Examples of questions

FYS3410 – Solid State Physics: List of questions
Periodic structures
1. Lattice: Main definitions – unit cell (primitive and conventional), Wigner-Seitz cell. Main symmetry
operations for a lattice, allowed rotation axes.
2. Bravais and-non Bravais lattices. Bravais lattices in two dimensions.
3. Bravais lattices and crystal systems in three dimensions.
4. Body-centered cubic (bcc), face-centered cubic (fcc), and hexagonal close packed (hcp) lattice:
Primitive and conventional cell. Packing ratio.
5. Diamond structure and cubic zinc sulfide structure.
6. Index system for crystal directions and crystal planes. Distance between the planes expressed
through Miller indices.
7. Notion about non-ideal crystal structures: Stacking defects and polytypes.
Wave diffraction and reciprocal lattice
1. Bragg’s law: General principle and typical numbers
2. Laue equations and reciprocal lattice. Rules for construction of reciprocal lattices.
3. Examples of reciprocal lattices for cubic and hcp crystals
4. Ewald’s construction and its justification.
5. Brillouin zones. Examples of Brillouin zones for sc, bcc, fcc and hcp lattices.
6. Diffraction amplitude: Expression through atomic form-factor.
7. Scattering from a lattice with basis: Structure factor.
8. Structure factor for bcc and fcc lattice.
9. Main experimental methods for wave diffraction in crystals.
Crystal binding
1. Van der Waals (molecular) bonding: Basic notion and estimates.
2. Ionic bonding: Basic notion and estimates. Madelung constant.
3. Covalent bonding: : Basic notion and estimates.
4. Metallic bonding: : Basic notion and estimates.
Elastic properties
1. Stress and strain tensors.
2. Hook’s law. Elastic constants: Meaning of different constants.
3. Elastic energy density for cubic crystals. Bulk modulus and compressibility.
4. Elastic waves in isotropic media and cubic crystals.
Lattice vibrations
1. Mono-atomic 1D lattice: Dispersion relation, phase and group velocity.
2. Diatomic 1D lattice: Dispersion relation, phase and group velocity.

3. Three-dimensional lattices: Acoustic and optical modes.
4. Quantization of lattice vibrations: Phonons, conservation laws for phonon-assisted scattering of X-
rays and neutrons.
5. Density of vibration states for different dimensions of the lattice. Debye and Einstein models.
6. Lattice contribution to heat capacity.
7. Anharmonic interactions and thermal expansion.
8. Lattice contribution to thermal conductivity.
Free electron Fermi gas
1. Electrons in a box: Wavefunctions and eigenvalues.
2. Electron density of states in 1, 2 and 3 dimensions.
3. Fermi distribution: Chemical potential and Fermi energy.
4. Electron heat capacity: Estimate and calculation.
5. Drude model for conductance: Main assumptions and expression for conductivity.
6. Origins for finite collision time: Basic scattering mechanisms and temperature dependence of
conductivity.
7. Electron contribution to thermal conductivity: Wiedemann-Franz law.
8. Motion in magnetic field: Cyclotron resonance and classical Hall effect.
9. Conductivity and resistivity tensors in magnetic field.
Energy bands
1. General properties of electrons in a crystal: Bloch theorem.
2. Dispersion relation for electrons in a periodic potential: Brilluoin zones and band structure.
3. Number of states in a band and velocity of a Bloch electron.
4. Band structure in a weak periodic potential.
5. Band structure in a tight-binding approximation.
6. Concept of effective mass: Weak and strong periodic potential.
7. Insulators, semiconductors, semimetals and metals.
Metals
1. Fermi surface: Basic concepts, reduced and extended zone schemes.
2. Fermi surfaces for free electrons and for typical metals (role of periodic potential).
3. Classical mechanics of electrons in metals in a magnetic field.
4. Bohr-Sommerfeld quantization of electrons in metals.
5. De Haas - Van Alphen effect in metals.
6. Main experimental methods to study Fermi surfaces in metals: Fermi surface of Cu as an example.
Semiconductors
1. Band structure of semiconductor and its manifestation in optical absorption.
2. Effective masses in semiconductors: Basic properties and typical numbers.
3. Intrinsic semiconductors: Density of states, chemical potential, concentration of charge carriers.
4. Impurity states: donors and acceptors. Temperature dependence of carrier concentration.

5. Mobility, its temperature dependence due to different scattering mechanisms.
6. Band structure of concrete semiconductors: Si and GaAs.
7. Thermoelectric effects.
Point defects and dislocations; surfaces and interfaces
1. Schottky and Frenkel defects, their origin and temperature dependence of their concentration.
2. Diffusion, Fick’s law.
3. Edge and screw dislocations, Burgers vector.
4. Surfaces, interfaces and basic semiconductor devices (MOSFET, HEMT)