First-principles calculation of the O vacancy in ZnO: A self-consistent gap-corrected approach

The electronic structure of the oxygen vacancy in ZnO has been found to be sensitive to the corrections applied to the local (spin) density approximation (LSDA) band gap underestimate. Here, the ``$\mathrm{LSDA}+U$'' approach, in which Hubbard-$U$ corrections are added to the local density approximation, is applied to both $\mathrm{Zn}\phantom{\rule{0.2em}{0ex}}d$ and $\mathrm{Zn}\phantom{\rule{0.2em}{0ex}}s$ orbitals. The justification of this approach is discussed. Transition state energies are calculated self-consistently instead of applying a posteriori corrections. The supercell size dependence and applicability of Makov--Payne corrections is investigated and an extrapolation approach inversely proportional to the cell volume is used. The $0∕2+$ transition level is found at $0.80\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ above the valence-band maximum and a small negative $U$ behavior is obtained with $U=\ensuremath{-}0.05\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The Kohn--Sham one-electron levels in the different charge states are also presented and relevant experimental results are discussed.

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