Comparative study of defect transition energy calculation methods: The case of oxygen vacancy in In2O3and ZnO

Theoretical calculation of defect properties, especially transition energy levels, is typically done by first-principles density-functional theory calculation using supercells with finite size. So far, three approaches---band-filling corrections (BFC), band-edge corrections (BEC), and no corrections (NC)---have been applied to deal with the potential inaccuracy caused by the finite size. In this paper, we compare these three approaches by calculating the (0/2$+$ ionization energies of the oxygen vacancy (V${}_{\mathrm{O}}$) in In${}_{2}$O${}_{3}$ and ZnO. We find that a correction must be included whether or not the defect level is deep or shallow, especially when the defect band has a large dispersion. The BFC approach gives the best correction. The BEC approach works well in GGA calculations only for certain systems in which the band gap underestimation is partially corrected by choosing effective band edges.