Back-reflection Second-harmonic Generation of (111)Si: Theory and Experiment

Abstract

We consider second-harmonic generation (SHG) from a (111) surface of a tetrahedrally bonded semiconductor illuminated at normal incidence by a focused pump beam of Gaussian cross section as a model of SHG by focused beams. Calculations are done in the anisotropic bond model (ABM) and the results are applied to Si. The unit-cell configuration is simple enough for the calculations to be done analytically, so the results can be compared directly to similar calculations done for amorphous material. Although the differences in unit-cell symmetry occur on the atomic scale, they lead to large differences in the spatial distribution of the emerging radiation. Lateral focusing, which might be expected to increase the bulk contribution to SHG by increasing the lateral field gradient, has little effect; the spatial-dispersion contribution remains dominated by the phase term. Focusing does not inhibit backscattered SHG from the bulk, although our data on the oxidation of H-terminated (111)Si clearly show that in some cases the interface contribution dominates by a wide margin.