Course outline

• Introduction     EN 6:45 
• Atoms
• The solutions to the Schrödinger equation for the hydrogen atom     W     DE 5:13 
• Constructing many-electron atomic wave functions from the hydrogen wave functions
• Many body problem     W
• The intractability of the Schrödinger equation
• The helium atom      W
• Singlet and triplet states
• Identical particles     W
• Pauli exclusion principle     W
• Slater determinants     W
• Exchange     W
• Molecules
• Molecular orbital theory      W
• Constructing the total molecular Hamiltonian     W
• The Born-Oppenheimer approximation     W
• The single electron molecular orbital Hamiltonian
• Solving the molecular orbital Hamiltonian
• Linear combination of atomic orbitals (LCAO)     W
• Hückel model     W
• Constructing many-electron molecular wavefunctions from the molecular orbitals
• Valence bond theory     W
• Hydrogen molecule
• 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
• Crystal structure
• Crystal structure     W
• Unit cell     W
• Bravais lattice     W
• Miller indices     W
• Wigner Seitz cell     W
• Asymmetric unit
• Symmetries
  • Point groups     W
  • Space groups     W
• Examples of crystal structures
• Program to plot crystals in 3-D
• Crystal diffraction
• Reciprocal space (k-space)     W
• Fourier transforms
• Expressing 2-D and 3-D periodic functions as a Fourier series
• Brillouin zones     W
• Animation of the construction of 2-d Brillouin zones
• Animation of the mapping of the higher zones onto the first Brillouin zone
• Brillouin zone applet
• Simple cubic Brillouin zone
• fcc Brillouin zone
• bcc Brillouin zone
• Hexagonal Brillouin zone
• Atomic form factor
• Atomic form factors
• Atomic electron densities
• Structure factor      W
• Bragg diffraction     W
• Laue condition     W
• Applications of diffraction
• powder diffraction     W
• Neutron diffraction     W
• LEED     W
• Crystal binding
• Molecular crystals     W
• Ionic crystals     W
• Madelung constant     W
• Bulk modulus      W
• Photons
• Photons in vacuum
• Review of Maxwell's unification of electromagnetism with optics      W
• Quantization of the normal mode solutions to the wave equation      W
• Thermodynamic properties of light
• Planck's radiation law      W
• Planck curve for black body radiation
• Wien's displacement law, λ_max = 2.8977685 × 10^-3/T m K     W
• Stefan-Boltzmann law, I = σT⁴ W/m²      W
• Internal energy density      W
• Specific heat      W
• Radiation pressure      W
• Entropy      W
• Table summarizing the results of the quantization of the wave equation
• Light in one-dimensional layered material
• Photonic crystals      W
• Empty lattice approximation
• Plane wave method
• Table of photonic crystals
• Phonons
• Calculating phonon dispersion relations by assuming the atoms are connected by linear springs
• Linear chain
• Using complex numbers to represent sinusoidal oscillations
• Linear chain with two different masses
• Einstein model      W
• Debye model      W
• fcc with linear springs to nearest neighbors
• bcc with linear springs to nearest neighbors
• Thermodynamic properties of phonons
• Dispersion relation
• Density of states
• linear chain
• Einstein model
• Debye model
• linear chain with two masses
• bcc, fcc
• Ag-fcc, Al-fcc, Au-fcc, Fe-bcc, Mg-hcp, Mo-bcc, Ta-bcc, Tb-hcp, Ti-hcp, W-bcc, 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
• Electrons
• Thermodynamic properties of free, noninteracting electrons
• Dispersion relation
• Density of states
• Internal energy density
• Specific heat
• Helmholtz free energy density
• Entropy
• Table of thermodynamic properties of free electrons
• Sommerfeld expansion
• Table of thermodynamic properties calculated with the Sommerfeld expansion
• Experimental methods
• Ultraviolet photoelectron spectroscopy (UPS)      W
• X-ray photoelectron spectroscopy (XPS)     W     DE 3:18 
• Angle resolved photoemission spectroscopy (ARPES)     W     3:37 
• Scanning tunneling spectroscopy      W
• Inverse photoemission spectroscopy
• Kinetic theory
• Ballistic transport
• Diffusive transport
• Ohm's law
• Mattheissen's rule
• Hall effect
• Thermal conductivity
• Wiedermann-Franz law
• Lorentz number
• Energy bands
• Bloch theorem
• Band structure calculations
• Kronig Penney Model
• One-dimensional potentials
• Empty lattice approximation
• simple cubic
• fcc
• bcc
• hexagonal
• tetragonal
• Plane wave method, central equations
• Approximate form of the bands near the Brillouin zone boundary
• Tight binding
• Table of tight binding band structure calculations
• 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)
• Calculated electron density of states
• Free electron model in 1-D
• Free electron model in 2-D
• Free electron model in 3-D
• Al fcc, Au fcc, Cu fcc, 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
• Separable square wave potentials
• 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
• Examples of how symmetries affect the properties of solids
• Piezoelectricity     W
• Nonlinear optics     W
• Birefringence
• Table of crystal classes and their associated point groups
• 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
• Examples of semiconductor band structures
• 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 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
• Seebeck effect     W
• Peltier effect     W
• Thermopower     W
• Bloch oscillations     W
• Magnetism
• Diamagnetism      W
• Paramagnetism     W
• Brillouin functions
• Ferromagnetism     W
• Curie temperature     W
• Curie-Weiss law     W
• Exchange
• Mean field theory
• Antiferromagnetism     W
• Neel Temperature     W
• Ferrimagnetism     W
• Magnetite      W
• Spinel crystal structure     W
• Magnetic domains     W
• Anisotropy energy
• Hard axis, easy axis
• Bloch walls     W
• Remnant magnetization
• Coersive field
• Hard magnets and soft magnets
• Superparamagnetism     W
• Spin glass     W
• Magnons     W
• Giant magnetoresistance     W
• Magnetoresistive Random Access Memory     W
• Magnetic force microscope      W