Ab initiocluster calculations for vacancies in bulk Si

Atomic and electronic structures of neutral and positively charged monovacancies in bulk Si are investigated from first principles using a cluster method. The calculations are performed in real space on bulk-terminated clusters containing up to 13 shells around the vacancy $(\approx$ 200 Si atoms). Vacancy-induced atomic relaxations, Jahn-Teller distortions, vacancy wave-function characters, and relaxation and reorientation energies are calculated as a function of the cluster size and compared with available experimental data. Potential-energy surfaces in the two-dimensional space of the relaxation normal modes are presented for neutral and positive charge states of the vacancy.