The Oxford Solid State Basics
Kaup valmöguleikar
The study of solids is one of the richest, most exciting, and most successful branches of physics. While the subject of solid state physics is often viewed as dry and tedious this new book presents the topic instead as an exciting exposition of fundamental principles and great intellectual breakthroughs. Beginning with a discussion of how the study of heat capacity of solids ushered in the quantum revolution, the author presents the key ideas of the field while emphasizing the deep underlying concepts.
The book begins with a discussion of the Einstein/Debye model of specific heat, and the Drude/Sommerfeld theories of electrons in solids, which can all be understood without reference to any underlying crystal structure. The failures of these theories force a more serious investigation of microscopics. Many of the key ideas about waves in solids are then introduced using one dimensional models in order to convey concepts without getting bogged down with details.
Only then does the book turn to consider real materials. Chemical bonding is introduced and then atoms can be bonded together to crystal structures and reciprocal space results. Diffraction experiments, as the central application of these ideas, are discussed in great detail. From there, the connection is made to electron wave diffraction in solids and how it results in electronic band structure. The natural culmination of this thread is the triumph of semiconductor physics and devices.
The final section of the book considers magnetism in order to discuss a range of deeper concepts. The failures of band theory due to electron interaction, spontaneous magnetic orders, and mean field theories are presented well. Finally, the book gives a brief exposition of the Hubbard model that undergraduates can understand. The book presents all of this material in a clear fashion, dense with explanatory or just plain entertaining footnotes.
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- Oxford University Press Academic UK
- 9780191502101
- 9780199680771
- Page Fidelity (PDF)
- 0
- Steven H. Simon
- English
- 2013-06-21
- 100
Kaflar
- The Oxford Solid State Basics
- Copyright
- Preface to the 2019 Reprint
- Preface to the 2016 Reprint
- Preface after Teaching this Course
- Preface
- About this Book
- Acknowledgments
- Contents
- 1. About Condensed Matter Physics
- 1.1 What Is Condensed Matter Physics
- 1.2 Why Do We Study Condensed Matter Physics?
- 1.3 Why Solid State Physics?
- Part I. Physics of Solids without Considering Microscopic Structure: The Early Days of Solid State
- 2. Specific Heat of Solids: Boltzmann, Einstein, and Debye
- 2.1 Einstein’s Calculation
- 2.2 Debye’s Calculation
- 2.2.1 Periodic (Born–von Karman) Boundary Conditions
- 2.2.2 Debye’s Calculation Following Planck
- 2.2.3 Debye’s “Interpolation”
- 2.2.4 Some Shortcomings of the Debye Theory
- Chapter Summary
- References
- 2.3 Appendix to this Chapter: ζ(4)
- Exercises
- 3. Electrons in Metals: Drude Theory
- 3.1 Electrons in Fields
- 3.1.1 Electrons in an Electric Field
- 3.1.2 Electrons in Electric and Magnetic Fields
- 3.2 Thermal Transport
- Chapter Summary
- References
- Exercises
- 4. More Electrons in Metals: Sommerfeld (Free Electron) Theory
- 4.1 Basic Fermi–Dirac Statistics
- 4.2 Electronic Heat Capacity
- 4.3 Magnetic Spin Susceptibility (Pauli Paramagnetism)
- 4.4 Why Drude Theory Works So Well
- 4.5 Shortcomings of the Free Electron Model
- Chapter Summary
- References
- Exercises
- Part II. Structure of Materials
- 5. The Periodic Table
- 5.1 Chemistry, Atoms, and the Schroedinger Equation
- 5.2 Structure of the Periodic Table
- 5.3 Periodic Trends
- 5.3.1 Effective Nuclear Charge
- Chapter Summary
- References
- Exercises
- 6. What Holds Solids Together: Chemical Bonding
- 6.1 Ionic Bonds
- 6.2 Covalent Bond
- 6.2.1 Particle in a Box Picture
- 6.2.2 Molecular Orbital or Tight Binding Theory
- 6.3 Van der Waals, Fluctuating Dipole Forces, or Molecular Bonding
- 6.4 Metallic Bonding
- 6.5 Hydrogen Bonds
- Chapter Summary (Table)
- References on Chemical Bonding
- Exercises
- 7. Types of Matter
- References
- Part III. Toy Models of Solids in One Dimension
- 8. One-Dimensional Model of Compressibility, Sound, and Thermal Expansion
- Compressibility (or Elasticity)
- Sound
- Thermal Expansion
- Chapter Summary
- References
- Exercises
- 9. Vibrations of a One-Dimensional Monatomic Chain
- 9.1 First Exposure to the Reciprocal Lattice
- Aliasing:
- 9.2 Properties of the Dispersion of the One-Dimensional Chain
- Sound Waves:
- Counting Normal Modes:
- 9.3 Quantum Modes: Phonons
- 9.4 Crystal Momentum
- Chapter Summary
- References
- Exercises
- 10. Vibrations of a One-Dimensional Diatomic Chain
- 10.1 Diatomic Crystal Structure: Some Useful Definitions
- 10.2 Normal Modes of the Diatomic Solid
- Chapter summary
- References
- Exercises
- 11. Tight Binding Chain (Interlude and Preview)
- 11.1 Tight Binding Model in One Dimension
- 11.2 Solution of the Tight Binding Chain
- 11.3 Introduction to Electrons Filling Bands
- 11.4 Multiple Bands
- Chapter Summary
- References
- Exercises
- Part IV. Geometry of Solids
- 12. Crystal Structure
- 12.1 Lattices and Unit Cells
- 12.2 Lattices in Three Dimensions
- 12.2.1 The Body-Centered Cubic (bcc) Lattice
- 12.2.2 The Face-Centered Cubic (fcc) Lattice
- 12.2.3 Sphere Packing
- 12.2.4 Other Lattices in Three Dimensions
- 12.2.5 Some Real Crystals
- Chapter summary
- References
- Exercises
- 13. Reciprocal Lattice, Brillouin Zone, Waves in Crystals
- 13.1 The Reciprocal Lattice in Three Dimensions
- 13.1.1 Review of One Dimension
- 13.1.2 Reciprocal Lattice Definition
- 13.1.3 The Reciprocal Lattice as a Fourier Transform
- 13.1.4 Reciprocal Lattice Points as Families of Lattice Planes
- 13.1.5 Lattice Planes and Miller Indices
- 13.2 Brillouin Zones
- 13.2.1 Review of One-Dimensional Dispersions and Brillouin Zones
- 13.2.2 General Brillouin Zone Construction
- 13.3 Electronic and Vibrational Waves in Crystals in Three Dimensions
- Chapter Summary
- References
- Exercises
- Part V. Neutron and X-Ray Diffraction
- 14. Wave Scattering by Crystals
- 14.1 The Laue and Bragg Conditions
- 14.1.1 Fermi’s Golden Rule Approach
- 14.1.2 Diffraction Approach
- 14.1.3 Equivalence of Laue and Bragg conditions
- 4.2 Scattering Amplitudes
- Neutrons
- X-rays
- Comparison of Neutrons and X-rays
- Electron Diffraction is Similar!
- 14.2.1 Simple Example
- 14.2.2 Systematic Absences and More Examples
- 14.2.3 Geometric Interpretation of Selection Rules
- 14.3 Methods of Scattering Experiments
- 14.3.1 Advanced Methods
- Laue Method
- Rotating Crystal Method
- 14.3.2 Powder Diffraction
- A Fully Worked Example
- 14.4 Still More About Scattering
- 14.4.1 Variant: Scattering in Liquids and Amorphous Solids
- 14.4.2 Variant: Inelastic Scattering
- 14.4.3 Experimental Apparatus
- Chapter Summary
- References
- Exercises
- Part VI. Electrons in Solids
- 15. Electrons in a Periodic Potential
- 15.1 Nearly Free Electron Model
- 15.1.1 Degenerate Perturbation Theory
- Simple Case: k Exactly at the Zone Boundary
- In One Dimension
- k Not Quite on a Zone Boundary (Still in One Dimension)
- Nearly Free Electrons in Two and Three Dimensions
- 15.2 Bloch’s Theorem
- Chapter Summary
- References
- Exercises
- 16. Insulator, Semiconductor, or Metal
- 16.1 Energy Bands in One Dimension
- 16.2 Energy Bands in Two and Three Dimensions
- 16.3 Tight Binding
- 16.4 Failures of the Band-Structure Picture of Metals and Insulators
- Magnets
- Mott Insulators
- 16.5 Band Structure and Optical Properties
- 16.5.1 Optical Properties of Insulators and Semiconductors
- 16.5.2 Direct and Indirect Transitions
- 16.5.3 Optical Properties of Metals
- 16.5.4 Optical Effects of Impurities
- Chapter Summary
- References
- Exercises
- 17. Semiconductor Physics
- 17.1 Electrons and Holes
- Effective Mass of Electrons
- Effective Mass of Holes
- The momentum and velocity of a hole
- Effective Mass and Equations of Motion
- 17.1.1 Drude Transport: Redux
- 17.2 Adding Electrons or Holes with Impurities: Doping
- 17.2.1 Impurity States
- Optical Effects of Impurities (Redux)
- 17.3 Statistical Mechanics of Semiconductors
- Law of Mass Action
- Intrinsic Semiconductors
- Doped Semiconductors
- Chapter Summary
- References
- Exercises
- 18. Semiconductor Devices
- 18.1 Band Structure Engineering
- 18.1.1 Designing Band Gaps
- 18.1.2 Non-Homogeneous Band Gaps
- Modulation Doping and the Two-Dimensional Electron Gas
- 18.2 p-n Junction
- The Solar Cell
- Rectification: The Diode
- Light Emitting Diode
- 18.3 The Transistor
- Chapter Summary
- References
- Exercises
- Part VII. Magnetism and Mean Field Theories
- 19. Magnetic Properties of Atoms: Para- and Dia-Magnetism
- 19.1 Basic Definitions of Types of Magnetism
- 19.2 Atomic Physics: Hund’s Rules
- 19.2.1 Why Moments Align
- Naive Argument
- More Correct
- Exchange Energy
- Magnetic Interactions in Molecules and Solids
- 19.3 Coupling of Electrons in Atoms to an External Field
- 19.4 Free Spin (Curie or Langevin) Paramagnetism
- 19.5 Larmor Diamagnetism
- 19.6 Atoms in Solids
- 19.6.1 Pauli Paramagnetism in Metals
- 19.6.2 Diamagnetism in Solids
- 19.6.3 Curie Paramagnetism in Solids
- Where to find free spins?
- Modifications of Free Spin Picture
- Chapter Summary
- References
- Exercises
- 20. Spontaneous Magnetic Order: Ferro-, Antiferro-, and Ferri-Magnetism
- 20.1 (Spontaneous) Magnetic Order
- 20.1.1 Ferromagnets
- 20.1.2 Antiferromagnets
- Detecting Antiferromagnetism with Diffraction
- Frustrated Antiferromagnets
- 20.1.3 Ferrimagnets
- 20.2 Breaking Symmetry
- 20.2.1 Ising Model
- Chapter Summary
- References
- Exercises
- 21. Domains and Hysteresis
- 21.1 Macroscopic Effects in Ferromagnets: Domains
- 21.1.1 Domain Wall Structure and the Bloch/N´eel Wall
- 21.2 Hysteresis in Ferromagnets
- 21.2.1 Disorder Pinning
- 21.2.2 Single-Domain Crystallites
- 21.2.3 Domain Pinning and Hysteresis
- Chapter Summary
- References
- Exercises
- 22. Mean Field Theory
- 22.1 Mean Field Equations for the Ferromagnetic Ising Model
- 22.2 Solution of Self-Consistency Equation
- 22.2.1 Paramagnetic Susceptibility
- 22.2.2 Further Thoughts
- Chapter Summary
- References on Mean Field Theory
- Exercises
- 23. Magnetism from Interactions: The Hubbard Model
- 23.1 Itinerant Ferromagnetism
- 23.1.1 Hubbard Ferromagnetism Mean Field Theory
- 23.1.2 Stoner Criterion
- 23.2 Mott Antiferromagnetism
- Chapter Summary
- References on Hubbard Model
- 23.3 Appendix: Hubbard Model for the Hydrogen Molecule
- Exercises
- A. Sample Exam and Solutions
- EXAM
- SOLUTIONS
- B. List of Other Good Books
- Indices
- Index of People
- Index of Topics