Generalized Koopmans Density Functional Calculations Reveal the Deep Acceptor State of NO in ZnO

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 (NO) 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 NO, 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 (NO - GaZn) or (CO - TiZn) have positively charged states in the gap that act as hole traps.