Silicon-Germanium alloy heterostructures offer the most viable opportunity to integrate
electronics with optoelectronic devices for widespread commercial application. Indeed
Germanium rich devices may be designed for application around 1.5 m by preying on
the direct-gap energy of 890meV. Low power optical modulators operating, under the
quantum confined Stark effect, at wavelength bands used in 3rd generation fibre optic
communication channels are developed in this thesis from a theoretical perspective.
An investigation into strained Germanium rich quantum well structures was performed,
revealing information about sub-band dispersion, joint density of states and absorption
coefficient using the double group formulation of k . p theory.
Using zone centre eigenstates as symmetrised half integer basis functions transforming
according to irreps of the double group, the spin orbit interaction is incorporated into
the unperturbed Hamiltonian. Along with semi-empirical input parameters available
in the literature, dispersion in bulk Silicon and Germanium reveals information about
hole effective masses and indirect conduction band minima in broad agreement with
experimental data.
In accordance with degenerate perturbation theory; effective mass Hamiltonians, with an
arbitrary quantisation axis through a canonical transformation, are constructed through
a series of matrix multiplications. Retaining operator ordering allows numerical modelling
of heterostructures grown on arbitrary growth planes with appropriate boundary
conditions across an abrupt interface under the envelope function framework. In this
thesis, the effect on the transition energy, hh1-e1, by the choice of growth plane in a
quantum well heterostructure is investigated.