Solid State Physics

Bands, Phonons and the Measured Properties of Crystals in 20 chapters — from “Symmetry and the classification of crystals” to “Collective and coupled excitations: plasmons, polaritons and polarons”.

Chapters

  1. Symmetry and the classification of crystals
    • From atomic positions to symmetry operations
    • Symmetry operations and crystallographic point groups
    • The crystallographic restriction theorem
    • The seven crystal systems and the fourteen Bravais lattices
    • Screw axes, glide planes and space groups
    • Site symmetry and Wyckoff positions
    • Neumann's principle and what symmetry forbids
    • Systematic absences forced by a symmetry operation
    • Summary
    • Problems
  2. Diffraction as measurement: form factors, thermal motion and refinement
    • Peak positions and peak intensities
    • The Ewald sphere and real experiments
    • The atomic form factor and neutron scattering length
    • What a diffractometer actually records
    • The Debye-Waller factor
    • Thermal diffuse scattering
    • Choosing between X-rays, neutrons and electrons
    • Whole-pattern refinement
    • Summary
    • Problems
  3. Seeing atoms: electron and scanning-probe microscopy
    • Image and diffraction pattern as Fourier-conjugate planes
    • Electron wavelength and the diffraction limit
    • Diffraction contrast and the two-beam condition
    • Lattice imaging and phase contrast
    • The scanning tunnelling microscope
    • What an STM image actually maps
    • Atomic force microscopy and the non-conducting case
    • Summary
    • Problems
  4. Point defects, dislocations and alloys
    • Vacancies and dislocations so far
    • Point-defect equilibria and charge neutrality
    • Diffusion by vacancy and interstitial jumps
    • Burgers vector, line energy and dislocation interaction
    • The Peierls stress and brittle against ductile
    • Obstacles to dislocation motion
    • The regular solution, the miscibility gap and ordering
    • Matthiessen's rule and the residual resistivity
    • Summary
    • Problems
  5. Solids without a lattice: glasses and quasicrystals
    • Silica glass without a Bravais lattice and basis
    • The static structure factor of a disordered solid
    • Zachariasen's rules and network formers
    • The glass transition as kinetic arrest
    • Viscosity, Vogel-Fulcher and fragility
    • The Kauzmann paradox, stated and left open
    • Two-level systems and the low-temperature anomalies
    • Quasicrystals: sharp diffraction without periodicity
    • Summary
    • Problems
  6. Lattice dynamics in three dimensions
    • Beyond monatomic and diatomic chains
    • Force constants in three dimensions
    • The dynamical matrix and its eigenvalues
    • Polarisation vectors and mode character
    • Born-von Karman boundary conditions and the mode count
    • The density of modes and van Hove singularities
    • The long-wavelength limit and the cubic elastic constants
    • Fitting a measured dispersion
    • Summary
    • Problems
  7. Phonons: quantisation, occupation and inelastic scattering
    • Normal coordinates and the decoupled Hamiltonian
    • The phonon as a quantum of a normal mode
    • The thermal occupation of a mode
    • Conservation in a one-phonon process
    • The one-phonon cross section
    • The triple-axis spectrometer and its competitors
    • Light scattering: Raman and Brillouin
    • Summary
    • Problems
  8. Anharmonicity: expansion, phonon lifetimes and thermal conductivity
    • The cubic term and what it does
    • Mode Gruneisen parameters
    • Three-phonon processes
    • Normal and Umklapp processes
    • The shape of κ(T)
    • Isotope and impurity scattering of phonons
    • Heat capacity beyond Debye and interface resistance
    • Summary
    • Problems
  9. The degenerate electron gas, finished
    • The Fermi function from one level
    • The Sommerfeld expansion
    • Thermodynamics of the degenerate gas
    • The thermal mass and what it contains
    • Thermionic emission and the Richardson equation
    • The photoelectric threshold and photoemission spectroscopy
    • What the free-electron gas still cannot do
    • Summary
    • Problems
  10. Bloch's theorem and the nearly-free-electron method
    • Degenerate perturbation theory for two nearly degenerate states
    • The lattice translation operators and the Bloch form
    • Crystal momentum and what it is not
    • The central equation
    • The nearly-free-electron gap
    • The empty-lattice bands and where the degeneracies are
    • Fermi surfaces in the higher zones
    • Aluminium's gapped Fermi surface and when nearly-free-electron fails
    • Summary
    • Problems
  11. Tight binding and the band structures of real materials
    • Bloch sums of atomic orbitals
    • Two-centre integrals in Slater-Koster form
    • sp3 hybrids and the valence bands of silicon
    • Why silicon's gap is indirect
    • Narrow d bands and the thermal mass
    • Graphene: two sites, one orbital, a linear crossing
    • Choosing a starting point
    • Summary
    • Problems
  12. The Fermi surface: semiclassical dynamics and its measurement
    • The semiclassical equations of motion
    • The effective-mass tensor
    • Holes, derived
    • Bloch oscillations and orbits on a Fermi surface
    • Landau quantisation and the Onsager relation
    • When oscillations can be seen
    • Four ways to see a Fermi surface
    • Summary
    • Problems
  13. The Boltzmann equation and electrical transport
    • What the semiclassical equations of motion leave out
    • The semiclassical distribution function and the Boltzmann equation
    • The relaxation-time approximation and the transport time
    • The displaced Fermi surface
    • The conductivity as a Fermi-surface integral
    • Screened impurity scattering
    • Phonon scattering and the Bloch-Gruneisen law
    • The conductivity tensor in a magnetic field
    • Summary
    • Problems
  14. Two currents, two forces: Wiedemann-Franz and thermoelectricity
    • Two currents, two forces
    • Solving the Boltzmann equation with two forces
    • Onsager reciprocity and the Kelvin relation
    • The electronic thermal conductivity and the Lorenz number
    • Where Wiedemann-Franz fails
    • The Seebeck coefficient from the Sommerfeld expansion
    • The Seebeck coefficient of a semiconductor
    • Peltier, Thomson and how a thermocouple works
    • The figure of merit ZT
    • Summary
    • Problems
  15. Semiconductors: masses, statistics, defect levels and mobility
    • Three averages of the effective-mass tensor
    • k⋅p and the origin of the effective mass
    • Valleys, anisotropy and the three averages
    • Heavy, light and split-off holes
    • Statistics beyond the Boltzmann tail
    • Where the chemical potential sits
    • Shallow and deep levels
    • Shockley-Read-Hall recombination
    • Mobility from screened impurity scattering and phonons
    • Summary
    • Problems
  16. Junctions and devices, finished
    • Two slopes of a p-n junction
    • Quasi-Fermi levels and the depletion region
    • The Shockley diode equation, derived
    • Generation, recombination and the ideality factor
    • The MOS capacitor
    • The MOSFET and the 60 millivolt floor
    • LEDs, photodiodes and the detailed-balance efficiency limit
    • What p-n junction theory leaves out
    • Summary
    • Problems
  17. Heterostructures, quantum wells and the two-dimensional electron gas
    • Mobility at a heterojunction
    • Band offsets and Anderson's rule
    • The quantum well and its subbands
    • The two-dimensional density of states
    • Modulation doping
    • The triangular well at a single heterojunction
    • Lattice matching, strain and critical thickness
    • What a 2DEG opens, and who owns it
    • Summary
    • Problems
  18. Dielectric response, local fields and ferroelectricity
    • Three ways a solid polarises
    • The local field and Clausius-Mossotti
    • Orientational polarisation and Debye relaxation
    • The ionic contribution and Lyddane-Sachs-Teller
    • The soft mode and the displacive transition
    • Domains, hysteresis and the two kinds of transition
    • Piezoelectricity, from symmetry to a number
    • Causality and the Kramers-Kronig relations
    • Summary
    • Problems
  19. Optical properties: interband absorption, excitons and luminescence
    • What is measured and what is wanted
    • Interband absorption and the joint density of states
    • Critical points and reading a spectrum
    • The direct absorption edge
    • The indirect edge needs a phonon
    • The exciton and its binding energy
    • Wannier, Frenkel and what comes back out
    • ε∞​ from the static Kramers-Kronig sum
    • Summary
    • Problems
  20. Collective and coupled excitations: plasmons, polaritons and polarons
    • Negative permittivity in two materials
    • The Drude dielectric function and the plasma frequency
    • The plasmon as a longitudinal mode
    • Plasmons in a doped semiconductor
    • The surface plasmon
    • The reststrahlen band
    • Phonon polaritons and the avoided crossing
    • The polaron
    • Single-particle, collective and coupled excitations
    • Summary
    • Problems