## 3 Results and Discussion
The energy of the interaction between graphene and aluminum nitride was calculated by the formula:  
\[E_{\text{b}}=(E(\text{C}_{\text{100}})+E(\text{Al}_{\text{64}}\text{N}_{\text{64 }}\text{H}_{\text{32}})-E(\text{C}_{\text{100}}\text{Al}_{\text{64}}\text{N} _{\text{64}}\text{H}_{\text{32}}))/S \tag{1}\]  
where \(S\) is the cell area. The resulting interaction energy was 0.194 J/m\({}^{2}\), which is very close to the energy of interlayer interaction in graphite. Thus, the graphene/graphene and graphene/AlN interfaces are almost equally energetically feasible. The optimal distance between graphene and AlN layers was equal to 3.66 A. Next, we investigated the effect of uniaxial stretching and compression, as well as characteristic defects in graphene (vacancies, Stone-Wales defect and impurity atom of nitrogen) by \(E_{\text{b}}\). Stretching and defects may occur as a result of the interaction of graphene with a silicon substrate if the number of graphene layers is not large enough. It is well known that graphene compression leads to its wave-like curv  
Figure 8: Periodic cell of the AlN–graphene heterostructure (**a**). Rippling of graphene under compression applied to the system (**b**). Purple, yellow, orange and blue balls represent C, Al, Ga and H atoms, respectively. shortening of C-C bonds. Therefore, the simulation of compressed graphene provides an estimation of the effect of sheet roughness on its interaction with AlN. In our study, the compression of the system by 5% led to roughness, at which the distance between the graphene and AlN layer was changed in the range of 3.2 to 4.3 A. The influence of various defects on the \(E_{\text{B}}\) value is represented in Table 1. Only one defect per cell shown in Figure 8 was introduced. Table 1 confirms that increased roughness due to graphene compression significantly enhances the interaction of graphene with AlN. In contrast, graphene stretching weakens this interaction. As for defects, only vacancies in graphene lead to a significant increase in the magnitude of \(E_{\text{B}}\). On Figure 9a,c fragments of XRD spectra are shown, including GaN (0002) (20 = 34.63\({}^{\circ}\)) and AlN (0002) (20 = 36.06\({}^{\circ}\)) maxima for FLG (Figure 9a) and MLG (Figure 9c). The FWHM value of the (0002) rocking curve for GaN grown on an FLG buffer is 6.95 arc. min. For GaN on MLG the FWHM of the (0002) rocking curve was 7.848. In turn, Figure 9b,d shows the \(\omega\) (rocking) scans for GaN/AlN samples, grown on FLG and MLG buffers, respectively. The peaks are centered at 34.56\({}^{\circ}\), and a higher number \begin{table}
\begin{tabular}{c c} \hline \hline
**Type of Defect** & \(E_{\text{b}}\)**, \(\text{J/m}^{2}\)** \\ \hline No defects & 0.194 \\ \hline Compression 5\% & 0.215 \\ \hline Stretching 5\% & 0.161 \\ \hline Stone-Wales defect & 0.196 \\ \hline Vacancy & 0.463 \\ \hline Nitrogen atom & 0.187 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Interaction energy of AlN surface with pristine, strained and defected graphene calculated with the density functional theory. Figure 9: HR-XRD spectra of the experimental samples: (**a**,**c**) 20-\(\omega\) scanning curve and (**b**,**d**) \(\omega\) scanning curve of the GaN/AlN films grown on the FLG (**a**,**b**) and MLG (**c**,**d**). of graphene layers results in the peaks broadening. The FWHM value increases from 55.55 to 60.00 arc. min. for samples grown on FLG and MLG buffers, respectively. The wider peaks observed in the case of using the MLG buffer confirm a poorer orientation and a large number of defects in the GaN grown on MLG.