Defect Formation Energies without the Band-Gap Problem: Combining Density-Functional Theory and theGWApproach 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 local-density approximation (LDA) to DFT. We demonstrate for the silicon self-interstitial that combining LDA with quasiparticle energy calculations in the $G_0{W}_0$ approach increases the defect formation energy of the neutral charge state by $\sim 1.1\mathrm{eV}$, 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 $G_0{W}_0$-corrected charge transition levels agree well with recent measurements.