Free carrier plasma edge and plasmonic excitations in heavily doped surface grated n-type Si

Abstract

Infrared spectroscopic ellipsometry (SE) in the MID IR region was applied at room temperature to heavily doped n++-Si to obtain information about the free carrier plasma edge and plasmonic excitations before and after the Si surface was grated with a period Λ of 294 nm to a nominal depth of 20 nm by using laser lithography. Besides, SE measurements were performed in the NIR-VIS-UV spectral range to validate the optical models for non-grated and grated Si. In the latter case a thin grated layer on silicon surface was alternatively modelled either within Bruggeman effective medium approximation (BEMA) or by treating this layer as an anisotropic thin film (ATF). A model that included SiO2 (2.1 nm), n++-Si substrate and a 24.5 nm-thick ATF for grated layer was found to be good enough to reproduce the obtained ellipsometric parameters in the accessed spectral range. Intraband optical transitions are shown to overwhelmingly contribute to the MID IR dielectric function (DF) below the free carrier plasma edge (FCPE) of non-grated n++-Si. The parameters obtained for conduction electrons from Drude fit to this function agree well with the relevant data reported for Si so far. FCPE of non-grated n++-Si is positioned at 1416 cm−1. For graded layer this value is preserved within determination accuracy. The life time of plasmonic excitations that appeared as a single peak with a perfect Lorentz line-shape in the dielectric energy loss function of non-grated Si and grated Si layer is about 70 fs. Shape induced optical anisotropy, along with presumably conical diffraction that identified itself through a distinct angle-dependent upturn in the reflection spectra of p-polarized light incident upon surface in the plane perpendicular to Λ is behind the whole set of ellipsometric data obtained for n++-Si with subwavelength grating on the surface.