Defect formation energies without the band-gap problem: Combining density-functional theory and the GW approach for the silicon self-interstitial

We present an improved method to calculate defect formation energies that overcomes the band-gap problem of Kohn-Sham density-functional theory (DFT) and reduces the self-interaction error of the localdensity approximation (LDA) to DFT.We demonstrate for the silicon self-interstitial that combining LDA with quasiparticle energy calculations in the G0W0 approach increases the defect formation energy of the neutral charge state by ~1.1 eV, which is in good agreement with diffusion Monte Carlo calculations (E. R. Batista et al., Phys. Rev. B 74, 121102(R) (2006); W.-K. Leung et al. Phys. Rev. Lett. 83, 2351 (1999)). Moreover, the G0W0-corrected charge transition levels agree well with recent measurements