Many-electron effects for interstitial transition-metal impurities in silicon

The interstitial iron-group transition-metal impurities are investigated by the self-consistent-field scattered-wave $X\alpha$ cluster method. The cluster ${\mathrm{Si}}_{10}$ ${\mathrm{H}}_{16}$ centered at the interstitial position represents the environment of each of the impurities V, Cr, Mn, Fe, Co, and Ni located at the origin. The single-particle electronic structure calculations reported in our previous publication are extended here to include many-electron effects in two different approximations. First, a spin-unrestricted calculation is performed with the hydrogen terminators moved in so that convergence is achieved. Second, a calculation based on a procedure introduced by Hemstreet and Dimmock is carried out. The first method includes spin-induced correlation between electrons; the latter includes space- and spin-induced correlation between electrons which are simultaneously in the transition-metal region. The results of both approaches indicate Hund's-rule ground states in all cases, consistent with the electron paramagnetic resonance studies of Ludwig and Woodbury. Term structures generated for V, Cr, Mn, and Fe provide optical transition energies and the corresponding symmetry selection rules for internal transitions.