Theory of interstitial transition-metal impurities in silicon

The electronic structure of interstitial iron-group transition-metal impurities in silicon is calculated by the spin-restricted scattered-wave $X\alpha$ method. A representation of pure crystalline silicon is provided by the cluster ${\mathrm{Si}}_{10}$ ${\mathrm{H}}_{16}$, which is centered on the high-symmetry ($T_d$) interstitial position. The sixteen hydrogen atoms serve to terminate the cluster by tying up the dangling bonds. The neutral transition-metal impurities, Cr, Mn, Fe, Co, and Ni, are placed at the center of this cluster. The results of the calculation indicate that the transition-metal $3d$ states interact primarily with $t_2$ and $e$ states of the ${\mathrm{Si}}_{10}$ ${\mathrm{H}}_{16}$ cluster which are located near the top of the valence band. Consequently, antibonding $t_2$ and $e$ states are pushed into the band gap for Cr, Mn, Fe, and Co with $t_2$ below $e$; the interaction with the $3d$ state of Ni is relatively weak. Partially occupied levels in the band gap are known to be electrically active and the results of the present calculation are in good agreement with the electron paramagnetic resonance experiments of Ludwig and Woodbury.