It was shown that lattice Monte Carlo simulations could be used to span the time and distance scales between underlying atomistic processes and macroscopic diffusion behavior. Ab initio calculations of binding energies versus configuration were used to calculate hopping rates of vacancies for use in lattice Monte Carlo simulations of diffusion and aggregation in silicon. The  lattice Monte Carlo simulations considered the biased nature of vacancy hopping frequencies in the neighborhood of dopants, with interactions up to sixth-nearest neighbors included. The simulations were used to investigate the expected macroscopic diffusion behavior, as well as the process of dopant/defect aggregation. The specific phenomena investigated included collective behaviors leading to greatly enhanced diffusivity at high doping levels, the time dependence of effective diffusivity due to the formation of dopant/vacancy clusters, and dopant fluxes in the presence of a vacancy gradient.

Lattice Monte Carlo Simulations as Link between ab-initio Calculations and Macroscopic Behavior of Dopants and Defects in Silicon. M.M.Bunea, S.T.Dunham: Journal of Computer-Aided Materials Design, 1998, 5[1], 81-8