Applying a generalized Koopmans condition to recover the linear behavior of the energy with respect to the fractional occupation number, we find that substitutional nitrogen $\left({\text{N}}_{\text{O}}\right)$ in ZnO is a deep acceptor with an ionization energy of 1.6 eV, which is prohibitively large for $p$-type conductivity. Testing the generalized Koopmans condition in computationally more demanding hybrid-functional calculations, we obtain a very similar result for ${\text{N}}_{\text{O}}$, but find that the simultaneous correction of defect (acceptor-level) and host (band-gap) properties remains challenging in hybrid methods. The deep character of anion-site acceptors in ZnO has important consequences for the concept of codoping, as we show that nominally charge-compensated impurity pairs such as $\left({\text{N}}_{\text{O}}\text{−}{\text{Ga}}_{\text{Zn}}\right)$ or $\left({\text{C}}_{\text{O}}\text{−}{\text{Ti}}_{\text{Zn}}\right)$ have positively charged states in the gap that act as hole traps.

• Received 27 January 2010

DOI:https://doi.org/10.1103/PhysRevB.81.205209