Defect levels through hybrid density functionals: Insights and applications

Hybrid density functional calculations applied to defect charge transition levels are explored in the attempt to overcome the band-gap problem of semilocal density functionals. Charge transition levels of a large set of point defects calculated with semilocal and hybrid density functionals are found to correspond closely when aligned with respect to the average electrostatic potential. This strongly suggests that the defect levels defined in this way are already accurately described at these levels of theory. In particular, this then also applies to the energy separation between different defect levels, which is directly accessible experimentally. At variance, within the same alignment scheme, the band edges obtained with hybrid functionals are found to undergo significant shifts with respect to those obtained with semilocal functionals. While these shifts systematically give larger band gaps, the agreement with experiment is not always satisfactory when a fixed fraction of exact exchange is admixed. This describes a current limitation of hybrid functional schemes. In the attempt of identifying a viable theoretical description within the class of one-parameter hybrid functionals based on bare exchange, we explore the validity of the empirical procedure which consists in tuning the fraction of nonlocal exchange to a value which gives a theoretical band gap reproducing the experimental one. Comparisons with experiment for band offsets and specific defect levels record very encouraging results. Despite its inherent limitations, such an empirical scheme based on hybrid functionals represents a definite improvement with respect to semilocal functionals. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim