Density-functional theory (DFT) calculations of defect levels in semiconductors based on approximate functionals are subject to considerable uncertainties, in particular due to inaccurate band-gap energies. Testing previous correction methods by many-body $GW$ calculations for the O vacancy in ZnO, we find that: (i) The $GW$ quasiparticle shifts of the $V_{\text{O}}$ defect states increase the spitting between occupied and unoccupied states due to self-interaction correction, and do not reflect the conduction- versus valence-band character. (ii) The $GW$ quasiparticle energies of charged defect states require important corrections for supercell finite-size effects. (iii) The $GW$ results are robust with respect to the choice of the underlying DFT or hybrid-DFT functional, and the $\left(2+/0\right)$ donor transition lies below midgap, close to our previous prediction employing rigid band-edge shifts.

• Received 13 October 2009

DOI:https://doi.org/10.1103/PhysRevB.81.113201