Theory of subband structure for semiconductor quantum wells and superlattices

The object of this study was to investigate the electronic properties of semiconductor heterostructures within the framework of an eight-band Envelope Function Approximation (EFA) model, which takes the two conduction and all six valence bands into account explicitly. The thesis presents an exact formulation for the calculation of the subband structure in semiconductor heterostructure systems. The model is designed to treat cases where: (a) the bulk bands of the constituent materials in the energy range of interest are degenerate or nearly degenerate, such as in the narrow gap semiconductors and the valence bands of III-V and II-VII semiconductors; (b) the energy levels to be considered are far from the band minimum where the bands are highly non-parabolic, and (c) the valence bands in one material are in close proximity to the conduction band in the other, such as occurs in type II superlattice systems. The eight-band {dollar}{lcub}bf kcdot p{rcub}{dollar} equation is solved in each constituent material, to obtain the bulk wave functions for a given energy. Proper boundary conditions at the interface between each material are applied to find the eigenvalues and eigenstates for the heterostructure systems. A new approximation which eliminates the un-physical wing bands from the general EFA model is established. A simple, accurate and fast algorithm has been developed and employed to calculate the subband structure of type I and II quantum well and superlattice systems with and without external magnetic field. The importance of including the coupling between bands in highlighted in the context of: (1) The effect of non-parabolicity of the GaAs bulk conduction band on the conduction subbands in GaAs/AlGaAs quantum well superlattices, (2) The strong couplings and resulting anti-crossings evident in the valence subband dispersion, (3) The valence band structure of a GaAs/AlAs quantum well system in an energy range far below the valence band edge, (4) Type II InAs/GaSb superlattice systems, where the overlapping valence and conduction bands prohibit accurate analysis with simpler models.