Solid state physics, the study and prediction of the fundamental physical properties of materials, forms the backbone of modern materials science and has many technological applications. The unique feature of this text is the MATLAB(R)-based computational approach with several numerical techniques and simulation methods included. This is highly effective in addressing the need for visualization and a direct hands-on approach in learning the theoretical concepts of solid state physics. The code is freely available to all textbook users.
Additional Features:
Uses the pedagogical tools of computational physics that have become important in enhancing physics teaching of advanced subjects such as solid state physics Adds visualization and simulation to the subject in a way that enables students to participate actively in a hand-on approach Covers the basic concepts of solid state physics and provides students with a deeper understanding of the subject matter Provides unique example exercises throughout the text Obtains mathematical analytical solutions Carries out illustrations of important formulae results using programming scripts that students can run on their own and reproduce graphs and/or simulations Helps students visualize solid state processes and apply certain numerical techniques using MATLAB(R), making the process of learning solid state physics much more effective Reinforces the examples discussed within the chapters through the use of end-of-chapter exercises Includes simple analytical and numerical examples to more challenging ones, as well as computational problems with the opportunity to run codes, create new ones, or modify existing ones to solve problems or reproduce certain results
Author(s): Javier E. Hasbun; Trinanjan Datta
Publisher: CRC Press
Year: 2020
Language: English
Pages: xx+550
Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Authors
Acknowledgments
1. Introduction
1.1 What Is Solid State Physics?
1.2 Crystal Structure Basics
1.2.1 The Lattice and the Basis
1.2.2 The Lattice Translation Vector
1.2.3 Primitive Translation Vectors
1.2.4 More on the Basis and the Crystal Structure
1.2.5 Primitive Cell
1.2.6 The Wigner-Seitz Cell
1.3 Basic Lattice Types
1.3.1 Crystal to Cartesian Coordinates
1.4 Properties of the Cubics
1.4.1 The Simple Cubic
1.4.2 The Body-Centered Cubic
1.4.3 The Face-Centered Cubic
1.5 Indexing of Crystal Planes (Miller Indices)
1.6 Examples of Crystal Structures
1.6.1 Sodium Chloride (Salt)
1.6.2 Cesium Chloride
1.6.3 Close-Packed: Hexagonal and Cubic
1.6.4 Diamond
1.6.5 Zinc-Sulfide or Zinc-Blende
1.7 Atomic Surface Microscopes
1.8 Element Properties Table
1.9 Chapter 1 Exercises
2. The Reciprocal Lattice
2.1 Introduction
2.2 Bragg’s Law
2.3 Reciprocal Lattice Vectors
2.3.1 Electron Concentration and Reciprocal Lattice Vectors in 1-D
2.3.2 Electron Concentration and Reciprocal Lattice Vectors in 3-D
2.4 Revisiting Bragg’s Law
2.4.1 G and its Perpendicularity to the (hkl) Plane
2.4.2 X-Ray Scattering Intensity from Crystals
2.4.3 Laue Equations
2.4.4 Scattering Intensity Calculation
2.5 Brillouin Zones
2.5.1 The Ewald Sphere
2.5.2 The First Brillouin Zone
2.5.3 Simple Cubic Reciprocal Lattice Vectors and BZ
2.5.4 Body Centered Cubic Reciprocal Lattice Vectors and BZ
2.5.5 Face Centered Cubic Reciprocal Lattice Vectors and BZ
2.6 Chapter 2 Exercises
3. Crystal Binding
3.1 Introduction
3.2 Inert Gas Solids
3.2.1 van der Walls Interaction
3.2.2 Lennard-Jones Potential
3.2.3 Lennard-Jones Potential for Crystals
3.3 Ionic Crystals
3.3.1 Ionic Crystal Potential and Madelung Energy
3.4 Covalent Bonding
3.4.1 The Molecular Hydrogen Ion (H+2 ) - An Analytical Calculation
3.4.2 The Hydrogen Molecule (H2) - A Numeric Calculation
3.4.3 Semiconductors
3.5 Metals
3.6 Chapter 3 Exercises
4. Lattice Vibrations
4.1 Introduction
4.2 Phonons: One Atom Per Primitive Cell (Linear Chain I)
4.2.1 Linear Chain of N+1 Atoms Simulation
4.2.2 Phase and Group Velocities
4.3 Phonons: Two Atoms Per Primitive Cell (Linear Chain II)
4.4 Phonon Momentum
4.5 Phonon Heat Capacity
4.5.1 Normal Mode Enumeration - Density of States
4.5.2 Debye Theory
4.5.3 Debye T3 Law
4.5.4 The Einstein Model
4.6 General Density of States
4.7 Thermal Expansion
4.8 Thermal Conductivity
4.9 Chapter 4 Exercises
5. Free Electron Gas
5.1 Introduction
5.2 Free One-Dimensional Electron Gas
5.3 The Fermi-Dirac Distribution
5.4 Free Three-Dimensional Electron Gas
5.5 Electron Gas Heat Capacity
5.6 Electrical Conductivity (Drude Model)
5.7 Electronic Motion in Magnetic Fields and the Classical Hall Effect
5.8 The Quantum Hall Effect
5.9 Electronic Thermal Conductivity of Metals
5.10 Chapter 5 Exercises
6. Introduction to Electronic Energy Bands
6.1 Introduction
6.2 Nearly Free Electron Model - Gaps at the Brillouin Zone Boundaries
6.3 Bloch Functions
6.4 The Kronig-Penney Model
6.5 Electron in a General Periodic Potential - the Central Equation
6.6 Empty Lattice Approximation
6.7 Solution of the Central Equation
6.8 Counting Band Orbitals
6.9 Chapter 6 Exercises
7. Semiconductor Crystal Properties
7.1 Introduction
7.1.1 Band Gap Significance
7.2 Electron and Hole Motion under Electromagnetic Fields
7.3 Electron and Hole Effective Masses
7.3.1 Effective Masses for Various Semiconductors
7.4 Intrinsic Carrier Concentration
7.4.1 Intrinsic Carrier Mobility
7.5 Impurities in Semiconductors
7.5.1 Impurity States and Conductivity
7.6 Extrinsic Carrier Concentration
7.6.1 Ohmic Contacts
7.7 Chapter 7 Exercises
8. Simple Band Structure Calculations
8.1 Introduction
8.2 The Single Band Tight Binding Model
8.2.1 The Simple Cubic (SC)
8.2.2 The Body Centered Cubic
8.2.3 The Face Centered Cubic
8.3 The Density of States and the Fermi Surface
8.3.1 The Simple Cubic Fermi Surface
8.3.2 The Body Centered Cubic Fermi Surface
8.3.3 The Face Centered Cubic Fermi Surface
8.4 Green’s Function and the Density of States
8.5 The Site Green’s Function
8.6 Density of States for the Cubics
8.6.1 The Simple Cubic Density of States
8.6.2 The Body Centered Cubic Density of States
8.6.3 The Face Centered Cubic Density of States
8.7 Simple Tight Binding Semiconductor Multiband Structures
8.7.1 The Band Structure
8.7.2 The Density of States
8.8 Chapter 8 Exercises
Appendix A: Singular Function Integration Using SingInt.m
Appendix B: Romberg Integration (rombergInt.m) and the Interpolating Function (interpFunc.m)
Appendix C: The Ray Method For K-Space Density of States Integration (TTareas.m)
Appendix D: Supporting Functions for Semiconductor Band Structures
9. Impurities and Disordered Systems
9.1 Introduction
9.2 The Single Impurity Level
9.3 Repeated Integrations Over 3-dimensional k-space - An Efficient Way
9.4 The Single Impurity Level Calculation
9.5 The Coherent Potential Approximation (CPA) for Disordered Systems
9.6 The Coherent Potential Calculation
9.7 An Insight into an Effective Medium
9.8 Chapter 9 Exercises
10. Magnetism I
10.1 Introduction
10.2 Bohr Magneton
10.3 Magnetization, Susceptibility, and Hysteresis
10.3.1 Magnetization and Susceptibility
10.3.2 Hysteresis
10.3.3 Stoner-Wohlfarth Model of Hysteresis
10.4 Diamagnetism
10.5 Paramagnetism
10.5.1 Langevin Theory of Paramagnetism
10.5.2 Curie-Weiss Law
10.6 Magnetocaloric Effect
10.7 Ferromagnetism
10.7.1 Mean Field Theory of Ising Model
10.7.2 Monte Carlo Simulation of Ising Model
10.8 Bohr-van Leeuwen Theorem
10.9 Chapter 10 Exercises
11. Magnetism II
11.1 Introduction
11.2 The Building Blocks of Atomic Magnetism
11.2.1 Spin, Orbital, and Total Angular Momentum
11.2.2 Atomic Orbitals
11.3 Spin-orbit Interaction
11.4 Ground State of an Ion: Hund’s Rules
11.5 Crystal Field Theory
11.6 Diamagnetism
11.7 Quantum Theory of Paramagnetism
11.7.1 S=12
11.7.2 General J Value
11.8 Exchange Interaction
11.9 Magnetic Resonance
11.10 Pauli Paramagnetism
11.11 Chapter 11 Exercises
12. Superconductivity
12.1 Introduction
12.2 Basic Properties of a Superconductor
12.3 Zero Electrical Resistance
12.4 Persistent Current
12.5 Meissner Effect
12.6 London Equation
12.7 Thermodynamics of Superconductors
12.8 Type I and Type II Superconductors
12.9 Vortices in Superconductors
12.10 Technological and Scientific Applications of Superconducting Materials
12.11 Chapter 12 Exercises
13. Optical Properties of Solids
13.1 Introduction
13.2 Basic Concepts in Electrodynamics
13.3 Complex Refractive Index and the Dielectric Constant
13.4 The Free Electron Drude Theory of Optical Properties
13.5 The Drude–Lorentz Dipole Oscillator Theory of Optical Properties
13.6 Optical Behavior of Glass, Metals, and Semiconductors
13.7 Optical Spectroscopy
13.8 Kramers-Kronig Relationship
13.9 Chapter 13 Exercises
14. Transport Properties of Solids
14.1 Introduction
14.2 The Boltzmann Transport Equation
14.3 Relaxation Time Approximation and Drude Conductivity
14.4 Boltzmann Equation in Electric Field and Temperature Gradients
14.5 Drift and Diffusion Current
14.6 Thermal Conductivity of Metals
14.7 Thermoelectric Phenomena
14.7.1 Seebeck Effect and Thermoelectric Power
14.7.2 Thomson Effect
14.7.3 Peltier Effect
14.7.4 Thermoelectric Figure of Merit, Z
14.8 Landauer Theory of Transport
14.9 Chapter 14 Exercises
Appendix A: Matlab Tutorial
A.1 Introduction
A.2 Tutorial Notation
A.3 General Features
A.4 Operands
A.5 M-Files and Functions
A.6 Built-in Functions
A.7 Plotting
A.8 Programming
A.9 Zeros of Functions
A.10 Numerical Integration
A.11 Differential Equations
A.12 Movies
A.13 Publish Code to HTML
A.14 Symbolic Operations
A.15 Toolboxes
A.16 MATLAB Websites, other Tutorials, and Clones
Appendix B: Distribution Functions
B.1 The Boltzmann Distribution Function
B.2 The Fermi-Dirac Distribution Function
B.3 The Bose-Einstein Distribution Function
Bibliography
Index
