## 3 Results and Discussion
The spectra consisted of a strong E2 (high) peak and A1 (LO) phonon peak, respectively, near 568 and 734 cm\({}^{-1}\), which coincides well with the Raman selection rule for wurtzite GaN. Compared with the Raman spectrum of the sample plane, PSS sample striped clearly observed significantly enhanced scattering efficiency. Due to the introduction of surface disturbance surface of the microstructure, more efficient coupling of light scattering and multiple scattered radiation, the sample can be observed from the striped PSS significant increase in the Raman intensity. E2 (high) for monitoring the line width of phonons in crystal quality, and its frequency may be used to monitor the stress of the film [21]. From Table 1, the E2 (high) phonon peaks of the films grown on different substrates are observed at 568.8 and 569.9 cm\({}^{-1}\), corresponding to the striped PSS and the planar substrate. The shift of E2 (high) phonon peak is the main indicator for the residual stress in wafers. Additionally, unstained GaN is characterized by standard E2 frequency of 568 cm\({}^{-1}\)[22]. It appears compressive stress when E2 frequency is larger than the standard value. As we all know, the amount of stress relaxation can be calculated by the following equation [23; 24]:  
\[\sigma=\frac{\Delta\omega}{4.3}\Big{(}\text{cm}^{-1}\text{ GPa}^{-1}\Big{)} \tag{3}\]  
where \(\sigma\) represents the residual stress and \(\Delta\omega\) is the E2 (high) phonon peak shift. It can be seen from Table 1 that the E2 (high) phonon frequency of striped sample is shifted to 568.8 cm\({}^{-1}\), while that of planar sample is shifted to 569.9 cm\({}^{-1}\). Obviously, the two samples show a slight red shift by about 0.82 and 1.90 cm\({}^{-1}\) corresponds to the compressive stress by an amount 0.19 Gpa and 0.45 Gpa, respectively for striped sample and planar sample. So, the compressive stress of striped sample is much smaller than that of planar sample. The value of striped sample demonstrates that the epilayers grown on striped PSS are almost fully relaxed. In contrast to those on planar substrate, as-grown epilayers on striped PSS have less lattice mismatch which can reduce dislocation in GaN films [25]. As we all know, high dislocations reduce the carrier mobility, reducing the minority carrier lifetime and depress the thermal conductivity [26]. Therefore, the result of FWHM also matches with the result of XRD which appears that the quality of GaN epitaxial layers grown on striped PSS has been improved. \begin{table}
\begin{tabular}{c c c c} \hline
**Samples** & **E2 Phonon Peak** & **E2 Phonon FWHM** & **Compressive Stress** \\  & **(cm\({}^{-1}\))** & **(cm\({}^{-1}\))** & **(GPa)** \\ \hline planar substrate & 568.8 & 8.1 & 0.45 \\ striped PSS & 569.9 & 6.7 & 0.19 \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of the Raman results recorded from planar substrate and fitted striped PSS (patterned sapphire substrate) samples at room temperature. FWHM (full width at half maximum). The amount of stress estimated from the E2 (high) phonon peak shift relative to a 400 \(\upmu\)m thick independent GaN without strain is displayed in Table 1.  
The crystallinity of the GaN films grown on striped PSS can also be researched by the absorption spectra. The transmittance of GaN films is about 80% in the wavelength range of 400-800 nm. From Figure 6, there is a sharp drop of the transmittance, which indicates the high crystallinity of the GaN epilayers. When GaN absorbs the light, the electrons in GaN can be activated and move from the valence band to the conduction band [27]. The amount of photon energy absorbed by GaN can be calculated by the following equation [28]:  
\[(\alpha hv)^{\frac{1}{n}}=A\left(hv-E_{\text{g}}\right) \tag{4}\]  
where \(A\) is a constant, \(hv\) represents the photon energy, \(E_{\text{g}}\) stands for the optical band gap of thin wafer, and the index n relies on the type of transition. For GaN, the n used to be \(\frac{1}{2}\)[29].