The vacancy-mediated diffusion of dopants was investigated by using Monte Carlo simulations of hopping diffusion, as well as analytical approximations which were based upon atomistic considerations. The dopant/vacancy interaction potentials were assumed to extend out to third-nearest neighbors, as required by pair diffusion theories. An analysis which concentrated on the third-nearest neighbor sites, as bridging configurations for uncorrelated hops, led to an improved analytical model for vacancy-mediated dopant diffusion. The Monte Carlo simulations of vacancy motion on a doped Si lattice confirmed the analytical results for moderate dopant levels. At very high doping levels (greater than 2 x 1020/cm3), the simulations indicated a very rapid increase in pair diffusivity that was due to the interaction of vacancies with more than one dopant atom. This behavior had been observed experimentally for group-IV and group-V atoms in Si, and the simulations predicted both the point of onset, and the doping dependence, of the experimentally observed diffusivity enhancement.

S.T.Dunham, C.D.Wu: Journal of Applied Physics, 1995, 78[4], 2362-6