Terrace and step contributions to the optical anisotropy of Si(001) surfaces

The contributions of atomically flat terraces as well as of $S_A,$ $S_B,$ and $D_B$ steps to the optical anisotropy of Si(001) surfaces have been calculated using a real-space multigrid method together with ab initio pseudopotentials. Our results for ideal $(1\mathrm{}\times 2),$ $p(2\mathrm{}\times 2),$ and $c(2\mathrm{}\times 4)$ reconstructed surfaces show a distinct influence of the dimer arrangement on the optical spectra. The calculated spectrum for the $\mathrm{Si}\mathrm{}\left(001\right)c(2\mathrm{}\times 4)$ surface agrees best with the signal measured for atomically smooth terraces. The significant optical anisotropy around 3 eV observed for vicinal surfaces, however, is induced by surface steps. Both electronic transitions directly at the surface as well as in deeper layers contribute to the optical anisotropy. We identify two mechanisms causing anisotropy signals from layers beneath the surface: the influence of the anisotropic surface potential on the bulk wave functions as well as minor contributions from atomic relaxations caused by surface-induced stress.