Vacancy clustering and diffusion in germanium using kinetic lattice Monte Carlo simulations

Abstract

We investigated vacancy-assisted self-diffusion in germanium by means of kinetic lattice Monte Carlo (KLMC) simulations below the melting temperature, for a vacancy concentration of 11018/cm3. At higher temperatures, fewer clusters formed, but there was less variation in the number of clusters than at lower temperatures as the time increased. Equilibrium diffusivities in the clustering region were 102 lower than those of free vacancies in the initial stage of KLMC simulations. They were expressed according to three temperature regimes: 6.510-4 exp(-0.35/kBT) cm2/s at temperatures above 1100K, 5.2105 exp(-2.32/kBT) cm2/s at temperatures of 900-1100K and 6.00-7 exp(-0.19/kBT) cm2/s at temperatures below 900K. The effective mean migration energy, 1.1eV, closely coincided with that of the 1.0-1.2eV in experiments and was very different from the migration energy of the free vacancy.