It was noted that calculations of the formation energies and charge transition levels of defects routinely relied on density functional theory for describing the electronic structure. Since bulk band gaps of semiconductors and insulators were not well described in semi-local approximations to density functional theory, band-gap correction schemes or advanced theoretical models, which properly described band gaps, had to be employed. However, it had become apparent that different methods that reproduce the experimental band gap could yield substantially different results regarding the charge transition levels of point defects. This problem was investigated in the case of the (+2/0) charge transition level of the O vacancy in ZnO; a benchmark case. Calculations based upon non-screened hybrid density functionals were first performed, and the results were then compared with those of other methods. Although the present results agreed very well with those obtained using screened hybrid functionals, they were very different when compared with those obtained using other bandgap-corrected schemes. It was nevertheless shown that all of the methods agreed well with each other and with the present calculations when a suitable alignment procedure was employed. The proposed procedure consisted of aligning the electron band structure through an external potential, such as the vacuum level. When the electron densities were well reproduced, this procedure was equivalent to an alignment through the average electrostatic potential in a calculation subject to periodic boundary conditions. It was stressed that, in order to give accurate defect levels, a theoretical scheme was required to yield not only band-gaps in agreement with experiment, but also band edges correctly positioned with respect to such a reference potential.

Band-Edge Problem in the Theoretical Determination of Defect Energy Levels: the O Vacancy in ZnO as a Benchmark Case. Alkauskas, A., Pasquarello, A.: Physical Review B, 2011, 84[12], 125206