An electronic and optical theory of semiconductor heterostructures

A semi-empirical theory based on the envelope function approach and k {dollar}cdot{dollar} p perturbation theory is developed and applied to the description of the electronic states and optical properties of two related classes of semiconductor heterostructures, superlattices and quantum wells. This theory treats semiconductor heterostructures as a new class of perfectly periodic, though highly anisotropic, crystals with their own crystal momentum and crystal coordinate representations. The only inputs to this theory are an empirical parameterization of the bulk III-V and II-VI zinc-blend constituent semiconductors and a value for the valence band offset at the heterointerfaces.; The envelope function approach is used to determine the zone center, K = 0, electronic states of the heterostructure. A superlattice K {dollar}cdot{dollar} p perturbation theory is formulated and used to determine the electronic states at finite K which form the basis for a crystal momentum representation. This technique for determining the superlattice band structure is applied to the II-VI HgTe/CdTe superlattice system in order to resolve an ongoing dispute concerning the valence band offset in this system.; The superlattice crystal momentum representation is transformed into a crystal coordinate representation in order to treat the effects of the electron-hole Coulomb interaction in superlattices and quantum wells. Wannier exciton binding energies and oscillator strengths as well as the fundamental optical absorption spectrum are calculated for three semiconductor superlattice systems, GaAs/Ga{dollar}sb{lcub}1-x{rcub}{dollar}Al{dollar}sb{lcub}x{rcub}{dollar}As, Ga{dollar}sb{lcub}1-x{rcub}{dollar}In{dollar}sb{lcub}x{rcub}{dollar}As/GaAs, and In{dollar}sb{lcub}1-x{rcub}{dollar}Ga{dollar}sb{lcub}x{rcub}{dollar}As/In{dollar}sb{lcub}1-y{rcub}{dollar}Al{dollar}sb{lcub}y{rcub}{dollar}As. The effects of applied electric and magnetic fields on superlattice exciton binding energies are calculated. The effects of quantum well asymmetry on the fundamental optical absorption spectrum are examined for the GaAs/Ga{dollar}sb{lcub}1-x{rcub}{dollar}Al{dollar}sb{lcub}x{rcub}{dollar}As system. In all cases agreement between theory and experiment is excellent.; The effects of Mn d bands on the electronic structure of superlattices incorporating diluted magnetic semiconductors are examined. The Mn d bands are described within the superlattice representation and their effects on the sp band structure are calculated for two example systems, CdTe/Cd{dollar}sb{lcub}1-x{rcub}{dollar}Mn{dollar}sb{lcub}x{rcub}{dollar}Te and ZnSe/Zn{dollar}sb{lcub}1-x{rcub}{dollar}Mn{dollar}sb{lcub}x{rcub}{dollar}Se.