Static and high-frequency electric fields in silicon MOS and MS structures probed by optical second-harmonic generation

We present a comprehensive analysis of the effects of static and high-frequency electric fields in silicon metal-oxide-semiconductor (MOS) and metal-semiconductor (MS) structures on optical second-harmonic generation (SHG). First, a general Green's function formalism developed by Sipe [J. Opt. Soc. Am. B 4, 481 (1987)] is applied to determine the voltage dependence of the SHG response from planar MOS structures. This approach takes directly into account the spatial distribution of the dc-electric-field across the silicon space-charge region. Predictions of the theory are in good agreement with experimental results of the SHG bias dependence from MS and MOS structures. Furthermore, the azimuthal SHG anisotropy from Si(111) MOS and Si(001) MS interfaces is determined in the presence of a reverse bias allowing a clear separation of various anisotropic contributions resulting from inhomogeneous bias fields and anisotropic ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ or ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ tensor elements. Finally, we demonstrate the capability of optical SHG for time-resolved measurements of free-running GHz signals on silicon millimeter-wave devices. Consequences for circuit testing are discussed.