Marius Grundmann

The Physicsof SemiconductorsAn Introduction Including Nanophysicsand Applications

Second Edition

With 247 Figures

.el Springer

Contents

1 Introduction 11.1 Timetable 11.2 Nobel Prize Winners 101.3 General Information 11

Part I Fundamentals

2 Bonds 192.1 Introduction 192.2 Covalent Bonds 19

2.2.1 Electron-Pair Bond 192.2.2 sp3 Bonds 192.2.3 spe Bonds 23

2.3 Ionic Bonds 252.4 Mixed Bonds 272.5 Metallic Bonding 302.6 van-der-Waals Bonds 302.7 Hamilton Operator of the Solid 32

3 Crystals 353.1 Introduction 353.2 Crystal Structure 353.3 Lattice 36

3.3.1 Unit Cell 363.3.2 Point Group 373.3.3 Space Group 393.3.4 2D Bravais Lattices 403.3.5 3D Bravais Lattices 403.3.6 Polycrystalline Semiconductors 453.3.7 Amorphous Semiconductors 45

3.4 Important Crystal Structures 473.4.1 Rocksalt Structure 473.4.2 CsC1 Structure 483.4.3 Diamond Structure 48

XI

XII Contents

3.4.4 Zincblende Structure

3.4.5 Wurtzite Structure

3.4.6 Chalcopyrite Structure

3.4.7 Fluorite Structure

3.4.8 Delafossite Structure

3.4.9 Perovskite Structure

3.4.10 NiAs Structure

3.4.11 Further Structures

4950515354555656

3.5 Polytypism 573.6 Reciprocal Lattice 57

3.6.1 Reciprocal Lattice Vectors 593.6.2 Miller Indices 603.6.3 Brillouin Zone 62

3.7 Alloys 633.7.1 Random Alloys 643.7.2 Phase Diagram 663.7.3 Virtual Crystal Approximation 683.7.4 Lattice Parameter 683.7.5 Ordering 69

4 Defects 734.1 Introduction 734.2 Point Defects 73

4.2.1 Point Defect Types 734.2.2 Thermodynamics 744.2.3 Diffusion 784.2.4 Dopant Distribution 804.2.5 Large Concentration Effects 84

4.3 Dislocations 874.3.1 Dislocation Types 884.3.2 Visualization of Dislocations by Etching 924.3.3 Impurity Hardening 94

4.4 Extended Defects 954.4.1 Micro-cracks 954.4.2 Stacking Faults 954.4.3 Grain Boundaries 974.4.4 Antiphase and Inversion Domains 99

4.5 Disorder 102

5 Mechanical Properties 1035.1 Introduction 1035.2 Lattice Vibrations 103

5.2.1 Monoatomic Linear Chain 1035.2.2 Diatomic Linear Chain 1065.2.3 Lattice Vibrations of a Three-Dimensional Crystal 110

Contents XIII

5.2.4 Density of St ates 1125.2.5 Phonons 1145.2.6 Localized Vibrational Modes 1145.2.7 Phonons in Alloys 1165.2.8 Electric Field Created by Optical Phonons 119

5.3 Elasticity 1225.3.1 Thermal Expansion 1225.3.2 Stress—Strain Relation 1225.3.3 Biaxial Strain 1275.3.4 Three-Dimensional Strain 1285.3.5 Substrate Bending 1305.3.6 Scrolling 1325.3.7 Critical Thickness 133

5.4 Cleaving 137

6 Band Structure 1396.1 Introduction 1396.2 Electrons in a Periodic Potential 139

6.2.1 Bloch's Theorem 1396.2.2 Free-Electron Dispersion 1406.2.3 Kronig—Penney Model 1426.2.4 Lattice Vector Expansion 1446.2.5 Kramer's degeneracy 147

6.3 Band Structure of Selected Semiconductors 1476.3.1 Silicon 1476.3.2 Germanium 1476.3.3 GaAs 1486.3.4 GaP 1496.3.5 GaN 1496.3.6 Lead Salts 1496.3.7 Chalcopyrites 1496.3.8 Delafossites 1516.3.9 Perovskites 152

6.4 Alloy Semiconductors 1536.5 Amorphous Semiconductors 1556.6 Systematics of Semiconductor Band Gaps 1566.7 Temperature Dependence of the Band Gap 1586.8 Electron Dispersion 161

6.8.1 Equation of Electron Motion 1616.8.2 Effective Mass of Electrons 1616.8.3 Polaron Mass 1656.8.4 Nonparabolicity of Electron Mass 167

6.9 Holes 1686.9.1 Hole Concept 1686.9.2 Hole Dispersion Relation 1696.9.3 Valence-Band Fine Structure 173

XIV Contents

6.10 Strain Effect an the Band Structure 6.10.1 Strain Effect an Band Edges 6.10.2 Strain Effect an Effective Masses 6.10.3 Interaction with a Localized Level

6.11 Density of States 6.11.1 General Band Structure 6.11.2 Free-Electron Gas

176176179179179179180

7 Electronic Defect States 1857.1 Introduction 1857.2 Fermi Distribution 1857.3 Carrier Concentration 1877.4 Intrinsic Conduction 1907.5 Shallow Defects 193

7.5.1 Donors 1937.5.2 Acceptors 2027.5.3 Compensation 2067.5.4 Multiple Impurities 2087.5.5 Amphoteric Impurities 2107.5.6 High Doping 211

7.6 Quasi-Fermi Levels 2157.7 Deep Levels 216

7.7.1 Charge States 2177.7.2 Double Donors 2187.7.3 Double Acceptors 2197.7.4 Jahn—Teller Effect 2217.7.5 Negative-U Center 2217.7.6 DX Center 2247.7.7 EL2 Defect 2267.7.8 Semi-insulating Semiconductors 2277.7.9 Isoelectronic Impurities 2287.7.10 Surface States 230

7.8 Hydrogen in Semiconductors 231

8 Transport 2358.1 Introduction 2358.2 Conductivity 2368.3 Low-Field Transport 238

8.3.1 Mobility 2388.3.2 Microscopic Scattering Processes 2398.3.3 Ionized Impurity Scattering 2398.3.4 Deformation Potential Scattering 2408.3.5 Piezoelectric Potential Scattering 2418.3.6 Polar Optical Scattering 2418.3.7 Dislocation Scattering 241

Contents XV

8.3.8 Grain Boundary Scattering 2428.3.9 Temperature Dependence 2438.3.10 Doping Dependence 2438.3.11 Piezoresistivity 246

8.4 Hall Effect 2478.5 High-Field Transport 251

8.5.1 Drift-Saturation Velocity 2518.5.2 Negative Differential Resistivity 2528.5.3 Velocity Overshoot 2548.5.4 Impact Ionization 254

8.6 High-Frequency Transport 2578.7 Diffusion 2578.8 Continuity Equation 2598.9 Heat Conduction 2598.10 Coupled Heat and Charge Transport 261

8.10.1 Seebeck Effect 2618.10.2 Peltier Effect 262

9 Optical Properties 2659.1 Spectral Regions and Overview 2659.2 Reflection and Diffraction 2669.3 Absorption 2689.4 Electron—Photon Interaction 2699.5 Band—Band Transitions 271

9.5.1 Joint Density of States 2719.5.2 Direct Transitions 2729.5.3 Indirect Transitions 2749.5.4 Urbach Tail 2789.5.5 Intravalence-Band Absorption 2789.5.6 Amorphous Semiconductors 2799.5.7 Excitons 2809.5.8 Phonon Broadening 2839.5.9 Exciton Polariton 2859.5.10 Bound-Exciton Absorption 2889.5.11 Biexcitons 2909.5.12 Trions 2909.5.13 Burstein—Moss Shift 2919.5.14 Band Gap Renormalization 2929.5.15 Electron—Hole Droplets 2939.5.16 Two-Photon Absorption 294

9.6 Impurity Absorption 2969.7 Free-Carrier Absorption 2999.8 Lattice Absorption 303

9.8.1 Dielectric Constant 3049.8.2 Reststrahlenbande 304

XVI Contents

9.8.3 Polaritons 3049.8.4 Phonon—Plasmon Coupling 307

10 Recombination 30910.1 Introduction 30910.2 Band—Band Recombination 309

10.2.1 Spontaneous Emission 30910.2.2 Absorption 31110.2.3 Stimulated Emission 31110.2.4 Net Recombination Rate 31210.2.5 Recombination Dynamics 31310.2.6 Lasing 314

10.3 Exciton Recombination 31510.3.1 Free Excitons 31510.3.2 Bound Excitons 31710.3.3 Alloy Broadening 323

10.4 Phonon Replica 32610.5 Self-absorption 33010.6 Donor—Acceptor Pair Transitions 33110.7 Inner-Impurity Recombination 33110.8 Auger Recombination 33310.9 Band—Impurity Recombination 335

10.9.1 Shockley-Read-Hall Kinetics 33510.9.2 Multilevel Traps 339

10.10 Field Effect 33910.10.1 Thermally Activated Emission 33910.10.2 Direct Tunneling 34010.10.3 Assisted Tunneling 340

10.11 Recombination at Extended Defects 34010.11.1 Surfaces 34010.11.2 Grain Boundaries 34110.11.3 Dislocations 341

10.12 Excess-Carrier Profiles 34210.12.1 Generation at Surface 34310.12.2 Generation in the Bulk 343

Part II Selected Topics

11 Heterostructures 347

11.1 Introduction 347

11.2 Heteroepitaxy 34711.2.1 Growth Methods 34711.2.2 Substrates 34811.2.3 Growth Modes 351

Contents

11.2.4 Heterosubstrates

11.2.5 Pseudomorphic Structures

11.2.6 Plastic Relaxation

11.2.7 Surfactants

XVII

352356356358

11.3 Energy Levels in Heterostructures 35911.3.1 Band Lineup in Heterostructures 35911.3.2 Quantum Wells 36111.3.3 Superlattices 36611.3.4 Single Heterointerface Between Doped Materials. . 368

11.4 Recombination in Quantum Wells 36911.4.1 Thickness Dependence 36911.4.2 Broadening Effects 37011.4.3 Quantum Confined Stark Effect 374

11.5 Isotope Superlattices 37511.6 Wafer Bonding 377

12 External Fields 37912.1 Electric Fields 379

12.1.1 Bulk Material 37912.1.2 Quantum Wells 381

12.2 Magnetic Fields 38212.2.1 Free-Carrier Absorption 38312.2.2 Energy Levels in Bulk Crystals 38412.2.3 Energy Levels in a 2DEG 38612.2.4 Shubnikov—de Haas Oscillations 387

12.3 Quantum Hall Effect 38912.3.1 Integral QHE 38912.3.2 Fractional QHE 39312.3.3 Weiss Oscillations 394

13 Nanostructures 39713.1 Introduction 39713.2 Quantum Wires 397

13.2.1 V-Groove Quantum Wires 39713.2.2 Cleaved-Edge Overgrowth Quantum Wires 40113.2.3 Nanowhiskers 40113.2.4 Nanobelts 40313.2.5 Quantization in Two-Dimensional Potential Wells . 404

13.3 Quantum Dots 40713.3.1 Quantization in Three-Dimensional

Potential Wells 40713.3.2 Electrical and Transport Properties 41013.3.3 Self-assembled Preparation 41313.3.4 Optical Properties 419

XVIII Contents

14 Polarized Semiconductors 42514.1 Introduction 42514.2 Spontaneous Polarization 42514.3 Ferroelectricity 427

14.3.1 Materials 42814.3.2 Soft Phonon Mode 42814.3.3 Phase Transition 42914.3.4 Domains 43214.3.5 Optical Properties 433

14.4 Piezoelectricity 43314.4.1 Piezoelectric Effect 43314.4.2 Zincblende Crystals 43414.4.3 Wurtzite Crystals 43514.4.4 Piezoelectric Effects in Nanostructures 438

15 Magnetic Semiconductors 44115.1 Introduction 44115.2 Magnetic Semiconductors 44115.3 Diluted Magnetic Semiconductors 44215.4 Spintronics 448

15.4.1 Spin Transistor 44815.4.2 Spin LED 448

16 Organic Semiconductors 45116.1 Materials 451

16.1.1 Small Organic Molecules, Polymers 45116.1.2 Organic Semiconductor Crystals 451

16.2 Electronic Structure 45416.3 Doping 45616.4 Transport Properties 45716.5 Optical Properties 457

17 Graphene and Carbon Nanotubes 46517.1 Graphene 465

17.1.1 Structure 46517.1.2 Band Structure 46517.1.3 Electrical Properties 46817.1.4 Other Two-Dimensional Crystals 472

17.2 Carbon Nanotubes 47317.2.1 Structure 47317.2.2 Band Structure 47417.2.3 Optical Properties 47517.2.4 Other Anorganic Nanotubes 476

Contents XIX

18 Dielectric Structures 48118.1 Photonic Band Gap Materials 481

18.1.1 Introduction 48118.1.2 General 1D Scattering Theory 48118.1.3 Transmission of an N-Period Potential 48318.1.4 The Quarter-Wave Stack 48518.1.5 Formation of a 3D Band Structure 48818.1.6 Disorder 49118.1.7 Defect Modes 49318.1.8 Coupling to an Electronic Resonance 497

18.2 Microscopic Resonators 50018.2.1 Microdiscs 50018.2.2 Purcell Effect 50218.2.3 Deformed Resonators 50318.2.4 Hexagonal Cavities 505

19 Transparent Conductive Oxide Semiconductors 51119.1 Materials 51119.2 Properties 512

Part III Applications

20 Diodes 51920.1 Introduction 51920.2 Metal—Semiconductor Contacts 520

20.2.1 Band Diagram in Equilibrium 52020.2.2 Space-Charge Region 52520.2.3 Schottky Effect 52720.2.4 Capacitance 52920.2.5 Current—Voltage Characteristic 53220.2.6 Ohmic Contacts 54320.2.7 Metal Contacts to Organic Semiconductors 546

20.3 Met al—Insulator—Semiconductor Diodes 54820.3.1 Band Diagram for Ideal MIS Diode 54820.3.2 Space-Charge Region 55120.3.3 Capacitance 55520.3.4 Nonideal MIS Diode 556

20.4 Bipolar Diodes 55820.4.1 Band Diagram 55820.4.2 Space-Charge Region 55820.4.3 Capacitance 56320.4.4 Current—Voltage Characteristics 56520.4.5 Breakdown 57520.4.6 Organic Semiconductor Diodes 580

XX Contents

20.5 Applications and Special Diode Devices 58220.5.1 Rectification 58220.5.2 Frequency Mixing 58420.5.3 Volt age Regulator 58620.5.4 Zener Diodes 58820.5.5 Varactors 58820.5.6 Fast-Recovery Diodes 58920.5.7 Step-Recovery Diodes 59020.5.8 pin-Diodes 59120.5.9 Tunneling Diodes 59220.5.10 Backward Diodes 59520.5.11 Gunn Diodes 59620.5.12 Heterostructure Diodes 597

21 Light-to-Electricity Conversion 59921.1 Photocatalysis 59921.2 Photoconductors 601

21.2.1 Introduction 60121.2.2 Photoconductivity Detectors 60121.2.3 Electrophotography 60321.2.4 QWIPs 60421.2.5 Blocked Impurity-Band Detectors 608

21.3 Photodiodes 61021.3.1 Introduction 61021.3.2 pn Photodiodes 61121.3.3 pin Photodiodes 61321.3.4 Position-Sensing Detector 61521.3.5 MSM Photodiodes 61621.3.6 Avalanche Photodiodes 62321.3.7 Traveling-Wave Photodetectors 62521.3.8 Charge Coupled Devices 62721.3.9 Photodiode Arrays 633

21.4 Solar Cells 63721.4.1 Solar Radiation 63721.4.2 Ideal Solar Cells 63821.4.3 Real Solar Cells 64321.4.4 Design Refinements 64321.4.5 Modules 64521.4.6 Solar-Cell Types 64621.4.7 Commercial Issues 651

22 Electricity-to-Light Conversion 65322.1 Radiometric and Photometric Quantities 653

22.1.1 Radiometric Quantities 65322.1.2 Photometric Quantities 653

Contents XXI

22.2 Scintillators 65422.2.1 CIE Chromaticity Diagram 65522.2.2 Display Applications 65822.2.3 Radiation Detection 65922.2.4 Luminescence Mechanisms 660

22.3 Light-Emitting Diodes 66122.3.1 Introduction 66122.3.2 Spectral Ranges 66122.3.3 Quantum Efficiency 66222.3.4 Device Design 66322.3.5 White LEDs 66822.3.6 Quantum Dot LED 67122.3.7 Organic LED 672

22.4 Lasers 67422.4 .1 Introduction 67422.4.2 Applications 67622.4.3 Gain 67822.4.4 Optical Mode 68022.4.5 Loss Mechanisms 68722.4.6 Threshold 68822.4.7 Spontaneous Emission Factor 68922.4.8 Output Power 69022.4.9 Temperature Dependence 69222.4.10 Mode Spectrum 69422.4.11 Longitudinal Single-Mode Lasers 69522.4.12 Tunability 69722.4.13 Modulation 69822.4.14 Surface-Emitting Lasers 70322.4.15 Optically Pumped Semiconductor Lasers 70722.4.16 Quantum Cascade Lasers 70822.4.17 Hot-Hole Lasers 709

22.5 Semiconductor Optical Amplifiers 710

23 Transistors 71323.1 Introduction 71323.2 Bipolar Transistors 714

23.2.1 Carrier Density and Currents 71523.2.2 Current Amplification 71823.2.3 Ebers—Moll Model 71923.2.4 Current—Voltage Characteristics 72123.2.5 Basic Circuits 72323.2.6 High-Frequency Properties 72523.2.7 Heterobipolar Transistors 72523.2.8 Light-Emitting Transistors 726

23.3 Field-Effect Transistors 727

XXII Contents

23.4 JFET and MESFET 72923.4.1 General Principle 72923.4.2 Static Characteristics 73023.4.3 Normally On and Normally Off FETs 73323.4.4 Field-Dependent Mobility 73423.4.5 High-Frequency Properties 736

23.5 MOSFETs 73723.5.1 Operation Principle 73723.5.2 Current—Voltage Characteristics 73823.5.3 MOSFET Types 74323.5.4 Complementary MOS 74323.5.5 Large-Scale Integration 74623.5.6 Tunneling FETs 75323.5.7 Nonvolatile Memories 75523.5.8 Heterojunction FETs 757

23.6 Thin-Film Transistors 76323.6.1 Annealing of Amorphous Silicon 76323.6.2 TFT Devices 76523.6.3 OFETs 765

Part IV Appendices

A Tensors 769

B Space Groups 773

C Kramers—Kronig Relations 775

D Oscillator Strength 777

E Quantum Statistics 783

F The k • p Perturbation Theory 787

G Effective-Mass Theory 791

References 793

Index 843