Hybrid density functional calculations are performed to study the electronic and optical properties of substitutional Li and Na in ZnO. Our calculations correctly show hole localizations at neutral ${\text{Li}}_{\text{Zn}}^0$ and ${\text{Na}}_{\text{Zn}}^0$, which lead to the formation of small polarons as observed experimentally. This is in contrast to previous local-density and generalized gradient calculations that showed delocalized holes. The calculated localization energies are, however, still noticeably smaller than the available experimental values. Our analysis of the discrepancies suggests that further improvement of the theory and a refinement of the experimental values are both required.

• Received 24 July 2009

DOI:https://doi.org/10.1103/PhysRevB.80.115217