Optimized hybrid functionals for defect calculations in semiconductors

Abstract

Defects influence the electronic and optical properties of crystals, so their identification is crucial to develop device technology for materials of micro-/optoelectronics and photovoltaics. The identification requires the accurate calculation of the electronic transitions and the paramagnetic properties of defects. The achievable accuracy is strongly limited in the case of the (semi)local approximations to density functional theory, because of the underestimation of the gap and of the degree of localization. In the past two decades, hybrid functionals, mixing semilocal and nonlocal exchange semiempirically, have emerged as an alternative. Very often, however, the parameters of such hybrids have to be tuned from material to material. In this paper, we describe the theoretical foundations for the proper tuning and show that if the relative positions of the band edge states are well reproduced, and the generalized Koopmans's theorem is fulfilled by the given parameterization, the calculated defect levels and localizations can be very accurate. As demonstrated here, this can be achieved with the two-parameter Heydt-Scuseria-Ernzerhof hybrid, HSE(α,μ) for diamond, Si, Ge, TiO2, GaAs, CuGaS(Se)2, GaSe, GaN, and Ga2O3. The paper describes details of the parameterization process and discusses the limitations of optimizing HSE functionals. Based on the gained experience, future directions for improving exchange functionals are also provided.