Results from hybrid density functional theory calculations on the thermodynamic stability and optical properties of the Zn vacancy $\left(V_{\text{Zn}}\right)$ complexed with common donor impurities in ZnO are reported. Complexing $V_{\text{Zn}}$ with donors successively removes its charge-state transition levels in the band gap, starting from the most negative one. Interestingly, the presence of a donor leads only to modest shifts in the positions of the $V_{\text{Zn}}$ charge-state transition levels, the sign and magnitude of which can be interpreted from a polaron energetics model by taking hole-donor repulsion into account. By employing a one-dimensional configuration coordinate model, luminescence lineshapes and positions were calculated. Due to the aforementioned effects, the isolated $V_{\text{Zn}}$ gradually changes from a mainly nonradiative defect with transitions in the infrared region in $n$-type material, to a radiative one with broad emission in the visible range when complexed with shallow donors.

• Received 24 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.104109