Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations

This thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.

Mechanically stacked solar cells for concentrator photovoltaics

The power output of dual-junction mechanically stacked solar cells comprising different sub-cell materials in a terrestrial concentrating photovoltaic module has been evaluated. The ideal bandgap combination of both cells in a stack was found using EtaOpt. A combination of 1.4 eV and 0.7 eV has been found to produce the highest photovoltaic conversion efficiency under the AM1.5 Direct Solar Spectrum with x500 concentration. As EtaOpt does not consider the absorption profile of solar cell materials; the practical power output per unit area of a dual junction mechanically stacked solar cell has been modelled considering the optical absorption co-efficients and thicknesses of the individual solar cells. The model considered a GaAs top cell and a Ge, GaSb, Ga0.47In0.53As or Si bottom cell. It was found that GaSb gives the highest power contribution as a bottom cell in a dual junction configuration followed by Ge and GaInAs. While the additional power provided by a Si bottom cell is less than these it remains a suitable candidate for a bottom cell owing to its lower cost

Investigation of electrically active defects at the interface of high-k dielectrics and compound semiconductors

As silicon based devices in integrated circuits reach the fundamental limits of dimensional scaling there is growing research interest in the use of high electron mobility channel materials, such as indium gallium arsenide (InGaAs), in conjunction with high dielectric constant (high-k) gate oxides, for Metal-Oxide-Semiconductor Field Effect Transistor (MOSFET) based devices. The motivation for employing high mobility channel materials is to reduce power dissipation in integrated circuits while also providing improved performance. One of the primary challenges to date in the field of III-V semiconductors has been the observation of high levels of defect densities at the high-k/III-V interface, which prevents surface inversion of the semiconductor. The work presented in this PhD thesis details the characterization of MOS devices incorporating high-k dielectrics on III-V semiconductors. The analysis examines the effect of modifying the semiconductor bandgap in MOS structures incorporating InxGa1-xAs (x: 0, 0.15. 0.3, 0.53) layers, the optimization of device passivation procedures designed to reduce interface defect densities, and analysis of such electrically active interface defect states for the high-k/InGaAs system. Devices are characterized primarily through capacitance-voltage (CV) and conductance-voltage (GV) measurements of MOS structures both as a function of frequency and temperature. In particular, the density of electrically active interface states was reduced to the level which allowed the observation of true surface inversion behavior in the In0.53Ga0.47As MOS system. This was achieved by developing an optimized (NH4)2S passivation, minimized air exposure, and atomic layer deposition of an Al2O3 gate oxide. An extraction of activation energies allows discrimination of the mechanisms responsible for the inversion response. Finally a new approach is described to determine the minority carrier generation lifetime and the oxide capacitance in MOS structures. The method is demonstrated for an In0.53Ga0.47As system, but is generally applicable to any MOS structure exhibiting a minority carrier response in inversion.