Predicting polaronic defect states by means of generalized Koopmans density functional calculations

Abstract

AbstractLattice 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.