## 3 Results and Discussion
### Free Charge Carrier Properties of MLG and QFS-MLG  
It is well-known that MLG on SiC is intrinsically \(n\)-type doped [49; 50; 51]. However, exposure to ambient can cause environmental doping of graphene via an acceptor redox reaction at the surface of the graphene involving various environmental gases (O\({}_{2}\), H\({}_{2}\)O, and CO\({}_{2}\)), which results in electron withdrawal [52]. Consequently, MLG can exhibit \(p\)-type conductivity depending on sample history [24; 53]. We have previously shown that the THz OHE is an excellent tool to precisely determine free charge carrier density and mobility parameters of graphene and monitor their in-situ variation under the influence of different gases [24; 37; 40; 54]. In order to determine the intrinsic properties of MLG and QFS-MLG, prior to the measurements they were annealed in vacuum (\(10^{-6}\) mbar) at 1000 \({}^{\circ}\)C and 500 \({}^{\circ}\)C, respectively. The annealing temperature was confirmed to not cause deintercalation or any changes in the QFS-MLG structural properties by LEEM, AFM, and \(\upmu\)-LEED. The samples were kept in dry N\({}_{2}\) during the measurements and storage. In addition, we have performed measurements after purging with dry N\({}_{2}\) for several days and air with RH of 45% for several hours. Both transient and static measurements were carried out. Finally, the samples were measured after being stored in ambient conditions for several months. We have selected for these investigations samples with the following \(T_{\rm Ar}\): (i) \(T_{\rm Ar}\) = 800 \({}^{\circ}\)C, for which the surface reconstruction happens entirely in Ar atmosphere and that shows completed buffer layer after heating to \(T_{\rm gr}\) = 1600 \({}^{\circ}\)C (0 s); (ii) \(T_{\rm Ar}\) = 1300 \({}^{\circ}\)C, for which the surface reconstruction happens entirely in vacuum, and which needed heating to \(T_{\rm gr}\) = 1800 \({}^{\circ}\)C for the buffer layer to form. Although no indications of surface oxidation were observed for the buffer layer sample with \(T_{\rm Ar}\) = 800 \({}^{\circ}\)C, a nano-scale oxidation cannot be excluded. Furthermore, the graphitization process is shifted to higher temperatures in comparison to \(n\)-type substrate as pointed out above. We, therefore, included in our investigation MLG and QFS-MLG samples, for which the Ar was introduced at (iii) \(T_{\rm Ar}\) = 640 \({}^{\circ}\)C. Growth temperature \(T_{\rm gr}\) = 1600 \({}^{\circ}\)C was employed to produce the buffer layer sample in this case. The QFS-MLG samples were obtained by hydrogen intercalation of the respective buffer layers as described in Ref. [28]. The MLG samples were fabricated using our optimized conditions of \(T_{\rm gr}\) = 2000 \({}^{\circ}\)C for 0 s growth time, which results in less than 1% BLG inclusions. The sample with \(T_{\rm Ar}\) = 1300 \({}^{\circ}\)C required a longer growth time of 5 min for a homogeneous MLG to form leading to increased BLG inclusions of 8%. Figure 7 shows the free charge carrier density (left panel) and mobility (right panel) of MLG (filled symbols) and QFS-MLG (open symbols) with different \(T_{\rm Ar}\) for different environmental conditions. The mobility parameters were found to be slightly anisotropic in accordance with our recent study [24]. The anisotropy, which is caused by the substrate step edges, does not have any bearing on the results discussed in the current work. Consequently, for brevity we present here the averaged mobility between the parameters determined along and perpendicular to the step edge. The freshly annealed MLG samples show \(n\)-type conductivity, as expected, with values in the range of 3.9 \(\times\) 10 \({}^{12}\) cm\({}^{-2}\) to 6.6 \(\times\) 10\({}^{12}\) cm\({}^{-2}\). Due to the semi-insulating nature of the substrates, the MLG doping should be entirely governed by charge transfer due to surface donor states [55].