## 3 Results and Discussion  
Figure 1 shows a low-temperature PL spectra (at 77 K) of GaN films grown on different substrates. PL spectra of GaN grown on different substrates are dominated by the near-band-edge emission at around 360 nm. The full width at half maximum (FWHM) of the GaN films produced on samples A (4 nm) and B (8 nm) are narrower than that of the films grown on samples C (10 nm) and D (13 nm), indicating the low defect density and high crystalline quality of the GaN films due to their lower lattice mismatch, which is consistent with the XRD results. Similar trends of the yellow band-emission peak on these samples were also observed (data not shown here). The yellow luminescence is related to deep level defects in GaN [25]. Figure 2 shows a comparison of the typical XRD patterns of GaN (0002) films grown on different substrates. It can be seen that there is a variation in the FWHM value of the (0002) diffraction peak, and intensities of the GaN diffraction peak on the different substrates were  
obtained at around 34.5 degrees. The intensity of GaN (0002) in sample A is the strongest among all samples, which indicates that the GaN films on the GaN/sapphire template are highly c-oriented and have better crystalline quality. The FWHM of GaN (0002) values for samples A, B, C, and D were measured at 0.19\({}^{\circ}\), 0.51\({}^{\circ}\), 0.79\({}^{\circ}\), and 1.09\({}^{\circ}\), respectively. However, the XRD peak intensity increases as FWHM decreases; this is attributed to the increase in the crystallite size due to either the aggregation of small grains or grain boundary movement during the growth process. Since the FWHM of the XRD diffraction peak is relative to the average crystallite grain size in the film [26], the grain size of GaN grown on the different substrates is calculated using the Debye-Scherer equation [27]:  
\[D=0.9\lambda/\text{FWHMcos}\theta \tag{1}\]  
where \(D\) is the crystallite size, \(\lambda\) is the X-ray wavelength, and \(\theta\) is the diffraction angle. The crystallite sizes of samples A, B, C, and D are estimated to be 57, 20, 13, and 9 nm, respectively. These results indicate that the crystalline quality of GaN films grown on samples A and B is better than that of the films grown on samples C and D.  
Figure 3 shows plane-view SEM pictures of GaN films grown on various substrates. The surface morphologies show different features, as they are strongly dependent on the types of substrates used. The surface of GaN films in samples A and B was mirror-like, indicating less of a lattice mismatch between GaN and sapphire (Figure 3a,b). The smooth surface might be due to the high kinetic energy needed by PLD for GaN precursor migration and diffusion on the substrates' surface [28]. A rough GaN  
Figure 1: Low-temperature photoluminescence (PL) spectra (at 77 K) of GaN films grown on different substrates. FWHM: full width at half maximum. Figure 2: X-ray diffraction (XRD) measurements results of GaN films grown on different substrates. film surface, meanwhile, was observed in sample C (Figure 3c). Sample D presented an incomplete island coalescence process with a hexagonal structure, as shown in Figure 3d. This result indicates that GaN films on Si(100) have a hexagonal phase. The different GaN film structure of the grains can be attributed to the different lattice structure of the Si substrate [29]. The surface morphology and roughness of the GaN films grown on different substrates were carried out by AFM measurements with the scanning area of 10 \(\times\) 10 \(\upmu\)m\({}^{2}\), as shown in Figure 4. In Figure 4, the root-mean-square RMS values for samples A, B, C, and D are 2.1, 3.4, 14.3, and 17.7 nm, respectively. The film grown in samples A and B exhibited quite a smooth surface, with the RMS roughness being 3.4 and 2.1 nm, respectively, and the RMS surface roughness of samples C and D was estimated as 14.3 and 17.7 nm, respectively.