New perspective on formation energies and energy levels of point defects in non-metals

We propose a powerful scheme to accurately determine the formation energy and thermodynamic charge transition levels of point defects in non-metals. Previously unknown correlations between defect properties and the valence-band width of the defect-free host material are identified allowing for a determination of the former via an accurate knowledge of the latter. These correlations are identified through a series of hybrid density functional theory computations and an unbiased exploration of the parameter space that defines the Hyde-Scuseria-Ernzerhof family of hybrid-functionals. The applicability of this paradigm is demonstrated for point defects in several insulators, including Si, Ge, ZrO$_{2}$ and ZnO