Semi-empirical modelling of SiGe hetero-structures

The k . p perturbation method, initially developed for bulk systems has subsequently been generalised to model heterostructures using the envelope function approximation. This semi-empirical modelling technique provides vital information on the electronic and optical properties of complicated material systems that form heterostructures. It is known that k . p theory can be formulated in two ways; either through use of single or double group basis functions, with the implication that spin orbit interaction is either treated as a perturbation in parallel with the k . p term, or as part of the unperturbed Hamiltonian. The critical difference between the two approaches is that under the former, single group selection rules are considered in the evaluation of the k-dependent Hamiltonian, and the subsequent treatment of spin orbit interaction as a perturbation places restrictions on the adapted double group bases. Under the latter approach, double group selection rules are considered, resulting in an explicit change in the k-dependent Hamiltonian for multiband models of 14-band models or higher, and implicit changes to material parameters describing lower band models. A key result, is the ability of the double group formulated k . π theory to properly account for the experimentally measured spin orbit band and conduction band effective masses. This in particular leads to a change in the bulk valence band dispersion relation. In heterostructures, double group-effective mass equations result in changes to the operator ordered Hamiltonian, and the use of double group material parameters impacts the confinement energies and in-plane dispersion of subbands in a quantum well. An investigation is made into the impact of these changes on the electronic properties of Ge/SiGe heterostructures, which have applications as optical modulator devices.EThOS - Electronic Theses Online ServiceGBUnited Kingdo