Broadband optical properties of graphene and HOPG investigated by spectroscopic Mueller matrix ellipsometry

Abstract

Optical properties of mono-graphene fabricated by chemical vapor deposition (CVD) and highly oriented pyrolytic graphite (HOPG) are comparatively studied by Mueller matrix ellipsometry (MME) over an ultra-wide energy range of 0.73–6.42 eV. A multilayer stacking model is constructed to describe the CVD mono-graphene, in which the roughness of the glass substrate and the water adsorption on the graphene are considered. We introduce a uniaxial anisotropic dielectric model to parameterize the optical constants of both the graphene and the HOPG. With the established models, broadband optical constants of the graphene and the HOPG are determined from the Mueller matrix spectra based on a point-by-point method and a non-linear regression method, respectively. Two significant absorption peaks at 4.75 eV and 6.31 eV are observed in the extinction coefficient spectra of the mono-graphene, which can be attributed to the von-Hove singularity (i.e., the π-to-π∗ exciton transition) near the M point and the σ-to-σ∗ exciton transition near the Γ point of the Brillouin zone, respectively. Comparatively, only a major absorption peak at 4.96 eV appears in the ordinary extinction coefficient spectra of the HOPG, which is mainly formed by the π-to-π∗ interband transition.