The vacancy mechanism for dopant diffusion was investigated at the microscopic level. The concentration dependence of the dopant diffusion coefficient in the high-concentration regime was simulated by using Monte Carlo methods and an atomistic model for clustering and precipitation. The simulation took account of the microscopic forces between particles (dopant atoms and vacancies) in a quantitative manner. Since sufficiently accurate data for the binding strength and shape of the interaction potentials were not available, various models for these interactions were analyzed in order to judge the likely macroscopic consequences of microscopic models. Purely attractive forces between dopants and vacancies were considered first. It was found that it was not possible to fit the experimental results by using this approach. Models with repulsive dopant-dopant potentials of Coulomb shape, together with attractive dopant-vacancy forces, were also found to give unrealistic results. On the other hand, a good fit to experimental data was obtained by assuming a non-binding dopant-vacancy interaction that increased the mobility of the vacancy only in the neighborhood of a dopant. The parameters of the atomistic potential were derived by fitting the simulations to experimental data. The simulation results for various microscopic approaches were also used to assess the validity of models, for high-concentration diffusion, that were based upon percolation theory.

S.List, H.Ryssel: Journal of Applied Physics, 1998, 83[12], 7595-607