Non-local screened-exchange calculations for defects in semiconductors: vacancy in silicon

The microscopic structure of a silicon vacancy is studied theoretically using first-principles supercell calculations. Both the standard Kohn-Sham local-density approximation (LDA) scheme and the generalized Kohn-Sham screened-exchange local-density approximation (sX-LDA) scheme are used. The latter approximation is expected to improve the description of electronic levels in the gap region substantially, while providing accurate total energies and bond lengths. The present LDA calculations are in line with the earlier corresponding calculations of the silicon vacancy, predicting an inward relaxation of the nearest neighbours of the vacant site. The LDA calculations also predict the Jahn-Teller distortions and negative effective-U effects for charged vacancies, qualitatively in agreement with the experimental results and the Watkins model. In contrast to LDA results, the present sX-LDA calculations predict an outward relaxation and sp(2) type hybridization for the ions surrounding the vacancy. This somewhat surprising result is explained by the removal of the systematic overbinding associated with LDA.