Semiconductor quantum wells. Electronic states in quantum wells in the conduction and valence bands; envelope function approximation. Density of states: electron and hole density. Transition selection rules: interband and intraband transitions. Absorption and gain in a quantum well. Intersubband absorption. Strained quantum wells. Transparency density and differential gain. Exciton in bulk and quantum well semiconductors.

Bulk semiconductors. Stimulated transitions: selection rules. Joint density of states. Absorption coefficient and gain in bulk semiconductors; Bernard-Duraffourg condition; transparency condition and differential gain. Spontaneous emission; bimolecular recombination: low and strong injection. Nonradiative recombination. Shockley-Read-Hall model. Auger recombination. Surface recombination. Radiative efficiency.

Basic concepts of quantum mechanics: Schroedinger equation; Dirac notation; the energy representation; expectation value; Hermite operators; coherent superposition of states and motion in the quantum world; perturbation Hamiltonian. Time-dependent perturbation theory: harmonic perturbation. Transition rate: Fermi’s golden rule. The density matrix; pure and mixed states. Temporal dependence of the density operator: von Neuman equation. Randomizing Hamiltonian. Longitudinal and transverse relaxation times. Density matrix and entropy.

Basic concepts of electromagnetic theory; Coulomb gauge; intensity of electromagnetic field. Electrons in an electromagnetic field: from the Lagrangian to the Hamiltonian; canonical momentum. Interaction Hamiltonian. Semiclassical approximation; weak-field limit. Electric dipole approximation. Calculation of the optical susceptibility by using the density matrix approach. From optical susceptibility to absorption coefficient. Momentum of an electron in a periodic crystal.

General structure of quantum cascade lasers: resonant tunnelling, minigap and miniband. Gain coefficient. Rate equations and threshold conditions. Output power, slope efficiency and wall-plug efficiency. Applications of quantum cascade lasers.

Semiconductor lasers: rate equations and threshold conditions for laser action. Confinement factor. Temperature dependence of the threshold current: characteristic temperature. Output power: external quantum efficiency and slope efficiency. Quantum well lasers. General structures of semiconductor lasers. Spectral and spatial characteristics of diode laser emission.

Crystal, lattices and cells; Bravais lattice; the reciprocal lattice; electrons in a periodic crystal: Bloch’s theorem; momentum of an electron in a periodic crystal; effective mass; electrons and holes in a semiconductor; calculation of the band structure: tight-binding method and k·p method; bandstructure of Si, GaAs and GaN.

Distributed feedback (DFB) lasers: general structure. Uniform and lambda/4-shifted gratings. Coupled-mode theory: coupling parameter; threshold conditions. DFB lasers with uniform grating; evaluation of oscillating frequencies and threshold gain. DFB laser with lambda/4-shifted grating. Distributed Bragg Reflector (DBR) lasers.

Born-von Karman boundary conditions; density of states in bulk materials, quantum wells, and quantum wires. Carrier statistics in semiconductors: Fermi-Dirac distribution function, electron and hole density in the conduction and valence bands. Nondegenerate semiconductors; effective density of states; intrinsic semiconductors. Mass-action law. Doped semiconductors: donors and acceptors; hydrogen-like model. Degenerate semiconductors. Quasi-Fermi levels in nonequilibrium systems. Charge transport in semiconductors. Diffusion current.

Vertical cavity surface-emitting lasers (VCSELs): general structure; threshold conditions. Distributed Bragg reflectors for VCSELs. Threshold conditions and current confinement. Applications.

Light emitting diodes (LEDs): photon flux, injection efficiency, internal quantum efficiency. Double-heterostructure LEDs. Burstein-Moss shift. Carrier overflow. Carrier leakage over the barrier. External efficiency of a LED: transmission efficiency and external quantum efficiency. Output power, responsivity, and wall-plug efficiency. Emission pattern of LEDs. Luminous efficiency. Blue LEDs.

Quantum dot lasers. Fabrication techniques of quantum dots: self-assembling formation of quantum dots (Stranski-Krastanov growth mode). General scheme of quantum dot lasers. Electronic states in quantum dots: particle in a cubic box; spherical quantum dots. Coulomb interaction. Carrier statistics in quantum dots. Optical transitions. Absorption and gain spectrum. Threshold current density and its temperature dependence. Linewidth enhancement factor.