Electronic states in semiconductor superlattices and quantum wells

The aim of this thesis is two-fold. Firstly to show how a complex bandstructure matching technique has been developed which allows detailed investigations to be made of various low dimensional structures. Secondly the method will be used to investigate interesting physical properties of quantum wells and superlattices. Consequently the thesis will begin with an exposition of the matching technique, giving an indication of the numerical methods used for computational calculations. Evidence will then be given, in the form of a comparison between the present work and the experimental and theoretical results to be found in the literature, of the efficacy of the method. A detailed description of results of calculations carried out on the valence band of AlAs/GaAs and AlGaAs/GaAs quantum wells will show how energy levels and wavefunctions have been calculated as well as giving an explanation of hybridisation and anti-crossing effects. In order to extend the method to strained systems it will be shown how strain can be incorporated into the model by simple empirical fits of calculated bulk properties to experiment. This method will be used to model two particular Si/Ge structures: a Ge(_0.25)Si(_0.75)/Si/Ge(_0.25)Si(_0.75) quantum well and a (Si)(_4)(Ge)(_4) superlattice. To allow a better comparison with experiment for the superlattice a description is given of a method for calculating optical matrix elements between superlattice states; and the results of such calculations are discussed.