Electronic structure of copper, silver, and gold impurities in silicon.

Abstract

The electronic structure of Cu, Ag, and Au impurities in silicon is studied self-consistently using the quasiband crystal-field Green's-function method. We find that a substitutional model results in a two-level (acceptor and donor), three-charge-state (${A}^{+}$, ${A}^{0}$, and ${A}^{\mathrm{\ensuremath{-}}}$) system, which suggests that these defects are amphoteric. Our results show that these substitutional impurities form e-type and ${t}_{2}$-type crystal-field resonances (CFR) near the center of the valence band and a dangling-bond hybrid (DBH) ${t}_{2}$ level in the gap. The ${e}^{\mathrm{CFR}}$ and ${t}_{2}^{\mathrm{CFR}}$ states are fully occupied and represent the perturbed and hybridized impurity atomic orbitals (not simply a ``${d}^{10}$'' configuration). They are magnetically and electrically inactive but are predicted to be optically active in the uv, producing both impurity-bound core excitons as well as localized-to-itinerantd\ensuremath{\rightarrow}s transitions with their attendant multiplet structure. The ${t}_{2}^{\mathrm{DBH}}$ gap level comprises antibonding hybrids of the central impurity orbitals with the vacancy dangling bonds. Its delocalization suggests that both the exchange splitting and the many-electron multiplet separations are small, as opposed to the situation encountered in main-group 3d impurities (e.g., Cr, Mn, Fe) in silicon. Consequently, for group-IB impurities, Jahn-Teller distortions should not be suppressed; the magnetic and electrical response of the system is then determined by these split-off components of the ${t}_{2}^{\mathrm{DBH}}$ orbital. Thecalculated donor and acceptor transition energies suggest a 0.15--0.25 eV lattice relaxation energy and that a spin S=(1/2) resonance may be observed for Si:${\mathrm{Au}}^{0}$ if the Fermi energy is located above the donor but below the acceptor energy. Study of the bonding in these systems suggests a depopulation of the atomic s and d orbitals and participation of the metal p orbitals in bond formation. The results of this study conflict both with the Ludwig-Woodbury ionic model and with the s electron (i.e., corelike d orbital) model. Calculations for interstitial gold in Si reveal a hyperdeep s-like ${a}_{1}$ state just below the valence-band minimum, few d-like resonances in the lower part of the valence band, anda virtually bound and delocalized ${a}_{1}$ state just near the conduction-band minimum. This state can lead to a simple shallow-donor behavior. Our model for the substitutional and interstitial group-IB impurities is used to discuss site-exchange reactions and to analyze various models employed previously to describe the electronic level schemes for these centers.