Solid State Physics
Crystals, phonons, electrons in solids and semiconductors, developed as a full course in condensed matter physics: the length and energy scales of solids and the range of their electrical behaviour; crystal structure as a Bravais lattice plus a basis, the cubic, hexagonal and diamond structures, packing, coordination, symmetry and Miller indices; the reciprocal lattice, the Laue and Bragg conditions, structure factors and extinction rules in powder x-ray diffraction, and Brillouin zones; van der Waals, ionic, covalent and metallic binding, with Lennard-Jones lattice sums, the Madelung constant, cohesive energies, bulk moduli and elastic constants; lattice vibrations in monatomic and diatomic chains and in three dimensions, acoustic and optical branches, phonons and inelastic neutron scattering; the Einstein and Debye heat capacities and the T-cubed law, thermal expansion and phonon thermal conductivity limited by umklapp processes; the Drude and Sommerfeld models of metals with conductivity, the Hall effect, the plasma frequency, the electronic heat capacity and the Wiedemann–Franz law; Bloch's theorem, crystal momentum and the nearly-free-electron model with gaps at zone boundaries and the Kronig–Penney model; tight-binding bands, effective masses, densities of states, holes, and the band-filling rules that separate metals, semimetals, semiconductors and insulators; semiconductors with intrinsic and extrinsic carriers, donors and acceptors, freeze-out and saturation, the p–n junction and the diode, LEDs, solar cells and transistors; diamagnetism, Curie and Pauli paramagnetism, exchange, Weiss mean-field theory, domains and hysteresis; and a capstone on superconductivity, from the Meissner effect and London theory to BCS pairing and high-temperature superconductors, graphene's Dirac cones and topological insulators, with runnable Python examples throughout.
PHYS-410 Year 4 3 credits 12 lessons · 4 h 11 min ▶ Video lessons coming soon
Offered by HSM University · Physics
This is the Canadian version of this course. See the American version.
What you'll learn
- Estimate the characteristic length and energy scales of a solid, including the thermal, phonon, cohesive and Fermi energies, and use them to decide which effects matter at a given temperature.
- Describe crystal structures as a Bravais lattice plus a basis, identify the common cubic and hexagonal structures, and compute coordination numbers, packing fractions and Miller indices.
- Construct the reciprocal lattice, derive the Laue and Bragg conditions, use structure factors and extinction rules to interpret powder diffraction patterns, and construct Brillouin zones.
- Classify crystal bonding, compute cohesive energies and bulk moduli for van der Waals and ionic crystals with lattice sums and the Madelung constant, and relate elastic constants to sound speeds.
- Derive phonon dispersion relations for monatomic and diatomic chains, distinguish acoustic and optical branches, and explain how inelastic neutron scattering measures dispersion with crystal momentum conservation.
- Derive the Einstein and Debye heat capacities and the \(T^3\) law, explain thermal expansion through anharmonicity, and estimate phonon thermal conductivity and mean free paths.
- Apply the Drude and Sommerfeld models to compute conductivity, relaxation times, Hall coefficients, plasma frequencies, electronic heat capacity and the Lorenz number of metals.
- Prove Bloch's theorem, explain crystal momentum and the absence of scattering in a perfect lattice, and show how a weak periodic potential opens gaps \(2|U_{\mathbf G}|\) at zone boundaries.
- Build tight-binding bands, compute effective masses and densities of states, and use band filling and band overlap to classify solids as metals, semimetals, semiconductors or insulators, including the role of holes.
- Compute intrinsic and extrinsic carrier densities with the law of mass action, explain freeze-out and saturation, and analyse the p–n junction, its built-in potential and the ideal diode equation.
- Explain diamagnetism, Curie and Pauli paramagnetism and ferromagnetism through exchange, solve the Weiss mean-field model, and interpret domains, hysteresis and the Curie–Weiss law.
- Describe superconductivity through the Meissner effect, London theory and BCS pairing, compute penetration depths, gaps and flux quanta, and explain the Dirac cones of graphene and the idea of topological insulators.
Course content
12 lessons · 4 h 11 min total · final exam
- 1 Why solid state physics: from atoms to materials 21 min · quiz
- 2 Crystal structure: lattices, bases and Bravais lattices 20 min · quiz
- 3 The reciprocal lattice, Bragg diffraction and Brillouin zones 22 min · quiz
- 4 Crystal binding and elastic properties 19 min · quiz
- 5 Lattice vibrations: phonon dispersion in one and three dimensions 21 min · quiz
- 6 Thermal properties: phonon heat capacity and thermal conductivity 21 min · quiz
- 7 The free electron model revisited: Drude, Sommerfeld and transport 21 min · quiz
- 8 Electrons in a periodic potential: Bloch's theorem and nearly-free electrons 21 min · quiz
- 9 Band theory: tight binding, metals, insulators and semiconductors 21 min · quiz
- 10 Semiconductors: carriers, doping, p–n junctions and devices 21 min · quiz
- 11 Magnetism in solids: diamagnetism, paramagnetism and ferromagnetism 20 min · quiz
- 12 Capstone: superconductivity and modern materials 23 min · quiz
- E Final exam 20 questions
Requirements
Recommended background. You can start any course at any time.
Description
Crystals, phonons, electrons in solids and semiconductors, developed as a full course in condensed matter physics: the length and energy scales of solids and the range of their electrical behaviour; crystal structure as a Bravais lattice plus a basis, the cubic, hexagonal and diamond structures, packing, coordination, symmetry and Miller indices; the reciprocal lattice, the Laue and Bragg conditions, structure factors and extinction rules in powder x-ray diffraction, and Brillouin zones; van der Waals, ionic, covalent and metallic binding, with Lennard-Jones lattice sums, the Madelung constant, cohesive energies, bulk moduli and elastic constants; lattice vibrations in monatomic and diatomic chains and in three dimensions, acoustic and optical branches, phonons and inelastic neutron scattering; the Einstein and Debye heat capacities and the T-cubed law, thermal expansion and phonon thermal conductivity limited by umklapp processes; the Drude and Sommerfeld models of metals with conductivity, the Hall effect, the plasma frequency, the electronic heat capacity and the Wiedemann–Franz law; Bloch's theorem, crystal momentum and the nearly-free-electron model with gaps at zone boundaries and the Kronig–Penney model; tight-binding bands, effective masses, densities of states, holes, and the band-filling rules that separate metals, semimetals, semiconductors and insulators; semiconductors with intrinsic and extrinsic carriers, donors and acceptors, freeze-out and saturation, the p–n junction and the diode, LEDs, solar cells and transistors; diamagnetism, Curie and Pauli paramagnetism, exchange, Weiss mean-field theory, domains and hysteresis; and a capstone on superconductivity, from the Meissner effect and London theory to BCS pairing and high-temperature superconductors, graphene's Dirac cones and topological insulators, with runnable Python examples throughout.
Part of the Science stream, typically taken in year 4.