1 Energy Band Structures of Semiconductors . . . . . . . . . . . . . . . 1
1.1 Free-Electron Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Bloch Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Nearly Free Electron Approximation . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Reduced Zone Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Free{Electron Bands (Empty{Lattice Bands) . . . . . . . . . . . . . . 9 1.5.1 First Brillouin Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5.2 Reciprocal Lattice Vectors of fcc Crystal . . . . . . . . . . . . 11
1.5.3 Free Electron Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.6 Pseudopotential Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.6.1 Local Pseudopotential Theo
ry . . . . . . . . . . . . . . . . . . . . . 15 1.6.2 Pseudopotential Form Factors . . . . . . . . . . . . . . . . . . . . . . 19
1.6.3 Nonlocal Pseudopotential Theory . . . . . . . . . . . . . . . . . . . 21
1.6.4 Energy Band Calculation by Local Pseudopotential
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.6.5 Spin{Orbit Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.6.6 Energy Band Calculations by Nonlocal
Pseudopotential Method with Spin{orbit
Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.7 k _ p Perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.7.1 k _ p Hamiltonian. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.7.2 Derivation of the
k _ p Parameters . . . . . . . . . . . . . . . . . . 40 1.7.3 15{band k _ p Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
1.7.4 Antisymmetric Potentials for Zinc Blende Crystals . . . 50
1.7.5 Spin{orbit Interaction Hamiltonian . . . . . . . . . . . . . . . . 51
1.7.6 30{band k _ p Method with the Spin{Orbit Interaction 53
1.8 Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2 Cyclotron Resonance and Energy Band Structures . . . . . . . 61
2.1 Cyclotron Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.2 Analysis of Valence Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
IX
X Contents
2.3 Spin{Orbit Interaction . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 74 2.4 Non-parabolicity of the Conduction Band. . . . . . . . . . . . . . . . . . 81
2.5 Electron Motion in a Magnetic Field and Landau Levels . . . . . 85
2.5.1 Landau Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.5.2 Density of States and Inter Landau Level Transition . . 90
2.5.3 Landau Levels of a Non-parabolic Band . . . . . . . . . . . . . 92 2.5.4 Landau Levels of the Valence Bands . . . . . . . . . . . . . . . . 96
2.5.5 Magneto{optical Absorption . . . . . . . . . . . . . . . . . . . . . . . 101
2.6 Luttinger Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 2.7 Luttinger Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3 Wannier Function and Effective Mass Approximation . . . . . 115
3.1 Wannier Function . . . . . . . . . . . . .
About the Author: Chihiro Hamaguchi graduated from Electrical Engineering (BS) in 1961, and MS Degree in 1963, and Graduate School of Engineering with Ph.D. Degree 1n 1966, all from Osaka University. He served as a research associate of Engineering Science in 1966, and an associate professor of Electronic Engineering in 1967, of Osaka University. He was a visiting research associate of Physics Department of Purdue University (USA), from 1967 to 1969. He was appointed full professor of Electronic Engineering Department of Osaka University in 1985 and retired in 2001, awarded Professor Emeritus. He was employed as an advisory board member of Sharp Corporation form 2001 till 2014, and also a visiting professor of Kochi University of Technology from 2001 till now. His major field of research is hot carrier transport, magnetotransport, modulation spectroscopy of quantum structures, and quantum transport in heterostructures, energy band calculations of superlattices and nitrides, publishing more than 350 papers. He was elected as 1990: Fellow of the American Physical Society (1990), Fellow of the Institute of Electrical and Electronics Engineers (IEEE) (1992), Fellow of the Institute of Physics, U.K .(1999), and Fellow of the Japan Society of Applied Physics (2008). He received the Award of Gold Rays with Neck Ribbon" (Zuiho-Chuju Shou in Japanese) from Japanese Government and the Emeror in 2016. He published several text books in Japanese, such as Introduction to Electronics and Physics of Materials, Semiconductor Devisce Physics, and Electromagnetic Theory (to be published).
He is a Fellow of American Physical Soviety, Instutute of Physics (U.K.), Institute of Electrical and Electronics Engineers (IEEE, U.S.A), and Japan Society of Applied Physics. He received the Award of Gold Rays with Neck Ribbon" (Zuiho-Chuju Shou in Japanese) in 2016.
