# Raman 2D Peak Line Shape in Epigraphene on SiC
## 3 Results
To verify further the origin of these inhomogeneities, we measured also AFM and LFM, see Figure 6. The topography of SLG-vac shows circular-like SiC terraces of 1-4 \(\upmu\)m in diameter. The SLG-Ar and QFMLG show regular SiC step bunching. The regular terraces are 1-4 \(\upmu\)m broad in SLG-Ar, and, they are 6-7 \(\upmu\)m broad in QFMLG. To identify these different areas in topography, we measured also LFM. The LFM can distinguish different materials if their friction with an AFM tip is different. The LFM images are shown in Figure 6d-f. We also plot friction force profiles in Figure 6g-i. We observe reduction of the friction force at the edges of homogeneous SiC areas in SLG-vac. Some edges show similar reduction of the friction force in SLG-Ar, too. In both cases, the friction force is reduced \(\approx\) 2\(\times\). Such reduction of the friction force was shown between single and bilayer graphene [43]. The friction force is increased in the step edge areas in QFMLG. The increase of friction force was related to the buffer layer [43], however; we observe increase by only \(\approx\) 2.5\(\times\). The expected increase is \(\approx\) 10\(\times\) for buffer layer. We note, that the step edge, or, sidewall area does not have the same structure as buffer, as shown in literature [44,45]. Figure 5: Maps of Raman scattering. The map of (**a–c**) 2D peak position and (**d–f**) 2D peak FWHM measured in (**a,d,g**) SLG-vac, (**b,e,h**) SLG-Ar and (**c,f,i**) QFMLG. We also show 2D peak line shape at three locations marked by black, red and blue circles. The spectra are plotted using corresponding black, red and blue curves in (**g–i**). We interpret the graphene at the SiC step edges as the sidewall graphene ribbons [46; 47]. We also observe in LFM that the friction displays large homogeneous areas, and, it also shows considerable amount of sub-micrometer sized inhomogeneities. These patches of different friction/material can contribute to the overall line shape of the 2D peak, too. Another contribution to the 2D peak broadening is the charge density and strain variation on the sub-micrometer length scale. We analyzed the positions of the G and 2D peaks measured by Raman mapping. The correlation of the G and 2D peak positions are plotted in the inset of Figure 7. We describe the relation between the G and 2D peak position \(\omega_{G}\), \(\omega_{2D}\) and mechanical strain and charge density by the following set of two equations. \[\omega_{G}=\omega_{G0}+\alpha_{G}|n_{2D}|-2\gamma_{G}\omega_{G0}\epsilon \tag{8}\]  
\[\omega_{2D}=\omega_{2D0}-\alpha_{2D}n_{2D}-2\gamma_{2D}\omega_{2D0}\epsilon, \tag{9}\]  
where proportionality constants are \(\alpha_{G}=6.8\) cm\({}^{-1}/10^{13}\) cm\({}^{-2}\) and \(\alpha_{2D}=2.7\) cm\({}^{-1}/10^{13}\) cm\({}^{-2}\). The effective Gruneisen parameters are \(\gamma_{G}=1.8\) and \(\gamma_{2D}=3.5\). The G and 2D peak positions in the charge neutral unstrained graphene are \(\omega_{G0}=1582\) cm\({}^{-1}\), and \(\omega_{2D0}=2680\) cm\({}^{-1}\). We chose the linear dependence of G and 2D peak position on strain in agreement with previous experimental works studying the G peak [7; 26] and 2D peak [24; 25; 26; 27]. We chose the functional dependence of the G peak position on the charge density as an approximation to the theoretically predicted dependence [7; 8; 9; 48]. The expected charge density dependence of G peak position is smoothed at room temperature [48] in comparison to \(T=0\) K. The measured dependence can be clearly approximated by absolute-value function, when compared to theory [48] and experiment [5; 7; 8; 9]. Our fitting parameters lead to 2.5\(\times\) stronger charge density sensitivity of G peak than the sensitivity of 2D peak. The absolute values and relative strength of G to 2D peak charge sensitivity is in agreement with previous works [7; 9].