The k-p method : electronic properties of semiconductors / Lok C. Lew Yan Voon, Morten Willatzen.

Format:

Book

Author/Creator:

Lew Yan Voon, Lok C.

Contributor:

Willatzen, Morten.

Language:

English

Subjects (All):

Semiconductors.

Hamiltonian systems.

Physical Description:

xxi, 445 pages : illustrations ; 25 cm

Place of Publication:

Dordrecht ; New York : Springer, [2009]

Summary:

This book presents a detailed exposition of the formalism and application of k.p theory for both bulk and nanostructured semiconductors. For bulk crystals, this is the first time all the major techniques for deriving the most popular Hamiltonians have been provided in one place. For nanostructures, this is the first time the Burt-Foreman theory has been made accessible. Thus, the reader will gain a clear understanding of the k.p method, will have an explicit listing of the various Hamiltonians in a consistent notation for their use, and a set of representative results. In addition, the reader can derive an excellent understanding of the electronic structure of semiconductors.

Contents:

1 Introduction 1

1.1 What Is k. p Theory? 1

1.2 Electronic Properties of Semiconductors 1

1.3 Other Books 3

Part I Homogeneous Crystals

2 One-Band Model 7

2.1 Overview 7

2.2 k. p Equation 7

2.3 Perturbation Theory 9

2.4 Canonical Transformation 9

2.5 Effective Masses 12

2.5.1 Electron 12

2.5.2 Light Hole 13

2.5.3 Heavy Hole 14

2.6 Nonparabolicity 14

2.7 Summary 15

3 Perturbation Theory - Valence Band 17

3.1 Overview 17

3.2 Dresselhaus-Kip-Kittel Model 17

3.2.1 Hamiltonian 17

3.2.2 Eigenvalues 21

3.2.3 L, M, N Parameters 22

3.2.4 Properties 30

3.3 Six-Band Model for Diamond 32

3.3.1 Hamiltonian 32

3.3.2 DKK Solution 40

3.3.3 Kane Solution 43

3.4 Wurtzite 45

3.4.1 Overview 45

3.4.2 Basis States 46

3.4.3 Chuang-Chang Hamiltonian 46

3.4.4 Gutsche-Jahne Hamiltonian 52

3.5 Summary 54

4 Perturbation Theory - Kane Models 55

4.1 Overview 55

4.2 First-Order Models 55

4.2.1 Four-Band Model 56

4.2.2 Eight-Band Model 57

4.3 Second-Order Kane Model 61

4.3.1 Löwdin Perturbation 61

4.3.2 Four-Band Model 62

4.4 Full-Zone k. p Model 64

4.4.1 15-Band Model 64

4.4.2 Other Models 69

4.5 Wurtzite 69

4.5.1 Four-Band: Andrew-O'Reilly 70

4.5.2 Eight-Band: Chuang-Chang 71

4.5.3 Eight-Band: Gutsche-Jahne 71

4.6 Summary 77

5 Method of Invariants 79

5.1 Overview 79

5.2 DKK Hamiltonian - Hybrid Method 79

5.3 Formalism 84

5.3.1 Introduction 84

5.3.2 Spatial Symmetries 84

5.3.3 Spinor Representation 88

5.4 Valence Band of Diamond 88

5.4.1 No Spin 89

5.4.2 Magnetic Field 90

5.4.3 Spin-Orbit Interaction 93

5.5 Six-Band Model for Diamond 114

5.5.1 Spin-Orbit Interaction 115

5.5.2 k-Dependent Part 115

5.6 Four-Band Model for Zincblende 116

5.7 Eight-Band Model for Zincblende 117

5.7.1 Weiler Hamiltonian 117

5.8 14-Band Model for Zincblende 120

5.8.1 Symmetrized Matrices 121

5.8.2 Invariant Hamiltonian 123

5.8.3 T Basis Matrices 125

5.8.4 Parameters 128

5.9 Wurtzite 132

5.9.1 Six-Band Model 132

5.9.2 Quasi-Cubic Approximation 136

5.9.3 Eight-Band Model 137

5.10 Method of Invariants Revisited 140

5.10.1 Zincblende 140

5.10.2 Wurtzite 146

5.11 Summary 151

6 Spin Splitting 153

6.1 Overview 153

6.2 Dresselhaus Effect in Zincblende 154

6.2.1 Conduction State 154

6.2.2 Valence States 154

6.2.3 Extended Kane Model 156

6.2.4 Sign of Spin-Splitting Coefficients 160

6.3 Linear Spin Splittings in Wurtzite 161

6.3.1 Lower Conduction-Band e States 163

6.3.2 A, B, C Valence States 164

6.3.3 Linear Spin Splitting 165

6.4 Summary 166

7 Strain 167

7.1 Overview 167

7.2 Perurbation Theory 167

7.2.1 Strain Hamiltonian 167

7.2.2 Löwdin Renormalization 170

7.3 Valence Band of Diamond 170

7.3.1 DKK Hamiltonian 171

7.3.2 Four-Band Bir-Pikus Hamiltonian 171

7.3.3 Six-Band Hamiltonian 172

7.3.4 Method of Invariants 174

7.4 Strained Energies 177

7.4.1 Four-Band Model 177

7.4.2 Six-Band Model 179

7.4.3 Deformation Potentials 179

7.5 Eight-Band Model for Zincblende 180

7.5.1 Perturbation Theory 181

7.5.2 Method of Invariants 182

7.6 Wurtzite 183

7.6.1 Perturbation Theory 183

7.6.2 Method of Invariants 184

7.6.3 Examples 186

7.7 Summary 186

Part II Nonperiodic Problem

8 Shallow Impurity States 189

8.1 Overview 189

8.2 Kittel-Mitchell Theory 190

8.2.1 Exact Theory 191

8.2.2 Wannier Equation 193

8.2.3 Donor States 194

8.2.4 Acceptor States 197

8.3 Luttinger-Kohn Theory 198

8.3.1 Simple Bands 199

8.3.2 Degenerate Bands 210

8.3.3 Spin-Orbit Coupling 213

8.4 Baldereschi-Lipari Model 214

8.4.1 Hamiltonian 216

8.4.2 Solution 217

8.5 Summary 219

9 Magnetic Effects 221

9.1 Overview 221

9.2 Canonical Transformation 222

9.2.1 One-Band Model 222

9.2.2 Degenerate Bands 230

9.2.3 Spin-Orbit Coupling 232

9.3 Valence-Band Landau Levels 235

9.3.1 Exact Solution 235

9.3.2 General Solution 239

9.4 Extended Kane Model 240

9.5 Land ̌g-Factor 240

9.5.1 Zincblende 241

9.5.2 Wurtzite 243

9.6 Summary 244

10 Electric Field 245

10.1 Overview 245

10.2 One-Band Model of Stark Effect 245

10.3 Multiband Stark Problem 246

10.3.1 Basis Functions 246

10.3.2 Matrix Elements of the Coordinate Operator 248

10.3.3 Multiband Hamiltonian 249

10.3.4 Explicit Form of Hamiltonian Matrix Contributions 253

10.4 Summary 255

11 Excitons 257

11.1 Overview 257

11.2 Excitonic Hamiltonian 258

11.3 One-Band Model of Excitons 259

11.4 Multiband Theory of Excitons 261

11.4.1 Formalism 261

11.4.2 Results and Discussions 266

11.4.3 Zincblende 267

11.5 Magnetoexciton 268

11.6 Summary 270

12 Heterostructures: Basic Formalism 273

12.1 Overview 273

12.2 Bastard's Theory 274

12.2.1 Envelope-Function Approximation 274

12.2.2 Solution 276

12.2.3 Example Models 277

12.2.4 General Properties 279

12.3 One-Band Models 280

12.3.1 Derivation 280

12.4 Burt-Foreman Theory 282

12.4.1 Overview 283

12.4.2 Envelope-Function Expansion 283

12.4.3 Envelope-Function Equation 287

12.4.4 Potential-Energy Term 294

12.4.5 Conventional Results 299

12.4.6 Boundary Conditions 305

12.4.7 Burt-Foreman Hamiltonian 306

12.4.8 Beyond Burt-Foreman Theory? 316

12.5 Sercel-Vahala Theory 318

12.5.1 Overview 318

12.5.2 Spherical Representation 319

12.5.3 Cylindrical Representation 324

12.5.4 Four-Band Hamiltonian in Cylindrical Polar Coordinates 329

12.5.5 Wurtzite Structure 336

12.6 Arbitrary Nanostructure Orientation 350

12.6.1 Overview 350

12.6.2 Rotation Matrix 350

12.6.3 General Theory 352

12.6.4 [11̄0] Quantum Wires 353

12.7 Spurious Solutions 360

12.8 Summary 361

13 Heterostructures: Further Topics 363

13.1 Overview 363

13.2 Spin Splitting 363

13.2.1 Zincblende Superlattices 363

13.3 Strain in Heterostructures 367

13.3.1 External Stress 367

13.3.2 Strained Heterostructures 369

13.4 Impurity States 371

13.4.1 Donor States 371

13.4.2 Acceptor States 372

13.5 Excitons 373

13.5.1 One-Band Model 373

13.5.2 Type-II Excitons 376

13.5.3 Multiband Theory of Excitons 377

13.6 Magnetic Problem 378

13.6.1 One-Band Model 379

13.6.2 Multiband Model 382

13.7 Static Electric Field 384

13.7.1 Transverse Stark Effect 384

13.7.2 Longitudinal Stark Effect 386

13.7.3 Multiband Theory 388

14 Conclusion 391.

Notes:

Includes bibliographical references (pages 431-442) and index.

ISBN:

9783540928713

3540928715

OCLC:

310401070