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 G0W0 approach increases the defect formation energy of the neutral charge state by approximately 1.1 eV, which is in good agreement with diffusion Monte Carlo calculations (E. R. Batista, Phys. Rev. B 74, 121102(R) (2006)10.1103/PhysRevB.74.121102; W.-K. Leung Phys. Rev. Lett. 83, 2351 (1999)10.1103/PhysRevLett.83.2351). Moreover, the G0W0-corrected charge transition levels agree well with recent measurements.