Supercell and cluster density functional calculations of the thermal stability of the divacancy in germanium

Large vacancy clusters, or voids, formed during growth have been reported in Ge. The divacancy is a precursor to such clusters, and is believed to be stable up to 150 or 180∘C. It is also believed to form in Ge irradiated at room temperature where single vacancies are mobile. Density functional theory calculations have been performed to calculate the energy barriers for migration and dissociation of the divacancy. We find the binding energy in the neutral charge state to lie in the range 1.1–1.5 eV, and this increases for more negative charge states. The migration energies were found to vary from 1.0 to 1.3 eV from the singly positive to the doubly negative state.