## 3 Results and Discussion
A possible explanation for the S-shaped behavior of the peak energy is illustrated in \[\omega_{LO}=290-18.6x-32.5x^{2}, \tag{4}\]0 \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & \(E_{\mathbf{g}}\)**(0) (eV)** & \(\alpha\) (eV/K)** & \(\beta\) (K) & \(\sigma\) (meV) \\ \hline
0\({}^{\circ}\) & 1.127 & 3.49 \(\times\) 10\({}^{-4}\) & 150 & \\
2\({}^{\circ}\) & 1.153 & 4.03 \(\times\) 10\({}^{-4}\) & 109 & 14.7 \\
15\({}^{\circ}\) & 1.089 & 2.84 \(\times\) 10\({}^{-4}\) & 120 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Fitting parameters, \(\alpha\), \(\beta\), and \(\sigma\), for the differently misoriented substrates. Figure 7: Temperature-dependent peak energies of the InGaAs/GaAsP QWs on (**a**) 0\({}^{\circ}\), (**b**) 2\({}^{\circ}\), and (**c**) 15\({}^{\circ}\)-misoriented substrates. At low temperatures, carriers are freely distributed throughout the QW layer (Figure 8a). With increasing temperatures, the weakly localized carriers are thermally activated and have a greater chance to relax to the deep localized states (Figure 8b); this results in a red shift in the PL peak energy. A further increase in the temperature leads to the carriers in the deep localized states obtaining sufficient energy to repopulate the shallow localized states (Figure 8c), which produces a blueshift in the emission peak energy. As the temperature continues to rise, the thermal carriers escape from the localized states into the barrier states and become free carriers (Figure 8d); at even higher temperatures, the peak energy exhibited redshifts owing to the shrinkage of the temperature-induced band gap upon thermal activation and delocalization of the carriers [39]. Typically, two factors are known to affect the PL linewidth of the InGaAs/GaAsP QWs, one is inhomogeneous broadening which is primarily determined by fluctuations of circumstance, for example, interface roughness, composition variation, and crystal disorder. The other one is homogeneous which is closely related to temperature and is primarily affected by the interaction between electrons and phonons [40; 41]. Figure 9 shows the behavior of the FWHM with respect to temperature. Inhomogeneous broadening and exciton interactions with phonons are considered. The trends of FWHM conform to the following expression [42]:  
\[\Gamma(T)=\Gamma_{0}+aT+\gamma/[(\exp(E_{LO}/k_{B}T)-1], \tag{7}\]  
where \(\Gamma(T)\) represents the FWHM of the photoluminescence spectra, \(\Gamma_{0}\) represents the inhomogeneous contribution to the FWHM that is related to the interface roughness and crystal disorder, \(a\) is a parameter representing the acoustic phonon scattering strength, \(\gamma\) is a parameter that is related to the exciton-phonon coupling, and \(E_{LO}\) is the longitudinal optical phonon energy of QW layer. The experimental data of the three samples were fitted using Equation (7) and shown in Figure 9; the fitted parameters are listed in Table 2. The value of \(\Gamma_{0}\) is noted to increase with increasing misorientation, which indicates that the interface roughness and alloy disorder increased as the substrate misorientation increased. Figure 8: Schematic diagrams illustrating the possible mechanism of the S-shaped temperature-dependent PL peak energy. (**a**) At the lowest temperature, carriers exist in all possible potential minimums. (**b**) At a slightly higher temperature, carriers relax to the deepest potentials. (**c**) As the temperature continues to rise, carriers redistribute to higher energies. (**d**) As the temperature rises very high, most carriers escape from the localization potentials. A higher value of \(E_{LO}\) is known to indicate a larger strain in the epitaxial layer [13; 42]. The highest \(E_{LO}\) value corresponded to the 0\({}^{\circ}\) sample and indicated the largest strain in this sample compared to those of the others; considerable strain relaxation was noted to occur in the 2\({}^{\circ}\) and 15\({}^{\circ}\) samples, which had also been implied by the Raman scattering results.