Formation energy and migration barrier of a Ge vacancy from ab initio studies

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Here we present local density functional calculations of the formation and migration energies of a vacancy in large Ge supercells and hydrogen-terminated Ge clusters. Migration barriers for neutral ( V 0 ), negatively charged ( V - ) and double negatively charged ( V = ) vacancies were calculated by using symmetry-constrained atomic relaxations, as well as a nudged elastic band scheme. The formation energy of the neutral vacancy is estimated at 2.6 eV, whereas 0.4, 0.1 and 0.04 eV are obtained for migration barriers of V 0 , V - and V = , respectively. These figures account well for the formation kinetics of vacancy-impurity complexes in Ge at cryogenic temperatures, and are also in line with measured self-diffusion activation barriers obtained at elevated temperatures.