Spectroscopy of semiconductors and dielectrics.

A.V.Chernenko

Annotation

Electrons in an ideal solid and band-gap formation. Adiabatic approximation. Single-electron picture: Hartree-Fock approximation. Effective masses, concept of positively charged holes. Crystal and band structure of silicon, germanium and gallium arsenide. Interband transitions and optical properties of semiconductors. Two-photon transitions. Optical properties of metal in a Drude-Lorentz model. Excitons in solids. Tight binding and Frenkel excitons. Wannier-Mott excitons. Effect of external static fields on exciton spectra. Retardation effects and a spatial dispersion in excitonic resonances. Impurity states in dielectrics and semiconductors. Optical orientation of electron and exciton spins in semiconductors. Spin-lattice and spin-spin relaxation. Two-dimensional semiconductor structures. Size quantization in low-dimensional systems. Quantum Hall effect.

1. Electrons in an ideal solid and band-gap formation. Born–Oppenheimer (adiabatic) approximation. Single-electron picture: Hartree-Fock approximation.
2. General properties of an electron in a periodic potential. Effective masses. Concept of positively charged holes. The Luttinger-Kohn Hamiltonian. (k•p) approximation and effective masses in semiconductors.
3. Crystal and band structure of common semiconductors: silicon, germanium, gallium arsenide.
4. Interband transitions and optical properties of semiconductors. General insight onto interband transitions: electron-radiation interaction, quantum theory of optical transitions in semiconductors. Connection with optical constants for an example of Lorentz oscillators. Dielectric function; coefficients of absorption, extinction and reflection; refraction index. Kramers-Kronig relations. Oscillator strength and a number of optically active electrons. Sum rules.
5. Analytical properties of optical constants near critical points in a (joint) density of states (Van Hove singularities, critical points of maximum, minimum, saddle-points). Cases of 3D, 2D, 1D.
6. Two-photon transitions and corresponding optical constants. Nonlinear optical phenomena: stimulated Brillouin scattering, harmonics generation, self-focusing.
7. Optical transitions in an external magnetic field. Landau oscillator and diamagnetic quantization of an electron energy spectrum. Magnetooptical oscillations in absorption spectra of semiconductors. Magnetooptical phenomena (Faraday, Cotton–Mouton and Kerr effects). Franz–Keldysh effect in an electric field.
8. Optical properties of metal in a Drude-Lorentz model. Plasma oscillations and plasma edge. Damping of plasma oscillations (Landau damping). Low-frequency properties of a normal metal.
9. Excitons in solids. Tight binding and Frenkel excitons. Longitudinal and Transverse Excitons.
10. Hydrogen-like (Wannier-Mott) excitons. Effective mass approximation for Mott excitons.
11. Effect of external static fields on exciton spectra: excitons in an electric field, in a magnetic field. Diamagnetic excitons (a strong magnetic field case).
12. Retardation effects and a spatial dispersion in excitonic resonances. Exciton polaritons, 2D-polaritons in microcavities. Surface-plasmon polaritons.
13. Donor and acceptor states in semiconductors. Shallow and deep levels of impurities. Donor-acceptor pairs and related optical recombination. Bound exciton complexes.
14. Optical orientation of electron and exciton spins in semiconductors. Spin-lattice and spin-spin relaxation. Optical detection of spin-oriented charge carriers and excitons.
15. Two-dimensional semiconductor structures: MOSFETs, heterstructures (quantum wells, superlattices and quantum dots).
16. Size quantization in low-dimensional systems. Two-dimensional excitons.