Course outline

PHY.K02UF Molecular and Solid State Physics

Course outline

Introduction

Review of atomic physics (pdf v.2018)

The solutions to the Schrödinger equation for the hydrogen atom

Atomic orbitals

Slater's rules

Helium
Many-electron wavefunctions
Slater determinants W
Singlet and triplet states
Exchange W
The intractability of the Schrödinger equation
Many-electron atoms

Molecules (pdf v.2018)

Molecular orbital theory W

A quantum mechanical description of molecules W

Harmonic oscillator

Solving the molecular orbital Hamiltonian

Valence bond theory

Heitler-London theory

Numerically calculated molecular orbitals

Carbon monoxide CO, Carbon dioxide CO₂, Water H₂O, Hydrogen sulfide H₂S, Nitrogen N₂, Ammonia NH₃, Methane CH₄, Ethene C₂H₄, Ethane C₂H₆, Butadiene C₄H₆, Benzene C₆H₆, Hexatriene C₆H₈

Programs to calculate molecular orbitals

GAMESS, Gaussian, Quantum Espresso, FHI-aims

Rotational and vibrational energy levels of some diatomic molecules
Chemical bonds

Covalent bond W
σ-bonds W
π-bonds W
sp, sp², sp³ orbitals
Double bond W
Triple bond W
Ionic bond W
Polar bond W
Metallic bond W
Van der Waals bond
Hydrogen bond W

Visualization tools

Crystal structure

Asymmetric unit
Symmetries
- Point groups W
- Space groups W
- Space Group → Bravais Lattice, Point Group
Examples of crystal structures

Crystal binding

Molecular crystals W
Ionic crystals W

Madelung constant W
Bulk modulus W

Periodicity, Fourier Series, and Reciprocal Space

Crystal diffraction

Lattice Vibrations and Phonons

Phonon dispersion of a bcc crystal

Phonon dispersion of a simple cubic crystal

Phonons of crystals with more atoms in the basis

Animations of some optical modes

Energy bands

Table of tight binding band structure calculations

Some band structure calculations: Cr, Li bcc, GaAs, GaN, GaP, Ge, InAs, 6H SiC, V

Photoemission Spectroscopy (UPS XPS, ARPES, PEEM)
Metals, semimetals, semiconductors, insulators

Numerical determination of the thermodynamic properties of metals

Calculated electron density of states

Al fcc, Au fcc, Cu fcc, Cr bcc, Li bcc, Na bcc, Pt fcc, W bcc, Si diamond, Fe bcc, Ni fcc, Co fcc, Mn bcc, Cr bcc, Gd hcp, Pd fcc, Pd₃Cr, Pd₃Mn, PdCr, PdMn, GaN, 6H SiC, GaAs, GaP, Ge, InAs, V bcc
Separable square wave potentials
Materials Project

Kinetic theory

Ballistic transport
Diffusive transport
Drift and diffusion simulation
Ohm's law
Mattheissen's rule
Hall effect
Thermal conductivity
Wiedermann-Franz law
Lorentz number

Summary: Electron Band Model

Crystal physics

Stress and strain

Einstein notation for tensors W
Review of statistical physics
Intrinsic symmetries
Maxwell relations W
Thermodynamic properties

Pyroelectricty W
Pyromagnetism
Piezoelectricty W
Piezomagnetism W
Electrocaloric effect W
Electrostriction W
Magnetostriction W
Thermal expansion W

Groups and symmetry
Table of crystal classes and their associated point groups
Flowchart to determine the point group of a crystal
Symmetric and asymmetric tensors
SGTE data for pure elements - The Gibbs energy as a function of temperature for many elements.

Semiconductors

Role of semiconductors in technology

Band structure of semiconductors

Conduction band E_c, valence band E_v, band gap E_g

Direct and indirect band gaps W
Absorption and emission of photons and phonons
Simplified band structures from the NSM Archive
- Direct band gap: InAs, InP, GaAs, InN, GaN (zincblende), GaN (wurtzite), AlN
- Indirect band gap: Ge, Si, GaP, Ga₂O₃

Electrons and holes

Effective mass W
Holes W
Crystal momentum W
Ohm's law

Boltzmann approximation

Intrinsic semiconductors W
Effective density of states N_c, N_v
The density of electrons in the conduction band n = N_cexp((μ - E_c)/k_BT)
The density of holes in the valence band p = N_vexp((E_v - μ)/k_BT)
Law of mass action: np = N_cN_vexp(-E_g/k_BT)
The intrinsic carrier density n_i =(N_cN_v)^1/2exp(-E_g/2k_BT)
Chemical potential of intrinsic semiconductors
Thermodynamic properties of intrinsic semiconductors
Intrinsic semiconductors with a split-off band
Table summarizing the thermodynamic properties of semiconductors in the Boltzmann approximation

Extrinsic semiconductors

Doping W
Extrinsic carrier densities
Chemical potential in extrinsic semiconductors W

Determining chemical potential from the charge neutrality condition

Semiconductor materials

Silicon, SiC 4H

Semiconductor devices

pn junctions
diodes

Light emitting diodes
Solar cells
Laser diodes

Transistors

Transport in semiconductors

Ohm's law: σ = (neμ_n + peμ_p)
Mobility W