Electronic states of (2 × 1) and (1 × 1) (111) surfaces of Ge,Si, diamond,GaAs and Ge on Si

The “dangling-bond” surface state dispersion curves, E(k), have been calculated for the (2 × 1) and (1× 1) (111) surfaces of Ge, Si, and diamond, for (1 × 1) GaAs, and for (2 × 1) Ge on Si. The calculations employ the sp³s1 empirical tight-binding model of Vogl et al. and the atomic relaxation of Feder et al. The surface state band gaps are in good agreement with optical-absorption and electron-energy-loss measurements for Ge and Si. For the assumed epitaxial geometry, Ge on Si is predicted to shift the dangling-bond states downward by ≈0.1 to 0.4 eV.