A study of the performance of tight-binding models for silicon and silicon-germanium alloys

An important challenge in achieving small-scale semiconductor devices is to confine dopants to small, well-defined regions because device performance depends on their accurate placement. However, semiconductor processing involves repeated annealing cycles which can cause dopants to diffuse away from their intended locations. For this reason, it is important to understand the basic physical processes of dopant diffusion on atomic length scales.; Tight binding models offer the possibility of studying diffusion in larger systems and for longer time scales than is possible with current LDA methods. However, while a wide variety of tight binding models exist for silicon, these models are not necessarily suited for dynamical studies and they are rarely extended to elements which are dopants in silicon, or to multicomponent systems. This dissertation addresses these issues.; We present the first systematic comparison of three parameterized, two-center, sp-based, tight binding models which, because of their simplicity, are suitable for dynamical studies. The models we considered are those by Goodwin et al. (GSP), Kwon et al., and Sawada. We evaluated these models for Si to determine their relative strengths and weaknesses in comparison to experimental and LDA results. Our results show that none of these models is outstanding over the others, and all give acceptable representations of the properties of Si which are of interest for dynamical studies.; Having carefully investigated the fitting process to find simple ways to fit tight binding parameters, we have provided information as to the role of each of the GSP parameters in the fitting procedure. As a result, we have recorded a detailed prescription for fitting which can be followed by researchers wanting to extend the models to additional species.; Based on our findings about the performance of the Si models, we extended the GSP model to second-nearest neighbors and produced new parameter sets for Si, Ge, and SiGe. This has resulted in a superior reproduction of a wide variety of physical properties of these systems, which is particularly evident in improved defect formation energies. We have also found that our SiGe model gives a good reproduction of Vegard's law for SiGe alloys containing up to 50% Ge. Given these results, we expect our Si, Ge, and SiGe models to perform well in dynamical studies of dopants and defects.