Y Galperin - Introduction to Modern Solid State Physics.pdf

Introduction to Modern
Solid State Physics
Yuri M. Galperin
FYS 448
Department of Physics, . Box 1048 Blindern, 0316 Oslo, Room 427A
Phone: +47 22 85 64 95, E-mail:
Contents
I Basic concepts 1
1 Geometry of Lattices ... 3
Periodicity: Crystal Structures . . . . . . . . . . . . . . . . . . . . . . . . . 3
The Reciprocal Lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
X-Ray Diffraction in Periodic Structures . . . . . . . . . . . . . . . . . . . 10
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Lattice Vibrations: Phonons 21
Interactions Between Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Lattice Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Quantum Mechanics of Atomic Vibrations . . . . . . . . . . . . . . . . . . 38
Phonon Dispersion Measurement . . . . . . . . . . . . . . . . . . . . . . . 43
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 Electrons in a Lattice. 45
Electron in a Periodic Field . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Electron in a Periodic Potential . . . . . . . . . . . . . . . . . . . . 46
Tight Binding Approximation . . . . . . . . . . . . . . . . . . . . . . . . . 47
The Model of Near Free Electrons . . . . . . . . . . . . . . . . . . . . . . . 50
Main Properties of Bloch Electrons . . . . . . . . . . . . . . . . . . . . . . 52
Effective Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Wannier Theorem → Effective Mass Approach . . . . . . . . . . . . 53
Electron Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Electric current in a Bloch State. Concept of Holes. . . . . . . . . . 54
Classification of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Dynamics