Predicting Polaronic Defect States by Means of Generalized Koopmans Density Functional Calculations

Lattice defects in semiconductors and wide-gap materials which create deep levels in an open-shell electronic configuration can give rise to so-called defect bound small polarons. This type of defects present a challenge for electronic structure methods because the localization of the defect state and the associated energy levels depend sensitively on the ability of the total-energy functional to satisfy the physical condition that the energy E(N) must be a piecewise linear function of the fractional electron number N. For practical applications the requirement of a linear E(N) is re-cast as a generalized Koopmans condition. Since most functionals do not fulfill this condition accurately, we use parameterized perturbations that cancel the non-linearity of E(N) and recover the correct Koopmans behavior. Starting from standard density functionals, we compare two types of parameterized perturbations, i.e., the addition of on-site potentials and the mixing of non-local Fock exchange in hybrid-functionals. Surveying a range of acceptor-type defects in II-VI and III-V semiconductors, we present a classification scheme that describes the relation between hole localization and the lattice relaxation of the polaronic state.