Ground-state properties of isolated interstitial iron in silicon: Electronic structure and hyperfine interactions.

Abstract

We have performed ab initio total energy calculations for interstitial iron in silicon with particular emphasis on the matrix elements for the hyperfine interactions with the iron nucleus and with several silicon ligand nuclei. The total energy calculations have been performed in the general framework of the density functional theory (DFT) treating many-particle effects in the local spin-density approximation (LSDA). We use a Dyson's equation approach to solve the Kohn-Sham equation of the density functional theory and calculate the Green's function with the help of the linear muffin-tin orbital theory using the atomic-spheres approximation (ASA). Unfortunately the use of the ASA prohibits the inclusion of lattice relaxation effects. Our total energy calculations lead to a model for the electronic structure which is dominated by covalent hybridization of iron d states with silicon p states. From the results of our calculations we can easily explain the reaction of the electronic system when passing from ${\mathrm{Fe}}_{\mathit{i}}^{0}$ to ${\mathrm{Fe}}_{\mathit{i}}^{+}$. To this aim we slightly modify the Ludwig-Woodbury model: In a first step we consider the exchange splitting of the iron d states which in a second step are further split by the crystal field. The hyperfine matrix elements for Si:${\mathrm{Fe}}_{\mathit{i}}^{0}$ are calculated directly from the magnetization density obtained by the LSDA-DFT calculation and show excellent agreement with data from electron nucleus double resonance (ENDOR) experiments. For Si:${\mathrm{Fe}}_{\mathit{i}}^{+}$ we have to take into account the spin-orbit interaction of the iron d orbitals. Since our total energy calculations neglect spin-orbit interactions, we switch to a description which uses symmetry-adapted many-particle wave functions. With these functions we calculate the matrix elements for the hyperfine interaction with the iron nucleus and with several silicon ligand nuclei. We use the localization properties of our magnetization density to determine the many-particle wave function and to obtain data for the hyperfine interactions. We show that the covalent hybridization of the iron d states with iron p states and with silicon orbitals alone cannot explain the discrepancy between calculated and measured data for the hyperfine interaction with the iron nucleus. However, the additional consideration of a dynamical Jahn-Teller effect as a Ham effect leads to consistent data. The calculated data for the ligand hyperfine interaction allow one to definitely assign ligand shells to the measured ENDOR data. \textcopyright{} 1996 The American Physical Society.