Kinetic lattice Monte Carlo simulation study on vacancy diffusion in germanium

We report kinetic lattice Monte Carlo simulations of vacancy-assisted self-diffusion in germanium below the melting point. We show that effective migration energies differ greatly from the migration energy of a free vacancy, which was calculated for a system with a low vacancy concentration. Vacancies are agglomerated in clusters and free vacancies are dissociated from clusters at temperatures above 657 °C, and the nucleation temperatures of vacancy clustering in germanium are estimated to be 617–657 °C. At temperatures below 617 °C, there are a few remaining free vacancies for low concentrations, and in that case the effective migration energy of 0.17 eV closely coincides with the migration energy derived from previous theoretical calculations for low vacancy concentrations. The effective migration energy of 1.17 ± 0.1 eV above 657 °C also closely coincides with that measured in previous experiments.