Electronic surface error in the Si interstitial formation energy

The results for Si interstitial formation energies differ substantially if calculated with quantum Monte Carlo (QMC) or density functional theory (DFT) techniques. In fact, not even DFT results using different exchange-correlation functionals agree well for these energies. We carefully quantify the differences between the DFT results by accurate calculations with large supercells. A similar discrepancy for vacancy formation energies in metals has previously been resolved by introducing the concept of an electronic surface error, and this view is adopted and shown relevant also for the present DFT results for interstitials in semiconductors. The origin of the surface error for the Si interstitial is explained by careful examination of the electron density. A postcorrection for the surface error brings all the results obtained with the tested functionals close to the results of the AM05 functional. However, it remains an important puzzle that while the surface error correction aligns the DFT results, they are still in large disagreement with QMC results.