Defect Formation Energies without the Band-Gap Problem: Combining DFT and \textit{GW} for the Silicon Self-Interstitial

For the self-interstitial in silicon, a defect of high technological relevance, density functional theory (DFT) in the widely applied local-density approximation (LDA) underestimates the formation energies of different configurations in the neutral charge state by $\sim$1.5 eV compared to diffusion Monte Carlo calculations [1,2]. We attriubte this to artificial self-interaction and the absence of the derivative discontinuity in the LDA exchange-correlation potential that give rise to the band-gap problem. We present a new formalism that combines LDA with quasiparticle energy calculations in the $G_0W_0$ approximation to overcome these deficiencies. The formation of the neutral defect is expressed as successive charging of its 2+ charge state, for which the defect level is unoccupied, permitting a decomposition into a lattice (LDA) and an electron addition part ($G_0W_0$) [3]. The $G_0W_0$ corrections increase the LDA formation energy by $\sim$1.1~eV. Moreover, the $G_0W_0$-corrected charge transition levels agree well with recent measurements [4]. [1] Batista {\it et al.} PRB {\bf 74}, 121102(R) (2006), [2] Leung {\it et al.} PRL {\bf 83}, 2351 (1999), [3] Hedstr\"om {\it et al.} PRL {\bf 97}, 226401 (2006), [4] Bracht {\it et al.} PRB {\bf 75}, 035211 (2007)