## 3 Results and Discussion  
Figure 2 shows the XRD patterns of the InGaAs/GaAsP QWs with different miscut angles. The strongest peak originated from the GaAs substrates, and the satellite peaks of the QW are clearly visible in samples with miscut angles of 0\({}^{\circ}\) and 2\({}^{\circ}\). However, the satellite peaks of the InGaAs/GaAsP QW disappeared in the XRD pattern of the 15\({}^{\circ}\) sample, which indicated its poor interfacial quality [12]. From the XRD patterns of the three samples in Figure 2, the relax are obtained by the simulation of the diffraction patterns, 5.03% strain relaxation occurs in the 0\({}^{\circ}\) sample while 19.26% strain relaxes in the 2\({}^{\circ}\) sample, as for the 15\({}^{\circ}\) sample, 90.58% strain relaxation occurs [13]. The XRD result show that the crystal quality degraded with increasing the angle of substrate misorientation. Raman scattering is an important technique used to investigate the optical properties of materials, wherein the disorder and local strain phenomena in materials can be adequately represented by vibrational spectra. The disorder and strain in materials can alter the phonon frequency and phonon lifetime, which can lead to the broadening of the Raman spectrum and breaking of Raman selection rules [14]. The frequency shifts of longitudinal optical (LO) phonons are extremely sensitive to strain; compressive and tensile strain are known to result in positive and negative frequency shifts, respectively [15]. Figure 2: Omega-20 scans around the (004) symmetric XRD patterns of InGaAs/GaAsP QWs grown on substrates with misorientations of (**a**) 0\({}^{\circ}\), (**b**) 2\({}^{\circ}\), and (**c**) 15\({}^{\circ}\). The samples prepared in this study feature a lattice mismatch between the In-rich InGaAs QW and the GAs substrate. The In-rich layer generates a lattice mismatch stress in the adjacent epitaxial layer. The residual stress in the epitaxial layer can be obtained by measuring the frequency shift of the characteristic peak of GaAs via Raman scattering. The stress in the InGaAs material can be evaluated using the frequency shift of the GaAs-like LO mode of the InGaAs material; Equation (4) was utilized to calculate the frequency of the GaAs-like LO mode in the InGaAs epitaxial layer [16]:  
\[\omega_{LO}=290-18.6x-32.5x^{2}, \tag{4}\]  
where \(x\) is the content of In and \(\omega_{LO}\) is the GaAs-like LO frequency in the strain-free InGaAs material as a function of \(x\). The GaAs-like LO frequency in an ideal strain-free In\({}_{0.38}\)Ga\({}_{0.62}\)As layer is evaluated to be 278.2 cm\({}^{-1}\). The residual strain in the epitaxial layer is evaluated using the deviation from the measured frequency of the GaAs-like LO mode to that of the ideal strain-free In\({}_{0.38}\)Ga\({}_{0.62}\)As layer [17]. GaAs-related LO phonons from InGaAs/GaAsP QWs are known to consist of two LO phonon modes [18]--one from the GaAs buffer layer because of the thin QW that can be penetrated into the GaAs buffer layer [19], and the other from the InGaAs layer that exhibits a GaAs-like LO phonon peak. As shown by the dashed line in Figure 3, the GaAs-like LO frequency in the ideal strain-free In\({}_{0.38}\)Ga\({}_{0.62}\)As epitaxial layer was obtained as 278.2 cm\({}^{-1}\). The GaAs-like LO frequency of the 2\({}^{\circ}\) GaAs substrate was observed at 283.4 cm\({}^{-1}\) via fitting of the Raman spectra; this sample features the smallest shift with respect to 278.2 cm\({}^{-1}\) compared to that of the 0\({}^{\circ}\) GaAs substrate (285.2 cm\({}^{-1}\)), which indicated that the strain induced via lattice mismatch was partially relaxed in the epitaxial layer in the 2\({}^{\circ}\) GaAs substrate. The GaAs-like LO frequency of the 15\({}^{\circ}\) GaAs substrate was observed at 279.8 cm\({}^{-1}\) which is very close to the ideal strain-free In\({}_{0.38}\)Ga\({}_{0.62}\)As layer and indicated that substantial strain had relaxed in 15\({}^{\circ}\) substrate.