# Raman 2D Peak Line Shape in Epigraphene on SiC
## 3 Results
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Sample** & **DOF** & \(\mathbf{RSS_{1}}\) & \(\mathbf{RSS_{2}}\) & **F** & **P** \\ \hline QFMLG & 163 & \(3.6\times 10^{6}\) & \(4.9\times 10^{5}\) & 1000 & 1 \\ SLG-Ar & 162 & \(5.8\times 10^{5}\) & \(8.4\times 10^{4}\) & 932 & 1 \\ SLG-vac & 163 & \(8.0\times 10^{5}\) & \(1.5\times 10^{5}\) & 675 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used to perform the F-test. Degrees of freedom (DOF), Residual Sum of Squares (\(\mathbf{RSS_{1}}\)) of the Lorentzian model and \(\mathbf{RSS_{2}}\) of the Voigt model. F is the value of the F-statistics. Number \(p\) is the p-number to reject the null hypothesis. Figure 2: Line shape of the 2D peak in (**a**) QFMLG, (**b**) SLG-Ar and (**c**) SLG-vac. The black dots are the experimental data, green curve is a Lorentzian fit and red curve is the Voigt fit to the experimental data. The upper insets show the residuals for the (green point) Lorentzian and (red points) Voigt line shape. The bottom insets show the histograms of thee residuals. We fitted the 2D peak spectra at four different positions on each sample. The statistics for the three samples is shown in Figure 4 and summarized in Table 2. The FWHM was obtained directly from the experimental data without using any fitting procedure. The parameters \(\gamma\) and \(\sigma\) are the fitting parameters of the Voigt line shape. We observe that the QFMLG shows the narrowest broadening. The QFMLG also shows the smallest contribution of the homogeneous and inhomogeneous broadening. It can be seen in Figure 4 that the homogeneous and inhomogeneous broadening are similar in QFMLG. However, the inhomogeneous broadening is larger by 2-3 cm\({}^{-1}\) with respect to the homogeneous broadening in SLG-Ar and SLG-vac. The role of inhomogeneous broadening is thus larger in SLG-Ar and SLG-vac than in the QFMLG. \begin{table}
\begin{tabular}{c c c c c} \hline
**Sample** & **Sample Position** & **FWHM (cm\({}^{-1}\))** & \(\gamma\) (cm\({}^{-1}\))** & \(\sigma\) (cm\({}^{-1}\))** \\ \hline QFMLG & 1 & 21.1 & 10.53 \(\pm\) 0.12 & 10.13 \(\pm\) 0.12 \\  & 2 & 21.1 & 10.56 \(\pm\) 0.13 & 10.06 \(\pm\) 0.13 \\  & 3 & 25.3 & 11.16 \(\pm\) 0.16 & 11.24 \(\pm\) 0.15 \\  & 4 & 23.2 & 10.94 \(\pm\) 0.17 & 11.06 \(\pm\) 0.16 \\ \hline Argon grown & 1 & 33.6 & 14.8 \(\pm\) 0.4 & 16.3 \(\pm\) 0.3 \\  & 2 & 31.5 & 13.7 \(\pm\) 0.3 & 15.4 \(\pm\) 0.3 \\  & 3 & 29.4 & 13.9 \(\pm\) 0.2 & 14.7 \(\pm\) 0.2 \\  & 4 & 33.6 & 12.1 \(\pm\) 0.6 & 17.6 \(\pm\) 0.5 \\ \hline Vacuum grown & 1 & 35.7 & 14.9 \(\pm\) 0.5 & 17.5 \(\pm\) 0.4 \\  & 2 & 31.5 & 13.5 \(\pm\) 0.3 & 15.5 \(\pm\) 0.2 \\  & 3 & 35.6 & 14.8 \(\pm\) 0.4 & 17.7 \(\pm\) 0.4 \\  & 4 & 31.4 & 13.7 \(\pm\) 0.3 & 16.4 \(\pm\) 0.2 \\ \hline \end{tabular}
\end{table} 
Table 2: Fitted parameters \(\gamma\) and \(\sigma\) of Voigt line shape and FWHMs for three samples (QFMLG, SLG-Ar, SLG-vac). The line shape was determined at four different positions on each sample. Figure 3: The high-energy tail of the 2D peak (black points) was fitted to the polynomial of the 2 nd order (red curve) to determine the experimental error. The normality of the residuals is tested by the Kolmogorov-Smirnov test (inset). We study sources of inhomogeneous broadening by measuring spatial Raman maps. We show the Raman maps of the 2D peak position and FWHM of 2D peak in Figure 5. We select three representative points (marked by black, red and blue circles in Figure 5a-f) and Raman spectra taken at these points are plotted in Figure 5g-i. The SLG-vac sample is the least homogeneous. The broad and blue-shifted 2D peak (red spectrum in Figure 5g) is a fingerprint of bilayer graphene. We observe similar small areas of broad and blue-shifted 2D peak in QFMLG, too (red spectrum in Figure 5i). Though SLG-Ar sample appears to be more homogeneous than SLG-vac and QFMLG, this could be due to the larger steps of SiC, or, due to the specific area chosen for the Raman map.