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Quantum Theory of Materials
Nicolas Bergeal & Arthur Marguerite
Syllabus
1. Specific heat of solids
- Classical specific heat, Dulong and Petit law, Boltzmann explanation
- Einstein’s model of the specific heat, canonical partition function, quantum harmonic oscillator
- Debye’s model of the specific heat, collective vibration of atoms, towards phonon modes
2. Cristal structure of solids
- Lattices and unit cells, Bravais lattices
- Reciprocal lattice, Brillouin zone
3. Phonons in solids
- Vibration of the 1D mono atomic chains, comparison with Debye model
- 1D diatomic chain, optical and acoustic modes
- Phonons
4. Free electrons and quantum transport
- Drude model, Hall effect, thermal transport
- Sommerfeld model, Fermi-Dirac statistics, electrons heat capacity
- Quantum transport, mesoscopic scales, coherent transport, ballistic transport
5. Electrons in solids
- Nearly free electrons models, perturbative approach, band representation, energy gap
- Bloch’s theorem, electron wave function in a solid
- Tight-binding model, 1D chain, band structure, Graphene band structure (TD)
6. Semiconductors and devices
- Band structure, electrons and holes
- Statistical mechanics of semiconductors, intrinsic and extrinsic doping, law of action mass
- Semiconductor devices, p-n junction, solar cell
Prerequisites
None
Evaluation
Written (2 h)
