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

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SEMICONDUCTORS AND SEMIMETALS VOLUME 20 20 Semi-Insulating GaAs Semi-Insulating

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SEMICONDUCTORS AND SEMIMETALS Edited Edited by R. K. ALBERT C. BEER VOLUME VOLUME 20 Semi-Insulating GaAs

1984 1984

Diego Diego SZo

@@ 1984, BY THIS BY A N Y

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32887 32887

by by

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Contents Contents OF CONTRIBUTORS .. PREFACE . .

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vii ix ix

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3 66 23 23 29 55 81 84 84

Chapter Chapter 11

of GaAs

D.

G. K. List ofSymbols ofSymbols .. .

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

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

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Chapter 2Chapter 2 C. List of Acronyms of

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I. Introduction Introduction .. ..

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11. Materials Materials Preparation . . . .Preparation . .

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

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Chapter 33 G aAs C,G.C, K. I.

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89 89 90 93 93 109 143 151 154 154

P. Oliver

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D. List ofSymbols ofSymbols .. .. .. . Introduction Introduction .. .. ..

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159 161

vi 11. LEC-Growth Technique Technique .. 111. Crystalline Quality Quality . .

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

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163 163 167 192 192 212 226 226 230 230

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S. 234 234 List of Symbols . . . . . . 235 235 I. Introduction Introduction .. . . 242 242 11. Quantum-Mechanical View Quantum-Mechanical of Flaw States States. . . . Ill. Effective Mass Formalism: Formalism: Its for Its Limitations Deep-Level Centers Limitations Centers .. 245 245 IV. Delta-Function Delta-Function and Quantum-Defect Potential Potential Quantum-Defect . . Models . . Models 25 1 1 V. Electronic Electronic Transition Transition Phenomena Flaws, and the Phenomena the Square-Well Involving Square-Well Involving Potential and Potential Billiard-Ball Models . . . . 267 267 309 VI. Techniques Based Techniques on Molecular Molecular. Orbitals . Orbitals Pseudopotential Pseudopotential Representations .. . . Representations . . 320 320 328 328 VIII. VIII. Green’s Function Function Method . . Method . . . . IX. Brief Notes on Other Other Approaches . . Approaches .. . . 349 353 References . . . . . . . .

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CONTENTS OF PREVIOUS VOLUMES. .

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363 363 376 376

List of Contributors Contributors

Defense Electronics Operations, Microelectronics Research and Development Center, Rockwell International International Corporation, Thou59) sand Oaks, Oaks, California 91360 (1 California D. D. Westinghouse Research Westinghouse and and Development Center, Pitts- Pittsburgh, Pennsylvania 15235 (1) S. Oregon Graduate Center, Graduate Beaverton, Oregon 97006 (233) T. Westinghouse Research Westinghouse and Development Center, Center, Pitts- Pitt burgh, Pennsylvania 15235 (1) R. R. Defense Electronics Operations,MicroelectronicsResearch and and Development Center, Rockwell International International Corporation, Thousand Thousand Oaks, California 91360 (159) G. WestinghouseResearch Westinghouse and Development and Center, Pitts- Pittsburgh, Pennsylvania 15235 (1) Defense Electronics Operations, Microelectronics Research and Development Center, Rockwell International International Corporation, Thou1 59) 59) sand Oaks, California Oaks, 91360 (91360 R. R. D. Defense Electronics Operations, Microelectronics Research and Development Center, Center, Rockwell Rockwell Corporation, International Interna Thousand Oaks, California 91360 (1 59) H. M. WestinghouseResearch Westinghouse and Development and Center, Pittsburgh, Pennsylvania 15235 ( 1()1 ) D. Defense Electronics Operations, Microelectronics Research and Development Center, Rockwell Rockwell International Corporation, International Thou- Thousand Oaks, California Oaks, 91360 (1 59) C. G. Defense Electronics Operations, MicroelectronicsResearch and Development Center, Rockwell International International Corporation, Thousand Oaks, California 91360 (159) 77 90278. 90278.

vii

viii

R. R. Defense Electronics Operations, Microelectronics Research and Development Center, Rockwell International Corporation, Thou- Thousand Oaks, California Oaks, 91360 (1 59) Oregon Graduate Center, Graduate Beaverton, Oregon 97006 (233) A. Hewlett-Packard Laboratories, Palo Alto, Alto, California 94304 (89) L. L. B. Westinghouse Research Westinghouse and Development Center, Pittsburgh, Center, Pennsylvania 15235 (1) (1) R. R. N. Westinghouse Research Westinghouse and and Development Center, Pitts- Pittsburgh, Pennsylvania 15235 (1) (1) WestinghouseResearch Westinghouse and Development Center,Pittsburgh, Center, Pennsylvania 15235 (1)

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88

Preface

The The advent of monolithic monolithic GaAs integrated circuits is is having a broad broad impact impact microwave on on signal processing and and power amplification. Impressive improvements are being are made in in the performance the and cost effectiveness of advanced systems for military radar and telecommunication as telecommunicatio well as in digital integrated circuits for ultra-high-speed or or fifth generation A multibillion dollar dollar market for for GaAs analog, digital, and computers. computers. optoelectronic integrated circuits is predicted for for the the with estimates 1993 made. as high as eight billion dollars in 1993 being In the the semi-insulatingGaAs was made by float-zone refining and the the by bombardment with bombardment electrons, neutrons, and neutrons, protons. In the the standard standard preparation preparation involved thetechnique the addition of technique chromium addition chromium the or or use of native defects (the EL2 (the center) center) Fe, and Zn, Zn, and Cd orimpurities-either or or or preferentially added. High-purity aluminum aluminum oxide, aluminum aluminum natural natural nitride, nitride, boronornitride or crucibles nitride were used. The purity of the gallium and the the arsenic was comparable with that that available today, as as was the the GaAs produced. the the group at the the Naval Research Laboratory, as as well as In the the others, revived much much of the the dormant technology dormantof the the and and added added further further improvements. High-purity undoped undoped semi-insulating GaAs was prepared. High-pressure liquid-encapsulated Czochralski (LEC) pullers, developed at the Royal the Radar and Radar Signals Establishment and and manufactured manufa by Cambridge Instruments, provided Instruments, an in in situ method situ of reacting gallium and and arsenic plus a technique for growing low-cost, large-diameter, stable, technique meeting high-resistivity GaAs single crystals. A low-pressure technique for the same the objectiveswas developed at Hewlett-Packard.In In this volume, this these methods of crystal growth, including means for for determining crystal determining quality, quality, electrical and and optical properties related to impurities impuritiesdefects, and andaspoint point well as use of direct ion ion implantation for implantation the preparation preparation of integrated circuits, are explained are by experts working in this field. this The group The at the Westinghouse Research and Development Center used the the Melbourn (Cambridge Instruments) puller Instruments) to grow highquality GaAs 1, details Chapter of this this crystals, with diameters ranging diameters from 2 to 4to4in. in. In In Chapter process are described, are including dislocation distributions and distributions the effect of water in in the boric theoxide on twinning. on Thermal gradients, Thermal asymmetries, and

ix

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

PREFACE

xi

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

R. R. K. WILLARDSON WILLA C. BEER


SEMICONDUCTORS AND SEMICONDUCTORS AND SEMIMETALS. VOL. 20

11

High-Purity LEC Growth and Growth Direct of GaAs for Monolithic Monolithic Implantation Implantation Microwave Circuits? G. W. K.

D. WESTINGHOUSE RESEARCH RESEARCH AND DEVELOPMENT CENTER PITTSBURGH, PENNSYLVANIA

LISTOF LIST OF SYMBOLS. . . . . . . . . . . . . . . . . . . I. INTRODUCTION .................... 11. LARGE-DIAMETER GaAs CRYSTAL GaAs GROWTH. CRYSTAL ....... I. ........... 2. ........... 3. .............. 111. COMPOSITIONAL PURITY COMPOSITIONAL . PURITY ............... 4. .................

5.

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

IV. ELECTRICAL PROPERTIES. PROPERTIES ............... 6. ............. I. .............. 8. ................. 9. 9. ................. 10. .............. V. DIRECTIONIMPLANTATION ION ............... 11. GaAs . . . . . . . . . . . . . . . . . 12. 12. .............. 13. 13. ... 14. of .......... 15. to Device Device . . . . . . . . VI. GaAs MATERIALS GaAs PROCESSING. . .PROCESSING. ........... REFERENCES. . . . . . . . . . . . . . . . . . . . .

11

33 66 66 88 12 23 23 26 29 30 30 32 36 36 44 52 55 56 56 62 66 71

I8 81 84 84

7 7Work Work supported supported by the in inDefense part part Advanced Research Projects Agency Projectsand moni- monitored by tored Office of Naval Research on Contract Contract NOOO14-80-C-0445. Present address: Present Microelectronics MicroelectronicsCenter, Center, McDonnell Huntington McDonnell Douglas Do Beach, California. California. 0 Present 0 Present address: Torrance Torrance Research Center, Hughes Aircraft HughesCompany, Company, CaliTorrance, Torrance fornia. fornia.

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

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Arc source emission source spectroscopy spectroscopy voltage Capacitance-Capacitance D D Diffusion constant constant sec-l) (cm2 (cm2 DLTS Deeplevel Deeplevelspectroscopy transient transient EL2 Main deepdonor level in undoped undoped GaAs GaAs DWS Differential weight gain signal Fraction Fraction melt solidified ff FET FET Field effect transistor transistor Ground-state degeneracy Ground-state factor factor g g cm-I)current Full channel channel current Effective segregation coefficient KK silicon implanted via donor/accept Mass action action constant constant governing governing role of implanted the the donor/acceptor interaction with interaction of arsenic arsenic vacancies on the vacancies Mass action action constant constant describing describing the the contribution contribution electron electron density density at measured measured LEC Liquid-encapsulated Liquid-encapsulatedCzochralski Czochralski LPE Liquid-phase epitaxy Liquid-phase LVM LVM Localized vibrational vibrational far-infrared mode mode spectroscopy spectroscopy MESFET Metal-semiconductor Metal-semiconductor field effect transistor transistor Ionized donor concentration (crn-9 concentration NA Residual ionized donor concentration concentration (~m-~) Ionized acceptor acceptor concentration ( c m 9 concentration Ni Residual ionized acceptor acceptor concentration (cm-’) concentration K O Intrinsic free-electron Intrinsic concentration (concentration cm3 Net donor concentration in concentration the the implanted implanted (cm-2) layer layer Free-electron concentration concentration in the the implanted layer implanted including including surface depletion depletion effects (cm+) (cm+) Free-electron concentration concentration in inlayer the the as determined implanted implanted determined by surface surface Hall-effect measurement (cm-*) measurement Concentration Concentration can be depleted that that at breakdown breakdown in an idealized parallel plate plate NSMO (ern+) geometry (ern+) geometry in the the encapsulant encapsulant Water content content Pyrolytic boron boron nitride nitride PBN Photoresist Photoresist PR Phosphosilicateglass Phosphosilicate PSG VV Electronic charge Electronic Depth of of maximum maximum implanted implanted concentration concentration Projected range of the the implanted ion implanted concentration concentration RP Projected range of the ionized ionized donor netconcentration net concentration Standard Standard cubic cubic centimeter centimeter per per minute minute sccm Secondary ion ion mass spectrometry spectrometry SIMS Spark Spark source mass spectrometry source spectrometry SSMS Implanted Implanted silicon concentration concentration (cm-7 {Si) Annealing Annealing temperature temperature Tailend section Tail of an ingot Tang Tang end Pinch-off voltage Vapor-phase epitaxy Breakdown voltage VB Electron saturation velocity saturation vast vast

c- v v

22

1. AA €€

AJ tl

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AND

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

++

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

44

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et al. al.

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

1.

AND

55

(b) (b) contain verycontain low total total concentrations of ionized concentrations impurities so impurities that that the the implanted FETimplanted channel mobility channel is not degraded; and and (c) permit fabrication of devices of predictable characteristics so that active and passive and elements can be matched in in monolithic circuit monolithic designs. Another Another important consideration important is the need the for uniformly round, largeround, by the the user and and systems area substrates. Broad acceptance of GaAs communities will communities occur only if a reliable GaAs IC manufacturing technolmanufacturing ogy capable of yielding high-performance monolithic circuits monolithic at reasonable the D-shaped slices of boatcosts is realized. Unfortunately, the characteristic grown GaAs material have been a serious deterrent to deterrent the the achievement of this goal, this since much of much the the standard semiconductor standard processing equipment equipment industry on on uniformly round round substrate developed for the the silicon IC industry relies slices. To address these needs for a reliable “siliconlike” technology base in in semi-insulatingGaAs materials processing, liquid-encapsulatedCzochralski (LEC) growth was selected over other other growth technologies because of its its ( and ( 1( 1111)1crystals ) of current capability current for producing for large-diameter, ( 100) 50- and 100-mm-diam wafers cut cut from (100)- (100)semi-insulating GaAs. The The oriented LEC oriented GaAs crystals are shown in Fig. in 1 to 1 illustrate to the significant economic benefits of large-area processing. The monolithic power amplifiers shown on on the 50-mm the slice are approximately 5 5X 2 X mm. 2 Device

1.

50-

of

GaAs slices

(100)

66

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et al.

processing on on 100-mm 1 wafers would increase the the die diefrom count 75count 5to to 300 per wafer, although the handling the and processing and costs in manufacturing manufacturing approximately independent of wafer size. In the following the sections, we report on on the growth the of high-purity, large-di(100) (100) crystals; on on assessments of the the structural perfection, structural ameter ameter compositional purity, and and electrical properties of these crystals; and upon upon evaluation of their suitability their and compatibility and for direct ion-implantation ion-implan device processing. Finally, the application of many of the wafer fabrication techniques now confined to the to silicon industry to industry produce uniform, largeuniform, area substrates in GaAs is discussed briefly. The underlying aim is aim to establish to a reproducible materials base in in order to order realizetothe the full potential of direct ion ion implantationaimplantation reliable, as as cost-effective fabrication technology of high-performance GaAs MESFET devices and integrated and circuits. 11.

1. 1.

GaAs LEC TECHNOLOGY

Liquid encapsulation was first demonstrated experimentally demonstrated by Metz et al. ( 1962) ( for the growth the of volatile PbTe crystals and has andsince been applied to the Czochralski the process by Mullin et al. (al. I 968) and and others (Swiggard otherset al., 1977; Henry and Swiggard, 1977; AuCoin et al., 1979; Ware and Rumsby, and liquid-encapsulated 1979) for the the growth of several 111-V crystals. In In Czochralski, the dissociation of the volatile As from the GaAs melt is avoided by encapsulating the the melt in in an an molten inert inert layer of boric oxide as or or and and pressurizing the the chamber with a nonreactive gas, such as nitrogen argon, to to counterbalance the As thedissociation pressure. The LEC technique has been developed intensively in in recent years, and high-pressure pullers are are now available commercially. One One is the the “Melbourn” bourn” high-pressure LEC puller (manufactured (manufactured by Cambridge Instru- Instruments, Ltd., in Cambridge, in England, and is and the the outcome of developmental outcome efforts at the the Royal Radar and Signals Establishment, Malvern, England), which is currently being introduced by introduced many laboratories many for the growth of GaP and InP crystals. With high-pressure large bulk GaAs as well as as out the the elemental elemen capability,in situ compound synthesis compound can be carried out from Ga and andcomponents, since the the boric oxide melts before excessive synthesis occurs sublimation starts starts taketoplace to (5460°C). Compound Compound rapidly and exothermally and at about about 820°C under aunder sufficient inert gas inertpres60 atm) atm) minimize to to significant sublimation of sublimation the arsenic the compo- composure (sure nent. nent.maintain maintain a nearly stoichiometric or slightly arsenic-rich melt, a slight excess of As is utilized to compensate to for inadvertent loss inadvertent of As during during the the heat-up cycle. After compound synthesis, compoundthe the chamber pressure chamber can be

1.

2.

II

AND

of

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

88

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et al. al.

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

GaAs MELTS MELTS

a.

At our laboratories, the the high-pressure Melbourn puller has been employed to develop to a reproducible growth technology for preparing for largeto nominally GaAs crystals. (100)-oriented Tech- Techdiameter diameter (up (up 100 mm), mm), (100)-oriented niques for producing crystals which are free are of major structural defects structural (such as twin as planes, lineage, inclusions, and precipitates), and and which and yield stable, semi-insulating properties without resorting to conventional Cr doping, have been successfully developed over the the course of about course 70 about experimental growths. The The work expands upon earlier LEC studies of Swiggard et al. (1977) and AuCoin and et al. (1979), who showed independently that improved that could grown from from undoped LEC purity, semi-insulating GaAs crystals could be melts when contained contained high-purity, in inpyrolytic boron nitride (PBN) nitridecruci(PBN) growth of much much larger crystals bles. The The present effort is directed at the the required for commercial GaAs processing, and exploits and the recent the availwith conjunction an an advanced ability of 150-mm-diam PBN crucibles in in conjunction technology as as embodied in the the Melbourn puller. For For high-pressure comparison purposes, GaAs crystals grown from Cr-doped melts and using and conventional fused silica crucibles have also been investigated. semi( GaAs crystalspulled from pyrolyticboron boron nitride crucibles nitride insulating ( 100) and and grown using the the differential weight signal for diameter diameter control contro 50 mm mm in in diameter and diamete shown in Fig. 3. The crystal The in Fig. 3a is nominally is 6 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 The of crystals of in the in ( 100) ( orientation has orientation relied upon upon ability the the to control the the crystal diameter diameter by continuously continuously monitoring crystal monitori of the weight gain signal (DWS). On weight and and the the instantaneous derivativeinstantaneous the the basis of these measured quantities quantities visual and monitoring and through monitoring the the TV system, adjustments to adjustments the power level made to correct to for undesirfor able changes in crystal in diameter. However, owing to reliance upon upon operator opera at times the the growth meniscus judgment judgment inability and and tothe seethe clearly at all as errors in the differential the through the boric the oxide layer, as well as systematic this method method weight gain signal due due capillary to to forces (Jordan, (Jordan, 198l), this growth results in crystalswith diameterswhich diameters vary (usually within k 5k5mm) along the boule the length, as demonstrated by demonstrated the crystals the in Figs. in 3a and 3b andand the the

1.

99

AND

H 20 mm

H

(a)

FIG.3. 3.

50-

((

3-

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

10

et al. al.

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Diameter Variation:

Control

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Diameter Variation: LEC Manual Control

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

b. “Coracle” Technology Technology

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

1.

AND

11

\loo>

TT

ll

00

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(100) (100)

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

12

R. R. N. THOMAS et

al. al.

3. CRYSTALLINE IMPERFECTIONS

Large-diameter GaAs crystals are usually are characterized by high densities the thermal thermal of dislocations ( 1(04- 1O5 cm-2), which arise as a result of the large stressesassociated with the LEC the growth of this material. this Although at present there there is scant evidence that that these relatively high-dislocation densities give rise to to harmful effects in in majority carrier carrier devices such as as MESFETs [in contrast contrast to to minority-camer devices suchminority-camer as LEDs as and laser and structureswhere structures dislocations are are known (Petroff and and Hartman, 1973) Hartman, to play a deleterious role in device performance], the the general consensus is that is GaAs of significantly lower dislocation densities will eventually be required for advanced monolithic circuit functions functions possibly andfrom and improved processing and and reliability considerations. I 1 5 mm, the the attendant attendan For LEC GaAs crystal growths at diameters diameters thermal stresses thermalare diminished are and andcrystals the thecan be grown entirely free of dislocations (Steinemann (Steinemann and Zimmerli, 1963). In these small crystals, successful dislocation-free growth depends depends primarily upon upon a Dash-type seeding (Dash, 1957) in in which dislocations in the the seed are are removed by growing a thin neck thin before increasingthe the diameter to form diameter the crystal the cone. Additional factors which have been found to found influence dislocation generation tion in these small crystals include melt stoichiometry (Steinemann (Steinemann an Zimmerli, 1963), temperature temperature gradients at the the growth interface (Brice, 1970) and and resulting the the shape of the the growth front front (Grabmaier (Grabmaier and maier 1972), and and angle the theof the the crystal cone as as emerges it it from from the the encapsulant (Roksnoer et al., 1977). Although large-diameterGaAs crystals can be cangrown free of twins and inclusions, a preponderance of experimental evidence indicates that dislocation that generation (and clustering) (and in large LEC crystals always occurs and is and almost exclusively controlled by local thermal thermal stresses. Successful growth of large dislocation-freeGaAs crystals has been observed only in in highly doped crystals, where dislocation generation is impeded by impurity-hardening effects (Seki et al., 1978). Factors governing twin formation formation dislocation and and generation in large-diin ameter GaAs ametercrystals are now are discussed.

a.

( 100) ( Crystals Crystals

The tendency The toward twinning in (in100)-oriented ( GaAs 100)-oriented crystals has often growth efforts in in the past. theAlthough the the frustrated large-diameter (100) (100) exact cause of twinning is rarely known, it has been empirically observed that the frequency the of twinning is affected is by deviations from stoichiometry (Steinemann and Zimmerli, 1963), excessive thermal stresses thermaldue duevariato to al., 1980),or instabilities in in the the of shape shape tions tions crystal in indiameter (Kotake el(Kotake the crystal the growth front associated with the emergence of the crystal the through through

1.

13

AND

the boric the oxide layer. Our early experiences indicated indicated twinning that comthat ( 100) ( to the the monly caused a change in in the crystal the growth direction from the the (22 1) )direction in in large-diameter GaAs crystals. Frequent Frequent twinning was associated with abrupt shouldering abrupt of the crystal the in the growth the of flat-topped crystals, and and the the initiation of a twin initiation plane was found to found be usually coincident with the the As facet when the the crystal diameter was diameter changed rapidly. In In this this regard, a gradual increase to the desired the crystal diameter has diameter proven to be highly effective in avoiding in twinning in in the early thestages of growth, as has as also been demonstrated in demonstrated the the case of LEC InP crystals (Bonner, 1981). To achieve reproducible growths of twin-free crystals, a growth procedure was adopted, which adopted, included the the use of vacuum baking of the boric oxide encapsulant to remove to residual moisture. This was Thisfound empirically found to be ( crystal growths and and an important factor important in reducing twinning in large in ( 100) in in maintaining high maintaining visibility of the the melt-crystal interface during growth during (Hobgood et af.,1981b). Similar findings have been reported by other other twinning that thatin in ( 100)-oriented ( 100)-orien workers (Aucoin et af.,1979), who found found crystals was associated with the use the of unbaked, high [OH]-content B20, B20, in in the the growth of LEC GaAs crystals. More recently, Cockayne et af. (1981) have definitively related the the water content content of the Bz03encapsulant to encapsulant the the generation of defect clusters in LEC in InP crystals. Statistics relating the the incidence of twinning for growths with “dry” ( and1000 ppm wt ppm [OH]) B203 [OH])are given are in in PBN crucibles. For both both types of Fig. 6 6for growths from fused Si02 and and crucibles, the the incidence of twinning within the first 75% of growth is ([OH] 500 < ppm). Appm). substantially lower when using vacuum-baked B203([OH] < growth methodology of gradual increase to crystal diameter, coupled with

- -

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IOH1 I 20 mm) is believed to be to due primarily due to thermally to induced stresses that accompany that large axial and radial and temperature gradients, temperature owing to the to large convective heat-transfer coefficient of the B20! the encapsulatinglayer and the the temperature tempera B203 near ambient the growth the differencebetween the crystal the intenor and the andB203ambient A of the thermal stresses thermalassociated with LEC growth interface. A comparison of GaAs and InP and relative to Czochralski to silicon pulled in aingaseous ambient ambient is illustrated in Fig. 7. In In contrast to contrast Czochralski-grown silicon crystals, et al., 1981) which can withstand a factor of three higher stresses (Jordan (Jordan and still be grown dislocation-free even at diameters of diameters 100 mm and larger, and can the resulting the thermal stresses thermalassociated with LEC growth of GaAs can easily

7.

of of excess (100) (100) of

al., 1981.) 1981.)

Si

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

100rnm

8.

(100)

slice

16

et al.

R. N.

silicon, have proven unsuccessful and confirm and that effects that other otherdislothan than cation multiplication from the seed the dominate dominate dislocation the the generation. To illustrate this point, point, Figs. 9a and and 9b show x-ray reflection topographs of longitudinal sections of seed-end cones for two ( 100) ( GaAs crystals corresponding to two to different cone angles: cone a relatively shallow cone approaching cone a flat top (Fig. top 9a) and aand steeper cone of cone 27 deg to the crystal the axis (Fig. 9b). 9b). Although in in both cases both dislocation-free growth was initiated by initiated the the Dashtype seeding, the dislocation-free seeding alone was alone insufficient to prevent diameters the 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-2 ( range) are confined are to the the center of the center crystal the and a layer near the crystal the periphery correspondingto regions of maximum maximum thermal stress; thermal however, severe glide plane activation in the in early stages of crystal growth, which is typically observed in in flat-topped growths (Fig. 9a), cone (Fig. (Thomas et(Thomas al., al., has been reduced by the use the of steeper cone angles 1981). At their full diameters, large 50- and 75-mm-diam and GaAs crystals exhibit radially nonuniform dislocation nonuniformdistributions with distributions maximum maximum dislocation lo4lo4range at the the center periphery center andofand the crystal the densitiesin in the the105-cm-2 with minima at about about one-half of the the radius, as shown in in Fig. 10. The The systematic variation in in dislocation density across the wafer the diameter replidiameter cates the the thermal stress thermal distribution in distribution the crystal in in excellent agreement

(a)

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1. HIGH-PURITY LEC GROWTH LEC AND DIRECT IMPLANTATION

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with the the Jordan model. Jordan The axial The dislocation distribution for distribution a 50-mm-diam crystal is observed to be relatively constant along constant the crystal the length, which again suggests that the the dislocation generation is driven by local thermal thermal stress rather than ratherby dislocation multiplication (which multiplication would produce an increase in dislocation density with length). GaAs crystals The current currentofstatus crystalline status quality in large relative to horizontal Bridgman-grown horizontal crystals of comparable comparable dimension (50-mm maximum maximum diameter)orisorillustrated in Fig. 11, where Lang reflection tion x-ray topographs of the the central wafer central areas are areas shown. In In spite of the commercial availability of small Bridgman wafers With very low dislocation (0- cm-2), Fig. 1 1suggests 11 that that in in large-area densities (0- 500 GaAs wafers somewhat similar dislocation densities ( 104-cm-2 ( range) are are observed in both Bridgman and and substrates. Since the magnitudes of the axial the and radial temperature gradients temperature exist- interface and across the the boric oxide boric layer itself help to ing at the melt the - B203 roleimportant in drive the the thermal stresses thermal in in the the solid, they play an an important determining whether determining the the crystal will dislocate at the the growth interface and during during therequired the timefor time the crystal to transit transit the boric oxide layer thickness. Reduction of Reduction thermal gradients thermal should lead to a corresponding decrease in in thermal stress thermal levels and a reduction reduction defect density. in in Thus, aThus,

1 1 . X-ray

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is 0.41

50

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19

AND

knowledge of the the thermal thermal distributions existing in indistributions the melt/encapsulant/ the high-pressure ambient ambient system is instructive in in establishing which growth parameters should be optimized to reduce dislocations. The influence The of crucible position in the the 150-mm hot zone of the the highpressure Melbourn furnace on on the the thermal profile along thermal the geometric the axis of the the system is illustrated in Fig. 12. The The profiles were measured using a a Pt- Pt1090Rh thermocouple attached attached movable to to the pullthe rod. The The data weredata measured with reference to to the crucible the bottom bottom extend and through and the the mm and 5 5cm into the the GaAs melt, the B203 the encapsulatinglayer (- 20 mm thick), inert argon inert ambient above ambient the encapsulant. the Even though the measurements the were made in the the absence of a crystal a growing (where effects due to latent latent heat dissipation and and heat conduction conduction growing up up crystal the the can can significantly modify the the thermal gradient thermal at the the growth interface), the the relative change in temperature temperature across the the system of melt/B,O, /ambient /ambient un- un der these conditions should approximate those corresponding to to the early the crystal is totally submerged in in the B203 the B203 stages of LEC growth when the the encapsulant. encapsulant . An axial thermal gradient thermal of 140°C/cm [Fig. 140°C/cm 12, curve (b)] was (b)] meaB203layer for normal normal operating conditions conditions (Le., PBN sured across the the crucible low in in heat zone, ambient pressure ambient 20 atm). When atm). the crucible is 25 mm in in the heat thezone, the the gradient increases to 18O"C/cm moved up up of the B203. TheB203. sensitivity owing to the 200°C the greater cooling at the surface the of the the B203 surface B203 to changes in in ambient pressure ambient is also is reflected in the

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GaAs

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(c) 40

20

20

R. N.

al. al.

thermal profile thermalof Fig. 12 [curve (a)], which corresponds to a factor of four four reduction in pressure. The surface temperature temperature of the the B203increases by - 100°C - when 100°C the the ambient pressure ambient is dropped from dropped 20 to 5 5atm. However, atm. the the thermal gradient thermal near the the melt surface is relatively unaffected. Moreover, growths carried out under 5-atm pressure yield crystal surfaces As loss), owing to the the higher ambient ambient with severe decomposition (due to to temperature. The The insensitivity of the the gradient across the the B203 layer to to variations in crucible position and and ambient pressure ambient indicates that varying the possibility of reducing the axial the the B203 the thickness itself may offer the best - interface. This observation This is suptemperature gradient temperature at the the melt - B203 the ported by a similar recent finding of Shinoyama al. (1980) on the growth of dislocation-free LEC crystals of InP. InP. In addition In to crystal rotation rate rotation and pull speed, the radial the uniformity of the the melt thermal thermal distribution is knowndistribution to play an an important important deter- part part in mining the the shape of the shape the growth interface and and radial the thevariations in impurity impurity incorporation, well asincorporation, having a significant as as effect on crystal diameter diameterMeasurements control. control. of the the radial temperature temperature profile at the the melt interface region of the the GaAs melt-B203 encapsulant encapsulant 150-mm in in the the hot zone of the Melbourn the puller indicate very shallow gradients of less than the melt the surface which tend tend 0.5 "C/mm 0.5 over the central the 60-mm diameter of diameter to promote relatively flat growth interfaces. Beyond this this central region, central the the radial gradient increases steeply (2"C/mm at 125-mm diameter) diameter) and is consistent with observations that that the the diameter isdiameter significantly control im-control improved by these steeper radial gradients in in the growths the of 75-mm-diam crystals in in the Melbourn the LEC system. Fluctuations Fluctuations microscopic in in growth the the rate in Czochralski in crystal growth arise because of thermal asymmetries thermal at the crystal-growth the interface. Symmetrical or or rotational impurity impurity striations are almoststriations always observed for impurities, with effective segregation coefficientsdiffering significantlyfrom seed- crucible rotation, rotation, which is conventionally em- emunity because of the the ployed. Nonrotational Nonrotational which striations, are are caused striations, mainly by turbulent turbulent melt, become increasingly important important in thermal thermal convection flows in the the al., 1977). Inhomogeneities such as these as large-volume melts (Carruthers (Carruthers are are of grave concern for device processing, particularly for submicron submicron deleterious effects on on geometries over large-area substrates, because of the the device performance and yields. and The The convective flows in a large-volume GaAs melt (viscosity 0.1 P) covered by a relatively viscous (30-P) BzO3 encapsulant encapsulant and in a and a situated turbulent high-pressure turbulent (20-atm) gas ambient ambient probably are are characterized by large Rayleigh numbers. Temperature Temperature fluctuations to convective fluctuations turbu- turbudue due lence in the melt can therefore can be expected to be quite severe. quite Measurements of the the temperature fluctuations temperature observed in ain150-mm-diam,3-kg, B,O,-en-

21

1. HIGH-PURITY LEC GROWTH LEC AND

capsulated GaAs melt in in the high-pressure the Melbourn system are shown are in melt was contained in in a PBN crucible that that was rotated at Fig. 13. The The 20 atm. The atm.measure15 rpm. The The inert argoninert ambient was ambient held constant at constant system. ments correspond to positions along the the geometric axis of the the interface (Fig. 13a) display a Temperature fluctuations Temperatureat the the AT, > 3°C > with individual temperature excursions temperature >2°C. > Over 2°C. the the total total 1Zmin time time interval shown, a somewhat systematic variation is observed is 1 min. Superimposed on this coarse this periodicity with a large period of about about is a more rapid fluctuation with a frequency of approximately 10 temperature excursions ture per minute. No minute. obvious cause (such as variations variations heater in in power or mechanical or vibrations) for the periodic the nature of nature these fluctuations was detected. Figure 13b shows the thermal fluctuations observed under under the the 1 cm 1 below the surface the of the G the aAs same conditions for conditions a position of about about melt. Here, the the amplitude of the amplitude the fluctuations is much larger than than at the the B,O,-GaAs interface. AT, is 9"C, with 9"C, individual excursions as large as as 6°C. The The fluctuation frequency is is also higher than at the the interface, -20 6 6

10

88

- 6 u u

f f

a a 44

22

(min)

13. 1

is 150

1

B203 B203

22

R. N.

et al. al.

excursions/min. Temperature Temperatureassociated fluctuations with fluctuations crystal and/or crucible rotation were rotation also explored by probing the the melt with the the thermo- thermocouple probe displaced to different positions from the the center of the center the melt. Temperature Temperaturewith fluctuations the exact fluctuations periodicity of the relative rotation rotation rate were rate observed. The The rotational rotational temperature were, temperature however, fluctuation quite small quite and were often difficult to observe because of the the larger, more more of these random random nonrotational fluctuations. nonrotational The The much largermuch magnitude magnitude temperature temperature indicates variations a much variations higher much degree of convectiveturbu- turbuGaAs melt relative to large-volume (unencapsu- (unencapsu lence for the encapsulated the are are lated) silicon lated) melts, where axial temperature temperatureof fluctuations about 1 1 fluctuations typical (Suzuki et al., 1981). 1). Preliminary investigations of impurity impuritybehavior striation in striation large-diameillustrated 14. For in in ter LEC ter GaAs crystals pulled from 3-kg melts are are illustratedFig. this this study, (1 1 1) 1 axial cross sections sliced from 50-mm 50-mm( 100)-ordiam, ( diam, 100)-orGaAs were polished to a mirror mirrorinfinish in Br-methanol Br-meth iented LEC ientedGaAs crystals a and then etched in an A-B solution to solution reveal longitudinal longitudinal striations striatio

1 11)

14.

- 0.04 - R

R

- - C2

( 100) ( LEC-grown

1.

23

AND

Nomarski Nomarski contrast contrast These interferometer. studies studies revealed interferometer. longitudinal longitudina striations striations (presumably due due to microscopic variations in in resistivity) for for undoped undoped semi-insulating GaAs grown from PBN crucibles (Fig. 14a) and low-resistivity n-type crystals pulled from fused Si02crucibles (Fig. 14b). In the the case of the the semi-insulating GaAs/PBN crystal, the the impurity impurity content c low, suggesting that the the observed striations striations correspond to to microscopic variations in variations compensation and compensation may arise from local fromfluctuations fluctuations stoichi- in in ometry. ometry. closely Thespaced The striations in striations the low-resistivity, the n-type material material (Fig. 14b) result from from variations dopant variations incorporation in in incorporation case, Si, (inSi, (in this th k,,- 0.1, - introduced from introduced the the SiO, crucible) due to fluctuations in fluctuations microscopic growth rate. rate. An even greater axially striated striated impurity impurity distrib and greater microscopic inhomogeneity is expected in Cr-doped GaAs GaAs because of the very the low segregation coefficient of chromium (k, chromium 6X 6X lo4). These investigations suggest that that further further optimization of the the thermal optimization thermal distributions distributions large-volume in in LEC melts is crucial to the the development of developm large-diameter GaAs crystals GaAs with highly uniform uniform properties a microproperties on o scopic as well as macroscopic scale. It is It speculated, based on recent on experiments with ments Czochralski-grown silicon (Suzuki et al., 1981; Braggins, 1; 1982), that that the the application of magnetic application fields across large-volumeLEC GaAs melts can have important beneficial importanteffects on on the suppression the of thermal fluctuathermal tions, with tions,corresponding correspondingin improvements microhomogeneity. improvements

--

111.

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

24 90

80

T -

70

60

11

R. N.

0 0 ((

10

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et al.

vi I

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

tt

1.

LEC

of

25

AND

&&

(s)

0.

well

~ r n were - ~ typically observed in material in grown by horizontal Bridgman horizontalor gradient-freeze methods. The reduced The concentration of concentration shallow donor imdonor purities in growths in from PBN crucibles permits undoped permits or, alternatively, Table I, I,where typical lower Crdoping levels to be utilized as shown in in X 3 X cm-3 at the crystal the seed end end Cr-dopant Cr-dopant concentrations range from 3concentrations 6 X 1015cm-3 near nearcrystal the thetang end. to 6 X The SIMS studies also indicate that LEC that growths, particularly from PBN ~ r n range) - ~ of boron. crucibles, generally result in high in concentrations concentrations 101I6cm-3 by Carbon Carbon oxygen andcannot and be cannot measured directly below about about lowthe 10I6 mass spectrometric techniques and are estimated are to be to in in the range or lower in (See Kirkpatrick et al., Chapter 3, Chapter Section 6, this this

26

N.

et al. al.

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

AND

Boric oxide is is now commercially available in six 9s 9s (0,999999) purity purity through high-purity recrystallization and vacuum-baking and procedures. Typical mass spectrometry measurements for highest grade B203 reveal the the 1-ppm wt presence of a few transition metals transition (principally, Cu and and at Fe) Fe) levels, with all other detectable other elements being below the detection the limit of limit the mass the spectrometry. Infrared absorption measurements show measurements [OH] con- condegree the the tents ranging tents from 150 ppm wt to 1000 ppm ppmdepending upon upon of vacuum baking to which to the the B203has been subjected (data supplied (data by Johnson-Mathey Chemical, Ltd.) encapsulant on encapsulant the the The influence The of the water the content content in [OH] the B203 the[OH] incorporation of Si and B and impurities B for impurities growths from fused SiO, and PBN and PBN crucibles has been investigated (Hobgood et al., 1981b). The The results are are shown in Figs. 16a and and 16b, respectively. In these measurements, low [OH] [OH] content was content assured by vacuum baking the the oxide at 1O0O0C/8hr immedi- immediately before use for crystal growth. For growths from fused SOz crucibles B Bcontent content of the the GaAs (as measured (as by SIMS) is a (Fig. 16a), the the Si and and encapsulant, with encapsulant, strong function of the the [OH] [OH]ofcontent the content having high [OH]content (> content 1000 ppm [OH]) yielding lower contents of contents Si and Bywhile concentrationsof concentrations Si nd B ndin B in the mid-10'6-cm-3 the range have been observed for growths utilizing vacuum-baked B203( 1000 >

5 X X corresponding to a total total ionized-impurity concentration concentration the low in in cm-3 range. These measurements suggest that high-purity, undoped GaAs/PBN mate1 X in X 1016-cm-3 rial contains contains residual, electrically active impurities impurities in the the range and, and, view in of in the low the concentration of concentration common shallow common donors and donors shallow acceptors detected by the SIMS analysis of this this material (lowmaterial the of 1015-cm-3range or less), this observation this poses a question as to the origin 1X 1 X 10l6cm-3 residual ionized impurity impurity concentration derived from concentration the the the the mobility analysis. Residual carbon impurity, aimpurity, shallow acceptor in in GaAs, has been suggested as the the source of this this residual electrical activity. Both secondary-ion and and spark source mass spectrometry indicate that thatpresthe the ence of carbon in both Bridgmanboth and LEC-grown and GaAs crystals, and recent et al., local vibration mode mode far-infrared spectroscopy studies (Holmes (Holmes 1982a,b; Kirkpatrick et al., Chapter Chapter 3, Section 8, this this volume) identify identify carbon as carbon the the predominant shallow predominant acceptor impurity in impurity undoped undoped Gas/ PBN substrates. Independent identification Independent and an an assessment of the the electrically active carbon carbon concentration concentration from the variable the are are temperaobtained obtained undoped, ture ture Hall-effect measurements shown in in Fig. 23 23 of two undoped, ptype, low-resistivityGaAs/PBN crystals pulled from Ga-rich melts. The data The are are al., 1978) by using a least-squares-fit fitted (Blakemore, 1962; Thomas et Thomas computer program computerto the charge the neutrality relation for the case the of compensated monovalent multiple acceptor levels:

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

38

et al. al.

R. N.

5 5 10

23. g= g 4=4

as

20 30 lRUl/T

of

40

50

of of

m* = 0.493 = m,. 0.493

concentration in concentration the low the 101s-cm-3range. The ionization energy ionization obtained obtained for the the deeper acceptor level in in the tang-end the substrate is is about 0.073 about eV, which is is about aboutlower than the the 5 5meV values of 0.077 eV (Yu et al., al., 1981) and 0.078 eV (Elliott al., al., 1982)determined from determined photoluminescence and level in in the the tang tang infrared absorption, respectively. The The occurrence of this this crystal is isin this this section suggests that that carbon the theconcentration concentration inextremely low and and thus compensated thus by residual donors. donors. Our Our studies indicate that that 0.073-eV the the acceptor level is associated with as by the photoluminescence the spectra excess Ga (Ta et al., 1982c),as illustrated 24. emission The peak (1.442 eV) associated with the free-to-bound the in Fig. 24. The al., 1)at the 0.073-eV the acceptor level is clearly is identified transition (Yu et al., 198 in Ga-rich samples (Fig. 24b) but but is conspicuously absent in all semi-insulating crystals pulled from stoichiometricor slightly or As-rich melts (Fig. 24a). Elliott et al. (1982) have recently shown that this acceptor concentration concentrati increases with increasing Ga atom atom fraction in the the melts. This observation This

1.

39

AND 1

1

1

1

1

1

1

1

1.4% eV

1

,

,

1.514 eV eV

Q Q c c

c

c

M M

1.442 eV

II

E E

24. of

10' > As illustrated in Fig. in 38, for for 15-min 1 implant these substrates the the deep-donor concentrations concentrations after after implant anneal are are still sufficiently high to provide complete compensation of residual shallow acceptor levels. However, increasing the the annealing annealing tim >> as as indicated by the the dashed curve) will further further reduce the the deepdonor donor concentration, ptype concentration, conversionand can and eventually occur. number undoped, semi-insuIn our laboratories, the growth of a large number of

50

et al. al.

R. N.

37.

of

(100) (100)

As of LEC As

LEC A-B

1. HIGH-PURITY

I a)I

51

AND

I clI

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

lating GaAs crystals GaAs from crucibles has been achieved reproducibly through very through close control of control the the time andtime temperature temperature during during the critical compounding cycle compounding and the the addition of about addition about 1 -2-mol 1 -2-mol excess to compensate for losses in this process. this Figure 39 39 shows the the Hall mobility measured on on as-grown, polished substrates substrates a a function offunction the the fraction of melt fraction solidified for several undoped, semi-insulating undoped, GaAs/PBN crystals. These crystals are characterized by high resistivities > 5> 5X X lo7 Sl cm (Fig. cm 19)and measured mobilities ranging from 4500 - 7000 cm2 V-' cm2sec-l over 90% of the crystal the length. The greatest variation usually occurs in the last-to-freeze the portion portion of the the crystal, where ionized impurity impurity scattering resulting from impurity segregation impurity effects and/or deviations of deviations the solid the from the stoichiometric composition metric may begin to dominate dominate the behavior. the transport transport loo00 r r 8 8

- -

66 44

I I

0 0

3

2

FIG.39. FIG. Measured Measured Hall Hall a function mobilityofmobility the fraction of melt solidified for solidified a number of undoped semi-insulating crystals crystalsfrom pulled stoichiometric pulled or As-rich As-rich melts. melts. by the different different data symbols. symbols. Different Differentare crystals indicated crystals

R. N. THOMAS et

52

af.

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

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

M

M

II

E, 1.0 1.0 0.8

V 0 0 V

b b0.2 0.2

v0 0

0.1

? 0.1 0.1 0.2

0. 3 3

lwl

of

40. 40.

29Si 1.4 X X lo1*

125

4.2 X Xlo’*

275

0.4

0.5 0.5

?

1.

AND

53

the the center of the center the wafer. More detailed investigations of corotated crystals corotated reveal only small radial resistivity variations in the the as-grown state, correstate, sponding to to the characteristic the M-shaped resistivity distribution observed distribution by et al., 1982) for LEC-grown GaAs substrates. However, after others others (Grand (Grand encapsulated annealing at 860°C/15860°C/1 min, significant min, radial variations ofthe measured sheet resistance and mobility are typically are observed. The results The for four four substrates selected from various positions along the the length of an undoped GaAs undoped crystal pulled at 6 mm/hr from a stoichiometric melt and employing corotation of corotation the seed the and crucible at 6 and and 15 rpm, respectively, rpm, this displayed high as-grown resistiviare shown are in Fig. in 4 1. Although this crystal (2 cm) and mobilities (- 5000 cm2 V-' cm2sec-l) over the full crystal ties (2lo7 length, annealing results in sheet resistances (Fig. 41a) and mobilities and (Fig. the of the wafers. the In particular, 4 1b), which decrease radially toward the center as the the tang tang of theend crystal theend is approached (wafer No. 63 corresponding 63 to to about about 55% of melt solidified), the development of distinct low-mobility, p-type cores becomes apparent. apparent. In In contrast these contrast results, to tohighly uniform GaAs crystals are produced when counter counter rotationreduced rotationgrowth and/or rates and/or are are employed during during illustrated in Fig. 42, where 42, high annealed sheet resistances growth. This is This (- lo9 R/sq) R/sq)mobilities and and (3000-6000 (3000-6000 V-I sec-I), cm2 which cm2 show little variation across the the full wafer area or or from slice to to slice, are observed are for as well as as corotated both crystals grown under under counter-rotation counter-rotation conditionscorotated conditi 29Si uniform crystals pulled at a reduced pull rate rate of 3 3mm hr-'. Under Under uniform implantation, these implantation, substrates enable uniform donor activation (+5%)to be achieved over the wafers the (Section 13). These results (and (and more recent studies using capless As overpressure annealing techniques) indicate conclusively that that coring the thephenomenon phenomeno cannot be cannot ascribed to faulty encapsulation or to or observed in in undoped undoped ( 1( 1 1) ) in in inhomogeneous implantation. Neither implantation. faceted growth (common (common Czochralskigrowth but unknown but in ( 100) ( growths) nor possible nor considerations related tions to to constitutional supercooling constitutional provide an adequate description adequate of this coring this effect at present. We suggest that that these effects are associated with localized stoichiometric defects that result that from the preferential the segrethe crystal. During subsequent During gation of excess Ga at Gathe center the of the growing crystal or or substrate annealing, these effects are also possibly enhanced by enhanced point defect gettering to to regions of frozen-in thermal stress thermal in in LEC-grown GaAs. Since these stoichiometric defects can exert a strong influence on on the the observed electrical activity (through, for example, modifying the EL2 con- concentration), local centration), increases in point-defect density can therefore affect the the local resistivity, thermal thermal stability, and, and, probably, site selection in in the im-the plantation plantation of ofsilicon. amphoteric Growth amphoteric Growth conditions of counter conditions counter rotation rota and reduced and growth rates are conducive are to to maintaining a uniform maintaining diffusion

54

et al. al.

R. N.

lo9

0 0

MM

25

(mml (a)

66

> >

II

II

II

00

50

25

Imm) ((

of 860°C/

41.

give

Si,N,).

of

of et al,, 1953). 1953). of

slice

1.

55

AND 1o1O 1

. U

- -

#81

1

U

--

X7

lo9 lo9

~~

#24

YI

z z

lo8

- -

-- --

- - -

- -

4 4

lo4 lo4

6 6

- -

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-I iI! -

-- -

> >

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- -

lo3

--

2 2 lo2

I

I

I

I

I

I

I

I

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I

I

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

V.

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

56

R. N.

et al. al.

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

GAS

a.

of

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

1.

57

AND

in in wafers annealed after receiving inert inert gas implants (Bozler implantset al., 1976) suggests that secondary that activation activation phenomena phenomenasuch are are not not i tests do not rule not out the possibility the that these that secondary phenomena phenomena be can ca associated with the the implanted species or or be masked by surface depletion effects. one-to-one correspondence between implanted implanted dose and net net donor donor activity per cubic centimeter has centimeter been employed to qualify stable semi-insulating substrates and and to infer an optimized implantation implantation process in the the past. Even this this interpretation is, however, interpretation in in sharp conflict sharpwith abundant abundant crystal growth (Kuznetsov et al., 1973), vapor-phase epitaxy (Wolfe and Stillman, 1975), and liquid-phase epitaxy (Casey et al., 1971) data showing data the n-dopants exhibit similar and significant and amphoteric amphoteric that all thatof the shallow character in character GaAs. the the activation of implanted implanted alsoions amphoteric, ions is isamphoteric any qualification and optimization optimization that seeks routine100% routine net net donor activation necessarily requires spurious activation spurious to compensate for compensate the net the activity “lost” through amphoteric doping amphoteric by the the implanted species. implanted Figure 43 illustrates the the present model of “ideal” activation of activation ion-imimplanted profile is planted n-layers in semi-insulating GaAs.The implanted silicon representative of channel channel implants employedimplants for power for FET fabrication. includes the effects the of gaussian implant profiles, implant dual-energy implants used implants to approximate aapproximate flat-channel profile, and and redistribution of the the implanted implant Si can implanted can act act as as donors, d species as a result of annealing. The The implanted II

of

43.

of

- &z)

is

II

II

II

n (nz )

29Si

58

et al. al.

R. N.

acceptors, or or neutral centers neutral by processes such as Si -+

+ e-,+ ++

++

(5)

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

--

q= q =

(Sic.

- Nz)/S(Si) Nz)/S(Si)

(8)

or or

rt = [W+, = - NA)/W+o -[W+, ++

+ NA)/4Si)1, +

(9)

where (Si) is the the implanted silicon implanted concentration. concentration. The differential activation efficiency can then then be written (10)

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

= =

- -

++

(1 1)

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

++

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

1.

59

AND

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

11

22

55

10

20

MX l0l6

nn

n= n

44. 44.

++

of -,

XX 1OI6

---,

+ + X X10I6

=

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ef al.. 1979.) 1979.)

60 60

et et al. al.

N.

ent concentrationsshould concentrations therefore yield the total ionized total impurity concenimpurity tration X, tration where

2 =2qx{Si) = +

+ ++

(13) The The scatter in the the data is a data measure of process reproducibility or substrate or q x > 1>1indicate incomplete and and uncontrolled acti- actiuniformity; q x < 1/(cs

- -+ +

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

68

et al.

R. N.

doped LEC and Cr-doped and (>5 5X X 10l6cm-3 Cr) crystals. The The undoped material (Fig. 47a) exhibits excellent reproducibility (*1 X 1 X 10l6 cm-j) and and a consistent, relatively broad transition transition into the the semi-insulatingsubstrate. Implantation of Implantation the Crdoped material to material achieve the same the net donor density donor and effective profile width requires higher doses at slightly higher energies. Reproducibility of the profile depth depth is poor, although the the profile abruptness can be excellent (Fig. 47b). A Adetailed analysis of both electrical activation and andchannel the the mobility in Cr-doped in GaAs shows that implanted implanted 29Si concentrations concentrations below 9 X 9X 10l6 cm-I3 exhibit no nomeasurable n-type activity, whereas implantation implantation t (0.9- (0.91.2) X 1.2) X 10’’ results in in poorly controlled n-activity in which the ionized chromium chromium appears absent as either compensating acceptors or or impurity-scattering centers. This This transition from an an apparent “Cr-free” apparent implanted layer to to a Cr-doped substrate results in in an abrupt abrupt interface between the channel the and andsemi-insulating the the substrate. Unfortunately, Unfortunately, depth of depth this interface this is is difficult to control. difficult

, I I

,

‘, ,\

\\

\\

11 1000

\* II

2000

3000

I I

I \ ,

4000

I

5000

.

II

6000

of 29Si 325

900-A 2 2X Xlo1*cm-* lo1* 125 figure Fig. 01. (1975). (1975).

5 5X X10l2

1.

69

AND

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.c

c

c

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,,

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4000

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5000

6000

125

7 7X X

b.

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

70

et al.

N.

1

2

3

4

5

6

7

8

9

-1 10

Dose (Dose lo1’ ( an-’)

48.

of 29Si

(NSM) 250 250

29Si+

donor donor concentration profile is flat is between the the Si3N4-GaAs interface and and concentration of the the channel channel and that implant implant the range the of maximum concentration (RM) = R=M implant depth depth the equivalent, the uniform concentration concentration implant is known. is The vertical The arrows in Fig. in 48 indicate the calculated the correction of NSMto assuming a 0.6-eV surface-depletion potential. The The horizontal horizon arrows correct the the total total implanted Si concentration implanted concentration for for 40% 40% deposition of the surface-fill the implant implantSi3N4 into into rather therather the than thanThe theslope the of the the GaAs. The corrected data data is the the net donor donor activation efficiency q = q qpqA, = and the the intercept on the vertical the axis divided by the effective the depth depth yields the net the residual acceptor density - - = = In Fig. In 48, 48, q q= 0.72 = and 0.72and = = 0.9 X X cm+. V of these samples yield volume concentrations concentrati Direct C- V measurements which agree within k5%kof those derived from the corrected the Hall data. data. The The effective depth agreement depth is k is 3%. kThe values The of q qand and - - can can be employed in an inverse an process to predict to undepleted charge and net andvolume carrier concentration at concentration other other channel implant implant energies down to to volume concentrationsas concentrations low as 1 1X X 10l6~ m - At ~ . high concentrations (>2 concentrations XX ~ m - ~however, ), this is complicated by sublinear activation. In the concenthe 29Siimplantation of implantation undoped tration tration range shown in Fig. 48, 48, consistentlyyields q = q 0.75 = k 0.03 k and and = (1=.O f 0.3) fXX 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 substrates ( >

-5 4ow 5-

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55

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55

lo1*

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50.

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300°K GaAs.

is

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

N, = 0.8 =XX 1OI6 + 0.12 +

(24) The differential The compensation ratio ratio 8= 8 = in turn indicates a differential net donor activation donor efficiency q,, q,, = 0.78. = This use Thisof the two the mobili8 and 8 overestimate and q,, . . ties is expected to underestimate to Figure 5 15 shows 1 the change the in carrier mobility achieved by reducing the the

1.

LEC LEC

-.- 40.000 > >

73

AND

t1t 1

-5 5 N

N

20,wo

Y Y 00

15.W

I-

c

c

c c .-- -10,000

8.000 8.000

--

6.000 4.000 I

1

0. 6 60. 8 81 1

II

I I

22

44

II

I

I

6 6 8 8 10

15X 10l6

N~ N~ 5 1.5

of

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

iV, = 0.9 = XX 1OI6 + 0.12 +

- -

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

b.

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

74

et al. al.

R. N.

2r

/-

10161/ 1016

II

22

II

55

II

I I

1017

22

of

< 55 X X 10l6 Cr) exhibits strikingly different behavior to implanted undoped GaAs, as was shown in Fig. 50. At low net donor donor concentrations, anomalously low carrier mobilities are are observed in imconcentrations, saturation is saturation planted Cr-doped GaAs,while at high concentrations, doping displaced to to higher levels as as the Cr the content is content increased. Measurements of implanted implanted channels formed in in lightly Cr-doped GaAs/PBN substrates (- 5 X 5 X cmF3Cr cmF3 content) indicate content)mobilities that that lie midway between the undoped the GaAs/PBN and the Cr-doped the GaAs curves shown in Fig. in 50. The role of Cr impurities Cr in in implanted GaAs implanted substratescan be substratescan analyzed from the perspective the of the the total equivalent total concentration of concentration ionized centers, derived from from mobility measurements, as a function function of the the implanted implant analogy with Eq. (26), the (26),the total ionized totalimpurity impurity silicon concentration. By concentration. in Z implanted Cr-doped implantedGaAs can be canrepresented by content Z content

is the Cr theimpurity concentration which concentration is assumed to be to a doubly where as aas content ionized deep acceptor. Plots of the the total ionized totalimpurity impurityZ,content function of the the implanted silicon implanted concentration concentration lightly doped for for (5 5X X10l6 ~ m Cr) - ~GaAs sub55, respectively. strates are shown in in Figs. 54 and and Implantation of Implantation lightly Cr-doped GaAs (Fig. 54) indicates two distinct 9 X concentratio regions: one above and and one below oneimplanted implanted concentrations of 9 X ~ m - ~At. implanted silicon concentrations greater concentrations than 9 X 9 X10l6 ~ r n - ~ , silicon implanted as donors donors acceptors or or complete (100%)activation of the the implanted the thecontent within the the lattice is observed. The The total ionized totalimpurity impurityofcontent and the the implanted layer is well represented by simply I:= = = 2=2X X expected influence of the doubly the ionized chromium acceptors chromium(4 10l6cmW3)and the the residual impurity concentration (KO concentration 1 1X X 1OI6 ~ r n - ~ ) 9the 9X X are noticeably are absent. At silicon implant implant concentrations below theconcentrations cm-3 threshold concentration, however, concentration, Fig. 54 54 illustrates clearly that the the observed total total impurity impurity reflects concentration the the effects concentration of the the Cr doping and and residual acceptor density in in accordance with Eq. (30). The The observed is distinct and and abrupt abrupt is not not well and and threshold dose at 0.9 X X understood at present. We speculate that that the the apparent presenceapparent or absence or of electrically active chromium chromium in in the layer themay implanted reflect possible implanted Cr interactions and and complex formation and/or out-diffusion to either either the the surface or deeper regions of residual implant damage. implant ionized totalimpurity impurity content a function content of function the the Figure 55 shows the the total

++

--

1,

54.

LEC LEC

29Si

of

as

77

AND DIRECT

5 55 5X X

55.

of

as 2 52 5X X10l6

29Si

78

R. N. THOMAS et al. al.

implanted implanted silicon concentration concentration in heavily Cr-doped GaAs (>5 X X 10l6 cm-3 Cr) pulled Cr) from fused silica crucibles. At silicon concentrations greater concentrations 1X 1 X 1017~ m - ~ complete , activation complete of the the implanted silicon implanted is again than than silicon. observed, except that that saturation occurs saturation at about about 3X 3 X10l8 Saturation is Saturation believed to be common to common all three types three of GaAs crystals, but X5 X lo1*- lo1*only the heavily the Cr-doped GaAs GaAs substrates were implanted substratesto implanted the 5the 9 X10l6cm-3 is cm-3 level. Again, a threshold silicon dose of approximately 9 X observed. In this case, this the the net netdensity donor is donor not sufficient not to overcome the the effects of Cr Cr doping, and measurable n-type activity cannot cannot be readily At implanted silicon implanted concentrations below concentrations achieved in the in implanted layer. implanted the the threshold dose, the the total ionized totalimpurity impuritytherefore content content becomes poorly defined and presumably and very large (mid-10I7~ m - from ~ ) the the simulta- simulta neous formation of formation donors and donors their their neutralization of the neutralization the chromium accepchromium 8 X 10l6 tor impurities. tor All ofthe mobility data at data net donor net densities below 8 X cm-3 in heavily Cr-doped GaAs (Fig. GaAs50) represent samples implanted at implanted the the same nominal silicon nominal concentration. concentration. We therefore conclude from these studiesofthe studies effects ofCr doping on doping the the quality of silicon-implanted layers that undoped, undoped, semi-insulating GaAs GaAs of achieving offers some important advantages important in in terms terms uniform, uniform, reproduc- re ible implant implant profiles, high electrical activation, and activation, high near-theoretical channel channel mobilities. In contrast, contrast, implantation of heavilyimplantation Cr-doped GaAs substrates appears generally appears unsuitable for for normal normal FET levels FET be-doping dopi cause of poor wafer-to-wafer reproducibility. Variations Variations in in Cr Cr conce tions tions wafers in in(due to Cr segregation Cr effects during growth), during Cr out-diffuCr sion characteristics, and possible Cr-implanted ion Cr-implanted interactions probably interactions contribute to contribute this poor this reproducibility. It is especially unsuitable ifunsuitable lightly doped n-layers are desired. 1015~ m - in ~ )in Our Our studies indicate also that indicate low Cr-doping levels (55 X5 X the GaAs the substrate have substrate no serious adverse effects on the electrical activation of directly implanted FET implanted layers and, and, in in instances, some some can be canutilized to some advantage. For example, For the the implanted layers implanted are noticeably more more substrates. undoped Unfortunately, Unfortunat abrupt in abrupt lightly Cr-doped GaAs than than in in undoped evidence (Magee, 1982) exists which suggests that that subsequent low-temperasubsequent ture ture processing, such as ohmic ohmic contact contact or prolonged formation,device formation, operation can can lead to the the reappearance of electrically active Cr Cr in in the the implanted implanted channel to highchannel concentrations and andat concentrations the drain the contact region. contact TO FET DEVICE DEVICE PROCESSING PROCESSING 15. IMPLICATIONS

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

1.

AND

79

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

(1) use of crystals grown from stoichiometric or slightly As-rich melts, [Gal/[Asl 5 1,51, (2) substrate resistivity 2 lo7 2 cm or sheet or resistance k lo9 k R/sq, R/sq, (3) measured mobility k 4500 k cmz sec-' with n-type conduction, conduction and and (4) sheet resistance 2 lo7 2 and and n-Hall an an coefficient following nitride encapsulation and and 860°C/1 5 5min860°C/1 annealing in forming in gas. At present, however, more exhaustive crystal selection or qualification procedures continue continue be usedtoand to rely upon evaluation of representative slices cut cut from different locations along each crystal. Control of Control selectiveimplantation processing implantation is performed through the use the of 29Sitest implants, implants, layers. implanted These Hall-effect measurements, and CandVprofiling of the the implanted evaluations amount amount to establishing the the magnitude and and reproducibility of parameters such as as the profile the shape, the the activation efficiency activation (for net donor donor and and total ionized totalimpurities), and andresidual the the electrical activity associated with the the substrate. In In practice, those parameters which can be directly related to probable FET performance are also are monitored and and include include (1) profile concentration, concentration, shape, depth, depth, and and (2) (2) zero-bias depletion width, (3) undepleted net net donor donor concentration, concentration, (4) channel mobility, ( 5 ) current per current unit unit periphery after source and drain processing, drain and (6) (6) pinch-off voltage.

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

80

et al,

R. N.

estimated to be below the the 101S-cm-3range and is and significantly lower than in in implanted layers implanted formed in Bridgman or GaAs prepared in fused in silica containers. Mass spectrometric analyses confirm directly the generally the highbackground concentrations of concentrations silicon in in GaAs compounded compounded grown in in and and fused silica crucibles using high-pressure LEC technology. Complete (100%)activation of silicon implants as implants either singly either ionized donors donors acceptors or oris obtained obtained in G inaA undoped undoped s at silicon concentrations concentrati up to to 1.5 X X10l8cm-3 with annealing. Decreasing the the anneal anneal temperature to to lowers this this limit6 X limit X to~tom - while ~ , raising it to it 950°C causes an increase an to 5toX X 10l8~ m - The ~ . influence The of the annealing the temperature ature on compensation on the the ratio ratio and and the the net netefficiency donor donor is of isactivation a more practical importance, and preliminary and measurements of the effects the of annealing temperature are temperature shown in Fig. in 56. These 56. experiments were camed out on unencapsulated substrates which were annealed in an an As overpressure at different temperatures after temperatures implantation. implantation. The donor donor activation activ efficiency is seen to increase to almost to 90%for anneals, reflecting the the reduced free electron concentration available concentration at the lower the annealing temper- temperature ature create to to silicon acceptors.

”$.

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0.05 0.05 66

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

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

82

R. N.

57.

et al.

of

50

( 110) (

ances (50 ances k 0.5-mm k diameter diameter 0.5 and 0.02-mm and thickness). The polished The ( 110) ( orientation flats orientation and are edge rounded. rounded. slices contain contain Recent experiencein wafer in fabrication and device processing on aonlabora- laboratory scale, however, reveals several areas where areas further further improvements improv be required. One One is the the need for improved surface improved wafer preparation will preparation flatness of GaAs wafers, especially when intended for intended large-area processing of submicron gate-length FETs. The The relatively unsophisticated rotary-polishing techniques techniques that that used are are today commonly in in GaAscommonly typically yield - pm across 50-mm-diam wafers and surfaces that are flat areto within only 5 - 10 so forth. forth.wafers Such Such offer poor control of control wafer parallelism, bow, taper, and taper, are are clearly unsuitable for modem modem high-throughput high-throughput optica processing in the the techniques that will be applied increasingly to GaAs IC IC future. future. example, For Fortoday’s direct-step-on-wafer photoaligners require require a pm/cm achieve micron and surface flatness of better better0.5 than than to to submicron gate submicron lengths in in sparse geometry FET structures over structures large-area

1.

83 83 HIGH-PURITY LEC GROWTH AND DIRECT IMPLANTATION IMPLANTATION

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

rr

88

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L

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= 4

II ( (9 9

z z 22

00

loo0

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2000

3000

4000

of = 50 =

of of

mm;

Si (100) (100) =0 = .5 mm;(100)

84

N. THOMAS et

al. al.

The authors authors wish to thank thank many of ourmany colleagues at the Solid Solid State Division Stateof the the Westinghouse Research and Development Development and at Center, the Advanced the Center,Technology Division Division for theirCenter their valuable valuableBaltimore, to contributions con of the Defense the and Electronic Electronic Systems Systems Center in in Baltimore, forTakei the x-ray the topographic topographic studies, studie this work. this We are particularly particularly to Dr. grateful W. J. J.grateful Takei A. A. Rohatgi for the DLTS studies, and Mr. R. C. Clarke Clarke for forinassistance implantation assistance implantation annealing a studies. We gratefully acknowledge valuable valuable consultations on powerconsultations FETs FETs and monolithic monolithic J. Oakes and Oakes M. C. Driver (Solid DriverState State Division) and Mr. Division) Mr. H. W. circuits provided circuits by Drs. J. G. J. Degenford (Advanced Technology (Advanced Division). The work was Cooper and Cooper Drs. M. Cohn, and Cohn, W.Bing, L. L. Wesoloski, and made possible made by the excellent the technical assistance technical of Messrs. W. E. Brandis in crystal growth, growth, Mrs. E. E. A. Halgas Halgas and Mrs.J. J.C. Henke Henke in substrate substrate T. A. A. in Hellett ion ion and R. L. R. Galley and Mrs. D. J. J. Hellett preparation and preparation evaluation, and evaluation, Messrs. P. implantation. implantation. We also gratefully acknowledge the valuable contributions contributions other colleagues of of to this work, work, G. W. Wicks of Cornell University Cornell for for providing providing the the photoluminescence data, ph including Dr. including Charlesand Associates for for the SIMS thedata, data, and Dr. R. M. Ware Ware of Dr. Dr. C. Evans of Charles Evans Cambridge Instruments Instruments his assistance for for assistance LECingrowth in theof theGaAs crystals. GaAs C.Dr. C. Nathanson Nathanson his moral moral for forsupport, support, The The authors authors especially also wish also thank thankH.Dr. Dr. R. A. A. Reynolds, Mr. Reynolds, Mr. S. Roosild Roosild (Materials Sciences (Materials technical advice, technical and guidance, and guidance, M. Yoder (Office Yoder of Naval Research) for for their their continued continued encour Office,DARPA), and Mr. Mr. K. Fox, State Division, Di ment ment and andFinally, support.wesupport. thank thankD.Mr. Mr. Manager of the the Solid Solid State for his continued continued andinterest permission interest to publish this this chapter. chapter.

Ashen, D. J., J., Dean, P. J., Dean, Hurle, D. Hurle, T. J., Mullin, J., J. Mullin, B., J. White, White, M., and Green, P. Green, D. ( 1975). ( 36, 1041. AuCoin, T. AuCoin, R., T. Ross, R. L., Wade, L., M. J., and Savage, and R. 0. R. (1979). (1979). 22,59. Bachelet, G. B., Baraf, G. and Schluter, M. Schluter, (1981). (1981). Rev. 24, 15. Baldereschi, A., and Lipan, N. Lipan, N. 0. (1974). (1974). 1525. Barrett, D. Barrett, L.,Ta, L. B., and Thomas, Thomas, N. (1982). R. R.Personal (1982). Personal communication. communication. S. ( 1962). ( “Semiconductor “Semiconductor Statistics,” Series Statistics,” of Monographs International on Monographs Internationa Blakemore, J. J. Semiconductors, Vol. Semiconductors, 3. 3. Pergamon, New Pergamon, York. York. Bonner, W. Bonner, A. A. ( 1 98 Cryst. Cryst. 54,2 Bozler, C. O., Donnelly, J.Donnelly, P., J. Lindley, W. Lindley, T., and Reynolds, R. Reynolds, A. A. (1976). (1976). 29, 698. Braggins, T. T. ( 1 982). Personal 982). communication. communication. J. (1970). (1970). Cryst. Cryst. 7,9. Brice, J. C. Brooks, (1955). (1955). 7 , 158. Burton, J. Burton, A., Prim, Prim, R. C., and Slichter, W. Slichter, P. (1953). (1953). 21, 1987. Carmthers, J. Carmthers, J. R., R., Witt, A. F., Witt, and Reusser, R. E. (1977). Proc. (1977). 3rd, 3rd,63,6 Casey, C., Parish, M. Parish, B., and Wolfstern, K. B. 97 I). 32,57 Cheng, ( 196 ( 33,76 1. Cockayne, B., Brown, G. T., G. and MacEwan, W. R. (1981). (1981). Cryst. Cryst. 51,461. Cullis, A. G., Augustus, P. D., P. and Stirland, D. Stirland, J. J. ( 1 980). 51,2556. Dash, W. Dash, C. (1957). (1957). Appl. 28,882. Debney, B. T., and Jay, P. Jay, R. (1980). 23,173. Eldridge, G . W. (1980). (1980). Device Device 1980,

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Magee, T. J. ( I 982). 982). Devices, dale, Makram-Ebeid, S., Makram-Ebeid, Gantard, D., Devillard, P., Devillard, and Martin, G. Martin, M. (1982). (1982). 40, 161. Whelan, M. (1976). (1976). Soc. 123, 1413. Malbon, R. Malbon, M., Lee, D. H., and Whelan, J. M.,G. M., Jacob, and Jacob, Poibland, G., G., G. Poibland, (1980a). 23, 37. Martin, G. Martin, Hallais, J. J. P., and Poibland, G. Poibland, (1980b). J. Martin, Martin,Farges, G. G. M., J. P.,M., Jacob, G., Jacob, 51,2840. 51,2840. Mears, L., and Stradling, R. Stradling, R. A. A. (197 I). (197 C 4, C L22. C., and Mazelsky, R. (1962). (1962). 33,2016. Metz, E. P. Miller, R. Miller, Hollan, Hollan, L., and Briere, (1976). (1976). Phys. 11, 153. Mircea, A., Mitonneau, Mitonneau, J. B., J. Heritage, R. Heritage, J., Holiday, C. Holiday, H., and Straughan, B. Straughan, W. (1968). (1968). Cryst. 34, 34, 281. K. H., Yee, C. M. L., and Wolfe, C. M. (1980). (1980). 23, 109. Nichols, K. Nichols, R. D., Chen, Chen, R. T., and Yu, P. Yu,W. (1981). 17, 839. 839. Oliver, J. R., Fairman, Fairman, Penning, P. Penning, (1958a). (1958a). 13,79. Rev. 19,357. Penning, P. Penning, (1957- (19571958b). 23,469. 23,469. Petroff, P., and and Hartman, R. L. (1973). (1973). L. (1975). In “Semiconductors “Semiconductors(R. andK. and Willardson K.Semimetals” and Willardson Semimetals” A. C. Beer, Rode, D. Rode, eds.), Vol. 10, Chap. Chap. I. Academic Press, New York. York. J., Huybregts, J. M. P. L., Van der Wiggert,W. M., and deKock, deKock, J. R. (1 R.977). J. Roksnoer, P. Roksnoer, Cryst. 40, 6. 6. Sealy, B. J., and Sumdy, R. K. (1975). 26, L19. Watanabe, H., Watanabe, and Matsui. J. J. (1978). J. 49,822. 49,822. Seki, Y., Seki, C., Yamamoto, Yamamoto, and Tokno, S. (1980). Jpn. J. Appl. 19, Uemura, Uemura, Shinoyama, Shinoyama, 1331. Steinemann, Steinemann, and Zimmerli, U. Zimmerli, U. (1963). (1963). 6, 597. “Semi-Insulating Materials” (G. Materials” Rees, ed.), Vol. Vol. I, p. 93. Shiva, Shiva, (1980). In “Semi-Insulating Ill-V Stolte, C. Stolte, Orpington, England. Orpington, K. (198 1). 981). Proc. Suzuki, Suzuki, Isawa, T.,N., T., Okubo, Okubo, and Y., Hoshi, Y., Hoshi, p. 90. Swiggard, E. M., Lee, S. H., H., and Von Von Batchelder, F. W. (1977). Conf: (1977). No. No. 33b, p. 23. C. (1966). J. J. 9, 143. Sze, S. M., and Irvin, Irvin, Rohatgi, and Thomas, R. Thomas, N. (1982a). J. 53,5771. Ta, L. B., Hobgood, H. M., Rohatgi, A., N., Eldridge, R. R. G. W., and Hobgood, H. Hobgood, H. M. (1982b). Conf: Conf: Ta, L. B., Thomas, Thomas, SOC.No. No. 65, p. 31. Ta, L. B., Hobgood, H. M., and Thomas, Thomas, R. N. (1982~).Appl. 41 (1 l), 109 I. Thomas, R. Thomas, N. Braggins, T. T. T., Hobgood, H. Hobgood, M., and Takei, W. Takei, J. J. (1978). J. 49, 2811. N., N., Hobgood, H. M., Barrett, D. Barrett, L. and Eldridge, G. W. (1980). In “Semi-lnsulat- “Semi-lnsulatThomas, R. Thomas, 111-V Materials’’ (G. J. (G. Rees, ed.), Vol. 1, p. 1, 76. Shiva, Shiva, Orpington, Orpington, England. Engl N., N., Hobgood, H. M., M., Eldridge, G. W., Barrett, D. Barrett, L., and and Braggins, T. T. (1 98 I).98 Thomas, R. Thomas, 24, 337. Walukiewicz, W., Lagowski, J., Jastrebski, L., Jastrebski, Lichtensteiger, M., and Gatos, Gatos, H. C. (1979). J. 50, 899. Walukiewicz, W., Lagowski, W., J., and Gatos, Gatos, H. C. (1982). 53,769. Cryst. Ware, R. M. (1977). Ware, R. Ware, M., and M., Rumsby, D. Rumsby, (1979). Devices, Ga.

1.

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87 87

Welch, B. Welch, M., Eisen, F. Eisen, H., and Higgins, J. A. J. (1974). J. (1974). Phys. 45,3685. S. H., H., Niehaus, W. Niehaus, C., Cox, Cox, H. M., Dihrenzo, J. V., and Schlosser, W. Schlosser, 0. (1980). (1980). Wemple, Wemple, Devices 1013. W. (1982). (1982). Cornell Cornell (private University communication). University Wicks, G. Wicks, R. K., K., and Allred, W. Allred, P. (1967). (1967). Phys. No. 3, p. 35. Willardson, Willardson, R., Brehm, G. Brehm, E., Doerbeck, Doerbeck, F. H., Frensley, W. Frensley, R., Macksey, H. M., Maxwell, Wisseman, W. Wisseman, J. J. W., W., Tserng, H. O., Tserng, and Williams, Williams, E. (1979). R. R. (1979). U.S. Air Air Force Interim ForceTech. Rep., Contract No. No. F336 15-78-C-05 F336 10. Wolfe, C. M., and Stillman, G. E. E. (1975). (1975). Phys. 27, 564. 564. G. E., and Dimmock, J. J. 0. (1970). J. (1970). 41,504. Wolfe, C. C. M., Stillman, Stillman, J. M. J. (1967). (1967). SOC. 239, 378. Woodall, Woodall, Y u, Y P. W., Holmes, Holmes, E., andD.Chen, D. R. T. R. ( 198 ( 1). 198 Oiso, Zucca, Zucca, R. R. (1977). J. (1977). Phys. 48, 1977. 1977.


SEMICONDUCTORS AND SEMICONDUCTORS SEMIMETAU, VOL. 20

22

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

LISTOF LIST ACRONYMS.. ACRONYMS. ....... I. INTRODUCTION ........... 11. MATERIALS PREPARATION. ..... 1. GaAs

2. 3. . 111. ION IMPLANTATION ..

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................ .................... 5. . . . . . . . . . . . . . . . 6. . . . . . . . . . . . . . . . . . I. . . . . . . . . . . . . . . . . . 8. ................ DEVICE RESULTS.. . . . . . . . . . . . . . . . . . . 9. 9. . . . . . . . . . . . . . . . . . . . 10. IC IC . . . . . . . . . . . . . . . . . . II .................... SUMMARY.. . . . . . . . . . . . . . . . . . . . . . REFERENCES. . . . . . . . . . . . . . . . . . . . . 4.

IV.

V.

89 90 93 93 103 106 109 109 111 119 119

125 125 134 143 143 143 146 148 151 151 154

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JFET Junction field effect transistor transistor Auger emission spectroscopy emission Arc source emission source LEC LEC Liquid-encapsulated Liquid-encapsulated Czochralski Czochralski spectroscopy LPE BFL Buffered FET logic Liquid-phase Liquid-phase epitaxy epitaxy c- v v Capacitance- Capacitancevoltage Large-scale integration integration CVD MBE deposition Chemical Chemical vapor vapor deposition Molecular beam Molecular epitaxy epitaxy DLTS DLTSDeep-level transient transient MESFET Metal-semiconductor Metal-semiconductor field effect transistor transistor spectroscopy spectroscopy ECL Emitter Emitter coupled logic coupled MSI Medium-scale Medium-scale integration integ FET OMVPE OMVPE Field effect transistor transistor Organo-metallic vapor-phase Organo-metallic IC epitaxy epitaxy Integrated Integrated circuit circuit AES ASES

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Academic Press. Academic Inc. reserved. ISBN 0- 12-752 120-8 12-752

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SSMS

RBS RBS logic logic

The materials The and and implantation procedures implantation used to produce to high-quality will be discussed regions for the fabrication the of GaAsintegrated circuits in this chapter. The present The state of state the the in artthe artthe preparation of materials, preparation the the ion implantation implantation technology, the the device processing procedures, the the has yielded circuits of the circuit design, and the the evaluation of GaAs 1 al., 1982a).This circuit, This which complexity of that shown that in Fig. in 1 (Liechti was designed, fabricated, and tested and at the Hewlett-Packard the Laboratories, is 400 transistors and a 5-Gbit/sec data rate dataword generator that that contains contains and 230 diodes on aon1.1 - by - 1A-mm 1 chip. The topics covered in this chapter are chapter many-faceted. Therefore, specific topics considered important important by some may not be addressed. The The main main experimental results included here are are representative of the the work of the the Appropriate author authorhisand colleagues and at Hewlett-Packard since 1975. 1975. references are made to to the the literature to complement literature complement theprethe information sented here with the results the obtained obtainedlaboratories. in in other other The intent intent of of this thi chapter is to cover to

( I ) the the important aspects important of the the selection and and characterization of the substrate materials that that serve as the the basis for all the the work, including the investigation of ion ion implantation implantation fabrication and of and the andthe (2) the the procedures used to produce the doped, active regions in in the the substrate material required to to form the the channel regions channel of MESFETs, the ohmic contact ohmic areas, and and other active other regions necessary for the the production product of

In Part 11, the the important aspects important of the growth, the properties, characterization, tion, and andstability thermalofthermal substrate materials are' presented. are' The The basic requirement for the the substrate material is that that provide it it electrical isolation between devices while at the same the time allowing time the the formation of high-moformation bility controlled-doping regions in in the areas thewhere devices are arebetofabrito is met met most in inapplications by selective region ion ion cated. This requirement This implantation into implantation bulk substrate material of sufficientquality or by or selective region ion implantation implantation high-purity intoepitaxial into layers produced by liqor epitaxy (VPE). These active regions uid-phase epitaxy (LPE) or vapor-phase

of

1.

32

1.1 X X 1.6

600 600

92 92

C. A.

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

2.

ION ION IMPLANTATION AND MATERIALS

93

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

11. Materials Materials Preparation Preparation

1. 1.SEMI-INSULATING GAASINGOT GAASGROWTH

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

94

C . A.

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

2. 2.

95

AND

France Franceet(Jacob al., al., 1980) (Jacob have compared compared gradient-freeze the the grown material with the high-pressure the LEC-grown material. The technique we technique have used (Ford and (Ford Larsen, 1975) for the for production production of semi-insulating GaAs ingots since 1974 is the low-pressure, 2-atm LEC procedure. This This technique has been technique used to produce produce standard Cr-dopedstandard (Cronin (Cronin Haisty, and1964), and semi-insulating substrates. This This material is usedmaterial as the the substrate material for for epitaxial growth of of the n-type the layers used to fabricate discrete FETs as well as for the the substrate substrate usedmaterial for for the material the growth of high-purity buffer layers, which is the starting starting material the material fo formation of formation n-type layers by ion implantation. Since implantation. 1978, this this technique techniq has also been used to produce nonintentionally nonintentionally high-purity, doped, semi-indoped, sulatingGaAs sulating ingots suitable ingots for use as substrates substrates epitaxialfor growth for as well as as for as the the production of n-type production regions by direct ion direct implantation implantation into the the bulk substrate material. substrateA cutaway A view of the LEC the puller employed for for the the 2-atm technique is technique shown in Fig. 2. The The apparatus consists apparatus of a aresistively heated crucible, either either quartz pyrolytic quartz boron or orboron nitride (PBN),nitride which holds the GaAs the melt. The GaAs starting material starting is either either compounded externally compounded to the puller the in a a standard standard quartz byquartz a a standard ampoule Asstandard vapor ampoule vapor transport trans technique technique 1975) (Mullin, or or by (Mullin, the the injection of As injection As into the Ga melt (Pekarek, 1970), (Pekarek, as will as be discussed below. These methods methods synthesis for for the the of GaAs eliminate eliminate need for the thethe high-pressure the LEC pullers. The appropri- appropriate ate dopants, if any, dopants, are any,added and the melt the is covered with a layer a of boric boric +SEED

ROD

SEED

Bzo3 Bzo3 (L)

2. cell is

is is rod.

96

A.

oxide (B203)which acts.as aacts.as protective encapsulant to encapsulant eliminate eliminate loss of the the the volatile the constituentsat constituents the growth temperature of temperature 1238°C 1238°C to isolate and and the melt from the crucible. the by inserting a seed of the proper the orientation to orientation The GaAs The crystal is pulled is the the surface of the the melt, which is held at 1238"C, and and extracting it itat a controlled rate while the seed the and andmelt the the are rotated are in opposite in directions. By careful and and judicious judicious of the the control rotation rates control rotation and the andpull rate, ingots with good crystallographic properties and reasonably and controlled diameters diameters are produced are using this technique. this The melt The charge is typically 2 kg, which produces ingots of approximately 65 65 mm in in diameter diameter 100 mmand mm in and in the the [ 1[1 11 or 11 the the [ 1001 [ direction; direction; in in length. The ingot The can be pulled in either [ 1[1the 11 direction. In In the the the past, the majority the of the ingots the were grown in in the case of the [the 1[11111ingots, the (100) the oriented wafers used for device fabrication are are cut from the the ingot and and typical the the D-shaped wafer is produced. The The control of control background impurities impurities crystals in inis the of utmost the utmost importance, imp independent of the the type of crystal being pulled. In the case of undoped undoped high-purity ingots, this this need is obvious. In In the the production of Cr-doped production ingots, it it is just as important important since the the Cr added to compensate the the background shallow donor donor diffuses during the the required anneal procedures anneal folet 1979). This diffusion This can lead to incon- inconlowing implantation (Evans implantation sistencies since the decrease the in the Cr theconcentration reduces concentration the the degree of as obtained, compensation, and layers and with inferior electrical properties are are obtained, discussed below. A novel and proven technique for technique in in situ synthesis situ of the the GaAs in the the 2-atm LEC puller has been refined and is and used to produce substrate material material al., al., 1981).The The apparatus used apparatus for this this technique is techniqu for our use our (Puttbach et (Puttbach this the Ga the and dopant species dopant are loaded are in in shown in Fig. 3. In this procedure, the crucible, the which can be caneither either quartz PBN,quartz and and or B203 or the the encapsulantisencapsulant placed over the melt. the The furnace The is heated and andGa themelt the brought to the the growth temperature, temperature, which time during the time during B203encapsulatesthe melt. the The The injection cell, either either quartz or PBN,quartz is lowered to position the injection the stem through the the B,03 into intoGa themelt. the Arsenic is injected into intomelt the the by a vapor-transport process driven by the the controlled temperature temperature of the the As injection cell. After the As thehas been incorporated in in the melt, thethe the injection injectio cell is extracted through an an air lockairand and seed the the crystal, mounted mounted on the the usual themanner. manner. control rod, control inserted into the melt in in the The The advantage of this this system is that that melt the the is compounded compounded situ, in in eliminating the the need for external synthesis and and potential the the of impurity impurity incorporation incorporation melt. In addition, in in the ifthe addition, all the parts, the including the the injection injectio cell and andcrucible, the the are fabricated from PBN, the the contamination by Sicontamination from necessary; the the quartz quartz is eliminated. parts parts In practice, In the use the of PBN is not not high-purity crystals have been grown in in all quartz systems, quartz as as documented docume

97 97

!! .L

3. 3. of GaAs.

of

cell used

the

below. The crucial The conditions required conditions to produce high-quality semi-insulating GaAs by these techniques include the use of very high-purity starting AA recent investigation by Oliver et al. ( 198 ( 1 ) ha\ material, at least six 9s. 9s. demonstrated demonstrated role of H,O the in in the the theencapsulant, which acts actsgettel as as a a content for Si. For their growth their conditions, in in a a quartz crucible, quartz an an content ot approximately 1000 ppm was necessary to reduce to the Si theconcentration and concentration obtain semi-insulating obtain GaAs. The The importance of theimportance the control of the control the ratio ratio duringgrowth duringofthe non-Cr-doped the semi-insulating ingots has been demonstrated by demonstrated Holmes ( 1982). ( The LEC The technique has technique historically produced ingots with higher disloca tion densities tion than thanBlidgman the the or gradient-freeze or technique. The densit The ICY are in arethe the 1 1X Xlo4- 1 1X Xlo5cm-2 range, depending on the dopant concc'n dopant tration tration and and manufacturer. paper by manufacturer. Holmes et al. The(1983) The presentj presentj experimental distributions of distributions the the dislocation densities, and the the EL2 l e (4~

98

A. A.

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

(four-level model)

or or (three-level model) if N ifA > ND, > then NDD > > - ND) (Swiggard et al., 1979),

where NsDand NSA and are are the the concentration of shallow concentration donors and donors acceptors, of deep concentration deep donors and donors respectively, and NDD and and NDA are are the the concentration in 4, acceptors, respectively. The energy The levels of these dopants, shown in Fig. have been measured by many laboratories. See the recent paper by Martin (1 980) for an overview an of these results. dueS and S and Si as as unintentional unintent The shallow The donors donors believed are are to be due to dopants dopants Te as oran oran to intentional to intentional used to dopant prevent to dopant ptype conversion of the Cr-doped material when it is it used as aassubstrate for substrate epitaxial growth of Teaddition Te for this this purpose is no no longer (Swiggard et al., 1979). The The addition necessary with the improved the purity of the growth the conditions possible conditions today. C, Mn, or Mn, other other impurities impurit The shallow The acceptors are believed are to be due to due the melt. The deep The acceptors are are duethe dueCrtointentionally to added to to the melt theto to compensate the shallow the donors donors intoinassure ordersemi-insulating order material 1X 1 X lo* R cm. R cm. The deepThe donor, donor, EL2the level, the with resistivitiesgreater than than et al. was originally ascribed to to oxygen (Milnes, 1973); however, Huber Huber (1979) demonstrated that thatEL2 the the level is not due to dueoxygen. It is believed is

2.

99 99

AND ??

1.43 1.43 eV eV

ND

eV

E,,

= =0.825 0.825 0.7 eV N,

eV eV 0.62 0.62 eV eV

EF

0.45 0.45 eV eV

0.15 0.15 eV eV

D+ D+ NN

-

4. 4. levels levels

&

of Crz+ Crz+

of

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

100

C . A.

copy (SIMS) (Clegg, 1982), Auger 1982),emission spectroscopy (AES) (Holloway, 1980),spark source mass spectroscopy (SSMS)(Brown el al., 1962), and 1962), arc arc The use of AES is source emission spectroscopy (ASES) (Wang, 1968). 1968). limited due due to the the lack of sensitivity. ASES has been successfully used in impurities such impurities as Cr, with Cr, a a these investigations for the determination of determination 1 X X1015~ m - Si, ~ ;with a detection a limit of limit 1XX 1015~ m - ~ ; detection limit of limit and and Mg, with a adetection limit limit of 4 X 4 X ~m-~ SIMS . analysis has been and to to used by many laboratories to evaluate the the redistribution of Cr Cr measure the the background impurity impurity concentration. In this this application, concentration. extreme care treme must be taken in the interpretation of interpretation results due to duematrix and and background effects. The most The sensitive technique for technique the analysis the of impurities isimpurities SSMS. This This technique requires precise preparation and use of calibration sources and careful operation of the the apparatusavoid apparatus instrumental to to background instrumentallevels which can lead to to erroneous results. erroneous The The data presented data in in Table I Iwere obtained by SSMS at three different facilities from samples taken from the the same regions same of two different high-purity semi-insulating ingots grown in our facilities. For For comparison purposes, results obtained obtained using ASES in these laboratories are included. There are large are discrepancies in the magnithe tudes of tudes the the impurities measured by the the three different threeSSMS facilities for andThe most The consistent and reliable and important species important such as Cr, as Si, S, and 0. results, and and those which are are agreement in in with the the measured electrical behavior, thermal stability, thermal and and implant and implant anneal resuIts, are those are obis is to note to that although that emission spectrostained by tained facility A. It It interesting copy lacks sensitivity, it is in agreement in with the SSMS the analysis of facility A. The The data Table dataI1inwere in obtained by obtained SSMS in facility in for a a number ofnumber different samples from different ingots produced by the the 2-atm LEC technique at nique Hewlett-Packard, F402 and and F450, and by andthe the high-pressure Melbourn puller bournat Metals Research using in situ synthesis. situ Using the three-level the CC is the the dominant shallow dominant model described above, and assuming that that acceptor (Brozel et al., 1978) and 1978) that and Si and S are S are the the dominant shallowdominant donors, donors, the the concentration of the the EL2 concentration level to to produce semi-insulating it material can be calculated. From From the theanalysis impurity given impurity in Table 11, it is seen that these that materials will be semi-insulating if an EL2 level concentra- concentra4X X 10l6cm-3 is assumed for the the LEC materials. This is This the the tion tion of about 4about concentration of concentration the the level that is that quoted quoted in in thefor thematerials literature literature grown by this this technique technique 1980).(Martin, 1980). (Martin, The properties The of these bulk materials, both bothCr-doped the the and and the the nonin- non tentionally doped, doped, high-purity semi-insulating materials, are are discussed in in detail in the sections that that follow and and compared are are with the the properties of bulk material from other sources other and grown and by other techniques. other In addi- addition, tion,properties the the of these bulk materials will be compared with the the properties obtained using obtained very high-purity buffer layers.

Ingot HP Ingot F402 labs labs Element Element (cm-%)

BB CC NN 00 Na

facility (~rn-~)

SSMS facility B B SSMS facility C C SSMS facility A A SSMS facility B B (~rn-~) (cm-3) (~rn-~) (~rn-~) 1.3x

6.6 X X

18.9 x x 1015 53.1 X X10l6

= 1.1 = 1.1 xx 1016

4.0 x x 1014 1014 < 1.2 < x 1015 x 1015 1>X1 X cm-2, the combination combination of the the incident incident ion flux and the substrate substrate temperature temperature the degree determine dete of implant-induced implant-induced damage and, in in extreme cases, extreme whether whether or or not not the the imimplanted planted region is driven driven amorphous. is generally amorphous. agreed It that It that subsethe the quent activation of activation the layer is less if the the sample is driven sample driven amorphous amorphous the implant implant et(Harris (Harris al., 1972). At 1972). moderate moderatedoses, implant in in the implant range 1 1X X 1X 1 X cm-2, the effect of the implant implant temperature on the the temperature

2.

119 119

ION IMPLANTATION AND MATERIALS

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

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

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of As from the surface during during anneal the the and and at the the same same avoidtime the time the species. dopant in-diffusion of contaminates or contaminates the the out-diffusion of the the dopant There are are numerous techniques numerous reported in in the the literature minimize literature the to theto loss of As during during the the including anneal,the anneal, the use of dielectric layers, capless and/or and/or proximity anneal anneal and and transient techniques. transientThe anneal technique annealtechnique used by a given organization is determined by the specific the technology which each has developed. In the the work reported in in this chapter, this the standard standard is thecap the chemical cap vapor deposition (CVD) Si,Ni, dielectric layer described earlier. Other cap Other materials have been evaluated during during investigation this this including reactively sputtered AlN and and Si3N, and CVD Si02. The A1N films had a very low oxygen concentration (less concentration than 2%) as compared to the high oxygen content content films reported in in the the literature (Pashley literature and Welch, 1975). It is believed that that poor adhesion observed is due to duethe the lack of oxygen. Reactively sputtered Si3N, films yielded good adherence but produced but inferior electrical proper( oxygen concentration concentration these films. in in ties. This is due duea to high to ( 15%) Thick, 7000-A CVD SiOz films grown in a Silox reactor at 450°C give 450°C better results for Si implants implants than than the theSi3N, standard cap. standard The CVD C cap anneal for Si implants is implants illustrated in in Fig. 15. The The influence of the the anneal increased doping efficiency for Si implants implants using Si02 caps is due due to the the cap (Vaidyanathan et al., 1977), which out-diffusion of Ga through the the produces Ga vacancies Ga near the surface. the These vacancies yield a higher Si on on a aGa-site concentration compared concentration to to the Si the on an an As-site concentration, concentrati which results in in a net increase in the the n-type concentration for concentration the the ampho- amphoteric Si teric dopant (Bhattacharya dopant et al., 1983). al., Although the the doping efficiency doping is higher using the the oxide cap, as compared as to the the nitride cap, there cap, can be a problem with the the reproducibility of results if the the Ga out-diffusion is is not consistent from run run to toInrun. the run. the case of the the nitride nitrideiscap, no cap, Ga there there out-diffusion; therefore, more consistent results can be canexpected. The The oppo- oppois as as site effect of the the cap material is observed in the the case of Se implants, implants, case, the the nitride nitride gives better cap cap doping illustrated in in Fig. 16. In this this efficiencyas as compared the compared efficiency to obtained to with obtained the oxide cap. The The nitride cap used in these investigations has been very reproducible and and has produced reliable results since the initiation of initiation the the work in in 1975. The thermal The expansion mismatch between the the nitride filmnitride and GaAs and produces cracks in in the nitride the for films thicker than approximately 2000 A. The The surface quality of the samples the is unchanged during during thecycle the anneal using the anneal the standard 1500-A-thick cap. The The nitride films produced are are pinhole free; there is there rarely evidence of a thermal etch thermal pit pit due to adue pinhole in in the the nitride nitrid film. An indication indication of the the integrity of the the nitride films nitride is the the successful annealing of samples with nitride nitride films as thin thin as 300A with excellent surface properties and and electrical characteristics. The The through-nitride-im-

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

122 122

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

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the evaporation the of metal contacts at room temperature. temperature. values in Table The in The VI are areagreement in in with those predicted by the theory the of Chang et al. (al. 197 ( 1) assuming a bamer height of 0.6 eV and andmeasured the the surface concentration. concentrati 1O-’ 1 IR cm2have cm2been obtained Layers with contact resistances contact as low as 2as2X X using nonalloyed CrAu contacts to high-dose laser annealed GaAs. The sheet The camer concentrationdecreases concentration rapidly during post-laser during anneal anneal Fig. 3 13for 1 the case the of high-dose Te Te implants implant heat treatments, treatments, illustratedas in as

3 1.3 The change in change the sheet the camer concentration concentration a function a of function the post-laser anneal anneal for a a Te Te implant into an implant LPE an buffer layer to a a dose ofdose 5 5X X cm-2 isochronal heat isochronal treatment treatment 250 at 250 keV.

142 142

C. A.

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

10-6 G-

I I

5" "5 a a

10-7 10-7

tt

101 00

II

200

II

400

II

I I

I I

I I

600 600 800 8001000 1000 1200

I I

32. Se

of 5ofX X

250

11 30

2.

ION IMPLANTATION AND MATERIALS

143

resistance changes rapidly for short short times and and then increases then with a time time 5000 hr. This stability This is better better than that reported for constant constant of about about et al., 1981). contacts The 1). values of e-beam annealed AuGe-Pt AuGe-Pt ohmic(Lee ohmic contacts contact contact resistance, maintained during during heatthe treatment, the treatment, with taken the the taken lOO-Q/sq value for the sheet resistance, indicate that these contacts would contacts be acceptable for MESFET applications. To apply the the laser mneal technique to technique the the fabrication of circuits, it itis necessary to laser to anneal anneal the the regions contact selectively contactwhile protecting the the channel regions. channel The laser The annealing of channel region implants produces implants very high-resistivity regions due duea to large to defect density produced during during the the rapid regrowth during during laser theanneal the anneal process. The The techniques for for selective laser annealing have been investigated in these laboratories. The The procedure developed to to provide this this selective anneal anneal uses an an A1 mask to to reflect the incident laser radiation to to protect the the quality of the channel channel - drain non- nonregions. MESFETs employing selectively laser annealed source-drain alloyed contacts have contacts been fabricated. The dc The characteristicsof these devices are comparable are to devices to fabricated using standard alloyed standard ohmic contacts. ohmic The long-term The stability of these devices is under investigation. under

IV. Device Results 9. IC FABRICATION

The materials The and and implantation technology implantation described have been used to to produce GaAs ICs of true MSI complexity. Examples of these circuits circuits are are the the generator (PRBS) (Fig. 33) operating at operating 1982b) and and MSI the the word generator (Fig. I), 2.5-Gbit/sec (Liechti et al., al., Gbit/secet 1982a). which operates at data data rates as high as 5 5Gbit/sec (Liechti These circuits employ selective ion ion implantation implantation high-purity LPE into into buffer layers, grown on Cr-doped substrates or grown or on on high-purity substrates, or implants implants directly into into high-purity substrates. Figure 34 shows cross sections of a transistor, a diode, and and interconnections as implemented interconnections implemente in these in circuits. Figure 35 illustrates schematically the process the steps used in in the fabrication the of the ICs. the The MESFET The channel is formed by selective ion implantation of implantation 6 X 10l2 500-keV Se ions into the intosubstrate (heated to 350OC) to atodose of 6 X cm-2 using an an 0.8-pm-thick A1 mask to to define the the implanted regions. implanted The The substrates are implanted bare; implanted no through-dielectric implants implants used. are A are second selective Si ion implant is implant used in addition addition Se to implant to the implant the in in the t active area of area diodes and under under the the ohmic regions ohmic ofcontact the transistors the contact to lower the sheet resistance. For this purpose, this Si is implanted at implanted 500 keV to a dose of 1 X XlOI3 cm-2 using an an A1 mask with the the substrate at room

144

C.

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of 400 MESFETS

33. 1.1

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temperature. temperature. After removal of the the A1 mask, both both implants implants are are sim for 15 min using the the Si3N4cap. The resultant resultant neously annealed at this this region has has sheet doping doping profile under under gate theisthe shown in Fig. 11; 11; The The dual species, dual Se plus Si, implant Si, region implantprofile is is resistance of 325 This has a sheet resistance of 120 shown in in Fig. 30. This region The The ohmic ohmic used contacts are are processed contacts in in a conventional conventional way by a multilayer evaporation of evaporation NiCr, Au, Ge, Au, and Au, lifting of the excess metal outside outside the the contact surface contact capping, patterns, andpatterns, alloying. The resulting the resistspecific contact resistance contact is typically 2 X X $2cm2, and the sheet

146

C. A. STOLTE STOLTE

ance of ance the alloyed the Au-Ge Au-Ge metal film is 1.3 As indicated, indicated, andohmic ohmi Schottky contacts have contacts been produced during during thefabrication the same same step by step use of the very the high doping doping concentration layers produced concentration by produced laser annealing annealing of high-dose implants. Laser-annealed implants. contacts have contacts not not been used in the the fabrication of the the described here. The gate The processing step step by isfaristhe the most crucial part part of the processing the sequence used to produce the integrated circuits. Here, Here, high resolution is resolution l-pm gate lines printed on printed the the required in the the lithography of thousands of thousands wafer. This is This a very complex procedure which, in in summary, is as summary, follows: The gate The lines are fabricated are by lifting evaporated metal with a combination combinatio of two positive resist layers. Prior Prior to the gate-metal gate-metal evaporation, evap channel channel region is precisely etched to a depth depth of 0.12 pm,leaving a gate trench above the FET the channel. channel. This lowers Thisthe trench level the trench of the Schottky the contact below contactthe the unpassivated GaAs surface. This gate Thisgeometry yields a lower series resistance of the the source and drain drain compared to a compared planar planar structure with structure the same the gate-cutoff voltage. It also reduces the modulation of modulation the the drain drain current to changing currentdepletion due due layer depletion widths at the free the surface during switching during transients. Finally, it allows it adjustment of adjustment the gate-cutoff the voltage during during processing. The circuits circuits are completed by an an intermetal intermet dielectric deposition, via deposition, patterning, and patterning, the deposition and and patterning of patterning the second the metal. metal. The The processed circuits ascircuits described as above, e.g., the PRBS the functional circuit shown circuit in Fig. in 33, have a 30% functional yield. This process technology differs in some fundamental ways fundamental from that used et al., 1980). In the Rockwell the process they at Rockwell International (Welch International implant implant through a Si,N, dielectric layer and and maintain thatmaintain passivation throughout throughout process,the except the for metallization regions. They do do not usenot a well-defined materials materials the the recessed gate process and therefore rely on on characterization and characterization implant implantto control provide control the the needed control of control the the 8X 8 8multi- multidevice parameters. This Thisproduced has has a high-performance 8 X 1000gates on aon2.7 X 2.25-mm X chip (Lee chip et plexer circuit that contains over contains a/., 1980). 10. IC PERFORMANCE

The 5-Gbit/sec The GaAs word generator IC shown in Fig. 1 consists 1 ofan 8 :81:1 parallel-to-serial converter, timing generator, generator, logic, control and control and emitter emitter coupled logic (ECL) interface (ECL) networks. The circuit generates circuit multiple multiple 8-bit 8words whose number number can be dynamically controlled. In the the circuit, circuit, data from eight parallel input input channels are amplified channels and applied to a tree of tree 2 :21:1 multiplexers that connects connects eight inputs the theto inputs a single output in a time-mul- time-mul:21:GaAs 1 multiplexer GaAs used in the the tiplexed sequence. The key featuresof features the 2the circuit are circuit its speed its and and its capability of generating clean waveforms with fast transition times. transition Even at a 5-Gbit/sec data rate, the the circuitperfectly circuit is is

2.

147 147

AND

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

c: 0 Ul

0

(2,5

SYNC.

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

148

C. A. A. STOLTE

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

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

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

150

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

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

The work The reported here has demonstrated demonstrated theofthe thecurrent the art current art in insta materials preparation and and ion implantation implantation technology required for the the

152

C.

production of MSI GaAs The The materials technology has made great strides during the last the four years; there is now available an ample supply ample of high-quality materials to provide the the necessary starting materials for for the the the of ion ion implantation, the implantatio further advancement further of IC technology. In the area necessary techniques and procedures and are available are to allow the the production product of selectively implanted regions, implanted with adequate quality adequate and reproducibility The growing The degree of complexity and and the the to satisfy to the needs the of today’s increased degree of integration, beyond the several the hundred transistor hundred level that is now being integrated on a chip, will require further further improvements impro the the materials and implantation technology. implantation In the area the of materials, the question the of the the importance of the importance dislocation the density has not been not resolved. Dislocations in in the the channel region could, channel for example, result in increased gate current current leakage, a decrease in the the gate breakdown voltage, and produce and diffusion spikes of the implanted species during during anneal thecycle. the These effects will become increasingly important as important the the relative area of the channel the region increases. It is expected that, that, as the the density of the devices the increases, it will it be necessary to reduce to the dislocation the 1X 1 X 10s-cm-2range, which is now available by at density from the 1 X1 Xlo4to to least an order an of magnitude in order in to provide reasonable yields at higher integration levels. At the present the time, it it appears that appears the dislocation the density be expected to change in in the the is not is the limiting the factor on yield, on but but that can that future. future. Another requirement for the the realization of large-scale integration (LSI) will be the availability the of large, at least 76-mm diameter, wafers grown in the the [ 1001 [ direction, with an an orientation flat,orientation to allow to the use the of modem processmodem ing equipment. equipment. Wafers with these characteristics have been successfully al., al., pulled by several laboratories with the the desired high purity (Thomas et (Thomas Chapter 1, this volume; this Kirkpatrick et al., al., Chapter 3, this volume). this Additional concerns now being formulated are are rapidly becoming firstorder effects rather rathersecond-order than than effects. These problems include include the the influence of the starting the material and and the the implant processing implant procedures and and on on the phenomena the of backgating, noise, gain compression, light sensitivity, As the technology the matures, these and other other and andreliability the the of GaAs as yet unidentified problems will occupy the efforts of the research labora- laboratories. In the the past two years, great strides have been taken taken to increase the the in all in phases of its development: its The production of production technology of GaAs improved quality material in in quantities thatquantities will support support development the the efforts; the the maturing of the maturing the implant implant technology and and anneal to to anneal the the point point IC design, where it is it more than than a laboratory technology; and sophisticated and circuits been demonstrated with demonstrated practical where true MSI true complexity circuits have yields. Finally, the the process technology necessary to produce these circuits has been demonstrated.

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The The MSI, < 1<X 1 X lo3 gate/chip, circuits described in in this this chapter were chapter fabricated using depletion-mode MESFETs in in BFL and andSDFL in in circuit configurations. The device The structures structures circuitand types and that that be canused canto to extend the level the of integration are described are in in detail detail articles in inby theEden the et al. (1979), al. Eden (1 982), Lehovec 982), and Zuleeg and (1980), and Bosch and (1980). It It is generally agreed that the the next step to step LSI, 1 X X lo3 to 1 X Xlo4gates/chip, lo4 can be accomplished using depletion mode MESFETs and and SDFL whenSDFL improvements improvements materials and in and active in layer uniformity, which are are well within the the realm of possibility, are are implemented. These circuits should operate in the 2the - 3-GHz/sec clock frequency range, lower than those dem- demonstrated with onstrated BFL but but with increased complexity. The use Theof enhancement mode enhancement MESFETs could increase the gate count count into the very the large-scale integration (VLSI)range, > 1>X X lo4gates/chip, with clock frequencies greater than than 1 1GHz/sec. These devices will require a very a stringent control of the doping the profile in in the active the channel region in in order to order produce a totally a depleted channel region for zero gate bias and still provide a good a device transconductance for gate voltages less than than about 0.5 V,about the the maximum gate maximum voltage which can be applied without drawing excessivegate current. Another current. candidate for candidate use in in the the regime is is the the enhancement enhan VLSI mode junction junction field effect transistor (JFET). transistor In this device, this the the channel-region doping is somewhat less stringent than thane-MESFET the the since the the junction junction characteristic allows a alarger gate voltage swing. However, the the investigations to to date date on device on this have thisindicated problems with the the control of control the geometry the of the device the due due tolateral to thediffusion the of the p-type the dopant dopant during during cycle, theinthe in the anneal case theofanneal implanted devices, implanted or during during the the diffusion of the the dopant for dopant diffused junction junction devices (Dohsen et al., al., 1981). 1981). In order order to to penetrate regime penetrate of VLSIthe complexity, the there thereseveral are are improvements which improvements must be made. First, the materials the used as substrates will have to have improved uniformity of electrical characteristics and and improved dislocation densities. Second, the the production of theproduction n-type the regions for enhancement mode enhancement MESFET devices or the p-type the regions for JFET JFET devices will require improved control of control the the doping profiles doping produced by ion ion implantation. implantation. In this this area, alternate alternate techniques such as organo-metallic vapor-phase epitaxy and molecular beam epitaxy (MBE), with appropriate isolation appropriate techniques, will be evaluated as an an alternative to ion alternative implantation. Finally, implantation. the the process techniques used to to produce these produce complex circuits will have to to be compatible with the materials and active-region - formation techniques formation in order order produce to to practical yields of functional circuits. It is the the author’s judgment judgment that the the decade of the the 1980s 1980s will see the the practical production production of GaAs circuits of LSI complexity operating with

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clock frequencies in in the 2 -2the 3-GHz/sec range. The The competition fromcompetition smalla in in the high-speed the geometry Si devices (Lepselter, 1980, 1981)will be a factor LSI devices. However, the the inherent advantages inherentofGaAs over ofGaAs Si, namely, the the higher electron mobility and electron and velocity at low fields and the availabilthe higher switching ity of semi-insulating substrates, makes possible much much as compared as to Si. The future for future GaAs indeed GaAs looks speeds for bright, and and we can look forward to to the thewhen time GaAs time is no no longer the the but the future the material of the present. material of the the future ACKNOWLEDGMENTS

The The author author his thanks extendsto thanks extends his colleagues at Hewlett-Packard who who contributed to thecontributed the particular, to particular, Grant Elliot, Bill Elliot, Ford, and Ford,Dick Dick Putback, who Putback, work reported in in this this chapter. chapter. used;material to Simone material Simone Malcolm and Mane Malcolm Amistoso, who grew who grew most of the the substrate substrate for his Hansen, his expertise in ion expertise ion implantation; implantatio and characterized the LPE the buffer layers; to Jim Jim Hansen, processing of samples. The samples. inclusion of inclusion results results and to Vibeke Bitsch and Jessie Kafia for the the of supplied by supplied Ed Stoneham, Stoneham, Chris Chris Kocot, andKocot, Joe Diesel Joe Pieroadded Piero to added Pianetta, the breadth Pianetta, breadth the chapter chapter and content is acknowledged. content The excellent excellentcooperation of Charlescooperation Charlesand Liechti his Liechti Noll, Ruth Devereaux, Devereaux, Lanick, andRod Falke Falke IC group, group, including including Elmer Elmer Gowen, Gowen, Ruth RuthRod The substrate substrate materialsby materials Ed supplied su Hennig has Hennig aided aided all phases in in of the work reported. reported. of Metals Roland Metals Ware Research, and Ware Ian Research, Ian Sanders of Sanders Swiggard of Naval Research Laboratory, Laboratory, Roland Plessey Research (Caswell) Ltd. increased the scope of the of the materials materials The evaluation. enthusias-evaluation. enthusiasthese investigations,the investigations, useful and stimulating discussions, stimulating and tic tic support support the course duringof course during of this this chapter by Bob chapter Archer, Charles Charles the constructive constructive comments regarding the content content Bittmann, Bittmann, and Liechti and Charles are are appreciated Charles appreciated acknowledged. and Finally, and the Finally, assistance by assistance of the illustrations illustrations and the the manuscript is manuscript Soyla Ybarra Ybarra and and Hill JoAnn in in the preparation JoAnn preparation appreciated. appreciated.

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Lee, F. F. S., Shen, E., Shen, Karlin, G. Karlin, R., Welch, B. M., M., Eden,C., Eden, and R. Long, R. S. Long, I. (1980). Paper Paper No. 3. and Zuleeg, R. R. (1980). Devices ED-27, 1074. Lehovec, K., K., Devices p. 42. Lepselter, M. P. (1980). (1980). Lepselter, M. P. (1981). (1981). S(Mar.) (news supplement supplement V. R., and Evans, C. A., Jr. (1978a). 32, 32, Lidow, A., Gibbons, J. Gibbons, F., Deline, V. Deline, 572. F., Magee, (1978b). 49, 5213. Lidow, A., Gibbons, Gibbons, J. J.T., and Peng, J. J. R., R., and Evans, C. A., Jr. (1980). J. 51,4130. Lidow, A., Gibbons, J. Gibbons, F., Deline, V. V. (1976). M’IT-24,279. Liechti, C . A. A. M., and Podell, Namjoo, A. Podell, F. (1982a). Liechti, C . A., Baldwin, G. L., Gowen, E., Joly, Joly, R., R., Namjoo, Devices ED-29, 1094. Gowen, and Joly, R. Joly, (1982b). (1982b). Liechti, C. A., Baldwin, G. L., Gowen, E., Conj, Dig Pap., p. p. 172. Liechti, CLiechti, . A., Stolte, C. Stolte, A., Namjoo, M., Namjoo, and Joly, R. (1982~).Final Final Rep. Rep. AFALTR-81-1082. AFA Air Force At. Lab., Air Force Syst. Command, Wright-Patterson Air Wright-Patterson Force Force Base, Ohio. Ohio. F. (1977). J. 48, 1262. Lindquist, P. Lindquist, “GaAs “GaAs FET Principles Principles and Technology” Lindquist, Lindquist, P. F., and Ford, Ford, W. M. (1982). (J. (J. DiLorenzo andDiLorenzo D. Khanderwal, eds.), Khanderwal, p. 1. Artech House, House, Dedham, Dedham, Massachusetts Gautard, D., Devillard, D., P., and Martin, G. Martin, M. (1982). 40, Makram-Ebeid, S., Makram-Ebeid, 161. 161. and Whelan, J. M. J. (1976). J. 123, 123, 1413. Malbon, Malbon, R. M., Lee, D. H., H., Materials” Materials” J. Rees,(G. ed.), (G.p. 13. Shiva, Shiva, “Semi-Insulating 111-V “Semi-Insulating Martin, Martin, G. M. (1980). (1980). Orpington, Orpington, England. P.,G., and Poiblaud, G. Poiblaud, (1980). 51, Martin, G. Martin, M., Fargas, J. J. P., P., Jacob, Hallais, Jacob,J.G., 2840. Mayer, J. W., Marsh, 0. J., Shifrin, G. Shifrin, A., and Baron, R. ( 1 967). Can. J. 45,4073. 45,4073. Mazelsky, R. (1962). J. 33,2016. Metz, E. P. A., Miller, R. C., and and in Semiconductors,” Impurities Impurities p. Semiconductors,” 57. Wiley, New York. York. Milnes, A. G. (1973). (1973). “Deep “Deep T., S., Hiyamizu, Fujii, T., Fujii, and Nanbu, K., (1980). Jpn. (1980). J. Jpn. 19, L225. Mimura, T., Hiyamizu, B. (1980). Appl. (1980). 36,927. Molnar, Molnar, Y. Y. (1979). Phys. Phys. 50,6413. 50,6413. Morkoc, H., Morkoc, and Cho, A. Cho, J. Cryst. 36, 109. Morkoc, H., Morkoc, and Eastman, Eastman, L. F. F. (1976). (1979). 35, 337. Mozzi, R. L., Fabian, W., Fabian, and Piekarski, F. J. J. B. Mullin, “Crystal Growth Growth and Characterization” (R. Characterization” Ueda and J. J. (R. Mullin, Mullin, Mullin, B. (1975). J. J. (1975). Publ., Amsterdam. Amsterdam. eds.), p. eds.), 6 1.6 North-Holland North-Holland Holliday, H., and Straughan, B. Straughan, W. (1968). J. Cryst. Mullin, Mullin, B., Heritage, J. J. R.J., Holliday, C. 3/4,28 I. Oliver, J. J. R., Fairman, Fairman, D., Chen, R. R. Chen, R. T., and Yu, P. W. (1981). (1981). 17, 839. 18, 977. Pashley, R. R. D., andD., Welch, B. M. 975). ( 1 970). J. 20,857. Pekarek, L. Pekarek, P. A., Stolte, Stolte, C. A., A., and Hansen, Hansen, J. L. (1980a). “Laser “Laser and Electron Electron Beam Pianetta, Pianetta, W. White White and P. S. Peercy, eds.), p. p. 328. Academic Press, Academic Processing of of Materials” (C.Materials” New York. Pianetta, P. Pianetta, A., Stolte, C. A., C. A., and Hansen, Hansen, L. (1980b). J. J. 36, 597. Amano, J., Amano, Woolhouse, G., G., and Stolte, C. Stolte, A. (1981). In “Laser and “Laser Electron- ElectronPianetta, P. Pianetta, Beam Solid Interactions and Interactions Material Processing” Material (J. F. Gibbons, L. Gibbons, D. Hess, and T. W. Sigmon, eds.), Sigmon, p. p. 239. ElsevierJNorth-Holland,New ElsevierJNorth-Holland, York. York. R. R. C., Elliot, G., Elliot, and Ford, Ford, W. M. (1981). Con6 Puttbach, Puttbach, ConJ Cryst. Diego, Calg

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Rode, Rode, D. L., and L., Knight, S. Knight, (197 1). 3,2534. (1973). Jpn. J. 12,242. Sato, Y. Sato, (1982). 13,21. Sealy, B. J. (1982). Microelectron. S., Stephens, K. Stephens, G., Croft, R., Croft, and Palmer, Palmer, (1978). (1978). 14, 14, Sealy, B. J., Kular, S. Kular, 720. Stevens, B. (1978). (1978). Proc. No. 50, 50,671. 671. Devices p. 585. Stolte, C. Stolte,(1975). (1975). ConJ Ion Ion Stolte, C. A. ( I 977). Colo., 1976 p. 149. Stolte, Stolte, C. A. A. (1980). (1980). In “Semi-Insulating 111-V “Semi-Insulating Materials” Materials” (G. J. Rees, ed.), p. 93. Shiva, Shiva, Orpington, England. Orpington, J. M. (1980). 47, 143. Stoneham, E. Stoneham, B., Patterson, G. Patterson, A., and Gladstone, J. Gladstone, (1977). SOC.124, 1806. Stringfellow,G. B., and Hom, G. (1977). J. J., Fischer, J., T.R.,T.R., and and Morkoc, H. (1983). Morkoc, Su, S. Su,L., Tejayadi, O., Drummond, Drummond, 130. Devices Devices M., Lee, S. H., and Von Batchelder, F. W. (1979). Con$ (1979). - No. 45, 45, Swiggard, E. E. p. 125. Eldndge, W., G. Barrett, D. Barrett, L., and Braggins, T. T, (1 98 Thomas, R. Thomas, N., Hobgood, H. M., Eldndge, G. 24, 387. L., Braggins, T. T., and Ta, L. B. Thomas, Thomas, N., Hobgood, R. R. H. Hobgood, M., Eldridge, G. W., Barrett, D. Barrett, “Semiconductors Semimetals” (R. Semimetals” K. Willardson and A. A. C. Beer, eds.), eds.), (1984). In “Semiconductors and I , this volume. this Academic Press, Academic New York. York. Chap. Chap. Troeger, G. L., Behle, A. A. F., Fnebertshauser, Fnebertshauser, E., Hu, K. L.,P.and P. Watanabe, Watanabe, S. H. (1979). Dig. - Devices p. 497. D. C., Gossard, A. Gossard, A. C., Kaminsky, G. Kaminsky, and and Wiegmann, W. (1Wiegmann, 98 39, Tsui, Tsui, 712. R., and Cardwell, M. M. J. (1979). Conf Jay, P. Jay, Tuck, B., Tuck, Adegoboyega, G. No. 45, 114. P. N., N., Delescluse, P., Delagebeaudeuf, D., Laviron, Laviron, M., Chaplart, Chaplart, J., J., and Linh, Linh, N. T. T. 18, 518. (1982). Vaidyanathan, K. Vaidyanathan, V., Helix, M. J., M.Wolford, D. J., Streetman, B. Streetman, G., Blattner, R. Blattner, J., and Evans, SOC.124, 124, 1781. C. A., Jr. Jr. (1977). J. (1958). 13, 1. van der Pauw, der L. J. J. Van Tuyl, R. Tuyl, L. (1978). ISSCC Dig. ISSCC Pap. Feb., p. p. 72. Van Tuyl, R. Tuyl, R. L. (1980). L. Dig. Pap. Feb., 118. Gowen, 977). J. Van Tuyl, R. Tuyl, L., Liechti, C. A., Lee, R. E., and Gowen, E. SC-I2,485. Van Tuyl, R. Tuyl, R. L., L., Kumar, Kumar, V., DAvanzo, D. C., Taylor, T. Taylor, W., Peterson, V. Peterson, E., Hornbuckle, Hornbuckle, and Estreich, D. B. (1982). Devices ED-29, D. P., Fisher, R. 1031. and Garrett, Garrett, J. P. J. P. (1972). 15,443. Vilms, J., J., 22, 761. Wang, M. S. (1968). Shen, Y., Shen, Zucca, R., Zucca, R., Eden, Eden, C., and R. R.Long, S. Long, 1. ( 1 980). 980). Welch, B. M., M., Devices Devices ED-27, 1 1 16. Wilson, R. R. G . (1976). (1976). 29, 770. G., and Deline, V. Deline, R. (1980). 37, 793. Wilson, R. R. E., andG. and G.Dimmock, J. 0.Dimmock, (1970). J. (1970). 41, 501. Wolfe, C. M., Stillman, Stillman, Woodcock, J. M. (1976). (1976). 28, 226. R., J. K., and K., Lehovec, K. (1978). Devices ED-25,628. ED-25,628. Zuleeg, R., Notthoff,

VOL. 20

AND AND

33

LEC C. G. Kirkpatrick, R. T. Chen, D. Chen, E. P. K. R. Elliott, R. Elliott, D. Fairman, f fand R. Oliver

Asbeck, Asbeck,

AND

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

159 161 161 . . . . . . . . . . . . . . . 163 . . . . . . . . . . . . . . . . 167 I. Dislocation Studies Studies . . . . . . . . . . . . . . . . . 168 168 2. Single-Crystal Yield Single-Crystal (Twinning) .(Twinning) . . . . . . . . . . . 182 182 3. Surface Surface Inclusions Ga Ga. . . . . . . . . . . . . . . . 187 4. 4.TEM Observed Microdejects . . . . . . . . . . . . . 187 5 . Conclusionson Conclusions Crystalline on Crystalline . .Quality . . . Quality ..... 190 190 Iv. Iv. AND . . . . . . . . . . . . 192 192 6. Chemical Chemical . Purity . . . Purity . . . . . . . . . . . . . . 192 7. Electrical and Optical Characterization. Characterization. . . . . . . . . 195 8. 8.Compensation Compensation . .Mechanism . . . . .Mechanism . . . . . . . 206 206 9. Residual Residual Impurities . . . . Impurities . . . . . . . . . . . . . 208 V. ........... 212 212 10. Approach . . . . . . . . . . . . . . . . . . . . . 212 1 1.1 Substrate Substrate Influence . . . . .Influence . . . . . . . . . . . . 216 216 12. Impact Impact of LEC GaAs . . . . . . . . . . . . . . . . 222 ..................... 226 226 227 227 13. Electrical Properties and Compensation Compensation . Mechanism . . Mechanism 14. Structural Perfection. . . . . . . . . . . . . . . . . 228 228 15. 15. Crystal Growth Crystal Technology. Technology. . . . . . . . . . . . . . 229 229 16. Application to Application ICs. . . . . . . . . . . . . . . . . . 229 229 ..................... 230 230

I. 11. 111.

of device

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Screening Screening parameters parameters Field effect Field transistor transistor Screening Screening parameters parameters Three-five Three-fiveof(columns (columns 44 Gallium Gallium substitutional on substitutional periodic periodic table) table) Ga, antimony site site Six nines (0.999999) six 9s Pyrolytic Pyrolytic boron boron nitride EPR EPR nitride Electron Electron paramagnetic paramagnetic PBN resonance resonance 11 1 crystal 1 axis orientation orientation (111) substitutional 100 crystal plane plane orientationA%. orientation Arsenic substitutional on (100) gallium gallium site site TEM TEM Transmission Transmission electron electron Electron trap Electron label microscopy microscopy EL2 Gallium Gallium vacancy site site density pit pit EPD EPD Etch Etch vo. Density of Density ionized ionized centers centers Burger vector Ni Electron Electron density density Burger vector bb Density of Density neutral neutral centers centers Extinction Extinction distance distance Extinction coefficient Extinction Equilibrium Equilibrium constant constant KK EE Shallow acceptor acceptor concentra- concentr Bragg absorption absorption SS tion tion SADP SADPSelected-area diffraction diffraction Shallow donor concentration concentration patterns patterns NDSD concentration concentration of Bright field BF Black and white residual residual acceptors acceptors B/W concentration of carbon carbon Scanning Scanning transmission transmission Net Net concentration STEM electron electron microscopy microscopy acceptors acceptors Concentration Concentration of EL2 deep deep Cone angle Cone 99 Secondary Secondary mass spectrosion ion donors SIMS PITS PITS Photoinduced Photoinduced transient transien COPY spectroscopy spectroscopy Local vibrational vibrational mode mode LVM angular angular momentum with momentum state R-PITSstate R-PITS PITS using rise in photocurrent photocurrent p,,2 PITS using PITS decay I= D-PITS Orbital Orbital angular momentum angular Al Change in Change current current II Current at time time Total Total angular momentum angular Current at time time Symmetry label Symmetry or electronic electronic r7 Emission Emission of traprate rate state state el - t,), -sampling sampling rate rate or electronic electronic Symmetry label Symmetry r* Time state state Type unknown unknown U? Optical cross Optical section section Vapor-phase epitaxy epitaxy WE Full-width-at-half-maximum Full-width-at-half-maximum AE Hole trap Holelabel label energy of spectral spectral feature feature UU Cross section section Tetrahedral Tetrahedral group group TD Semi-insulating Semi-insulating Angular momentum Angular state state SI Electron trap Electron label label EL3 EL3 with I = I 0,= 4 4 Electron label E M threefoldElectron trap Point Point group group of of threefold Electron trap Electron label label symmetry symmetryaxis about aboutEL7 an Schottky Schottky field barrier effectbarrier Boron substitutional on substitutionalMESFETs MESFETs BAI transistor transistor arsenic arsenic site site Junction field effect transistor transistor JFETs Gallium Gallium substitutional on substitutional GaAs Metal Metal insulator insulator semiconducto MISFETs MISFETs arsenic arsenic site site field effect transistor transistor Arsenic vacancy v*, Buffer field effect transistor transistor BFL Spherical Spherical spin- spin- orbit orbit splitting splitting P P logic parameter parameter Schottky Schottky fielddiode effectdiode Cubic Cubic spin spin -orbit -orbitSDFL splitting splitting 6 6 transistor logic transistor parameter parameter - VLSI splittingVery large-scale integration integration Effective spin-orbit spin-orbit splitting AA FET FET 111- v-

cc

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161

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

162 162

G.

et al. al.

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

3. 3.

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GaAs

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

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

-- --

OXIDE

1.

of

of

164

c. G .

et al.

GaAs. Although the initial the cost of crucibles is high is (generally $4000- $6000, depending on on quantity quantity manufacturer), and and the crucibles can can be crucibles is favored is cleaned and reused and about aabout dozen times. The use of due due tohigher to the yield the of high-resistivity single crystals, as will as be discussed later. GaAs melt can can be changed by varying the the The The stoichiometry of the the composition of the charge. the To make an accurate accurate determination of the the determination initial initial As from the the melt composition, it it necessary is is to take to into account the account loss of As from charge during the the heat-up cycleheat-up resulting from incomplete wetting incomplete of the the B203 to the the crucible (particularly crucibles) before synthesis. The The weight loss is determined by comparing the weight the of the initial charge initial with the weight the of the the crystal and the charge the remaining in the the crucible after the the growth process. The Theconcentration of concentration melts has effectively been vaned vaned fraction. When samples for for characterization were from 0.46-0.51 1atom atom obtained along the the length of the the crystal, the the melt composition for composition each sample was determined by determined adjusting the the initial meltinitial composition for for the the crystal weight at the the time of growth. time The crystal weight and and length are recorded during growth during as a function of function time. time. is loaded on top of The Ga, Thewhich is solid to to just above justroom temperature, room the theGa serves to encapsulate the the As. Starting with a the the As so that that liquid crucible is heated to between 450 450 and and chamber pressure of 600 psi, the the 5OO0C,at which point the B203 the softens, flows over the charge the of Ga and As, and seals at the the crucible wall. The The boric oxide flows at relatively low occurs. The The temperatures (450"C) before significant arsenic sublimation sublimation Bz03floats on on top of the topthe melt and wets and the surface of the the crucible and the the = GaAsmUJ = occurs growing crystal. The synthesis The reaction (Ga%~d at about about 800°C. 800°C. The The presence of the the B 2 0 3 and and use the the of high argon overpressures (- 1000 psi) prevent significant loss of As As due duesubliminato to tion tion evaporation and and during and during subsequent to the the exothermic synthesis. exothermic The GaAs The melt is effectively sealed by the boric the oxide, suppressing not only not As loss As but also but shielding the melt against contamination from contamination the crucible the and growth ambient. ambient. melt The reaction The is then allowed to to equilibrate equilibrate an the growth the procedure begins. Growth is initiated by initiated dipping the the seed, which is held on on the pullthe shaft, B203 and and into the melt. into The The seeds are are generally through the the transparent transparent sliced from low dislocation material. The The crystal is grown by gradually withdrawing the the seed from the the melt. The The system configuration during during The diameter diameter gradually is and is controllably and growth is shown in Fig. in 2. The crystal increased to to full dimension. The The seed and the the crucible are are rotated in the the 6 and 15 rpm,respectively. The pull Therate for ratethis work this was same direction at 6 and 7.0 mm hr-', and and crucible lift rate was 1.4 mm mm h r l . When the the growth process was terminated, terminated, crystal was thepositioned the above the B203 the encapsu-

++

3.

165

GaAs

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.:.

of

2. 2.

of

B203during

OXIDE

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during

Si,N,

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166

4. 4.

et al.

sections of

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

3.

167

GaAs

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

111. Crystalline Quality

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

168

c.

al. al.

and and distribution, conedistribution, angle, and andeffects the theof B203 height, ambient presambient sure, seed quality and and necking, diameter control, control, stoichiometry. and and 1.

STUDIES STUDIES

Current Current interest in in large-diameter GaAs crystals grown by the the LEC at., at., 1981;(Fairman Thomas Thomas al., al., 1981) stems from stemsthe need the technique technique (Fairman for substrate material for digital and and monolithic integrated monolithic circuit fabricaAs these circuits become larger and and more complex, more possible adverse tion. tion. effects from dislocations on device on performance and reliability may appear. appear. However, at this stage this of development, there have therebeen virtually no systema first step, the the atic atic studies reporting the the possible role of dislocations. density and and distribution of dislocations distributionacross large-diameter substrates have been characterized and the andmeans by means which these are controlled are by the crystal growth process is determined. This determined. understanding understanding also important is important is for the the application of large-diameter LEC material to minority-carrier devices such as solar as cells, where low dislocation densities are required are to achieve high minority-camer lifetimes minority-camer and and diffusion lengths. A principal A cause of dislocationsin bulk in GaAs crystals is stress induced by induced thermal gradients thermal (Penning, 1958;Mil’vidskii and Bochkarev, and 1978;Jordan Jordan al., 1980; Jordan, Jordan, 1980) during crystal during growth. Radial gradients Radial are of particular concern in Czochralski-type growth configurations (LEC, Grem- Grempublished dislocation studies on GaAs concern concern melmaire). Most of the the small-diameter (10,000 large-scale integration (VLSI) levels gates). The The circuit of Fig. 25c is direct-coupled FET logic (DCFL), which employs enhancement-mode enhancement-mode FETs,(normally and typically (normally has theoff) theoff) al., 1980; Zuleeg et lowest power consumption requirements consumption (Mizutani et (Mizutani al., 1978). The logic The voltage swings are lowest are with this approach; this they are are limited by the the Schottky bamer turn-on turn-on voltage to avoid conduction conduction of substantial current current from gate from to thethe source. thethe The allowable variations in variations pinch-off voltage, processing, and substrate characteristics are are also the the smallest. Fabrication yield is currently currently a significant problem with this this approach. In In addition to addition these three three types of circuits, a variety of other other circuit approaches and FET and approaches have been demonstrated (Nuzillat, demonstrated 1980). For all cases, however, at the high the switching speeds achievable with GaAs,it is of major concern to maintain low-energy maintain dissipation per switching operaa high level of circuit integration can can be obtained obtained without tion so that that excessive power dissipation per chip. The high The level of integration is particuis larly advantageous because it reduces the system the burden of burden long-delay-time chip-to-chip interconnection, which interconnection, might negate the the system advantage obtained by obtained using high-speed gates. On On the thehand, otherfor other low switching energy, logic swings and voltage noise margins are reduced, are placing stringent FETs.This requireThis demands demands on onover the pinch-off the control voltage control in the the ment is ment further emphasized further by the need the for very high yield of FETs in order order to produce circuits with large numbers of numbers gates. The high degree of device reproducibility required for high system performance places stringent demands on the fabrication the processes and and substrate material substrate characteristics. Active regions for the FETs, the diodes, and resistors have been produced by both (growth both epitaxial growth, by ion ion implantation, by implantation, combinations andof combinations and of an an epitaxial “buffer” layer, followed by ion ion implantation). implantation). most Th that that of ion implantation directly implantation into semi-insucost-effective approach is approach lating substrates, which will be emphasized here. A Atypical fabrication 1980) is is illustrated in in Fig. 27. Polished wafers of sequence (Welch et al., al., ( 100) ( semi-insulating GaAs are coated are with a thin thin ( 1000 ( A) layer of Si3N4, , which protects the the surface from mechanical and chemical damage during during the process the and serves and as an annealing an cap, as described here. Donor ions ions are are implanted implanted desired in indevice the the areas, with the the remaining regions of the the

--

26. 26.

of 8 X 8 X 88

on

The

contains 1008 gates. 1008

3. 3.

215

GaAs

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

2.

N- IMPLANT (PHOTORESIST MASK)

3.

Nt IMPLANT (PHOTORESIST M A S K )

4.

DEPOSIT REST REST OF CAP INSULATOR

5.

ANNEAL IMPLANTS

6.

OHMIC METAL

7.

ALLOY ALLOY OHMIC CONTACTS

8.

SCHOTTKY SCHOTTKY METAL < PRETEST>

N+ IMPLANT

ENCAPSULATION AND ANNEAL ANNEAL

OHMIC CONTACT METALLIZATION

SCHOTTKY-BARRIER AND INTERCONNECT METALLIZATION

SECOND-LAY ER METALLI ZATl ON 9. 2ND INSULATOR SECOND-LEVEL SECOND-LEVEL INTERCONNECT INTERCONNECT I I /INSULATOR 10.

CUT WINDOWS

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

27. 27.

of

GaAs is

is is

sample protected by photoresist. The The implanted implanted activated, ions and ions theare are lattice damage from the the implantremoved implant by is isa post-implant anneal. Subsequently,metallizations are deposited are on the GaAssurface, in windows etched in in the Si3N4 thecap. The metallizations The include, first, an an ohmic ohmic contact c - -Ge Ni - (which requires a subsequent alloy cycle) and, and, layer typically of Au -Ge second, a layer of Ti-Pt- Au, which serves both as Schottky gates and and as interconnects devices. The metallizations are typically are first level of interconnectsbetween Schottky the gate region are are defined by a lift-off process; metal linewidthsin in the 1 or less. or To complete the circuits, the a second level of intercontypically 1 pm nects is produced (in this (in case using Au) after appropriate deposition appropriateof an via and holeand opening (Lee et al., 1980). insulating layer of silicon nitride nitride

216

c.

et al.

The The multiple, localized ion ion implant implantdescribed approach earlier approach has a significant number of number advantages over alternative alternativefor techniques producing techniques the doped the areas of the devices. the The The implantation implantation very flexible. technique techniqu AA number of separate implants may implants be used, allowing independent independent optimi zation of the the doping profile in in different device regions. This capability This is employed to to obtain, forobtain, example, relatively heavily doped regions near near the the source and and drain contacts drainto minimize series resistance in in the switching the FETs as well as as to produce produce a low carrier carrier density (8 X X10l6 ~ m - ~thick ) (>3000 A) active region for the Schottky diodes, to minimize diode capacitance. Isolation between devices is automatically obtained obtained in in the the un planted areas through the semi-insulating substrate. The technique technique cost is is effective since the throughput can throughput be very high. Finally, the degree the of control control attainable attainable doping in in concentration the the and concentration thickness of the device the areas is areas superior to most epitaxial techniques. A drawback of direct direct implantation is implan that the thatdevice characteristicsare relatively are sensitive to the substrate properties-a relationship which has motivated much of the the recent research in in LEC growth. 11.

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

217

3.

2 2

00

t t

2t 2t z z

ww

0 0 2 2

0 0

0

0

a a

wa wa a a

a a0

0

FET

28.

in surface

shape

(1) a slight amount of amount channeling of the the implanted implanted (despite theions fact theions (100) orientation in orientation 8 off the the that that ions the the are directed at the the crystal 8 deg order to minimize the channeling); (2) (2)a slight amount of diffusion of the the implanted Se during implanted during the the post-implant anneal; anneal; and and (3) (3) the the fact that the the C- V V technique technique used to to get the the doping profile doping exhibits artifacts due to duethe proximity the of the semi-insulating the substrate.

the the param From Fromcircuit the the standpoint, standpoint, of the the one principal one principalofparameters measured in in implanted region implanted is the pinch-off (threshold) voltage or in or Schottky diodes. The value The of corresponds to

where

is the the net net donor donor concentration concentration region (asin in the the

218

c. G.

et al. al.

discussed here), xis the distance the from the surface, the is the effective the depth of depth built-in potential of the the Schottky bamer, is is the the the the profile, V, is the the is e the is static dielectric constant of constant Variations electronic charge, and eand a of changes in in the doping the distribution distribution in V, occur principally as a result induced by variations in in the substrate the or in in the the implantation process. implantation As discussed earlier, it it is of is interest for the fabrication the of digital ICs to control control to within to a relatively a narrow range. For circuits of the SDFL the type, control control of (V,) to within to mV is desirable for high-yield for fabrication of inteaverage the pinch-off voltage of FETs in in an an ( is is the grated circuits, where ( V,) area corresponding to to an an entire circuit.entire (V,) is affected by ingot-to-ingot and run-to-run reproducibility, run-to-run as The The the wafers. Too high a value a of well as by long-range uniformity of the processed ( V,) ( will result in FETs in that will that not turn off, turnwhile too low too a value a will lead to excessively slow circuit operation. An additional additional is constraint that that of constraint short-range uniformity of V,; i.e., the deviations the of V, from ( ( among among the the FETs of the same the circuit must be small. This This necessary is is to ensure that the input drive inputrequirements of each gate will be met by the output capabilities output of the the preceding gates (after allowing for for their their The fanout). maximum fanout).maximum dependent the the tolerable standard deviation standard a, of within a acircuit is dependent on to be needed for LSI circuits circuit size; values of a, of 50 mV appear appear (> 1000 gates). To maintain maintain average thepinch-off the voltage within the required k 200k arethe order the of 8 8X X mV range, the maximum the tolerable deviations in in are of ~ r n - ~assuming , a a uniformdeviation uniformover the the 2000-&thick channel. The maximum The tolerable deviations in in channel thickness channel are of arethe the order of order stringent than what is rou80 A. These tolerances are significantly more more tinely achieved with epitaxial growth techniques. V, is principally through through The influence The of the substrate the on on the measured the & ,as & , already as mentioned. Here, mentioned. is given by the the the net thedonor donor distribution distribution expression

- - - NDA - + NSD +

(9) where is the doping the density introduced introduced due due to to the the implant NsDrepresent the substrate substrate contributions of shallowcontribution and and NDA,and and acceptors, deep acceptors, and shallow and donors, respectively, donors, in the region the of the the implant. implant. do do not influence the FET the behavior since they are The deep The donors donors neutral in the n-type the channel region. There is, There however, an effect of the deep the donors in donors producing slow shifts in FET in characteristicswhen the the channels channelsar nearly pinched off. As detailed earlier, it is typical of semi-insulating un- unthere is is net a a excess of doped LEC GaAs grown in PBN crucibles that that shallow acceptors over shallow donors. There There are, are, inmore in addition, than addition = =

33

3.

219

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

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

220

c. Gc..

et al.

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

3.

221

FOR

This result corresponds to to the factthe that at the surface the of the substrate the there is there an an excess of shallow donors donors over shallow and deep deep acceptors while the the substrate remains semi-insulating,In fact, In this results this from the the phenomenon phenom of Cr redistribution during during post-implant the the anneal. anneal. the horizontal In In Bridgman technique, typically, considerableamounts of amounts Si contaminate contaminate th ingots due to duedecomposition of the quartz-crystal-growth apparatus at apparatus the the growth temperature. With the the silicon donors, the the predominant shallow predominant GaAs only by the inten- intenimpurity, it impurity, is possible to to obtain semi-insulating obtain tional tional incorporation of deepincorporation acceptors (Cr) to pin the the Fermi levelFermi near process, implantation however, a post-implant midgap. part of the ion ion implantation anneal (typically anneal at 850°C)is needed to ensure proper dopant dopant activation. activa has been shown by SIMS measurements that during during heatthis treatment, this treatment, considerable motion of the Cr thetypically occurs near near the the substrate surface. substrate Figure 30 shows, for example, the Cr profile Cr obtained before obtained and after an 85O0C/30-minanneal. anneal. Cr The is depleted The over several microns from microns the the may become concentration under- undersurface. As a result, the silicon donor donor concentration compensated, yielding an an n-type surface layer. If, however, the net donor donor 1015 1 ~ m - and ~ ) extends only extends over a thin layer, thin concentration isconcentration small ( r,. > (13) Here, the subscript M denotes M the model the potential, is a general function of function electron energy (indicative of well depth), is the the projection operator operator 2 is2the the ion ionnumb associated with the angular the momentum momentum quantum quantum number, valency. This This kind of approach has been used for shallow impurities impurities in i elements (Jaros (Jaros Kostecky, and and1969;Jaros, 197la) and has led in Group IV Group turn turn tomodel to thepotential the of Ning and Sah and (197 1a), which is described in Section 8.

248

S.

AND S.

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

++

++

++

249

4. 4. A A

It It is often desired to model radiative transition transition probabilities involving flawstates- whether they are shallow are or deep. few remarks are made here concerning photoionization photoionization and andfor photoneutralization shallow (effective photoneutra mass) flaws. This This subject occurs again in in Sections 5, 6, 7, 9, and 10. The mathematical framework is treated most fully in Section in 9, and the effects of phonon phonon assistance are discussed are in Section 10. That That framework requires a description of the lower and and upper states upper photoionization, luminescence. involved in a process of photoexcitation, photoionization, or The The upper state state involved is is excited (but (but still localized) for processes of photoexcitation, and of “internal “internal transition” transition” luminesbound-to-bound cence. Photoionization Photoionization “noncharacteristic” and and(free-to-bound) luminescence both involve a band state. A photoionization A photoionization for hv not treatment far notabove treatment threshold ought to ought take take into into accountcoulombic account the interaction the between interaction the ejected electron and and the the resulting localized flaw charge. That That involves coulomb coulomb wave functions functions Photoionization is often treated simply treatedin practice in with a (Gottfried, 1966). (Gottfried, plane wave final state assumed. state That amounts to amounts the Born approximation approximat a procedure that thatproperly is is appropriate appropriate when hv only is is only (Schiff, 1968), 1968), much larger than than the ionization energy. ionization is normal practice, normal in in any event, to use the electric dipole approxima- approximaIt It tion in working out the out radiative transition probability. transition For, conveniently, the the electric quadrupole and quadrupole magnetic dipole contributions contributions are are both smaller than thanelectric the thedipole term. term. For simple For the supposition the of a shallow hydrogen atom, atom, the the donor donor thatbethat represented can can by a scaling of the the normalized ground-state wave function has function the the radial formradial = = exp (exp (14) parametrized by the dielecHere the scaled Bohr radius is is = = IC and and by the the effective mass m,. The The ground-state binding ground-state tric tric constant constant energy is = = for a genuinely hydrogenic donor, which donor,does not not require a central cell central “chemical shift” correction. And so and are are interrelated by = =

= =

(15)

Part Part IV of this this chapter will chapter go on on discuss to to the the quantum defect and and delta-function potential models intended for intended rather deeper-lying rather flaws, with > > and and of characteristic radius U, < < It ItWill be binding binding energy = = = = for those more strongly more bound bound noted there there that that usedisinis paramein situations, when the effective mass m, for just one band band trizing the the bound bound state. state.

250

A N D S.

S. S.

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

(hv - -

(16) (16) This This falls off as as for hv > > the energy range for which this this approximation should be a reasonable one. one. Equation (16) also purports purports show atomaximum to maximum of when cHowever, the the plane wave final state state is isless much appropriate much appropriate for photon photon energies that that small, when the the wave vector k isk small compared with The photoionization The spectrum for a hydrogenic shallow impurity has impurity also been examined with a coulomb wave coulomb function adopted functionfor for final the the state. In In the electric the dipole approximation, this approximation, gives OC

a exp(a

4y cot-'

1 - exp(- 2~y)]+~,

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

4. 4.

251 251

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

+ +-

-

+ + - EJ- + +

( 1 8) While the the rise of this expression this is determined by determined the the numerator, numerato maximum is maximum soon reached, for a a photonenergy photon = =-

-1 1-

(19) (19) and and the subsequent the decline eventually resembles - behavior. This hardly matters from a apractical point point of view, since that that spectral region overlaps the the intrinsic rangeintrinsic and is and undetectable. Indeed, with hv,,, is is quite close quite to to the the the the band parameters band of GaAs (Blakemore, is of impurity impurity band-gap energy. Thus photoneutralization for photoneutralization aa = = - - [or, interest mostly concerning the the threshold energy - - for a a donor] donor]rise andofand a , from the the threshold- that is, linear at linear first, soon becoming sublinear. The The study of photoneutralization is photoneutralization more profitable for a adeeper-lying that thatoptical the thethreshold energy is further removed further from the the impurity, so impurity, intrinsic edge intrinsic energy. Toward that that end, we now end, move, via the delta-function the potential and and quantum-defect models, quantum-defect toward models better suited to some some description of mid-gap centers.

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

252 252

S. S.

A N D S. S.

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

We shall have more to say to in Section in 8 about 8 about consequences the the of a model a of finite potential in the form the of a spherically a symmetric square well square radius r,. Lucovsky was interested in the the solution of the the Schrodinger equation for the the short-range limit-that limit-that is, the the combination of r,combination --* 0 0 while Vo+ CQ,+ CQ, in in such a a manner manner the “strength,” that that gauged by ( ( remains finite. That That “strength” of the the delta-function potential potential determines de the ground-state the binding energy, and no andexcited states are are bound unless bound the the strength is far too too large to be useful in a a semiconductor: flaw semiconductor: situation. situation. in the the Those featureswere explored by Bethe and Morrison (1956) in modeling binding neutronin a a deuteron, and deuteron, they showed that thatsolutions the the proton - neutron of short-range potential. were relatively insensitive to the exact the When the the ionization energy (for a a certain kind certain of flaw in ingiven a a host) is host) known, the the strength of the impurity pseudopotential impurity (represented in Lube adjusted to be consistent covsky’s case by a delta-function a potential) can potential) for afordeep-donor a flaw. with that that ionization energy, which we shall call This adjustment procedure adjustmentreminds one one of pseudopotential methods for band calculations (Chelikowsky and and Cohen, 1976;Cohen, Ihm Ihm and and Joannopoulos, Jo 1981). 1). With the &potential the strength set to produce a localized a state of state binding binding a,, such that the corresponding wave function has function a radius a energy

aD =

(20) (20) Note thereby that (that a s D )= = = = where ad and refer to the the radius and and ionization energy ionization for a shallow a hydrogenic donor. donor. scaling, This This with =

(21) in the the is an implicit consequence of using the conduction-band mass conduction-band the the valence-band description of the the bound state. bound One would One similarly = =

4.

253

FOR

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

(22) Apart from the difference the in the normalization the constant, this constant, differs signifihaving the the factor preceding the the exponential. cantly from Eq. (14) in in 3 show 3 that that (for a given a,) this describes this a bound bound electron Figures 2 2and and distribution with distribution a much muchdistinct more more outer outer limit. limit. A Abound-state radial radial wave function function Y(r) has has a radial charge density = = The two The curves in in Fig. 2 2show associated with it it of plotted, versus normalized radius (r/ad)or or for the hydrogenic the wave delta-function potential wave potential function of function Eq. (14) [curve (A)] and for the the 2 ordinate ordinate suchunits that units that the the function of function Eq. (22) [curve (B)]. Figure 2 uses integrated area under each undercurve is unity. It does not look not quite like quite that, that, but but only because of the logarithmic the ordinate scale. ordinate Elementary texts on modern physics or physical chemistry often include the 1s1wave s function. These function. artistic, airbrushed visualizationsof the hydrogenic = =

z z

0 0 U U 0 0 WW J J WW

2. 2.

of of

so

is

Eq. (14). Eq. (22).

(B) (B)

254

S. S.

AND S. S.

..

22

0 0

NORMALIZED

3.

3 3

44

(r/o)

of of

of of of

as

(A)

( 1 4). (B) 4). (B)

(22).

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

255

4. 4.

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

- -

(23)

where (24) (24) features of Eq. (23) Eq. most (23) often compared with compared experiment is experiment One of the the that that o, achieves for = = Just Just above threshold, a, should rise should as as (hv - - while for sufficiently large photon energy, photon oxis supposed, is by this model, this to vary to as (ash ~ ) - ~ ” . Lucovsky chose to compare his photoionization expression [Eq. with some of the the original photoabsorption data data (Newman, 1955) for the the = 0.15 = eV). Figure 4 shows moderately deep acceptor indium in indium silicon the Lucovsky the expression compared with more recent experimental data data for for that same acceptor. same The experimental The curves are affected are by the photoexcitation tation opportunities near theopportunities the continuum threshold, continuum but but there a considerthere is is (23) to appear have similar able spectral range for which experiment and Eq. and(23) appear trends. = =

0 0 Y

Y

b ‘ ii

256

S.

AND S.

The maximum The cross section of Lucovsky’s model, om,, of (24), can be can seen to depend to on the semiconductor-specific the quantities Kquantities and K m, andand also on on an “effective an field ratio” (squared!). Dexter (1958) presented arguments as to the the possible enhancement of enhancement a photon’s effective electric vector, when one visualizes one a highly highly localized center as center localized a sphericalcavity in ain lattice of high dielectric constant. That viewpoint That would allow to be as large as (K( K 2)/3 in in an extreme an case-that-is, as large as as as4 for 4 GaAs. One One would expect the the effective field ratio ratio to depart depart much less seriously from unity for a flaw level that is that only “moderately deep,” with a wave function function radius a, or a, several times times larger than the the nearest-neighbor atomic atomic of us (J.S.B.) has found found effective field ratios to ratios be virtually spacing. One One indistinguishable from unity unity analyzing in in experimental photoabsorption photoabsor data for dataMn in GaAs in = 0.1 = 1 eV, a, = 0.8 = nm; see nm;Brown et al. (1973)l al. and for andIn In Si in in = 0.15 = eV, aA = 0.6 = nm; see nm;Messenger and Blakemore and (197 l)]. an experimental an note-and thus outside the the nominal scope nominal of this chapter-it this can be remarked that any underestimate any of the the neutral flawneutral density tends to boost one’s estimate of estimate a ,, having an effect an that resembles that > 1.> As As with other other analytic models, the the elegant and and simple approach approach that be adopted intact intact for any deeplying center, Lucovsky adopted cannot cannot especially if this is this a very deep one. deepLucovsky recognized these limitations limitations and and remarked, for example, that that a coulombic long-range potential would have to be to used for excited states. Moreover, the model the as indicated in (20)- (24) - uses (24)the effective the mass ofjust one (parabolic) one band rn, for donors, donors, rn, for acceptors. In addition, addition, simplethe choice the of plane-wave-like band band states for the expression the of truncates atruncates large part part of the the nature of the nature the impurity, the impurity, perfect host crystal, and their relationship. their Pantelides and Grimmeiss and (1 980) have shown, both experimentally and and theoretically, that deep-level that optical spectra are often are dominated by dominated transitions to to bound bound and andfinal quasibound states induced quasibound by the the strong shortrange potentials. Thus, Thus, short-range the the potential which potential Lucovsky approximated by a delta-function potential affects potential both the the initial and initial final states in an an act of photoionization. Kravchenko et al. (1 al.98 1) discussed some variations on the delta-function the potential approach in in connection withconnection the nature of nature the impurity impurity potential, po the size the of the wave the functions at functions the the flaw site, the the allowance for the charge the state in state photoionization, and the consequences the of electron of -phonon phonon inter- int action. They applied one of these variations variations (on of (on the thethe the potential) nature nature potenti to the case of two deep centers often centers found found in in “undoped” GaAs and“undoped” were able to to arrange parameters for a fit between their model their and experiment. However, it itshould not be assumed that an an ad hocadarrangement of arrangement Lucovsky’s model, which appears to to yield desired results for one one deep-level center, will necessarily be a reliable a guide to a variety of deeplying deeplying states.

++

--

4.

257

It was argued by Grimmeiss and Ledebo and (1975) that 975)that, rather , ratherrn,, than than should be used in Eq. in (20)for the deeper-lying the kinds of kinds flaw. When > rn, > (as is the the case for GaAs, and and for many manysemiconductors), other other this has this the the a Their argument was argument based on on the the effect of making U, smaller for a given premise that that a alocalized quite quite ground ground should statenot state be notmuch influenced much by the the crystal periodic potential; and and it is the the crystal potential potential which produces Bloch functions functions behavior andwhich and one simulates one by an effective mass. Since the the particular concern of Grimmeiss and and Ledebo was the the GaAs (a state state attributed by them attributed at them the the well-known 0.79-eV deep donor in donor time time“oxygen” to to and and now more more likely described as then then = 0.2 = 0.2 nm, nm, handsomely consistent with their argument argument in favor of the the use of m0. m0 . With the the plane wave final state state (Born approximation) approximation) for assumptio photoionization to a aparabolic band, band, Grimmeiss and and Ledebo thereby deduced that

- -

++

- -

(25) It is interesting to to compare Eq.compare (25)with Eq. (23),the spectral the dependence for Lucovsky’s version of the the delta-function potential potential photoionization p problem. Both equations equations rise initially from threshold in in a a fashion. Similarly, both both equations eventually equations decline as as for sufficiently high photon photon energies. Yet the the two equations equations have appreciably and and the the maximum fdr maxim different spectral dependences for intermediate intermediate Eq. (25) occurs right at = = only when rn, = = Since this is this germane to to our consideration our of mid-gap states in GaAs, Fig. 5 5shows the photoionization the data of data Grimmeiss and Ledebo for the 0.79-eV the “oxygen” level in in GaAs, compared most favorably with Eq. (25), as as displayed by curve (a). Curves (a). (b) and (b) (c) both show apparently less favorable comparisons with delta-function potential models potential using rn, for for the the bound- bou state wave function. Curve (b) is (b)the the conventional Lucovsky conventional result [Eq. while curve (c) is the result the of using a a coulomb wave coulomb function for function the the final state. state. The superficial appearance of the the curves and and data of Fig. data5 5is is that that the the yielding curve (a) looks (a) the best the by far. However, far. it should it model [Eq. be borne in mind mind that spectral that the range the for the comparison the did did extend not not through and beyond and the maximum (which maximum would, of course, take take intoitthe it the that the wave the(Born approximation) approxima inaccessible > >region), and and thatplane simplification cannot be cannot expected to be a a trueguide true in in the near-threshold the region. Blow and Inkson and (1980a), and Inkson (198 l), have pointed pointed out out that the the choice of different effective masses for bound bound electrons or holes in in a a delta-potential model lacks clear justification. Those Thosewriters latter latter do not not believe that that this could be applied successfully to a avariety of deep-level situations. a a

258

S.

A N D S.

II

II

I .o I

II

.o

II

JJ

12

hU (eV)

(1975), (1975), 0.79 eV

5.

GaAs.

is (25), (25), = =

(c)

use

Despite all these caveats, the the simplicity of Lucovsky’s expression, [Eq. or or of the the Grimmeiss and Ledebo modification [Eq. automati- automatically appeals to many experimentalists who have data derived data from optical absorption, photoconductivity, etc. one one illustration of this, Fig. 6 pro6 vides data data and an an analysis from the the work of Vasudev and and Bube (1 978), showing results for oxygen-dopedGaAs as investigated by photocapacitance measurements. These data points, data covering a seven-decade range of ampli- amplitude, were tude,fitted to to the sum the of three terms, each having the form of Eq. (25). With six parameters needed for fitting (three thresholds, as as noted in the the it it is hard is to imagine that the thatsix figure caption, caption, threeand values andfor a,,), choices arrived at by Vasudev and and Bube were all uniquely optimized. Yet the the analysis of experimental data data often calls for some kind of fitting to to data cover equations that that are arecumbersome, not not too too even when the available the much less than the ideally the broad spectral range. 975) with a discussion The paper of Grimmeiss and Ledebo ( I 975) proceeded of further ways that that a delta-function potential model potential might be generalized. Here they were concerned with transitions from transitions the the ground ground to a band state band state that is that warped and/or and/or nonparabolic, having decided that the GaAs the conduc- conduction-band nonparabolicity tion-band was insufficient to affect Fig. 5 . They also considered transitions transitions multiple to bands, to such as as the heavy-hole, the light-hole, and and and, and, I11 - V-V semiconsplit-off band combination for the various the Group IV Group ductors.

4.

259 259 I0I’

6.

II

I I

clo2

(1 978), 978),

of of 6 6

They illustrated the the consequences of the the latter specifically latter for for the goldthe - splitting orbit donor and donor acceptor states in silicon. in Since Si has a small spin - orbit (As-, = 0.045 = eV), photoionization photoionization split-off valence to to the band theband becomes possible shortly above the the threshold for hole creation creation in either either of the the - orbit splitting $-, = = uppermost valence bands bands of that that solid. The The spin - orbit 0.341 eV is nearly an order order magnitude of larger in in GaAs (Nishino et (Nishino al., 1969;Aspnes and and Studna, 1973). Studna, Yet a shoulder at -I-$-,) is is apparent in apparent the the photoabsorption spectral response for moderately deep acceptors in in and GaAs, such as Mn (Chapman (Chapman and and 1967), Hutchinson, or Co (Brown Hutchinson, Blakemore, 1972).The spectral The behavior of Mn in GaAs will be illustrated a little later later Fig.in8.in Banks et al. (al. 1980) ( used Green’s function techniques function (further discussed (further in to to calculate optical cross sections for deep-level flaws, and in so Part VIII) VIII) doing commented on commented the weakness the of the Lucovsky the approach in describing the the impurity waveimpurity function through functionconcepts derived from just one one band band edge. They pointed out that that a deep-donor wave function might function well have nodal properties coinciding with those of the valence the band, and band, showed that that this would this lead to to a photoionization spectral photoionization dependence

- -

+ p)’.+

(26) p p= 0,= and and a,transition, tr For a “forbidden” donor- donor- conduction-band conduction-band (modest in in size, clearly) rises sublinearly from threshold, is maximized for = 1= and falls and quite rapidly quite as increases further. T further. his is illustrated is a a

260

J. S. S.BLAKEMORE AND S. S.RAHIMI

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

- (l-+ + (27) when the deep-donor the wave function does function have nodal properties coincident with the valence band nodes; and and this valuethis of p pwould be several times times forintrinsic any mid-gap donor in donor larger than than the the gap intrinsic Dzwig et al. al. ( 198 ( la) have recently reported an an interesting expansion of the Lucovsky the model approach, approach, formin of in anthe an the impurity super impurity lattice. This This approach is discussed in Part IX. Part

p p= =

6. THEQUANTUM-DEFECT MODEL MODEL

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

II

7. follows (23) of (26), (26), (26), > >

II

II

22

33

4 4

of a of, (B) is

of

et al. (1980). (1980).

/?= 0=0

of of

261

4.

general. The model was based on that that developed by Burgess and and Seaton ( 1(960) 1 in connection with connection astrophysical spectroscopic problems. The The aim of the the model is to to obtain anobtain approximate solution for the the is r, defined is impurity wave impurity function outside function the ion ion core site. core Thus, a radius r,radius (of the order of the the nearest neighbor spacing) outside of which the the QDM formulation is expected to be valid. As with the delta-function potential approach discussed approach in in the preceding the section, a knowledge of the the observed In In conformity binding energy is required to to achieve the goal the of the QDM. the with the terminology the already used, will be used to signifythe (empirical) binding energy of a deep deep donor. And so, donor. instead of solvingthe effective the mass the eigenvaluesand eigenfunctions,the energy the equation, Eq. equation, (1 l), for the energy is inserted as a requirement. Assuming the validity the of Eq. (1 1) used in wayr > r r,, > one obtains one the asymptotic the form of the envelope the function function this way this for Let us express radii in in units of units the the “hydrogenic Bohr radius” ad, and energy in units in of the hydrogenic donor Rydberg energy [asrelated by Eq. (1 Then Then radial the the part of Eq. (1 1) can be written as as

- /(I-+ l)/r2 + - -++

= 0, =

r> r >. .

(28) Substituting the coulombic the potential for this large-radius part ofthe part solution -2/r this system of units) in in Eq. (28), the the (which is is just justin this dimensionless ( 1967) ( Chapman to be expressible was shown by Bebb and and Chapman solution for is, in in the form theof a Whittaker function (Whittaker function and Watson, 1964)-that -that as a linear combination combination of two confluent hypergeometric confluent functions. For each of the the specific quantum quantum states, the the correct form of the the Whittaker p, defined by function is function determined by a (29) Here IE IEis is the principal the quantum quantumand number Y= Y = number The reader The may wish to note to that Bebb and Chapman’s and original terminol- terminolp pand and v vof Eq. (29). The The ogy is is retained here in in writing the the quantities quantities dimensionlessquantity vquantity here v should be kept distinct in distinct one’s mind from mindthe from use of v as v as an electromagnetic an wave frequency! A simplified form of the envelope the wave function may function then be written in the form the

(r/ad)‘l (r/ad)‘l rc, (30) (30) and and sees one that one the thatwave function is function scaled by the characteristic the distance CC

(3 1) comparison with Eq. (21) then then shows at once oncevad thatis that the same same the , used in discussing in the delta-function the potential model. potential As noted noted quantity aquantity = =

262

A N D S.

S. S.

by Bebb (1969), and and by Bebb and Chapman Chapman (1971), the function function provides a continuum continuum of opportunities for opportunities the the range 0 < 0 v-

200

U U

aa

LL

I00

t t LL

a au 50

u

-+ + X X

20

X X

WW

10

-33 5 5 22

FIG.10. Log- log plots ofF(x) plots for the shallow boron boron acceptor in silicon, acceptor and silicon, for for four four I of acceptor inkinds various various I 0.2 rather rather deeper deeper kindsacceptor 0.5 1.0 2 2 55 et al., semiconductor semiconductor hosts. (Afier Rynne Rynne NORMALIZED RADIUS = = 1976.) 1976.)

266

A N D S.

S.

[ [

[q(h~)]'/~

Q Q

dr.

(35)

Here, j,(kr) is the nthe = n 1=member 1 of member the family the of spherical Bessel functions, functions, given by = (kr)-2[sin(kr) = - (kr) - cos(kr)].

(36) (36)

Now, since

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

[ [

r-l r-l

Q Q

k3/2j,(kr)(a/v)1/2 dk.k3/2j,(kr)(a/v)1/2 (38)

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

(39)

in terms of the normalized radius x = = Here, F(x) is constant constant a for for x-' for the the shallow hydrogenic acceptor, vanes as xY-l for QDM,and as as = = delta-potential limit. Thus, the radial dependence of the the quantity quantity Y(x) exp(+x) should exp(+x)be indicative of how effective a given kind of flaw is at keeping its bound charge within a defined radius (as discussed in in connection connecti Rynne al. (1 al.976), shows the form the of F(x) for with Fig. 3). Figure 10, after Rynne et B Si and :In, : and for andthree additional moderately additional deep acceptors: Ge :Ge Hg, : Si :B:and GaAs :Mn, : and GaAs and :Cu. : So far as the the curves in in Fig. 10 are concerned, are that that for Si:B has already deep-level impurities. For all four of the been disposed of as irrelevant to to The others, the slope of F(x) on this logthis log plot is slightly steeper than - 1.3 3arise because of imperfections in in the input the anomalous wiggles anomalous for optical data: This large-radius This portion of portion the curve is especially affected by the the part of the the photoionization curve nearest to threshold, with 1.

4.

FOR

267

That defect That of several curves in Fig. in 10 is a reminder to reminder the experimentalist the as close to can have great value. that that data dataas possible to threshold optical is informaAt the opposite end of end the abscissa the scale for Fig. 10, it it is or or which has the greatest the bearing on one’s ability to tion for hv >> discern the the bound charge bound density distribution nearest distribution to the the flaw site. We recognize, of course, that that photoionization for a mid-gap center center cannot be cannot sets a limit on limit the the kinds of information information detected for hv > > = = That That that that be canextracted can from photoionization data data with a very deep level. Despite this limitation, limitation, models the to to be thediscussed now, in in Parts Parts often have to to be scrutinized in terms of terms the optical the properties they imply. V.

As already remarked, the the signature of a flaw in aingiven semiconductor host ductor should include information information the following: about about (i) (i) the eigen-energies the for bound electrons bound and/or and/or holes, (ii) the wave the functions of functions the various the charge states (in ground ground form state state plus any excited any states), (iii) the the symmetry (or lack (or thereof) of thereof) the the site for each state of state charge and excitation, and (iv) the multiplet the fine structure resulting structurefrom crystal field asymmetry, (v) the strength the of electron-lattice (vibronic) coupling, and (vi) the probabilities the of any energy/charge transfer mechanisms. transfer

That is That a tall order. The models The discussed so far do farlittle more morescratch than than body of desired information, information, only and transition and thetransition the the the surface of that that so mentioned far has been photoionization. photoionization. More is said phenomenon phenomenon mentioned 9, while Section 10 (also in this this part) part) outlines outlines ph about this about in Section in participation in in optical transitions. Nonradiative multiphonon multiphonon emission (MPE) (MPE) relaxation and Auger-assisted capture capture noted areinareSection 11. However, that still thatleaves many more detailed more aspects of transition transition phenom- p ena without an explicit treatment. treatment. Some Some of those topics can can be handled only by elaborate numerical methods, since analytical approaches do do not have notenough generality. Despite this, analytical methods can can sometimes relate experimentally measured quantities to quantities various flaw attributes attributes a simpler in(albeit in inexact) way. This section This briefly notes the the localized states that are compatible are with the the Schrodinger equation for equation a spherically symmetric square-well symmetric (S3W)poten- potential and goes on on discuss to to in in some detail the the so-called billiard-ball model of Ridley (1980). This model This sets out out to put put a severe limit limit on on the the the flaw state state bound charge bound density outside a certain radius, and so the occupied

268

J. S. BLAKEMORE AND S. RAHIMI

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

8. 8. THESPHERICALLY SPHERICALLY SYMMETRIC SYMMETRIC SQUARE-WEL POTENTIAL MODEL MODEL

The delta-function potential model of Lucovsky (1965) (1965) some andofand the the ensuing modifications of that model were discussed in Section 5. That approach amounts amounts to toofadoption a spherically adoption symmetric square-well potential of vanishingly small radius yet nonvanishing binding strength. It It should now be noted that that a square-well potential offinite potentialradius, == - r < r,,
r,, > (40) can also can bind a camer-potentially camer-potentially a quite deep quitestate. inThe in terminology The of Eq. (40) follows that of that Eq. (1 3) in in using r, to denote adenote critical radius at radius which the the form of the the model potential undergoes a stepfunction change. Part (a) of (a)Fig. 1 1 illustrates 1 the the simple form of Eq. (40). The principal The characteristicsof a quantum-mechanical system quantum-mechanical subject to the potential the of Eq. (40) have been described in in the the standard standard quantumchanical textbook literature (see, literature e.g., SchiE, 1968). Those characteristics were rescaled by Walker and Sah (1973) for the version of flaw states statesin in a semiconductor, and applied and by them to deep-lying to species of radiation-induced defects in in silicon. The The bridging model version of the the (Amato and Ridley, and 1980)also amounts amounts S3Wtosituation, to an an with situation, [as in the model the potential of Eq. (1 3)] the the option of coulombic option wings to to the potential the for . shall return to return that more complicated more situation situation Sectionin9.in r > r,>. We = 0, =

269

4.

vfrlO0 O0

-

c

SYMBOLIC ACT uAuL" BEHAVIOR

-V0

of

1 1. 1 1.

of Eq. of (40). ( 197 ( 1197 1

(41) (41)(42).

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

(41)

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

++

++

270

. I . S.

AND S. S.

The much simpler model potential of Eq. (40), illustrated in in part (a) of 973).That adoption allowed adoption them them to to Fig. 1 I,1 was used by Walker and Sah (1973). That scale the the standard standard mechanical quantumsolutions quantum(Schiff, 1968)for a potena tial of that that radial step-function form. States that can thatbe bound by the the potential of Eq. potential (40) include some include that are are bound states of finite angular angular purely radial, 1=0. However, additional additional > 0)>can 0) also be included in the the total picture, totalif the well the depth depth momentum (1 momentum is large enough. [As will be seen shortly, the actual the criterion is controlled Even so, the principal the interest in an in model for a a by the size the of (of( deep-level flaw in in semiconductor aa is obliged to be concentrated on concentrated the the simple wave function for function the the Is ground Is state: n = n 1,=11,= 1 0.= Following the the terminology already used in in previous sections, let let denote denote ground-state the the binding energy for for deep-donor aa type of flaw. We shall find it convenient, it in what follows, to define quantities a quantities and a pand p(with dimensions of reciprocal length), as follows:

a =a =

VO - -

p p= =

(43) (43) The 1 s1 ground s state, for the potential the of Eq. (40),then (40),has thena form a that thatbe can can expressed as ee

Yl(r) = (C/r) = sin(ar), sin(ar), r,, (44) = (C/r) = sin(ar) exp[-p(r - r r> r,,> where C isCa anormalization constant. Since constant. it it is necessary that that (Y = = (Y (Y for r r= r,, = then the the three three quantities r,, a,andquantities pand pmust be interre- interrelated by the the condition condition

p p= -=a-tan(ar,). a

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

- -

= Vo = C0S2(ar,) = Vo = COS2[(r~/h)(2mc)1/2( VO VOED)"^].

ED)"^]. (46)

An potential has no no bound bound at all,state unlessstate its its depth V, exceeds V, depth the the minimum value

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

271

4. = =

+p) += =

= =

(48) (48)

= =

= =

Equation (46) Equation can then then be re-expressed in the the form

+ cos[n(x + -

= 1= 1

-

(49) (49)

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

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

y y< 1.< 1.

(50) Let us now consider the the numerical specifics for gallium arsenide. The The are less are severe if acceptorlike flaw states states considare are requirements for several times larger than than It Itwould seem ered, since rn, = = Y, = 0.12 = nm, nm, half the the nearest-neighbor reasonable to tosuppose that that (47) (47) yields = 13 = eV. Since this is this nearly interatomic spacing. interatomic Then Eq. Then 20 times 20 larger times than thanbinding the theenergy (- 0.7 0.7 eV) for a mid-gap center, one one quite For the the specific can see that that use the of theEq. (50) will be quite justifiable. = 0.7 = 0.7 eV, Eqs. (49) (49) and instance of a mid-gap acceptor in GaAs,with (50) have (50) the solution the = 1.35, = y1.35, y= 0.06. = 0.06. The strong The sensitivity of the ground-state the binding energy to any modest any y y< 1< 1conditions conditions Eq. (50), change in potential well depth, depth, under under the the of should provide a warning that thatSthe 3W S the model needs to be to approached with as above, a change in in of appropriate caution. appropriate With GaAs, as discussed & 10% & is sufficient to to move the the acceptor ground state state all the way from (E, to - Perhaps because of that that sensitivity to parameter parameter choices, the the study of study ( for radiation-induced flaws in silicon has not been not Walker and and Sah ( 1973) followed up by many other other applications of this this “muffin-tin potential” in the the latter latter approach approach to to other other flaw semiconductor: systems. As described semiconductor: part of Section 9, the “bridging” version of the the does revive the the as at least the major the part part a model of of potential. In that In case, a coulombic tail is Y> > with attractive or repulsive flaws [the procedure [the suggested added for Yfor in Eq. ( 1 3)].

++

9.

AND

In order to to develop the the goals of the the model, it was necessary to to at the critical the radius r, . . prescribe an an abrupt change abrupt in in the effective the In contrast, contrast, BBM the makes the its most its important important assumption concerning a form form the electron the at a particular radius. particular That That change in in the theof radius is here denoted r, denoted for a deep donor (or donor r, when the flaw the in question in is known to be to an an acceptor). Of course, the the model also entails a change in in the form theof at the the

272 272

S.

A N D S. S.

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

o,(hv) = = = =

(51)

The terminology The of Eq. ( 5 1) is as is follows: a, = = = 0.0529 = nm is is the the Bohr radius for a hydrogen atom; atom; a,, = = = = is the the fine structure structure = (q,P‘/2h2) = = 13.6 = eV is the hydrogen the atom Rydberg atom energy; constant;RH constant; and Vis the volume the of the cavity the containing containing flaw site.the [The thefinal [Theresult for V.] Also, n,(= is the the refractive index while does not depend on on is the the conduction-band density conduction-band of states, for kinetic energy & = (hv -(hv ED) - in in the band bandcorresponding and and wave vector k. Of course, Ek=Ek =

4.

273

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

P =P(Dlexp(=

(52) is the matrix the element for a transition from transition a donor donorDstate to a conduction state conduction Since the wavelength the of the the photon greatly photon exceeds the flaw diamestate C. state q = 0=applies, 0 and and so P =P = (That becomes (That ter, the the longwave limit qlimit P =P= I I I IV) for an acceptor an to valence-band transition.) transition.) The p is p The is quantity the the momentum momentum And operator. for for theoperator. dipole approximation, approximation, with then = = electric dipole moment moment The matrix The element P can P be evaluated when the envelope functions functions are a of massband m,,band and , with the specified. Thus, for a parabolic conduction conduction Eq.(52) reduces to to longwave limit presumed, limit

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

(53)

Here, of course, the the crystal momentum momentum hk = = - Equation (Equation 5 1) can be further simplified further when the response to unpolarized light is considered. is Then Thencan one write one (54)

= =

where the overall the magnitude is magnitude scaled by

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

(55)

and the andspectral function function is given by (DlC) 1'.

= =

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

ZB

nL

exp(& exp(&

(57)

214

I. S.

AND S.

(Here, n signifies n neither electron density nor refractive nor index, but but rather rather the th of (57) should index identifyinga band.) Ridley remarked that theform that apply to both to the bound the state state andfinal andconduction the the conduction of a photoionstate state photoionand ization process, although with different sets of coefficients, respectively. The The momentum matrix momentum element of (52) may then then be written (in (in the longwave the limit) as limit) (58)

where = I/-’ =

exp(-ik” exp(-ik”

exp(zlr’

(59)

This looks much much more forbidding than than needs it itto, to, for the the near vertical space of an optically an induced transition eliminates transition all contribu- contribunature in nature tions except tions those for k ” = = And so, so,

For any band n, the the diagonal terms of terms the momentum momentum matrix are are matrix is the the group velocity. group where vg = (=( simply Having gone through all of the the above, which is applicable for any of the the combinations combinations of bound bound state final state state andstate wave and function function that be that can c conjectured, let us now be specific for the billiard-ball the model. This provides This a very simple model for the the and andcoefficients (or and as the the case may be) in in (57) and (58). As noted at noted the begining the of this section, this Ridley proposed that thatwave the the function be function constructed as as the the product of a product (using Bloch functions) and andenvelope an an function function periodic part

xk

= =

(61)

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

4. 4.

275

GALLIUM

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

case for

++

(62) The participation of the the conduction conduction valence bands andinand in formation of formation b, .. the flaw the wave function is function thus determined thus through through coefficients the theb, and One would expect = 1,= = 0=0for a ashallow donor, donor, dominated by the the dominated conduction band; conduction but but that should thatnot not be the the case for any mid-gap flaw in in it be remarked that complication further for GaAs,it may GaAs. a a further should probably be replaced by a a sum ofsum contributions from contributions the first the several and and conduction conduction bands, with the the large densities of states for the conduction minima having a powerful a influence. The The is is not complete not until the untilenvelope functions functions and and have also been specified. In constructing Ridley was mindful of the the scattering of an electron an by a a coulomb potential coulomb with a noncoulombic a core. He deduced that that an an approximation envelope approximation function function for the final state state the (valid for > (67) ~d,cr)= = exp(should be appropriate. While we have previously used v v= = the the quantum-defect parameter, Eq. (67) uses the the quantities =quantities = and = = vl Z vl1. Thus, = -= for a center with center2 < 20, That the the same formsame as Eq. (26) (26) behavior was shown as curve as (C) in Fig. 7. It is thus not thusimmediately clear what new insights the BBM the may have to to offer concerning the photoionization the response spectrum of a flaw. However, 4 1.5) C that should that it is it actually the region the not very not far above theshold (1 < 4 r

>

(72) as sketched as in Fig. in 12 for 12 both charge both sign options. One options. may assume that this this r, of r, the the order of the order Debye the tail will become essentially flat beyond a radius a That That quantity veryquantity large forisaisa screening length = = semiconductor with small free carrier densities, as in semi-insulating in GaAs. = (-=

++

of

12. Form of

is is

4.

279

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

r r< < (73) where A, is is the needed the normalization constant and constant jo(z) = Z1 = sin@)is the is in Eq. (73),quantity with zero order order spherical Bessel function. function. The a, Theinquantity a a dimensions of reciprocal length, may be compared with the the quantity quantity with CU, of Eq. (66). One One write (Y, = = defined in inEq. (43), and and Vo- in in an an attempt to relate attempt a,to atopotential well potential depth, depth, but but this is a rather empty rather exercise in in the lack of any any reliable perspective as as to to within appropriate the core the radius. what effective mass m* is is appropriate Amato Amato Ridley and quite and naturally quite chose to to represent the envelope function > by the the asymptotic form of a Whittaker function, as function, for r r> rM encountered encountered inEq. in the (30),the and QDM as and further QDMmentioned further as as earlier in this in thatmatching requirements requiremen section by means of Eq. (67). They showed that the r rM = provide the the normalization coefficients for and and at r = In In using their bridging model for describing photoionization processes, photoionization Amato and and Ridley considered two possible forms of forms final state wave state function. tion.of One these, One not surprisingly, not was a simple plane wave plane(PW) function. function. weakly This can be expected to to be most reliable when hv > >and for afor scattering (neutral) site. (neutral) Their Their choice other other was a type of coulomb wave coulomb function (CW), function simplified to to

&,PI

= =

= =

exp(zk

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

280

S.

A N D S. S.

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

Flaw charge, with charge, electron electron removed removed wave final state Plane state PlaneCoulomb wave Coulomb final state state ~~

~~ ~~

~~

~~ ~~

_ _ _ _ _ ~

~~

> 0.1, > .3 v> v 0.5 > 0.5 Not Not applicable applicable

4.

281

FOR

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

++

I I

I I

II / /

V=0.4 I I

1.0

1.2

1.4

I I

II

1.6

1.8

16

1.0

+ = hV/E,

0.4 of v v= 0.1. = 0.1.

= v=v= 0.4 =

is is

I I

2.0

1.2

1.4

I I

1.6

I I

1.8

II 2.0

is is

282 282

J. S. BLAKEMORE AND S. RAHIMI

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

++

++

10. PHONON-ASSISTED OPTICAL OPTICAL TRANSITIONS TRANSITIONS

The complete The photoionization cross section for a flaw a must be expressed emission and abas a a summationwhen summation concurrent processes concurrentof phonon phonon sorption are taken into account. For account. a a “neutral “neutral type donor” of situation, donor” situation, as the spectral function before any any phonon phonon which yields Eq. 4 (hv/ = (hv/ effects are allowed for, that that summation for reduced summation photon energy photon4 = can (with a simplified a treatment) be treatment) expressed as

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

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

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

(77)

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

4.

283

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

++

++

EMPTY

CONFIGURATION COORDINATE, Q Q

14.

of levels,

284

S.

A N D S.

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

285

4. 4.

+= FIG.15.

of = 0; =

= =

1980.) G(4)

= 11 = S= S 0. = For

8* =

=

= = = 0.1. =

0.1.Also (c) (c) AlsoS = S 3,=3, 0.15ED(=

S= S 3) =3) with 8*= 0.4. = 0.4.

differences between curves b and cand arise from differences in in their assumed their temperatures. 8* = = Let temperature be temperature expressed in dimensionless form as as Then curve Then b in Fig. in 15 corresponds to O* = 0.1, = and curve and c to a tempera- temperature ture four timesfour larger. It Itcan be seen that that higher the thetemperature temperature curve extends slightly to to the low energy side of its low-temperature its counterpart counterpart is very is small, but but that it is that slightly is to the right the of curve bcurve for the the when the upper part of the register. What temperatures would temperatures those situations correspond situations to for In In this semiconductor, this the the largest maximum in maximum the the phonon density phonon of states 1013 rad/sec for ho = 33 = meV. That That means that that occurs for o =o5=X5 X 8*= 0.4 = [the [the condition supposed condition for curve for c in Fig. 151 when T '-T. 150 K. One One more curve in Fig. 15 15 remains remains be mentioned. to to mentioned. is curveThis d, This the curve bodily translated to translated the right the by a Franckwhich is the zero-phonon = (= It can be seen that this agrees this (rather (rather Condon shift Condon = 0.154,

286

S.

A N D S.

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

++

44

FIG. 16.

of

of a@)

Rhys

= 0) = 0)

S.

8+ = 198 1 .)1

=

= 1.=

287

4.

affected by phonon phonon emission and and absorption would absorption like to onebeone able to deduce -at least -thethe threshold shift If one one had had confidence, any any moreover, concerning concerning the the predominant energy predominant phonon then thenresults the the phonon of the the analysis could be expressed in terms terms of a aHuang-Rhys Huang-Rhys factor = = Any of the above the requires that the the phonon influences phononbe decon- deconvolved from experimental optical experimental data, data, as obtained obtained in in measurements m of absorption, absorption, photoconductivity, luminescence. photoconductivity, or or Figure 17 provides a a rather simple ratherexample of such an such analysis. The The data data points points in figure in this trace this trace out out the the room spectral room temperature form of thetemperature the photoneutralization cross photoneutralization section a,(hv) for the for electron-producing the reaction tion Cr2+ hv Cr2+ + Cr3+ + +eCr3+at a a substitutionalCr,substitutional site in in GaAs. (That (That constitutes constitutes photoneutralization, since Cr3+isCr3+ photoneutralization, the lattice lattice neutral charge state neutral state of this mid-gap this flaw.) The The data Fig. data 17in areinof areextrinsic extrinsic photoconductivity ph measured near near room room temperature, and were analyzed temperature, by Ridley and Amato Amato (198l), (198 assuming a a transition transition an s-like from bound fromstate to state a a(perceptibly nonparabolic) r, nonparabolic) conduction conduction band. band. The The curve in in Fig. 17 resulting from that that modeling was based on a a simplifying assumption assumption all phonon thateffects phonon that could be simulated by simulated the use the

++

I I

- lo3- lo3 z z 3 3

>> a a

a:

Em mE

102

a:

-a a-' - ' -0 c 1 c

II

06

07

08 09 (eV)

10

I !

FIG.17. A A of for of CrZ+ hv + + e- eof is of (198 for - - = 0.66 = eV as ho = 0.03 = eV S= S 3, = = Sho = = 0.09 = eV, eV,

++

++

(see (see

et a[., 1980) a[., 296 296

0.76 eV

++

- -

Also Also = 0.75 = eV.

288

S.

A N D S.

of a phonon energy phonon = 30 = meV. That assumption can be canViewed as effecting a compromise with respect to to the energy the ranges of various LA and LA LO participating phonons in phonons the GaAs the normal mode normal spectrum (Waugh and and Dolling, 1963). The The caption Fig.caption 17 indicates in in that thatcurve the the was fitted to to the the chromium chrom - -= = data data for a “zero-phonon” room-temperature room-temperature threshold of 0.66 eV, and with and the various the phonon emission phonon and absorption and opportuni- opportuni= = = = 90 = 90 meV. [This makes [This the the room room ties rendered by S =S3.0, - - dF-c)== dF-c) photoneutralization threshold photoneutralization temperature temperature 0.75 0.75 eV, in parametrizing in the upper the part of the curve.] the That Franck-Con- Franck-Con and its decomposition its into effective into values for don shift don for Cr, in GaAs, in and ha,provide the first the entry in entry Table 111. The second The entry in Table in I11 is is the the phonon shift deduced phononby Arikan et al. al. (1980) for the the 0.4-eV oxygen-related (?)donor donor in [Look and Chau- Chaudhuri dhuri (1983) argue that that is this a pure this defect, which does not incorporate incorporate oxygen.] The result The quoted by quoted Arikin (1980) was obtained from obtained an analysis an and the the of the the of the the temperature dependence temperature of both the much extrinsic photoconductive edge. Table I11 does not not list a much larger (dF-c= 240 = meV), which was reported by Malinauskas et al. (1979), al. also based on on the photoconductive the threshold temperature dependence temperaturefor (apfor parently) the same the donor. donor. chosen onefor The smaller The value, that that suggested by Arikan et al., is the the one tabulation here, tabulation since those workers measured and commented on commented the large ==1.2 - X Xlo4 eV/K] for eV/K] the effective the temperature dependence threshold energy. When the temperature temperature dependences of the the threshold and and were jointly analyzed, jointly it became clear that that multiphonon multip effects account for account slightly less than half thanof The remainder arises true as a consequence of lattice dilation. from a true (&&it), as as by Makram-Ebeid The The next three three entries in Table I11 are arereported ( 1980); ( based in part on analysis of his measurements of field-aided tunnel- tunnelvalues from various experiments ing from flaw sites, supplemented by reported by others. One of the systems Makram-Ebeid measured was the E3 This becomes This evident near near- 0.6 -eV) after MeV electron level in GaAs. in E3 is V,, is while Pons et Pons al. al. irradiation. Lang et al. (1977) concluded that that (1980) were more conservative more in assigning this simply this to a Ga sublattice native defect. Another system that Makram-Ebeid that examined was the well-known the (even EL2 mid-gap flaw in GaAs.The third third if not fully not identified and explained) and 0 complex in GaP, in an isovalent entity entity that that system was the so-called the Zn -0-pair is well known for its red its luminescence properties. A A more proper name for name signifying an oxygen donor on donor a this (as indicated in Table 111) is phosphorus site with a zinc acceptor zinc on a nearest-neighbor gallium site.

++

111 SHIFTS

%ME %ME

1N

AND

SS ~~~~~~~~~~~ ~~~~~~~~~~~

90

GaAs GaAs GaAs GaP GaP

0.4-eV

110 100 120 200

4 - Z b

Op Op

85

30 31 11 20 19

[n

3.0 3.5 9 6 11

1.7 1.7 1.1

(1981) et al. (1980)

(1980) (1980) (

(1 980)

(1976)

290

S.

AND S.

AA comparison of the first the four entries four in Table 111, all for flaws in GaAs, shows that that a breakdown of as the the product of a product Huang-Rhys Huang-Rhys factor and an and phonon energy, phonondoes not always yield the same the value for ho. That ought That not to be to surprising,for one oneexpect can can “normal mode” “normal phonons phonons (Waugh and and Dolling, 1963; see also Blakemore, 1982b), with energies essentially continuous from continuous zero to some 35 meV, to have varying degrees of effectivenessin in communicating between communicating the GaAs the lattice and various and kinds of flaw. Additionally, of course, there are local are phonon modes phonon(Dawber and and the flaw differs in mass in and/or Elliott, 1963),which arise specifically charge from neighbors. In writing Eq. (79, the ‘‘single the flaw energy” ho was used together with a notation that that this was this a asimplification of convenience. The The various ho entries for GaAs in Table I11 demonstrate demonstrate required thatphonon that thephonon the “mix” “m does differ from one flaw one species to another. another. indicates a Franck-Condon Franck-Con The fourth fourth entry Table entry 111, that in inthat for shift only slightly larger than for the other the three flaw threespecies. Rather than Rather let this pass this without further further comment, shouldcomment, be remarked it itthat thatwealth the theof experimental reports concerning this flaw indicate more complexity more than In In particular, EL2particular, behaves as as just ajust simple deep deep donor with adonor modest though it has a metastable excited state (Vincent state and Bois, and 1978;Mitonneau Mitonneau and and Mircea, 1979), with resulting properties including low-temperature persistent photoconductivity, photocapacitance quenching, luminescence 1982), quenching (Leyral et al., 1982), etc. Such phenomena are reminiscent of various low-temperature, long-persistence effects that that have been noted in in connection with connection flaws (many (many not not fully identified) in a number number of semiconductor hosts. These have been ascribed (Lang and Logan, and 1977; Langer, 1980) to atolarge lattice relaxation lattice around around flawthe site.the That That amounts extrinsic amounts self-trapping to to of an electron. It can be described in terms of terms “small polaron” polaron” theory (Toyozawa, 1961, 1973),and aand suitably drawn one-dimensional configurational1980; Emin, Emin, coordinate diagram (Langer, 1980; Lang, 1980) can model some of the the principles involved in a simplified form. The CC diagram view of nonradia- nonradiathe transitions istransitions discussed in in Section 1 1c, with the large-lattice-relaxation situation illustrated there as Fig. 22. major characteristicof a large-lattice-relaxationsituation is situation a very large ( 1980) ( cites examples of this this I11in- V, in - I1-VI, Franck- Franck- shift. Condon Langer Condon and and - VII - types of host lattice. For example, the donor-related the types of flaw in Ga,,Al,As alloys (Lang and and Logan, 1977) have an an apparent apparen of thermal optical threshold exceding 0.6 eV, despite an an apparent apparent thermal only 0.1 eV. of relaxation required to account for account situations such situations as as The extent The of lattice a major fraction of those noted above may be regarded as one extreme, one

--

4.

CENTERS

291

an eV. At the the opposite extreme, some flaws do not appear to appear show any shift Condon at all. Reported values in I11 in - V-compounds lie compounds all the the Franck - Condon way in-between. Thus, Thus,= 120 = meV for EL2, for as listed in in Table 111,Table is ais middle-of-the-road value. That That value gives no no clue as to the metastable excited state. al. (1982)] al. can can Perhaps EL2 in GaAs in [and [and related in inalloys (Matsumoto et(Matsumoto be fully identified and understood by the the time time bookthis is inthis in print. Such print. is not not case the the as as this this chapter goes to chapter press, however. models for this this mid-gap state presumed that thatwas thisoxygen this - at least oxygen-relatedand and those ideas no longer hold. [However, Yu and Walters (1982) find a level they attribute to attribute oxygen fairly near the the energy of EL2, as a separate entity.] A proposal by Lagowski et al. (1 al.982a,b) was noted noted Section in in2 -that -that is, This be an an that that EL2 is caused by an an isolated A s , anti-site defect. This should 1982) of GaAs isocoric double donor; donor; photo-ESR and and studies (Weber et al., al., in which anti-sites have been generated by plastic deformation do deformation show band, conduction with the mid-gap the levels some 0.7 some eV and 1 1eV below the the conduction level displaying photoquenching characteristics reminiscent of those in in al., al., 1982, 1983) show a EL2. However, ion ion implantation studies implantation (Martin et (Martin differentiationbetween anti-site density and EL2 and activity. Such information information has encouraged other hypotheses. other The metastable The properties could could indicate indic A s , with an a two-site complex, such as a near-neighbor combination of combination 1983; acceptor such as C, (Ledebo, 1983) or or a vacancy (Lagowski et al., al., 1983). Kaminska et al., al., These and and other hypotheses other have fueled an interesting an debate debate active and and - period, and one must one assume that experimental research in in the 1980 the- 1983 complete accounting for accounting EL2 the puzzle will eventually be fully solved. A A must include the the status of lattice statusrelaxation for each of the various the states of charge and excitation. and Before Table 111 is left too far behind, there is a sixth entry which entry merits entry5 , this this concerns Gap, rather rather than than some consideration. As with entry No. largetoHuang-Rhys large factor that GaAs, as the the host solid. In In contrast contrast to the the Huang-Rhys ( deduced for the 0,the nearest-neighbordonor donorMakram-Ebeid ( 1980) acceptor pair complex, entry No. No. 6 deals with a situation of situation relatively small (but (but observably and interesting complicated) phonon phonon coupling to to optical transitions. transitions. flaw in question in The Theis oxygen, substituted on aonphosphorus site phosphorus as a deep monovalent donor, 0, donor, an acceptor an as a nearest neighbor. = 0.90 = eV This This donor has itsdonor ground state statefar notfrom not mid-gap, with and and- - = 1.45 = eV for low temperatures. The The luminescence associated with the the Gap: 0,system was analyzed in in detail by Monemar and Samuelson (1976,1978; Samuelson (1976,1978; and Monemar, Monemar, 1978), using a variety of photoluminescence (PL) techniques, including

292 292

AND S.

S. I I

I I

I

1 I I

I I

4

1.2

1.3

1

1

Ic Iiiwp 4

1.4

I I

c

55

(eV)

FIG.18. A two-stage A deconvolution deconvolution of of phononanphonon optical influences optical transition influences transition upon upon invol for afor donor-acing aing deeplevel deeplevel flaw. Data Data here hereofare Monemar are thoseand Monemar those Samuelson (1976) Samuelson 4K).The deepphotoluminescen deep ceptor ceptor transition in Gap,transition observed by low-temperature low-temperature photoluminescence carbon, both carbon, on phosphorus sites. phosphorus (a) The (a) observed donor is oxygen and the shallow the acceptor is acceptor CC With phonons = eV) deconvoluted. deconvoluted. The (c) (c) PL PL spectrum. spectrum.effects (b) (b)ofWith of the phonons the = 0.048 = 0.019 = eV) subtracted. subtracted. electronic electronic with spectrum, the effects thespectrum, of CC phonons phonons

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

4.

293 MODELS FOR MID-GAP MID-GAP CENTERS IN GALLIUM GALLIUM ARSENIDE ARSENIDE

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

= S,ho, =

++

= 85 = meV,

(79) as was noted noted last in inline theof the Table 111. Similar conclusions were reached ho,and and phonons phonons upon transitions transitions concerning the the influences of the the or or another another of the the bands of GaP bands(Monemar (Monemar and and and one one between Samuelson, 1978), using a modification of the the Grimmeiss and Ledebo (1975) version of the the Lucovsky (1965) delta-function potential potential model to describe the deep the donor. donor. 11.1 NOTESON CARRIER CARRIER AND CAPTURE EMISSION CAPTURE MECHANISMS

This chapter chapter aims to provide a review of various model concepts for deep-level flaws, of the kinds that may that be encountered in encountered the middle the part of the GaAs the intrinsic gap. intrinsic In order to keep to the coverage the within bounds, it is it not not feasible to account in detail for all the transition transition phenomena such aphenomena t mid-gap flaw may exhibit. Nevertheless, the the reader may find it ituseful to include some brief notes here concerning various topics in electron in capture capture and emission, and including the nonradiative the processes which so often dominate dominate transition rates. transition with the the semiconductor :flaw : systems exemplified in the preceding

294

A N D S.

S.

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

a.

of

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

exp(-ED/kT)I (80) Here = = is is theeffective the density of conduction-band states for nondegenerateconditions, g, and g,are the statistical the weights of the the flaw electronic configurationswhen “empty” “empty” “filled” andwith andthe electron the in question, in and Eand D is the the Gibbs free Gibbs energy of the the transition. transition. The The q can be regarded as a mass-action density characteristic of the flaw the depth. depth. : systems, the the quantity E D can quantity be canexpected For most semiconductor :flaw = =

4.

295 295

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

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

/gf)ex~(ASn/k)l ~xP(-m n IkT) exp(-AH,,/kT).

(82)

Engstrom and Alm and (1978)use the name the “entropy factor” “entropy for the the quantity quantity = [(ge/gf) = exp(AS,,/k)]in Eq. (82). Note that that includes the the factor of the the Maxwell- Boltzmann mean speed, over and above any temperature temperatur dependence that 5 that ,may have in a given a case, while contains acontains T312 a factor if the band band is not far from parabolic. Because of those two explicit factors, one can can think of Eq. think (82) as being crudely equivalent to to

exp(AH,,/kT). (83) (83) T2/e,, For this reason, emission data is data often displayed as a plot a of log(T2/e,,)versus l/T. [For [For examples with flaws in in GaAs, see Martin Martin et al. (1977) and and Mitonneau et Mitonneau al. (1977).] When this is the the display procedure, some caution caution is advisable as to the the significance of the the slope of the plotted the data-a data-a quantity one is tempted quantitytempted to to regard as a a thermal activation thermal energy. As the simplest the example of how this activation energy may relate to the the thermodynamic thermodynamic suppose first quantities, qua that that EDvaries linearly with T, for all temperatures: all E D = (ED0 = - CUT). - In In this case, AS,, = a, = while a, the the apparent apparent activation thermal energy thermal is AH,, is = = EDo, regardless of the the range of measurement temperatures temperatures of the the (and (and actual values of EDat those temperatures). Far more more commonly, however, commonly, EDvaries with temperature in temperature a a nonlinear nonlinear way. That nonlinearity That may, of course, be small enough so that the thatemission probability can resemble = exp(-AE,,/kT) (84) en= CT2 over a reasonably a broad temperature range temperature of measurements. Under these Under circumstances, AEem indicates a avalue for for somewhere near the the center of that measured that range. When E D (typically)declines in ainnonlinear a nonlinear way with rising temperature, any temperature, value deduced for AE,, will tend tend exceed to to E D of any any temperature. temperature. behavior is That exemplified That by the the curves in in Fig. 19. Complications of this this character beset comparisons of optical transition transition

296

S.

AND S.

TI

T T(KI-

with

19.

of

ED

T,, ,

of of

ED(T)

(8

of ED(T) thermal thermal

= 0. =Thus,

ED

of

any

--

energies, “thermal activation “thermal energies,” and the like, the in deducing Franck Condon shifts, actualground-state energies, actualground-state etc., for mid-gap flaws in GaAs. In GaAs,as for for other crystalline other solids with zinc-blendeor diamond lattices, diamond the lattice the constant vanes constant with temperature in temperature a complicated way, with two reversals in in the the sign of the expansion the coefficient as as temperature risestemperature [information recently summarized by one one of us (Blakemore, 1982b)I. Those complicateddilatationalcharacteristics dilatational naturally result naturally in a nonlinear variation tion of Eiwith temperature temperature (Thurmond, 1975), but but they (Thurmond, inevitably affect also the separation the of deeplying donors and donors acceptors from one one band or theband the other, in in a way that that is not not conducive to a simple linear linear temperature temp dependence. This can Thisbe exemplified by analyses for Cr Cr in in The work of Martin et Martin al. (1980) (1980) has provided extensive data, data, over the the temperature range temperature 300- 500 - K, 500for for the the processes four four of electron and hole and emission and capture capture Cr3+ A comparison of the the electron emisinvolved in in Cr2+ Cr3+transitions. sion/capture data sion/capture with Eq. (82) was found (Blakemore, found 1982a) to yield an entropy factor = 40. = This provided a clear warning that the “thermal “thermal activation energy” would be an inflated one. Similarly, an an entropy entropy factor = 2=12was found for found the hole the emission/capture processes. And so it was it no surprise that that activation the the energies for electron and and hole processes in the the

**

297

4.

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

b. Detailed Detailed We have already discussed the physics the which provides for a finite probability that a neutral neutral should donor donor be photoionized in the the presence of adequate energy. adequate The same physics same also prescribes the probabilphotons of photons of kinetic energy can can suffer a radiative ity that that a conduction electron conduction capture process captureat an empty donor site. donor The relationship The between the cross the sections for “induced” “induced” upward processes and and “spontaneous” (as well as be traced by arguments of arguments detailed “induced”) “induced”) downward processes can can A sophisticated more argument follows argument Fermi’s balance (Blakemore, 1967). A more “golden rule’ (Bebb and Williams, and 1972). section is is the capture cross capture From From either of these approaches, the radiative (85)

= =

from the conduction-band states states of kinetic energy - - down into one of one the the ground states ground of an empty donor. donor. orderIntoIn express the the radiative capture coefficient capture c, = c, = = = an averaging process must be carried out out with respect to the relative speeds and and occuthe the semiconductor semiconductor con pancy probabilities for the the various Ek inEk band. For a nondegenerate semiconductor (q, this results this in

l-

C, = (2Kg,/gf~ckTCf)(2amckT)-”2 =

exp(-E,/kT)q(hv) exp(-E,/kT)q(hv) (86)

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

298

S. S.

AND S.

dependence may change further above further threshold, but that but will not matter for matter the present the intended purpose. intendedAnd so, suppose so, that that O~(hv) - (87) For the first 100 meV or so or above threshold. Equation (88) Equation is scaled by the the which would be the the apparent result apparent of extrapolating Eq. (87) to to quantity uM, quantity = [i.e., much further further needed than than for Eq. (86).] a photon a energy = 2& In substituting Eq. (87) into Eq. (86), let a dimensionless a energy terminol- terminolz= be incorporated in in reexpression of the the ogy x = integral. The result then is then

Now our principal our interest here is with flaws that that are deep enough deep to be to in the the central portion portion of the the intrinsic gapintrinsic for GaAs, and then then z= >> 1 even at room temperature. And temperature. so for all practical purposes, the the e the - ~ integral the , is is just r(3) just = = integrand can be regarded as ~as ~ / ~and This results in a thermally a averaged radiative capture coefficient capture (89) For those who prefer to to think think of in ainradiative aterms terms capture cross capture section, the corresponding the expression for that that quantity is quantity C, = =

- -

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

4.

299 h+

++

-+

+ hv, +

(91)

- -+ +

is to isit find one oneneutral, neutral, than than it findalready h+

++

C F

(92)

hv’,

in in creating a a hole-trap hole-trap (Blakemore situation situation et af., 1982).For For radiative the the capture reaction capture of (9 I), (9 most emitted emitted photons will havephotons an energy near near 0.7 eV. = K 13 = for GaAs and a ahole We may assume a a staticdielectric static constant Kconstant mass m, 0.5 m,,providing a amean thermal hole thermal speed Vp = lo6 = cm sec-I. Kaufmann Kaufmann and Schneider (1980b) 980b) report = 4, =report gf= 5=5for this flaw, this of thestrength optical the and the extensive the and varied literature concerning literature the the strength transition transition could encourage us to suggest that 0, = 3=3X X cm2. These cm2. values yield 5 =510-23 = cm2, (93) = = T T cm3/sec, =I

II

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

c. Radiationless (Multiphonon) Transitions (Multiphonon)

Having said so much much about about optical optical transition is only transition phen proper to comment about comment radiationfesstransitions radiationfess that transitions involve exclusively the the absorption or emission absorption of many many phonons.energy phonons. transformation This This transformat mechanism provides by far the the most efficient means means carrier of carrier capture in capture many cases manyand has andbeen the subject the ofa substantial substantial literaturee.g., HuangliteratureHuang and Rhys and (1950), Kubo and Kubo Toyozawa (1 955), Kovarskii (1 962), Sinyavskii and Kovarskii (1967), Englman and Jortner (1970), Jortner Stoneham Stoneham (1975,1977), ( Henry Henry and Lang (1977), (1977), Passler (1978a,b), Ridley (1978a, 1982), Lang (1980), Langer (1980), Sumi (1980, 198I), and I), Burt Burtl), (198 among (198others. among can can start start with It Itwas remarked in Section 3 3 thatelectron that capture capture (phonon-emission-aided)capture into capture a very a shallow excited state of state a flaw. a Then Thensuccessive the the steps in in a a “phonon cascade” “phonon (Lax,1960; Smith and Smith 1978) may make the the eventual moves eventual Landsberg, 1966; Abakumov et al., al., toward a a ground ground of thestate flaw the state an inevitable progression. Modeling of a a sequential passage through excited throughstates tends to tends predict a a capturecoefficapture cient that increases with falling temperature, in temperature, a a mannerresembling manner c, a a

300

A N D S.

S.

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

++

IOOO/T

20.

EL3,

a,

a,,.

of

of

Op Op

B levels B of

1980,

(1975). of

1977.) 1977.)

4.

301

In a different concept for a two-stage process, Ralph and Hughes (197 1) speculated that that electron capture at capture positively charged (coulomb (coulomb attractive) a deep flaws in in the partly the ionic solid ionicGaAs might occur with occuremission of an an energetic polar phonon phonon as the first 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 capture at one data species one data of flaw with an an apparent apparent 0.475-eV 0.475-eV depth, depth,a and room-temperature and room-temperature thermally averaged lo7 istimes is times capture cross capture section Z,(300) = 3=X 3 X cm2. [Observethat this this larger than than a, of (93).] Phonon Phonon cascades play no no part, either part, as a first stage or or as a subsequent stage, in ainmodel that has been advanced (Lang and Henry, Henry and Lang, to account account for carrier carrier capture at a variety capture of Lang, 1980) 1980) deep-level flaws in GaAs and and Gap. Lang and and Henry concluded that that these situations, with situations, patterns of patterns capture cross-section capture behavior as exemplified as by the the data of Fig. data20, could be accounted for by a emission (MPE) process of radiationless lattice relaxation. Such a process is conceptualized as taking an electron directly from a band band to state stateground a flaw state, with no preliminaries. no Lang and Henry and ( 1975) ( remarked 1975) that that their view their of the the transition process transition has analogies to a phonon-assisted radiative transition transition model (the (the diagram of Fig. 14), except that they that evaluate the oscillator overlap factor for the situation situation of vanishingly small emitted emitted photon energy, 0. Description of capture by capture means of a diagram does give doesuseful insights into intophysics the the of the the process, and and Fig. 21 draws the the kind of diagram necessary to account account a healthy for for rate. By means of means such a a

--

Qa

Qb

Q Q

2 12. of

with is is

14)

MPE,

302

AND S.

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

4.

303

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

00 z z a> K O

Lz 52 w w nJ Ui-

z z z+ U W

g:

>> I I

II

Q,

Qh

I I

FLAW CONFIGURATION COORDINATE, COORDINATE, Q Q

of of

22. 22. AA 14 2 1). 2

= Q:, =

Q,

of

304

S.

AND S. S.

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

d.

at a

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

4. 4.

305

FOR

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

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

I I r-L L YY T2

23.

of

T3

of Eq. (96). (96).

306

AND S.

S. S.

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

v =v =

exP(-

(97) (97)

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

---

as modeled for the specific the instance of Cu in germanium. It is interesting that that and and(each of which starts with startsone mobile electron and and one mobile hole, of which the former is captured for captured and and the the forlatter T,) ended latterup as - for the the bands of germanium. bands comparable in size -at least

4. 4.

307

Such calculations for Auger capture rates capture at mid-gap flaws in GaAs would have one area one of general similarity (the valence (the bands), but would but involve a ordering of the the various minima minima conduction-band system conduction-band with a of Ge. (Aspnes, 1976) and, of and, course, an an intrinsic gapintrinsic twice as wide as that that Therefore, an an electron raised in energy by Auger hole capture (process capture would probably be transferred from the the r 6 lowest conduction band conduction into & of minima (Blakemore, minima 1982b). either the L6 theor & or sets Despite these disclaimers, let us see us what carrier densities carrier in GaAs might make the the Auger capture capture coefficients of Eq. (96) competitive (96) with MPE through are all areof relaxation, on on the assumption the that the coefficients the several flaws in GaAs in the the order of ordercm6 sec-I. cm6 Note from Fig. 20 that that have room-temperature MPE room-temperature capture cross capture sections around around i.e.,cm2; cm2; cm3 Equivalence of the MPE the capture coefficients capture approximating lo-* cm3sec-I. and Auger capture probabilities capture thus requires a free-carrier density of some l0l8 ern-,. ern-,. The The Auger processes of Eq. (96) (96) can can be safely thus thus ignored in in camer-depleted GaAs- that that is, in in semi-insulating material, or in aindevice heavily doped depletion layer. They should not be casually overlooked in in GaAs, or or in in the the conductingofconducting a field effect channel transistor. channel As remarked earlier in in this section, this allowance for Auger capture processes capture does not not end withend a consideration only of the simple the forms represented by Eq. (96). Belorusets (96). and Grinberg and (1978) argue that an Auger-type an transition transition to to a flaw ground state is state more probable from a shallow excited state state than than from the conduction band conduction itself. Their model Their supposes an electron under- undergoing the first the few steps of a phonon cascade phonon through excited throughstates. At this this point, apoint, passing free carrier (electron or hole) is accelerated, while the the first electron drops drops into the the deep-lying ground state state [which Belorusets and Grinberg modeled by the wave the function of function Eq. Jaros (1978) Jaros proposed a different Auger capture model, captureappropriate for appropriate a units of units mid-gap center of the kind that that change can canits occupancy its by charge. (There (There many are such are deep level flaws, including Group I Iand and transition transition element impurities, as well as as various native defects and and com24 the kind the of process Jaros conjectured, Jaros drawn in in plexes.) Figure 24 illustrates the the manner he suggested. manner (A Feynmann diagram would have shown the the suppose that that sequence of events, possibly more convincingly.)For Fig. 24, 24, flaw flaw is initially occupied by two electrons, with no mobile carriers the the around. When around. a free hole (of ordinary ordinaryspeed) thermal amves, thermal amves, could this bethis annihilated by annihilated one of one the bound the electrons. If the energy released in in that that transition is transition more than half the the intrinsic gap,intrinsic it is possible that the the Auger capture could capture be effected by ejection of the the second bound bound electron to to the the - Ei). - Jaros remarks Jaros that that this conduction band, conduction with kinetic energy energetic electron will rapidly thermalize by phonon phonon emission. Jaros proceeded Jaros to evaluate the overlap the integrals associated with this kind

308

S.

AND S.

free elec- elec-

of

24.

will is

if if

> >. .

is is as

if if

lose

1978.) 1978.)

of process, amving at amving a capture cross capture section of some cm2(i.e., cm2capture capture coefficient of some lo-’ cm3 sec-*) cm3 for the most favorable circumstances (i.e., cetc.). Note that the processes the that that Jaros was considering Jaros are are not not dependent on on the presence the of a second free canier to to carry off the the transferred energy; and and so-unlike the the circumstances of Eq. (96)- these Auger capture coefficients capture are are independent of n independent and n p. Their Their opportunities oppo to contribute to contribute the the total totalprobability capture capture are are thus thus diminished not notin a crystal or device or region of very small caner densities. caner Thus, Thus, large theAuger the capture capture probabilities deduced by Jaros Jaros (1978) appeared large enough to dominate the the nonradiative transition transition probabilities to mid-gap states in in materials such as However, Riddoch and and Jaros (1980) Jaros have created a more more sophisticated model for the the probability of this kind this of Auger capture. That That subsequent work made extensive numerical calculations, using a localized state wave state function that function was constructed to avoid the “effective the mass contamination” contaminat of more conventional more approaches. The result was an Auger capture cross capture cm3 sec-l), cm3 six section more like cm2 cm2 (capture coefficient (capture orders of magnitude smallerthan the the 1978estimate! It Itto is be is hoped that the the continued continued development of more more complete models for bound-state wave bound-state functions will have the reassessment the of Auger capture probabilities capture as one of its corollary its calculations. cm2 cm2is is not,event, not, inautomatin any any automatAn Auger capture cross capture section of ically negligible. The two Thelower curves of Fig. 20 show cross sections of that size, with little temperature dependence; temperature comparable behavior is known is for various other other mid-gap flaw types. For those those regions of relatively small temperature dependence, temperaturethere there a three-way is is split of the the capture probability capture among radiative capture, tunneling tunneling between vibronic states, and and Auger capture. The mechanism which dominates dominates flaw forone those one lower temper- temperature ature conditions is not conditions necessarily the the important important for anotherone flaw. another oneIn In each case, we should like to know about all about three processes. three

--

4. 4.MODELS MODELS FOR MID-GAP MID-GAP

CENTERS GALLIUM CENTERS ARSENIDE IN IN

309

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

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

310

AND

S. S.

S.

ANTIBONDING ANTIBONDING (CONDUCTION) II I II I

II

tI tI

EGO EP

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

.)-

EGO

\-

1% 7

EN

\ L BONDING (VALENCE)

7

II

ii

-II

A’

HYPERDEEP HYPERDEEP TRAP

ATOM- ATOMMOLECULE GaP HOST

25. 25.

MOLECULE

- ATOM -

WITH SUBSTITUENT

of GaP of P of P

As is is is is 1981.) 1981.)

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

4. MODELS

FOR FOR MID-GAP CENTERS IN GALLIUM ARSENIDE

311

involved Koster- Slater calculations- to to be discussed in in the following the sections. Thus, one one of these is a a antibonding state, antibonding which we can identify with the concept the of a deep-flaw a state within state the gap. the The other other is is an an impuritylike bonding “hyperdeep state,” lying or the valence band. However, Bernholc et al. (1981) (198 have compared the results the of applying this this simple approach (for several impurities impurities silicon) with in inthose of a a Green’s function calculation. function They concluded that predictions from a defect a molecule approach can can miss some resonant states entirely. In the next two sections, we consider the extended the Huckel theory (EHT) (EHT) and andmultiple the the scattering approach, which approach, Slater and and Johnson ( 1972) ( Johnson have termed the the Xa method. 13. THEEXTENDED HUCKELTHEORY (EHT) (EHT) APPROACH CLUSTER

Extended Huckel theory methods have been applied to molecular problems over the the years (see, e.g., Gilbert, 1969). A Aproposal was made by Messmer and and Watkins (1970) that an an EHT cluster EHTapproach be used for dealing with deep-lying states of a flaw a in a semiconductor. a This allows This one one to solve to the Schrodinger equation (approximately), equation using a a linear linear combina- com tion of atomic atomic orbitalsmolecular orbitalsorbital (LCAO- MO) method, method, numeri- nu cally evaluated. Messmer and Watkins and (1970) investigatedthis approach for approach nitrogen in in diamond, simulating diamond, the crystal the by a 35-atom a cluster surround- surrounding the the flaw site. Note that that in a acluster calculation, in in contrast to contrast the the defect molecule method, all method, of allthe one-electron the orbitals xVof the cluster the atoms atoms taken areinto are calculation: A donor A wave donorfunction 4D function is expanded in in terms of four terms orbitals four of each bonded atom. atom. Thus, cluster Thus, of four a a host four atoms atoms contributes 16 contrib orbitals:

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

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

where

894) = 894) =

4).

(102)

312 312

Here

AND S.

S.

is is the spherical the harmonic harmonic part, radial part, part andisand defined is the by the = Nr*-le-O =

(103) (103)

In Eq. In (103), Nis the the normalization normalization while n denotes nconstant, denotes constant, principal the the quantum quantum number number and and C isC the the orbital exponent. [Messmer and Watkins Watkins (1970) (1970) took C = C 1.625 = for the the host carbon atoms atoms diamond.] in in The matrix elements are are then calculated then from = =

+ HvV)S,v/2. +

(104)

p pand anddenote denote valence orbitals, and and are are chosen to represent the the empirical atomic ionization atomic energies Ip of the pth the valence orbital. That is, H, = = and KPvis defined by

KPv= 1, p = v, K, p Zp Z v. Here, 1 < 1 K >would be almost impossible to to verify experimentally,even with the the modem sophisticated modem versions of modulation spectroscopy. Some other things that that be cancalculated can are are more easily more compared with - that does that not ensure ensure lack ofa controversy a concernexperiment-although ing the interpretation. Considerable interpretation.interest has interest been aroused (and (and some spirited discussion also) by studies of chemical trends trends flaw in energy, in camed Vogl(198 This work out by Hjalmarson et al. (1980a,b), as reviewed by Vogl(198 1). used a aGreen’s function calculation to predict the the activation energies activation of numerous elements, numerousacting as anion-site as and cation-site sp3-bondedsubsti-

347

4. 4.

r Ir

A A

-12

AA

rl r

1 1

0

REDUCED WAVE VECTOR

FIG.35. Electron energy dispersion dispersion curves high symmetry curves along symmetry along in directions the the zone, directions for zone, the valence and lower conduction conduction of GaAs, bands asbands calculated by calculated Chelikowsky and Cohen Cohen states statesoccurs where occurs is s ismall over aover substantial substantial of k. of range range (1976). A large density of density See Fig. 36 for the the resulting formresulting of

1.5 I I

II

II

II

E-E,

II

II

11

(eV)

FIG.36. Density ofelectron ofelectron with respect states states to energy, for the valence bandsand valence the of GaAs. The solid curve shows curve the the calculated result calculated of Chelikowsky lower conduction conduction bands bands of Ley et al. al. (1974) the and and Cohen (1976). Cohen The dashed dashediscurve the experimental curve experimental result result for for valence bands. bands.

348

AND

S.

II

S.

II

II

- -

00

+(REPULSIVE)

FLAW SITE POTENTIAL

FIG. 37. FIG. schematic schematic of theplot variation plot variation with flaw site site potential of the potential localized state state with the the arguments arguments by advanced adv energy; for a atwo-state model (as in Fig. 2 5 ) and in line line al. (1980a,b) and (1980a,b) Vogl(198 1). Vogl(198 This This indicates indicates energy the the limit pinning which limit pinning is Hjalmarson et Hjalmarson repulsive local sitepotential. local approached for approached a avery large attractive or attractive

tutional tutional impurities. The The emphasis is entirely on the the consequences of a a short-range impurity impurity potential; long-range potential; coulombic the thecoulombic partpotenpart potenof the the tial is tial ignored, to allow any shallow any impurity to impurity have zero binding energy. bindingA A key element in this this approach is theapproach the “pinning energy” “pinning dividing the the energy regions in the the intrinsic gap intrinsic associated with bonding-type and antibonding- antibonding the energy is envisaged is type states. Figure 37 shows schematically how the flaw C C

B 51 B

Band E d g e

-- -

T, States Cation Site

-II

-10

--

--

--

11

00

-5

F L A W p - O R B I T A L ENERGY

(eV)

FIG.38. Predicted Predicted bound-state energy, relative bound-state to the conduction band conduction edge, for T2 for(p-like) (p-like) flaw levels arising from from a a cation cation siteinsite thesubstitution, eight solids indicated substitution, indicated Vogl,(after 1981). (after 1). The abscissa at at the bottom bottom shows a ascale of the porbital energy of of the flaw site. Values considered appropriate appropriate for for various various atomic atomic substituents top edge. substituents See are are i Talwar Ting Ting (1982) surveyed. (1982) Fig. 39 for a larger a range of abscissa energy, which Talwar and

349

4.

-40 -40 -30

10

20

I M P U R I T Y POTENTIAL

(eV)

-20

-10

00

30

40 40

39. 39.

of

1982). 1982

of of

for of

of be

37, 37,

38. 38.

as depending on on the strength the of the local site potential, for a two-state simplified model (Fig. 25). 25). Where the the pinning energy pinning ends up ends in the gap the depends, of course, on the the band band structure of the structure host the (GaAs being the solid of principal concern here), concern (= As site in GaAs) or cation on whether on the the substitution is onsubstitution an on anion site anion site (Ga (Ga site in GaAs), and on on whether one onedealing is is with a symmetric (I = = or or (I # # representation. Figure 38 shows the the curves of Vogl (1981) for predictions of the the bound flawbound state state energy, versus p-orbital energy, for states resulting from substitutions on substitutions the cation the site of site GaAs IV solids. Group and seven and other 111-V other and and Group The The curve for GaAs curvein Fig. in 38 formsjust one part one of the the broader energy broader from the the work of Talwar and Ting (1982) for range curve in in Fig. 39, 39, symmetry states in the five 111-V hosts as indicated. as The two The portions of portions those the idealized the curve in in each curve in Fig. in 39 may be compared with those of and showed also a family of curves for symmetric (A,) Fig. 37. Talwar and Ting states on on cation sites, while the the families of curves provided by Vogl dealt with both A, and andrepresentations for both cation cation andsites. and anion Theseanion two investigations did did not yield identical results (that rarity (that in in this world), this nor nor even the the same conclusions, but but both represent interesting avenues for andother mildly other polar 111-V polar further modeling further of mid-gap flaws in GaAs and the compounds.

The The precedingparts of thisprecedingparts this chapter have chapter not, by any means, exhausted the the opportunities for opportunities reviewing theoretical models that could be applied to

350

S.

AND S.

deep-level flaws in GaAs. in In In this this brief part, comments part, comments made, concerning are are concerning a number of other other approaches that that have been proposed in in recent years. Some of these correspond, in certain in respects, to to the various the categories that that have already been ennumerated. For ennumerated. several of the models the to be to mentioned mentioned here, the photoionization the spectralresponse has been a major preoccupation. major Nazareno and and Amato (1982) suggested a simple model for identifying a deep-level member of the the flaw in a semiconductor as being a species. Their model concentrates on on the peculiarities the of the the photoionizaas related as to to critical points in in the density the of final tion tion cross section A similar consideration had led us, in in Part VIII, Partto note the the states for GaAs in in Fig. 36, for comparison with the the features of maxima of Figs. 33 and 34. andAt any rate, Nazareno and and Amato Amato comment (with some comment some that t simplification) a,depends on the the transition transition matrix matrix element elem and and on on for the final the state energy. state From From kind thisofthis analysis, they drew 0 in 0 conclusions concerning iron ironsilicon, in in oxygen in in Gap, and and Cr and and GaAs.Their deductionsfor deductions the two the impurities species impurities in in the thehost latter were latter (Ei-Eq)=0.55eV for Cr,, and and ED=0.67eV for with the the conduction conduction alone taken band band taken into account. account. was That probably Thatnot not a wise assumption to have to made for those situations, situations,not but invalidate but it it does the does the basic opportunities for opportunities this this kind of approach. kind deep-level photoionization photoioniza Burt (1 980) evaluated a simple form of the the problem, with GaAs specifically in mind. in For For computational ease and computational other other delta-function potential. There was There some interestreasons, he used a ing logic behind the the adoption of this adoption potential, this for its eigenvalues its include band-gap states analogousto surface states. This made This it possible it for Burt to Burt perform the calculation the using evanescent waves (Heine, 1963). These waves describe non-Bloch states, related to to the the ordinary Bloch states ordinary of the crystal the by an extension an into complex wave vector, There has been a general recognition for afor half-century that athat state which state delocalized through- throughcan be described by a complex wave vector cannot be cannot out aout crystal. However, that was that put to putuse two decades ago for the modeling the of surface states properties (Heine, 1963), and and possible the the value of an an evanescent wave approach for deep-lying flaw states in the the was not analyzed until until much more recently. These topics, of the complex the band band structure, usestructure, of evanescent the the states, how this can thisbe used to describe photoionization of photoionization a deep flaw, deepwere and of and further examined further in a series of papers by Inkson (1 980, 198 and by Blow ( The reader’s The attention attention drawn tois aiscomment comment made m and Inkson and ( 1980a,b). gap by Blow and Inkson and (1980a) that that the the works method well method for an semiconductor because (a) flaw (a) states are then then not not distorted by the low-lying thedistorted r minimum, r minimum, (b) the and the and (Penn model (Penn dielectric) band band gap is then then more nearly constant over constant the surface the of the the Jones zone.Jones One One implication of these implication

351

4.

comments comments is that flaws in GaAs may not not provide an ideal test of this this approach. approach. In a series a of papers which papersalso draw draw upon evanescent upon the wave the approach approach (and with (andBurt and Inkson Inkson among among Dzwig the the authors), authors), et al. (198 al. la,b, 1982) 1982) have proposed a aslightly different model for calculation of calculation optical optical matrix mat elements and elements cross sections associated with deep-level flaws in GaAs. This This is is a asuperlattice approach, approach, based on the the assumption of aassumption alattice lattice of flaw S S potentials. In this way, this some of the symmetry the is restored to the problem the (as (as in the electrostatic the problems solved by the the method of images). methodAn isolated flaw is then then modeled as as the limit limit of the the superlattice superlattice going to constant cons infinity. In their investigation their of a 2a 2X X 2 superlattice, 2 Dzwig et al. (1 al.982) were able to trace trace change the thein the the character of the character the bound flawbound state state asisasmade this this deeper (it gets (it more p-like). more They took took various the theconduction minima conduction at the the r, L, and X Xpoints points into account account calculating in in curves for for the spectral the dependence of and of Figure 40 shows an example of their their results, q(hv)for for donor a a of = 0.625 = eV in GaAs. in This may Thisbe be compared compare with the optical the cross-section curves for for lower the theconduction conduction region band of band Fig. 34, from 34, the work the of Banks et al. (1980). al. One can see some similarities some and and also some differences, for the the “true and“true complete” complete”for solutions deep- solutions level flaws and their their photoionization properties photoionization still elude us. AA tight-binding LCAO approach approach has been taken taken by Peiia and Mattis Mattis

--

of

40.

‘3

GaAs(ED=0.625 = 0.625 eV), eV), Dzwig ef a/. (1982) 2 2X X 22

for

5 5

b“

of

0.6

I .o I

1.4

(eV)

18

352 352

J. S. BLAKEMORE AND S. S.RAHIMI

(198 l), with both both host and flaw states expanded as as a complete set of site-localized orbitals. Unlike many of the the other theories otherwe have noted up up Wannier Wannier to now, their their approach approach require did thatdid thatnot host thenot the orbitals be orbitals included in the the functions-only that that they be compatible with the bands bands calculation. Fermi’s golden rule was employed in in deducing the the electronic part of part oplically induced transition rates. transition The The latter was applied latter to problems of moderately deep acceptors in in silicon, and the the applicability of these techniques for the the mid-gap types of flaw in a polar solid such as GaAs remains (as this is this written) to be tested. Additionally, we might note anote viewpoint growing out of remarks made made in in the of Monemar and Monemar Samuelson (1978) and reexamand Appendix A of the work al. (1 al.98 1). This concerns two opposite extremes for the the ined by Chantre et Chantre = constant = constant for an allowed form of the the matrix element. matrixThus, process. However, transition, transition, as characteristic of a photoneutralization photoneutralization a kafor k a first-order forbidden transition, transition, typicalasfor as is many is many kdependence of the the matrix element matrix for a photoionization transitions. The kThe - need not coincide not with either extreme. real situation of semiconductor- flaw Allowance for this this obliges a numerical evaluation, evaluation, using the the real band band structure (including structure nonparabolicity, upper upper conduction bands,conduction etc.). Folal. applied al. lowing the the formalism of Monemar and Monemar Samuelson, Chantre et Chantre aAs conduction conduction system,band and used and bandthis this this method this specifically for the G the to fit their photocapacitance spectra for several well-known flaw species in in EL6, etc. that that semiconductor: Cu, Cr, Cu, The subject The matter of matter this chapter this is is not not one which oneaon conclusion on can can usefully be expressed, since the methods the by which mid-gap flaws (in GaAs and and in other other semiconductors, of both direct and indirect indirect gaps) may be modeled and calculated and are still are in in a state of state rapid evolution. analyticare now are Some glaring limitations of certain of the simpler analytic models quite well quiterecognized. However, their value their for an approximate approximate and and u numerical standable representation does not allow them them to away. The The methods, as conducted with large computational resources, computational probably do represent the way the of the the future. is essential future. Itthat It thatuse theofthe such methods be methods inextricably entwined with human human input and monitoring, and that the the attributes the experithe results printed printed provide out out such a variety of flaw attributes that mentalist has independent independent opportunities for testing the opportunities validity. the As we have “right” binding energy is not not enough! said all the way the through, to get the the ACKNOWLEDGMENTS ACKNOWLEDGMENTS 79 16454 79

of

8305731, also

of of D. D. Dow,

4. MODELS MODELS FOR FOR MID-GAP IN GALLIUM MID-GAP GALLIUM CENTERS CENTERS ARSENIDE 353 ARSENIDE G. Ferenczi, H. Ferenczi, G. H. Grimmeiss, M. Grimmeiss, Jaros, U. Jaros, Kaufmann, L-A. Kaufmann, Ledebo, J. R. k i t e , D. C. Look, S. Makram-Ebeid, S. G. Makram-Ebeid, M. Martin, A. Martin, G. G. Milnes, S. T.Milnes, Pantelides, B. Pantelides, K. Ridley, L. I. Samuelson, Samuelson, alltheir allthe oftheir of following respects: and and J. Schneider, Schneider, among among valued others, help forin help others, any orfor useful discussions, interesting interestingand preprints, (in some preprints, some cases) comments comments on the draft draft manu- manuthe figures we number as script. We script. are are additionally additionally to Dr. Dr. Baraff indebted for his indebted for originals of originals Figs. 31 and 32.

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transient transient technique, 140- 140-technique, 143 143 ASES (arc (arc source source emission emission spectrosco Absorption coefficient, Absorptionsee also Optical Optical 100, 132 analysis), 26, 26, absorption absorption studies studies Auger recombination, recombination, 304- 304- 308 308 at 1.1 pm, 35 35 capture coefficients, capture 305-305 308 - 308 Acceptors, 32, 34, 37-44,98, 99, see 99, also diagram of diagram capture processes, capture 305 305 Compositional Compositional purity; levels purity; Impurity Impurity 0.026-eV level, 0.026-eV 37, 38 B B 0.073-0.078-level, 0.073-0.078-level, 201 -206, -206, 38-44, 208, 38-44, 208, 211 211 Backgating, 148-151, 148-151, 195 195 anti-site defect, anti-site205, 205, 206 Barrier height, A1 on GaAs, 67 boron boron complex, 40 -44 40 complex, Billiard-ball model, 263, model, 264,271 263, -278, C, 32, 32, 34, 37-40,42,47, 48, 48, 79, 98, 280,281 100- 102, 192, 193,203,206-208, photoionization photoionization cross section, 272-277, section, 272-277, 2 1 1,1 see also Carbon Carbon 280, 280, 281 29, 29, 30, 36, 37,98, 106-109, 106-109, see Cr, Cr, Boat-grown GaAs, 5 also Chromium Chromium Boric oxide oxide encapsulant, 6, 6, 10, encapsulant, 14, 17,10, 14, Mn, 47,98, 101, 102, 193 193 see 19-21,26-28, 163- 165, 194,211, 165, Si, Si, amphoteric amphoteric 57-59, behavior, 57-59, 73-81 behavior, also Encapsulation Encapsulation Activation efficiency, Activation69 -69 7-1, see also Ion [OH] content, [OH] 13,26-28,97, 163, 163, 194, implantation implantation 195,211 Activation energy Activation prevalence of prevalence 0.65-eV trap, 21 1 1 37-44, see also Acceptors acceptors, 37-44, acceptors, temperature temperature 19gradients, gradients, 29,42,43, deep deep donor, donor,see atso Donors Donors viscosity, 20 - 7-1, see also electrical activation, 69 activation, Born approximation, approximation, 249, 249, 257, 264 257, 264 Direct Direct ion ion implantation implantation Boron, 24-28, Boron, 101, 102, 192-195,204, see implants, implants, 56, see 56, also Ion implantation implantation also Impurities Impurities resistivity, see also Resis?;vity 4 1 -44 boron boron -defect -defect complex, complex, 19 semi-insulating semi-insulating materiai, materiai, effect of [OH] in [OH] in B,O, encapsulant, encapsulant, 13, AES (Auger emission spectroscopy), 100 26-28,97, 194, 195,21 I I Amphoteric Amphoteric 57 behavior, 59,73 -8behavior, I , 297 Boron nitride, pyrolytic, nitride, 8, 28, 28, 49, 163, 164, Si, 57-59,73-81 see also PBN crucible crucible Annealing, 45-47, Annealing, 54,65, 80, 80, 113125,113- Breakage, GaAs wafers, GaAs 83 135-143, 135-143, 221,222, seealso Thermal Thermal Breakdown voltage, FET, 6FET, 11 annealing annealing Bridging version of square-well potential potential activation efficiency, activation 80, 80, 123 123 effect on effect model, 271,278-281 model, effect on camer concentration, concentration, 107, 108 profiles, 67 Broadening of implant implant implanted implanted layers, 113-1 18, 127, 128 Buffer layer, 103- 103105, 109 effect on on compensation compensation 80 ratio, ratio, camer concentration, concentration, 104, 105 thermal thermal conversion, 4,46 - 49, -conversion, 109,221, camer mobility, mobility, 104- 104105 222 growth, growth, 103- 103105 AA

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reduction reduction of electron electron mobility, 44 mobility, with Te, Te, 106 Capacitance Capacitance spectroscopy, transient transient 196, 197 various charge variousstates of states Cr, (calculated), (calculated), Capture coefficient, Capture 236-238, 236-238, see also also 319 Carrier Carrier capture and emission capture mecha- mechaCompensation Compensation nisms nisms 192,206 - 208 - 208 mechanism, mechanism, 305-305 308, - 308,also producing producing semi-insulating29, semi-insulating 29, beha Auger recombination, recombination, Auger recombination recombination 44, 161,206- 208 - 208 300, 300, ratio, ratio, multiphonon multiphonon crossemission section, emission section, 74,75, 80 302, 307, see also Radiationless Radiationlesseffect of annealing, 80 annealing, transitions transitions role of role carbon, carbon, 208, see 208,also Carbon Carbon -299, see also Radiative Radiativerole of EL2 defect, radiative, 297 radiative, EL2 208, see 208,also EL2 level transitions transitions Complexes, Complexes, also Acceptors Acceptors Carbon, 4,24-26, Carbon, 34, 37-40,47,48, 79, 79, 40-42 boron-defect, boron-defect, 98, 101, 102, 192, 193, 203, 206-208, 23-29, 23-29, 192-212, see Compositional Compositional purity, purity, see also Impurities: Impurities: 2 121,1 227,236,29 1, 1, also Stoichiometry Stoichiometry Impurity levels Impurity determination determination also ASES, 26, see also ASES effective segregation coefficient, 39 39 measurement with measurement LVM, LVM 26, 192, see also LVM LVM, 26, LVM, possible component component of EL2 complex, 291 complex, SIMS, 23-25, see also SIMS with EL2, 207,208,227 SSMS, 23,26, see also SSMS impurity impurity elements, elements, Impurities see also Impurities Camer capture and capture emission mechanisms, mechanisms, 293-308, 293-308, see also Capture coefficient; Capture B, 24-28, see also Boron see also Carbon Carbon Emission coefficient; Photoionization; Photoionization; C, 24-26, 24-26, 8, 24-26, 24-26, 36-38, seealso Cr, 4, Cr,4, Radiationless Radiationless transitions transitions Chromium Chromium 304-308, 304-308, also Auger recombination recombination 0 , 4 , 2 4 , see also Oxygen Auger recombination recombination see also Silicon also Si, 22-28, 22-28, 296 287, Cr2+-Cr3+ transitions, 287, transitions, 24, 24, 25,impurities, tabulation tabulation of major major impurities, enthalpy of enthalpy transition, transition, 295, 296 295, 101, 102, 193 193 entropy factor, entropy295 295 impurity impurity sources, 23-28 entropy of entropy transition, transition, 295 influence of influence water [OH] water in [OH] in encapsulant, encapsulant, free energy of ionization, 296 ionization, 194, 195, 195, seealso 211, 211, seealso multiphonon multiphonon emission capture capture cross cross 26-28, 26-28, Encapsulation Encapsulation 300, 307 section, 300, 302, 283, 283, Configurational Configurational coordinate coordinate diag radiationless radiationless 299 transitions, - 304, - 307, 304, transitions, 290,301-303 see also Radiationless Radiationless transitions transitions self-trapping, 303, self-trapping, 304 303, 304 297 - 299 radiative radiativecoefficient, capture capture Conversion, Conversion, 109,221,222 thermodynamic thermodynamic 294relationship, 294 -297 -297 relationship,4,46-49,51, thermal, thermal, 4,46-49, 109,221, 222 two-stage capture capture process, 300 - 302 - 302 Crucible Crucible Charge carrier carrier scattering, ionized scattering, impurity, impurity, 73 73 PBN, PBN, 8,28, 163, 164, 192-195,211,see 164, also PBN 8, 8, 23-26, 29, 30, 36-38, 76, Chromium, 4, Chromium, 150,106-109, 193, 163, 192- 192- 195 195 quartz, quartz, 92,95,98- 102, 102, 106-109, 209-211,221,223,236,237,242,287, silica, 8, silica, 27, 27, 31 288, 296, 340, see 340,also Impurities; Impurities; Crystal growth, Crystal see also Crystalline Crystalline imperfections; imperfections; Crucible; Crucible; Enca Impurity levels Impurity growtk Materials growtk Materials Dislocations; LEC Dislocations; Crz+-Cr3+ transitions, 287,296 transitions, preparation; preparation; Uniformity Uniformity diffusion, 108, 221 4, 17, 24, 29, 24, 29, 93,94 Bridgman, 4, Bridgman, effect on ion implantation, implantation, 69-72,76, 77 coneangle, 16, 170, 174, 176-179, 176-179, 191 redistribution, 4, redistribution, 22 1 1 CC

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crucible crucible material, see Crucible material, Crucible 327, 337-340, 337-340, energy level calculations, 327, calculations, differential weight gain signal, 7, 10, 167 167 347-349, 347-349, also Green’s Green’s function function encapsulation, see encapsulation, also Encapsulation Encapsulationmethod method B203,6, 10, 14, 17, 19-21,26-28,97, - 238 phenomena phenomena affected, 235 - 238 163, 164 Defects, see also Crystalline Crystalline imperfections; impe effect on electrical properties, 30 properties, - 32 - 32 Dislocations; Dislocations; levels; Impurity Twinning Impurity Twinning LEC technique, technique, 5-23, 163-167, 163-167, see acceptor level, acceptor 42 also LEC growth 0.073-defect-compIex, 42 0.073-defect-compIex, plasma plasma 62 nitride, -6265, - see nitride, also Silicon Silicondonor level nitride nitride 0.45-eV, 42, 43 24, 29 gradient-freeze technique, 24, technique, EL2, see EL2 level inclusions inclusions 187, see also TEM detection by detection TEM, TEM, As, As, 190 190 16, 326, 326, 327, 327, energy level calculations, 3calculations, As As precipitates on precipitates dislocations, 50 dislocations, 50 337-340, 337-340, 347-349, 347-349,Green’s see also Green’s Ga, 187 function function method method large melts, 8melts, 252-260potential model, mo Delta-function Delta-function potential automatic automatic diameter 8, diameter 9, 167 control, control, 25 applicability, applicability, 1, 1, 252 coracle technology, 8 - 1-1, 166 photoionization photoionization section, 255 section, cross - 260 - 260 manual manual diameter diameter 8- 10, 166 control, Depletion control, voltage, Depletion 225, 225, 226 LEC, 5 -23, see also LEC growth Depletion Depletion 150width, 150 width, 17, 19-22 thermal thermal gradients, gradients, Device fabrication, 63-65, fabrication, 212-226, see pull speed effects, 20-22, 52-55, 164 also FET; IC FET; devices; MESFET MESFET seed rotation rotation effects, 20-22, 52-55, 164 164 implantation implantation 64 sequence, sequence, Crystalline Crystalline imperfections, 12-23, 12-23, see also imperfections, logic approaches, 2approaches, 12,213 Crystal growth Crystal steps, 213-216 steps, 12, 14- 17, 17, 50, 50, 97, 97, 167-wafer 167- breakage, 182, 182, 83 dislocations, 12, dislocations, breakage, 187, 187, 190,226,228, see also Direct Direct ion ion implantation, 3, 4, 4, 55 - 8-implantation, 1, 55 Dislocations Dislocations 109- 109- 143, 143, 212-226, 212-226, see also Electrical 12, 168,226,227 effectson devices, effectson12, 152, properties; properties; Ion Ion implantation implantation generation, generation, 14- 1417, 168 65, 80, 81, 65, 80,125, 81, 113- 113annealing effects, annealing influence of influence thermal stress, thermal12, 14- 17, - 17, 135-143,221,222 19,20, 168, 171, 172 channel channel mobility, 71 -73 mobility, reduction, reduction, 12, 12, 16, 15, 97,98, 16, 168,228 Cr-doped Cr-doped 76 substrate, - 78, - 78, 129 substrate, - 132 impurity impurity striations, 20-23 striations, electrical activation, 56-58,69-71, activation, inclusions inclusions 76-78 190 experimental experimental 62-66 procedure, procedure, As precipitates precipitates on on 50dislocations, dislocations, evaluation evaluation techniques, 65 techniques, Ga, 187 nitride nitride encapsulation, 62 - 65, - encapsulation, 65, 1 13-13 123 - 123 microdefect microdefect studies, 187, 190, studies, see TEM, TEM, PSG encapsulation, 63 encapsulation, also TEM TEM Si02encapsulation, encapsulation, 1 15 1 15 twinning, twinning, 12- 14, - 182- 187, - see also flat-channel profile, flat-channel 57 Twinning Twinning implications, implications, device processing, FET FET 60, Czochralski puller, 7, see also Crystal growth growth 61,78-81 measured profiles, measured57, 66-69, 57, 113- 113118, 121, 122, 127, 128, 132, 137, 132, 139, DD 140,2 17, see also Electrical properties properties Deep-level centers, see centers, also Flaw; Flaw 57, 128 Hall mobility, 57, mobility, states states (quantum (quantum theory) theory) mobility, see mobility, Mobility Mobility classification scheme, 238-242 238-242 plasma plasma nitride nitride62-65, encapsulant, encapsulant, detection detection technique, 24 1, see also technique, DLTS DLTS 113-123 113-123

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Direct ion ion implantation (cont.) implantation (cont.) thermal thermal gradients in melt, melt, gradients 17, 19-22, 168 power FET applications, 60,6 applications, 1, 1, 78 -78 8-18 x-ray topographs, topographs, 16, 16, 18 Seimplantation, 81, 81, 115-118, 115-118, 122, 123, DLTS DLTSlevel (deep transient (deep transient spectroscopy), spectro 127, 130, 132, 137, 132, 139, 140,217, 45-47, 149,241 see see also Selenium also Selenium Donors, 29,32-35,39,40,42-53,56-60, Donors, - 65- 65 selected area, 63 area, 66-71,73-81,98,99, 195-206, 195-206, see see selective implantation implantation fabrication fabrication also Compositional Compositional purity; purity; Impu Impurity levels Impurity sequence, 63-65 sequence, implants, 81, implants, 81, 114, 119, 128, 129, see 129, 0.45-eV level, 42-44 also Sulfur Sulfur 35, 44-51, 53,913EL2 level, EL2 29, 32, 34, 34, 137, 115, 121, 121, 100, 108, 108, 109, see Siimplantation, 56-81, 56-81, 115, EL2 also level 148,also 109, 148, Silicon also 139, 140,219, 220, see 220,see also out-diffusion, 49, out-diffusion, 51 of Si, 57-59,behavior 0 , 2 9 , 195, see also amphoteric amphoteric behavior see Oxygen 73-81 - 44,208 - 2-I I I I residual, 36 residual, concentration profile, concentration 57, 57, 1 15, 137, effective donor segregation coefficient, 139, 140 39 98, see see also Sulfur alsoSulfur effect ofannealing, 80, 119- 119125, 8 see also Selenium Selenium Se, 8 1, nealing Si, 56-60,66-69, 73-81,98, seealso 71-73, 75 mobility, 59-61, mobility, Silicon uniformity, 68, uniformity, 133, 134, see also also amphoteric amphoteric 57-59,73-81 behavior, behavior, Uniformity Uniformity diffusion coefficient, 125 125 14- 18, - 50, 97, 97, 98, 152,98, profile of implants, implants, 57, 57, 1 15, 1 137, 139, 139, Dislocations, 12, Dislocations, 167- 182, 187-192,226,228,242, see 140 140 also Crystal growth; Crystalline Te, Te, 98, see 98, see also Tellurium also Tellurium imperfections imperfections 14, 17, 19-21 augmented by augmented encapsulant, encapsulant, E E decoration, 50 decoration, 50 EL2 level, 29, 29, 32, 34, 35,44-51, 53, 53, effect on devices, on 152, 168,226, 227 generation, 14generation, 1417, 168 98-100, 108, 109, 148, 196,200,201, 205-208,227,228,236,241,290,291, influence of influence thermal thermal stress, 12, 1412, 17, 19, 19, 20, 168, 171, 172 304 304 longitudinal longitudinal distribution, 174, 174, 175distribution, 175 with with carbon, 207,208 carbon, dependence dependence on on29, stoichiometry, 32, 29, 35, 32, stoichiome networks, 173, 174 174 parameters affecting parameters density, density, 170, 174, 44,49,201,227 electron electron paramagnetic paramagnetic resonance r 190, 191 ambient pressure, ambient 170, 174, 179-181 179-181 35 35 identifications identifications coneangle, 16, 16, 170, 174, 176-179, 176-179, 191 anti-site defect anti-site (As on Ga site), 35, 99, 99, crucible crucible position, 19 position, crystal rotation rotation and rate pull rate speed, speed, 196,205,206,227,241,291 complex, 29 complex, 129 1 20-22 174,control, 182, 182, 1 19 metastable metastable 290, 29 state, 1, 1, 304 state, 304 diameter diameter170, control, 35, 35, 196,absorption, 200,201 height of encapsulant, encapsulant, 14, 19, 20, 20, optical optical absorption, out-diffusion, 49, out-diffusion, 51 1 170, 174, 179, 180, 191 melt melt stoichiometry, 170, 174, stoichiometry, 182 182 photoconductivity, 196 photoconductivity, 196 photoluminescence, 20 photoluminescence, I20 , 202 seed quality and quality necking, 16, 17, 17, 170, 174, 181, 182, 191 role in conversion, 46,49, conversion, 5 I , 109 transient capacitance studies, studie radial radial distribution, 15, 17,distribution, 170-173, 170-173, 190 190 transient capacitance196 properties, 57-62,65, reduction, reduction, 12, 15, 16, 97, 98, 98, 168, 228 228 Electrical properties, 29-55, 71-79, 128-132, 128-132, 195-206, seealso TEM TEM studies, 18'7- 190, - see aiso see TEM

LEC techniques, 5-23, techniques, 163- 163- see 167,also 167, also Impurity Impurity levels; Ion implantation; implantation; LEC Semi-insulating Semi-insulatingmaterial material LEC growth phosphosilicate glass phosphosilicate (PSG), 63 axial variation of variation resistivity, 30, 31 plasma plasma nitride, 62-65, nitride, see also Silicon Silicon carrier carrier concentration concentration nitride nitride 57-60, 113- 113118, implanted layers, implanted 115, 138, SiO,, 115, 138, 139 121, 122, 124, 127-129, 127-129, 132, 135-142,217-220, seealso Ion Ion Implantation Implantation various crystals, various 38, 40-44, 40-44, 48, 52, 52, 63-65, FET (field effect transistor), 3-6, transistor), 107, 108, 197 78-81,92,212-226, seealso MESFET MESFET crucible/encapsulant effects, crucible/encapsulant 30- 3032 device fabrication, 2fabrication, 12- 226, - see 226,also also 31 resistivity variations, 30, variations, Device fabrication fabrication depletion voltage, depletion225, 225, 226 device processing, 78 -78 8-1 melt melt composition effects, composition 32-36,41-44, discrete vs. discrete monolithic monolithic 3 -6 circuit, circuit, Stoichiometry see also Stoichiometry also flat-channel profile, flat-channel 57 36, 51, 51, 53-55, 198, seealso mobility, 34, mobility, implants, implants, see also see Electrical properties; properties; Mobility Mobility Direct Direct ion ion implantation; Ion implantation; implanted layers, implanted 57-61,71-75, implantation implantation - see also see Ion implantation implantation 128- 132, breakdown 61 pinch-off voltage, 65,79, 213, 222-225 222-225 breakdown voltage, channel channel mobility, 71, 73 resistivity, 29-31, 29-31, 33, 34, 43,52, 196, full-channel full-channel 6 1 current, current, 199, see also Resistivity also undepleted undepleted donor concentration, net net concentration, Se-implanted layers, Se-implanted 115- 118, 127, 132, 60,61 133, 135, 139, 140, 216, 217, seealso logic approaches, 2approaches, 12,2 2 I3 Selenium Selenium semi-insulating semi-insulating behavior,Semi-insubehavior, see Semi-insupinch-off voltage, 65, 79, 65, 79, 213,222-225 power applications, implantation, applications, 60 lating lating material material 63 - 65 - 65 57-59, 71-78, 115, 115, selected-area implantation, implantation, Si-implanted layers, Si-implanted 137, 139, 140, 2 19, see also Silicon also Silicon zero-bias depletion depletion width,79 width,79 see Carrier Carrier capture and emission captureemission Flaw, see also Te-implanted layer, Te-implanted 1 13, 141 mechanisms; centers; centers; thermal thermal stability, 44- 44- 52, stability, 52, see Heat seeHeat also also mechanisms; Deep-level Defects; Flaw states (quantum states theory); theory); treatment; treatment; Thermal Thermal annealing annealing Impurity Impurity levels; Phonon-assisted Phonon-assisted optic 52-55, see also Uniformity also Uniformity uniformity, 52-55, uniformity, transitions; transitions; Pbotoionization; Pbotoionizatio Electron mobility, Electron see Mobility Mobility tralization tralization 239, EMA (effective mass approximation), 239, approximation), amphoteric, 297, amphoteric, see 297,also Amphoteric Amphoteric 245-248,250 behavior behavior hydrogenic model, 247, model, 247, seeHydrosee alsoHydroalso 304- 308, see 308,also also Auger recombination, recombination, genic impurity impurity Auger recombination recombination see also also Emission coefficient, 236-238, 236-238, billiard-ball model, 263, model, 263, 264, 271 -278, 264, Carrier Carrier capture and emission capture mechasee see also Billiard-ball also model model nisms nisms carrier carrier capture and emission, capture293-308, emission,293-308, also see Crystal growth Encapsulation, see Encapsulation, see see also Carrier alsocapture Carrier and emission emission 10, 14, 17, 19-21,26,27, BZO,, 6, 6, 163-165, 163-165, 194, 195,211,seealso mechanisms mechanisms Boric oxide encapsulant encapsulant 240 240 classification chart, chart, impurity, impurity, 240 240 [OH] content, 13,26, effect of water [OH] content, native defect, native 240 240 27,97, 163, 164, 194, 164, 195,211 prevalence of 0.65-eV trap, 0.65-eV trap, 2 1 11 complexes, 4complexes, 1 -44, -44,1, 24 24224242 definition, 238 definition, 238 vacuum baking, vacuum26 26 effect on electrical properties, 30-32 properties, 30-32 delta-function delta-function potential 252 252potential -260, -260, model, m

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Flaw (cont.) (cont.) photoionization, photoionization, -25 I , see also249 249 see also Delta-function Delta-function potential potential Photoionization Photoionization model photoneutralization, photoneutralization, 249,25 1, 1, see also hydrogenic model, 247, model, 250, 25 1, see also Photoneutralization Photoneutralization Hydrogenic Hydrogenic impurity impuritywave function, function, andspatial spectral spatial spectral information information for complete required required complete also Flaw properties, properties,see 264-266, 264-266, signature, 267,268 signature, Franck-Condon shift, 283-285,287-293, multiphonon multiphonon processes, 299- 299304, 307 296 Phonon- Phonon- tabulation, tabulation, 289 289 phonon phonon coupling effects, see coupling assisted optical optical transitions transitions see also quantum-defect quantum-defect model, model, 260-264, 260-264,G G Quantum-defect model Quantum-defect radiative capture cross capture section, section, 297-299 Gradient-freeze 297-299 Gradient-freeze growth technique, crystal crystal 4, technique, radiative radiative transitions,1,transitions, 297-299, 297-299, 249-25 24,29, 249-25 93, 94, see 94, also Crystal growth growth Green’s Green’s function function method, method, 328-34 also Radiative Radiative transitions transitions square-well potential potential model, 267-271, 267-271, calculated energy calculated levels, 327, 327, 337-340, 337-340, 347 - 349 see also Square-well 279-281, 279-281, flaw bound-state energy bound-state dependence on dependence potential model potential -1 1 site site potential, 349 potential, bridging version, 27 1,278- 28 wave function function cation cation site site substitution, 348 substitution, spatial properties, properties, 264-266 264-266 continued continued fraction339 fraction method, method, electron energy electrondispersion curves, dispersion 347 spectral properties, 264, properties, 265 see Flaw states (quantum states theory), 242ff, theory), Cia-site substitutional substitutional impurities, impurit also Flaw tight-binding tight-binding approximation, 329 approximat - 264, - see also Flaw choice of potential, 247 potential, V , , VG., V,-V,, complex, complex, 327, 327, 338 3 impurities, 0 impurities, divacancies, billiard-ball model, 263, model, 264, 271 -278, -278, vacancies, divacancies, 0 vacancy-0 pairs, pairs, 327,337-340 280, 28 1, see also Billiard-ball change change in of in density states states density from from removal remo model ofGa, 342 bridging version of square-well charge charge density contourdensity plots, 343,344 potential, 271, potential, 278-281 278-281 see also also 252-260, delta delta function, function, 252-260, density of density states of states principal principal 347 bands, bands, flaw-state energy flaw-state variation with variation site site Delta-function Delta-function potential potential model model 1, 1, see also Hy- Hyhydrogenic, 247, 247, 250,25 potential, potential, 348 fundamental fundamental336 limitation, limitation, drogenic impurity impurity quantum-defect quantum-defect 260-264,280, model, model, suggested remedy, remedy, 336 general general formulation, formulation, 328-336 328-3 also Quantum-defect Quantum-defect 28 1, convergence convergence 334problems, problems, model inclusion of inclusion long-range long-range potential, potential, see square well, square 267-271, 267-271, 279-281, 279-281, simplicity ease of simplicity also Square-well potential potential modelimproving model improvingand see also245-248, calculation, 335 effectivemass effective theory, theory, 245-248, calculation, optical cross optical sections of sections various levels, various Green’s function function method, method, see 328-349,345,346 328-349, 1 11 Grinding Grinding of crystal, 1 1,8 also Green’s function function method method molecular molecular orbital orbital approaches, approaches, 309-329, 309-329, see also Molecular Molecular orbital orbital approaches approaches pseudopotential pseudopotential representations, representations, Heat treatment, Heat 44-49, 80, 81, see 81, also see also Pseudopotential Pseudopotential 320-328, 320-328, Thermal Thermal annealing annealing representations representations radiative transitions, transitions, 1, 297-299, 249-25 249-25 297-299, High-pressure LEC High-pressure technology, 6-23, 6-23, 94, 94, see 159-229, also LEC growth LEC 95, 95, 159-229, see also Radiative Radiative transitions transitions

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SIMS, 23-25,48, 100, 126, seealso 126, SIMS also SSMS, 23,26, 100- 102, see also SSMS see also see also Acceptors; Defects; Acceptors; Impurity levels, Impurity Donors; Donors; Impurities, Impurities, Ionized Ionized 20138-44, -206, -206, 0.073-0.078-level, 34, 34, 38-44, 208 208 anti-site defect, anti-site205, 205, 206 206 boron boron complex, 4 1-44 complex, IC devices, 143-143 154, - see see also MESFET also excess Ga, 38, 39 151, 195 195 backgating, 148- 148fabrication, fabrication, 143- 146, - see see also MESFET also boron-defect boron-defect 41 -44 41 complex, complex, 146- 15 - 115 C, 4, 34, 37, 37, 39,47,48, see see also also Carbon Carbon performance, performance, 327, 337327, 340, calculated energies, calculated use of LEC material, 229, material, see 229,see also LECalso 347 - 349, - see 349,also see also Green’s Green’s function func growth Crystalline see Crystalline imperfections; imperfections; Imperfections, see Imperfections, method method 74,75, 80, see 80, ratio, see also compensation compensation ratio, Defects also Acceptors; Composi- Composi- Compensation Compensation Impurities, see Impurities, 80 annealing, 80 effect ofImpurity of annealing, tional purity; tional purity; Donors; levels; Donors; Impurity complexes, 40-44, 241,242, see also see also Ionized Ionized impurities impurities B, 24-28, 101, 102, 192-195,204, see see Complexes Complexes also Boron also seealsoChromium Cr, 4,8,29,30,36-38, Cr, C, 4,24-26,34, C, 100- 100- 102, 102, EL2,29,32, 34,35,44-51,53,98-100, effective segregation coefficient, 39 108, 109, 148, 196,200,208, see see also also Cr, 4, Cr,23-26, 29, 30, 36-38, 36-38, 76, 92, 95, 92, 95, EL2 EL2 level 98-102, 106-109, 106-109, 150, 193, optical optical absorption, 35 absorption, 209-21 209-21 1,221,223,237,242,287, out-diffusion, 49, out-diffusion, 49, 51 1 288, 288, 296,340, see see also also Chromium Chromium 0 , 4 , 2 9 , see also Oxygen also 208 208centers, Si, 4, 4, 23-28, 23-28, 56-60, see see 56-60, also Direct also 81,Direct 81, major major electrically active active centers, 0.073-0.078-eV acceptor, 208, acceptor, see also see also ion ion implantation; implantation; Ion Ion implantat Acceptors Silicon Silicon 208, see 208, see afso carbon carbon acceptor, acceptor, 1 13, 1 141, see also see Tellurium Tellurium Te implant, Te Acceptors; Carbon Carbon also also PITS; PITS; traps, 209-21 traps, 1,236-238, see see 208, see 208, see also Donors; also Donors; Trap EL2 deep deep donor, donor, EL2 level -2 20811 LEC material, 208 material, 0,4,24,25,29, 100- 102, see 102,also see Oxygen also Inclusions Inclusions 1 residual, 36-44, residual,208-21 208-21 As precipitates on precipitates dislocations, 50 dislocations, effective segregation coefficient, donors, donors, Ga, 187 Integrated Integrated 3, circuits, 5, 152- 154, circuits, - see also see also 39 39 S, 24, 25, 81, 24, see 25, also 81, 98, Sulfur 98, Sulfur IC devices Se, 8 1, see also Selenium Selenium 3,4,implantation, 55-81,90-93, Ion Ion implantation, 66-81, 98, 101, Si, 4, 23-28, 56-60, 56-60, 109- 109146,212-226, see see also also Direct Direct ion ion 102, see 102,also also Silicon Silicon implantation; implantation; Electrical properties properties 57, 66-69, 57, 115, profiles of implants, implants, 56 -60, activation efficiency activationof implants, implants, 121, 137, 139, 140 140 69-71,76-78, 123 123 striations, 22, striations, 23 22, effect of annealing, 8, annealing, 123, see also see tabulation, tabulation, 24,25, 101, 102, 193 193 Annealing Annealing Impurity analysis, Impurity 99- 102, 197,208-21 102, 11 65, 80, 65, 8 1,conditions, 1, annealing annealing conditions, AES, 100, see see also AESalso 1 19- 19- 125, 125, 143,221, 135- 135see see also also 132,see also ASES also Thermal Thermal annealing annealing ASES, 23,26, 100, 132, see also also PITS PITS beam beam energy, PITS, 197,209- 2-1 1,1 see see 66 - 7-1,energy, 112 LEC LEC material, 209-21 material, 209-21 1 carrier carrier concentration profiles,concentration 57,66-69, Huang-Rhys Huang-Rhys 282-291,302 factor, factor, Hydrogenic Hydrogenic 247,250 impurity, impurity, photoionization cross photoionization section, 250,25 section,1 1 photoneutralization, 25 photoneutralization, 125 1

Ion implantation implantation Activation Ionization energies, Ionizationsee Activation energy see also Acceptors; also Ionized Ionized impurities, impurities, 18, 121, 122, 127, 128, 132, 113-1 113-1 Donors; Donors; Impurities; Impurities; levels Impurity Impu 137, 139, 140,217-222, seealso seealso concentration, concentration, 36,48,52, 57, 66 specific dopant implanted implanted Si, 52, 52, 57, 66, 68-72, 68-72, 74, 74, Cr implant, 221 implant, 77, see also Silicon also Silicon Seimplant, 115-118, 115-118, 127, 132, 139, 132, seecenters, 208, 208, major major electrically active active centers, also Selenium 140, 2 16, 2 2 17, 2 see also Selenium Si implant, implant, 115, 137, 57, 57, 139, 140, 219, also specific also dopants 0.073-0.078 0.073-0.078 208,acceptor, see also acceptor, 220, see also Silicon implant, implant, 114, 128, 129, see also Sulfur Sulfur Acceptors carbon carbon acceptor, 208, seeacceptor, also 1 13 1 - 123 Si3N, cap, cap, SiO, cap, cap, 115, 120- 122 Acceptors; Carbon Carbon EL2 deep deep donor, 208, see donor, also Donors; also Donors; Te Te implant, implant, 141 113, 113, co-implantation co-implantation EL2 level Isocoric impurity, impurity, 240 240 Se, Ga, 139 Isoelectronic Isoelectronic 239impurity, impurity, Se, Si, 140 Isovalent Isovalent impurity, 239,240 impurity, S, S, Si, 81 differential activation efficiency activationof implant, implant, 58 diffusion broadening, 67 broadening, JFET. 2 12 2 Cr, 6972,76,77 effect of Cr, 69FET fabrication, fabrication, 13-226, -226, see2 also 2 FET also FET Hall mobility, 57-61, 57-61, 71-73, 71-73, 75, 75, I28 -I28 132, - see also Mobility also LEC (liquid-encapsulated (liquid-encapsulated Czochralski) high doses, 134- 143 see growth, 5-23,93-99, growth, 159-229, 159-229, see IC fabrication, fabrication, 146,213-226, 143- 143also Crystal growth growth also MESFET also 109, 161, 211,222-226, advantages, 5, advantages, implant implant conditions, 119conditions, 110- 110229 implanted Si implanted concentration, concentration, 52, 57,66, 2 1211I96 1 I96 characterization of characterization product, product, 68,69, 70-72, 70-72, 74, 77, 112, 115, 121, capacitance capacitance spectroscopy, transient transient 196, 135, 137, 139, 140,219,220 197 implant implant profiles, 57,66-69, see also also Mobility; Hall effect, Hall 196, see also Mobility; specific dopant dopant 113 1 - 1-18, 1concentration, see Electrical properties properties carrier carrier concentration, optical optical absorption, 196, 197,200-202, absorption, also Electrical properties properties donor donor concentration, concentration, see also 66-69, 66-69, see also Optical Optical absorption absorption stud photoluminescence, photoluminescence, 197, see also Donors Donors Photoluminescence Photoluminescence effect of variability, 162 variability, PITS,197, see also PITS also uniformity, uniformity, 133, 13468, 68, resistivity, 196, 199, 208, see also also MESFET MESFET fabrication, see fabrication, Resistivity range of implant, implant, 65-69, 112 see Crystalline Crystalline crystalline crystalline imperfections, imperfections, recoil implantation, implantation, 63 imperfections imperfections selective implantation implantation fabrication fabrication crystal crystal quality,192 quality, 167- 167sequence, 63-65 see Crucible Crucible crucible crucible material, material, sheet resistance depletion voltage, depletion225, 226 Se implant, implant, 138 -applications, see also also device device applications, 12- 226, 22 Si implant, implant, 135 Device fabrication; FET; fabrication; IC devices; 11 Te implant, implant, 14 14 substrate substrate influence, 119, 120, influence, 125 -125 135, diameter diameter control control 216-222 216-222 8, 9, 8, 167 automatic, automatic, temperature effect, temperature 119, 119, 120 120

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impurity impurity 99analysis, 102, see 102, analysis, also also coracle technology, coracle 8 -8 1-I,1 166 Impurity Impurity analysis analysis 8- 10, 166 manual, manual, Dislocations Dislocations dislocation dislocation densities, densities, semi-insulating semi-insulating material, material, ingot i high-pressure technique, 6-23, technique, 94, 95 94, 93-102 IC applications, applications, 159-229, also Device also 159-229, Bridgman, Bridgman, 7,24,29,4,93, 4, 93, 94 94 fabrication; fabrication; devices; FET; FET; IC IC gradient freeze, gradient 4, 4, 24, 29, 29, 93, 93, 94 94 MESFET also also LEC growth LEC LEC, 93-99, impurity impurity striations, striations, 22, 22, 23 LPE, 23 94, 105, also LPE LPE LPE,103-103 low-pressure technique, technique, 95 - 102 MBE, 92,94, 103, 105, see also MBE Melbourn Melbourn 5-8,puller, 94, 94, 163 puller, OMVPE, OMVPE, 103, 105, see also also OMVPE OMVPE also pinch-off voltage, pinch-off 222-225, 222-225, also VPE VPE VPE, 94, 94, 103, 105, Pinch-off voltage -1 see 83, also LEC also Materials processing, Materials 8 8-183, reproducibility of reproducibility product, product, 222-224, 222-224, 227 227 Materials Materials preparation prepar growth; growth; seed rotation, rotation, 20-22, 164 20-22, 52-55, 52-55, 11 grinding grinding of 1of, 8crystal, crystal, 1 1 - I67 - I67 technique technique description, description, 163 163 importance importance of substrate substrate8quality, 1-83 8 quality, 2 121 fluctuations temperature temperature fluctuations in melt, melt, MBEin(molecular beam (molecular epitaxy), epitaxy), 92, 92, 94, 94, thermal thermal gradients in melt, melt, gradients 17, 19-22 103- 103105 traps, traps, 209-21 1,236-238, 209-21seealsoTrap buffer layer layer growth, growth, 103- 103- 105 105 twinning, twinning, 167, 12-14, 182-187, 12-14, 182-187, 192, 55 8,crystal - 94, 94,puller, 163 163 Melbourn Melbourn crystal puller, 194, see also also Twinning Twinning Melt composition, see also Stoichiometry Stoichiometry composition, uniformity uniformity of of product, product, 20-23, 52-55, 52-55, properties, 32-36, 32-36, effect 20-23, on on electrical properties, also also Uniformity Uniformity 41 -44, -44, 196- 196222-221, 222-221, see also also 198,Electrical 198, Liquid-encapsulated Liquid-encapsulated Czochralski properties Czochralski method, method, properties see LEC growth LEC MESFET MESFET (metal (metalfield -semiconductor effect -semicond Liquidus, 44 Liquidus, transistor), 3-6,90-92, transistor), 113, 123, 125, Localized vibrational mode vibrational far-infrared far-infrared 128, 133, 134, 133, 143, seealsoFET LVM LVM spectroscopy, spectroscopy, device fabrication, 63-65, fabrication, 78-81,90-93, - 102, - see Low-pressure LEC technology, 95 technology, 143-146,212-216 also LEC growth Microwave applications, applications, 3 3 LPE (liquid-phase epitaxy), (liquid-phase 94, 103- 103105 see also Deeplevel Mid-gap centers, 233x centers, buffer layer growth, 103- 103105 centers; Flaw centers; Photoluminescence Photoluminescence Luminescence, Luminescence, insulatorinsulator- semiconductor semico MISFET (metal -(metal LVM (localized vibrational vibrational mode mode far-infrafield effectfar-infratransistor), transistor), 12 22 red red spectroscopy), 26, 26, 192 Mobility, Mobility, 51,34, 53-55, 34, 36, 53-55, 57-62, 36, 71-75, 71-75, boron boron determination, 204 determination, 119, 121-123, 121-123, 128-132, 198,seeaho 128-132, carbon carbon determination, 26, 192,determination, 207 Electrical properties properties carrier-concentration carrier-concentration 59 dependence, d 1 1 dependence, 6 6 depth dependence, depth implanted implanted layers, 57, 57, 128 128 drift vs. driftelectron electron concentration, 59 concentration, Mass spectrometry, spectrometry, 26, see also23, 23, SSMS also vs. electron electron concentration, 59,72,73,75 concentration, ASES, 26, 26, also ASES implanted implanted layers, 57-61, 57-61, 71-75 71-75 also SIMS SIMS analysis, 23-25, 23-25, S, 128, 129 128, also also Materials Materials preparation, 93- 109, see preparation, Se, 130, 132 130, Crystal growth; LEC growth; growth; growth; Materials Materials Si, 71 -75 processing melt composition effect, composition 34, 34, 198 105 buffer layer growth, 103- 103radial radial variation, 54, 55 variation, camer concentration, concentration, 104, 105 stoichiometry effects, stoichiometry 34, 198 camer mobility, mobility, 105 104, 104, surface, also Crucible crucible crucible material, material,Crucible surface, 61 - 55, - see considerations, uniformity PBN, 8,28,96, PBN, 192- 192195, see also PBN PBN uniformity considerations, 52 quartz/silica, 8, quartz/silica, 27, 31, 96, 96, 192-195 192-195 also Uniformity Uniformity

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Molecular orbital orbital approaches, 309 - 329 -approaches, 329 photoneutralization, photoneutralization, 287, see also cluster-Bethe-lattice cluster-Bethe-lattice 319, 320 method, method, Photoneutralization Photoneutralization defect molecule method, method, 309 - 3-131 1 1 small small polaron polaron 290 theory, theory, extended Hiickel theory theory cluster clusterPhotocapacitance approach, approach, Photocapacitance 197,258, measurements, measure 311-313 311-313 259 259 Xa-scattered-wave self-consistent Xa-scattered-wave cluster cluster Photoinduced Photoinduced transientsee transient spectroscop method, method, 313-319 313-319 PITS calculated charge charge distribution, 18 distribution, 33 Photoionization, Photoionization, 249-251,283-286,294, 297,298,350-352, see also Camer calculated energy-levelspectra, spectra, 16 33 of 17-atom 17-atom forcluster cluster capture and capture emission emission mechanisms; mechanism 315-318 315-318 Flaw; Phonon-assisted Phonon-assisted optical optical t various charge variousstates of states Cr,,, 3 19 3 tions also Multiphonon Multiphonon transitions, 304, see transitions, 299-section 299cross cross Radiationless Radiationlesstransitions transitions billiard-ball billiard-ball model, 280, model, 28 1 1272-277, 272-2 bridging bridging model, 279-281 model, 279-281 delta-function delta-function potential potential model, 00 255-260,263 OMVPE OMVPE (organometallic (organometallic vapor-phase vapor-phase evanescent wave evanescent approach, approach, 350,351 epitaxy), 103, 105 experimental experimental 255,258-260,263 data, data, Optical Optical absorption 35, absorption 196, 197, studies, 197, studies, 1 1 donor, hydrogenic hydrogenic 250,25 donor, see also Absorption Absorption 200-202, 200-202, quantum-defect quantum-defect 262-264,280, model, model, coefficient;Radiative Radiative transitions transitions28 1 1 0.073-0.078-eV 0.073-0.078-eV 38,201acceptor, -203 -203acceptor, related to related critical criticalinpoints density points density of of EL2 level, 35, 200, 201 200, states, 350 states, Oxygen, 4,24,25,29, 100- 102, 195,211 350, states, 35 350, II evanescent evanescentof,states, Cr - O- O doping, doping, 29 29 free energy of ionization, ionization, 296 Ga20, 28 28 information information available,267 available, limitation, l Ga20,, 28 phonon phonon coupling effects, 285,286, couplingsee also getter, getter, 196 Phonon-assisted Phonon-assisted optical optical trans in semi-insulating semi-insulating I95 material, material, phonon phonon emission and absorption absorption - 293, - see also considerations, considerations, 282also 282 Phonon-assisted Phonon-assisted optical optical trans photocapacitance photocapacitance 197,258, measurements, measu 259 PBN (pyrolytic boron boron nitride) nitride) 8, crucible, crucible, II superlattice superlattice 35approach, approach, 28,49,96, 163, 164, 192- 192195,211 Photoluminescence, Photoluminescence, 39,48, 197, 197,38, 38, Phase Phase diagram, 44 diagram, -1203 20 120 Phonon-assisted optical optical transitions, transitions, 0.073-0.078-eV 0.073-0.078-eV 38, 39,acceptor, 39, acceptor, see also Photoionization; Photoionization; 282 -293, -293, 201 -203 1, 202 1, 202 transitions EL2 level, EL2 20transitions Radiationless Radiationless(multiphonon) (multiphonon) spectra,diagram, 38, spectra, 39, 48, 201, 202 201, configurational configurational coordinate 283, coordinate diagram, Photoneutralization, Photoneutralization, 1,287,288,352 249-25 249-25 290, see also Configurational Configurational 25 1, 287 section, 287 coordinate coordinate diagram diagram cross cross section, experimental 287 data, data, electron-phonon electron-phonon coupling, coupling, 282-287 experimental 282-287 11 hydrogenic acceptor, Franck- Franck- Condon Condon shift, shift, 283 283 -285, hydrogenic -285, 25acceptor, phonon coupling effects, coupling 287 287-293,296, see also Franckthreshold, 288 threshold, Condon Condon shift shift 65, 218, Huang-Rhys Huang-Rhys 282-291,302 factor, factor, Pinch-off voltage, 65, 79,213,217, 222-225 222-225 Stokes shift, 283,284 PITS (photoinduced (photoinduced spectroscopy), transient transient see also283-286, 283-286, photoionization, photoionization, 197,209-21 1 1 Photoionization Photoionization

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stoichiometry effects, stoichiometry 196, see also traps observed traps in LEC GaAs, 208 - 2-I2I1 1 Stoichiometry Stoichiometry Precipitates Precipitates uniformity, uniformity, 52-55, 52-55, 133, see also As, 190 As (dislocation (dislocation decoration), 50 decoration),Uniformity Uniformity Ga inclusions, inclusions, 187 Pseudopotential Pseudopotential320representations, 328 representations, calculated calculated energies, electronV,electron and V,, defects, 326 Charge Charge carrier carrier scattering scatt Scattering, see Scattering, Schottky Schottky46barrier, barrier, Selenium, 8Selenium, 181 diffusion coefficient, 125 Quantum-defect Quantum-defect 260-264, model, 260-264, 280, 281 model, implant, implant, 81, 81, 115-119, 122-125, 122-125, 127, applicability, 25 applicability, I, 252, 280 130, 132,135,135,139,140,216,217 132,135,135,139 photoionization photoionization section, 262,263, section, cross with Ga, 139 280,28 1 1 with Si, 140 Semi-insulating Semi-insulating 3, 4, 4, 8, material, 298, 3 1,3 material, 34-36,90-103, 195-211,seealsoEL2 R R level; Impurity Impurity levels; LEC growth; Radiationless Radiationless (multiphonon) (multiphonon) transitions, transitions, Substrates Substrates 299-304, 299-304, 307, see also see Carrier Carrier capturecontrol capturecontrol of of metal metal 32 -composition, 36 compositio and emission mechanisms; mechanisms; PhononPhononcrucible/encapsulant effects, crucible/encapsulant 30- 3032, see see assisted optical optical transistions transistions also Crystal growth; Crystal Encapsulation Encapsulation capture cross capture section, 300,302, section, 307, see see energy diagram of diagram shallow levels and deep deep also Capture coefficient Capture 99 traps, traps, 283, coordinate configurational configurational coordinate diagram, diagram, residual impurities, impurities, 36-45, 36-45, alsosee see - see also see Configurational Configurational 301 - 303, Impurities Impurities coordinate coordinate diagram diagram Silicon, 4, Silicon, 22-28, 22-28, 56-60, 66-81,56-60, 98, 98, 101, phonon phonon cascade, 299, 300 102, 192- 192195, see also see Donors; Donors; two-stage capture process, capture 300 - 302 Electrical properties; properties; Impurities; Impurities; Radiative Radiative transitions, 249 -25 -25 1, 297-299, transitions, 297-299, rity levels; Ion Ion implantation implantation coefficient;Camer see also see Capture Capture 57-59,73-81 amphoteric amphoteric behavior, behavior, capture capture and emission emission mechanisms; mechanisms; diffusion coefficient, 125 tical tical absorption absorption studies; studies; PhotoionizaPhotoionizaeffect of [OH] in [OH] B,O, encapsulant, encapsulant, 26, tion; tion; Photoluminescence; Photoluminescence; Encapsulation Encapsulation 27,Photoneutra194, see also seePhotoneutra1iz1iaz at t i io on n 52, 56-81, 56-81, 112, 115, 121, implantation, implantation, see see capture capture coefficient, 279 -299, -299,also 135, 137, 139, 140,219, 220, seealso Capture coefficient Capture Direct Direct ion ion implantation implantation photoionization, 249 photoionization, -25 1, see also see 115, 137, profiles, 52, 57,66-69, 115, 121, Photoionization Photoionization 139, 140,219,220 photoneutralization, photoneutralization, 249,25 I, see also see co-implantation with co-implantation S, 8 181 Photoneutralization Photoneutralization co-implantation with co-implantation Se, 140 Recombination Recombination 236-239,center, 236-239, also center, see see Silicon nitride, nitride, 62-65, 62-65, 75, 113-123, 113-123, 133, Auger recombination recombination 135-140, 135-140, 165, 166 33, 34, 43, 52, 196, 199, Resistivity, 29-31, 29-31, coracle coracle application, 10, 166 application, 208, see also see Electrical Electrical properties properties refractive index, 62,63 index, implanted implanted layers, sheet resistance, 133, SIMS (secondary (secondary mass spectroscopy), ion ion spectroscopy), 142 135, 138, 141, 141, 23-25,48, 100, 126, 192,204,221 melt melt composition effects, composition 32-36 32-36 24-28,48,204 boron boron determination, determination, semi-insulating semi-insulating 30 material, material, chromium determination, determination, 22 122 1 sheet resistance, 53-56, 53-56, 133- 135, 138, iron iron determination, 48 determination, 141, 142 141, manganese manganese determination, 48 determination,

374

Square-well potential potential 267-27 model,267-27 I Imodel, microdefect studies, studies, 187 bridging version, 27 I , 278 -28 2781 BF (bright-field) micrographs, micrographs, 187- I89 photoionization cross photoionization section, 279 section, -28 1 black-and-white black-and-white contrast contrast micros SSMS (spark source mass source spectroscopy), 23, 190 190 26, 26, 100- 102 - 190 dislocations, 187 dislocations, Stoichiometry Stoichiometry precipitates, 190 precipitates, 190 As-rich melts, 32-34, 44, 45, 50, 79, 108, Thermal Thermal annealing, 4,29,45-49,54, annealing, 65, 65, 192, 199,202 80, 81, 113-125, 113-125, 221,seealso As vaporization, As 33 vaporization, 33 Annealing Annealing effect on 0.073-0.078-eV acceptor, 34, acceptor, effect on effect deep on levels, deep 29,45 38-42,203-205,211,227, 228 228 45 -47 -47 DLTS measurements, 45 measurements, effect on on dislocations, 170,dislocations, 174, 182 182 implanted implanted layers, 65, 80, 81, 119- 119125, effect on on EL2 concentration, concentration, 29, 32, 35, 135-143,221,222 EL2 plasma plasma nitride nitride encapsulation, 62 - 65, - 65, encapsula 44,49, 196,227, see also EL2 level 75, 75, 113-123, 133, 113-123, 135-140 effect on resistivity and mobility, 33 - 36, 41 -44, -44, 196- 196SiOz encapsulated, encapsulated, 115, 138, 139 effect on thermal thermal stability, 5 51, see also stability, unencapsulated, 75 unencapsulated, Thermal Thermal stability stability thermal thermal conversion, 4,46 - 49, -conversion, 5 1, 5 109, 109, effect on on twinning, 184-186, twinning, 184-186, 192 192 22 1,222 Ga-rich melts, Ga-rich 32-34, 38-44, 38-44, 108, 199, Thermal Thermal conversion, 4, 46 - 49, - conversion, 5 1, 5 109, 109, 221,222 202,227 key to to reproducibility in growth, reproducibility 227, growth, 228 Thermal Thermal 44-52, stability,106stability, 109, 142 142 melt composition composition determination, determination, implanted implanted layers, 142 142 weight-in/weight-out technique, 33 technique, 33 influence of influence stoichiometry, 5stoichiometry, I5I Stokes Stokes 283, shift, 284shift, 284 Trap, 209-21 Trap, 209-21 1,236-238 Substrates, 3Substrates, - 5,-see also Semi-insulating Semi-insulating detected by detected PITS, 208 -2 2081 1 material material energy level diagram, 99 diagram, 99 107, 108 self-trapping, 303, self-trapping, 303, 304 304 carrier carrier concentration profiles,concentration importance of importance quality, 8quality, 1-83, 162, Twinning, Twinning, 12-14, 167, 167, 182-187, 192,182-187, 194 2 16-222 16-222 impeding impeding large-diameter 12large-diameter growth impurities, 4, impurities, see also Impurities; Impurities; importance importance of moisture moistureencapsuin in encapsuSemi-insulating Semi-insulatingmaterial material 13,27, 194, see 194,also Encapsula- Encapsulalant, lant, tion tion influence on implanted implanted layer, 119, 120, 184- stoichiometry, 184186, 192 melt melt stoichiometry, 125-135,216-222 temperature effect, temperature I I19, 120 material material requirements, 3,4, 8 1, 8 83 1, requirements, UU qualification qualification 55procedure, procedure, thermal thermal stability, 44-52, 106stability, 106- 109 109 Uniformity, 20-23, Uniformity, 52-55, 68, 68, 132- 132- 134, 134, Sulfur, 24, Sulfur, 25, 81, 98, 81, 114,98, 119, 128, 129 128, 222-227 222-227 co-implantation with co-implantation Si, Si, 8 181 horizontal horizontal Bridgman vs. LEC substrates, substrates, diffusion coefficient, 125 222-226 222-226 implant,81, 114, 114, 119, 128, 129 see implant implant profiles, 68, 133, 134, see also Direct Direct ion implantation; ion implantation; Ion implantation implantation T T impurity impurity striations, 20 -20 23 - striations, pull-speed effects, 52- 5 5 Tellurium, 98, Tellurium, 98, 106, 113, 125, 141 with chromium, 106 radial radial variations, 52-55 52-55 variations, electrical properties, 52 properties, - 54- 54 diffusion coefficient, 125 round substrates, 5, substrates, 11 implant, implant, 113, 141 seed rotation rotation effects, 52-55 TEM TEM (transmission (transmission microscopy), electron electron

375 VV

of

94, 94, 103, 103, 105 103, 103, 105 73 103, 105

8 1-183 -

8 181 82

Contents Contents of Previous Previous Volumes Volume 1 1 Physics of 111-V C. Hilsum, Some Key Features Features of 111-V Compounds Compounds

Franco Bassani, Methods of Methods Band Calculations Applicable Calculations to 111-V Compounds Compounds E. 0. Kane, The The k . p.pMethod V. L. Bonch-Bruevich. Effect of Effect Heavy Heavy Doping the Semiconductor Band Semiconductor Structure Donald DonaldEnergy Band Structures Structures of Mixed Crystals Crystals of 111-V Compounds Compounds Laura Laura M. Roth and Petros Petros N. Argyres, Magnetic Quantum Quantum Effects Effects Geballe, Thermomagnetic Thermomagnetic in the the Effects Quantum Region Effects Quantum S.M. Puri Puri andH.and W . M . Becker, Band Characteristics Characteristics Principal Minima near near from Magnetoresistance Magnetoresistance E. H. Putley, Freeze-Out Freeze-Out Effects, Effects, Hot and Hot Submillimeter Electron Electron Submillimeter Effects, Effects, Photoconduc. tivity tivity in H. Weiss. Magnetoresistance Magnetoresistance Betsy Ancker-Johnson, Plasmas in Semiconductors and Semiconductors Semimetals Semimetals

Volume 2 2 Physics of 111-V

M. C. Holland, Thermal Thermal Conductivity Conductivity S. S. 1. Novkova. 1. Thermal Thermal Expansion Expansion U.Piesbergen, Heat Heat Capacity and Debye Capacity Temperatures Temperatures C. Giesecke, Lattice Lattice Constants Constants 1.R. Drabble. Drabble. Elastic Elastic Properties Properties A . U.Mac Rae and G. W . Gobeli, Energy Electron Electron Diffraction Diffraction Studies Studies Robert Lee Lee Mieher, Nuclear Nuclear Magnetic Resonance Resonance Bernard Bernard Goldstein, Electron Electron Paramagnetic Paramagnetic Resonance Resonance 7. S. S. Moss. Photoconduction in Photoconduction 111-V Compounds Compounds E. Antontik and andTauc, Quantum Efficiency Quantum o f the the Internal Internal Photoelectric in InSb Photoelectric Effe G. W . Gobeli and and F. C. Allen. Photoelectric Photoelectric andThreshold Work Function Work Threshold Function P . S.Pershan, Nonlinear Nonlinear in 111-V OpticsCompounds Optics Compounds M. Gershenzon, Radiative Radiative Recombination in the the 111-V Recombination Compounds Compounds Frank Frank Stern. Stimulated Emission Stimulatedin in Semiconductors Semiconductors

Volume 3 3 Optical of Properties 111-V

Marvin MarvinLattice Lattice Reflection William William G. Spitzer, Multiphonon Lattice Lattice Absorption Absorption D. L. Stienvalt and and R. F. Potter. Potter. Emittance Emittance Studies Studies H. R. Philipp Philipp H. and Ehrenreich. and Ehrenreich. Ultraviolet Ultraviolet Optical Optical Properties Properties Manuel Cardona, Optical Optical Absorption Absorption above Edge above the the Fundamental Fundamental Earnest Earnest 1. Absorption near near the Fundamental Fundamental Edge 0.Dimmock, Introduction Introduction the the Theory of Exciton Theory Exciton States in Semiconductors Semiconductors Lax and and J . G. Mavroides, Interband Interband Magnetooptical Magnetooptical Effects Effects

376

377

H. Y. Effects of Effects Free Free Carriers Carriers on on Optical Optical Properties Properties Edward Edward D. Palik and and George B. Wright, George Free-Carrier Free-Carrier Magnetooptical Magnetooptical Effec Richard Richard H. Bube. Photoelectronic Photoelectronic Analysis Analysis B. 0. Seraphin and and H. E. Bennett, Optical Optical Constants Constants

Volume 4 4 Physics of 111-V

N . A. Goryunovu, A. S. Borschevskii, and and D. N . Treriakov, Treriakov, Hardness Hardness N . N . Sirota, Heats of Formation Formation and Temperatures Temperatures and Heats of of Fusion Fusion of of Compounds C AmBV AmBV Don Don L. Kendall, Diffusion A. G.Chynoweth, Charge Charge Multiplication Phenomena Phenomena Robert Robert W. Keyes, The The Effects of Hydrostatic Effects Hydrostatic Pressure Roperties Pressure of 111-V on onSemiconthe the Semiconductors L. W. Aukermun, Radiation Radiation Effects Effects N . A. F. P. Kesamunly. and and D. N. Nasledov, Phenomena in Phenomena Solid Solutions Solutions R. T. Bate, Electrical Electrical Properties of Nonuniform Properties Nonuniform Crystals Crystals

Volume 5 5 Infrared Detectors

Henry Henry Levinstein, Characterization of Characterization Infrared Infrared Detectors Detectors Paul W. Kruse, Indium Antimonide Indium Photoconductive Photoconductive and and Photoelectromagnetic Pho M. B. Prince, Narrowband Narrowband Self-Filtering Self-Filtering Detectors Detectors Ivars Ivars MelngailisT. Melngailis C. Hurmun. and Single-Crystal and Single-Crystal Lead-Tin Lead-Tin Chalcogenides Ch Donald Donaldand and Joseph L. Schmir, Mercury-Cadmium Mercury-Cadmium and Closely Telluride CloselyTelluride Related Relate Alloys E. H.Pulley. The The Pyroelectric Pyroelectric Detector Detector Norman B. Stevens, Radiation Radiation Thermopiles Thermopiles R. J . Keyes and and T. M.Quisr, Quisr, Low Level Level Coherent and Incoherent CoherentIncoherentinDetection the the Infrared Detection Infrared M. C. Teich, Coherent Coherent Detection in the Infrared Detection Infrared F. R. Arams, E. W. Surd, B. J . Peyton, and and F.P. Pace, Infrared Infrared Heterodyne Heterodyne with Detectio Gigahertz IF Gigahertz Response Response H. S.Sommers, Jr., Microwave-Based Photoconductive Photoconductive Detector Detector Robert Robert Sehr and and Rainer Zuleeg, Rainer Imaging and and Display

Volume 6 6 Murruy Murruy A. Lampert and and Ronald B. Schilling, Ronald Current Current Injection in Solids:Injection The Solids: Regional Approximation Method proximation Richard Richard Williums, Injection Injection by Internal Internal Photoemission Photoemission Allen M. Burnett, Current Filament Formation Formation R. Baron Baron J. and W . Muyer, and Double Injection Injection in Semiconductors Semiconductors W. Ruppel, The Photoconductor-Metal Photoconductor-Metal Contact Contact

Volume 7 7

Part A

John A. Copeland Copeland Stephen andKnight, and Applications Utilizing Applications Bulk Negative Negative Resistance Resista F. A. Pudovuni, The Voltage-Current Voltage-CurrentofCharacteristics Metal-Semiconductor Characteristics Metal-Semiconductor Contacts P. L. Hower, W . W. Hooper, B. R. Cuirns, R. D. Fairman, and andA. D.Tremere, D. The GaAs GaAs Field-Effect Field-Effect Transistor Transistor

378

CONTENTS CONTENTS OF PREVIOUS VOLUMES

Marvin H. White. MOS Transistors Transistors G.R.G. Anfell. Gallium Arsenide Transistors Transistors T.L. Tansley, Heterojunction Heterojunction Properties Properties

Volume 7 7

BB

and

T. Misawa, IMPA'IT IMPA'IT Diodes H . C. Tunnel Tunnel Diodes Robert Campbell and Hung-Chi Chang, Silicon Silicon Carbide Carbide Junction Junction Devices De R. E. Ensrrom. H . Kressel, and Krassner, High-Temperature High-Temperature ofPower Power R GaAs,-,P,

Volume 8 8Transport and and Richard Srirn. Srirn. Band Structure Structure and and Galvanomagnetic in 111-V Galvanomagnetic Compounds Compounds with Effects Effects Indirect Indirect Band Gaps Gaps Rofand W . Ure, Thermoelectric Thermoelectric in 111-VEffects Compounds EffectsCompounds Herbert Piller. Piller. Faraday Faraday Rotation Rotation H . Barry Barry Bebb and E. W . Williams, Photoluminescence IPhotoluminescence : Theory Theory E. W . Williams and H . Barry Barry Bebb. Photoluminescence Photoluminescence Gallium Arsenide Arsenide

Volume 9 9

B. 0.Seraphin, Electroreflectance Electroreflectance R. L.R. Aggonoal, Modulated Interband Interband Magnetooptics Magnetooptics Daniel Daniel F. Blossey and Paul Handler, Electroabsorption Electroabsorption Bruno Bruno Batz. Thermal Thermal and Wavelength Modulation Spectroscopy Spectroscopy Ivor Balslev. Piezooptical Piezooptical Effects Effects D. E. Aspnes and and N. Electric-Field Electric-Field Effects Effects on onofthe Semiconthe Dielectric SemiconDielectr ductors ductors and lnsulators lnsulators

Volume 10 Transport R. Rode, Low-Field Electron Electron Transport J. D. Wiley, Mobility of Holes in 111-V Compounds Compounds C. M. Wove and G. E. Stillman, Apparent Apparent Mobility Enhancement in Enhancement Inhomogeneous CWSInhomogeneous tals tals Peterson, The Magnetophonon Magnetophonon Effect Effect

Volume 11 11Solar Cells

Hovel, Introduction; Introduction; Camer Collection, Collection, Spectral and Spectral Photocument; Response,Photocument; Response, Cell Electrical Electrical Characteristics; Characteristics; Other Efficiency; Solar Cell Solar Efficiency; Devices; Thickness; Devices; Th Radiation Effects; Effects; Temperature TemperatureCell andTechnology and Intensity; Technology Intensity; Solar Solar

Harold

Volume 12 Infrared

(11)

D. Merriam, and R . F. Potter, Operational Operational Characteristics of Infrared Infrared Characteristic Photodetectors Photodetectors Perer Perer R. Bran. R. Impurity Germanium Impurity and Silicon Infrared Infrared Detectors Detectors

W.L. Eiseman,

VOLUMES

379 379

E. H. Putley, InSb InSb Submillimeter Submillimeter Photoconductive Photoconductive Detectors Detect G. G. E. Stillman, C. M. and and J . 0.Dimmock, Far-Infrared Far-Infrared Photoconductivity in High Photocond Purity Purity GaAs GaAs G. G. E. E. Stillman and and C. M. Avalanche Avalanche Photodiodes Photodiodes P. L. Richards, The Josephson JosephsonasJunction a a Detector Junction ofDetector Microwave and Microwave Far-Infrared Far-Infrared Radiation diation E. H. Putley, The The Pyroelectric Detector-An Pyroelectric Update Update

Volume 13 13 Kenneth

Materials Materials Preparation; Preparation; Physics; Physics; Defects; Defects; Applica

Volume 14 Lasers, N . Holonyak, Jr. and M. H. Lee, Photopumped 111-V Photopumped Semiconductor Semiconductor Lasers Lasers Henry Henry Kressel Jerome KresselK.and Butler, and Heterojunction Heterojunction Laser Diodes A. Van der der Ziel. Space-Charge-Limited Solid-state Space-Charge-Limited Diodes Peter Peter J. Price, Price, Monte Carlo Carlo Calculation of Electron Calculation Electron Transport in SolidsTransport Solids

Volume 15 L. Sharma, Ohmic Contacts Contacts to 111-V Compound Semiconductors Semiconductors Allen Allen Nussbaum, The Theory Theory of Semiconducting Semiconducting Junctions Junctions S. S. Escher, NEA Semiconductor Semiconductor Photoemitters Photoemitters

Volume 16

Kressel, The The Effect Effect of of Crystal on Optoelectronic Crystal Defects Optoelectronic Defects Devices Devices C. R. Whitsett, J . G. Broerman, and and C. J . Summers, Crystal Crystal Growth Growth of and and Properti

Hg,-=Cd,Se Alloys

M. H. Weiler, H. Magnetooptical Magnetooptical of Hg,-,Cd,Te Properties Alloys Properties Paul Paul W. Kruse Kruse John and G. andReady, Nonlinear Nonlinear Optical in Hg,-,Cd,Te Optical Effects Effects

Volume 18

Paul Paul W. Kruse, The The Emergence of (Hg,-,Cd,)Te Emergence as a a Modem Modem Infrared Infrared Sensitive Sensi H. E. Hirsch, S. S. C. Liang, andA. G. White, G. Preparation of Preparation High-Purity High-Purity Cadmium, Cadmium, M and and Tellurium W.F. H.Micklethwaite, The Crystal Crystal Growth of Cadmium Growth Mercury Mercury Telluride Telluride Paul Paul E. Petersen, Auger Recombination Recombination in in Mercury Mercury Cadmium Cadmium Tellu R. M. Broudy Broudy V. J. andMazurczyck, and (HgCd)Te (HgCd)Te Photoconductive Photoconductive Detectors D M.B. B. A . K. Sood, and T.J . Tredwell, Tredwell, Photovoltaic Photovoltaic Infrared Infrared Detectors Detec M.A. Kinch, Metal-Insulator-Semiconductor Metal-Insulator-Semiconductor Infrared Infrared Detectors

Volume 19 G.

Neumark and and K. Kosai, Kosai, Deep Levels Deep in Wide Band-Gap 111-V Band-Gap Semiconductors Semiconductors David C. Look, The Electrical and Photoelectronic Properties Photoelectronic of Semi-InsulatingGaAs Semi-Insulating R. Brebrick, Brebrick, Ching-Hua and Ching-Hua and Pok-Kai Liao, Pok-Kai Associated Solution Solution Model for for Ga-In-Sb and Hg-Cd-Te Yu. Ya. Gurevich and and Yu. Pleskov, Photoelectrochemistry Pleskov, of Photoelectrochemistry Semiconductors Semiconductors


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

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

Semiconductors and Semimetals: Deep Levels, GaAs, Alloys, Photochemistry

Semiconductors and Semimetals Volume 72 Silicon Epitaxy (Semiconductors and Semimetals)

Semiconductors and Semimetals Volume 72 Silicon Epitaxy (Semiconductors and Semimetals)

Semiconductors and Semimetals: Defects, HgCd, Se, HgCdO and Te (Semiconductors and Semimetals, Vol. 16)

SEMICONDUCTORS & SEMIMETALS V38, Volume 38 (Semiconductors and Semimetals)

SEMICONDUCTORS & SEMIMETALS

SEMICONDUCTORS & SEMIMETALS

Semiconductors and Semimetals v. 4

Semiconductors and Semimetals Infrared Detectors

SEMICONDUCTORS & SEMIMETALS

SEMICONDUCTORS & SEMIMETALS

Semiconductors and Semimetals, Volume 67: Ultrafast Physical Processes in Semiconductors (Semiconductors and Semimetals)

Semiconductors and Semimetals. Volume 25: Diluted Magnetic Semiconductors (Semiconductors and Semimetals)

Semiconductors and Semimetals, Volume 67: Ultrafast Physical Processes in Semiconductors (Semiconductors and Semimetals)

Semiconductors and Semimetals, Vol. 12: Infrared Detectors II (v. 12)

Semiconductors and semimetals: Indentification of defects in semiconductors

The Spectroscopy of Semiconductors: Volume 36 (Semiconductors and Semimetals)

Semiconductors and Semimetals, Volume 71: Recent Trends in Thermoelectric Materials Research: Part Three (Semiconductors and Semimetals)

Semiconductors and Semimetals: Transport Phenomena v. 10

Conducting Organic Materials and Devices, Volume 81 (Semiconductors and Semimetals) (Semiconductors and Semimetals)

Semiconductors and Semimetals, Volume 21, Part A: Hydrogenated Amorphous Silicon : Preparation and Structure (Semiconductors and Semimetals)

Semiconductors and Semimetals, Volume 51A Identification of Defects in Semiconductors

Hydrogen in Semiconductors II, Volume 61 (Semiconductors and Semimetals)

Nanostructured Systems, Volume 35 (Semiconductors and Semimetals)

Semiconductors and Semimetals, Volume 14 Cadmium Telluride

Semiconductors and Semimetals, Volume 60 Self-Assembled InGaAs GaAs Quantum Dots

Semiconductors and Semimetals, Volume 59 Nonlinear Optics in Semiconductors II

Semiconductors and Semimetals, Vol. 17: C W Beam Processing of Silicon and Other Semiconductors

Semiconductors and Semimetals. Volume 27: Highly Conducting Quasi-One-Dimensional Organic Crystals (Semiconductors and Semimetals)

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