# Raman 2D Peak Line Shape in Epigraphene on SiC
## 3 Results  
We show in Figure 1 the typical Raman spectra of graphene grown in high vacuum, argon and the intercalated buffer, so called QFMLG. All spectra show the typical graphene characteristics as the D peak, G peak and 2D peak. The Raman spectra also show typical characteristics of the single-layer graphene. These are the ratio of the integrated 2D peak to G peak intensity larger than 2, and, the single-component line shape of the 2D peak. The characteristic distinction between the hydrogen intercalated and non-intercalated samples can be also found by the absence/presence of the peaks labeled (1), (2) and (3) in inset of Figure 1. These peaks were attributed to the buffer layer [18; 42]. The hydrogenated (QFMLG) and non-hydrogenated (SLG-vac, SLG-Ar) samples can be also distinguished by a low intensity background in the spectral range of the D peak. This background was assigned to the buffer layer, too [42]. We observe rather similar Raman spectra of graphene grown in argon and high vacuum. Their differences are discussed in the following detailed analysis. The 2D peaks of the three samples are shown in Figure 2 by black circles. We obtained the spectra by two 30 s integration periods. The 30 s integration reduced the noise level and the two accumulations allowed us to remove spikes in recorded spectra. The low level of the noise is essential to fit the 2D  
Figure 1: Raman spectra of quasi free-standing monolayer graphene (QFMLG), single layer graphene grown in vacuum (SLG-vac) and single layer graphene grown in argon (SLG-Ar). Graphene related D, G and 2D peaks are labeled by arrows. Inset shows details of Raman spectra including three buffer related Raman modes, labeled by arrows (1), (2) and (3). peak line shape at low-energy and high-energy tails from the central peak position. Before we analyzed the 2D peak line shape, we subtracted a linear background. The background was determined using five experimental points at 2530 and at 2870 cm\({}^{-1}\). The 2D peaks are fitted by the Lorentzian (green curves) and Voigt (red curves) line shapes in Figure 2. The residuals are displayed in the top insets and the corresponding histograms of the residuals are shown in the bottom insets of Figure 2.  
The fit improvement by the Voigt line shape is tested by the F-test. The Degrees of Freedom (DOF) and Residual Sum of Squares of the Lorentzian (model 1) and Voigt (model 2) line shape are summarized in Table 1. The null hypothesis for the F-test is: the Lorentzian and Voigt line shapes are the same. The F-number in Table 1 results from the comparison of the two models. The p-number determines the cumulative probability that the expected F number is lower than the experimentally determined F-number. The F-test shows that the Voigt line shape describes the 2D peak line shape better. As the Voigt line shape has four fitting parameters (one more with respect to the Lorentzian broadening), we need to verify that the Voigt line shape model is not overparametrized. We verify the overparametrization by determining the \(\chi^{2}\) statistics of the fitted models. The \(\chi^{2}\) statistics requires the experimental error \(\sigma_{exp}\). We determine the experimental error from the high-energy tails of the 2D peak, as depicted in Figure 3. The high-energy tail is fitted by the second order polynomial to describe the trend of the experimental data. The residuals are considered as a random experimental error. The normality of these residuals is tested by the Kolmogorov-Smirnov test, as depicted by the cumulative distribution function in the inset of Figure 3. The normality is verified at the 95% confidence level. The experimental error is estimated to be \(\sigma_{exp}\approx 10\) cm\({}^{-1}\). The centered and normalized \(\chi^{2}\) for the Lorentzian and Voigt model is 1000 and 260, respectively.