Dielectric properties of the Si(111) 2×1 surface: Optical constants and the energy-loss spectrum

We present a method of computation of the optical constants of the surface layer of a solid, starting from a differential reflectivity spectrum. The differential reflectivity was obtained by comparing the overall reflectivity of the same sample in the case of a clean and oxidized surface. The method assumes sharp interfaces at the vacuum surface and at the surface bulk side. The physical properties of the bulk and of the surface layer are described by an energy-dependent dielectric constant. This method is applied to the Si(111)2×1 surface. The surface optical constants are derived in the (0.3-4.0)-eV range. With the use of the same model and the calculated optical constants, the electron-energy-loss spectrum of the Si(111)2×1 surface has been calculated. The agreement with the experiment is good. This is assumed as a proof of the reliability of the optical constants. In addition the comparison of the calculated energy-loss spectrum and the experiment allows the explanation of the apparent disagreement between optical and energy-loss experimental data in the near-infrared range. We demonstrate the different nature between the energy-loss peak and the optical one, the first due to the excitation of the two surface interface modes of the Si(111)2×1 surface layer and the second to an interband transition.