Application of the pseudopotential method to the theory of semiconductors

The Empirical Pseudopotential Method (EPM) has been used in this thesis to investigate four areas of interest in sennconductor research, namely, strain-induced valence subband splittings, simple analytical k.p expressions for conduction and valence band dispersions, 'universal' behaviour of conduction band non-parabolicity, and r-L mixing in [111] grown superlattices. In the first of these the EPM was used to calculate directly the valence band structure of strained nlaterials. From this the strain-induced matrix elelnent, C4 , which is proportional both to the axial strain, Cax , and the in-plane wave-vector, kJ.' was deduced for all common III-V materials and selected II-VI's. The effect of C4 on properties of quantum wells is discussed with particular emphasis on layers under biaxial tension. The EPM was then used to test analytical k.p expressions that attempt to describe the conduction band anisotropy and valence bands along the [001] direction around the zone centre r point. A number of expressions have been derived which span a wide range of band gap and spin-orbit splitting energies. The EPM has allowed the range of applicability of these expressions to be deternlined. The conduction band dispersion around the r point generated by the EPM was also used to verify the 'universal' behaviour of common senliconductor Inaterials when energy and wavevector are scaled in an appropriate manner. Surprisingly we find the universality of this type is still present even when non-parabolicity effects are expected to be important. This analysis was initially done on the direct gap III-V senliconductors but was then extended to the indirect gap III-V and group IV materials, as well as the direct gap II-VI's. A modified 2-band k. p model was devised which reproduced the universal behaviour and allowed interpretation of the results using Harrison's model-solid theory. Finally superlattice (SL) bandstruct ures were generated using the supercell method of Jaros et ale with bulk Inaterial wavefunctions and energies calculated by the EPM. The technique was used to study f-L mixing in [111] superlattices using the GaSb/GaAlSb system. This was done for a wide range of barrier and superlattice compositions and then compared with f-X mixing in GaAs/GaAlAs [001] superlattices. It was then proposed that f-L mixing can be more readily modelled in device applications than can f -X mixing.