Semiconductor heterojunctions and nanostructures

578 Pages·2005·5.279 MB·English

by  Omar Manasreh

Semiconductor
Heterojunctions and
Nanostructures
Omar Manasreh
UniversityofArkansas
Fayetteville,Arkansas
McGraw-Hill
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DOI: 10.1036/0071469680
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555
TomyPhDadvisor,DonO.Pederson
andmyfriendGregJ.Salamowhoinspiredmein
manyways
ABOUTTHEAUTHOR
OmarManasreh,Ph.D.,isafullprofessorintheDepartment
ofElectricalEngineeringattheUniversityofArkansasin
Fayettevilleandtheauthorofover150journalarticles.He
editedandcoeditedovertenbooksandorganizedoverten
symposia.Dr.Manasrehisalsoaserieseditorforatechnical
bookseries,NanoscienceandTechnology,publishedby
McGraw-Hill.Hehasextensiveexperienceinthe
experimentalandtheoreticaloptoelectronicpropertiesof
III-Vsemiconductors,superlattices,nanostructures,and
relateddevices.
Copyright © 2005 by The McGraw-Hill Companies, Inc. Click here for terms of use.
For more information about this title, click here
Contents
Preface xi
Acknowledgments xv
ListofSymbolsandAbbreviations xvi
Chapter1. IntroductiontoQuantumMechanics 1
1.1 Introduction 1
1.1.1 Blackbodyradiation 2
1.1.2 Thespecificheatcapacityofsolids 2
1.1.3 Photoelectriceffect 4
1.1.4 TheBohrmodeloftheatom 6
1.2 ThedeBroglieRelation 8
1.3 WaveFunctionsandtheSchro¨dingerEquation 9
1.4 WavePacketataGivenTime 10
1.5 SeparationofVariables 15
1.6 DiracNotation 17
1.7 ImportantPostulates 18
1.8 ImportantMathematicalTools 19
1.8.1 Thescalarproduct 19
1.8.2 Linearoperators 20
1.8.3 Actionofalinearoperatoronabra 21
1.8.4 TheadjointoperatorA†ofalinearoperatorA 21
1.8.5 Eigenvaluesandeigenfunctionsofanoperator 22
1.8.6 TheDiracδ-function 24
1.8.7 FourierseriesandFouriertransforminquantummechanics 26
1.9 VariationalMethod 28
1.10 Perturbation 29
1.11 AngularMomentum 33
Summary 34
Problems 35
Chapter2. PotentialBarriersandWells 37
2.1 StationaryStatesofaParticleinaPotentialStep 38
2.2 PotentialBarrierwithaFiniteHeight 42
2.3 PotentialWellwithanInfiniteDepth 49
v
vi Contents
2.4 Finite-DepthPotentialWell 51
2.5 Unbound Motion of a Particle ( E >Vo) in a Potential Well with a
FiniteDepth 56
2.6 TriangularPotentialWell 58
2.7 Parabolic Potential Well 61
2.8 Delta-FunctionPotentials 64
2.9 TransmissioninFiniteDouble-BarrierPotentialWells 70
2.10 Wentzel-Kramers-Brillouin(WKB)Approximation 72
2.11 EnergyLevelsinDoubleQuantumWellStructure 78
Summary 80
Problems 81
Chapter3. ElectronicEnergyLevelsinPeriodicPotentials 83
3.1 Bloch’sTheorem 84
3.2 TheKronig-PenneyModel 85
3.3 BlochElectroninaWeakPeriodicPotential 89
3.4 One-ElectronApproximationinaPeriodicDiracδ-functions 93
3.5 Superlattices 95
3.6 EffectiveMass 98
3.7 BandStructureCalculationMethods 99
3.7.1 Tight-bindingmethod 99
3.7.2 k·pmethod 102
3.7.3 Envelopefunctionapproximation 113
Summary 119
Problems 120
Chapter4. TunnelingThroughPotentialBarriers 123
4.1 TransmissionThroughPotentialBarriers 124
4.2 TunnelingThroughPyramidalPotentialBarriers 131
4.3 Double-BarrierPotential 135
4.4 The pn-JunctionTunnelingDiode 139
4.5 ResonantTunnelingDiodes 143
4.6 CoulombBlockade 147
Summary 149
Problems 150
Chapter5. DistributionFunctionsandDensityofStates 153
5.1 DistributionFunctions 156
5.2 Maxwell-BoltzmannStatistic 157
5.3 Fermi-DiracStatistics 161
5.4 Bose-EinsteinStatistics 164
5.5 DensityofStates 166
5.6 DensityofStatesofQuantumWells,Wires,andDots 171
5.6.1 Quantumwells 171
5.6.2 Quantumwires 175
5.6.3 Quantumdots 178
Contents vii
5.7 DensityofStatesofOtherSystems 179
5.7.1 Superlattices 179
5.7.2 Densityofstatesofbulkelectronsinthepresenceofa
magneticfield 181
5.7.3 Densityofstatesinthepresenceofanelectricfield 184
Summary 188
Problems 189
Chapter6. OpticalProperties 191
6.1 Fundamentals 192
6.2 LorentzandDrudeModels 196
6.3 TheOpticalAbsorptionCoefficientoftheInterbandTransition
inDirectBandgapSemiconductors 199
6.4 TheOpticalAbsorptionCoefficientoftheInterbandTransition
inIndirectBandgapSemiconductors 205
6.5 TheOpticalAbsorptionCoefficientoftheInterbandTransition
inQuantumWells 206
6.6 TheOpticalAbsorptionCoefficientoftheInterbandTransition
inTypeIISuperlattices 208
6.7 TheOpticalAbsorptionCoefficientoftheIntersubbandTransition
inMultipleQuantumWells 210
6.8 TheOpticalAbsorptionCoefficientoftheIntersubbandTransition
inGaN/AlGaNMultipleQuantumWells 216
6.9 ElectronicTransitionsinMultipleQuantumDots 217
6.10 SelectionRules 222
6.10.1 Electron-photoncouplingofintersubbandtransitions
inmultiplequantumwells 222
6.10.2 Intersubbandtransitioninmultiplequantumwells 223
6.10.3 Interbandtransition 223
6.11 Excitons 225
6.11.1 Excitonsinbulksemiconductors 225
6.11.2 Excitonsinquantumwells 231
6.11.3 Excitonsinquantumdots 233
6.12 CyclotronResonance 234
6.13 Photoluminescence 239
6.14 LatticeVibrationsandPhonons 245
Summary 255
Problems 256
Chapter7. ElectricalandTransportProperties 261
7.1 Introduction 261
7.2 TheHallEffect 265
7.3 QuantumHallandShubnikov–deHaasEffects 269
7.3.1 Shubnikov–deHaaseffect 272
7.3.2 QuantumHalleffect 275
7.4 ChargeCarrierTransportinBulkSemiconductors 277
7.4.1 Driftcurrentdensity 278
7.4.2 Diffusioncurrentdensity 282
7.4.3 Generationandrecombination 286
7.4.4 Continuityequation 288
viii Contents
7.5 BoltzmannTransportEquation 294
7.6 DerivationofTransportCoefficientsUsingtheBoltzmann
TransportEquation 298
7.6.1 Electricalconductivityandmobilityinn-typesemiconductors 300
7.6.2 HallcoefficientRH 302
7.7 ScatteringMechanismsinBulkSemiconductors 304
7.7.1 Scatteringfromanionizedimpurity 306
7.7.2 Scatteringfromaneutralimpurity 307
7.7.3 Scatteringfromacousticphonons 307
7.7.4 Opticalphononscattering—polarandnonpolar 309
7.7.5 Scatteringfromshort-rangepotentials 310
7.7.6 Scatteringfromdipoles 311
7.8 ScatteringinaTwo-DimensionalElectronGas 312
7.8.1 Scatteringbyremoteionizedimpurities 314
7.8.2 Scatteringbyinterfaceroughness 315
7.8.3 Electron-electronscattering 317
7.9 CoherenceandMesoscopicSystems 318
Summary 324
Problems 325
Chapter8. SemiconductorGrowthTechnologies:Bulk,ThinFilms,
andNanostructures 329
8.1 Introduction 329
8.2 GrowthofBulkSemiconductors 334
8.2.1 Liquid-encapsulatedCzochralski(LEC)method 334
8.2.2 HorizontalBridgmanmethod 341
8.2.3 Float-zonegrowthmethod 343
8.2.4 Lelygrowthmethod 346
8.3 GrowthofSemiconductorThinFilms 347
8.3.1 Liquid-phaseepitaxymethod 348
8.3.2 Vapor-phaseepitaxymethod 349
8.3.3 Hydridevapor-phaseepitaxialgrowthofthickGaNlayers 352
8.3.4 Pulsed-laserdepositiontechnique 355
8.3.5 Molecularbeamepitaxygrowthtechnique 357
8.3.6 Metal-organicchemicalvapordepositiongrowthtechnique 372
8.4 FabricationandGrowthofQuantumDots 377
8.4.1 Nucleation 379
8.4.2 Fabricationsofquantumdots 387
8.4.3 Epitaxialgrowthofself-assemblyquantumdots 388
Summary 399
Problems 400
Chapter9. ElectronicDevices 403
9.1 Introduction 403
9.2 SchottkyDiode 406
9.3 Metal-SemiconductorField-EffectTransistors 411
9.4 JunctionField-EffectTransistor 420
9.5 HeterojunctionField-EffectTransistors 423
9.6 GaN/AlGaNHeterojunctionField-EffectTransistors 428
9.7 HeterojunctionBipolarTransistors 433