Zn vacancy-donor impurity complexes in ZnO

Results from hybrid density functional theory calculations on the thermodynamic stability and optical properties of the Zn vacancy ($V_{\text{Zn}}$) 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 non-radiative defect with transitions in the infrared region in \textit{n}-type material, to a radiative one with broad emission in the visible range when complexed with shallow donors.