not provide many free electrons moving fast enough to effect impact ionization, it can be concluded that those two equal and opposite rates are likely to be very small. While this is so, it does not mean that Auger recombination will necessarily be negligible under nonequilibrium conditions. An appreciable Auger contribution should always be considered as a contender when the concentration of free electrons and/or holes is large enough. Moreover, as Jaros (1 978) has pointed out, there are some types of extrinsic Auger process for which the effective capture cross section is not dependent on carrier density. Auger-facilitated capture is far from being a single process. One can contemplate processes involving one or more bound carriers, one or more

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

305

free carriers, possibly also involving free or bound excitons, and so forth. An active exponent of the possibilities of this subject has been Landsberg (1 970) and collaborators (Landsberg el al., 1964; Landsberg and Adams, 1973; Landsberg and Robbins, 1978). The most recent of the papers just cited seemed to take a perverse delight in enumerating no less than 70 types of Auger process, most of them flaw-related. Even though many of the flaw-related Auger processes one can conceive of do involve a miscellany of participants, the basic set of four processes is that indicated in Fig. 23. These involvethe capture of one electron (with rate constants TIor T,) depending on whether a second electron, or a hole, is the beneficiary of the energy transfer, or the capture of one hole (rate constants T3or T4).Thus, one can write the capture coefficientsof a flaw for electrons and holes as

c,=nT,+pT,, c,=nT3+pT4. Figure 23 does not draw the familiar parabolas for E- k of the conduction and valence bands, since energy conservation is important but k conservation is not. That is in marked contrast with band-to-band Auger recombination (Beattieand Landsberg, 1959; Blakemore, 1962). The distinction lies in the presence of a flaw, perturbing the periodic distribution of mass in the lattice. Then, one or more phonons (normal mode and/or local mode) can take care of all the momentum conservation requirements for a small fraction of the total energy cost. Auger capture processes for shallow flaws in semiconductors were examined by Sclar and Burstein (1955). Bess (1957, 1958) commented on the possible importance of the processes noted above With coefficients TI through T4,in controlling the Hall -Shockley- Read lifetime in a semicon-

I r-L Y

T2

T3

FIG.23. The set of four Auger capture processes incorporated in the terms of Eq. (96).

306

J. S. BLAKEMORE AND

S. RAHIMI

ductor containing flaws in the central part of the energy gap. Contributions to the subject have continued to appear, although many of them have been (if the reader will excuse the pun) flawed in one way or another. An Auger-facilitated capture process is induced by an electron - electron coulombic interaction. Landsberg et al. ( 1964) have shown how this can be expressed by an overlap integral. Such an integral is nonvanishing in view of the difference between the actual interaction and the Hartree- Fock (mean-field) value. However, a fully realistic model on which to base an overlap integral evaluation is not a simple matter. Thus, Grebene (1968) attempted to evaluate the coefficients TI and T, by extrapolation from the Beattie and Landsberg (1959) model of band-toband Auger transitions, an approach that failed to take into account the important relaxation of the k-conservation requirement. Several treatments have used a plane wave function for the accelerated electron (or hole), yet a coulomb wave function would be more realistic. Screening of the e-e, h-h, or e-h interaction to account for the influence of the filled valence bands may well be adequately accomplished in terms of an appropriate dielectric constant: V = (e/xrI2).However, allowance for screening by conductionband electrons (or by unfilled valence states) could well modify this to

v=

(eh.12)

exP(-

r12/L).

(97)

That would not represent a serious problem for a semiconductor with the large Debye length of very small free-carrier densities (as in semi-insulating GaAs), but neglect of the screening factor (as in most models) could lead to an overestimate of the Auger trapping strength in a heavily doped crystal, or one highly excited with band-gap illumination. It should be almost superfluous to remark here that the most critical ingredient in an overlap integral must be a good description of the boundstate wave function Y(4,8, r) and its parity. Thus, a major drawback to the early calculations of Bess (1957, 1958) was his use of hydrogenic wave functions for a deep-level flaw, with the dielectric constant arbitrarily lowered to make ED come out large enough. The calculations of Landsberg et al. (1964) concerning the coefficientsin Eq. (96) suggest the values TI cm6 sec-l, T2- T3 3 X cm6 sec-', (98) T, 5 X cm6 sec-I,

-

as modeled for the specificinstance of Cu in germanium. It is interesting that T2 and T3 (each of which starts with one mobile electron and one mobile hole, of which the former is captured for T2and the latter for T,) ended up as comparable in size -at least for the bands of germanium.

4. MODELS

FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

307

Such calculations for Auger capture rates at mid-gap flaws in GaAs would have one area of general similarity (the valence bands), but would involve a conduction-band system with a T-L-X ordering of the various minima (Aspnes, 1976) and, of course, an intrinsic gap twice as wide as that of Ge. Therefore, an electron raised in energy by Auger hole capture (process T,) would probably be transferred from the r6 lowest conduction band into either the L6 or & sets of minima (Blakemore, 1982b). Despite these disclaimers, let us see what carrier densities in GaAs might make the Auger capture coefficients of Eq. (96) competitive with MPE relaxation, on the assumption that the coefficients TIthrough T4are all of the order of cm6 sec-I. Note from Fig. 20 that several flaws in GaAs have room-temperature MPE capture cross sections around cm2;i.e., capture coefficients approximating lo-* cm3sec-I. Equivalence of the MPE and Auger capture probabilities thus requires a free-carrier density of some l0l8 ern-,. The Auger processes of Eq. (96) can thus be safely ignored in camer-depleted GaAs- that is, in semi-insulating material, or in a device depletion layer. They should not be casually overlooked in heavily doped GaAs, or in the conducting channel of a field effect transistor. As remarked earlier in this section, allowance for Auger capture processes does not end with a consideration only of the simple forms represented by Eq. (96). Belorusets and Grinberg (1978) argue that an Auger-typetransition to a flaw ground state is more probable from a shallow excited state than from the conduction band itself. Their model supposes an electron undergoing the first few steps of a phonon cascade through excited states. At this point, a passing free carrier (electron or hole) is accelerated, while the first electron drops into the deep-lying ground state [which Belorusets and Grinberg modeled by the wave function of Eq. (22)]. Jaros (1978) proposed a different Auger capture model, appropriate for a mid-gap center of the kind that can change its occupancy by two units of charge. (There are many such deep level flaws, including Group I and transition element impurities, as well as various native defects and complexes.) Figure 24 illustrates the kind of process Jaros conjectured, drawn in the manner he suggested. (A Feynmann diagram would have shown the sequence of events, possibly more convincingly.)For Fig. 24, suppose that the flaw is initially occupied by two electrons, with no mobile carriers around. When a free hole (of ordinary thermal speed) amves, this could be annihilated by one of the bound electrons. If the energy EAreleased in that transition is more than half the intrinsic gap, it is possible that the Auger capture could be effected by ejection of the second bound electron to the Jaros remarks that this conduction band, with kinetic energy (2EA - Ei). energetic electron will rapidly thermalize by phonon emission. Jaros proceeded to evaluate the overlap integrals associated with this kind

308

J. S. BLAKEMORE AND S. RAHIMI

FIG. 24. Auger capture of a thermal free hole by a flaw containing two bound electrons. This process will “go” only if EA > jEi . When that inequality is satisfied, the electron is ejected into the conductionband with finite kinetic energy. One can envisage a comparable process for electron capture as being workable, if a conduction electron can lose energy exceedingjEi in being captured, while the flaw simultaneously acquires an electron from a suitable energy within the valence band. (After Jaros, 1978.)

of process, amving at a capture cross section of some cm2(i.e., capture coefficient of some lo-’ cm3 sec-*) for the most favorable circumstances (i.e., EA c- EJ2, etc.). Note that the processes that Jaros was considering are not dependent on the presence of a second free canier to carry off the transferred energy; and so-unlike the circumstances of Eq. (96)- these Auger capture coefficients are independent of n and p. Their opportunities to contribute to the total capture probability are thus not diminished in a crystal or device region of very small caner densities. Thus, the large Auger capture probabilities deduced by Jaros (1978) appeared large enough to dominate the nonradiative transition probabilities to mid-gap states in materials such as GaAs. However, Riddoch and Jaros (1980) have created a more sophisticated model for the probability of this kind of Auger capture. That subsequent work made extensive numerical calculations, using a localized state wave function that was constructed to avoid the “effective mass contamination” of more conventional approaches. The result was an Auger capture cross cm3 sec-l), six section more like cm2 (capture coefficient orders of magnitude smallerthan the 1978estimate! It is to be hoped that the continued development of more complete models for bound-state wave functions will have the reassessment of Auger capture probabilities as one of its corollary calculations. cm2is not, in any event, automatAn Auger capture cross section of ically negligible. The two lower curves of Fig. 20 show cross sections of that size, with little temperature dependence; comparable behavior is known for various other mid-gap flaw types. For those regions of relatively small temperature dependence, there is a three-way split of the capture probability among radiative capture, tunneling between vibronic states, and Auger capture. The mechanism which dominates one flaw for those lower temperature conditions is not necessarily the important one for another flaw. In each case, we should like to know about all three processes.

-

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

309

VI. Techniques Based on Molecular Orbitals

In the preceding parts, we have discussed a number of analytical approaches toward the problem of deep-level flaws in semiconductors. The limitations in applicabilityof those models have led researchers to look for a numerical treatment of this rather complex problem. This search, along with the ever increasing speed and availability of computers, has resulted in a remarkable wealth of information regarding the signature of deep levels. The numerical techniques are not trouble-free, however, and may among other deficiencies suffer from limitations inherent to the nature of the technique itself. In this part, we briefly review models based on a molecular orbital (MO) treatment of deep-flaw levels. What makes this method distinguishable from the others is not how the equations are solved. Rather, it is how the equations are set up. The effect of the introduction of a defect into an otherwise perfect host crystal is often considered as a perturbation to the Hamiltonian of the host crystal (in perturbative methods). The Hamiltonian Ho and the band structure of the perfect solid are known, and the effect of a flaw potential in the total Hamiltonian is represented by a perturbation h. MO methods as an entirely different (nonperturbative) approach start with the local environment of the defect, and determine the defect’s electronic structure by utilizing the atomic orbitals of the neighboring atoms to obtain a molecular orbital. The MO approach should be distinguished from crystal field techniques, since the latter methods are based on an assumption that an isolated central atom may govern the properties of a polyatomic system in the form of the zero-order perturbation. The interaction of this central atom with the rest of the system is then considered as a sequence of higher perturbations. 12. THEDEFECTMOLECULE METHOD

Before engaging ourselves in details of cluster methods and their results, it seems appropriate to make a few remarks concerning the defect-molecule method, which was first proposed by Coulson and Kearsley (1957). The principal feature of this model is that one chooses several one-electron band orbitals of the nearest neighbors surroundingthe defect and then constructs a several-electron wave function consistent with these orbitals. The defectmolecule method has mostly been applied to vacancies in covalent semiconductors. Each defect has four nearest neighbors that each contributes a dangling sp3hybrid orbital. The defect wave function may then be obtained by a linear combination of these four orbitals. An appropriate potential is constructed from the atomic potentials of the nearest neighbors, and a quantum mechanical calculation leads to an evaluation of the defect-energy

310

J. S. BLAKEMORE

AND

S. RAHIMI

ANTIBONDING (CONDUCTION) I II

I

tI

EGO EP

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

.)-

EGO

\-

1% 7

\ L BONDING (VALENCE)

I

EN

I

i

-I

A’

HYPERDEEP TRAP

ATOM- MOLECULE GaP HOST

MOLECULE

- ATOM

WITH SUBSTITUENT

FIG.25. The defect molecule viewpoint, exemplifiedby Np in Gap. At the left are visualized the bonding (valence) and antibonding (conduction) states of GaP itself. As indicated at the right, a substitution of P by N creates two flaw states. The hyper deep state is an impurity-like bonding state, in or below the valence band, while the observed “deeplevel” flaw state is a hostlike antibondingstate. (After Hjalmarson el a!., 198Oa and VogI, 1981.)

levels and the coupling of the defect to the lattice. The main disadvantageof this method is that the defect energy levels may not be linked to the band edges at all accurately.This shortcoming is the immediate result of accounting for only one of each four sp3 hybrids in the defect-wave function expansion. This, however, leads to an exclusion of the problem of dangling bonds, otherwise present in most cluster model calculations. The case of more delocalized wave functions has been considered by Coulson and Larkins (1969, 1971). A review of applications of the defect molecule method and the extended Huckel theory (see Section 13) to vacancies in silicon and diamond, and divacancies in diamond, has been made by Lidiard (1973). More recently, Hjalmarson et al. (1980a) and Vogl (1981) have shown that a physical insight may be gained by comparing the simple defect molecule method with more elaborate calculations of substitutional deep impurities in compound semiconductors, such as GaAs. Figure 25 shows the bonding and antibonding states of two molecules, for the example of GaP that Hjalmarson et al. and Vogl singled out. The first molecule, representing a Gap perfect crystal, consists of one P anion with four neighboring Ga cations. The second, representing a doped crystal, has a nitrogen anion (replacingP), still with four Ga cation neighbors. This results in two flaw states. These two states appear to agree qualitatively with the results of more

4. MODELS

FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

311

involved Koster- Slater calculations- to be discussed in the following sections. Thus, one of these is a hostlike antibonding state, which we can identify with the concept of a deep-flaw state within the gap. The other is an impuritylike bonding “hyperdeep state,” lying inside or befowthe valence band. However, Bernholc et al. (1981) have compared the results of applying this simple approach (for several impurities in silicon) with those of a Green’s function calculation. They concluded that predictions from a defect molecule approach can miss some resonant states entirely. In the next two sections, we consider the extended Huckel theory (EHT) and the multiple scattering approach, which Slater and Johnson ( 1972)have termed the Xa method. 13. THEEXTENDED HUCKELTHEORY (EHT) APPROACH CLUSTER Extended Huckel theory methods have been applied to molecular problems over the years (see, e.g., Gilbert, 1969). A proposal was made by Messmer and Watkins (1970) that an EHT cluster approach be used for dealing with deep-lying states of a flaw in a semiconductor. This allows one to solve the Schrodinger equation (approximately),using a linear combination of atomic orbitals- molecular orbital (LCAO- MO) method, numerically evaluated. Messmer and Watkins (1970) investigatedthis approach for nitrogen in diamond, simulating the crystal by a 35-atom cluster surrounding the flaw site. Note that in a cluster calculation, in contrast to the defect molecule method, all of the one-electron orbitals xVof the cluster atoms are taken into calculation: A donor wave function 4Dis expanded in terms of four orbitals of each sp3bonded atom. Thus, a cluster of four host atoms contributes 16 orbitals:

Use of such 4Din the Schrodinger equation leads to the secular equation

where H is a one-electron Hamiltonian and the matrix elements are Hpv= (XJHIX,,)and S,,= (x,lxvl). In order to solve Eq. (101), each set ofXvis chosen to be the outer sp3orbitals of each atom in the form of Slater orbitals (Slater, 1930):

fir, 894) = R(r)Y(@,4).

(102)

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J. S. BLAKEMORE AND S. RAHIMI

Here Y(O,$)is the spherical harmonic part, and the radial part is defined by R(r) = Nr*-le-O (103) In Eq. (103), Nis the normalization constant, while n denotes the principal quantum number and C is the orbital exponent. [Messmer and Watkins (1970) took C = 1.625 for the host carbon atoms in diamond.] The matrix elements HPvare then calculated from HPV= K,”(H, + HvV)S,v/2. (104) p and v denote valence orbitals, and Hw are chosen to represent the empirical atomic ionization energies Ip of the pth valence orbital. That is, H, = -I,,, and KPvis defined by KPv= 1, p = v, KPv=K, p Z v. Here, 1 < K < 2 and is usually taken to be = 1.75. [See Pople and Segal (1965) for experimental values of IP, and Hoffman (1963) for values of K.] As a result, the secular equation (101) may be solved for the energy levels ED. Furthermore, by minimizing the total energy Etot= Z njEj (where nj is the occupation number of the jth molecular orbital),Messmer and Watkins (1970) could calculate the lattice elastic constants and determine the JahnTeller coupling coefficients for the N impurity in carbon. One serious limitation of the cluster method is the existence of dangling bonds. These produce “surface states” in the band gap of the semiconductor, which may be indistinguishablefrom the levels introduced by the flaw. Another problem is due to the finite cluster size. In a later paper, Messmer and Watkins (1973) increased the size of the cluster to 71 atoms and imposed a periodic boundary condition (a super lattice of flaws) in order to eliminate the cluster surface effects. Meanwhile, others tried to saturate the dangling bonds with hydrogen atoms (see, e.g., Larkins, 1971). A comprehensive EHT calculation, applied to the substitutional nitrogen -atom impurity and to the lattice vacancy in diamond, along with the effect of cluster size, was reported by Messmer and Watkins (1973). However, the main shortcomings of the EHT cluster approach remain untouched with the above improvements. Thus, the energy bands and the electronic structure of the host crystal cannot be predicted accuratelyby this method. Moreover, an EHT model appears to be applicable only for a semiconductorwith a uniform charge density. Thus, it should not seemingly be applicable for flaws in any compound semiconductor,such as 111-V and I1 - VI materials. Despite this, a cluster method (somewhat different from EHT) has been

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used by Lowther (1976, 1977). He used parameters obtained from other band - structure calculations in numerically evaluatingthe cluster modeling of flaw states. Results obtained for flaws in diamond, and for neutral vacancies in GaAs,were in good agreement with those obtained from more elaborate calculations. Despite these apparent successes, for the host electronic structure and for flaw properties, Lowther’s version of cluster calculations was criticized in several respects by Pantelides (1978). It may be noted in passing that further changes in the EHT cluster approach were made by Astier et al. (1979). These workers used a self-consistent field version (see the next section) of a LCAO-MO cluster method, which drew upon the work of Berthier ef al. (1 965). Astier et al. treated the problems of boron and nitrogen impurities in diamond, using clusters of 17 and 47 atoms. The total energy of the cluster, in the form of a Hartree- Fock approximation, was minimized through variation of locations of atoms in the cluster. This permitted, for example, evaluation of the Jahn-Teller distortion (see, e.g., Englman, 1972) around a nitrogen donor in diamond. Such results are clearly interesting, although the application of the method to a partly polar solid such as GaAs would not be straightforward. 14. THEXa-SCATTERED-WAVE METHOD

For problems the EHT approach cannot handle, a new tool for MO treatment of flaws in compound semiconductors has emerged from the Xa-scattered-wave (Xa-SW) self-consistent cluster method. This grew out of a suggestion by Slater (1965), which was explored by Johnson (1966) and appeared in subsequent work by these two authors (Slater and Johnson, 1972; Slater, 1974; Johnson, 1973, 1975). The alternative name MS-Xa signifies that this is a multiple-scatteringapproach. In contrast to the EHT approach, Xa-SW is a non-LCAO method. The main objective of the method is to solve the following one-electron Schr6dinger equation (Slater, 1974). In Rydberg units, V,+ vx,]q=Ejq, (106) where V, are the one-electron spin orbitals, V,, introducesthe contributions of exchange correlation to the Hamiltonian, and V ,represents the coulomb potential due to all other electronic and nuclear charges. The term V, conveys the unknown parameter a into the equations (named Xa), to be determined by minimization of the total energy through a variational method. Thus, the method exhibits two distinct features. One is the Xa approximation. [For a comparison of this approximation and the Hartree Fock approximation, see Johnson (1973). For an example of a H-F calculation, see Watson (1958).] The other feature is the self-consistent multiple-scatteringtechnique (Johnson, 1973), which allows for charge-re[-v2+

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J. S. BLAKEMORE AND S. RAHIMI

laxation effectsaround the flaw. In the words of Slater and Johnson (1972, p. 845): In carrying through a self-consistent calculation, we may imagine that we start with an assumed potential, solve the one-electron equation for that potential, finding certain spin orbitals Ujwith eigenvalues Ej, then decide by use of suitable criteria which spin orbitals will be occupied. We then take the charge density arising from these occupied spin orbitals, as well as the nuclei, determine the potential arising in this way, carry out the averaging required by the muffin-tin method, and use the resulting potential as the starting point of the next iteration. For application of the method in a crystal, the volume is divided into clusters, Each in turn is divided into three regions, in accordance with the muffin-tin approximation. The potential is assumed to be spherically symmetric within spheres of arbitrary radius (region I, radius rr) and flat in the space between the spheres (region 11). The region outside the clusters (region 111, radius r!II)is defined such that in going from one cluster to another the wave functions behave as periodic Bloch functions, as in the Korringa, Kohn, and Rostoker (KKR) method (Komnga, 1947; Kohn and Rostoker, 1954). For an isolated cluster, the potential in region I11 is assumed to be spherically symmetric. The wave functions in each region are accordingly defined, and it is the continuity of these functions and their derivativesat the boundariesthat lead to some secular equations. The energy eigenvaluesmay be obtained through these equations. The Xa-SW cluster method has been used in a number of deep-level flaw investigations. For examples, see Cartling (1975) and Hemstreet (1977) for applicationsof an Xa-SW method to impurities in Si, and Hemstreet ( 1975) for applicationsto lattice vacancies in PbTe and SnTe. However, it was not until recently that the method was used to study mid-gap centers in GaAs. We have already mentioned the significance of the boundary conditions in cluster model calculations. We saw that the problem of dangling bonds at the surface of the cluster could be handled by introduction of periodic boundary conditions, or by saturation of dangling bonds with hydrogen atoms. In the following, we shall discuss an alternative method of dealing with this problem. Fazzio d al. (1978) suggested that by promoting the electrons, filling the dangling bonds, to a Watson sphere (Watson, 1958), one may obtain a good representationof the host crystal band structure-as distinguished from the cluster energy-level structure. The number of electrons to be promoted to the Watson sphere may be found by subtracting from the total number (N) of valence electrons for all cluster atoms, the number (S) required for bulk valence states. Having done this, S is the effective number of electrons taking part in the calculation.

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Fazzio et al. (1979a) chose for GaAs a 17-atom cluster with an As atom at the center (i.e., lAs, 4Ga, then 12As). Since Ga and As atoms contribute 3 and 5 valence electrons, respectively, then N = 77 for this cluster. Also, S = 32 if the electronic structure of the cluster is described by sp3hybrids. That leaves 45 electrons to fill dangling bonds. Fazzio et al. proceeded to do two calculations, with the dangling bonds handled different ways. In both cases, the parameters used included a = 0.706, muffin-tin atomic radii of r,(Ga) = 2.45 a.u. and rI(As) = 2.17 a.u., and an outer sphere radius r,, = 9.47 a.u. All 77 electrons were used for one of these calculations, assuming that hydrogen atoms were attached to the cluster periphery. This yielded Ei = 0.9 eV for GaAs, with a valence band total width of 6.5 eV. Those do not compare well with Ei = 1.5 eV in practice and an observed valenceband span of 12.9 eV (Grobman and Eastman, 1972). More satisfactory results (Ei= 1.17 eV, valence-band span 11.7 eV) were obtained by a 32electron calculation; the other 45 electrons being promoted to the Watson sphere. Although Ei for the 17-atomAs-centered cluster was then still on the low side, a value on the high side (Ei= 1.92 eV) was obtained by calculation for a 17-atom Ga-centered cluster. That version of the calculation reduced the valence-band range to some 10.9 eV. Differences on this scale are not surprising, in view of the relative smallness of the cluster chosen. The value Ei= 1.92 eV controls the ordinate scale of Fig. 26, which shows energy levels in the vicinity of the GaAs intrinsic gap in part (a), as deduced for the Ga-centered 17-atom cluster. The apparent successes of this cluster model for GaAs itself paved the way for a similar treatment by Fazzio et al. ( 1979b)of clusters representing GaAs containing a point flaw. They used the Xa-SW cluster method to study GaAs containing neutral vacancies (V, or V&), Se shallow donors, and Cu deep acceptors. A 17-atom cluster was still used, with four Ga, or four As atoms, as needed, for nearest neighbors of the central flaw site. Numbers a = 0.706, for the radii of regions I and 111, and for the orbital quantum numbers used in partial-wave expansions, followed previous practice (Fazzio et al., 1979a).As in that earlier paper, lattice-relaxation effects were still ignored. Levels of two symmetry types were found in the gap for a (V, 4Ga, 12As) cluster with an As vacancy. A symmetric (s-like) A, state at (E, - 0.50 eV) was fully occupied. A (p-like) T2state at (E, - 0.13 eV) was concluded as holding one electron for neutrality. For a cluster with a Ga vacancy (V, 4As, 12Ga), the only kind of state found in the intrinsic gap was of T, symmetry, at (En 0.73 eV), and with three of the six orbitals occupied. [See part (b) in Fig. 26.1 Remember that

+

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J. S. BLAKEMORE AND S. RAHIMI

I

h /

W 2

Z

0

E

-I W

E

f

T2

I

IGa-4As-IZGa

-2T

V-4As-12Ga

Cu-4As-12Ga

[ b)

(C)

T2 (0)

FIG.26. Energy level spectra, in the vicinity of the intrinsic gap, for (a) a 17-atom cluster representingGaAs (Ga as center atom), (b) a cluster with V, as the central native flaw feature, and (c) a cluster with Cu, as the center (after Fazzio et af., 1979b).The scale of energy is set by E, 1.92 eV found by Fazzio et al. for the 17-atom Ga-centered “pure” GaAs cluster. Note that V, provides one kind of state in the gap, with three of the six orbitals occupied in neutrality. The Cu, acceptor is shown as rather comparable in energy, with four of the six orbitals occupied in neutrality. Lattice reconstruction effects were not accounted for in this calculation.

-

the “pure” Ga-centered cluster had indicated Ei = 1.92 eV (as used in drawing the ordinate of Fig. 26), and so this implies that EA= 0.4Ei for V,. Fazzio et al. (1979b) compared their results (for V, and V, centered clusters)with those of two other calculations: An imperfect crystal model of Il’in and Masterov (1976) and a semi-empiricaltight-binding model (Bernholc and Pantelides, 1978). Both of these other models had indicated a relatively small EAfor V, in contrast to the position near mid-gap shown in Fig. 26b. The deeper location was noted by Fazzio et al. as agreeingbetter with the experimental reports of Bois (1974) and of Chiang and Pearson (1975). One might add that identification of V, with the E3 radiation defect (Lang et al., 1977; see also Pons et al., 1980) is also indicative of a position near mid-gap. As noted above, Fazzio et al. (1979b) also made Xa-SW cluster calculations for 17-atomclustersin GaAs,where the central atom is a substitutional impurity. The calculation for the cluster (Se, 4Ga, 12As)indicateda 0.03-eV shallow-donor state ofA, symmetry. That is reassuring, but not so relevant

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for the present purposes as their calculation for a (Cu, 4As, 12Ga) cluster. The results of this for the eigenvalues close to the intrinsic gap are shown in part (c) of Fig. 26. The states in the gap are of T2symmetry, with four of the six occupied in neutrality (Le., a double acceptor). The energy came close to that ofthe V, triple acceptor in this calculation. However, calculations with larger clusters, and allowing for lattice reconstruction, would not necessarily render these eigenvalues as being so close. Brescansin and Fazzio (1981) applied the Xa-SW method, as outlined above, to 17-atom clusters of GaSb, including clusters with a V, or V,, site at the middle of the cluster; see also Fazzio et al. (1982) for V-. in GaP. These calculations yielded vacancy levels roughly comparable wth those noted above for GaAs.The reader should note, however, that more rigorous Green’s function methods (Bachelet et al., 1981; Talwar and Ting, 1982),as discussed in Part VIII, can give results differing from those of the Xa-SW approach. In order to explore the effects of lattice distortion around a flaw site in GaAs, Fazzio et al. ( 1979c)performed a Xa-SW calculation for GaAs :0,. Calculations were made for three cases: unrelaxed, and with inward and outward symmetrical changes of the nearest-neighbor bonds (+5% along 0 - Ga directions). The ED 0.4 eV binding energy for this level of substitutional oxygen (Arikan et al., 1980) would be consistent with an inward relaxation of the Ga nearest neighbors by a few percent. Of course, this very simple symmetric adjustment of bond lengths does nothing to test the sensitivity of the solution to an asymmetric lattice reconstruction around the flaw site-such as a Jahn-Teller distortion (Englman, 1972). Moreover, a satisfactory flaw signature requires much more than the appearance of a bound state in the correct energy region. Fazzio and Leite (1980) went on to investigate the applicability of their Xa-SW cluster approach to four kinds of 17-atom cluster, each representing GaAs with an impurity atom replacing the central Ga atom. One of these was the copper-doped cluster (Cu, 4As, 12Ga) that had previously been reported by Fazzio et al. (1979b). The other three clusters considered had Ni, Coyor Fe as the central atom, as examples of the important effects that 3d transition element impurities have for GaAs. (It was assumed that the impurity in each case was substitutional on a Ga site.) The work of Fazzio and k i t e continued to use the same values for radii of regions I and I11 as in the earlier work and continued to neglect lattice relaxation. The calculations for clusters containing Ni, Coyor Fe had to take into consideration the relationship between the partially filled 3d subshell of the impurity and levels found in or near the intrinsic gap region of energy. Values as reported by Schwartz ( 1972)were used for the exchange parameter (Y appropriate for the central impurity atom of these 17-atom clusters. Table IV shows one feature of the results obtained by Fazzio and Leite

-

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J. S. BLAKEMORE A N D S. RAHIMI

TABLE IV CHARGE DISTRIBUTION, EXPRESSED IN NUMBER O F ELECTRONS PER SPHERE, FOR 17-ATOM “PURE” A N D “DOPED” G a s CLUSTERS, AS CALCULATED BY THE Xa-SW Methoda

Region Central atom As sphere Ga sphere Interatomic region Extramolecular region

Number of electrons, for central cluster atom comprising Cu Ni Co Fe Ga 30.92 31.60 28.52 7.53 0.02

28.93 31.57 28.53 7.50 0.02

28.23 31.52 28.54 7.32 0.02

27.43 31.47 28.54 7.25 0.02

26.25 31.51 28.54 7.34 0.02

As reported by Fazzio and k i t e ( 1 980); in each case, the central atom (host or impurity)is surrounded by four As nearest neighbors, with 12 Ga atoms as second nearest neighbors.

(1980); the charge distribution (in numbers of electrons per sphere) for a “pure” GaAs 17-atom cluster (Ga-centered); and for clusters with C b , N&,, Co,,, or FeGaat the center. Although the number of electrons on the central atom is within 1% of the atomic number for the copper-centered complex, the numbers for clusters including any of the three transition elements indicate the transfer of a fraction of an electronic charge from the As sphere to the central impurity atom. The calculationsreported by Fazzio and k i t e (1980) also took account of spin polarization, in view of the partly filled atomic 3d subshell for the transition element impurities. They concluded that, from copper to cobalt, the d states behave as core states, interacting only weakly with the lattice. In contrast, the d states for Fe,, were found to be strongly affected by the tetrahedral crystal field, and the impurity states in the gap were influenced by those atomic orbitals, to an extent depending on the spin options. Thus, the papers by Fazzio and co-workers have provided some interesting insights into multivalent flaw sites in GaAs, despite their neglect of various complicating effects: non-muffin-tin corrections (Ferreira et al., 1976),relativistic coriections (Chadi, 1977),many-electron effects (Watkins and Messmer, 1974),etc. Only in one of the Fazzio et al. papers noted above (Fazzio et al., 1979c) was lattice relaxation accounted for at all, and then only in a highly simplified way. Hemstreet (1980) has used the spin-restricted version of the Xa-SW cluster method to treat Cu in GaAs, and also several of the 3d transition element group: Ni, Co, Fe, Mn, and Cr. The cluster used in his work consisted of a central gallium atom (or its substituent impurity), four

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nearest-neighbor As atoms, and 12 hydrogenlike “saturator” atoms as the outer periphery. Overall charge neutrality was effected by surrounding the cluster with a Watson sphere. Bearing in mind the difference of this cluster’s construction from that of Fazzio’s group, the results are in good agreement for similar circumstances (i.e., spin-restricted calculations). Hemstreet and Dimock (1979a,b) investigated solutions for the various charge states (Cr2+,Cr3+,and C14+)of substitutionalCr? in GaAs, using the above Xcw-SW method. The results of the spin-restncted version of the method were disappointing. Improvements were then made by (i) application of the spin-polarizedmethod and (ii) accounting for the electron-electron interactions as a perturbation to their original spin-restricted calculations. This was done in the form of a strong field limit version of a crystal field calculation (see, e.g., Figgis, 1966). The work of Hemstreet and Dimmock does not, however, take Jahn -Teller distortion into account; this has been shown to be significant for several of the charge states of GaAs :Cr, (Krebs and Stauss, 1977a,b; Kaufmann and Schneider, 1976, 1980b, 1982; Abhvani et al., 1982). 15. THECLUSTER - BETHE- LATTICE METHOD

Among several cluster approaches to the problem of calculating the electronic structure of imperfect crystals, the Cluster- Bethe-Lattice (CBL) method of Yndurain et al. (1974) seems to be particularly useful for theoretical treatment of complex lattice defects. Joannopoulos and Yndurain (1974) applied the method to the case of amorphous and homopolar solids. The CBL method was later used to study vacancies in silicon surfaces (Louis and Vergks, 1980). The theory was eventually applied to vacancies, anti-sites, and vacancies surrounding the anti-sites of GaAs by Louis and Verges (1981). The essence of the CBL method lies in the fact that the material is divided into two parts: a cluster, surrounding the defect, and an infinite Bethe lattice attached to the ends of the crystal, representing the rest of the material. Every cluster atom, unlike the Bethe lattice atoms, may be considered as being located on one (or more) ring passing through the defect at the center of the cluster (see Joannopoulos and Yndurain, 1974). Four sp3-likeorbitals are placed on each atom, and a first nearest-neighborHamiltonian is formed for treatment of anti-site defects. For applications to vacancies in GaAs, the second nearest-neighbor interactions between the atoms around the vacancy are also taken into account (Louis and Verges, 1981). The density of states is obtained using the local Green’s function formalism (see Section 17 for details). Bulk parameters of GaAs were used in a tight binding calculation (Louis, 1977), where it was assumed that the presence of defects did not affect the

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J. S. BLAKEMORE A N D S. RAHIMI

parameters. The CBL calculations of Louis and Verges (1981) predict two levels for the Ga on As anti-site, of A, and T2symmetry, with energies -6.97 eV and 0.36 eV. (All energies are measured from top of the valence band.) For the As on Ga anti-site, three Al symmetric levels are predicted (- 1 1.32 eV, -6.94 eV, 2.68 eV). Ga vacancies around Ga on As anti-sites, and As vacancies around As on Ga anti-sites, are also treated in the above work. Six levels are predicted for the former: three of s-like (A) symmetry, two E symmetric, and one of undetermined symmetry. Five levels were found for the latter defect: four Al states, and one E symmetric state. Despite the agreement between the predictions of the CBL method (Louis and Vergks, 1981) and those of Bernholc and Pantelides (1978) concerning vacancies in GaAs, these results appear to lack quantitative significance. Thus, the calculationsyield an energy gap of about 2.7 eV for a perfect GaAs cluster. However, the CBL method seems to be a desirable one for qualitative interpretation of complex defects in GaAs, if the complications of more involved methods are to be avoided. VII. Pseudopotential Representations

Over the past half-century, the quest for a proper potential, representative of the true atomic core potential has always been a challenging question. The idea of utilizing a pseudopotential in the quantum mechanical wave equation, for application in solids, did not receive much attention until the work of Phillips and Kleinman (1959). This was followed by several significant publications, among which the work of Heine and Abarenkov (1964), and Abarenkov and Heine (1965), should be noted. Cohen and Bergstresser (1966) investigated the band structure of diamond and zinc-blende semiconductors, employing an empirical pseudopotential method. The pseudopotential form factors thus obtained have found extensiveuse in the subsequent studies of these solids. The methodology was camed a major stage further with the nonlocal pseudopotential calculations of Chelikowsky and Cohen (1976). Calculation of the band structure for a solid by pseudopotential methods has been the subject of comprehensivereviews by Heine (1970), Cohen and Heine (1 970), and Heine and Weaire (1970). A recent “layman’s’’ review of the subject (Cohen et al., 1982)elegantly describes the physical nature and historical evolution of pseudopotential theory. With regard to the pseudopotential treatment of deep centers in semiconductors, a substantial portion of the major review articles cited up to now in this chapter have discussed this problem. Masterov and Samorukov (1978) have discussed the matter in the specific context of I11-V compounds. The essential idea behind any pseudopotential treatment is to replace the

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321

original wave equation with a pseudowave equation. The new pseudopotentials and pseudowave functionsare chosen such that the new eigenvaluesare the same as the original ones. Thus, for a wave equation

+

[T V]lY) = El") then a pseudowave equation has the form

+ V,]I@)

(107)

(108) The true wave function 1") may be expressed in terms of the pseudowave function (orthogonalized plane wave representation), [T

W)=I@)

=El@).

- ~IIwC)(WCl@)Y

(109)

C

where the summation runs over the core states. Note that the true wave function 1" ) is orthogonal to the core states IyC ) .The pseudopotential may be shown to be (Heine, 1970)

v,

=

v+

c (EC

~ c ) l y / , )( kl,

(1 10)

where lye) ( tycl is a projection operator and the Ecs are electron core energies. We have chosen this simple picture only to emphasize the important physical nature of a pseudopotential. It is obvious from Eq.(109) that, outside the core region, the pseudowave function is the same as the true wave function. The two terms on the right-hand side of Eq. (1 10) are of opposite sign. It is this cancellation that makes the magnitude of the pseudopotential smaller than the true potential in the core region (Cohen and Heine, 1961). Now let us introduce an impurity atom in the host crystal. The core states and the electronic core energies are now different for the impurity and the host atoms. (T+UH)IWCH) =&-~wcH),

(1 11)

(T + UI)IV/CI ) = Ecrl~cr), (1 12) where IyCH), ECH and IwCr), Ea are the core electron eigenstates and eigenvalues for host and impurity atoms, respectively. For the case of a substitutional impurity, U, represents the sum of the electronic and atomic contributions to the impurity potential, and U, is the sum of the potential associated with the host atoms and the host-crystal electron potential. In order to show the significance of the Phillips and Kleinmann type of pseudopotential, one may start with a Schradinger equation involving the total electronic Hamiltonian of the system. This can be reduced to a one-electron equation, with some approximations. That equation, once

322

J. S. BLAKEMORE AND

S. RAHIMI

expressed in terms of orthogonalized plane waves, reveals (Jaros, 1980) the importance of the host-crystal and impurity pseudopotentials in a form similar to Eq. (1 10):

v,

= UIi

+ host C ( E - EcH)IvcH)( vCHL

(1 13)

The effective substitutional impurity pseudopotential then may be represented as j = V, - Vm.

(1 15)

A somewhat similar conclusion may be drawn for other classes of flaws. Once the smooth pseudopotentials of Eqs. (1 13) and (1 14) are known, the energy eigenvalues may be obtained by a proper perturbative solution of a pseudowave equation similar to Eq. (108). Equation (109) will subsequently lead to an evaluation of the true flaw wave function. Calculation of smooth pseudopotentials, corresponding to proper pseudowave functionsis not, however, an easy task. This brought about the idea of model potentials (Heine and Abarenkov, 1964; Abarenkov and Heine, 1965). A model potential is simply a smooth potential, behaving like a pseudopotential but without a restriction of the type of Eq. (109) applied between the pseudowave function and the true wave function. Thus, the terms “model potential” and “pseudopotential” may be used interchangeably, depending on whether or not the condition of Eq. (109) is met. The only constraint set on these potentials is that, over the range of their applicability, they must result in energy eigenvalues of the true potentials. Therefore, a model potential may be constructed by employing the energy levels obtained experimentally. For a nonempirical calculation of model potentials (applied to GaN and A 1N), see Jones and Lettington ( 1972). A survey of the form of model potentials and empirical pseudopotentials for isovalent impurities is given by Allen (1971). Some remarks were included in Section 3 concerning the Abarenkov and Heine type of model potential [Eq. (1 3)], in the context of effective mass theory. The S ’W model potential of Eq. (40),in Section 8, also provided a highly simplified example. However, model potential and pseudopotential approaches have a much wider range of application. One of the earlier uses for semiconductor- flaw problems was demonstrated by Callaway and Hughes (1967) in studying the neutral vacancy in silicon. A Green’s function (GF) method was used (the principal topic of Part VIII), with the vacancy potential represented by the negative of an atomic pseudopotential. (A pseudopotential method was also used to solve for the host-crystal energy levels and wave functions.j

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MID-GAP CENTERS IN GALLIUM ARSENIDE

323

The contributions of Jaros and co-workers concerningflaw states derived by pseudopotential methods have been considerable. In one of the first of these, Jaros and Kostecky (1969) constructed an impurity model potential, based on V, of Eq. ( 13), to study the substitutional Sb donor in semimetalic gray tin. Subsequently,Jaros ( 1971a) used a similar model potential, in the framework of an improved effective mass method, to treat shallow donors in Si and Ge. Far more relevant to the motivations of this chapter, Jaros (1971b) constructed what he called a "pseudo-pseudopotential" for dealing with problems of deeper-lying flaws. This potential contained both the (core) short-range and (screened coulombic) long-range components. Assuming a predominantly s-like ground-state impurity wave function, Jaros applied the method to six substitutionalimpuritiesin G a s : CryMn, Fe, Co, Ni, and Cu, in ascending atomic number. In calculations having much in common with the quantum-defect method of Bebb (1969), Jaros deduced approximate bound-state wave functions of the form Y(r) b: rrl exp(- r/b),and also deduced corresponding forms for the photoionization cross section q(hv). (The latter assumed plane wave final states.) We do not reproduce here the tabulation of Jaros for the quantities v and b (and for the pseudopotential amplitude V )that he quoted for each of the six substituents, since pseudopotential methods have been developed much more since the date of that work. However, it is interesting to observe that Jaros apparently had no difficulty in accommodating facts such as the relatively small EA= 0.1 1 eV for Mn (see, for example, Fig. 8), while its immediate neighbors in the 3d transition elements series have E A = 0.7 eV for Cr and E A = 0.5 eV for Fe. As it happened, the next several papers from the Jaros group did not concern GaAs. In one of these, the goal of Jaros ( 1972)was the ground-state energy and wave function for the Zn deep double donor in Si, including photoionization properties. A pseudopotential model was used to generate the host-crystal band structure. The impurity potential was taken to be the difference between the ionic pseudopotentials of host and impurity atoms. The latter were approximated by the semilocal model potentials of Animalu ( 1965; see also Animalu and Heine, 1965). In a subsequent paper, Jaros and Ross ( 1973a) calculated bound-state energies for various substitutional impurities in silicon: zinc (again); B, Al, Ga, and In acceptors of Group 111; and isovalent Ge, Sn, and Pb substituents. A model potential representation was used for the ionic pseudopotentials in that paper of Jaros and Ross (1973a). The impurity wave function (Y(r)) was expanded in terms of the pseudowave functions ( o n , k ( r ) of ) the Si valence bands:

1 y(r)

)=

I,,

d3kAn,k [

- 2 I v C ) ( v C l ] I @n,k(r) C

)*

(1 16)

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J. S. BLAKEMORE AND S. RAHIMI

In Eq. (1 16), the summation over n is over the bands under consideration, and the integral is over the Brillouin zone. For numerical calculation of the coefficientsA,,, [see Eq. (1 19) in what follows and also Eq. (142) in Section 161, the integral was replaced-as an approximation-by a sum over a set of sampling points representing the entire Brillouin zone. Now, for crystals with Tdsymmetry (fcc, diamond, zinc blende), one can draw a volume of &th part of the Brillouin zone, which is equivalent to any other &th part by symmetry. Then one can sample throughout the Brillouin zone, by appropriate choice of a relatively small number of sampling points in any &th zone. With the number of distinguishable sampling points kept small, the problem of matrix inversion is greatly eased. Jaros and Ross ensured that the zone center r(OO0) was included in their sample. (1 16) were expanded in The valence band pseudowave functions for terms of 16 plane waves. Jaros and Ross remarked that a two-band calculation required 90 min on an IBM 360-67 computer. Since then, calculations have often tended to become more extensive, but faster computers are also available. Several ensuing flaw pseudopotential papers by Jaros concerned nitrogen and oxygen in GaP. The method as indicated above was used by Jaros and Ross (1973b) for Gap: 0,, treated (at this stage) as a monovalent donor. This time, the impurity wave function was expanded in terms of a complete set of I@n,k(r) )

m.

Y

IW

)=

c 1,d3k - u ~ ~ , ~ ( r ) ),

(1 17)

where the symbols have the same significance as in Eq. (1 16). For the calculation concerning GaP :Op, two valence bands and two conduction bands were used in the expansion, with 21 sampling points in the &th Brillouin zone. The 1965 table of Animalu was used in establishing a suitable model potential for the oxygen substituent. Jaros and Ross concluded that the ground state of 0, should be dominated by the second lowest set of conduction-band valleys, the L6band. Incidentally, they deduced that the ground state of 0,should lie 0.7 eV below the lowest (X,)conduction band of Gap. That value falls some 0.2 eV short of the actual donor binding energy. The difference is not significant, particularly when one remembers that lattice relaxation was not taken into account in the work of Ross and Jaros (1973). That refinement was added in later work of Jaros (1975a), as discussed below. In making a pseudopotential calculation, the Schrodinger equation

(Ho+ h)lW) ) = EIW))

(1 18)

needs to be reduced to the form of a secular equation. The latter form is the

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

325

key to solving pseudopotential calculations such as that noted above. This secular equation can be expressed as

The details on how Eq. ( 1 19) is solved will be discussed when this reappears as Eq. ( 142) in Section 16. In two of the investigationsjust cited, the 1965 tables (unpublished) of Animalu for semilocal model ion potentials were noted as being useful. The real quantity at issue here is an efective Fermi energy, representative of the electron density in the ion core. Jones and Lettington (1972) had suggested a value for nitrogen in Gap, and Jaros and Ross (1973b) asserted that the values for substitutional N, and Op should be very similar in modeling GaP :Op. The reader should not be surprised to be advised that Ross and Jaros (1973) described a comparable pseudopotential calculation for GaP :N,. That particular piece of work involved some convergence problems, which Jaros and Brand (1979) subsequently pointed out and corrected. In the interim. Ross and Jaros (1977) had used a self-consistent pseudopotential method in calculating the electronic charge distribution around an unrelaxed Np site in Gap. With GaP once again-rather than GaAs-as the host lattice being explored, Jaros (1975a) investigated the well-known ability of 0,to capture a second electron in a deep-lying state, using a pseudopotential calculation. [Henry and Lang (1977) review the experimental evidence from various investigations about “State 2” of GaP :0,. J The various improvements in the pseudopotential calculation procedure since Jaros’s earlier work on this flaw (Jaros and Ross, 1973b)resulted in a prediction of ED = 0.9 eV for the ordinary one-electron state. This, of course, was in accordance with experiment. In order to describe the two-electron state, it was necessary to include a screened electron- electron interaction. Additionally, Jaros (1975a) made allowance in a crude and simple way for lattice relaxation by examining the effect on the system energy of a simultaneous shortening of all four of the O-Ga nearest-neighborbonds. He thus found that a second electron could be bound with an energy of from 0.6 eV upward, depending on the scale of the supposed lattice relaxation. Since the experimentalevidence that Henry and Lang (1977) reviewed indicated an electron binding exceeding 1 eV, their conclusion was a large lattice relaxation (see Section 1 lc). An allowance for lattice relaxation was, quite properly, made by Jaros (1975b) in a pseudopotential calculation for gallium and arsenic vacancies in GaAs. (Finally, we are back to GaAs.) As illustrated in Fig. 27, he concluded that neutral V, could produce bound states in the lower half of

326

J. S. BLAKEMORE AND S. RAHIMI

r

X

WAVE VECTOR

FIG.27. Calculated electron energies for isolated Vo. and V ,defects in GaAs,as obtained from the pseudopotential calculation of Jaros (1975b). The T2representations, three-fold degenerate for an unrelaxed vacancy, are shown also with splitting symbolic of an axial relaxation.

the intrinsic gap. In contrast, he deduced that V , creates a conduction-band resonant state, degenerate with the r6lowest conduction minimum. Since this piece of work was completed prior to the surprising demonstration that the GaAs conduction bands have a r- L- X ordering (Aspnes, 1976), Fig. 27 shows the x6 conduction band as the first indirect one. One might think of the work that produced Fig. 27 as being a progenitor of some Green's function calculations for native defects and flaw complexes in semiconductors. These GF results will be described further in Section 17. Thus, the GF results of Jaros and Brand (1976) dealt With GaAs containing V,, V,, V,-VA, pairs, or V,-0 complexes. The levels they found for these entities by GF methods are shown in Fig. 28, which can be compared with Fig. 27. Other GF calculations for native defects in GaAs (and other I11-V semiconductors)include the work of Bernholc and Pantelides(1978), Bachelet et al. (198 l), and Talwar and Ting (1982). The consequences of a vacancy in silicon have similarly inspired several GF calculations, including Bernholc and Pantelides (1 978) once more, Jaros et al. (1979), and Baraff and Schluter (1 979). Still within the purview of the pseudopotential approach, Jaros and Srivastava (1977) examined the comparable problem of a phosphorus vacancy in GaP and did find localized states in the lower half of the gap, of both A, and T2 symmetry. The order of these depended on the scale supposed for the vacancy potential, but the levels were not very sensitive to the details of the form of the potential. Jaros and Srivastava considered this to provide at least partial support for the concept that V, might cause the

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

1

327

/

-0.2

FIG. 28. Energy levels calculated by Jaros and Brand (1976), using a non-self-consistent Green’sfunction method, for isolated unrelaxed Ga and As vacancies in GaAs (at the left);for a nearest-neighbor nearest-neighbor VG,-V, vacancy pair (in the center); and for a V,-O,, complex (at the right). The short lines indicate the degeneracy of a level. As with a previous pseudopotential calculation (Jaros, 1975b; see Fig. 27), the isolated vacancy A , states are resonant with the valence band (see Table V) while the T2triplet of V,, is resonant with the conduction band.

+

hole trap seen at (E, 0.75 eV) in Gap. [The reader will recall that this trap was mentioned in section 1 1c, in connection with the “two-stage” capture process envisaged by Gibb et al. ( 1977).] Among other theoretical developments of the pseudopotential method, we should mention a self-consistenttreatment by Louie et al. (1976) of the vacancy in silicon. Admittedly, we are again wandering away from GaAs as the host, but Vsiis certainly of interest for deep-level native defect states. The paper of Louie et al. is particularly useful in demonstrating the procedure of a self-consistentpseudopotentialcalculation;and it is not without relevance that two of the authors of that study were at about the same time conducting a major study of energy bands for diamond and zinc-blende solids by a self-consistentnonlocal pseudopotential method (Chelikowsky and Cohen, 1976). In connection with the work of Louie et at. (1976), an interesting comment was later made by Baraff and Schluter(1979). (Schluterhad also been a co-author for the 1976 paper.) They remarked that, in order to prevent the (vacancy) defect wave function from overlapping with other unit cells, one may need to increase the size of the unit cells involved. This, in turn, results in a more complicated, and more time and energy consuming, kind of calculation. Jaros et al. (1979) observed that, although the work of Louie et

328

J. S. BLAKEMORE AND S. RAHIMI

al. (1976) may not have yielded accurate energy levels for Vsi, it was successful in demonstratingthe character of the vacancy potential. Another interesting application of pseudopotential methods to the problems of flaws in semiconductors can be seen in the pseudo-impurity theory developed by Pantelides and Sah (1972). This method, which was originally conceived of as a pseudo-EMT, was further developed over the next two years. It was applied to various shallow and deep (substitutional and interstitial) donor impurities in silicon (Pantelides and Sah, 1974a), and also to impurities in Gap (Pantelides, 1974). Applications of that 1972 pseudo-impurity theory appear, however, to be limited to isocoric impurities in a semiconductor-such as phosphorus and sulphur in silicon. A more general form of pseudo-impurity theory capable of dealing with nonisocoric impurities was subsequentlyprovided by Pantelides and Sah (1974b). The latter would reduce to an EMT approach for isocoric situations. Of course, as mentioned earlier in connection with the point charge model, use of a model potential in the context of EMT is apt not to give satisfactory results for deep-lying flaws in heteropolar semiconductors (Bernholc and Pantelides, 1977). Pantelides et al. (1980) pointed out that a fundamental problem involved with pseudopotential EMT calculations (in trying to deduce wavefunctions for deep-level flaws) arises from the use of Bloch functions only from a small region of the Brillouin zone, around the nearest band extremum. In summary, pseudopotential approaches can be quite valuable in the modeling of deep-level flaws, but they also have opportunities to lead one astray. The efficiency of the method, and the accuracy of the results, obviously depend a great deal on wehether the computational technique is reasonably matched to the problem. Some of the examples noted in this section indicate how sensitive the results can be to the strength of the supposed pseudopotential more than to its form. Such calculations show that, in the presence of short-range potentials, the predicted position for a flaw bound state energy may result from a delicate cancellation of contributions from among the various valence and conduction bands taken into consideration. The influencesof higher conduction bands (or lower valence bands), of lattice relaxation, and of electron correlation effects all enter into that delicate task. VIII. Green’s Function Method

16. GENERAL FORMULATION In contrast to several of the deepcenter models discussed above, the perturbative methods employing a Green’s function technique use a band-

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

329

structure calculation as a means of obtaining the energy levels and wave functions of the host crystal. The Green’s function method, initiated by Koster and Slater ( 1954a,b),and by Koster (1954), makes it possible to take the perturbations induced by the flaw directly into consideration. In this approach, one does not need to include the details of the extended parts of the sum of the host and the flaw potentials simultaneously. The GF method calculations are carried out numerically, and the extent of the numerical calculations depends on the spatial range of the localized potential. This may be considered as an advantage of the GF method over all other models, whose calculation size is governed by the spatial range of the flaw wave function. (The flaw wave function is often more extended than its potential.) The calculations yield flaw energy levels clearly defined with respect to the host-crystal band edges and show the changes in electronic properties of the crystal, without having to compare the properties of the perfect and flawed lattices. The Koster - Slater method was extended by Callaway (1964, 1967) into calculation of scattering amplitudesand energy levels of localized imperfections in solids. By incorporating the solid-state scatteringtheory with the GF method, Callaway (1964) was able to provide a convenient method for study of localized defects. Callaway and Hughes (1967) carried out an early numerical calculation of the GF method, applied to the neutral vacancy in silicon. The wave functions and energy levels of the host crystal were obtained by a psuedopotential band calculation. The negative of an atomic pseudopotential was used to represent the vacancy potential, and the matrix element calculations were based on Wannier functions. Expansion of the defect wave functions on the basis of Wannier functions proved to make the calculations so cumbersome that only a few further similar calculationswere attempted (Callaway, 1971; Parada, 1971; Singhal, 1971, 1972). A different approach was made by Bassani et al.(1969), who expanded the defect eigen functions in terms of Bloch functions of the extended Brillouin zone. This method was later modified and used by Jaros (1975a,b), and by Jaros and Brand (1976), as a powerful means of deep-center calculations. Alternatively, Lannoo and Lenglart (1969) combined the Green’s function method with a tight-binding approximation and, followingthe work of Leman and Friedel (1962), expressed the defect wave function as a linear combination of atomic orbitals. They defined a set of s and p orbitals on each atom. Taking only the nearest-neighbor interactionsinto account, they applied their simplified GF-tight-bindingmodel to a vacancy in diamond. A comparison was then made between their numerical results and the conclusions drawn from a simple analytical calculation. The basic ideas proposed in the work of Lannoo and Lenglart, although not conclusive, were the beginning of a series of GF method studieswhich until today form one of the most accurate treatments of deep-level problems in semiconductors

330

J. S. BLAKEMORE A N D S. RAHIMI

(Krieger and Laufer, 1981; Talwar and Ting, 1982). The advantages and disadvantages of each of the above GF method approaches will be pointed out after a brief description of the general formulation of the method, and in the context of the results of the calculations in Section 17. Once again we start with the Schrodinger equation for the perfect and imperfect crystal: =EfY:k.

(120)

This is to be compared with HY = E Y ,

(121)

where

+

H = (Ho h)

(122) and h is the perturbation introduced into the perfect crystal by a flaw. Following the treatments of Bernholc and Pantelides (1978), and Bernholc et al. ( 1 980),we define the Green's function operators Go(E)and G(E)for the perfect and perturbed crystals, respectively.

+

Go(E)= Iim ( E iq - H0)-', 1-0

+

G ( E )= lim ( E iq - H)-'. ?l+O

These two Green's functions are related by the equation

G ( E )= [ 1 - Go(E)h]-'Go(E).

(125)

Using the definition for Go(E),Eq. (121) may now be written as Y = Go(E)hY

(126)

for energies within the band gaps. Within the energy bands of the host crystal, Y may be expressed in terms of the Lippman - Schwinger equation (Lippman and Schwinger, 1963): Y = Y$

+ Go(E)hY.

(1 27)

We can rewrite Eq. (126) as [ 1 - Go(E)h]Y= 0,

(128)

while Eq. ( 127) may similarly be written as [ 1 - Go(E)h]Y= YO,.

Note that Eq. (128)indicates that, for the bound states to exist, the determinant D(E)associated with the left-hand side of the equation must vanish:

4.

331

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

D ( E ) = detlll

- Go(E)hll= 0

( 130)

for any complete set expansion of Y. Within the energy bands of the perfect crystal, Eq. (129) yields solutions for all energies. It is important, however, to realize that the eigenstates of these energies are different from the perfect crystal wave functions Y:k, as evidenced by Eq. (120). Apart from the calculation of bound states within the gaps and energy bands, Green's function methods are capable of evaluating the changes in the electronic properties of the crystal induced by the presence of the flaw. The change in density of the states in the vicinity of the flaw can be expressed in the following form: AN(E)= (2/n) Im Tr{(d/dE)[GO(E)]h[1 - Go(E)h]-l},

(13 1)

where Im Tr stands for the imaginary part of the trace of the operator on the right-hand side of the equation. Following Callaway (1964, 1967), AN(E) may also be obtained by AN@) = (2/a)[dd(E)/dE].

(132)

6 ( E )in Eq. (132) denotes the phase shift defined by 6(E)= -tan-l[Im D(E)/Re D(E)],

(1 33)

where Im and Re stand for the imaginary and real parts, respectively. Equation (1 32) can be rewritten in the following useful form: AN(E) = ( r / 2 r ) [ ( ~- ~

~

+ (+)r21-l. 1

2

(1 34)

The quantity r in Eq. (1 34) is defined by where E, is the energy at which Re D(E)= 0. Equation (1 33) suggests that, for E = E,, the phase shift 6(E)will be an odd multiple of n/2.According to Eq. ( I 34), positive peaks will occur in AN@) if r > 0 (resonance), and negative peaks arise for r < 0 (anti resonance). The half-width of each type of peak is l r l (Newton, 1966). The final definition concerns N,, the number of bound states introduced into the gap by the perturbation. According to the solid-state analog of Levinson's theorem (Callaway, 1976, Section 5.2.3), if the total number of states in the gaps and bands remain unchanged by the perturbation, N, will be given by N,

+

I

bands

AN(E) dE = 0,

(136)

332

J. S. BLAKEMORE AND S. RAHIMI

where the integral is taken over the density changes within the bands. Equation (1 36) may be used to obtain the Fermi level in the perturbed crystal (Bernholc and Pantelides, 1978). For application of the above GF formulation, one must choose a proper Hamiltonian and represent the operators in some basis set. Let us expand Y in a complete set of orthonormal basis functions +a

Substituting Y in Eq. (1 28) will result in a set of linear matrix equations. Then, for the bound states to exist, the followingcondition correspondingto Eq. ( 130) must satisfy:

O , where the matrix element G Gk#=

is given by

(alnk) ( n k l a ’ ) / ( E - E $ J ,

(1 39)

and hmr is a matrix element of the perturbation

hm, = (alhla’).

(140)

The size of the calculation involved in Eq. ( 138) depends on the number of nonzero matrix elements hm,, which itself is limited by the range of the localized potential. It can be shown (Krieger and Laufer, 1981) that the basid form of Eq. ( 138) will be preserved if one expands Y in a nonorthogonal basis set. The matrix elements of the Green’s function operator, however, have to be modified slightly. Earlier, we discussed the emergence of LCAO-type basis functions as an alternative to the localized Wannier functions. Baraff and Schluter (1978, 1979)applied their GF method, in an LCAO basis set, to the case of an ideal vacancy in silicon. A self-consistent GF method study of Si :V was also reported by Bernholc et al. (1978; see also Bernholc et al., 1982). On theotherhand,aseriesofpapersbyJaros(l975a,b,1977,1979),Jaros and Brand ( 1976,1979),Jaros and Srivastava (1 977), and Jaros et al. (1979) extended the GF method of Bassani et al. (1 969), and applied this to oxygen, Ga and As vacancies, and oxygen-vacancy pairs in GaAs and GaP. Y was expanded in terms of the Bloch functions of the perfect crystal [see Eq. (1 1711,

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

333

where n and k denote the bands and the points in the reciprocal lattice, respectively. The coefficients An,k can be determined from the following set of linear equations [see Eq. (1 19)]:

In order to achieve fast convergence in solving Eq. (142), the impurity potential h was factorized as h = hahb, (1 43) and the matrix elements of Eq. (142) were separated in the following form: ( b n > , WIh14n,k)

=

2 <4n9.k31halgm) m

hbtdn,k)

*

( 144)

Here, g, are a complete orthonormal set of functions. The angular part ofg, were chosen to be the spherical harmonics Yl,m(Oy +), and the radial part were represented by (Jaros and Brand, 1976)

In the above equation, I‘ and L indicate the gamma function and the associated Laguerre polynomials, respectively. Following the Bassani-1adonis- Preziosi (BIP) method (Bassani et al., 1969), Eq. (142) is reduced to a set of linear equations, which will yield the values of the bound-state energies E by finding the zeros of the following determinant:

The functionsfh(n, k) are defined as (i = a, b),

fh(n~k)= (+n,kI

-

hit&) (147) Note that the integral in Eq. (146) was changed into a sum over a mesh of sampling points in the dgth irreducible segment of the Brillouin zone (see Part VII). The size of the determinant in Eq. ( 146) is given by the number of functionsg,(r) employed-i.e., 10(Jarosand Brand, 1976). Jaros(1979) points out that the significant feature of this Green’s function method is the inclusion of all sampling points and all bands in Eq. (146). Calculation of E from Eq. (146) and consequently calculation ofAkkfrom Eq. (142), laid a positive basis for establishing a relationship between the localization of the flaw wave function and the depth of the localized state in the gap. Contrary to valid conclusions drawn for shallow impurities, it was

-

334

J. S. BLAKEMORE AND S. RAHIMI

found that the wave-function localization was not a sensitive function of the position of the deep level in the energy gap (Jaros, 1975a, 1977).Jaros (1979) argued that the properties of a deep flaw (concerning its wave function) may hardly be derived from a knowledge of its precise position in the gap. In order to obtain information regarding the signature of the flaw, one has to calculate quantities such as the transition probabilities and relate them to experimentalphotoionization and capture data through their variation with temperature and pressure. One problem involved with the above GF method was the question of convergence of the flaw energy level during the course of calculation. Brand (1978) has introduced a parameter a into the exponent of the exponential term in Eq. (1 4 9 , changing it to exp(- ar/2).Then, the optimization in the choice of this parameter, along with a proper choice and factorization of the defect potential h, into h‘ and hb,led to the desired convergence properties. The two defect potentials used in Brand‘s (1978) study for a vacancy in silicon were

h, = hqhf = [(A?

+ B) exp(-pr)][(Ar2 + C ) exp(-j?)],

(148)

(149) h2 = h$h$= [(Ar + B) exp(-fip)][(Ar - B ) exp(-fip)]. Banks et al. (1 980) used the same expression as in Eq. (149) to represent h for deep impurities in GaAs and Gap. In an earlier work, Jaros and Brand (1 976) had used the form

h, = hfh$ = (A2rz- B2)rZnexp(-pr).

(150) Brand et al. (1981) chose ha = V and hb = 1 in their self-consistent GF study of the silicon vacancy, thus avoiding the separation of the localized potential. Jaros and Brand (1979) discussed the problems involved in finding a self-consistent impurity pseudopotential for use in the above GF method. The realistic potentials found for nitrogen impurity in GaP,As,-,, were later used in a GF study of the wave functions associated with the nitrogen impurity in GaP (Banks and Jaros, 1981). These self-consistent GF calculations were carried out (Jaros et a!., 1979), first with a host-crystal band structure calculation. Next, a trial potential h was chosen. Then the bound states in the gap, the total energy, and the charge density were calculated for that particular choice of h. Finally, by readjusting h, a self-consistent potential was obtained through iteration. In yet a further study, Rodriguez et al, (1 980) pointed out the importance of including the long-range potential in deep-level flaw calculations. They divided h into a short-range potential h,, and a long-range potential h,, where

h, = - [ 1-exp(- a r ) ] / ~ r .

(151)

Their GF method calculations showed that for a large number of deep levels

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

335

found in the energy gap, a contribution of about 0.1 eV to the binding energies could be attributed to the long-range part of the potential (except for the case of isoelectronic impurities). Another class of GF calculations with an LCAO basis set was initiated by Hjalmarson et al. ( 1980a) and applied to substitutional deep impurities in covalent semiconductors. The essential goal of that work was the establishment of a relationship between the atomic structure of the impurity and its depth in the forbidden gap. Two s orbitals and three p orbitals (five basis functions per impurity ion) were involved in the calculations. The longrange part of the flaw potential was neglected, and the localized central cell potential was assumed to be strong enough to bind the impurity states. Only the nearest-neighborinteractions were considered, and the effects of lattice distortions and charge state splittings were neglected. The main feature of the above technique was the proper choice of the impurity potential matrix elements. The diagonal elements h, (for an unrelaxed host) of Eq. (140) were chosen according to the symmetry of the site. Thus for an s orbital, the bound state was A l symmetric, and for any of the three p orbitals associated with a specific site the bound state was T2 symmetric. The A, and the T2parts of the defect matrix were thus given by

h*, = EL* - ELt

(152)

and

h, = ELp - ELt (153) where E s and EP denote the s- and p-orbital energies of host and impurity. E sand EP for impurity and host atoms were chosen to be proportional to the atomic orbital energies (Vogl, 1981), as given by Clementi and Roetti (1974), and by Fisher (1972). The constants of proportionality were 0.8 for the s energies and 0.6 for the p energies. The attractive feature of this version of the GF method is its simplicity (and low-cost calculations), compared to the more sophisticated GF methods described above. Sankey and Dow (198 1) applied the method to study chemical trends of substitutional defect pairs in G a s . The deep energy levels associated with 84 1 nearest-neighbor defect combinations were predicted. According to Sankey and Dow, the computer cost of these calculations was less than $5.00. The method was also applied to sp3-bonded substitutional impurities in several semiconductors including GaAs (Hjalmarson et al., 1980a), sp3bonded impurities at GaAs/AlAs( 1 10)interface (Hjalmarson et al., 1980b), and substitutional defect pairs in GaAs,,P, (Sankey et al., 1980). We present some predictions of this GF method, relevant to G a s , in Section 17. Up to this point, we have been describing GF formulations in the basis

336

J. S. BLAKEMORE A N D S. RAHIMI

sets of Wannier functions and LCAO, and the basis sets used by Jaros and co-workers. Lindefelt and Pantelides (1979) have discussed the advantages and disadvantages of each representation. They have also suggested the wave functions of a harmonic oscillator as a basis set for application to the GF method study of point defects: @)n/(r)= f i d r ) &rn(O,4)* ( 154) The angular part Y,JO, 4) is a spherical harmonic, and the radial part is defined by Rn,(r)= (BW~ exp(-~+/2)

~/+(I~ n2) - L ~ ~ , ~ V ~ (155) 2),

where the last term is an associated Laguerre polynomial and the parameter j? is a scaling factor. The method was applied to the T2bound state of the vacancy in Si. After achieving convergence, the value obtained for the bound-state energy was similar to those obtained by other GF methods. However, Lindefelt and Pantelides warn that such a single-center basis set may not be suitable for defects which undergo strong lattice relaxation. For cases where more than one atomic site is involved, the LCAO basis sets were recommended. More recently, Lindefelt and Zunger (198 1) have examined the theoretical problems involved in GF method calculations. They have shown that the fact that the point defect wave function may be represented both in localized basis functions and in the wave functions of the host crystal, in a GF formulation, leads to a fundamental limitation of the method. This limitation concerns the common belief that the GF formalism efficiencyimproves with the degree of localization of the defect potential. Lindefelt and Zunger have argued that an enormous number of host-crystal wave functions are needed to obtain relatively accurate energies and wave functions for impurities which are chemically mismatched to the host-crystal atoms. This argument, however, as a result of the aforementioned duality in the nature of conventional GF methods, questions the accuracy of the predictions of the GF methods regarding the chemical trends of impuritiesin semiconductors. This criticism addresses the procedure of Hjalmarson el al. (1980a), in particular, and all the following investigationsbased on that study. However, Lindefelt and Zunger (1981) suggested a remedy, offering a “quasi-band-structure” representation that they argued was formally exact. They demonstrated comparisons of this with conventionalGF calculations for a solvable problem: a parabolic flaw potential in a “free-electron” silicon host. They also considered a transition element impurity (Cr) in the same simplified host format. Substitutional Cu was modeled self-consistently in crystalline silicon, using nonlocal first-principles atomic pseudopotentials. [See Zunger and Lindefelt (1 982), for this approach extended to substitutional and interstitial 3d impurities in silicon.]

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

337

17. GREEN’S FUNCTION METHOD RESULTS In order to assess the validity of theoretical results of a deeplevel model, one has to make a comparison with existing experimental data. Unfortunately, despite the quantity of data available for deep centers in GaAs, there is still a great deal of uncertainty regarding the nature of the deep defects and impurities and their various charged states (see, e.g., Rees, 1980; MakramEbeid and Tuck, 1982). The one-electron energies obtained by numerical calculations, on the other hand, may not be realistic enough to be compared with experimentally observed activation energies. As Jaros (1980) points out, the observed energies can be interpreted as the total differencebetween the initial and the final electron configurations, and this obviously depends on the charge states of the center. Jaros and Brand (1976) note that differences between levels for various charge states of the Ga vacancy in GaAs may be a fraction of an eV. Thus, the study of transition energiesof multiparticle centers need inclusion of electron-electron correlation energies in the calculations. Despite arguments that these deficiencies are not strong enough to prove the results of one-electron calculations invalid, it appears at this time that the shortcomings of the theoretical models, and the inadequacies of the interpretation of experimental data, are bound in a vicious circle. However, some of the available theoretical results do agree, to a large extent, with existing experimental observations. Our intention in this section is merely to mention such numerical results of the Green’s function methods as apply to deep centers in GaAs. In the preceding section, we pointed out differences in the G F method approaches leading to these results. Jaros and Brand (1 976) reported on a rather comprehensive GF study of vacancies, divacancies, oxygen impurities, and vacancy -oxygen pairs in GaAs. These (non-self-consistent)results are summarized in Fig. 28. The eigenvaluesfrom these GF calculations may be compared with those for V, and V, shown in Fig. 27, from a slightly earlier pseudopotential calculation (Jaros, 1975b). (See pages 326-327.) It can be seen from Fig. 28 that each (unrelaxed) isolated vacancy was found to produce two types of level: one of A, symmetry, the other (triply degenerate)of T2symmetry. The A, levels of both VGpand V ’ are shown as being in resonance with the valence band system. The p-like states of V, were deduced as lying fairly close to the valence band (indicative of a weak Ga vacancy potential), whereas the p states of V, were found to lie above E, (a much stronger As vacancy potential). Jaros remarked that these eigenvalues were relatively insensitive to the strength chosen for the vacancy potential. [Observe how different this is from a single-band type of S3W simulation of a deep-level flaw, when the eigenvalue is sensitivelydependent

338

J. S. BLAKEMORE AND S. RAHIMI

upon the value of (Vor&),if this is not far above the necessary threshold for having a bound state. This was discussed in Section 8, apropos the conditions for a mid-gap center in GaAs.] Jaros and Brand remarked that V, and V, would behave as acceptor and donor, respectively, probably monovalent. However, they went on to remark that the T, triplet state of the V, defect could be a good candidate for sensitivity to a Jahn-Teller distortion. They simulated a trigonal distortion mode for this defect by supposing a movement of the vacancy along one of the trigonal axes, and calculated how this should affect the eigenvalues. In practice, this resulted in a rather modest rate of lowering for the ground-state energy with distortion. The first row of entries in Table V summarizes (approximately)the A and T2 state energies deduced by Jaros and Brand in their 1976 GF study of isolated vacancies in GaAs (including that simple attempt at allowing for Jahn - Teller distortion). The reader should be advised that all entries in Table V have been rounded off to the nearest 0.1 eV, since that table is intended to provide a basis for comparison and is not a detailed substitute for the original papers. The calculations which provided numbers for the remaining rows of Table V will be discussed shortly. Meanwhile, we note that the GF calculations of Jaros and Brand (1976) also dealt with V,- V, nearest-neighbor divacancies, and with the V,O,, nearest-neighbor complex in GaAs.In each case, the site symmetry can be no higher than C,,(trigonal group) contrasted with the Td (tetrahedral) symmetry of an unrelaxed single substitutional flaw. The C,, symmetry permits a separation of the triply degenerate T2state. As shown in the central section of Fig. 28, the divacancy was deduced as having a doubly degenerate pair of states (Esymmetric)not far above the valence band, and an A, singlet TABLE V ISOLATEDVACANCY ENERGY LEVELSIN THE INTRINSICGAPOF GaAs, AS DEDUCED FROM GREEN'S FUNCTION CALCULATIONS"

v,

Vacancy type State symmetry Jaros and Brand (1976) Il'in and Masterov ( 1976) Bernholc and Pantelides (1978) Bachelet ef al. ( 1 98 I) Talwar and Ting ( 1982)

Vh

A,

T2

A,

-0.2 (eV) +0.2

+0.2 (eV) +0.3

==O

=O

- 1.0 -

+0.1

-0.1 (eV) 1.2 +0.7 -0.8

+0.1

+

-

Tl

+ 1.6 (eV) + 1.3 + 1.5

+ 1.1 + 1.0

All entries expressed with respect to the top of the valence band and rounded off to the nearest 0.1 eV.

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

339

further into the gap. Jaros and Brand found that these arose from the Ga site potential; states affected by the As site potential were predicted to lie above E,. Similarly, the lower-lying states of the multiplet for V,- Oh, as indicated in the right portion of Fig. 28, were also Ga-site dominated. Jaros and Brand remarked that the oxygen ion simply supplies an electron to fill the lowest of these. Il’in and Masterov (1976) also made GF calculations for states of neutral vacancies in GaAs (and in Gap). Their calculations were based on the GF method of Decarpigny and Lannoo (1 973). This is a modified Koster-Slater approach, which requires a detailed knowledge of the host-crystal band structure. Their results for energy levels are shown as the second row of numbers in Table V. For V, thcy concluded that two of the five electrons would be on the A, level (resonant with the valence band), and three would be on the T, level. Since this can accommodate six electrons altogether, V, is an acceptor. On the other hand, the As vacancy yields three electrons:Two occupying the A, state and one for the T, level (not very far below E,) to make this defect a donor. Subsequently,Il’in and Masterov (1 977) expanded their GF calculational approach into a continued fraction technique. They noted that this method had been used with apparent success for the modeling of surface states (Haydock et al., 1972). This continued fraction method, as discussed also in the subsequent review by Masterov and Samorukov (1 978), was applied to GaAs containing copper or a member of the 3d transition series (Ti, V, Cr, Mn, Fe, Co, and Ni in ascending atomic number). The extent of d-level splitting for the transition elements depended on the strength of the interaction supposed between the ion and its neighbors, scaled by a parameter 3, in the range 0 IA I1; g factors from experimental ESR information were used to set suitable values for A That 1977 calculation of Il’in and Masterov resulted in predictions of E-symmetric and T, states within (and in some cases below) the GaAs intrinsic gap region, and additionally A, and T, states resonant with the conduction band. Table V1 shows their suggestions for the states within the gap, with values (all expressed with respect to E,) again rounded to the nearest 0.1 eV, and noting (without itemizing here the various citations)the experimental flaw energies they tabulated for comparison. Bernholc and Pantelides (1978) made a tight binding GF calculation for ideal vacancies in GaAs, with results indicated to the nearest 0.1 eV as the third row in Table V. The levels of V, were calculated to be very near to the top of the valence band, lacking the moderately deep acceptor status that the two previous calculations had indicated. The (completely filled) A, state of V,, was located near mid-gap, and only in regard to the (donorlike) T, level of V, did the results agree reasonably with those of Jaros and Brand (1976),

Dopant atom

Ti

( E - E,) (ev) Symmetry

[ [i: [ F2 [?: 2:

E*

V

Cr

E*

Mn

E*

Calculated

Experimenp

0.5 1.3 1.5 0.5 1.2

( E - Ev)(ev) Dopant Atom

Fe

Symmetry

[

z: E*

0.7

Calculated

Experimenp

0.2

0.4

0.5 0.7

0.5

0.1

0.2 0.4 0.5

0.3 0.7

0.2-0.4 0.4-0.5

0.2 0.6

0.2 0.5

Go

1.3 0.4

0.9

0.8

0.1

0.1

1.o

0.3 0.7 0.9

Ni

*: [

Il’in and Masterov cite the sources of the energies quoted in the “experiment” columns.

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

341

and Il’in and Masterov (1 976). It was pointed out by Bernholc and Pantelides ( 1978) that, in any case, a defect such as V, should be subject to a large Jahn - Teller distortion. They caution accordingly that results for “ideal” unrelaxed vacancy situations should not be compared directly with experiment. Yet, solutions of the unrelaxed vacancy situations do provide an important stepping stone toward understanding deep-lying states of “real” flaws. The final two rows in Table V indicate results from the calculations of Bachelet et al. (198 1) specifically for ideal vacancies in GaAs, and of Talwar and Ting (1982), which tackled the gamut of vacancy situations in 111-V compounds. The calculations of Bachelet et al. were obtained by a self-consistent GF method, based on that used by Baraff and Schliiter (1978, 1979) for vacancies in silicon. They remarked that the use of a self-consistent treatment was considered necessary in view of the partly polar nature of GaAs. The concluding comments of their paper did include an assessment of how the results would be likely to be affected by Jahn-Teller relaxation, but the Td site symmetry of ideal vacancy sites was used for the calculations themselves. These calculations were on a substantial scale, with wave functions evaluated on a grid of 70 sampling points per &th (Brillouin) zone, and energies on a grid of 203 points per &th zone. Figure 29 shows a spherical average of one of the self-consistent potentials deduced by Bachelet et al. (1 98 I), that for an unrelaxed V, site. The curves prior to and following the final iteration are compared here. It was apparent 40

I

I

I

I

I

c BEFORE F I N A L ITERATION

’

-40

0

AFTER I

I

11

I

I

2 RADIUS

I

4 (0

u)

FIG. 29. A spherical average of the self-consistent potential around an isolated ideal Ga vacancy in Gas, as developedby successiveiteration in the work of Bachelet et al. ( 198 1). The solid line shows the result of the penultimateiteration, used as input for the final iteration,with the output of that shown as the dashed curve.

342

J. S. BLAKEMORE AND S. RAHIMI

1

4t l 2-

II

BOUND STATE -I.OeV

0

"U

[L

I-

v -4-

w

v

-

I

w

a"

I

I

-I W

L

601JND

5-

STC4TE -IOeV

0

7

BOUND STATE

/

-5 -10

-

I -15%

-10

-8

-'6 -;-'2 6 (E-E,)

(ev)

4'

FIG.30. Contributions of the A , and T, representations to the change in the density of electronic states resulting from a neutral unrelaxed Ga vacancy in GAS.(After Bachelet et al., 1981.)

from the range of this potential that the LCAO expansion needed to include 20 orbitals from each of the four nearest-neighbor sites, but not for the 12 Ga atoms of the second nearest-neighbor sphere. As a result of this, Bachelet et al. were not obliged to invert a matrix of size larger than 14 X 14. [The need for that arose in connection with the T2(p-like) representation.] Figure 30 shows the deduction of Bachelet et al. (1981) concerning the change in the electronic density of states produced by removal of one Ga atom (without subsequent lattice reconstruction) from a GaAs crystal, indicating the A, and T2contributionsto this change. Similar plots ofAg(E) versus energy had been provided in the paper of Bernholc and Pantelides (1978), and were also provided in the subsequent work of Talwar and Ting (1982). Note that the entire 13-eV range of the GaAs valence bands is affected -and also, of course, conduction bands extending beyond the range of this figure. Figure 30 also indicates the positions of the A, resonance at (E, - 1.O eV), and the T2 bound state at (E, 0.1 eV), as listed in the fourth row of Table V. Figure 3 1 shows charge density plots for this A resonance and for the weakly bound T2state, projected onto the (1 10)plane, for a cut through the

+

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

343

FIG.3 1. Charge density plots associated with (a) the A l resonance at (E, - 1.O eV), and (b) the weakly bound T, state at (E, 0. I eV), resulting from a neutral unrelaxed Ga vacancy in GaAs. Plotted in the ( I 10) plane, with V, at the center of each part of the figure. (From Bachelet et al., 1981.)

+

unit cube with the vacancy at the center of each part of the figure. A comparable (1 10) plane plot of charge density contours is shown in Fig. 32 for GaAs containing an unrelaxed As vacancy. The two parts of this figure are for the A, resonance at (E, - 0.8 eV) and for the T, bound state at (E, 1.1 eV). (Those energies are also as listed in Table V.) Having calculated this and much else for ideal unrelaxed vacancy sites, Bachelet et al. (198 1) then allowed themselves some speculations concerning how their results could be reconciled with various experimental results, as affected by lattice reconstruction around a vacancy site. They commented that Jahn - Teller distortion (expected to be significant for VGa)would also depend on the state of charge-just as it is for Cr, (Stauss and Krebs, 1980; Kaufmann and Schneider, 1980b, 1982). Bachelet et al. speculated that, after an ideal Vka has been split by Jahn-Teller distortion into two levels,

+

344

J. S. BLAKEMORE AND S. RAHIMI

FIG.32. Charge density contour plots, in the (1 10) plane ofGaAs, associatedwith (a) the A , resonance at (E, - 0.8 eV) and (b) the T, bound state at (E, 1 1 eV), for an unrelaxed neutral As vacancy. The V,, site is at the center of each part of the figure. (From Bachelet et al.. 198 I .)

+

I

the transitions in the V&, V& system might be those responsible for what is described as the E3 or EL3 radiation defect in GaAs (Lang et al., 1977; Pons et al., 1980). The LCAO Green’s function calculations of Talwar and Ting ( 1982)have already been noted briefly, in respect of their GaAs unrelaxed vacancy energies, listed as the final entries in Table V. Theirs was, in fact, an ambitious set of calculations. This involved band calculations for Seven 111-V binary compounds, as well as the effect of ideal vacancies, and of other point flaws with short-range potentials. Talwar and Ting were interested in trends of binding energy with local potential strength. Their specific results on the latter topic are deferred for the moment (an example appears as Fig. 39) in order to illustrate them concurrently with some from the similarly motivated work of Hjalmarson er al. (1980a,b) and Vogl(1981). In another type of GF development, Banks et al. (1980)expanded the

4. MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

345

deep-level flaw wave function in terms of host Bloch functions, in the manner of Eqs. (141)-( 146), in order to calculate optical transition cross sections, to the valence and conduction bands. It was assumed that photoionization leaves behind a neutral center. Banks et al. found that only 1 = 0 (for the symmetric A, representation) and I = 1 and 2 (for the T2 representation) needed to be considered to make the energy level convergent. They cautioned that their results should not be compared exactly with experiment because of the use of host-crystal pseudowave functions for final states and the neglect of electron -phonon coupling. However, their curves for a,(E)do show interesting possibilities. These are exemplified by Fig. 33, showing the expected variation of optical cross section with final state energy for levels of A, symmetry in the intrinsic gap of G a s . Here, the solid curve (a) corresponds to ED= 0.4eV, while the dashed curve (b) is for a deep donor near mid-gap, E D = 0.7 eV. Curves with some contrasting features are shown in Fig. 34, which provides the curves that Banks et al. calculated for flaws of T2symmetry in the gap of GaAs. This contrast emphasizes the important effect of the flaw symmetry on the magnitude and form of the optical cross section. It is important to remember that these numerical calculations of Banks et al. employed a multiband formulation. Not only were final states in all bands considered, but the flaw state itself was constructed to represent the influences of these bands, and is delocalized in k space. Thus, optical transitions can occur in any part of the Brillouin zone, to a part of a band which is not

-5

-4

I

I

I

-3

-2

-I

E-E,

I

0

+I

(eV)

FIG. 33. Variation with final state energy of the optical cross sections for levels of A , symmetry in the gap of GaAs,as calculated by Banks ef al. (1980). (a) For a level 0.4 eV below the r, conduction minimum. (b) For a level of ED = 0.7 eV. It is supposed that the flaw is neutral after photoionization (to the conduction band). Thus, an optical transition from a valence-band state to the flaw leaves this with a charge of - e.

346

J. S. BLAKEMORE AND S. RAHIMI

E-E,

(eV)

FIG.34. Optical cross section versus final state energy, as in Fig. 33, but for bound states of Tz symmetry in the gap of GaAs, again as calculated by Banks el al. (1980). Functions with both I = 1 and 1 = 2 were used in constructing the supposed bound states, which were envisaged as lying (a) 0.5 eV below the r, conduction band, (b) 1.0 eV below the conduction band, and (c) 0.1 eV above the valence-band maximum.

“forbidden” for reasons of parity -and preferentially to where the density of final states is large. The latter condition is satisfied, where VJ5 remains small over a substantial range of k. As a reminder of promising areas of large final state density, Fig. 35 reproduces results from the nonlocal pseudopotential calculations of Chelikowsky and Cohen (1976), for GaAs valence-band and conduction-band dispersion curves along high symmetry directionsin the Brillouin zone. The result of that for the total density of band states, g(E),is shown as the solid curve in Fig. 36. [Thedashed curve shows, for comparison, the experimental result of Ley et al. (1974) for g ( E ) in the valence bands.] While curves such as those of Figs. 33 and 34 are of intrinsic interest in revealing aspects of deep-level flaw behavior, one must remember that any featuresinvolving a photon of energy hv > Eiwould be almost impossible to verify experimentally,even with the modem sophisticatedversions of modulation spectroscopy. Some other things that can be calculated are more easily compared with experiment-although that does not ensure a lack of controversy concerning the interpretation. Considerable interest has been aroused (and some spirited discussion also) by studies of chemical trends in flaw energy, camed out by Hjalmarson et al. (1980a,b), as reviewed by Vogl(198 1). This work used a Green’s function calculation to predict the activation energies of numerous elements, acting as anion-site and cation-site sp3-bondedsubsti-

4. MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

-12 L

rI

A

A

rl

1

X U 0, K

347

REDUCED WAVE VECTOR

FIG.35. Electron energy dispersion curves along high symmetry directions in the zone, for the valence and lower conduction bands of GaAs,as calculated by Chelikowsky and Cohen (1976). A large density of states g ( E )occurs where V,E is small over a substantial range of k. See Fig. 36 for the resulting form of g(E).

1.5 I

I

I

I

E-E,

I

I

1

(eV)

FIG.36. Density ofelectron states with respect to energy, g(E),for the valence bandsand the lower conduction bands of GaAs. The solid curve shows the calculated result of Chelikowsky and Cohen (1976). The dashed curve is the experimental result of Ley et al. (1974) for the valence bands.

348

J. S. BLAKEMORE A N D S. RAHIMI

I

- (ATTRACTIVE)

I

I

0

+(REPULSIVE)

FLAW SITE POTENTIAL

FIG. 37. A schematic plot of the variation with flaw site potential of the localized state energy; for a two-state model (as in Fig. 2 5 ) and in line with the arguments advanced by Hjalmarson et al. (1980a,b) and Vogl(198 1). This indicates the pinning energy limit which is approached for a very large attractive or repulsive local sitepotential.

tutional impurities. The emphasis is entirely on the consequences of a short-range impurity potential; the long-range coulombic part of the potential is ignored, to allow any shallow impurity to have zero binding energy. A key element in this approach is the “pinning energy” dividing the energy regions in the intrinsic gap associated with bonding-type and antibondingtype states. Figure 37 shows schematically how the flaw energy is envisaged C I

A s 1 1 Bi

B 51

Band E d g e

-

T, States Cation Site

1.6’

I

1

-10

-5

F L A W p - O R B I T A L ENERGY

-

-

0

(eV)

FIG.38. Predicted bound-state energy, relative to the conduction band edge, for T2(p-like) flaw levels arising from a cation site substitution, in the eight solids indicated (after Vogl, 1981). The abscissa at the bottom shows a scale of the porbital energy of the flaw site. Values considered appropriate for various atomic substituents are indicated along the top edge. See Fig. 39 for a larger range of abscissa energy, which Talwar and Ting (1982) surveyed.

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

-40

-30

10

20

I M P U R I T Y POTENTIAL

(eV)

-20

-10

0

30

349

40

FIG.39. Predicted variation ofbound-state energy within the intrinsic gap upon the flaw site potential, for deep-level flaws of T, symmetry on cation sites (after Talwar and Ting, 1982). The two parts of the various curves may be compared with the schematic of Fig. 37, and the upper portions of the antibondingcurves for GaAs, Gap, AIAs, and InP may be compared with the corresponding curves of Fig. 38.

as depending on the strength of the local site potential, for a two-state simplified model (Fig. 25). Where the pinning energy ends up in the gap depends, of course, on the band structure of the host (GaAs being the solid of principal concern here), on whether the substitution is on an anion site (= As site in GaAs) or cation site (Ga site in GaAs), and on whether one is dealing with a symmetric (I = Ow, or (I # O)T, representation. Figure 38 shows the curves of Vogl (1981) for predictions of the bound flaw state energy, versus p-orbital energy, for T, states resulting from substitutions on the cation site of GaAs and seven other 111-V and Group IV solids. The curve for GaAs in Fig. 38 formsjust one part of the broader energy range curve in Fig. 39, from the work of Talwar and Ting (1982) for T, symmetry states in the five 111-V hosts as indicated. The two portions of each curve in Fig. 39 may be compared with those of the idealized curve in Fig. 37. Talwar and Ting showed also a family of curves for symmetric (A,) states on cation sites, while the families of curves provided by Vogl dealt with both A, and T, representations for both cation and anion sites. These two investigations did not yield identical results (that rarity in this world), nor even the same conclusions, but both represent interesting avenues for further modeling of mid-gap flaws in GaAs and the other mildly polar 111-V compounds. IX. Brief Notes on Other Approaches The precedingparts of this chapter have not, by any means, exhausted the opportunities for reviewing theoretical models that could be applied to

350

J. S. BLAKEMORE AND S. RAHIMI

deep-level flaws in GaAs. In this part, brief comments are made, concerning a number of other approaches that have been proposed in recent years. Some of these correspond, in certain respects, to the various categories that have already been ennumerated. For several of the models to be mentioned here, the photoionization spectralresponse has been a major preoccupation. Nazareno and Amato (1982) suggested a simple model for identifying a flaw in a semiconductor as being a bona Jide deep-level member of the species. Their model concentrates on the peculiarities of the photoionization cross section q(hv), as related to critical points in the density of final states g(E). A similar consideration had led us, in Part VIII, to note the maxima of g(E) for GaAs in Fig. 36, for comparison with the features of Figs. 33 and 34. At any rate, Nazareno and Amato comment that (with some simplification) a,depends on the transition matrix element squared lM12 and on g(E)for the final state energy. From this kind of analysis, they drew conclusions concerning iron in silicon, oxygen in Gap, and Cr and 0 in GaAs.Their deductionsfor the two impurities species in the latter host were (Ei-Eq)=0.55eV for Cr,, and ED=0.67eV for Oh, with the Ta conduction band alone taken into account. That was probably not a wise assumption to have made for those situations, but it does not invalidate the basic opportunities for this kind of approach. Burt (1 980) evaluated a simple form of the deep-level photoionization problem, with GaAs specifically in mind. For computational ease and other reasons, he used a planar delta-function potential. There was some interesting logic behind the adoption of this potential, for its eigenvalues include band-gap states analogousto surface states. This made it possible for Burt to perform the calculation using evanescent waves (Heine, 1963). These waves describe non-Bloch states, related to the ordinary Bloch states of the crystal by an extension into complex wave vector, There has been a general recognition for a half-century that a state which can be described by a complex wave vector cannot be delocalized throughout a crystal. However, that was put to use two decades ago for the modeling of surface states properties (Heine, 1963), and the possible value of an evanescent wave approach for deep-lying flaw states in the bulk was not analyzed until much more recently. These topics, of the complex band structure, the use of evanescent states, and of how this can be used to describe photoionization of a deep flaw, were further examined in a series of papers by Inkson (1 980, 198I), and by Blow and Inkson ( 1980a,b). The reader’s attention is drawn to a comment made by Blow and Inkson (1980a) that the method works well for an indirect gap semiconductor because (a) flaw states are then not distorted by the low-lying r minimum, and (b) the (Penn model dielectric) band gap is then more nearly constant over the surface of the Jones zone. One implication of these

4.

MODELS FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

351

comments is that flaws in GaAs may not provide an ideal test of this approach. In a series of papers which also draw upon the evanescent wave approach (and with Burt and Inkson among the authors), Dzwig et al. (198 la,b, 1982) have proposed a slightly different model for calculation of optical matrix elements and cross sections associated with deep-level flaws in GaAs. This is a superlattice approach, based on the assumption of a lattice of flaw S potentials. In this way, some of the symmetry is restored to the problem (as in the electrostatic problems solved by the method of images). An isolated flaw is then modeled as the limit of the superlattice constant going to infinity. In their investigation of a 2 X 2 superlattice, Dzwig et al. (1982) were able to trace the change in the character of the bound flaw state as this is made deeper (it gets more p-like). They took the various conduction minima at the r, L, and X points into account in calculating curves for the spectral dependence of lM12 and of q(hv). Figure 40 shows an example of their results, q(hv)for a donor of ED = 0.625 eV in GaAs. This may be compared with the optical cross-section curves for the lower conduction band region of Fig. 34, from the work of Banks et al. (1980). One can see some similarities and also some differences, for the “true and complete” solutions for deeplevel flaws and their photoionization properties still elude us. A tight-binding LCAO approach has been taken by Peiia and Mattis

FIG. 40. Spectral dependence of the photoionization cross section for a mid-gap donor in GaAs (ED=0.625 eV), as calculated by Dzwig ef a/. (1982) from a model supposing a planar 2 X 2 super-lattice of these donors, each represented by a Spotential.The evanescent wave approach used, and band nonparabolicity taken into account, in addition to allowance for the four lowest conduction bands.

-a ‘3 5

b“

0.6

I .o

1.4

hu ( e V )

18

352

J. S. BLAKEMORE AND S. RAHIMI

(198 l), with both host and flaw states expanded as a complete set of site-localized orbitals. Unlike many of the other theories we have noted up to now, their approach did not require that the host orbitals be Wannier functions-only that they be compatible with the bands included in the calculation. Fermi’s golden rule was employed in deducing the electronic part of oplically induced transition rates. The latter was applied to problems of moderately deep acceptors in silicon, and the applicability of these techniques for the mid-gap types of flaw in a polar solid such as GaAs remains (as this is written) to be tested. Additionally, we might note a viewpoint growing out of remarks made in Appendix A of the work of Monemar and Samuelson (1978) and reexamined by Chantre et al. (1 98 1). This concerns two opposite extremes for the form of the matrix element. Thus, = constant for an allowed transition, as characteristic of a photoneutralization process. However, (klplk) a k for a first-order forbidden transition, as is typical for many photoionization transitions. The k dependence of the matrix element for a real situation of semiconductor- flaw need not coincide with either extreme. Allowance for this obliges a numerical evaluation, using the real band structure (including nonparabolicity, upper conduction bands, etc.). Following the formalism of Monemar and Samuelson, Chantre et al. applied this method specifically for the GaAs conduction band system, and used this to fit their photocapacitance spectra for several well-known flaw species in that semiconductor: Cu, Cr, EL2, EL6, etc. The subject matter of this chapter is not one on which a conclusion can usefully be expressed, since the methods by which mid-gap flaws (in GaAs and in other semiconductors, of both direct and indirect gaps) may be modeled and calculated are still in a state of rapid evolution. Some glaring limitations of certain of the simpler analytic models are now quite well recognized. However, their value for an approximate and understandable representation does not allow them to go away. The numerical methods, as conducted with large computational resources, probably do represent the way of the future. It is essentialthat the use of such methods be inextricably entwined with human input and monitoring, and that the results printed out provide such a variety of flaw attributes that the experimentalist has independent opportunities for testing the validity. As we have said all the way through, to get the “right” binding energy is not enough! ACKNOWLEDGMENTS The authors Wish to acknowledge the support of the National Science Foundation, through DMR Grants 79 16454 and 8305731, for studies of semi-insulatinggallium arsenide which led to the writing of this chapter. We also wish to thank G. A. Baraff, J. D. Dow, P. DzWig,

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G. Ferenczi, H. G. Grimmeiss, M. Jaros, U. Kaufmann, L-A. Ledebo, J. R. k i t e , D. C. Look, S. Makram-Ebeid, G. M. Martin, A. G. Milnes, S. T. Pantelides, B. K. Ridley, L. I. Samuelson, and J. Schneider, among others, for their valued help in any or all of the following respects: useful discussions, interesting preprints, and (in some cases) comments on the draft manuscript. We are additionally indebted to Dr. Baraff for his originals of the figures we number as Figs. 31 and 32.

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Index A

Absorption coefficient, see also Optical absorption studies at 1.1 pm, 35 Acceptors, 32, 34, 37-44,98, 99, see also Compositional purity; Impurity levels 0.026-eV level, 37, 38 0.073-0.078-level, 38-44, 201 -206, 208, 211 anti-site defect, 205, 206 boron complex, 40 -44 C, 32, 34, 37-40,42,47, 48, 79, 98, 100- 102, 192, 193,203,206-208, 2 1 1, see also Carbon Cr, 29, 30, 36, 37,98, 106-109, see also Chromium Mn, 47,98, 101, 102, 193 Si, amphoteric behavior, 57-59, 73-81 Activation efficiency, 69 - 7 1, see also Ion implantation Activation energy acceptors, 37-44, see also Acceptors deep donor, 29,42,43, see atso Donors electrical activation, 69 - 7 1, see also Direct ion implantation implants, 56, see also Ion implantation resistivity, see also Resis?;vity semi-insulating materiai, 19 AES (Auger emission spectroscopy), 100 Amphoteric behavior, 57 - 59,73-8 I , 297 Si, 57-59,73-81 Annealing, 45-47, 54,65, 80, 113- 125, 135-143, 221,222, seealso Thermal annealing effect on activation efficiency, 80, 123 effect on camer concentration, 107, 108 implanted layers, 113-1 18, 127, 128 effect on compensation ratio, 80 thermal conversion, 4,46 - 49, 109,221, 222

363

transient technique, 140- 143 ASES (arc source emission spectroscopic analysis), 26, 100, 132 Auger recombination, 304- 308 capture coefficients, 305- 308 diagram of capture processes, 305

B Backgating, 148-151, 195 Barrier height, A1 on GaAs, 67 Billiard-ball model, 263, 264,271 -278, 280,281 photoionization cross section, 272-277, 280, 281 Boat-grown GaAs, 5 Boric oxide encapsulant, 6, 10, 14, 17, 19-21,26-28, 163- 165, 194,211, see also Encapsulation [OH] content, 13,26-28,97, 163, 194, 195,211 prevalence of 0.65-eV trap, 21 1 temperature gradients, 19 viscosity, 20 Born approximation, 249, 257, 264 Boron, 24-28, 101, 102, 192-195,204, see also Impurities boron -defect complex, 4 1 -44 effect of [OH] in B,O, encapsulant, 13, 26-28,97, 194, 195,21 I Boron nitride, pyrolytic, 8, 28, 49, 163, 164, see also PBN crucible Breakage, GaAs wafers, 83 Breakdown voltage, FET, 6 1 Bridging version of square-well potential model, 271,278-281 Broadening of implant profiles, 67 Buffer layer, 103- 105, 109 camer concentration, 104, 105 camer mobility, 104- 105 growth, 103- 105

364

INDEX

C

Capacitance transient spectroscopy, 196, 197 Capture coefficient, 236-238, see also Carrier capture and emission mechanisms Auger recombination, 305- 308, see also Auger recombination multiphonon emission cross section, 300, 302, 307, see also Radiationless transitions radiative, 297 -299, see also Radiative transitions Carbon, 4,24-26, 34, 37-40,47,48, 79, 98, 101, 102, 192, 193, 203, 206-208, 2 1 1, 227,236,29 1, see also Impurities: Impurity levels effective segregation coefficient, 39 measurement with LVM, see LVM possible component of EL2 complex, 291 with EL2, 207,208,227 Camer capture and emission mechanisms, 293-308, see also Capture coefficient; Emission coefficient; Photoionization; Radiationless transitions Auger recombination 304-308, see also Auger recombination Cr2+-Cr3+ transitions, 287, 296 enthalpy of transition, 295, 296 entropy factor, 295 entropy of transition, 295 free energy of ionization, 296 multiphonon emission capture cross section, 300, 302, 307 radiationless transitions, 299 - 304, 307, see also Radiationless transitions radiative capture coefficient, 297 - 299 thermodynamic relationship, 294 -297 two-stage capture process, 300 - 302 Charge carrier scattering, ionized impurity, 73 Chromium, 4, 8, 23-26, 29, 30, 36-38, 76, 92,95,98- 102, 106-109, 150, 193, 209-211,221,223,236,237,242,287, 288, 296, 340, see also Impurities; Impurity levels Crz+-Cr3+ transitions, 287,296 diffusion, 108, 221 effect on ion implantation, 69-72,76, 77 redistribution, 4, 22 1

reduction of electron mobility, 4 with Te, 106 various charge states of Cr, (calculated), 319 Compensation mechanism, 192,206 - 208 producing semi-insulating behavior, 29, 44, 161,206- 208 ratio, 74,75, 80 effect of annealing, 80 role of carbon, 208, see also Carbon role of EL2 defect, 208, see also EL2 level Complexes, see also Acceptors boron-defect, 40-42 Compositional purity, 23-29, 192-212, see also Stoichiometry determination ASES, 26, see also ASES LVM, 26, 192, see also LVM SIMS, 23-25, see also SIMS SSMS, 23,26, see also SSMS impurity elements, see also Impurities B, 24-28, see also Boron C, 24-26, see also Carbon Cr, 4, 8, 24-26, 36-38, seealso Chromium 0 , 4 , 2 4 , see also Oxygen Si, 22-28, see also Silicon tabulation of major impurities, 24, 25, 101, 102, 193 impurity sources, 23-28 influence of water [OH] in encapsulant, 26-28, 194, 195, 211, seealso Encapsulation Configurational coordinate diagram, 283, 290,301-303 self-trapping, 303, 304 Conversion, 4,46-49,51, 109,221,222 thermal, 4,46-49, 109,221, 222 Crucible PBN, 8,28, 163, 164, 192-195,211,see also PBN quartz, 163, 192- 195 silica, 8, 27, 31 Crystal growth, see also Crystalline imperfections; Crucible; Encapsulation; Dislocations; LEC growtk Materials preparation; Uniformity Bridgman, 4, 17, 24, 29, 93,94 coneangle, 16, 170, 174, 176-179, 191

INDEX

crucible material, see Crucible differential weight gain signal, 7, 10, 167 encapsulation, see also Encapsulation B203,6, 10, 14, 17, 19-21,26-28,97, 163, 164 effect on electrical properties, 30 - 32 LEC technique, 5-23, 163-167, see also LEC growth plasma nitride, 62 - 65, see also Silicon nitride gradient-freeze technique, 24, 29 inclusions As, 190 As precipitates on dislocations, 50 Ga, 187 large melts, 8 automatic diameter control, 8, 9, 167 coracle technology, 8 - 11, 166 manual diameter control, 8- 10, 166 LEC, 5 -23, see also LEC growth thermal gradients, 17, 19-22 pull speed effects, 20-22, 52-55, 164 seed rotation effects, 20-22, 52-55, 164 Crystalline imperfections, 12-23, see also Crystal growth dislocations, 12, 14- 17, 50, 97, 167- 182, 187, 190,226,228, see also Dislocations effectson devices, 12, 152, 168,226,227 generation, 14- 17, 168 influence of thermal stress, 12, 14- 17, 19,20, 168, 171, 172 reduction, 12, 15, 16, 97,98, 168,228 impurity striations, 20-23 inclusions As, 190 As precipitates on dislocations, 50 Ga, 187 microdefect studies, TEM, 187, 190, see also TEM twinning, 12- 14, 182- 187, see also Twinning Czochralski puller, 7, see also Crystal growth D Deep-level centers, see also Flaw; Flaw states (quantum theory) classification scheme, 238-242 detection technique, 24 1, see also DLTS

365

energy level calculations, 327, 337-340, 347-349, see also Green’s function method phenomena affected, 235 - 238 Defects, see also Crystalline imperfections; Dislocations; Impurity levels; Twinning acceptor level, 42 0.073-defect-compIex, 42 donor level 0.45-eV, 42, 43 EL2, see EL2 level detection by TEM, 187, see also TEM energy level calculations, 3 16, 326, 327, 337-340, 347-349, see also Green’s function method Delta-function potential model, 252-260 applicability, 25 1, 252 photoionization cross section, 255 - 260 Depletion voltage, 225, 226 Depletion width, 150 Device fabrication, 63-65, 212-226, see also FET; IC devices; MESFET implantation sequence, 64 logic approaches, 2 12,213 steps, 213-216 wafer breakage, 83 Direct ion implantation, 3, 4, 55 - 8 1, 109- 143, 212-226, see also Electrical properties; Ion implantation annealing effects, 65, 80, 81, 113- 125, 135-143,221,222 channel mobility, 71 -73 Cr-doped substrate, 76 - 78, 129- 132 electrical activation, 56-58,69-71, 76-78 experimental procedure, 62-66 evaluation techniques, 65 nitride encapsulation, 62 - 65, 1 13- 123 PSG encapsulation, 63 Si02encapsulation, 1 15 flat-channel profile, 57 implications, FET device processing, 60, 61,78-81 measured profiles, 57, 66-69, 113- 118, 121, 122, 127, 128, 132, 137, 139, 140,2 17, see also Electrical properties Hall mobility, 57, 128 mobility, see Mobility plasma nitride encapsulant, 62-65, 113-123

366

INDEX

Direct ion implantation (cont.) power FET applications, 60,6 1, 78 - 8 1 Seimplantation, 81, 115-118, 122, 123, 127, 130, 132, 137, 139, 140,217, see also Selenium selected area, 63- 65 selective implantation fabrication sequence, 63-65 S implants, 81, 114, 119, 128, 129, see also Sulfur Siimplantation, 56-81, 115, 121, 137, 139, 140,219, 220, see also Silicon amphoteric behavior of Si, 57-59, 73-81 concentration profile, 57, 1 15, 137, 139, 140 effect ofannealing, 80, 119- 125, 135-143,seealsoThermalannealing mobility, 59-61, 71-73, 75 uniformity, 68, 133, 134, see also Uniformity Dislocations, 12, 14- 18, 50, 97, 98, 152, 167- 182, 187-192,226,228,242, see also Crystal growth; Crystalline imperfections augmented by encapsulant, 14, 17, 19-21 decoration, 50 effect on devices, 152, 168,226, 227 generation, 14- 17, 168 influence of thermal stress, 12, 14- 17, 19, 20, 168, 171, 172 longitudinal distribution, 174, 175 networks, 173, 174 parameters affecting density, 170, 174, 190, 191 ambient pressure, 170, 174, 179-181 coneangle, 16, 170, 174, 176-179, 191 crucible position, 19 crystal rotation rate and pull speed, 20-22 diameter control, 170, 174, 182, 191 height of B20Jencapsulant, 14, 19, 20, 170, 174, 179, 180, 191 melt stoichiometry, 170, 174, 182 seed quality and necking, 16, 17, 170, 174, 181, 182, 191 radial distribution, 15, 17, 170-173, 190 reduction, 12, 15, 16, 97, 98, 168, 228 TEM studies, 18'7- 190, see aiso TEM

thermal gradients in melt, 17, 19-22, 168 x-ray topographs, 16, 18 DLTS (deep level transient spectroscopy), 45-47, 149,241 Donors, 29,32-35,39,40,42-53,56-60, 66-71,73-81,98,99, 195-206, see also Compositional purity; Impurities; Impurity levels 0.45-eV level, 42-44 EL2 level, 29, 32, 34, 35, 44-51, 53,913100, 108, 109, 148, see also EL2 level out-diffusion, 49, 5 1 0 , 2 9 , 195, see also Oxygen residual, 36 - 44,208 - 2 I I effective donor segregation coefficient, 39 S , 98, see also Sulfur Se, 8 1, see also Selenium Si, 56-60,66-69, 73-81,98, seealso Silicon amphoteric behavior, 57-59,73-81 diffusion coefficient, 125 profile of implants, 57, 1 15, 137, 139, 140 Te, 98, see also Tellurium

E EL2 level, 29, 32, 34, 35,44-51, 53, 98-100, 108, 109, 148, 196,200,201, 205-208,227,228,236,241,290,291, 304 with carbon, 207,208 dependence on stoichiometry, 29, 32, 35, 44,49,201,227 electron paramagnetic resonance studies, 35 identifications anti-site defect (As on Ga site), 35, 99, 196,205,206,227,241,291 complex, 29 1 metastable state, 290, 29 1, 304 optical absorption, 35, 196, 200,201 out-diffusion, 49, 5 1 photoconductivity, 196 photoluminescence, 20 I , 202 role in conversion, 46,49, 5 I , 109 transient capacitance studies, 196 Electrical properties, 29-55, 57-62,65, 71-79, 128-132, 195-206, seealso

INDEX

Impurity levels; Ion implantation; Semi-insulatingmaterial axial variation of resistivity, 30, 31 carrier concentration implanted layers, 57-60, 113- 118, 121, 122, 124, 127-129, 132, 135-142,217-220, seealso Ion Implantation various crystals, 38, 40-44, 48, 52, 107, 108, 197 crucible/encapsulant effects, 30- 32 resistivity variations, 30, 3 1 depletion voltage, 225, 226 melt composition effects, 32-36,41-44, see also Stoichiometry mobility, 34, 36, 51, 53-55, 198, seealso Mobility implanted layers, 57-61,71-75, 128- 132, see also Ion implantation pinch-off voltage, 65,79, 213, 222-225 resistivity, 29-31, 33, 34, 43,52, 196, 199, see also Resistivity Se-implanted layers, 115- 118, 127, 132, 133, 135, 139, 140, 216, 217, seealso Selenium semi-insulating behavior, see Semi-insulating material Si-implanted layers, 57-59, 71-78, 115, 137, 139, 140, 2 19, see also Silicon Te-implanted layer, 1 13, 141 thermal stability, 44- 52, see also Heat treatment; Thermal annealing uniformity, 52-55, see also Uniformity Electron mobility, see Mobility EMA (effective mass approximation), 239, 245-248,250 hydrogenic model, 247, see also Hydrogenic impurity Emission coefficient, 236-238, see also Carrier capture and emission mechanisms Encapsulation, see also Crystal growth BZO,, 6, 10, 14, 17, 19-21,26,27, 163-165, 194, 195,211,seealso Boric oxide encapsulant effect of water [OH] content, 13,26, 27,97, 163, 164, 194, 195,211 prevalence of 0.65-eV trap, 2 1 1 vacuum baking, 26 effect on electrical properties, 30-32

LEC techniques, 5-23, 163- 167, see also LEC growth phosphosilicate glass (PSG), 63 plasma nitride, 62-65, see also Silicon nitride SiO,, 115, 138, 139

F FET (field effect transistor), 3-6, 63-65, 78-81,92,212-226, seealso MESFET device fabrication, 2 12- 226, see also Device fabrication device processing, 78 - 8 1 discrete vs. monolithic circuit, 3 -6 flat-channel profile, 57 implants, see also Electrical properties; Direct ion implantation; Ion implantation breakdown voltage, 6 1 channel mobility, 71, 73 full-channel current, 6 1 undepleted net donor concentration, 60,61 logic approaches, 2 12,2I3 pinch-off voltage, 65, 79, 213,222-225 power applications, implantation, 60 selected-area implantation, 63 - 65 zero-bias depletion width,79 Flaw, see also Carrier capture and emission mechanisms; Deep-level centers; Defects; Flaw states (quantum theory); Impurity levels; Phonon-assisted optical transitions; Pbotoionization; Photoneutralization amphoteric, 297, see also Amphoteric behavior Auger recombination, 304- 308, see also Auger recombination billiard-ball model, 263, 264, 271 -278, see also Billiard-ball model carrier capture and emission, 293-308, see also Carrier capture and emission mechanisms classification chart, 240 impurity, 240 native defect, 240 complexes, 4 1 -44, 24 1, 242 definition, 238 delta-function potential model, 252 -260,

368

INDEX

Flaw (cont.) see also Delta-function potential model hydrogenic model, 247, 250, 25 1, see also Hydrogenic impurity information required for complete signature, 267,268 multiphonon processes, 299- 304, 307 phonon coupling effects, see Phononassisted optical transitions quantum-defect model, 260-264, see also Quantum-defect model radiative capture cross section, 297-299 radiative transitions, 249-25 1, 297-299, see also Radiative transitions square-well potential model, 267-271, 279-281, see also Square-well potential model bridging version, 27 1,278- 28 1 wave function spatial properties, 264-266 spectral properties, 264, 265 Flaw states (quantum theory), 242ff, see also Flaw choice of potential, 247 - 264, see also Flaw billiard-ball model, 263, 264, 271 -278, 280, 28 1, see also Billiard-ball model bridging version of square-well potential, 271, 278-281 delta function, 252-260, see also Delta-function potential model hydrogenic, 247, 250,25 1, see also Hydrogenic impurity quantum-defect model, 260-264,280, 28 1, see also Quantum-defect model square well, 267-271, 279-281, see also Square-well potential model effectivemass theory, 245-248, see also EMA Green’s function method, 328-349, see also Green’s function method molecular orbital approaches, 309-329, see also Molecular orbital approaches pseudopotential representations, 320-328, see also Pseudopotential representations radiative transitions, 249-25 1, 297-299, see also Radiative transitions

photoionization, 249 -25 I , see also Photoionization photoneutralization, 249,25 1, see also Photoneutralization wave function, spatial and spectral properties, 264-266, see also Flaw Franck-Condon shift, 283-285,287-293, 296 tabulation, 289

G Gradient-freeze crystal growth technique, 4, 24,29, 93, 94, see also Crystal growth Green’s function method, 328-349 calculated energy levels, 327, 337-340, 347 - 349 bound-state energy dependence on flaw site potential, 349 cation site substitution, 348 continued fraction method, 339 electron energy dispersion curves, 347 Cia-site substitutional impurities, 340 tight-binding approximation, 329 V , , VG., V,-V,, complex, 327, 338 vacancies, divacancies, 0 impurities, vacancy-0 pairs, 327,337-340 change in density of states from removal ofGa, 342 charge density contour plots, 343,344 density of states of principal bands, 347 flaw-stateenergy variation with site potential, 348 fundamental limitation, 336 suggested remedy, 336 general formulation, 328-336 convergence problems, 334 inclusion of long-range potential, 334 improving simplicity and ease of calculation, 335 optical cross sections of various levels, 345,346 Grinding of crystal, 1 1,8 1 H Heat treatment, 44-49, 80, 81, see also Thermal annealing High-pressure LEC technology, 6-23, 94, 95, 159-229, see also LEC growth

INDEX

Huang-Rhys factor, 282-291,302 Hydrogenic impurity, 247,250 photoionization cross section, 250,25 1 photoneutralization, 25 1 I IC devices, 143- 154, see also MESFET backgating, 148- 151, 195 fabrication, 143- 146, see also MESFET performance, 146- 15 1 use of LEC material, 229, see also LEC growth Imperfections, see Crystalline imperfections; Defects Impurities, see also Acceptors; Compositional purity; Donors; Impurity levels; Ionized impurities B, 24-28, 101, 102, 192-195,204, see also Boron C, 4,24-26,34, 100- 102, seealsoCarbon effective segregation coefficient, 39 Cr, 4, 23-26, 29, 30, 36-38, 76, 92, 95, 98-102, 106-109, 150, 193, 209-21 1,221,223,237,242,287, 288, 296,340, see also Chromium major electrically active centers, 208 0.073-0.078-eV acceptor, 208, see also Acceptors carbon acceptor, 208, see afso Acceptors; Carbon EL2 deep donor, 208, see also Donors; EL2 level 0,4,24,25,29, 100- 102, see also Oxygen residual, 36-44, 208-21 1 effective segregation coefficient, donors, 39 S, 24, 25, 81, 98, see also Sulfur Se, 8 1, see also Selenium Si, 4, 23-28, 56-60, 66-81, 98, 101, 102, see also Silicon profiles of implants, 57, 66-69, 115, 121, 137, 139, 140 striations, 22, 23 tabulation, 24,25, 101, 102, 193 Impurity analysis, 99- 102, 197,208-21 1 AES, 100, see also AES ASES, 23,26, 100, 132, see also ASES PITS, 197,209- 2 1 1, see also PITS LEC material, 209-21 1

369

SIMS, 23-25,48, 100, 126, seealso SIMS SSMS, 23,26, 100- 102, see also SSMS Impurity levels, see also Acceptors; Defects; Donors; Impurities, Ionized impurities 0.073-0.078-level, 34, 38-44, 201 -206, 208 anti-site defect, 205, 206 boron complex, 4 1-44 excess Ga, 38, 39 boron-defect complex, 41 -44 C, 4, 34, 37, 39,47,48, see also Carbon calculated energies, 327, 337- 340, 347 - 349, see also Green’s function method compensation ratio, 74,75, 80, see also Compensation effect of annealing, 80 complexes, 40-44, 241,242, see also Complexes Cr, 4,8,29,30,36-38, seealsoChromium EL2,29,32, 34,35,44-51,53,98-100, 108, 109, 148, 196,200,208, see also EL2 level optical absorption, 35 out-diffusion, 49, 5 1 0 , 4 , 2 9 , see also Oxygen Si, 4, 23-28, 56-60, 81, see also Direct ion implantation; Ion implantation; Silicon Te implant, 1 13, 141, see also Tellurium traps, 209-21 1,236-238, see also PITS; Trap LEC material, 208 -2 11 Inclusions As precipitates on dislocations, 50 Ga, 187 Integrated circuits, 3, 5, 152- 154, see also IC devices Ion implantation, 3,4, 55-81,90-93, 109- 146,212-226, see also Direct ion implantation; Electrical properties activation efficiency of implants, 56 -60, 69-71,76-78, 123 effect of annealing, 8, 123, see also Annealing annealing conditions, 65, 80, 8 1, 1 19- 125, 135- 143,221, see also Thermal annealing beam energy, 66 - 7 1, 112 carrier concentration profiles, 57,66-69,

INDEX

Ion implantation (con?.) 113-1 18, 121, 122, 127, 128, 132, 137, 139, 140,217-222, seealso specific dopant Cr implant, 221 Seimplant, 115-118, 127, 132, 139, 140, 2 16, 2 17, see also Selenium Si implant, 57, 115, 137, 139, 140, 219, 220, see also Silicon S implant, 114, 128, 129, see also Sulfur Si3N, cap, 1 13- 123 SiO, cap, 115, 120- 122 Te implant, 113, 141 co-implantation Se, Ga, 139 Se, Si, 140 S, Si, 81 differential activation efficiency of implant, 58 diffusion broadening, 67 effect of Cr, 69- 72,76,77 FET fabrication, 2 13-226, see also FET Hall mobility, 57-61, 71-73, 75, I28 - 132, see also Mobility high doses, 134- 143 IC fabrication, 143- 146,213-226, see also MESFET implant conditions, 110- 119 implanted Si concentration, 52, 57,66, 68,69, 70-72, 74, 77, 112, 115, 121, 135, 137, 139, 140,219,220 implant profiles, 57,66-69, see also specific dopant carrier concentration, 113- 1 18, see also Electrical properties donor concentration, 66-69, see also Donors effect of variability, 162 uniformity, 68, 133, 134 MESFET fabrication, see MESFET range of implant, 65-69, 112 recoil implantation, 63 selective implantation fabrication sequence, 63-65 sheet resistance Se implant, 138 Si implant, 135 Te implant, 141 substrate influence, 119, 120, 125 - 135, 216-222 temperature effect, 119, 120

Ionization energies, see Activation energy Ionized impurities, see also Acceptors; Donors; Impurities; Impurity levels concentration, 36,48,52, 57, 66 implanted Si, 52, 57, 66, 68-72, 74, 77, see also Silicon major electrically active centers, 208, see also specific dopants 0.073-0.078 acceptor, 208, see also Acceptors carbon acceptor, 208, see also Acceptors; Carbon EL2 deep donor, 208, see also Donors; EL2 level Isocoric impurity, 240 Isoelectronic impurity, 239 Isovalent impurity, 239,240

JFET. 2 12 L LEC (liquid-encapsulated Czochralski) growth, 5-23,93-99, 159-229, see also Crystal growth advantages, 5, 109, 161, 211,222-226, 229 characterization of product, I96 - 2 1 1 capacitance transient spectroscopy, 196, 197 Hall effect, 196, see also Mobility; Electrical properties optical absorption, 196, 197,200-202, see also Optical absorption studies photoluminescence, 197, see also Photoluminescence PITS,197, see also PITS resistivity, 196, 199, 208, see also Resistivity crystalline imperfections, see Crystalline imperfections crystal quality, 167- 192 crucible material, see Crucible depletion voltage, 225, 226 device applications, 2 12- 226, see also Device fabrication; FET;IC devices; MESFET diameter control automatic, 8, 9, 167

INDEX

coracle technology, 8 - 1 I, 166 manual, 8- 10, 166 dislocation densities, see Dislocations high-pressure technique, 6-23, 94, 95 IC applications, 159-229, see also Device fabrication; FET; IC devices; MESFET impurity striations, 22, 23 low-pressure technique, 95 - 102 Melbourn puller, 5-8, 94, 163 pinch-off voltage, 222-225, see also Pinch-off voltage reproducibility of product, 222-224, 227 seed rotation, 20-22, 52-55, 164 technique description, 163- I67 temperature fluctuations in melt, 2 1 thermal gradients in melt, 17, 19-22 traps, 209-21 1,236-238, seealsoTrap twinning, 12-14, 167, 182-187, 192, 194, see also Twinning uniformity of product, 20-23, 52-55, 222-221, see also Uniformity Liquid-encapsulated Czochralski method, see LEC growth Liquidus, 44 Localized vibrational mode far-infrared spectroscopy, see LVM Low-pressure LEC technology, 95 - 102, see also LEC growth LPE (liquid-phase epitaxy), 94, 103- 105 buffer layer growth, 103- 105 Luminescence, see Photoluminescence LVM (localized vibrational mode far-infrared spectroscopy), 26, 192 boron determination, 204 carbon determination, 26, 192, 207

M Mass spectrometry, 23, 26, see also SSMS ASES, 26, see also ASES SIMS analysis, 23-25, see also SIMS Materials preparation, 93- 109, see also Crystal growth; LEC growth; Materials processing buffer layer growth, 103- 105 camer concentration, 104, 105 camer mobility, 104, 105 crucible material, see also Crucible PBN, 8,28,96, 192- 195, see also PBN quartz/silica, 8, 27, 31, 96, 192-195

371

impurity analysis, 99- 102, see also Impurity analysis semi-insulating material, ingot growth, 93-102 Bridgman, 4, 7,24,29, 93, 94 gradient freeze, 4, 24, 29, 93, 94 LEC, 93-99, see also LEC growth LPE, 94, 103- 105, see also LPE MBE, 92,94, 103, 105, see also MBE OMVPE, 103, 105, see also OMVPE VPE, 94, 103, 105, see also VPE Materials processing, 8 1- 83, see also LEC growth; Materials preparation grinding of crystal, 11 , 81 importance of substrate quality, 8 1-83 MBE (molecular beam epitaxy), 92, 94, 103- 105 buffer layer growth, 103- 105 Melbourn crystal puller, 5 - 8, 94, 163 Melt composition, see also Stoichiometry effect on electrical properties, 32-36, 41 -44, 196- 198, see also Electrical properties MESFET (metal -semiconductor field effect transistor), 3-6,90-92, 113, 123, 125, 128, 133, 134, 143, seealsoFET device fabrication, 63-65, 78-81,90-93, 143-146,212-216 Microwave applications, 3 Mid-gap centers, 233x see also Deeplevel centers; Flaw MISFET (metal - insulator- semiconductor field effect transistor), 2 12 Mobility, 34, 36, 51, 53-55, 57-62, 71-75, 119, 121-123, 128-132, 198,seeaho Electrical properties carrier-concentration dependence, 59 depth dependence, 6 1 implanted layers, 57, 128 drift vs. electron concentration, 59 vs. electron concentration, 59,72,73,75 implanted layers, 57-61, 71-75 S, 128, 129 Se, 130, 132 Si, 71 -75 melt composition effect, 34, 198 radial variation, 54, 55 stoichiometry effects, 34, 198 surface, 61 uniformity considerations, 52 - 55, see also Uniformity

372

INDEX

Molecular orbital approaches, 309 - 329 cluster-Bethe-lattice method, 319, 320 defect molecule method, 309 - 3 1 1 extended Hiickel theory cluster approach, 311-313 Xa-scattered-wave self-consistent cluster method, 313-319 calculated charge distribution, 3 18 calculated energy-levelspectra, 3 16 use of 17-atom cluster for GaAs, 315-318 various charge states of Cr,,, 3 19 Multiphonon transitions, 299- 304, see also Radiationlesstransitions 0

OMVPE (organometallic vapor-phase epitaxy), 103, 105 Optical absorption studies, 35, 196, 197, 200-202, see also Absorption coefficient;Radiative transitions 0.073-0.078-eV acceptor, 38,201 -203 EL2 level, 35, 200, 201 Oxygen, 4,24,25,29, 100- 102, 195,211 Cr - O doping, 29 Ga20, 28 Ga20,, 28 getter, 196 in semi-insulatingmaterial, I95 P PBN (pyrolytic boron nitride) crucible, 8, 28,49,96, 163, 164, 192- 195,211 Phase diagram, 44 Phonon-assisted optical transitions, 282 -293, see also Photoionization; Radiationless(multiphonon) transitions configurational coordinate diagram, 283, 290, see also Configurational coordinate diagram electron-phonon coupling, 282-287 Franck- Condon shift, 283 -285, 287-293,296, see also FranckCondon shift Huang-Rhys factor, 282-291,302 Stokes shift, 283,284 photoionization, 283-286, see also Photoionization

photoneutralization, 287, see also Photoneutralization small polaron theory, 290 Photocapacitance measurements, 197,258, 259 Photoinduced transient spectroscopy,see

PITS Photoionization, 249-251,283-286,294, 297,298,350-352, see also Camer capture and emission mechanisms; Flaw; Phonon-assisted optical transitions cross section billiard-ball model, 272-277, 280, 28 1 bridging model, 279-281 delta-function potential model, 255-260,263 evanescent wave approach, 350,351 experimental data, 255,258-260,263 hydrogenic donor, 250,25 1 quantum-defect model, 262-264,280, 28 1 related to critical points in density of states, 350 evanescent states, use of, 350, 35 I free energy of ionization, 296 information available, limitation, 267 phonon coupling effects, 285,286, see also Phonon-assisted optical transitions phonon emission and absorption considerations, 282 - 293, see also Phonon-assisted optical transitions photocapacitance measurements, 197,258, 259 superlattice approach, 35 I Photoluminescence, 38, 39,48, 197, 20 1 - 203 0.073-0.078-eV acceptor, 38, 39, 201 -203 EL2 level, 20 1, 202 spectra, 38, 39, 48, 201, 202 Photoneutralization, 249-25 1,287,288,352 cross section, 25 1, 287 experimental data, 287 hydrogenic acceptor, 25 1 phonon coupling effects, 287 threshold, 288 Pinch-off voltage, 65, 79,213,217, 218, 222-225 PITS (photoinduced transient spectroscopy), 197,209-21 1

373

INDEX

traps observed in LEC GaAs, 208 - 2 I 1 Precipitates As, 190 As (dislocation decoration), 50 Ga inclusions, 187 Pseudopotential representations, 320- 328 calculated electron energies, V, and V,, defects, 326

Q Quantum-defect model, 260-264, 280, 281 applicability, 25 I, 252, 280 photoionization cross section, 262,263, 280,28 1

R Radiationless (multiphonon) transitions, 299-304, 307, see also Carrier capture and emission mechanisms; Phononassisted optical transistions capture cross section, 300,302, 307, see also Capture coefficient configurational coordinate diagram, 283, 301 - 303, see also Configurational coordinate diagram phonon cascade, 299, 300 two-stage capture process, 300 - 302 Radiative transitions, 249 -25 1, 297-299, see also Capture coefficient;Camer capture and emission mechanisms; Optical absorption studies; Photoionization; Photoluminescence; Photoneutra1izat ion capture coefficient, 279 -299, see also Capture coefficient photoionization, 249 -25 1, see also Photoionization photoneutralization, 249,25 I, see also Photoneutralization Recombination center, 236-239, see also Auger recombination Resistivity, 29-31, 33, 34, 43, 52, 196, 199, 208, see also Electrical properties implanted layers, sheet resistance, 133, 135, 138, 141, 142 melt composition effects, 32-36 semi-insulating material, 30 sheet resistance, 53-56, 133- 135, 138, 141, 142

stoichiometry effects, 196, see also Stoichiometry uniformity, 52-55, 133, see also Uniformity S Scattering, see Charge carrier scattering Schottky barrier, 46 Selenium, 8 1 diffusion coefficient, 125 implant, 81, 115-119, 122-125, 127, 130, 132,135,135,139,140,216,217 with Ga, 139 with Si, 140 Semi-insulating material, 3, 4, 8, 29- 3 1, 34-36,90-103, 195-211,seealsoEL2 level; Impurity levels; LEC growth; Substrates control of metal composition, 32 - 36 crucible/encapsulant effects, 30- 32, see also Crystal growth; Encapsulation energy diagram of shallow levels and deep traps, 99 residual impurities, 36-45, see also Impurities Silicon, 4, 22-28, 56-60, 66-81, 98, 101, 102, 192- 195, see also Donors; Electrical properties; Impurities; Impurity levels; Ion implantation amphoteric behavior, 57-59,73-81 diffusion coefficient, 125 effect of [OH] in B,O, encapsulant, 26, 27, 194, see also Encapsulation implantation, 52, 56-81, 112, 115, 121, 135, 137, 139, 140,219, 220, seealso Direct ion implantation profiles, 52, 57,66-69, 115, 121, 137, 139, 140,219,220 co-implantation with S, 8 1 co-implantation with Se, 140 Silicon nitride, 62-65, 75, 113-123, 133, 135-140, 165, 166 coracle application, 10, 166 refractive index, 62,63 SIMS (secondary ion mass spectroscopy), 23-25,48, 100, 126, 192,204,221 boron determination, 24-28,48,204 chromium determination, 22 1 iron determination, 48 manganese determination, 48

374

INDEX

Square-well potential model, 267-27 I bridging version, 27 I , 278 -28 1 photoionization cross section, 279 -28 1 SSMS (spark source mass spectroscopy), 23, 26, 100- 102 Stoichiometry As-rich melts, 32-34, 44, 45, 50, 79, 108, 192, 199,202 As vaporization, 33 effect on 0.073-0.078-eV acceptor, 34, 38-42,203-205,211,227, 228 effect on dislocations, 170, 174, 182 effect on EL2 concentration, 29, 32, 35, 44,49, 196,227, see also EL2 level effect on resistivity and mobility, 33 - 36, 41 -44, 196- I98 effect on thermal stability, 5 1, see also Thermal stability effect on twinning, 184-186, 192 Ga-rich melts, 32-34, 38-44, 108, 199, 202,227 key to reproducibility in growth, 227, 228 melt composition determination, weight-in/weight-out technique, 33 Stokes shift, 283, 284 Substrates, 3 - 5, see also Semi-insulating material carrier concentration profiles, 107, 108 importance of quality, 8 1-83, 162, 2 16-222 impurities, 4, see also Impurities; Semi-insulatingmaterial influence on implanted layer, 119, 120, 125-135,216-222 temperature effect, I 19, 120 material requirements, 3,4, 8 1, 83 qualification procedure, 55 thermal stability, 44-52, 106- 109 Sulfur, 24, 25, 81, 98, 114, 119, 128, 129 co-implantation with Si, 8 1 diffusion coefficient, 125 implant,81, 114, 119, 128, 129

T Tellurium, 98, 106, 113, 125, 141 with chromium, 106 diffusion coefficient, 125 implant, 113, 141 TEM (transmission electron microscopy),

microdefect studies, 187 BF (bright-field) micrographs, 187- I89 black-and-white contrast microstructures, 190 dislocations, 187- 190 precipitates, 190 Thermal annealing, 4,29,45-49,54, 65, 80, 81, 113-125, 221,seealso Annealing effect on deep levels, 29,45 DLTS measurements, 45 -47 implanted layers, 65, 80, 81, 119- 125, 135-143,221,222 plasma nitride encapsulation, 62 - 65, 75, 113-123, 133, 135-140 SiOz encapsulated, 115, 138, 139 unencapsulated, 75 thermal conversion, 4,46 - 49, 5 1, 109, 22 1,222 Thermal conversion, 4, 46 - 49, 5 1, 109, 221,222 Thermal stability, 44-52, 106- 109, 142 implanted layers, 142 influence of stoichiometry, 5 I Trap, 209-21 1,236-238 detected by PITS, 208 -2 1 1 energy level diagram, 99 self-trapping, 303, 304 Twinning, 12-14, 167, 182-187, 192, 194 impeding large-diameter growth, 12 importance of moisture in B,O, encapsulant, 13,27, 194, see also Encapsulation melt stoichiometry, 184- 186, 192 U

Uniformity, 20-23, 52-55, 68, 132- 134, 222-227 horizontal Bridgman vs. LEC substrates, 222-226 implant profiles, 68, 133, 134, see also Direct ion implantation; Ion implantation impurity striations, 20 - 23 pull-speed effects, 52- 5 5 radial variations, 52-55 electrical properties, 52 - 54 round substrates, 5, 11 seed rotation effects, 52-55

375

INDEX V

VPE (vapor phase epitaxy), 94, 103, 105 buffer layer growth, 103, 105 mobility of n-Si layer, 73 OMVPE (organometallic VPE), 103, 105

W

Wafer processing techniques, 8 1- 83 edge grinding, 8 1 wafer flatness requirement, 82

Contents of Previous Volumes Volume 1 Physics of 111-V Compounds 111-V Compounds Franco Bassani, Methods of Band Calculations Applicable to 111-V Compounds E. 0. Kane, The k . p Method V. L. Bonch-Bruevich. Effect of Heavy Doping on the Semiconductor Band Structure Donald Long. Energy Band Structures of Mixed Crystals of 111-V Compounds Laura M. Roth and Petros N. Argyres, Magnetic Quantum Effects S.M. Puri and T . H. Geballe, Thermomagnetic Effects in the Quantum Region W . M . Becker, Band Characteristics near Principal Minima from Magnetoresistance E. H. Putley, Freeze-Out Effects, Hot Electron Effects, and Submillimeter Photoconduc. tivity in InSb H. Weiss. Magnetoresistance Betsy Ancker-Johnson, Plasmas in Semiconductors and Semimetals C. Hilsum, Some Key Features of

Volume 2 Physics of 111-V Compounds M. C. Holland, Thermal Conductivity S. 1. Novkova. Thermal Expansion U.Piesbergen, Heat Capacity and Debye Temperatures C. Giesecke, Lattice Constants 1.R. Drabble. Elastic Properties A . U.Mac Rae and G. W . Gobeli, L o w Energy Electron Diffraction Studies Robert Lee Mieher, Nuclear Magnetic Resonance Bernard Goldstein, Electron Paramagnetic Resonance 7. S. Moss. Photoconduction in 111-V Compounds E. Antontik and J . Tauc, Quantum Efficiency o f the Internal Photoelectric Effect in InSb G. W . Gobeli and F. C. Allen. Photoelectric Threshold and Work Function P . S.Pershan, Nonlinear Optics in 111-V Compounds M. Gershenzon, Radiative Recombination in the 111-V Compounds Frank Stern. Stimulated Emission in Semiconductors

Volume 3 Optical of Properties 111-V Compounds Marvin Hass. Lattice Reflection William G. Spitzer, Multiphonon Lattice Absorption D. L. Stienvalt and R. F. Potter. Emittance Studies H. R. Philipp and H. Ehrenreich. Ultraviolet Optical Properties Manuel Cardona, Optical Absorption above the Fundamental Edge Earnest 1.Johnson, Absorption near the Fundamental Edge John 0.Dimmock, Introduction to the Theory of Exciton States in Semiconductors E . Lax and J . G. Mavroides, Interband Magnetooptical Effects

376

CONTENTS OF PREVIOUS VOLUMES

377

H. Y. Fun, Effects of Free Carriers on Optical Properties Edward D. Palik 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. Goryunovu, A. S. Borschevskii, and D. N . Treriakov, Hardness N . N . Sirota, Heats of Formation and Temperatures and Heats of Fusion of Compounds AmBV Don L. Kendall, Diffusion A. G.Chynoweth, Charge Multiplication Phenomena Robert W. Keyes, The Effects of Hydrostatic Pressure on the Roperties of 111-V Semiconductors L. W. Aukermun, Radiation Effects N . A. Goryunovu, F. P. Kesamunly. and D. N. Nasledov, Phenomena in Solid Solutions R. T. Bate, Electrical Properties of Nonuniform Crystals

Volume 5 Infrared Detectors Henry Levinstein, Characterization of Infrared Detectors Paul W. Kruse, Indium Antimonide Photoconductive and Photoelectromagnetic Detectors M. B. Prince, Narrowband Self-Filtering Detectors Ivars Melngailis and T. C. Hurmun. Single-Crystal Lead-Tin Chalcogenides Donald Long and Joseph L. Schmir, Mercury-Cadmium Telluride and Closely Related Alloys E. H.Pulley. The Pyroelectric Detector Norman B. Stevens, Radiation Thermopiles R. J . Keyes and T. M.Quisr, Low Level Coherent and Incoherent Detection in the Infrared M. C. Teich, Coherent Detection in the Infrared F. R. Arams, E. W. Surd, B. J . Peyton, and F.P. Pace, Infrared Heterodyne Detection with Gigahertz IF Response H. S.Sommers, Jr., Microwave-Based Photoconductive Detector Robert Sehr and Rainer Zuleeg, Imaging and Display

Volume 6 4 e ~ t i o nPhenomena Murruy A. Lampert and Ronald B. Schilling, Current Injection in Solids: The Regional Approximation Method Richard Williums, Injection by Internal Photoemission Allen M. Burnett, Current Filament Formation R. Baron and J. W . Muyer, Double Injection in Semiconductors W. Ruppel, The Photoconductor-Metal Contact

Volume 7 Application and Devices: Part A John A. Copeland and Stephen Knight, Applications Utilizing Bulk Negative Resistance F. A. Pudovuni, The Voltage-Current Characteristics of Metal-Semiconductor Contacts P. L. Hower, W . W. Hooper, B. R. Cuirns, R. D. Fairman, and D. A. Tremere, The GaAs Field-Effect Transistor

378

CONTENTS OF PREVIOUS VOLUMES

Marvin H. White. MOS Transistors G.R. Anfell. Gallium Arsenide Transistors T.L. Tansley, Heterojunction Properties

Volume 7 Application and Devices: Part B T. Misawa, IMPA'IT Diodes H . C. Okean. Tunnel Diodes Robert 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. Srirn. Band Structure and Galvanomagnetic Effects in 111-V Compounds with Indirect Band Gaps Rofand W . Ure, Jr., Thermoelectric Effects in 111-V Compounds Herbert Piller. Faraday Rotation H . Barry Bebb and E. W . Williams, Photoluminescence I : Theory E. W . Williams and H . Barry Bebb. Photoluminescence 11: Gallium Arsenide

Volume 9 Modulation Techniques B. 0.Seraphin, Electroreflectance R. L. Aggonoal, Modulated Interband Magnetooptics Daniel F. Blossey and Paul Handler, Electroabsorption Bruno Batz. Thermal and Wavelength Modulation Spectroscopy Ivor Balslev. Piezooptical Effects D. E. Aspnes and N.Borrka, Electric-Field Effects on the Dielectric Function of Semiconductors and lnsulators

Volume 10 Transport Phenomena R . L. Rode, Low-Field Electron Transport J. D. Wiley, Mobility of Holes in 111-V Compounds C. M. Wove and G. E. Stillman, Apparent Mobility Enhancement in Inhomogeneous CWStals Roberr L. Peterson, The Magnetophonon Effect

Volume 11 Solar Cells Harold J . Hovel, Introduction; Camer Collection, Spectral Response, and Photocument; 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. Eiseman, J . D. Merriam, and R . F. Potter, Operational Characteristics of Infrared Photodetectors Perer R. Bran. Impurity Germanium and Silicon Infrared Detectors

CONTENTS OF PREVIOUS VOLUMES

379

E. H. Putley, InSb 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. Wove, 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 Zunio, Materials Preparation; Physics; Defects; Applications

Volume 14 Lasers,Junctions, Transport N . Holonyak, Jr. and M. H. Lee, Photopumped 111-V Semiconductor Lasers Henry Kressel and Jerome K. Butler, Heterojunction Laser Diodes A. Van der Ziel. Space-Charge-Limited Solid-state Diodes Peter J. 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 Nussbaum, 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. Whitsett, J . G. Broerman, 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

Volume 18 Mercury Cadmium Telluride Paul W. Kruse, The Emergence of (Hg,-,Cd,)Te as a Modem Infrared Sensitive Material H. E. Hirsch, S. C. Liang, andA. G. White, Preparation of High-Purity Cadmium, Mercury, and Tellurium W.F. H.Micklethwaite, 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. Sood, and T.J . Tredwell, Photovoltaic Infrared Detectors M.A. Kinch, Metal-Insulator-Semiconductor Infrared Detectors

Volume 19 Semi-Insulating GaAs G. F. Neumark and K. Kosai, Deep Levels in Wide Band-Gap 111-V Semiconductors David C. Look, The Electrical and Photoelectronic Properties of Semi-InsulatingGaAs R. F. Brebrick, Ching-Hua Su, and Pok-Kai Liao, Associated Solution Model for Ga-In-Sb and Hg-Cd-Te

Yu. Ya. Gurevich and Yu. V. Pleskov, Photoelectrochemistry of Semiconductors

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