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

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 (V0V0), negatively charged (V-V-) and double negatively charged (V=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 V0V0, V-V- and V=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.