## 3 Results and Discussion
In the spectra of epitaxial layers, it is possible to identify the combination peaks of graphene (D-band, G-band, and 2D-band), as well as the characteristic \(E_{\text{2(high)}}\)-peak of GaN allowed for a c-oriented wurtzite structure. These data indicate that graphene remained under the nitride film. To characterize areas with a different number of graphene layers (SLG and FLG), maps of the G-peak intensity (Figure 7b,e) and maps of the E\({}_{\text{2(high)}}\) peak intensity (Figure 7b,e) and position (Figure 7c,f) were constructed. Raman spectral mapping of high peak GaN E\({}_{\text{2}}\) (Figure 7a,c) confirmed the selectivity of the GaN cores with respect to graphene-coated wafer areas. Analyzing the Raman spectral maps of the G-peak intensity (Figures 7a,d and S7a,b), it can be seen that the areas with a high intensity value (>200) of the G-peak can be attributed to FLG, and areas with a lower intensity value (<200) to SLG (Figures 7a and S7a). Analyzing the maps of the position and intensity of the E\({}_{\text{2(high)}}\)-peak  
Figure 7: Raman analysis: (**a,d**) Raman mapping of G peak intensity and of the E\({}_{\text{2(high)}}\) peak intensity (**b,e**) and position (**c,f**) from random areas on the continuous FLG (**a–c**) and MLG (**d–f**) after nitrides PA-MBE growth acquired at a laser excitation wavelength of 532 nm. of GaN (Figures 7b,c and S7c-f), it can be concluded that the characteristic areas of SLG and FLG experience different stress values in the epitaxial layers of nitrides (Figure 7c). The difference in stress values may be associated with stress relaxation due to the occurrence of additional defects during growth on more defective sections of graphene that correspond to SLG. Thus, nitride nucleation occurs more qualitatively on the FLG regions, which are less defective than the SLG regions. The observed differences in the surface morphology of the obtained epitaxial layers of III-nitrides can be explained by the initial difference between graphene areas. For SLG sections, the average value of the E\({}_{\text{2(high)}}\) band position is \(\omega\)\(-\)567.6 (Figures 7b and S7e). At the same time, we observed a slight red shift of the E\({}_{\text{2(high)}}\) band (\(\omega\) = 567.4 cm\({}^{-1}\)), as indicated in Figures 7b and S7f. Figure 7e and Figure S7h show a significant shift for GaN grown on the MLG buffer (\(\omega\) = 568.4 cm\({}^{-1}\)). Red shift of E\({}_{\text{2(high)}}\) mode frequency usually indicates a tensile strain, typical for epitaxial GaN grown on Si (111) substrate. The coefficient 4.2 cm\({}^{-1}\) GPa\({}^{-1}\) describes the linear dependence between biaxial stress and spectral shift of the E\({}_{\text{2}}\) phonon mode. Therefore, we calculated a tensile stress of GaN equal to 0.05 \(\pm\) 0.01 GPa and \(-\)0.2 \(\pm\) 0.01 GPa for GaN grown on FLG and MLG, respectively. This value is much lower than the typical stress of GaN on silicon substrate (0.4-0.68 GPa). The results of the Raman spectroscopy show that the formation of nitrides on graphene with higher roughness leads to a significant increase in graphene defects and deterioration in the quality of the nitride layers. We investigated the interaction of graphene with AlN crystal and the effect of defects on the interaction energy between the layers. As an atomistic model, a rectangular C\({}_{\text{100}}\)Al\({}_{\text{64}}\)N\({}_{\text{64}}\)H\({}_{\text{32}}\) cell was considered, containing one graphene layer and two layers of aluminum nitride (see Figure 8). The outer surface of aluminum nitride was passivated by hydrogen atoms. The ratio of the AlN and graphene lattices constants is close to 5:4, therefore the aluminum nitride and graphene layers contained 4 \(\times\) 4 and 5 \(\times\) 5 elementary cells, respectively. The positions of atoms and the lattice vectors were optimized simultaneously. As a result, we obtained the optimal cell size of 12.37 \(\times\) 21.33 A\({}^{\text{2}}\).