Theory of dielectric-function anisotropies of (001) GaAs (2×1) surfaces

We present theoretical studies of the surface dielectric functions of (001) GaAs with As-terminated (2×1) and Ga-terminated (1×2) reconstructions as approximations to the (2×4) and (4×2) reconstructions observed in molecular-beam epitaxy. We assume a surface geometry of symmetric As or Ga dimers. A nearest-neighbor tight-binding model with six orbitals (s,x,y,z, ${\mathrm{x}}^2$-${\mathrm{y}}^2$, 3${\mathit{z}}^2$-${\mathit{r}}^2$) per atom is used in the calculation. The interaction parameters and optical matrix elements between atomic orbitals are determined by fitting the band structure and optical matrix elements between Bloch states over the entire Brillouin zone to the corresponding empirical pseudopotential results. The calculated dielectric-function anisotropies for GaAs (2×1) surfaces are analyzed with reference to the electronic structures, and are compared to data.