## 2 Materials and Methods  
In this article, to conduct a systematic research study on the different buffer layers containing graphene layers, four different buffer layers were prepared between the GaN epilayer and sapphire substrate. The growth of GaN epilayers in all samples were prepared by using a conventional low temperature-high temperature two-step growth method of metal organic chemical vapor deposition (MOCVD). The buffer layer structure used in the four samples is shown in Table 1 and Figure 1 below. For the experiment preparation of sputtered AlN film, the growth temperature of the sputtered AlN buffer layer was set at 550 \({}^{\circ}\)C and the radio frequency (RF) sputter system pressure was adjusted to 10\({}^{-7}\) Torr. Then, high-purity (99.99%) Al target was used to deposit 25-nm-thick sputtered AlN films in the radio frequency (RF) sputter system with 50 W of RF power. In the traditional two-step growth method of MOCVD, the formation mechanism of the epitaxial layer is to nucleate at low temperature and coalesce into a thin film at high temperature. Therefore, the MOCVD AlN epitaxial layer was first nucleated at a lower temperature of 550 \({}^{\circ}\)C while the temperature increased to 1220 \({}^{\circ}\)C, coalescing into a film. Hexagonal honeycomb graphene was grown on the polished copper foils via chemical vapor deposition (CVD) and transferred on the surface of the sample via wet transfer. In the process of growing GaN films, trimethylgallium (TMGa) and ammonium (NH3) were used as the source of Ga and N for the growth of GaN epilayer, respectively. Firstly, low temperature GaN films were deposited at about 550 \({}^{\circ}\)C and kept for 5 min. Then, the temperature was raised to 1050 \({}^{\circ}\)C and heated for 70 min to form high temperature GaN films, and finally a GaN epitaxial layer with a thickness of about 2 \(\upmu\)m was obtained. Experimental analysis provided reliable evidence that the stress in GaN could be indicated by the E2 (high) phonon peak in the Raman spectrum. Furthermore, the full width at half maximum (FWHM) of the Raman scattering peak of A1 (LO) also better characterized the process of Raman scattering in GaN from the perspective of phonon lifetime. On the one hand, the frequency shift of the E2 (high) phonon was analyzed, so that we could deduce the magnitude of the strain in the GaN films grown with different buffer layers. If the E2 (high) phonon peak moved to the lower frequency relative to the corresponding peak position of stress-free GaN films, it indicated that there was tensile stress in the GaN films. Otherwise, we judged that the stress that GaN films subjected to was compressive stress. [16; 17]. On the other hand, the destruction of the long-range order due to the defects or impurities would impair the intensity of E2 (high) phonon peak and A1 (LO) phonon peak. The above phenomenon would also be manifested as the broadening of the phonon peak. Therefore, through the energy-time uncertainty relation, the phonon lifetime was determined by observing the phonon line width of the A1 (LO) phonon [18; 19]. In addition, the Raman spectra of the GaN layer was measured at room temperature in the range from 300 cm\({}^{-1}\) to 800 cm\({}^{-1}\) using micro-Raman testing technology with back scattering geometry. We focused the 514 nm line of an Ar+ laser onto a 10-um-diameter spot and used it as the excitation source, and the scattered light was detected by the charge-coupled detector (CCD). The Raman spectra resolution was better than 0.1 cm\({}^{-1}\) to ensure the accuracy of the measured spectrum. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & **Substrate** & **Buffer Layer** & **Epitaxial Layer** \\ \hline sample 1 & sapphire & sputtered aluminum nitride (AlN)/graphene & gallium nitride (GaN) \\ sample 2 & sapphire & MOCVD AlN/graphene & GaN \\ sample 3 & sapphire & graphene/MOCVD AlN & GaN \\ sample 4 & sapphire & MOCVD AlN & GaN \\ \hline \hline \end{tabular}
\end{table}