Electronic structure of deepsp-bonded substitutional impurities in silicon

The recently-developed Green's-function method for defects in semiconductors is used to investigate the electronic properties of deep substitutional $\mathrm{sp}$-bonded impurities in Si. These impurities are grouped according to the value ${\Delta }_z=z_{\mathrm{imp}}-z_{\mathrm{host}}$ where $z$ is the chemical valence. We choose a typical representative impurity from each group: sulfur with $\Delta z=2\mathrm{}$ (double donor), zinc with $\Delta z=-2\mathrm{}$ (double acceptor), and hydrogen with $\Delta z=-3\mathrm{}$ (triple acceptor). In each case we obtain the impurity-induced state-density changes in the valence bands, and the energy positions and wave functions of the bound states in the forbidden gaps. These results are compared with earlier results for the vacancy, which may be viewed as a $\Delta z=-4\mathrm{}$ nominal quadruple acceptor. We describe a simple physical model which explains the chemical trends as a function of $\Delta z$ and compare with available experimental data.