Relationship of Surface-State Band Structure to Surface Atomic Configuration of Zinc Blende (110)

Intrinsic surface-state band structure has been computed for zinc blende (110) from an adaptation of the Slater-Koster representation of the bulk electronic states. In particular, $s$ orbitals are assigned to the $M$ ions, and $p_x,p_y,p_z$ orbitals to the $X$ ions; the bulk conduction band is then $M$-like and the valence band is $X$-like with the correct symmetry. Also, the zone center bandgap and curvature are adjusted to fit experiment or other theory. In this scheme, it has proved possible to explicitly include displacements of $M$ and $X$ surface ions from their ideal positions, consistent with the low-energy electron-diffraction (LEED) result that no reduction of the surface periodicity takes place (no new spots are observed). It was found that both $M$ (acceptor)-like and $X$ (donor)-like surface-state bands appeared most easily when such ion displacements were combined with the modification of the surface "Coulomb integrals" customarily considered. To a first approximation, both $M$- and $X$-like surface-state effective masses are found equal to those of the adjoining bulk bands. An analysis such as this is shown to interrelate surface ion geometry with surface electrical properties. In the present case, we find indications that the $X \mathrm{}\left(M\right)\mathrm{}$ ion is displaced into (out of) the nominal surface plane.