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The k p Method - Electronic Properties of Semiconductors
von: Morten Willatzen, Lok C. Lew Yan Voon
Springer-Verlag, 2009
ISBN: 9783540928720, 452 Seiten
Format: PDF, OL
Preis: 117,65 EUR
Foreword
6
Preface
9
Contents
11
Acronyms
18
Chapter 1 Introduction
19
What Is kp Theory?
19
Electronic Properties of Semiconductors
19
Other Books
21
Part I Homogeneous Crystals
22
Chapter 2 One-Band Model
23
Overview
23
kp Equation
23
Perturbation Theory
25
Canonical Transformation
25
Effective Masses
28
Electron
28
Light Hole
29
Heavy Hole
30
Nonparabolicity
30
Summary
31
Chapter 3 Perturbation Theory -- Valence Band
32
Overview
32
Dresselhaus--Kip--Kittel Model
32
Hamiltonian
32
Eigenvalues
36
L,M,N Parameters
37
Properties
45
Six-Band Model for Diamond
47
Hamiltonian
47
DKK Solution
55
Kane Solution
58
Wurtzite
60
Overview
60
Basis States
61
Chuang--Chang Hamiltonian
61
Gutsche--Jahne Hamiltonian
67
Summary
69
Chapter 4 Perturbation Theory -- Kane Models
70
Overview
70
First-Order Models
70
Four-Band Model
71
Eight-Band Model
72
Second-Order Kane Model
76
Löwdin Perturbation
76
Four-Band Model
77
Full-Zone kp Model
79
15-Band Model
79
Other Models
84
Wurtzite
84
Four-Band: Andreev-O'Reilly
85
Eight-Band: Chuang--Chang
86
Eight-Band: Gutsche--Jahne
86
Summary
92
Chapter 5 Method of Invariants
93
Overview
93
DKK Hamiltonian -- Hybrid Method
93
Formalism
98
Introduction
98
Spatial Symmetries
98
Spinor Representation
102
Valence Band of Diamond
102
No Spin
103
Magnetic Field
104
Spin-Orbit Interaction
107
Six-Band Model for Diamond
128
Spin-Orbit Interaction
129
k-Dependent Part
129
Four-Band Model for Zincblende
130
Eight-Band Model for Zincblende
131
Weiler Hamiltonian
131
14-Band Model for Zincblende
134
Symmetrized Matrices
135
Invariant Hamiltonian
137
T Basis Matrices
139
Parameters
142
Wurtzite
146
Six-Band Model
146
Quasi-Cubic Approximation
150
Eight-Band Model
151
Method of Invariants Revisited
154
Zincblende
154
Wurtzite
160
Summary
165
Chapter 6 Spin Splitting
166
Overview
166
Dresselhaus Effect in Zincblende
167
Conduction State
167
Valence States
167
Extended Kane Model
169
Sign of Spin-Splitting Coefficients
173
Linear Spin Splittings in Wurtzite
174
Lower Conduction-Band e States
176
A,B,C Valence States
177
Linear Spin Splitting
178
Summary
179
Chapter 7 Strain
180
Overview
180
Perturbation Theory
180
Strain Hamiltonian
180
Löwdin Renormalization
183
Valence Band of Diamond
183
DKK Hamiltonian
184
Four-Band Bir--Pikus Hamiltonian
184
Six-Band Hamiltonian
185
Method of Invariants
187
Strained Energies
190
Four-Band Model
190
Six-Band Model
192
Deformation Potentials
192
Eight-Band Model for Zincblende
193
Perturbation Theory
194
Method of Invariants
195
Wurtzite
196
Perturbation Theory
196
Method of Invariants
197
Examples
199
Summary
199
Part II Nonperiodic Problem
200
Chapter 8 Shallow Impurity States
201
Overview
201
Kittel--Mitchell Theory
202
Exact Theory
203
Wannier Equation
205
Donor States
206
Acceptor States
209
Luttinger--Kohn Theory
210
Simple Bands
211
Degenerate Bands
222
Spin-Orbit Coupling
225
Baldereschi--Lipari Model
226
Hamiltonian
228
Solution
229
Summary
231
Chapter 9 Magnetic Effects
232
Overview
232
Canonical Transformation
233
One-Band Model
233
Degenerate Bands
241
Spin-Orbit Coupling
243
Valence-Band Landau Levels
246
Exact Solution
246
General Solution
250
Extended Kane Model
251
Landé g-Factor
251
Zincblende
252
Wurtzite
254
Summary
255
Chapter 10 Electric Field
256
Overview
256
One-Band Model of Stark Effect
256
Multiband Stark Problem
257
Basis Functions
257
Matrix Elements of the Coordinate Operator
259
Multiband Hamiltonian
260
Explicit Form of Hamiltonian Matrix Contributions
264
Summary
266
Chapter 11 Excitons
267
Overview
267
Excitonic Hamiltonian
268
One-Band Model of Excitons
269
Multiband Theory of Excitons
271
Formalism
271
Results and Discussions
276
Zincblende
277
Magnetoexciton
278
Summary
280
Chapter 12 Heterostructures: Basic Formalism
282
Overview
282
Bastard's Theory
283
Envelope-Function Approximation
283
Solution
285
Example Models
286
General Properties
288
One-Band Models
289
Derivation
289
Burt--Foreman Theory
291
Overview
292
Envelope-Function Expansion
292
Envelope-Function Equation
296
Potential-Energy Term
303
Conventional Results
308
Boundary Conditions
314
Burt--Foreman Hamiltonian
315
Beyond Burt--Foreman Theory?
325
Sercel--Vahala Theory
327
Overview
327
Spherical Representation
328
Cylindrical Representation
333
Four-Band Hamiltonian in Cylindrical Polar Coordinates
338
Wurtzite Structure
345
Arbitrary Nanostructure Orientation
359
Overview
359
Rotation Matrix
359
General Theory
361
[110] Quantum Wires
362
Spurious Solutions
369
Summary
370
Chapter 13 Heterostructures: Further Topics
372
Overview
372
Spin Splitting
372
Zincblende Superlattices
372
Strain in Heterostructures
376
External Stress
376
Strained Heterostructures
378
Impurity States
380
Donor States
380
Acceptor States
381
Excitons
382
One-Band Model
382
Type-II Excitons
385
Multiband Theory of Excitons
386
Magnetic Problem
387
One-Band Model
388
Multiband Model
391
Static Electric Field
393
Transverse Stark Effect
393
Longitudinal Stark Effect
395
Multiband Theory
397
Chapter 14 Conclusion
399
Appendix A Quantum Mechanics and Group Theory
401
Löwdin Perturbation Theory
19
Variational Principle
401
Perturbation Formula
402
Group Representation Theory
19
Great Orthogonality Theorem
405
Characters
406
Angular-Momentum Theory
21
Angular Momenta
407
Spherical Tensors
407
Wigner-Eckart Theorem
408
Wigner 3j Symbols
408
Appendix B Symmetry Properties
409
Introduction
19
Zincblende
19
Point Group
405
Irreducible Representations
406
Diamond
21
Symmetry Operators
407
Irreducible Representations
407
Wurtzite
415
Irreducible Representations
418
Appendix C Hamiltonians
420
Basis Matrices
19
s=12
401
l=1
402
J=32
420
|JMJ"526930B States
19
Hamiltonians
21
Notations
407
Diamond
407
Zincblende
408
Wurtzite
408
Heterostructures
423
Summary of kp Parameters
415
References
438
Index
450
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