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Density functional theory with local density approximation including on-site Coulomb interaction has been used to calculate the formation energy of the neutral and charged vacancy in germanium as a function of the Fermi level. The calculations suggest that vacancies in germanium are multiple-level acceptors with a first level at 0.02eV and a second level at 0.26eV above the valence band maximum in agreement with published experimental data. The formation energies of the neutral and charged vacancies line up well with the experimental values estimated from quenching experiments.

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