Drude Lorentz model for dielectric constant of multilayer epitaxial graphene on C-face SiC measured by synchrotron radiation

Abstract

We report on the procedure for determining the dielectric constant of multilayer epitaxial graphene (MEG) film grown epitaxially on the carbon face (C-face) of SiC substrate. The dielectric constant is determined by fitting the reflectance spectra of C-face MEG film measured from synchrotron radiation over a broad wavenumber from 5000 – 165000 cm−1 by using Drude-Lorentz (DL) model. To calculate the dielectric constants of C-face MEG, the system is modeled with Fresnel coefficient for an optically stratified multilayer film system. The model is composed of the air, a layer that represents C-face MEG film, and a layer that represents SiC substrate. We have used forty DL oscillators and have found all parameters that give the best match to the reflectance data. Of those forty oscillators, we find five oscillators (i.e., at 5000 cm−1, 40000 cm−1, 45000 cm−1, 50000 cm−1, and 90000 cm−1) that contribute dominantly in the dielectric constant of MEG Film. Those dominant oscillators that appear at low wavenumbers (i.e., 5000 cm−1 and 40000 cm−1) related to the intraband transitions and many-body effects that have been observed and reported by earlier study while those at higher wavenumbers probably may come from the electronic transitions involving higher energy states. The results show that DL model can be used to determine the dielectric constant of MEG.