## 3 Results and Discussion
### Free Charge Carrier Properties of MLG and QFS-MLG
Since the MLG samples are grown at the same \(T_{\rm gr}\) and have a similar history we do not  
Figure 7: Free charge carrier density (left panel) and mobility (right panel) of MLG (filled symbols) and QFS-MLG (open symbols) with \(T_{\rm Ar}\) = 640 \({}^{\circ}\)C (black circles), \(T_{\rm Ar}\) = 800 \({}^{\circ}\)C (red squares) and \(T_{\rm Ar}\) = 1300 \({}^{\circ}\)C (blue triangles) for different environmental conditions: after annealing in vacuum (Annealed), after being purged with dry N\({}_{2}\) for several days (N\({}_{2}\) RH 0%), after being purged with moist air (RH 45%) for several hours (Air RH 45%), and after being exposed to the ambient for several months (Ambient). anticipate a difference in impurity levels. It is thus plausible to suggest that in the MLG with \(T_{\text{Ar}}\) = 1300 \({}^{\circ}\)C the interface phonon scattering is reduced as a result of different interface properties. We recall that the buffer layers grown at different \(T_{\text{Ar}}\) on SI substrates exhibit very similar \(sp^{3}\) contents and defect densities (Figure 6). Furthermore, the Raman scattering spectral features associated with the buffer layer in the respective MLG samples with different \(T_{\text{Ar}}\) are practically identical. Hence, the reduced interface phonon scattering is likely a result of a different interface between MLG and the buffer layer rather than between buffer layer and SiC substrate. This suggestion is further supported by the similar free charge carrier density in the ambient doped MLG with different \(T_{\text{Ar}}\) indicating similar surface state densities. To gain further insight into the origin of the different interface properties between MLG and the buffer layers we turn now our attention to the free charge carrier properties of the QFS-MLG samples. In QFS-MLG the intercalated hydrogen saturates the Si dangling bonds passivating the interface donor states. Consequently, QFS-MLG exhibits \(p\)-type doping induced by the spontaneous polarization of the SiC substrate [28, 59, 60]. The resulting free hole density in QFS-MLG on SI 4H-SiC was reported to be 8.6 \(\times\) 10\({}^{12}\) cm\({}^{-2}\) as determined by angular resolved photo-electron spectroscopy (ARPES) [60]. As expected our freshly annealed QFS-MLG samples show \(p\)-type conductivity (see Figure 7 left panel). We find very similar free hole densities in the QFS-MLG with \(T_{\text{Ar}}\) = 640 \({}^{\circ}\)C and \(T_{\text{Ar}}\) = 800 \({}^{\circ}\)C of 1.2 \(\times\) 10\({}^{13}\) cm\({}^{-2}\) and 1.5 \(\times\) 10\({}^{13}\) cm\({}^{-2}\), respectively. These values are slightly higher than the free hole density expected from pure polarization doping [60]. It is possible that some residual ambient doping is present as the annealing temperature for the QFS-MLG samples was relatively low in order to prevent deintercalation. Purging in dry N\({}_{2}\) for several days lead to a small reduction of the free hole density in these two samples to \(\sim\)1.0 \(\times\) 10\({}^{13}\) cm\({}^{-2}\), which is suggested to be the intrinsic value for our QFS-MLG resulting from polarization doping. We consider this to be a good agreement with the previously reported value of 8.6 \(\times\) 10\({}^{12}\) cm\({}^{-2}\)[60] given the different experimental techniques used in the two works and the various fitting parameters employed to deduce the free hole concentration from ARPES. Both the freshly annealed and the dry N\({}_{2}\) purged QFS-MLG with \(T_{\text{Ar}}\) = 1300 \({}^{\circ}\)C show significantly lower free hole density of 4.4 \(\times\) 10\({}^{12}\) cm\({}^{-2}\) and 2.1 \(\times\) 10\({}^{12}\) cm\({}^{-2}\), respectively. According to the polarization doping model, the negative pseudo-polarization charge, which is a constant parameter for the 4H-SiC, is balanced by the free holes in the QFS-MLG and the positive space charge in the substrate depletion layer [60].