Introduction to Solid-State Physics

Crystals, phonons, bands and the materials built from them

About this course

The structure and bonding of crystals, lattice vibrations and thermal properties, electrons in metals and semiconductors, and magnetism, superconductivity, dielectric response and defects.

What you will be able to do

  • Describe crystal lattices and use the reciprocal lattice to interpret diffraction
  • Compute phonon dispersion and heat capacity in the Einstein and Debye models
  • Explain how a periodic potential produces energy bands, and classify metals, insulators and semiconductors
  • Explain the operation of the p-n junction and the transistor
  • Use the Hall effect and the Fermi surface to describe electronic transport in metals

What this course covers

  • Paramagnetism, Brillouin Function, and Effective Moment
  • Diamagnetism and Larmor Precession
  • Exchange Interaction and Failure of Magnetic Dipole Forces
  • Weiss Mean-Field Theory and Self-Consistent Magnetization
  • Ising Lattice and Limits of Mean-Field Theory
  • Iron's Saturation Magnetization and the Weiss Field as Exchange Energy
  • Magnetism as Collective Phenomenon: Lecture Synthesis
  • Lattice plus basis: definition and atom counting
  • Coordination numbers and neighbor shells
  • Sphere packing fractions and the five structures
  • Density formula and lattice-constant determination
  • Miller indices and plane spacings
  • Crystallographic restriction theorem
  • The fourteen Bravais lattices
  • Monatomic chain dispersion relation
  • Diatomic chain: acoustic and optical branches
  • Normal-mode count and periodic boundary conditions
  • Phonon as quantum of a normal mode
  • Crystal momentum and its conservation
  • Measuring phonons: Brockhouse's neutron spectrometer
  • Density of states and Van Hove singularity
  • Debye temperature from sound speeds
  • Drude Classical Gas, Ohm's Law, and the Heat Paradox
  • Sommerfeld's Fermi Sphere and Fermi Energy
  • Three Speeds and the Degeneracy Mirage
  • Limits of the Free Electron Gas and What Comes Next
  • Fermi-Dirac Distribution and Electronic Heat Capacity
  • Pauli Paramagnetism and the Wiedemann-Franz Law
  • Copper Worked Example: Five Predictions from N and ρ
  • Dulong-Petit Law and Its Failures
  • Einstein's Single-Frequency Oscillator Model
  • Debye's Spectrum and the T³ Law
  • The Debye Temperature Table and Electronic Heat Capacity Crossover
  • Zero-Point Energy and the Third Law
  • Thermal Expansion from Anharmonicity
  • Phonon Thermal Conductivity and Mean Free Path
  • The Reciprocal Lattice
  • Bragg's Law and the Powder Method
  • Ewald's Sphere Construction
  • The Structure Factor
  • The Brillouin Zone and Copper's Fermi Sphere
  • Unifying Principle: One Lattice, Five Names
  • Indexing an Unknown Powder Pattern
  • Two founding experiments: Onnes and Meissner
  • London equations and penetration depth
  • Cooper pairing and the phonon glue
  • BCS gap equation and the universal ratio 3.53
  • Macroscopic wave function, flux quantisation, and Josephson effect
  • High-TC cuprates and hydrides: beyond BCS
  • MRI magnet wire: BCS in a wire
  • Bloch's Theorem and Crystal Momentum
  • The Band Gap at the Zone Boundary
  • Kronig-Penney Model and Exact Band Structure
  • Tight-Binding Bands and Effective Mass
  • Electron Count, Wilson's Rule, and Metal vs. Insulator
  • Reading a Band Structure: Gaps, Masses, and Filling
  • Copper's Effective Mass and D-Band Hybridisation
  • Polarizability and the local field (Clausius-Mossotti)
  • Kramers-Kronig relations and causality
  • The Lorentz oscillator and the reststrahlen band
  • Drude dielectric function and the plasma frequency
  • Colors of noble metals and D-band absorption
  • The plasmon as a collective mode
  • ITO low-emissivity window: dielectric function applied
  • Four types of crystal bonding
  • Van der Waals bond and Lennard-Jones solid
  • Quantum zero-point motion and the de Boer parameter
  • Madelung constant and conditional convergence
  • Ionic lattice energy of NaCl
  • Metallic bond and jellium model
  • Cohesive energies and the 30 kTM rule
  • Intrinsic carrier density and effective density of states
  • Temperature dependence of ni and the Arrhenius plot
  • Doping: hydrogen-atom model and law of mass action
  • Fermi level as a dial for carrier density
  • Shallow vs. deep impurity levels
  • Mobility, conductivity, and the million-to-one ratio
  • Intrinsic limit and device failure temperature
  • Vacancies: equilibrium fraction and Boltzmann count
  • Diffusion via vacancy hopping and Arrhenius law
  • Theoretical shear strength and the dislocation
  • Defect dimensionality and the mirage of perfection
  • F-centre: colour from an electron in a vacancy box
  • Quantum dot: particle in a sphere and size-tunable colour
  • Graphene's Dirac cone and the course capstone
  • Built-in voltage at a P-N junction
  • Depletion layer width and capacitance
  • Shockley diode equation and rectification
  • Generation current and limits of Shockley's law
  • Solar cell operation and open-circuit voltage
  • Unifying theme: every junction number is kT/e times a logarithm
  • End-to-end worked example: ten numbers from three inputs
  • Mean Free Path at the Fermi Speed
  • Matthiessen's Rule and Residual Resistivity
  • Bloch–Grüneisen T-to-the-fifth Law
  • Hall Effect and Carrier Sign
  • Cyclotron Orbits and the Fermi Surface
  • Boltzmann / Displaced Fermi Sphere Picture
  • Worked Example: Copper's Resistivity Curve

Syllabus

  1. Crystal Structure and Bonding

    1. L1 · Crystals: Lattices, Bases and Symmetry
    2. L2 · Diffraction and the Reciprocal Lattice
    3. L3 · Bonding and Cohesion

  2. Lattice Vibrations

    1. L4 · Lattice Vibrations: Phonons
    2. L5 · Thermal Properties: Einstein, Debye and Heat Capacity

  3. Electrons in Solids

    1. L6 · The Free Electron Gas
    2. L7 · Electrons in a Periodic Potential: Bands
    3. L8 · Semiconductors
    4. L9 · Semiconductor Devices: the p-n Junction and the Transistor
    5. L10 · Metals: Transport, the Fermi Surface and the Hall Effect

  4. Collective and Optical Phenomena

    1. L11 · Magnetism
    2. L12 · Superconductivity
    3. L13 · Dielectrics, Optical Properties and Plasmons
    4. L14 · Defects, Nanostructures and the Close