Download 固態物理 - 交通大學

交通大學 電子工程學系 電子研究所 「磐石課程」課程綱要
課程名稱：（中文）固態物理
（英文）Solid State Physics
學分數
3
必/選修
選修
開課單位
電子研究所
永久課號
IEE5501
開課年級
電子碩博
先修科目或先備能力:
工程數學/近代物理/電磁學
Engineering Mathematics/Modern Physics/Electromagnetics
課程概述與目標:
課程中將探討固態量子力學中最重要的原理和基礎。本課程聚焦在固態單晶的討論，包括最重要的
晶體的形成及其結構、電子和聲子能帶特性的探討；以及固態中電子在磁場和電場下的特性、弛豫
過程、電導和基本的熱特性都將被討論。
The course treats the central principles and foundation of the quantum physics of solids. The course emphasizes
crystalline solids. Most important properties of crystal binding and structures, electronic and phononic band
structures are considered. Electronic properties of solids under magnetic and electric fields, relaxation processes
and electrical conductivity are discussed. Basic thermal properties of solid states are considered as well.
課程大綱
單元主題
內容綱要
Introduction
Introduction to basic concepts of the quantum description of solids.
Drude and Sommerfeld models for free
electron in solids
Basic assumptions of the Drude model, DC and AC conductivity of
metals. Hall effect. Thermo-conductivity. Errors in the Drude
description.
The Sommerfeld theory. Impact of the quantum statistics. Free
electrons in three dimensions and Born-von Karman boundary
conditions. Fermi momentum, energy, and temperature. Thermal
properties of the free electron gas. Heat capacity. Sommerfeld theory
of conduction in metals. Discussion of failures of the free electron
model .
Crystal structure
Bravais lattice. Primitive unit cell and Wigner-Seitz cell. Lattice
with basis. Some simple crystal structures. The reciprocal lattice
Diffraction of waves by crystals. First Brillouin zone. X-Ray
diffraction. Bragg and von Laue considerations. Geometrical
structure and atom form factors.
Electron energy bands
Periodic potential and Bloch’s theorem and its proofs. Born-von
Karman boundary conditions for the Bloch wave function. General
consequences of the Bloch’s theorem. Effective mass. KronigPenney model. Electrons in a weak periodic potential. Energy levels
near a single Bragg plane. Brillouin zones and Fermi surface.
Density of the electronic states (levels). The tight-binding model.
Semi-classical model of electron
dynamics
Wave packets of Bloch electrons. Description of the semi-classical
model. Semi-classical motion in DC uniform electric and magnetic
fields. Holes. Quasi-particles.
Semi-classical theory of conduction in
metals
The relaxation time approximation. Non-equilibrium distribution
function. The Boltzmann equation. Electron scattering. DC electrical
conductivity and thermal conductivity in metals with complex
electron dispersion relations.
Classical theory of the harmonic crystal
Harmonic and adiabatic approximations. Specific heat of a classical
crystal. Normal modes of one-dimensional Bravais lattice and
lattice with basis. Normal modes of a three-dimensional lattice.
Quantum theory of the harmonic crystal
Normal modes and phonons. Planck distribution. Density of states
for phonons (density of normal modes). Debye and Einstein models
for the phonon density of states. Specific heat in the quantum
theory.