## 3 Results
### Raman E\({}_{2}\) (High) Phonon of GaN Epilayer  
For the E\({}_{2}\) vibration mode, the positive and negative charges in the unit cell are not shifted, so the E\({}_{2}\) vibration mode was a non-polar mode. Moreover, since the E\({}_{2}\) phonon mode corresponded to the stretching and compression of the atoms in the lattice, so the E\({}_{2}\) (high) phonon could characterize the biaxial strain existing in the GaN [17; 29; 30]. Generally, the large lattice and thermal mismatches between these substrates and epitaxial layer lead to a high defect density and large biaxial stress, and the residual stress will affect the phonon scattering frequency. Furthermore, the frequency shift of the E\({}_{2}\) (high) phonon was very sensitive to the biaxial strain in GaN layer, and the stress in GaN therefore could be measured based on the Raman shift of the E\({}_{2}\) (high) scattering peak in the geometry scattering configuration (z(y,y)z). Figure 4a clearly shows the E\({}_{2}\) (high) phonon scattering peak's position in the spectrum of the GaN film grown on four different types of substrates. From the Figure 4a, we found that when the GaN epilayer was grown on the graphene/sputtered AlN/sapphire substrates, the frequency of E\({}_{2}\) (high) phonon was 568.2 cm\({}^{-1}\), close to the 568 cm\({}^{-1}\) corresponding to the stress-free GaN films [31]. Therefore, we thought the GaN epilayer with graphene/sputtered AlN buffer layer was almost stress free. However, when the GaN epilayer was grown on sapphire substrates without sputtered AlN buffer layer (sample 2-4), the frequency of the E\({}_{2}\)(high) phonon exhibited movement toward the high frequency (569.1 cm\({}^{-1}\), 570.7 cm\({}^{-1}\), 572.3 cm\({}^{-1}\), respectively), compared with stress-free GaN films (568.0 cm\({}^{-1}\)) [31], showing that the GaN epilayer was subjected  
Figure 3: (**a**) Raman spectra of the GaN films grown on sapphire substrate with graphene/sputtered AlN buffer layer (sample1), graphene/MOCVD AlN buffer layer (sample 2), MOCVD AlN/graphene buffer layer (sample 3), and MOCVD AlN buffer layer (sample 4) in the low-wave region of 300–800 cm\({}^{-1}\); (**b**) the intensity of the A\({}_{1}\) (LO) phonon, E\({}_{1}\)(LO), and E\({}_{2}\) (high) of Raman spectra of the GaN films in the four different samples. to compressive stress. On the contrary, the degree of frequency shift of the E\({}_{2}\) (high) phonon scattering peak in the GaN films with graphene/sputtered AlN buffer layer was so slight that it was almost close to the frequency value of stress-free (568 cm\({}^{-1}\)) [31], indicating evidently that the stress induced by defects and lattice mismatch in GaN films was lowest under this growth mode. Moreover, the release of stress due to graphene introduction could be estimated to a large extent by the following formula,  
\[\Delta\omega=\text{K}\sigma, \tag{1}\]  
in which \(\Delta\omega\) is the difference of the E\({}_{2}\) (high) peak with the stress-free GaN crystal value of 568.0 cm\({}^{-1}\)[31], K represents the stress coefficient \(\approx\)2.56 cm\({}^{-1}\) GPa\({}^{-1}\), and \(\sigma\) is the stress value of the GaN epitaxial layer [32]. It is acknowledged that the biaxial stress value of GaN films grown on the sapphire substrate with graphene/sputtered AlN buffer layer (sample1) was 0.07 GPa and was clearly the lowest compared to the other samples (2-4) in Figure 4d, suggesting that the effective stain relaxation in the GaN epitaxial layer by the introduction of graphene films and the sputtered method would create more nucleation points than the MOCVD method. A large number of studies have shown that the phonon intensity and the full width at half maximum (FWHM) of the E\({}_{2}\) (high) phonon scattering peak reflected the discrepancy in the crystal quality of the material. The GaN films with high dislocation density had smaller strength and larger full width at half maximum (FWHM).