Role of screening in the density functional applied to transition-metal defects in semiconductors

Abstract

We study selected transition-metal-related point defects in silicon and silicon carbide semiconductors by a range-separated hybrid density functional (HSE06). We find that HSE06 does not fulfill the generalized Koopmans' theorem for every defect, which is due to the self-interaction error in the functional in such cases. Restoring the so-called generalized Koopmans' condition with a simple correction in the functional can eliminate this error and brings the calculated charge transition levels remarkably close to the experimental data as well as to the calculated quasiparticle levels from many-body perturbation theory.

Theoretical unification of hybrid-DFT andDFT + Umethods for the treatment of localized orbitals

“…(38) was demonstrated in Ref. [53], where we determined the strength of the on-site correction potential w by the fulfillment of the ionization potential (IP) theorem [9,56,57] or, in other context, the generalized Koopmans' theorem (gKT) [35][36][37]. These theorems state that the KS eigenvalue of the highest occupied KS orbital is equal to the negative ionization energy and remains constant under the variation of its occupation number in the case of the exact exchange correlation functional.…”

“…On this basis we suggested, in a previous work [53], the hybrid-DFT + V w scheme. It introduces an additional on-site screening potential…”

“…The case of V impurity in 4H-SiC has been examined in our previous article [53], however, here we reconsider this case with a more faithful treatment of the spurious electrostatic interaction of the charged point defect and carefully investigate the differences of the results of our scheme and the HSE06 functional. Additionally, we calculate the matrix elements of the hyperfine interaction of the vanadium and correlate the KS energy differences with excitation energies.…”

“…This connection is used to provide a theoretical foundation for the recently proposed hybrid-DFT + V w method of Ref. [53].…”

“…On the other hand, a large part of the exchange and correlation effects are still described in (semi)local DFT, which suffers from the self-interaction error and the absence of the derivative discontinuity. In the case of correlated points defect in the host of conventional semiconductors, neither hybrid functionals nor DFT + U can provide an accurate description, however, a corrected hybrid functional, presented in a previous paper, the HSE06 + V w , can overcome the difficulties [53]. In this article we present the theoretical motivation and foundation of this method, as well as deeper insights into the connection between the hybrid-DFT and DFT + U methods.…”