Kinetic Lattice Monte Carlo Simulations of Vacancy Diffusion in Silicon Below the Melting Point

We investigated vacancy diffusion in silicon via kinetic lattice Monte Carlo simulations of temperatures below the melting point. Equilibrium diffusivities in the cluster region were two orders of magnitude lower than those of free vacancies, which were calculated from a known low density system. While the mean cluster size was almost constant at temperatures below 1,200 K, it increased at temperatures from 1,300 K to 1,400 K and then decreased after the peak temperature of 1,400 K was reached. The number of clusters slightly increased at temperatures from 800 K to 1,200 K whereas it abruptly decreased at temperatures above 1,300 K. While high temperatures resulted in fewer large vacancy clusters, many small clusters at low temperatures resulted in fewer free vacancies in intermediate phases between aggregation and dissociation of smaller clusters. Effective migration energies of a silicon vacancy below the melting point were 2.5 eV and 0.47 eV at temperatures above and below 1,300 K, respectively.