A recently-developed ab initio theory of second harmonic generation (SHG) spectroscopy of semiconductor surfaces is used to develop a new ‘modified’ semi-empirical tight binding model (SETBM) of SHG spectroscopy. Some key quantitative features of experimental SHG spectra for H- and Ge-covered Si(001) are not well explained by a simple two-parameter SETBM, despite its success in explaining linear semiconductor surface spectra. The ab initio theory identifies the source of this short-coming as the stronger contribution of optical transitions involving surface atom/adatom states to the SHG response, and is then used to quantify additional SETBM parameters describing these transitions, resulting in a complete, accurate, and convenient description of surface orbital hybridization and experimental results.

We present a systematic analysis of the intensity anisotropy of fourth harmonic generation (FHG) in reflection from centrosymmetric crystals of classes m3m (e.g. diamond structure) and 6/mmm (e.g. graphite) and non-centrosymmetric crystals of class 4̄3m (e.g. zincblende structure). Surface dipole FH contributions are analyzed for six symmetry classes (2mm, 4mm, 3m, m, 6mm, 5-fold) which encompass the (001), (111), and (110) surfaces of the diamond-zincblende crystals, the (001) surface of graphite. and the (00001) surface of an icosahedral quasicrystal.