## 3 Results and Discussion
It was previously shown [28; 65; 66], the RHEED technique can be applied for visualization of graphene reciprocal structure and to analyze the ordering of its crystalline domains. Previously [38], it was shown that in the case of a single-crystal 2D material, its reciprocal space structure consists of vertical rods. Because of the relatively large wave vector of electrons in RHEED, the Ewald sphere is large and crosses the rods in reciprocal space. In general, bands form in RHEED patterns in 2D materials (Figure S4a). We obtained the reciprocal lattice of the 2D material by the measuring of streaks as a function of the momentum transfer parallel to the surface (k\({}_{\parallel}\)) at different azimuthal angles \(\varphi\)[28; 65; 66]. We constructed a reverse space map for graphene with two types of crystallites with a mutual rotation of 30\({}^{\circ}\) (Figure S4c), which is synthesized on a Cu (100) catalyst using the CVD method [28]. The RHEED method was used to analyze the graphene in situ and control the processes of nucleation and subsequent stages of III-nitride growth (Figures 4 and 5). Figure 4 shows the RHEED patterns from the FLG (Figure 4a) and MLG (Figure 4d) transferred to a SiO\({}_{2}\)/Si substrate. The in-plane structures of graphene and GaN/AlN films can be derived from their observed structures in 2D reciprocal space. In the reciprocal space, the radius and polar angle correspond to the reciprocal distance from the (00) spot and azimuthal angle, respectively. Figure 4b,e shows the intensity profiles of line scans as a function of k\({}_{\parallel}\) (the distances from (hk) to (00)) at a fixed value k\({}_{\perp}\)[28; 65]. Since a sample with FLG is more characterized by SLG regions, the widened peaks characteristic of graphene are noticeable in the RHEED images (Figure 4a-c). In the case of MLG, the main peaks are characterized by a smaller FWHM (Figure 4e), which leads to the more contrasting RHEED reciprocal space structure (Figure 4f). A smaller half-width value is associated with a larger value of the thickness of the MLG film compared to FLG. Figure 4: Images of RHEED patterns obtained of FLG (**a**) and MLG (**d**) at azimuthal angles \(\varphi=0^{\circ}\) (**a**,**d**). Intensity profiles for azimuthal angles \(\varphi=0^{\circ}\) (**b**,**e**) for FLG (**b**) and MLG (**e**), respectively. (**c**,**f**) The RHEED reciprocal space structures for the FLG (**c**) and MLG (**f**) samples. The growth kinetics of the AlN wetting layer on graphene to improve the quality of the GaN epitaxial layers is not well-studied. Nevertheless, in this work, we used the standard nucleation process, which showed itself well during the growth of heterostructures on SiC (30-40 nm-thickness of the AlN layer under a N\({}_{2}\)-rich regime at \(T_{\text{S}}\) = 710 \({}^{\circ}\)C). PA-MBE growth at this stage was also controlled by the RHEED method (Figures S5.1 and S5.2). The next RHEED patterns (Figure 5a,e) measured along the axes of the [01\(\overline{10}\)] band follow the PA-MBE growth of GaN/AlN epilayers on different regions of the graphene buffer: FLG (Figure 5a) and MLG (Figure 5e). Note that the axes of the [01\(\overline{10}\)] band correspond to \(\varphi\) = 0\({}^{\circ}\). Figure 4c,f shows the reciprocal space structures of the transferred FLG and MLG. Figure 4c,f, shows twelve mutually symmetrical spots at the reciprocal distances of 2.9 and 5.1 A\({}^{-1}\) from the center. These correspond to graphene domains randomly oriented with respect to each other. According to our previous study [28], the direction of graphene growth is rotated by 30\({}^{\circ}\) because of the 60\({}^{\circ}\) crossing of in-plane grain boundaries. Therefore, twelve observed peaks point to two graphene domains disoriented by 30\({}^{\circ}\). Figure 5c,g shows constructed structures of the 2D reciprocal space derived from our experiments Figure 5c,g). Characteristic peaks from GaN grown on FLG (Figure 5a-c) demonstrate a greater intensity value with a smaller FWHM compared to nitride on MLG (Figure 5e-g).