Semiconductor Alloys: Physics and Materials Engineering

357 Pages·1996·31.73 MB·English

by  An-Ban Chen

Semiconductor Alloys
Physics and Materials Engineering
MICRODEVICES
Physics and FabricationTechnologies
SeriesEditors: IvorBrodieandArden Sher
SRIInternational
MenloPark. California
COMPOUNDAND JOSEPHSONHIGH-SPEEDDEVICES
Edited byTakahikoMisugiandAkihiro Shibatomi
ELECTRONAND IONOPTICS
Miklos Szilagyi
ELECTRONBEAMTESTINGTECHNOLOGY
Edited byJohn T. L. Thong
GaAsDEVICES ANDCIRCUITS
Michael Shur
ORIENTEDCRYSTALLIZATIONONAMORPHOUS SUBSTRATES
E. I. Givargizov
PHYSICS OF HIGH-SPEEDTRANSISTORS
Juras PoFela
THE PHYSICS OF MICRO/NANO-FABRICATION
IvorBrodie and Julius J. Muray
PHYSICS OF SUBMICRONDEVICES
DavidK. Ferryand Robert O. Grondin
THE PHYSICS OF SUBMICRONLITHOGRAPHY
Kamil AValiev
SEMICONDUCTORALLOYS
Physicsand Materials Engineering
An-BanChenandArdenSher
SEMICONDUCTORLITHOGRAPHY
Principles, Practices, and Materials
Wayne M. Moreau
SEMICONDUCTORPHYSICALELECTRONICS
Sheng S. Li
AContinuationOrderPlanisavailableforthisseries.Acontinuationorderwillbringdeliveryofeachnewvolumeimmediately
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Semiconductor Alloys
Physics and Materials Engineering
An-Ban Chen
Auburn University
Auburn. Alabama
Arden Sher
SRIInternational
Menlo Park, California
Plenum Press • New York and London
LlbrBry of Congress CBtBloging-ln-PubllcBtlon OBIB
ChBn, An-BBn.
SeBleonduetor Blloys physics and Baterlals engIneering I An-Ban
Chen. Arden Sher.
p. CB. -- lHlcredevlces)
ISBN978--1-46U·7994·2
1. Seelconducters--Huerlals. 2. Alleys. 3. Free electron theory
of uUls. I. Sher, Arden. II. Title. lIt. SerIes.
OC611.B.A40C4B 1995
537.6'22--<le20 95-41549
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Front cover: Lattice arrangement ofGaO.51nO.5As. This is therelaxed atom arrangement
in acation·substituted disordered alloy, GaO.5Ino.sAs. The cations are located neartheir
face-centered cubicsublattice sites, butthe anionsassume relaxed positions delennined
by theirnearest-neighborcation site occupancy. Other bond length mismatchedalloys
have similar arrangements.
ISBN 978-1-4613-7994-2 e-ISBN-13:978-1-4613-0317-6
001: 10.1007/978-1-4613-0317-6
01995 Plenum Press.NewYork
Softcoverreprintofthehardcover1sledition1995
ADivisionofPlenum PublishingCorporation
233SpringStreet,New York,N.Y. 10013
Allrightsreserved
1098765432 I
Nopartofthisbookmaybereproduced,storedinaretrieval system,ortransmittedinanyformorbyany
means,electronic,mechanical,photocopying,microfilming,recording,orotherwise,withoutwritten
permission from lhePublisher
To ourwivesMayurase Chen andLoisSher
Preface
Semiconductor alloys, with tailorability of their electronic structures and other material
properties, have found wide applications in optic and electronicdevices. Literatureon the
fundamental properties ofthese materials isgrowing rapidly. MllP.Y majordiscoveries and
advances have been made in the past decade. However, owing to difficulties in treating
disorder in these materials, it probably will take another decade for semiconductor alloy
theory to reach the same level ofmaturity as that for current crystalline semiconductors.
Against this background, there is a need for a book which provides simple, yet practical,
theorieslinkingthepropertiesofsemiconductoralloystotheirconstituentcompounds.The
mainpurposeofthis bookis toprovidesuch alinkage.Often,even now, itispossibletodo
thisatalevelofaccuracycapableofservingasengineeringdesign tools.
The topics treated in this book include crystal structures, bonding, elastic properties,
phase diagrams, band structures, and transport. We begin with the constituent compounds
andgraduallypasstoalloys.Afairfractionofthesubjectmatterselectedreflectsourprevious
work, butabroaderview isadopted wheneverpossible.Ab initiotheories arediscussed to
provideanappreciationofthestatusofcurrenttheory. However,semiempiricaltheoriesare
emphasized. Theidea is to assemble thought-provoking models and simplecomputational
tools thatstillcorrelatewithexperiments. Extensivetables and figures areprovidedsothat
thebookcan serveas auseful referencefor workers in the field. Thisisparticularlytruein
Chapter 7, where detailed quantitative band structures of all common III-V and II-VI
compounds and alloys are compiled. At the end ofeach chapter, we comment on future
developments. Problemsetsarealso includedsothatthebookcan beused as atext.
Readers withabackgroundinintroductorysolid-statephysicsandquantummechanics
shouldbeabletounderstandthemajorityofthematerial,althoughsometreatmentsrequire
aknowledgeofthesetopicsat thegraduatelevel.
ACKNOWLEDGMENTS
Many resufts discussed in this book originated from collaborativeresearch with Srini
Krishnarnurthy, Mark van Schilfgaarde, Marcy Berding, Chin-Yu Yeh, and Tony Paxton.
WaltHarrisonandTomCasselmanprovidedvaluableinsightsforimprovingthecontentand
presentation ofmany sections ofthe book. We are deeply in debt to Joyce Garbut, Robin
Burns,andJulieKirkpatrick,withoutwhoseskilledandpatientworkonthemanuscriptthis
book would never have materialized. Some financial aid to An-Ban Chen for manuscript
preparationwassuppliedbyONR.WealsoacknowledgeAFOSR,ONR,ARPA,andNASA
vii
viii PREFACE
forhelpingsupportaspectsoftreatmentspresentedherethat,inseveralinstances,werenever
previouslypublished.Finally,butnotleast, wethankourwivesfortheircontinuoussupport
and understanding.
An-BanChen
Arden Sher
Contents
CHAPTER1. CrystalStructures
1.1. Diamond,ZincBlende,andWurtziteStructures 1
1.2. BulkAlloys 4
1.3. Alloy StructureDeterminedby EXAFS. . . 5
104. Long-RangeOrdered SemiconductorAlloys 10
1.4.1. ABC2Structures 15
1.4.2. BondLengths 18
1.5. ConcludingRemarks 18
References . . . . . . 19
CHAPTER2. BondinginOrdered Structures
2.1. CohesiveEnergyintheBom-QppenheimerAdiabaticApproximation . 21
2.2. DensityFunctionalTheory . 22
2.3. BondsandBands from Local DensityFunctional Theory . 23
204. Tight-BindingApproach. . 27
2.5. TheBond-OrbitalModel ..... . 29
2.6. Polarityand Ionicity . . . . . . . . . 34
2.7. ExcessEnergiesofOrderedAlloys 35
2.8. ConcludingRemarks 38
References . . . . . . . . . . . . . 39
CHAPTER3. Elasticity
3.1. DefinitionsandAnalysis. . 41
3.2. AbInitioCalculations . . . 44
3.3. Valence-Foree-FieldModel . 46
3.3.1. DiamondStructure . . 46
3.3.2. ZincBlendeStructureand CoulombForce . 47
304. "Exact"Tight-BindingCalculation . . . . . . . . . 49
3.5. Analytical Expressions in theBond-Orbital Model. . 50
3.6. QuantitativeTight-BindingModel ... . 54
3.6.1. Full-Band-StructureCalculation. . . . . . . . 55
ix
x CONTENTS
3.6.2. QuantitativeExtendedBond-Orbital Model 56
3.7. ElasticityinAlloys ... 57
3.7.1. OrderedAlloys . 58
3.7.2. DisorderedAlloys 60
3.8. ConcludingRemarks 63
References . 65
CHAPTER4. AlloyStatisticsand PhaseDiagrams
4.1. MixingFreeEnergy,MiscibilityGap,andOrder-DisorderTransitions 67
4.2. AnalyticalModels . . . . . . 70
4.2.1. Ideal-SolutionModel 71
4.2.2. ZerothApproximation . . . . . . . . . . . . . . . . . . . . 71
4.2.3. FirstApproximation-TheQuasi-Chemical!-pproximation 72
4.3. PhaseDiagram: CommonTangentLineand ActivityCoefficient 75
4.4. Vie1and's Methodand BinaryLiquidus. . . . . . . . . . . 78
4.5. TernaryPhaseDiagrams. . . . . . . . . . . . . . . . . . . 81
4.6. PhaseDiagramDataandSimpleMixingEnthalpyModels. 87
4.7. GeneralizedQuasi-ChemicalTheory 92
4.8. Internal StrainandClusterEnergies. 95
4.9. Sixteen-BondMicroclusters . 98
4.10. ClusterVariationalMethod . 108
4.11. AbInitioCalculations . 110
4.12. ConcludingRemarks ... . 116
References . . . . . . . . . . 117
Appendix4A: AnalyticalFormulasofGQCA . . 117
Appendix4B: CriticalTemperatureinGQCA . . 118
Appendix4C: GQCAatLowTemperature .. . 120
CHAPTER5. BandStructureTheory
5.1. FormationofEnergyBands . . . . . . . . . . . . . . . 123
5.2. LCAO andtheEmpirical Tight-BindingMethod. . . . 127
5.3. Plane-WaveMethodand EmpiricalPseudopotentials . .130
5.4. BandGapsand EffectiveMasses . . . . . . . . . . . .133
5.5. BandStructureofSemiconductorAlloys: Problemsand Applications. .142
5.6. GreenFunctionandSpectral DensityofStates . . . . . . . . . . . .. . 143
5.7. PerturbationTheory and BowingofFundamental Gaps . . . . . . .. .145
5.8. MultipleScatteringTheoryandtheCoherentPotential Approximation .148
5.9. ASingle-BandAlloyModel. . . . . . . . . . . . . . . . . . . . . .. . 150
5.1O. MolecularCPAForZincBlendeAlloys. . . . . . . . . . . . . . . .. .153
5.11. EffectsofDiagonal andOff-Diagonal DisorderonBand-EdgeProperties .. 165
5.12. ConcludingRemarks .171
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
CONTENTS xi
CHAPTER6. Transport
6.1. MasterandBoltzmannEquations . . . . . . . . . . 175
6.1.1. MasterEquationfor aSupersystem . . . . . . 175
6.1.2. MasterEquationfor aSystemin aHeatBath . 176
6.1.3. Single-ParticleStates . . . . . . . . . . . . . 178
6.1.4.TheBoltzmannEquation .. . . . . . . . . . 178
6.2. Electron-PhononInteractionandSingle-ParticleMasterEquation 179
6.3. Low-FieldTransportforNondegenerateElectronsinCollision-Time
Approximations .... . . . . . . . . . . . . . . . . . . . . . . . 181
6.4. MobilitiesinAlloys: Example,SixGel-x . . . . . . . . . . . . . . . 185
6.5. Hot-Electronv-ECharacteristics: ComparisonofMaterials'Merits 190
6.5.1. Example: Inl-xGaxAs . . . . . . . . . . . . . 192
6.5.2. MeritsofOtherAlloysComparedwithGaAs 192
6.6. ScatteringMechanisms . . . . . . . . . . 197
6.6.1. IonizedImpurityScattering. . . . 198
6.6.2. BareElectron-PhononInteraction 198
6.6.3. PolarOpticalPhonon Scattering 199
6.6.4. AlloyScattering. . . . . . . . . 200
6.6.5. Electron-ElectronScattering . . 200
6.7. Expansion SolutionoftheBoltzmannEquation . 201
6.8. Near-BallisticTransport 206
6.9. IntervalleyScattering. 221
6.10. Narrow-GapMaterials 223
6.11. ConcludingRemarks 229
References . . . . . . 230
CHAPTER7. BandStructuresofSelectedSemiconductorsandTheirAlloys
7.1. HybridPseudopotentialandTight-BindingModel(HPT) . . . . . 233
7.2. BandStructures andHamiltonianParametersforIII-VConstituent
Compounds 238
7.2.1. AlP . 240
7.2.2. AlAs 241
7.2.3. AISb 242
7.2.4. GaP . 244
7.2.5. GaAs 246
7.2.6. GaSb 249
7.2~.fuP. ~1
7.2.8~ InAs 252
7.2.9. InSb 254
7.3. TheHPTModelAppliedtoIII-VPseudobinary Alloys 255
7.4. BandStructuresofSelectedIII-VZincBlendeAlloys 257
7.4.1. Gal-xAlxAs 257
7.4.2. Gal-xAlxSb 259
7.4.3. Gal-xAlxP. 262
7.4.4. Inl-xGaxP . 263