Level positions of interstitial transition-metal impurities in silicon

The single-donor and single-acceptor level positions associated with defect- to band-state excitations are calculated for the interstitial transition-metal impurities V, Cr, Mn, Fe, Co, and Ni in silicon. Electronic relaxation and many-electron corrections are included. The single-particle electronic structures have been calculated by us previously according to the self-consistent-field scattered-wave $X\alpha$ cluster method, and reported in earlier papers. The effects of electronic relaxation are here estimated by the Slater transition-state procedure. Many-electron corrections are considered in two approximations: A spin-unrestricted approach which includes only spin-induced correlation between electrons, and an approach suggested by Hemstreet and Dimmock which includes both space- and spin-induced correlations between electrons, but in an approximate way. The level positions computed using the latter approximation scheme are in good agreement with experiment with the possible exceptions of the Fe single-acceptor level and the V single-donor level. It is found that the many-electron corrections to the computed level positions are relatively small (∼0.1 eV) provided that the effect is properly included in both the initial and final states. Electronic relaxation is found to separate single-donor and single-acceptor levels by ∼0.3 eV.