## 3 Results and Discussion
### Buffer Layer Formation
In our experiments, when Ar is introduced at 800 \({}^{\circ}\)C the entire surface reconstruction process up to 1600 \({}^{\circ}\)C proceeds under enhanced Si pressure, which should shift the formation of the buffer layer to higher temperatures. In contrast, for \(T_{\rm Ar}\) = 1300 \({}^{\circ}\)C the reconstruction occurs in vacuum up to this temperature and the formation of buffer layer should already take place [29]. We have previously shown that no etching by Ar occurs in the sublimation process in closed crucible [45] as confirmed here by step height distribution (See supplementary information Figure S1). Therefore, one would expect a better developed buffer layer for \(T_{\rm Ar}\) = 1300 \({}^{\circ}\)C compared to \(T_{\rm Ar}\) = 800 \({}^{\circ}\)C. Surprisingly, we find the opposite trend from the Raman scattering spectroscopy, reflectance mapping and \(\mu\)-LEED results. These findings are not compatible with scenarios (i) and (ii) in which oxidation of uncovered areas occurs after buffer layer formation. A potential explanation for the observed suppression of buffer layer formation at higher \(T_{\rm Ar}\) is provided by scenario (iii) in which the observed oxidation occurs during the annealing process. It has been shown that intermediate SiO\({}_{\rm x}\) on the Si-face of SiC is stable up to a temperature of 1200 \({}^{\circ}\)C and it is difficult to be fully eliminated even at 1400 \({}^{\circ}\)C [46]. Thus, if oxidation occurs during annealing and Ar is introduced at temperatures higher than 1200 \({}^{\circ}\)C the oxide layer will prevent the buffer layer formation. As the oxide layer starts to gradually be removed above 1200-1400 \({}^{\circ}\)C Ar effectively enhances the Si gas pressure and suppresses the phase transformation to (6\(\sqrt{3}\)\(\times\) 6\(\sqrt{3}\))-R30\({}^{\circ}\) surface reconstruction. As a results after heating up to 1600 \({}^{\circ}\)C, the sample with \(T_{\rm Ar}\) = 1300 \({}^{\circ}\)C (BL4) shows only the initial stage of the buffer layer and is mostly uncovered SiC (Figure 3d). At \(T_{\rm Ar}\) lower than 1200 \({}^{\circ}\)C (BL1, BL2, BL3), Ar reduces the mean free path of oxygen suppressing oxide  
Figure 4: Si 2p oxide X-ray photoelectron emission microscopy (XPEEM) image taken at photon energy of 133 eV and electron energy of 26 eV with 40-\(\mu\)m field-of-view for the buffer layer sample with \(T_{\rm Ar}\) = 1150 \({}^{\circ}\)C. The bright areas correspond to higher content of SiO\({}_{\rm x}\) but even the dark areas of the image have some oxide component. formation and allowing complete (partial) buffer layer formation for \(T_{\rm Ar}\) = 800 \({}^{\circ}\)C (900 \({}^{\circ}\)C-1150 \({}^{\circ}\)C.) We note that no charging or any indication of oxidation is observed in the buffer layer sample with \(T_{\rm Ar}\) = 800 \({}^{\circ}\)C, which may be understood in view of the reduced mean free path of oxygen at lower temperatures. Scenario (iii) has several important implications for the growth strategies to obtain high-quality graphene by high-temperature sublimation. As the buffer layer becomes the first graphene layer upon annealing, forming the buffer layer and, consequently, graphene at higher temperatures should be favorable in terms of surface roughness and uniform restructuring as they affect positively free charge carrier mobility. At the same time, one can argue that if the buffer layer forms at lower temperatures it can be conditioned during the annealing process until the temperature of graphene formation is reached, reducing the density of defects such as vacancies or/and \(sp^{3}\)-defects. Another interesting question is to compare the properties of QFS-MLG obtained from buffer layers grown using different \(T_{\rm Ar}\) and understand which mechanism has a decisive role. To address these questions we have investigated the free charge carrier properties of MLG and QFS-MLG samples for which the Ar was introduced at different \(T_{\rm Ar}\) (Table 1).