Transition levels of defects in ZnO: total energy and Janak's theorem methods

Transition levels of defects are commonly calculated using either methods based on total energies of defects in relevant charge states or energy band single particle eigenvalues. The former method requires calculation of total energies of charged, perfect bulk supercells, as well as charged defect supercells, to obtain defect formation energies for various charge states. The latter method depends on Janak's theorem to obtain differences in defect formation energies for various charge states. Transition levels of V(Zn), V(O), and V(ZnO) vacancy defects in ZnO are calculated using both methods. The mean absolute deviation in transition level calculated using either method is 0.3 eV. Relative computational costs and accuracies of the methods are discussed.