A super-cell approach for the study of localized defects in solids: carbon substitution in bulk silicon

Carbon substitution in bulk silicon has been investigated using the super-cell approach, in conjunction with the periodic ab initio Hartree-Fock method. The convergence of the defect formation energy and of the relaxed defect geometry as a function of the super-cell size is discussed with reference to super-cells containing 8, 16, 32 and 64 atoms. It turns out that the convergence of the unrelaxed defect formation energy is rapid, in spite of the large local charge redistribution around the defect (the net charge on carbon is 1.2 mod e mod ); the relaxation effects are very large (about 2.0 eV) and involve mainly the first and second neighbours; however, the relaxation of the fifth neighbours of the defect (which is possible only with the biggest super-cell considered) lowers the energy by a further 0.06 eV. The defect formation energy and the atomic displacements obtained with the 32 and 64 atoms super-cells are similar, whereas the energy difference between the 16 and 32 atoms cells is as large as 0.4 eV.