Fundamentals of Semiconductors: Physics and Materials Properties / Edition 2

1 Introduction 1

1.1 A Survey of Semiconductors 2

1.1.1 Elemental Semiconductors 2

1.1.2 Binary Compounds 2

1.1.3 Oxides 3

1.1.4 Layered Semiconductors 3

1.1.5 Organic Semiconductors 4

1.1.6 Magnetic Semiconductors 4

1.1.7 Other Miscellaneous Semiconductors 4

1.2 Growth Techniques 5

1.2.1 Czochralski Method 5

1.2.2 Bridgman Method 6

1.2.3 Chemical Vapor Deposition 7

1.2.4 Molecular Beam Epitaxy 8

1.2.5 Fabrication of Self-Organized Quantum Dots by the Stranski-Krastanow Growth Method 11

1.2.6 Liquid Phase Epitaxy 13

Summary 14

Periodic Table of "Semiconductor-Forming" Elements 15

2 Electronic Band Structures 17

2.1 Quantum Mechanics 18

2.2 Translational Symmetry and Brillouin Zones 20

2.3 A Pedestrian's Guide to Group Theory 25

2.3.1 Definitions and Notations 25

2.3.2 Symmetry Operations of the Diamond and Zinc-Blende Structures 30

2.3.3 Representations and Character Tables 32

2.3.4 Some Applications of Character Tables 40

2.4 Empty Lattice or Nearly Free Electron Energy Bands 48

2.4.1 Nearly Free Electron Band Structure in a Zinc-Blende Crystal 48

2.4.2 Nearly Free Electron Energy Bands in Diamond Crystals 52

2.5 Band Structure Calculations by Pseudopotential Methods 58

2.5.1 Pseudopotential Form Factors in Zinc-Blende- and Diamond-Type Semiconductors 61

2.5.2 Empirical and Self-Consistent Pseudopotential Methods 66

2.6 The k-p Method of Band-Structure Calculations 68

2.6.1 Effective Mass of a Nondegenerate Band Using the k-p Method 69

2.6.2 Band Dispersion near a Degenerate Extremum: Top Valence Bands in Diamond and Zinc-Blende-Type Semiconductors 71

2.7 Tight-Binding or LCAO Approach to the Band Structure of Semiconductors 83

2.7.1 Molecular Orbitals and Overlap Parameters 83

2.7.2 Band Structure of Group-IV Elements by the Tight-Binding Method 87

2.7.3 Overlap Parameters and Nearest-Neighbor Distances 94

Problems 96

Summary 105

3 Vibrational Properties of Semiconductors, and Electron-Phonon Interactions 107

3.1 Phonon Dispersion Curves of Semiconductors 110

3.2 Models for Calculating Phonon Dispersion Curves of Semiconductors 114

3.2.1 Force Constant Models 114

3.2.2 Shell Model 114

3.2.3 Bond Models 115

3.2.4 Bond Charge Models 117

3.3 Electron-Phonon Interactions 121

3.3.1 Strain Tensor and Deformation Potentials 122

3.3.2 Electron-Acoustic-Phonon Interaction at Degenerate Bands 127

3.3.3 Piezoelectric Electron-Acoustic-Phonon Interaction 130

3.3.4 Electron-Optical-Phonon Deformation Potential Interactions 131

3.3.5 Frohlich Interaction 133

3.3.6 Interaction Between Electrons and Large-Wavevector Phonons: Intervalley Electron-Phonon Interaction 135

Problems 137

Summary 158

4 Electronic Properties of Defects 159

4.1 Classification of Defects 160

4.2 Shallow or Hydrogenic Impurities 161

4.2.1 Effective Mass Approximation 162

4.2.2 Hydrogenic or Shallow Donors 166

4.2.3 Donors Associated with Anisotropic Conduction Bands 171

4.2.4 Acceptor Levels in Diamond and Zinc-Blende-Type Semiconductors 174

4.3 Deep Centers 180

4.3.1 Green's Function Method for Calculating Defect Energy Levels 183

4.3.2 An Application of the Green's Function Method: Linear Combination of Atomic Orbitals 188

4.3.3 Another Application of the Green's Function Method: Nitrogen in GaP and GaAsP Alloys 192

4.3.4 Final Note on Deep Centers 197

Problems 198

Summary 202

5 Electrical Transport 203

5.1 Quasi-Classical Approach 203

5.2 Carrier Mobility for a Nondegenerate Electron Gas 206

5.2.1 Relaxation Time Approximation 206

5.2.2 Nondegenerate Electron Gas in a Parabolic Band 207

5.2.3 Dependence of Scattering and Relaxation Times on Electron Energy 208

5.2.4 Momentum Relaxation Times 209

5.2.5 Temperature Dependence of Mobilities 220

5.3 Modulation Doping 223

5.4 High-Field Transport and Hot Carrier Effects 225

5.4.1 Velocity Saturation 227

5.4.2 Negative Differential Resistance 228

5.4.3 Gunn Effect 230

5.5 Magneto-Transport and the Hall Effect 232

5.5.1 Magneto-Conductivity Tensor 232

5.5.2 Hall Effect 234

5.5.3 Hall Coefficient for Thin Film Samples (van der Pauw Method) 235

5.5.4 Hall Effect for a Distribution of Electron Energies 236

Problems 237

Summary 241

6 Optical Properties I 243

6.1 Macroscopic Electrodynamics 244

6.1.1 Digression: Units for the Frequency of Electromagnetic Waves 247

6.1.2 Experimental Determination of Optical Functions 247

6.1.3 Kramers-Kronig Relations 250

6.2 The Dielectric Function 253

6.2.1 Experimental Results 253

6.2.2 Microscopic Theory of the Dielectric Function 254

6.2.3 Joint Density of States and Van Hove Singularities 261

6.2.4 Van Hove Singularities in εi 262

6.2.5 Direct Absorption Edges 268

6.2.6 Indirect Absorption Edges 269

6.2.7 "Forbidden" Direct Absorption Edges 273

6.3 Excitons 276

6.3.1 Exciton Effect at M0 Critical Points 279

6.3.2 Absorption Spectra of Excitons 282

6.3.3 Exciton Effect at M1 Critical Points or Hyperbolic Excitons 288

6.3.4 Exciton Effect at M3 Critical Points 291

6.4 Phonon-Polaritons and Lattice Absorption 292

6.4.1 Phonon-Polaritons 295

6.4.2 Lattice Absorption and Reflection 298

6.4.3 Multiphonon Lattice Absorption 299

6.4.4 Dynamic Effective Ionic Charges in Heteropolar Semiconductors 303

6.5 Absorption Associated with Extrinsic Electrons 305

6.5.1 Free-Carrier Absorption in Doped Semiconductors 306

6.5.2 Absorption by Carriers Bound to Shallow Donors and Acceptors 311

6.6 Modulation Spectroscopy 315

6.6.1 Frequency Modulated Reflectance and Thermoreflectance 319

6.6.2 Piezoreflectance 321

6.6.3 Electroreflectance (Franz-Keldysh Effect) 322

6.6.4 Photoreflectance 329

6.6.5 Reflectance Difference Spectroscopy 332

6.7 Addendum (Third Edition): Dielectric Function 333

Problems 334

Summary 343

7 Optical Properties II 345

7.1 Emission Spectroscopies 345

7.1.1 Band-to-Band Transitions 351

7.1.2 Free-to-Bound Transitions 354

7.1.3 Donor-Acceptor Pair Transitions 356

7.1.4 Excitons and Bound Excitons 362

7.1.5 Luminescence Excitation Spectroscopy 369

7.2 Light Scattering Spectroscopies 375

7.2.1 Macroscopic Theory of Inelastic Light Scattering by Phonons 375

7.2.2 Raman Tensor and Selection Rules 378

7.2.3 Experimental Determination of Raman Spectra 385

7.2.4 Microscopic Theory of Raman Scattering 394

7.2.5 A Detour into the World of Feynman Diagrams 395

7.2.6 Brillouin Scattering 398

7.2.7 Experimental Determination of Brillouin Spectra 400

7.2.8 Resonant Raman and Brillouin Scattering 401

Problems 422

Summary 426

8 Photoelectron Spectroscopy 427

8.1 Photoemission 431

8.1.1 Angle-Integrated Photoelectron Spectra of the Valence Bands 440

8.1.2 Angle-Resolved Photoelectron Spectra of the Valence Bands 443

8.1.3 Core Levels 451

8.2 Inverse Photoemission 456

8.3 Surface Effects 457

8.3.1 Surface States and Surface Reconstruction 457

8.3.2 Surface Energy Bands 458

8.3.3 Fermi Level Pinning and Space Charge Layers 460

Problems 465

Summary 468

9 Effect of Quantum Confinement on Electrons and Phonons in Semiconductors 469

9.1 Quantum Confinement and Density of States 470

9.2 Quantum Confinement of Electrons and Holes 473

9.2.1 Semiconductor Materials for Quantum Wells and Superlattices 474

9.2.2 Classification of Multiple Quantum Wells and Superlattices 478

9.2.3 Confinement of Energy Levels of Electrons and Holes 479

9.2.4 Some Experimental Results 489

9.3 Phonons in Superlattices 494

9.3.1 Phonons in Superlattices: Folded Acoustic and Confined Optic Modes 494

9.3.2 Folded Acoustic Modes: Macroscopic Treatment 499

9.3.3 Confined Optical Modes: Macroscopic Treatment 500

9.3.4 Electrostatic Effects in Polar Crystals: Interface Modes 502

9.4 Raman Spectra of Phonons in Semiconductor Superlattices 511

9.4.1 Raman Scattering by Folded Acoustic Phonons 511

9.4.2 Raman Scattering by Confined Optical Phonons 516

9.4.3 Raman Scattering by Interface Modes 518

9.4.4 Macroscopic Models of Electron-LO Phonon (Frohlich) Interaction in Multiple Quantum Wells 521

9.5 Electrical Transport: Resonant Tunneling 525

9.5.1 Resonant Tunneling Through a Double-Barrier Quantum Well 526

9.5.2 I-V Characteristics of Resonant Tunneling Devices 529

9.6 Quantum Hall Effects in Two-Dimensional Electron Gases 533

9.6.1 Landau Theory of Diamagnetism in a Three-Dimensional Free Electron Gas 534

9.6.2 Magneto-Conductivity of a Two-Dimensional Electron Gas: Filling Factor 537

9.6.3 The Experiment of von Klitzing, Pepper and Dorda 538

9.6.4 Explanation of the Hall Plateaus in the Integral Quantum Hall Effect 541

9.7 Concluding Remarks 545

Problems 546

Summary 551

Appendix A Pioneers of Semiconductor Physics Remember... 553

Ultra-Pure Germanium: From Applied to Basic Research or an Old Semiconductor Offering New Opportunities Eugene E. Haller Haller, Eugene E. 555

Two Pseudopotential Methods: Empirical and Ab Initio Marvin L. Cohen Cohen, Marvin L. 558

The Early Stages of Band-Structures Physics and Its Struggles for a Place in the Sun Conyers Herring Herring, Conyers 560

Cyclotron Resonance and Structure of Conduction and Valence Band Edges in Silicon and Germanium Charles Kittel Kittel, Charles 563

Optical Properties of Amorphous Semiconductors and Solar Cells Jan Tauc Tauc, Jan 566

Optical Spectroscopy of Shallow Impurity Centers Elias Burstein Burstein, Elias 569

On the Prehistory of Angular Resolved Photoemission Neville V. Smith Smith, Neville V. 574

The Discovery and Very Basics of the Quantum Hall Effect Klaus von Klitzing von Klitzing, Klaus 576

The Birth of the Semiconductor Superlattice Leo Esaki Esaki, Leo 578

Appendix B Solutions to Some of the Problems 582

Appendix C Recent Development 673

Appendix D Recent Developments and References 687

References 719

Subject Index 755