The substrate effects are studied in detail. Once chemical bonds are formed, there is no guarantee that electrons are confined within a designated adatom structure. This is not appropriate in device applications and must be avoided. Examples for this type of substrate is a usual silicon crystal, a germanium crystal, a gallium arsenide crystal, and many metallic crystals like copper. Oppositely, if the lattice spacing is longer than the s-p crossing point, then there are no surface states of this kind, and all the modes penetrate deep into the substrate.
Examples are alkali halide crystals, like sodium chloride.
Apparently, we need to stick to the former s-p crossing substrate as long as the chemical bonding scheme is sought. As a gedanken experiment, the lattice spacing is changed from infinity to a finite value as the crystal is conceived of using the same tight-binding method. This is a mathematically simplified one-dimensional model to study the origin of surface states, and the surface states in this context correspond to edge states, where electrons strongly localize at the dangling bonds of the edge atoms. The figure shows that the edge states always appear in the middle of the band gap once after the s-p crossing has occurred. The edge states are quite robust, and their existence is not influenced by the detail of the lattice symmetry.