The convergence of first-principles super-cell calculations for defects in semiconductors was studied, with the vacancy in bulk Si being used as a test case. The ionic relaxations, defect formation energies, and ionization levels were calculated for super-cell sizes of up to 216 sites by using several k-point meshes in the Brillouin-zone integrations. The energy dispersion which was inherent to deep defect states in the super-cell approximation, and the long range of the ionic registrations, were shown to postpone convergence. Conclusive results for the physical properties could thereby be obtained before the super-cell size was of the order of 128 to 216 atomic sites.

Convergence of super-cell calculations for point defects in semiconductors M.J.Puska, S.Pöykkö, M.Pesola, R.M.Nieminen: Physical Review B, 1998, 58[3], 1318-25