The K P Method

Electronic Properties of Semiconductors

By: Lok C. Lew Yan Voon, Morten Willatzen

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Hardcover | 23 June 2009

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I ?rst heard of k·p in a course on semiconductor physics taught by my thesis adviser William Paul at Harvard in the fall of 1956. He presented the k·p Hamiltonian as a semiempirical theoretical tool which had become rather useful for the interpre- tion of the cyclotron resonance experiments, as reported by Dresselhaus, Kip and Kittel. This perturbation technique had already been succinctly discussed by Sho- ley in a now almost forgotten 1950 Physical Review publication. In 1958 Harvey Brooks, who had returned to Harvard as Dean of the Division of Engineering and Applied Physics in which I was enrolled, gave a lecture on the capabilities of the k·p technique to predict and ?t non-parabolicities of band extrema in semiconductors. He had just visited the General Electric Labs in Schenectady and had discussed with Evan Kane the latter's recent work on the non-parabolicity of band extrema in semiconductors, in particular InSb. I was very impressed by Dean Brooks's talk as an application of quantum mechanics to current real world problems. During my thesis work I had performed a number of optical measurements which were asking for theoretical interpretation, among them the dependence of effective masses of semiconductors on temperature and carrier concentration. Although my theoretical ability was rather limited, with the help of Paul and Brooks I was able to realize the capabilities of the k·p method for interpreting my data in a simple way.

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You Can Find This Book In

Non-Fiction Engineering & Technology Electronics & Communications Engineering Electronics Engineering Electronic Devices & Materials Semi-Conductors & Super-Conductors Science Physics Materials & States of Matter Condensed Matter Physics including Liquid State & Solid State Physics Technology in General Nanotechnology

Chemistry Physical Chemistry Applied Physics Astrophysics Analytical Chemistry Spectrum Analysis

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Published: 19th October 2010

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Acronyms	p. xxi
Introduction	p. 1
What Is k. p Theory?	p. 1
Electronic Properties of Semiconductors	p. 1
Other Books	p. 3
Homogeneous Crystals
One-Band Model	p. 7
Overview	p. 7
k. p Equation	p. 7
Perturbation Theory	p. 9
Canonical Transformation	p. 9
Effective Masses	p. 12
Electron	p. 12
Light Hole	p. 13
Heavy Hole	p. 14
Nonparabolicity	p. 14
Summary	p. 15
Perturbation Theory - Valence Band	p. 17
Overview	p. 17
Dresselhaus-Kip-Kittel Model	p. 17
Hamiltonian	p. 17
Eigenvalues	p. 21
L, M, N Parameters	p. 22
Properties	p. 30
Six-Band Model for Diamond	p. 32
Hamiltonian	p. 32
DKK Solution	p. 40
Kane Solution	p. 43
Wurtzite	p. 45
Overview	p. 45
Basis States	p. 46
Chuang-Chang Hamiltonian	p. 46
Gutsche-Jahne Hamiltonian	p. 52
Summary	p. 54
Perturbation Theory - Kane Models	p. 55
Overview	p. 55
First-Order Models	p. 55
Four-Band Model	p. 56
Eight-Band Model	p. 57
Second-Order Kane Model	p. 61
Löet;wdin Perturbation	p. 61
Four-Band Model	p. 62
Full-Zone k. p Model	p. 64
15-Band Model	p. 64
Other Models	p. 69
Wurtzite	p. 69
Four-Band: Andrew-O'Reilly	p. 70
Eight-Band: Chuang-Chang	p. 71
Eight-Band: Gutsche-Jahne	p. 71
Summary	p. 77
Method of Invariants	p. 79
Overview	p. 79
DKK Hamiltonian - Hybrid Method	p. 79
Formalism	p. 84
Introduction	p. 84
Spatial Symmetries	p. 84
Spinor Representation	p. 88
Valence Band of Diamond	p. 88
No Spin	p. 89
Magnetic Field	p. 90
Spin-Orbit Interaction	p. 93
Six-Band Model for Diamond	p. 114
Spin-Orbit Interaction	p. 115
k-Dependent Part	p. 115
Four-Band Model for Zincblende	p. 116
Eight-Band Model for Zincblende	p. 117
Weiler Hamiltonian	p. 117
14-Band Model for Zincblende	p. 120
Symmetrized Matrices	p. 121
Invariant Hamiltonian	p. 123
T Basis Matrices	p. 125
Parameters	p. 128
Wurtzite	p. 132
Six-Band Model	p. 132
Quasi-Cubic Approximation	p. 136
Eight-Band Model	p. 137
Method of Invariants Revisited	p. 140
Zincblende	p. 140
Wurtzite	p. 146
Summary	p. 151
Spin Splitting	p. 153
Overview	p. 153
Dresselhaus Effect in Zincblende	p. 154
Conduction State	p. 154
Valence States	p. 154
Extended Kane Model	p. 156
Sign of Spin-Splitting Coefficients	p. 160
Linear Spin Splittings in Wurtzite	p. 161
Lower Conduction-Band e States	p. 163
A, B, C Valence States	p. 164
Linear Spin Splitting	p. 165
Summary	p. 166
Strain	p. 167
Overview	p. 167
Perurbation Theory	p. 167
Strain Hamiltonian	p. 167
Löet;wdin Renormalization	p. 170
Valence Band of Diamond	p. 170
DKK Hamiltonian	p. 171
Four-Band Bir-Pikus Hamiltonian	p. 171
Six-Band Hamiltonian	p. 172
Method of Invariants	p. 174
Strained Energies	p. 177
Four-Band Model	p. 177
Six-Band Model	p. 179
Deformation Potentials	p. 179
Eight-Band Model for Zincblende	p. 180
Perturbation Theory	p. 181
Method of Invariants	p. 182
Wurtzite	p. 183
Perturbation Theory	p. 183
Method of Invariants	p. 184
Examples	p. 186
Summary	p. 186
Nonperiodic Problem
Shallow Impurity States	p. 189
Overview	p. 189
Kittel-Mitchell Theory	p. 190
Exact Theory	p. 191
Wannier Equation	p. 193
Donor States	p. 194
Acceptor States	p. 197
Luttinger-Kohn Theory	p. 198
Simple Bands	p. 199
Degenerate Bands	p. 210
Spin-Orbit Coupling	p. 213
Baldereschi-Lipari Model	p. 214
Hamiltonian	p. 216
Solution	p. 217
Summary	p. 219
Magnetic Effects	p. 221
Overview	p. 221
Canonical Transformation	p. 222
One-Band Model	p. 222
Degenerate Bands	p. 230
Spin-Orbit Coupling	p. 232
Valence-Band Landau Levels	p. 235
Exact Solution	p. 235
General Solution	p. 239
Extended Kane Model	p. 240
Landé g-Factor	p. 240
Zincblende	p. 241
Wurtzite	p. 243
Summary	p. 244
Electric Field	p. 245
Overview	p. 245
One-Band Model of Stark Effect	p. 245
Multiband Stark Problem	p. 246
Basis Functions	p. 246
Matrix Elements of the Coordinate Operator	p. 248
Multiband Hamiltonian	p. 249
Explicit Form of Hamiltonian Matrix Contributions	p. 253
Summary	p. 255
Excitons	p. 257
Overview	p. 257
Excitonic Hamiltonian	p. 258
One-Band Model of Excitons	p. 259
Multiband Theory of Excitons	p. 261
Formalism	p. 261
Results and Discussions	p. 266
Zincblende	p. 267
Magnetoexciton	p. 268
Summary	p. 270
Heterostructures: Basic Formalism	p. 273
Overview	p. 273
Bastard's Theory	p. 274
Envelope-Function Approximation	p. 274
Solution	p. 276
Example Models	p. 277
General Properties	p. 279
One-Band Models	p. 280
Derivation	p. 280
Burt-Foreman Theory	p. 282
Overview	p. 283
Envelope-Function Expansion	p. 283
Envelope-Function Equation	p. 287
Potential-Energy Term	p. 294
Conventional Results	p. 299
Boundary Conditions	p. 305
Burt-Foreman Hamiltonian	p. 306
Beyond Burt-Foreman Theory?	p. 316
Sercel-Vahala Theory	p. 318
Overview	p. 318
Spherical Representation	p. 319
Cylindrical Representation	p. 324
Four-Band Hamiltonian in Cylindrical Polar Coordinates	p. 329
Wurtzite Structure	p. 336
Arbitrary Nanostructure Orientation	p. 350
Overview	p. 350
Rotation Matrix	p. 350
General Theory	p. 352
[1&1bar;0] Quantum Wires	p. 353
Spurious Solutions	p. 360
Summary	p. 361
Heterostructures: Further Topics	p. 363
Overview	p. 363
Spin Splitting	p. 363
Zincblende Superlattices	p. 363
Strain in Heterostructures	p. 367
External Stress	p. 367
Strained Heterostructures	p. 369
Impurity States	p. 371
Donor States	p. 371
Acceptor States	p. 372
Excitons	p. 373
One-Band Model	p. 373
Type-II Excitons	p. 376
Multiband Theory of Excitons	p. 377
Magnetic Problem	p. 378
One-Band Model	p. 379
Multiband Model	p. 382
Static Electric Field	p. 384
Transverse Stark Effect	p. 384
Longitudinal Stark Effect	p. 386
Multiband Theory	p. 388
Conclusion	p. 391
Quantum Mechanics and Group Theory	p. 393
Löet;wdin Perturbation Theory	p. 393
Variational Principle	p. 393
Perturbation Formula	p. 394
Group Representation Theory	p. 397
Great Orthogonality Theorem	p. 397
Characters	p. 398
Angular-Momentum Theory	p. 399
Angular Momenta	p. 399
Spherical Tensors	p. 399
Wigner-Eckart Theorem	p. 400
Wigner 3j Symbols	p. 400
Symmetry Properties	p. 401
Introduction	p. 401
Zincblende	p. 401
Point Group	p. 402
Irreducible Representations	p. 403
Diamond	p. 406
Symmetry Operators	p. 406
Irreducible Representations	p. 407
Wurtzite	p. 407
Irreducible Representations	p. 410
Hamiltonians	p. 413
Basis Matrices	p. 413
s = 1/2	p. 413
l = 1	p. 413
J = 3/2	p. 413
JM_J> States	p. 414
Hamiltonians	p. 414
Notations	p. 416
Diamond	p. 416
Zincblende	p. 416
Wurtzite	p. 416
Heterostructures	p. 416
Summary of k. p Parameters	p. 416
References	p. 431
Index	p. 443
Table of Contents provided by Ingram. All Rights Reserved.

The K P Method

Electronic Properties of Semiconductors

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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Paperback

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