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

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 1 × 1018/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: 6.5 × 10− 4 exp(–0.35/k B T) cm2/s at temperatures above 1100 K, 5.2 × 105 exp(–2.32/k B T) cm2/s at temperatures of 900–1100 K and 6.0 × 0–7 exp(–0.19/k B T) cm2/s at temperatures below 900 K. The effective mean migration energy, 1.1 eV, closely coincided with that of the 1.0–1.2 eV in experiments and was very different from the migration energy of the free vacancy.