Spectroscopic imaging ellipsometry and Fano resonance modeling of graphene

Abstract

In this work, we have examined the optical properties of exfoliated graphene on an Si/SiO2 substrate using spectroscopic imaging ellipsometry in the visible range (360–800 nm). Measured spectra were analyzed by an optical model based on the Fresnel coefficient equations. The optical model was supported by correlated Raman and atomic force microscopy measurements. The complex refractive index of graphene was obtained by inversion of the measured ellipsometry data. The Fano line-shape was used to parameterize the optical properties. Measurements were highly reliable due to the numerous advantages of the spectroscopic imaging ellipsometric technique combined with the proper choice of substrate and experimental set-up. Thickness maps of the graphene sample were obtained from spatially resolved imaging ellipsometry spectra with a spot size of 1 μm. The data showed the presence of a water layer on the surface of the sample, and the thickness was mapped showing the distribution of water over graphene in ambient conditions.

Large-area microfocal spectroscopic ellipsometry mapping of thickness and electronic properties of epitaxial graphene on Si- and C-face of 3C-SiC(111)

“…24 Imaging ellipsometry was used to determine thickness of small flakes of exfoliated graphene. [25][26][27] We have recently reported the visible-ultravacuum dielectric functions of EG grown on different polytypes of SiC, where we developed a parameterized dielectric function model for graphene. 21 frequencies combined with optical Hall effect measurements revealed and quantified conductive channels in EG on 6H-SiC.…”

Calculation of dielectric constant of buffer layer graphene on SiC measured by spectroscopy ellipsometry using Gauss-Newton numerical inversion method

“…It can be mentioned that due to this constant value of dielectric constant, the buffer layer graphene might become transparent. Regarding the value of dielectric constant, it might be said that the thickness of our grown buffer layer graphene might be between 0.5 ML and 1 ML since the dielectric constant of bulk SiC substrate is lied in the range of 0 to 12 while the dielectric constant of graphene is lied around -5 to 15 [4][5][6][7][8][9][10]. However, detail spectroscopic ellipsometry experiment, for example by varying the incident angles, would help in determining the exact thickness of our buffer layer graphene.…”

“…The inversion method has been carried out by Kravets et al [3] and Matkovic et al [4,5] while Santoso et al [6,7,9], Boosalis et al [8], and Gogoi et al [10] have employed the modeling of a dielectric constant method to calculate the refractive index and dielectric constant of nanostructured graphene from measured spectroscopy ellipsometry data using Drude-Lorentz model and model dielectric function.…”

Calculation of refractive index of multilayer epitaxial graphene on C-face SiC measured by synchrotron using Kramers-Kronig and Newton-Raphson method

“…150004-5 Similar to that of SiC substrate, we observed no difference between the value of the resulting complex refractive index of MEG films on SiC for difference Newton-Raphson tolerance, step size h, and initial guess used indicating that the resulting complex refractive index calculated using Newton-Raphson method converge very fast. At lower wavenumber (up to 40000 cm -1 ), the complex refractive index resembles that of graphene on SiO2 and epitaxial graphene on Si-Face obtained using low energy spectroscopic ellipsometry and absorption spectroscopy [4,[9][10][11][12][13][14][15][16] in which the refractive index is nearly constant at this particular wavenumber range indicating the transparency of MEG film on SiC substrate. 150004-6…”