Syllabus
1. Crystal Structure
1.1 Periodic Array of Atoms. 1.1.1 Lattice Translation Vectors. 1.1.2 Primitive Lattice Cell. 1.2 Fundamental Types of Lattices. 1.2.1 Two-Dimensional Lattice Types. 1.2.2 Three-Dimensional Lattice Types. 1.2.3 Index Systems for Crystal Planes and Directions. 1.3 Simple Crystal Structures. 1.3.1 Sodium Chloride Structures. 1.3.2 Cesium Chloride Structures. 1.3.3 Diamond Structure. 1.3.4 Zinc Blende Structure. 1.4 Problems.
2. Reciprocal Lattice
2.1 The Bragg Diffraction Law. 2.2 Reciprocal Lattice. 2.2.1 Fourier Analysis of Scattered Wave. 2.2.2 Reciprocal Lattice Vectors. 2.2.3 Diffraction Conditions. 2.2.4 Laue Equations. 2.3 Brillouin Zones. 2.3.1 Reciprocal Lattice to Cubic Lattice. 2.3.2 Reciprocal Lattice to Face-Centered Cubic Lattice. 2.3.3 Reciprocal Lattice to Body-Centered Cubic Lattice. 2.4 Fourier Analysis of the Basis. 2.4.1 Structure Factor of Body-Centered Cubic Lattice. 2.4.2 Structure Factor of Face-Centered Cubic Lattice. 2.4.3 Atomic Form Factor. 2.5 Problems.
3. Band Structures
3.1 Introduction. 3.2 Free Electron Fermi Gas. 3.2.1 Single Electron Model. 3.2.2 Fermi Sphere. 3.2.3 Density of States. 3.2.4 Fermi Distribution 3.3 Non-Interacting Electrons in a Periodic Potential. 3.3.1 Definition of Periodic Potential. 3.3.2 Bloch Theorem. 3.3.3 Band Index. 3.3.4 Fermi Surface. 3.3.5 Kronig-Penney Model. 3.3.6 Energy Bands in 1D lattice. 3.4 Nearly Free Electrons in a Weak Periodic Potential. 3.4.1 General Approach to Schrodinger Equation. 3.4.2 Energy Levels near a single Bragg Plane. 3.4.3 Energy Bands in a 1D lattice. 3.5 Tight-Binding Model. 3.5.1 General Approach. 3.5.2 Energy Bands in a 1D Lattice. 3.6 Energy Bands in Three Dimensions. 3.6.1 Introduction. 3.6.2 High Symmetry Points. 3.6.3 Energy Bands in a Cubic Lattice. 3.6.4 Energy Bands in a Body-Centered Cubic Lattice. 3.6.5 Energy Bands in a Face-Centered Cubic Lattice. 3.7 Orthogonalized Plane-Wave. 3.8 Pseudopotential.
4. Boltzmann’s Transport Equation
4.1 Introduction. 4.2 The Electron Distribution Function. 4.2.1 Equation of Motion. 4.2.2 Steady-state Transport. 4.2.3 Relaxation Time Approximation. 4.3 Electrical and Thermal Transport. 4.3.1 Isothermal Electrical Conductivity. 4.3.2 Thermo-electric Transport. 4.3.3 Thermal Conductivity. 4.4 Drift-Diffusion Model. 4.4.1. Diffusion Equation. 4.4.2. Continuity Equation. 4.4.3. Poisson Equation. 4.5 Solution of Finite Element Equations. 4.5.1 Introduction to Finite Element Method. 4.5.2 Discretization of the Domain. 4.5.3 Application of Finite Element Method: a Simple Example. 4.5.4 Physical Limitations on Numerical Drift-Diffusion Schemes.
SLIDES
1. CRYSTAL STRUCTURE
2. RECIPROCAL LATTICE
3. BAND STRUCTURES
4. BOLTZMANN’S TRANSPORT EQUATION
TEXTBOOKS
N. W. Ashcroft and N. D. Mermin – Solid State Physics, Cencage.
C. Kittel – Introduction To Solid State Physics, John Wiley & Sons Inc.