Second-harmonic generation from single-domain Si(1 0 0) surfaces

We apply a microscopic formulation based on the semi-empirical tight-binding method to calculate the second-harmonic spectra of a clean single-domain Si(1 0 0)c(4×2) surface. The dimer formed between the top-most Si atoms and the sublayer atoms give a surface with a C1v symmetry class, characterized by ten non-zero elements of the non-linear surface susceptibility tensor χ↔. This symmetry gives rise to a second-harmonic signal that is anisotropic in the azimuthal angle φ which the incident plane of the fundamental beam of frequency ω makes with the surface plane. The anisotropy depends on the surface or bulk nature of the SH resonance. In particular, the spectral range around the Si E1 critical point is investigated.