Lattice Monte Carlo simulations as link between ab-initio calculations and macroscopic behavior of dopants and defects in silicon

Abstract

In this work, we show that lattice Monte Carlo simulations can be used to span the time and distance scales between underlying atomistic processes and macroscopic diffusion behavior. We use ab- initio calculations of binding energies versus configuration to calculate hopping rates of vacancies for use in lattice Monte Carlo (LMC) simulations of diffusion and aggregation in silicon. The LMC simulations consider the biased nature of vacancy hop frequencies in the neighborhood of dopants, with interactions up to sixth-nearest- neighbor distances included. We use these simulations to investigate the expected macroscopic diffusion behavior, as well as the process by which dopant/defect aggregation occurs. Specific phenomena investigated include collective behavior 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.