## 3 Results and Discussion
The full width at half maximum (FWHM) values of the GaAs-like LO frequencies for the 0\({}^{\circ}\) and 2\({}^{\circ}\) substrates were obtained as 3.0 and 5.6 cm\({}^{-1}\), respectively, by fitting the Raman spectra. The increase in the FWHM of GaAs-like LO phonons suggests that the residual strains released through defect generation and structural disorder [15; 20]. Consequently, the epitaxial layer on the 2\({}^{\circ}\) GaAs substrate exhibited a poorer crystalline quality than that of the 0\({}^{\circ}\) GaAs substrate. Figure 3: Raman spectra of InGaAs/GaAsP QWs grown on a GaAs (001) substrate with misorientations of 0\({}^{\circ}\), 2\({}^{\circ}\), and 15\({}^{\circ}\) using a 488 nm laser. Raman selection rules are often applied for analyzing the crystal quality; the LO phonon is allowed and the TO phonon is forbidden for the (001) plane of a sphalerite crystal structure [21; 22; 23; 24]. The disorder in InGaAs films can be assessed by the ratio between the TO and LO peak intensities because the presence of the TO phonon is an indicator of crystal structural disorder. As shown in Figure 3, the TO mode at 267.4 cm\({}^{-1}\) appeared only in the 15\({}^{\circ}\) sample, confirming its extremely large degree of crystal disorder compared to that of the other two samples [25]. The above results show that the strain relaxes gradually with the increase of the misorientation. These results follow trends similar to those observed in the XRD results. AFM analysis was subsequently conducted to verify the growth model of the InGaAs/GaAsP QWs. Figure 4 shows the AFM results on the surface morphologies of the three samples with different misorientations. Figure 4 reveals that the 0\({}^{\circ}\) sample exhibited a step-flow characteristic with RMS surface roughness of 0.147 nm, which indicated the high quality of the heterointerface in the 0\({}^{\circ}\) sample. Figure 4 indicated the narrowing of the terrace width in the 2\({}^{\circ}\) sample; the RMS surface roughness increased from 0.147 to 0.363 nm due to the composition-related inhomogeneity of In clusters that lead to a partial internal strain relaxation. In this case, the localization potential was formed because of the In clusters. Figure 4 reveals the presence of self-assembled quasi-quantum dots in the 15\({}^{\circ}\) sample. Randomly positioned growth nuclei were formed and the local strain subsequently relaxed at the locations of these nuclei [26; 27]; a surface roughness of 0.479 nm was obtained. Based on these results, a growth model is proposed to elucidate the different morphologies with the substrates featuring different misorientations. Figure 5 illustrates a surface on a substrate that is composed of steps and terraces. The growth condition in this scenario is presumed to involve surface coverage of the misoriented substrate with As atoms, because of the high V/III ratio (-150). Two dangling bonds are present on the terrace and three dangling bonds are at the kinks of the terrace edges. The incorporation probability of group III atoms into step kinks is presumed to be higher than that on the terraces. Upon reaching the growing surface, the group III species preferentially adhere to the step and kink sites on the terrace edge. This results in a step flow growth mode. The width of the terrace is known to decrease with increasing substrate misorientation, owing to the high density of growth steps on the tilted substrates [28]. Figure 4: AFM images of InGaAs/GaAsP QWs in a 3 \(\times\) 3 \(\upmu\)m\({}^{2}\) scan area with different misoriented substrates: (a) 0\({}^{\circ}\), (b) 2\({}^{\circ}\), and (c) 15\({}^{\circ}\). The disparity in the samples from the 0\({}^{\circ}\) to the 2\({}^{\circ}\) substrate was possibly caused by the inequality of diffusion lengths of the In and Ga cations for the growth of InGaAs. Ga cations possess smaller diffusion lengths than those of In; therefore, In atoms are likely to be mobile enough to incorporate at the step edges of the 2\({}^{\circ}\) substrate.