A newly developed method which incorporates a parametrized, quantum mechanical, nearest neighbor total energy expression for silicon into a "ficticious Lagrangian" molecular dynamics scheme developed by Car and Parinello will be expanded to model the germanium- silicon solid solution system. A novel full range, parametrized total energy expression for the germanium-silicon system based on the local density approximation with complete transferability will be constructed. This total energy expression is parameterized against a large data base which is derived from experiment and state of the art local density approximation calculations. Computationally, it will only be slightly more demanding than the calculations for silicon alone, and finite temperature simulations of hundreds of atoms could be performed in tens of Cray YMP hours, a factor of about 50 more rapidly than the best local density approximation calculations. The study of the epitaxial growth of germanium-silicon will be done by breaking the problem into smaller components which can be studied individually; namely, relaxation of surfaces, steps and kinks, sticking and diffusion of an atom on this surface, dynamics of atoms near a relaxed kink, and growth of kinks into steps. %%% Computational techniques will be developed to model the total energies of germanium-silicon mixtures - an important material for the electronics industry. The proposed technique will accelerate the calculation of important properties. The proposed techniques have the potential to have a major impact on the way that these properties are calculated and can be applied to other materials of scientific and commercial interest.
