MAS.020UF Introduction to Solid State Physics

Course outline

• Crystal structure
• Crystal structure     W
• Unit cell     W
• Bravais lattices     W
• Miller indices     W
• Wigner Seitz cell     W
• Drawing Wigner-Seitz cells in two dimensions
• Drawing Wigner-Seitz cells in three dimensions
• Asymmetric unit
• Examples of crystal structures
• simple cubic, fcc, bcc, hcp, diamond, silicon, zincblende, ZnO wurzite, NaCl, CsCl, perovskite, graphite, sugar
• More crystal structures, CIF files, and programs to visualize crystal structures
• The AFLOW standard encyclopedia of crystallographic prototypes
• Symmetries
  • Point groups     W
  • Table of crystal classes and their associated point groups
  • Flowchart to determine the point group of a crystal
  • Space groups     W
  • Space Group → Bravais Lattice, Point Group
• Crystal physics
• SGTE data for pure elements - The Gibbs energy as a function of temperature for many elements.
• Stress and strain
• Einstein notation for tensors     W
• Equilibrium thermodynamic properties
• Internal energy, Helmhotz free Energy, Gibbs free energy, Enthalpy, Specific heat, Pyroelectricty  W, Pyromagnetism, Piezoelectricty  W, Piezomagnetism  W, Electrocaloric effect  W, Electrostriction  W, Magnetostriction  W, Thermal expansion  W
• Nonequalibrium properties
• Electrical conductivity, thermal conductivity, Seebeck effect, Peltier effect, Hall effect, Enrst Effect, Ettingshausen effect
• Intrinsic symmetries
• Maxwell relations     W
• Symmetric and asymmetric tensors
• Crystal diffraction
• Periodic functions
• Fourier series
• Fourier series in 1-D
• Reciprocal lattices
• Fourier series in 2-D
• Fourier series in 3-D
• Plane waves and reciprocal space
• Interference of scattered waves
• Intensity of the scattered waves
• Plotting the intensity of the scattered waves
• Laue condition $\Delta\vec{k}=\vec{G}$      W
• The number of diffraction peaks observed
• Ewald sphere
• Brillouin zones     W
• Brillouin zones of 2D Bravais lattices
• Brillouin zones of 3D Bravais lattices
• Drawing 3D Brilouin zones
• Symmetry points and lines: Simple Cubic, Face Centered Cubic, Body Centered Cubic, Hexagonal, Rhombohedral, Simple Tetragonal, Body Centered Tetragonal, Simple Orthorhombic, Base Centered Orthorhombic, Face Centered Orthorhombic, Body Centered Orthorhombic, Simple Monoclinic, Base Centered Monoclinic, Triclinic
• Symmetry points of 2D lattices: Square, Hexagonal, Rectangular, Centered Rectangular, Oblique
• Atomic form factors
• X-ray atomic form factors
• Electron atomic form factors
• Structure factor      W
• Bragg diffraction     W
• The reciprocal lattice vector G_hkl is orthogonal to the (hkl) plane.
• Applications of diffraction
• powder diffraction     W
• American Mineralogist Crystal Structure Database (contains diffraction data)
• Neutron diffraction      W
• Electron diffraction      W
• LEED     W
• Lattice Vibrations and Phonons
• Normal modes and phonons
• Using complex numbers to represent sinusoidal oscillations
• Linear chain
• Linear chain with two different masses
• fcc with linear springs to nearest neighbors
• bcc with linear springs to nearest neighbors and next nearest neighbors
• simple cubic with linear springs to nearest neighbors and next nearest neighbors
• Jupyter python notebook for calculating phonon dispersion equations
• Animations of some optical modes
• Thermodynamic properties of phonons
• Dispersion relation
• Density of states
• linear chain
• linear chain with two masses
• Ag-fcc, Al-fcc, AlN, Fe-bcc, GaN, Mg-hcp, Mo-bcc, Si-diamond, α-Sn, β-Sn, Ta-bcc, Tb-hcp, Ti-hcp, W-bcc, ZnO (rocksalt), ZnO (zincblende), ZnO (wurtzite), Zr-hcp
• Energy spectral density u(ω,T)
• Internal energy density u(T)
• Specific heat c_v(T)
• Helmholtz free energy density f(T)
• Entropy density s(T)
• Table summarizing the thermodynamic properties of phonons
• Kinetic theory
• Thermal conductivity
• Electron energy bands
• Free electrons
• Fermi function
• Free electron density of states
• Free electron model in 1-D
• Free electron model in 2-D
• Free electron model in 3-D
• Table of thermodynamic properties of free electrons
• Bloch theorem
• One dimension
• Bloch waves in one dimension
• Kronig Penney Model
• One-dimensional potentials
• Empty lattice approximation: simple cubic, fcc, bcc, hexagonal, tetragonal, body centered tetragonal, orthorhombic, simple monoclinic
• Fermi surfaces
• Fermi surface of a two-dimensional square lattice
• Fermi surfaces of some three-dimensional lattices
• Electronic band structure calculations
• Plane wave method, central equations
• Nearly free electron model
• Tight binding
• Table of tight binding band structure calculations
• Some band structure calculations: Cr, Li bcc, GaAs, GaN, GaP, Ge, InAs, 6H SiC, V
• Periodic table of electronic bandstructures
• Separable square wave potentials
• Materials Project
• Metals, semimetals, semiconductors, insulators
• Numerical determination of the thermodynamic properties of metals
• Chemical potential μ(T)
• Energy spectral density u(E,T)
• Internal energy density u(T)
• Specific heat c_v(T)
• Helmholtz free energy density f(T)
• Grand potential density φ(T)
• Sommerfeld expansion
• 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
• Experimental methods
• Ultraviolet photoelectron spectroscopy (UPS)      W
• X-ray photoelectron spectroscopy (XPS)     W     DE 3:18 
• Angle resolved photoemission spectroscopy (ARPES)     W     3:37 
• Inverse photoemission spectroscopy
• 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
• 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
  • Silicon, SiC 4H
• Electrons and holes
• Effective mass     W
• Holes     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