Preface xv

Acknowledgments/Dedication xvii

1 Structural Properties 1

1.1 Ionicity 1

1.1.1 Definition 1

(a) Phillips ionicity 2

(b) Pauling ionicity 2

(c) Harrison ionicity 2

1.1.2 Ionicity Value 3

1.2 Elemental Isotopic Abundance and Molecular Weight 3

1.2.1 Elemental Isotopic Abundance 3

1.2.2 Molecular Weight 4

1.3 Crystal Structure and Space Group 4

1.3.1 Crystal Structure 4

(a) Diamond, zinc-blende and wurtzite structures 4

(b) Hexagonal and rhombohedral structures 7

(c) Rocksalt structure 9

1.3.2 Space Group 10

1.4 Lattice Constant and Related Parameters 12

1.4.1 Lattice Constant 12

(a) Room-temperature value 12

(b) Near-neighbor distance 12

(c) External perturbation effect 13

1.4.2 Molecular and Crystal Densities 13

1.5 Structural Phase Transitions 14

1.6 Cleavage 15

1.6.1 Cleavage Plane 15

1.6.2 Surface Energy 18

(a) Theoretical value 18

(b) Experimental value 20

References 20

2 Thermal Properties 23

2.1 Melting Point and Related Parameters 23

2.1.1 Phase Diagram 23

2.1.2 Melting Point 23

2.2 Specific Heat 26

2.3 Debye Temperature 28

2.4 Thermal Expansion Coefficient 30

2.5 Thermal Conductivity and Diffusivity 33

2.5.1 Thermal Conductivity 33

2.5.2 Thermal Diffusivity 39

References 39

3 Elastic Properties 41

3.1 Elastic Constant 41

3.1.1 General Remarks 41

3.1.2 Room-temperature Value 42

3.1.3 External Perturbation Effect 48

(a) Temperature effect 48

(b) Pressure effect 50

3.2 Third-order Elastic Constant 51

3.3 Young’s Modulus, Poisson’s Ratio and Similar Properties 53

3.3.1 Young’s Modulus and Poisson’s Ratio: Cubic Lattice 53

3.3.2 Bulk Modulus, Shear Modulus and Similar Properties: Cubic Lattice 56

3.3.3 Young’s Modulus and Poisson’s Ratio: Hexagonal Lattice 60

3.3.4 Bulk Modulus, Shear Modulus and Similar Properties: Hexagonal Lattice 61

3.4 Microhardness 62

3.5 Sound Velocity 68

References 72

4 Lattice Dynamic Properties 73

4.1 Phonon Dispersion Relation 73

4.1.1 Brillouin Zone 73

(a) Face-centered cubic lattice 74

(b) Hexagonal lattice 74

(c) Rhombohedral lattice 75

4.1.2 Phonon Dispersion Curve 75

(a) Cubic lattice 75

(b) Hexagonal lattice 77

4.1.3 Phonon Density of States 79

4.2 Phonon Frequency 80

4.2.1 Room-temperature Value 80

4.2.2 External Perturbation Effect 84

(a) Temperature effect 84

(b) Pressure effect 86

4.3 Mode Grüneisen Parameter 87

4.4 Phonon Deformation Potential 88

4.4.1 Cubic Lattice 88

4.4.2 Hexagonal Lattice 91

References 92

5 Collective Effects and Some Response Characteristics 95

5.1 Piezoelectric and Electromechanical Constants 95

5.1.1 Piezoelectric Constant 95

(a) Piezoelectric stress constant 95

(b) Piezoelectric strain constant 98

5.1.2 Electromechanical Coupling Constant 99

5.2 Fröhlich Coupling Constant 99

References 101

6 Energy-band Structure: Energy-band Gaps 103

6.1 Basic Properties 103

6.1.1 Energy-band Structure 103

(a) Diamond-type semiconductor 104

(b) Zinc-blende-type semiconductor 106

(c) Wurtzite-type semiconductor 108

6.1.2 Electronic Density of States 111

6.2 E 0 -gap Region 114

6.2.1 Effective Ɣ-point Hamiltonian 114

6.2.2 Room-temperature Value 115

6.2.3 External Perturbation Effect 120

(a) Temperature effect 120

(b) Pressure effect 124

(c) Temperature and pressure coefficients 124

6.2.4 Doping Effect 126

6.3 Higher-lying Direct Gap 130

6.3.1 Cubic Semiconductor 130

(a) Room-temperature value 130

(b) External perturbation effect 133

6.3.2 Hexagonal and Rhombohedral Semiconductors 137

6.4 Lowest Indirect Gap 137

6.4.1 Room-temperature Value 137

6.4.2 External Perturbation Effect 138

(a) Temperature effect 138

(b) Pressure effect 139

(c) Temperature and pressure coefficients 142

6.5 Conduction-valley Energy Separation 142

6.6 Direct–Indirect-gap Transition Pressure 142

References 143

7 Energy-band Structure: Effective Masses 147

7.1 Electron Effective Mass: Ɣ Valley 147

7.1.1 General Remarks 147

7.1.2 Numerical Value 149

7.1.3 Polaron Effect 151

7.1.4 External Perturbation and Doping Effects 152

(a) Temperature effect 152

(b) Pressure effect 153

(c) Doping effect 155

7.2 Electron Effective Mass: Satellite Valley 158

7.2.1 Camel’s Back Structure 158

7.2.2 Numerical Value 159

7.3 Hole Effective Mass 159

7.3.1 Effective Ɣ-valence-band Hamiltonian and Luttinger Parameter 159

7.3.2 Numerical Value 164

(a) Cubic semiconductor 164

(b) Hexagonal and rhombohedral semiconductors 167

7.3.3 Polaron Effect 168

7.3.4 External Perturbation and Doping Effects 170

(a) Temperature effect 170

(b) Pressure effect 170

(c) Doping effect 170

References 171

8 Deformation Potentials 173

8.1 Intravalley Deformation Potential: Ɣ Point 173

8.1.1 Conduction Band 173

8.1.2 Valence Band 175

8.1.3 E 0 Gap 179

8.1.4 Optical Phonon Deformation Potential 181

8.2 Intravalley Deformation Potential: High-symmetry Points 183

8.2.1 L Point 183

(a) Hydrostatic and shear deformation potentials: conduction band 183

(b) Optical phonon deformation potential 185

(c) Valence-band deformation potential 186

(d) Hydrostatic and interband deformation potentials: E 1 and E 1 + ∆ 1 gaps 186

8.2.2 X Point 188

(a) Hydrostatic and shear deformation potentials: conduction band 188

(b) Hydrostatic and interband deformation potentials: E 2 gap 189

8.3 Intervalley Deformation Potential 189

8.3.1 General Remarks 189

8.3.2 Numerical Value 192

References 192

9 Electron Affinity and Schottky Barrier Height 195

9.1 Electron Affinity 195

9.1.1 An Overview 195

9.1.2 Numerical Value 196

9.2 Schottky Barrier Height 198

9.2.1 An Ideal Schottky–Mott Contact 198

9.2.2 Case Study: Au/Semiconductor Contact 202

9.2.3 Surface Reconstruction and External Perturbation Effect 204

(a) Surface reconstruction 204

(b) Temperature effect 205

(c) Pressure effect 205

9.2.4 Breakdown Voltage 206

References 208

10 Optical Properties 211

10.1 Summary of Optical Dispersion Relations 211

10.1.1 Dielectric Permittivity 211

10.1.2 Optical Dispersion Relation 213

10.1.3 Optical Sum Rule 214

10.1.4 Optical Spectra 216

10.2 The Reststrahlen Region 217

10.2.1 Static and High-frequency Dielectric Constants 217

(a) Room-temperature value 217

(b) External perturbation effect 219

10.2.2 Reststrahlen Spectra 222

(a) Zinc-blende-type and rocksalt-type semiconductors 222

(b) Hexagonal semiconductor 226

(c) External perturbation effect 227

10.2.3 Multiphonon Optical Absorption Spectra 228

10.3 At or Near the Fundamental Absorption Edge 230

10.3.1 Free-exciton Binding Energy and Related Parameters 230

(a) Exciton states: direct exciton 230

(b) Exciton states: indirect exciton 232

(c) Exciton binding energy and related parameters 233

(d) Spin-exchange interaction constant 236

10.3.2 Refractive Index 236

(a) Theoretical dispersion model 236

(b) Long-wavelength n value: empirical formula 240

(c) External perturbation effect 241

10.3.3 Optical Absorption at the Fundamental Absorption Edge 244

(a) Critical point: definition 244

(b) Free electron–hole pair transition 245

(c) Excitonic transition 251

(d) Experimental 253

10.3.4 Urbach Tail 256

10.4 The Interband Transition Region 258

10.4.1 Model Dielectric Function 258

(a) Fundamental absorption edge 259

(b) E 1 and E 1 + ∆ 1 transitions 259

(c) E ′ ′ 0 , E 2 and E 1 transitions 260

(d) Plasma and d-band effects 262

10.4.2 Fundamental Optical Spectra 263

(a) Si 263

(b) GaAs 265

(c) w-CdS 265

10.4.3 External Perturbation and Doping Effects 268

(a) Temperature effect 268

(b) Pressure effect 268

(c) Doping effect 269

10.5 Free-carrier Absorption and Related Phenomena 270

10.5.1 Free-carrier Absorption 270

10.5.2 Interconduction-band and Intervalence-band Absorption 274

(a) Interconduction-band absorption 274

(b) Intervalence-band absorption 275

10.5.3 Free-carrier-induced Change in Refractive Index 278

References 278

11 Elasto-optic, Electro-optic and Nonlinear Optical Properties 283

11.1 Elasto-optic Effect 283

11.1.1 Theoretical Expression 283

11.1.2 Experimental Value 285

11.2 Linear Electro-optic Constant 291

11.2.1 Theoretical Expression 291

11.2.2 Experimental Value 294

11.3 Quadratic Electro-optic Constant 295

11.3.1 Theoretical Expression 295

11.3.2 Experimental Value 298

11.4 Franz–Keldysh Effect 300

11.4.1 Theoretical Expression 300

11.4.2 Experimental Value 301

11.5 Nonlinear Optical Constant 302

11.5.1 Second-order Nonlinear Optical Susceptibility 302

11.5.2 Third-order Nonlinear Optical Susceptibility 308

11.5.3 Two-photon Absorption 309

References 311

12 Carrier Transport Properties 315

12.1 Low-field Mobility: Electrons 315

12.1.1 Electron Scattering Mechanism 315

(a) Intervalley scattering 317

(b) Polar optical scattering 317

(c) Nonpolar optical scattering 318

(d) Piezoelectric scattering 318

(e) Deformation potential scattering 318

(f) Ionized impurity scattering 319

(g) Neutral impurity scattering 319

(h) Space-charge scattering 319

(i) Alloy scattering 320

(j) Carrier–carrier scattering 320

12.1.2 Three-valley Model 320

12.1.3 Room-temperature Value 321

12.1.4 External Perturbation and Doping Effects 324

(a) Temperature effect 324

(b) Pressure effect 325

(c) Doping effect 326

12.1.5 Hall Factor 328

12.2 Low-field Mobility: Holes 331

12.2.1 Hole Scattering Mechanism 331

12.2.2 Room-temperature Value 333

12.2.3 External Perturbation and Doping Effects 333

(a) Temperature effect 333

(b) Pressure effect 337

(c) Doping effect 337

12.3 High-field Transport: Electrons 339

12.3.1 Electron Drift Velocity–Field Characteristic 339

12.3.2 Electron Saturation Drift Velocity 347

(a) Temperature dependence 347

(b) LO phonon scattering-limited electron saturation drift velocity 348

12.4 High-field Transport: Holes 349

12.4.1 Hole Drift Velocity–Field Characteristic 349

12.4.2 Hole Saturation Drift Velocity 352

12.5 Minority-carrier Transport: Electrons in p-type Materials 353

12.5.1 Minority-electron Mobility 353

12.5.2 Minority-electron Drift Velocity 356

12.5.3 Minority-electron Lifetime and Diffusion Length 356

12.6 Minority-carrier Transport: Holes in n-type Materials 359

12.6.1 Minority-hole Mobility 359

12.6.2 Minority-hole Lifetime and Diffusion Length 360

12.7 Impact Ionization Coefficient 362

12.7.1 Theoretical Consideration 362

12.7.2 Experimental Value 365

(a) Electric-field dependence 365

(b) Temperature dependence 366

(c) Crystallographic direction dependence 368

References 369

Index 373