## 3 Results and Discussion
The evolution of FWHM vs. temperature revealed a unique tendency before 70 K for the 2\({}^{\circ}\) sample. The FWHM increased slowly below 40 K, sharply decreased in the 40-70 K range, and increased above 70 K. The FWHM trends exhibited a reverse temperature-dependent relationship compared to that of the PL peak energy. The FWHM data for the 2\({}^{\circ}\) sample are plotted against the corresponding peak energies in Figure 10, with the temperature spanning the entire region from 15 to 300 K. The fitting linear curve was obtained by the least square method drawn by the solid red line, a clearly negative linear relationship can be observed between them, which indicates that the evolutions of peak energy and FWHM of QW with temperature obey a similar or associated mechanism [43]. At low temperature (<40 K), carriers are thermally activated upon an increase in the temperature and have a significant opportunity to transit to deeper localization potentials; therefore, the range of energy levels of the carrier distribution widens, which leads to an increment in the FWHM. As the temperature increases to a critical level, the carriers obtain sufficient energy to enable their delocalization. The decrease in FWHM in the temperature range of 40-70 K was due to the process of carrier escape from the located states. The increment in FWHM at temperatures above 70 K presumably occurred because of a combination of the thermalization of carriers and phonon scattering caused by the increase in temperature. It is worth noting that the variations of PL peak position and FWHM of the 15\({}^{\circ}\) sample were not similar to the 2\({}^{\circ}\) sample. In addition, the value of the PL peak and FWHM of the 15\({}^{\circ}\) sample were much higher than the 0\({}^{\circ}\) and 2\({}^{\circ}\) samples, this is because large misorientations yield substantial strain relief and random quantum dots can form, therefore the luminescence characteristics are dominated by quantum dots. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & \(\mathbf{\Gamma_{0}}\) **(meV)** & \(a\) **(meV/K)** & \(\mathbf{\gamma}\) **(meV)** & \(\mathbf{E_{LO}}\) **(meV)** \\ \hline
0\({}^{\circ}\) & 14.36 & 0.058 & 1 & 0.83 \\
2\({}^{\circ}\) & 20.91 & 0.015 & 43 & 0.05 \\
15\({}^{\circ}\) & 28.00 & 0.081 & 12 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: FWHM-fitting parameters for samples with different misoriented substrates. Figure 9: PL full width at half maximum (FWHM) as a function of 1000/T of the InGaAs/GaAsP QWs on substrates misoriented by (**a**) 0\({}^{\circ}\), (**b**) 2\({}^{\circ}\), and (**c**) 15\({}^{\circ}\). The fitting curves of the FWHM data of the PL spectra are predictions based on the exciton–optical phonon coupling model. The temperature-dependent PL intensity data can be fit using the Arrhenius equation shown below to study the mechanism of PL quenching with increasing temperatures [44]:  
\[I(T)\propto 1/(1+\sum_{i}C_{i}\exp(-E_{i}/k_{B}T)). \tag{8}\]  
\(I(T)\) represents the integrated PL intensity at temperature \(T\), \(C_{i}\) represent the factors related to the densities of nonradiative recombination centers, and \(E_{i}\) represent the activation energies of the relevant nonradiative recombination centers. Two types of nonradiative recombination channels have been proposed for the quenching mechanism of PL intensities in epitaxially grown materials. The modified Arrhenius equation used to fit these experimental data can be expressed as [45; 46; 47]  
\[I(T)\propto 1/(1+C_{1}\exp(-E_{A}/k_{B}T)+C_{2}\exp(-E_{B}/k_{B}T)), \tag{9}\]  
where \(E_{A}\) and \(E_{B}\) are the activation energies of the corresponding nonradiative recombination processes, and \(C_{1}\) and \(C_{2}\) are two constants that are related to the number of nonradiative recombination centers in the QWs.