Ab initio study of vacancy and self-interstitial properties near single crystal silicon surfaces

The microscopic model of the Si(001) crystal surface was investigated by first principles calculations to clarify the behavior of intrinsic point defects during crystal growth and thermal annealing. A c(4 × 2) structure model was used to describe the crystal surface in contact with vacuum. The calculations show that a vacancy in the first or second atomic layer has about a 2.0 eV lower formation energy than deeper inside the bulk and that there is a diffusion barrier to penetrate into the deeper crystal region. Furthermore, a vacancy in the first or second atomic layer is stabilized by the fact that Si atoms with dangling bonds attract each other due to ionic and/or covalent bonding. There is, however, no barrier for the diffusion of a vacancy from the first layer to the second one. The tetrahedral (T)-site and dumbbell (DB)-site, in which a Si atom is captured from the surface and forms a self-interstitial, are found as stable sites near the third atomic layer. The T-site has a barrier of 0.48 eV, whereas the DB-site has no barrier for the interstitial to penetrate into the crystal from the vacuum. Self-interstitials in both the T- and DB-sites in the third atomic layer have a 1.7 to 2.8 eV lower formation energy than deeper in the bulk and there is a diffusion barrier to penetrate into the deeper crystal region; 32 sites were found as stable sub-surface vacancy positions, whereas only 8 sites were found as stable self-interstitial positions. Using these results, a mechanism for the elimination of crystal-originated pits by thermal annealing is proposed. It is shown that the microscopic model is consistent with and allows to fine-tune existing macroscopic models that are used to calculate the intrinsic point defects behavior during crystal growth from a melt.