Semi-empirical modelling of SiGe hetero-structures
Author(s)
Elder, Warren James
Type
Thesis
Abstract
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.
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.
Date Issued
2012
Date Awarded
2012-07
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Zhang, Jing
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)