Understanding the negative vacancy in silicon without configuration interaction theory

Abstract

We have calculated the electronic structure of the lattice vacancy in silicon in the negative charge state ${V}^{\ensuremath{-}}$ using the self-consistent charge density-functional theory based tight-binding scheme for the computation of large supercells containing up to 512 atoms in combination with the linear muffin-tin orbitals method in the atomic-spheres approximation. Many-body effects are treated in the local spin density approximation of the density functional theory (LSDA-DFT). We find the ground state of the ${V}^{\ensuremath{-}}$ to be the low-spin ${}^{2}{B}_{1}$ state of the group ${C}_{2v},$ which is lower in energy by 0.09 eV than the ${}^{4}{A}_{2}$ high-spin state of the group ${T}_{d}.$ We have also calculated the hyperfine interactions with 18 shells containing 46 ${}^{29}\mathrm{Si}$ ligand atoms. We find the largest HF interactions in the (11\ifmmode\bar\else\textasciimacron\fi{}0) plane in agreement with experimental data. The HF interactions with nuclei in the (110) plane, which are about two orders of magnitude smaller than those with nuclei in the (11\ifmmode\bar\else\textasciimacron\fi{}0) plane, also agree with the experimental data. We conclude that the LSDA-DFT describes the magnetization density of the ${\mathrm{V}}^{\ensuremath{-}}$ well. It is therefore not necessary to include configuration interactions as has been proposed by M. Lannoo [Phys. Rev. B 28, 2403 (1983)].