Self-consistent electronic structure of the chlorine-adsorbed silicon (111) surface

A first-principles self-consistent-field calculation of the electronic structure of the Si(111) surface with a layer of chemisorbed Cl atoms has been performed by means of the method of linear combinations of atomic orbitals. A thin-film crystal consisting of twelve infinite (111) Si layers plus one layer of Cl on each side is considered. The crystal potential is expressed as a superposition of localized function at each site, and the basis functions consist of two-dimensional Bloch sums of the $1s$,$2s$,$2p$,$3s$,$3p$ atomiclike functions and of contracted-Gaussian orbitals for each layer of the film. By means of the Gaussian techique, all the multicenter integrals are evaluated exactly and the Hamiltonian matrix elements are computed by summing these integrals over all the lattice points to convergence. The solution of the one-electron Hamiltonian is carried to self-consistency. Application of Mulliken's method of population analysis enables us to determine the fraction of electron charge allocated to each layer for a given wave function and quantitatively characterize the localization of the surface states. At the $\overline{\Gamma }$ point of the two-dimensional Brillouin zone, we find a surfacelike $\sigma$ state at -13.4 eV (relative to the vacuum level) and a $\pi$ surface state at -10.7 eV. The localized behavior of the latter persists at ${\overrightarrow{\mathrm{k}}}_{\parallel }$ points on the $\overline{\Gamma }\overline{M}$ line. The calculated local density of states (LDS) for the valence band agrees well with the experimental photoemission data. In the lower conduction band we find one LDS peak due to surface states at -3.4 eV which corresponds closely to the electron-energy-loss data. Estimates of the LDS for the upper conduction band have been made and the results are in reasonable accord with experiment. A population-analysis calculation indicates a net charge of -0.35 $e$/ atom ($e$ being proton charge) for the Cl layer and 0.27 $e$/ atom for the adjacent Si layer with some residual ionicity in the next few layers.