Ionic Surface States from a Band-Edge Method

Abstract

The properties of surface states on ionic or partially ionic crystals such as NaCl, CdS, and GaAs have been computed using the method of linear combination of atomic orbitals (LCAO) in a novel way. The method consists of simulating an ionic crystal by assigning $s$ and $p$ orbitals on alternate sites in a one-dimensional crystal so that the resonance integral alternates in sign along a chain. This feature causes the band gap to lie at the center of the Brillouin zone, as required for these crystals. Also, the unperturbed reference energies are conveniently chosen to be the band-edge energies, rather than the separated-atom energies as in the more usual LCAO method. In an $\mathrm{MX}$ crystal, $M$-like states appear somewhat below the conduction band when the lattice is terminated at an $M$ atom. Similarly, $X$-like states appear somewhat above the valence band when the lattice ends on an $X$ atom. The results complement and support the previous Madelung and Mathieu theories for ionic surface states, and have the proper qualitative behavior to agree with experiment.