## 3 Results
### X-ray Diffraction of GaN Epilayer  
The density of dislocations of GaN epilayers grown on graphene/sputtered AlN/sapphire and graphene/MOCVD AlN/sapphire substrates were further evaluated via X-ray diffraction (XRD). It is well known that dislocations in the materials caused the distortion to crystallographic planes and were accompanied by the broadening of the FWHM in the corresponding XRD \(\omega\)-scan (rocking curves). The screw and edge dislocations could be determined by obtaining the FWHM in the XRD \(\omega\)-scan (rocking curve). Figure 6a,b showed the (0002) and (10-12) reflection peaks of GaN films grown on graphene/sputtered AlN/sapphire and graphene/MOCVD AlN/sapphire substrates, respectively. The XRD rocking curves demonstrated that the FWHMs in both (0002) and (10-12) reflection peaks were narrower for the GaN films with the graphene/sputtered AlN/ buffer layer than those with the graphene/MOCVD AlN buffer layer, indicating that the densities of screw and edge dislocations in the GaN film grown on graphene/sputtered AlN/sapphire substrate had been reduced. Generally speaking,the densities of dislocations in the XRD \(\omega\)-scan (rocking curve) for GaN films could be estimated using the following empirical formula [35].  
\[N=\frac{\beta^{2}}{4.35\times\left|b^{2}\right|}, \tag{3}\]  
in which \(\beta\) was the FWHM of the XRD \(\omega\)-scan (rocking curve) and \(b\) was the Burgers vector of the corresponding dislocations. The (0002) FWHM of the X-ray x-scan (rocking curve) of the GaN epilayer was significantly reduced from 542 to 133 arcsec with the assistance of the graphene/sputtered AlN buffer layer, and the (10-12) FWHM was reduced from 597 to 246 arcsec. The estimated densities of the screw and edge dislocations of the GaN epilayer with the graphene/MOCVD AlN buffer layer were \(2.85\times 10^{8}\) and \(3.45\times 10^{8}\) cm\({}^{-2}\), respectively. In addition, the reduction in dislocation had been to \(1.71\times 10^{5}\) and \(5.87\times 10^{7}\) cm\({}^{-2}\) with the assistance of the graphene/sputtered AlN buffer layer. Therefore, the stress of the epitaxial layer was largely released, and the decreasing of dislocation density in the GaN epilayer could be attributed to the alleviation of the mismatch effects between the substrate and GaN epilayer. Furthermore, in the growth of the sputtered AlN buffer, the collision between electrons and gas molecules was strong in the magnetic field, so that the growth rate was greatly improved, which was helpful to increase the energy of the atoms on the surface of the substrate and improve the quality of AlN film to a large extent compared to the MOCVD AlN film. It could be seen that the results of XRD were consistent with the Raman spectrum.  
Figure 5: (**a**) A\({}_{1}\) (LO) peak of Raman spectra of GaN films grown on sapphire substrate with graphene/sputtered AlN buffer layer (sample 1), graphene/MOCVD AlN buffer layer (sample 2), MOCVD AlN/graphene buffer layer (sample 3), and MOCVD AlN buffer layer (sample 4) in the wave region of 700–800 cm\({}^{-1}\). (**b**) The relationship between the FWHM of A\({}_{1}\) (LO) phonon and the phonon lifetimes in the four different samples.  
Figure 6: (**a**) (002) and (**b**) (102) rocking curves of the GaN epilayer grown on graphene/sputtered AlN/sapphire and graphene/MOCVD AlN/sapphire substrates.