Scattering-theoretical method for relaxed and reconstructed surfaces with applications to GaAs(110) and Si(100)-(2×1)

The tight-binding scattering-theoretical method for the calculation of electronic properties of relaxed and reconstructed surfaces is described in detail and applied to the relaxed GaAs(110) surface and the reconstructed Si(100)-(2×1) surface. For the underlying bulk electronic structure, we employ realistic empirical tight-binding Hamiltonians retaining first- and second-nearest-neighbor interactions. In our calculations we have used surface-structural models, proposed in the literature on the basis of total energy minimization calculations. These models are in good agreement with low-energy electron-diffraction data. Relaxation- and reconstruction-induced changes in the interaction matrix elements with interatomic distance $d$ are taken into account by the $d^{-2\mathrm{}}$ scaling law, as proposed by Harrison. We discuss our results in terms of surface band structures and wave-vector—integrated as well as wave-vector—resolved layer densities of states. These theoretical data allow for a detailed discussion of the origin and physical nature of the surface-induced features. In particular, the effects of relaxation or reconstruction on the ideal surface electronic properties can transparently be analyzed in the framework of the current method. Comparison of our results with both angle-integrated and angle-resolved photoemission data shows very good agreement confirming the charge-transfer bond-angle relaxation model for GaAs(110) and the asymmetric dimer model for Si(100)-(2×1).