Lok С. Lew Yan Voon Morten Willatzen. The k-p Method. Electronic Properties of Semiconductors. Springer
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1 Lok С. Lew Yan Voon Morten Willatzen The k-p Method Electronic Properties of Semiconductors Springer
2 Acronyms xxi 1 Introduction What Is к p Theory? Electronic Properties of Semiconductors Other Books 3 Part I Homogeneous Crystals 2 One-Band Model Overview к p Equation Perturbation Theory Canonical Transformation Effective Masses Electron Light Hole Heavy Hole Nonparabolicity Summary 15 3 Perturbation Theory - Valence Band Overview Dresselhaus-Kip-Kittel Model Hamiltonian Eigenvalues L, M, N Parameters Properties Six-Band Model for Diamond Hamiltonian DKKSolution Kane Solution 43 xiii
3 xiv 3.4 Wurtzite Overview Basis States Chuang-Chang Hamiltonian Gutsche-Jahne Hamiltonian Summary 54 4 Perturbation Theory - Kane Models Overview First-Order Models Four-Band Model Eight-Band Model Second-Order Kane Model Löwdin Perturbation Four-Band Model Full-Zone к p Model Band Model Other Models Wurtzite Four-Band: Andreev-O'Reilly Eight-Band: Chuang-Chang Eight-Band: Gutsche-Jahne Summary 77 5 Method of Invariants Overview DKK Hamiltonian - Hybrid Method Formalism Introduction Spatial Symmetries Spinor Representation Valence Band of Diamond No Spin Magnetic Field Spin-Orbit Interaction Six-Band Model for Diamond Spin-Orbit Interaction /t-dependent Part Four-Band Model for Zincblende Eight-Band Model for Zincblende Weiler Hamiltonian Band Model for Zincblende Symmetrized Matrices Invariant Hamiltonian 123
4 xv T Basis Matrices Parameters Wurtzite Six-Band Model Quasi-Cubic Approximation Eight-Band Model Method of Invariants Revisited Zincblende Wurtzite Summary Spin Splitting Overview Dresselhaus Effect in Zincblende Conduction State Valence States Extended Kane Model Sign of Spin-Splitting Coefficients Linear Spin Splittings in Wurtzite Lower Conduction-Band e States А, В, С Valence States Linear Spin Splitting Summary Strain Overview Perturbation Theory Strain Hamiltonian Löwdin Renormalization Valence Band of Diamond DKK Hamiltonian Four-Band Bir-Pikus Hamiltonian Six-Band Hamiltonian Method of Invariants Strained Energies Four-Band Model Six-Band Model Deformation Potentials Eight-Band Model for Zincblende Perturbation Theory Method of Invariants Wurtzite Perturbation Theory Method of Invariants 184
5 xvi Examples Summary 186 Part II Nonperiodic Problem 8 Shallow Impurity States Overview Kittel-Mitchell Theory Exact Theory Wannier Equation Donor States Acceptor States Luttinger-Kohn Theory Simple Bands Degenerate Bands Spin-Orbit Coupling Baldereschi-Lipari Model Hamiltonian Solution Summary Magnetic Effects Overview Canonical Transformation One-Band Model Degenerate Bands Spin-Orbit Coupling Valence-Band Landau Levels Exact Solution General Solution Extended Kane Model Lande g-factor Zincblende Wurtzite Summary Electric Field Overview One-Band Model of Stark Effect Multiband Stark Problem Basis Functions Matrix Elements of the Coordinate Operator Multiband Hamiltonian Explicit Form of Hamiltonian Matrix Contributions
6 xvli 10.4 Summary Excitons Overview Excitonic Hamiltonian One-Band Model of Excitons Multiband Theory of Excitons Formalism Results and Discussions Zincblende Magnetoexciton Summary Heterostructures: Basic Formalism Overview Bastard's Theory Envelope-Function Approximation Solution Example Models General Properties One-Band Models Derivation Burt-Foreman Theory Overview Envelope-Function Expansion Envelope-Function Equation Potential-Energy Term Conventional Results Boundary Conditions Burt-Foreman Hamiltonian Beyond Burt-Foreman Theory? Sercel-Vahala Theory Overview Spherical Representation Cylindrical Representation Four-Band Hamiltonian in Cylindrical Polar Coordinates Wurtzite Structure Arbitrary Nanostructure Orientation Overview Rotation Matrix General Theory [110] Quantum Wires Spurious Solutions Summary 361
7 xviii 13 Heterostructures: Further Topics Overview Spin Splitting Zincblende Superlattices Strain in Heterostructures External Stress Strained Heterostructures Impurity States Donor States Acceptor States Excitons One-Band Model Type-II Excitons Multiband Theory of Excitons Magnetic Problem One-Band Model Multiband Model Static Electric Field Transverse Stark Effect Longitudinal Stark Effect Multiband Theory Conclusion 391 A Quantum Mechanics and Group Theory 393 A.l Löwdin Perturbation Theory 393 A. 1.1 Variational Principle 393 A.1.2 Perturbation Formula 394 A.2 Group Representation Theory 397 A.2.1 Great Orthogonality Theorem 397 A.2.2 Characters 398 A.3 Angular-Momentum Theory 399 A.3.1 Angular Momenta 399 A.3.2 Spherical Tensors 399 A.3.3 Wigner-Eckart Theorem 400 A.3.4 Wigner 3y Symbols 400 В Symmetry Properties 401 B.l Introduction 401 B.2 Zincblende 401 B.2.1 Point Group 402 B.2.2 Irreducible Representations 403 B.3 Diamond 406 B.3.1 Symmetry Operators 406 B.3.2 Irreducible Representations 407
8 xix B.4 Wurtzite 407 B.4.1 Irreducible Representations 410 С Hamiltonians 413 C.l Basis Matrices 413 C.1.1 s = i 413 C.1.2 / = C.1.3 J = \ 413 C.2 \JMj) States 414 C.3 Hamiltonians 414 C.3.1 Notations 416 C.3.2 Diamond 416 C.3.3 Zincblende 416 C.3.4 Wurtzite 416 C.3.5 Heterostructures 416 C.4 Summary ofkp Parameters 416 References 431 Index 443
The k p Method. Electronic Properties of Semiconductors. Bearbeitet von Lok C Lew Yan Voon, Morten Willatzen
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