# Raman 2D Peak Line Shape in Epigraphene on SiC
## 4 Discussion  
The detailed analysis of 2D peak line shape shows that the Voigt line shape describes the 2D peak better than the Lorentzian line shape. Although the improvement is significant, the \(\chi^{2}\) statistics suggests that further corrections are needed. These deviations from the Voigt model are probably due to the larger areas of non-normally distributed strain, or, due to the patches of side wall graphene at the SiC step edges. Such areas cause side bands or local extrema in the normal distribution of the strain. We propose these deviations from the normal strain distribution can be reduced by defocusing the laser spot. However, defocusing will also reduce the Raman signal, and, it will also cause broader 2D peak. We assumed only biaxial strain contributing the total broadening of 2D peak. Though the uniaxial strain was neglected, it could contribute to the 2D peak broadening, too. The uniaxial strain splits the 2D peak [24; 25; 26; 27]. If the 2D peak splitting is smaller or comparable to the spectral resolution (2 cm\({}^{-1}\)),  
Figure 7: The variation of the charge density and strain as determined from the spectral position of the G and 2D peaks in the three samples (QFMLG, SLG-Ar, SLG-vac). The inset shows the correlation between the G and 2D peak positions. The left and bottom histograms depict the distribution of the charge density and strain, respectively.  
the 2D peak could be misinterpreted as a single-component peak. We assume that the uniaxial strain would effectively contribute to the 2D peak broadening only. Also, since the 2D peak splitting also leads to unequal intensities of the two split components, we expect contribution to the asymmetry of the 2D peak.  
Another contribution to the inhomogeneity of epitaxial graphene on SiC is the stacking alignment between graphene and underlying SiC substrate [49]. These stacking domains can lead to strain inhomogeneity. However, since the size of these domains is well below the laser spot size (1 \(\upmu\)m) we assume these stacking domains will mainly contribute to the Gaussian broadening, and, they could be studied by the Voigt line shape fitting.  
We note it is necessary to fit the data of the 2D peak in the large enough spectral range. We used a 300 cm\({}^{-1}\) broad spectral window. The spectral window broader than 300 cm\({}^{-1}\) can not be used due to the presence of the combination Raman mode at \(\approx\)2450 cm\({}^{-1}\). The narrower spectral range can lead to better fit [17; 50], however, the fitting parameters might not be as reliable. As the Raman signal is low in the low and high energy tails, the signal might become weaker than the noise level. For the reason of high signal-to-noise ratio the Raman spectra have to be collected with a high numerical aperture objective and the data have to be integrated for at least 60 s.  
Our analysis also shows a promise for growth improvements of the epitaxial graphene. The correlation between the width of the 2D peak and carrier mobility has been demonstrated [22]. Hence, we assume, if the strain inhomogeneity is reduced, the graphene carrier mobility could be improved, too.  
Contrary to improving graphene, the effect of inhomogeneous broadening can also result in large deviations from the here presented line shapes. We have studied samples where the inhomogeneous broadening is comparable to the homogeneous broadening. However, if the inhomogeneous broadening dominates, the Gaussian component is expected to be prevalent in the 2D peak line shape.