## 3 Results and Discussion
The large values for the surface roughness of the GaN films in samples C and D might be due to the large lattice mismatch between the film and the substrates. A decrease in surface roughness occurs with an increase in grain size, as mentioned in the XRD results. The electrical resistivity of the GaN films grown on different substrates is shown in Figure 5a. The electrical resistivity of the four samples was found to be in the range 16.2-32.8 \(\Omega\cdot\)cm. The electrical resistivity of sample D was the largest, while that of sample A was the smallest. The electrical resistivity correlates with defect density, and the high defect density in the films may cause a decrease in the electrical resistivity [30]. The values of electrical resistivity of samples C and D were very close, which is consistent with the structural features of the films grown on these substrates, as discussed  
Figure 4: Atomic force microscopy (AFM) observations of GaN films grown on different substrates. RMS: root-mean-square. Figure 3: Scanning electron microscopy (SEM) surface image of GaN films grown on different substrates: (**a**) GaN/sapphire template (sample A); (**b**) sapphire (sample B); (**c**) Si(111) (sample C); (**d**) Si(100) (sample D). above. As electrical resistivity is inversely proportional to the carrier concentration and carrier mobility, the electrical resistivity of the films grown on the different substrates can be determined from their measurements. Low-temperature Hall measurement data from GaN films grown on the different substrates are shown in Figure 5b,c. Sample A showed the lowest carrier concentration and highest carrier mobility, thereby resulting in an increased number of conductive paths. The carrier concentration in sample D was higher than that in the others, whereas its carrier mobility was the lowest. This can be attributed to the existence of a high intrinsic defect and several grain boundaries in the film. These defects trap and scatter moving electrons, thus decreasing their mobility in the GaN films [31,32]. To further clarify the stress behaviors among the four samples, Raman scattering spectroscopy was performed, and the results are shown in Figure 6. The E\({}_{2}\)-high phonon mode is very sensitive to biaxial strain, and is extensively used to characterize the in-plane stress state of the GaN epilayer [33]. Figure 5: Variation in (**a**) resistivity; (**b**) carrier concentration; and (**c**) mobility of GaN films with different substrates. Figure 6: Raman spectra of GaN films for samples MGS (metalorganic chemical vapor deposition (MOCVD)-grown GaN on sapphire), A, B, C, and D.  
The relationship between biaxial stress and Raman shift can be shown by the formula:  
\[\sigma=\Delta\omega/k \tag{2}\]  
where \(\sigma\) is the biaxial stress, \(\Delta\omega\) is the Raman shift, and \(k\) is the Raman stress coefficient of 6.2 cm\({}^{-1}\cdot\)GPa\({}^{-1}\) for GaN [34]. Generally, a blue shift in an E\({}_{2}\)-high phonon peak indicates compressive stress, while a red shift indicates tensile stress [35]. It has been found that an E\({}_{2}\)-high peak position is substrate dependent, which implies that there are different stress states in those samples. In the present case, the GaN E\({}_{2}\)-high peaks of samples MGS (MOCVD-grown GaN on sapphire), A, B, C, and D were evaluated as 520.7, 569.7, 565.5, 565.7, and 566.3 cm\({}^{-1}\), respectively. Compared to the intrinsic value of 566.8 cm\({}^{-1}\) for the stress-free GaN, samples B, C, and D were under tensile stress, while sample A was under compressive stress [36]. This can be due to the rapid release of stress in the nucleation of GaN films during the initial growth by high-temperature (1000 \({}^{\circ}\)C) PLD. This observed result is also consistent with those reported by [PERSON] et al. [37]. Sample D had minimum stress, likely caused by the growth of polygonal island structures and defects generated in the films, which is consistent with the SEM results [38].