## 4 Discussions  
### Emission Peak Energy vs. Tj  
The emission peak shift can be described by a band-tail model [22]:  
\[EgT=Eg(0)-\frac{\alpha T^{2}}{\beta+T}-\frac{\sigma^{2}}{kT} \tag{1}\]  
where \(\alpha\) and \(\beta\) are Varshni parameters, and \(Eg(0)\) and \(Eg(T)\) are the band gap values at 0 K and at temperature \(T\), respectively. The second term is about the band gap shrinkage with increasing temperature, leading to the redshift of the emission peak in the temperature range of \(\sim\)175-373 K. The last term describes the redshift of the Stokes type, where \(\sigma\) is the degree of the localized effect of the carriers, and \(k\) is the Boltzmann constant [23]. Indium composition fluctuations lead to the spontaneous formation of indium-rich regions, and the presence of such regions in addition to the presence of doping elements and crystalline quality of the hetero- and homoepitaxial material lead to potential fluctuations in the InGaN alloy layers [24]. The band-tail states also mean the potential fluctuations in energy band structure, and they would capture the carriers and excitons to generate the localized carriers and bound excitons. The larger the \(\sigma\) value is, the deeper extension of the tails into the forbidden band and the greater degree of the localized effect of the carriers [25]. The potential fluctuations are sufficiently strong to provide efficient luminescence centers because these states can confine electrons and holes at the same sites [26]. Due to the fact that the density-of-states of the tails is much lower, the occupation of the higher energy states of the tails is more obvious than the occupation in regular energy bands with the increasing \(T_{j}\)[24]. In the temperature range of \(\sim\)120-175 K, thermalized bound excitons occupy higher energy states, and the effect of the blueshift is stronger than the effect of the temperature-induced band gap shrinkage with temperature increasing, leading to the blueshift of the emission peak energy [22; 27]. Using Equation (1) to fit the blue LED data, the fitting curve is presented in Figure 8a and shows good agreement with the experimental data. Two maxima were found in the curve of the emission peak energy as a function of the \(T_{j}\) of green LED, indicating that a transition between two different main luminescence mechanisms occurs as the \(T_{j}\) of the green LED changes. Therefore, the data cannot be fitted with a single set of parameters. As reported previously, excitons play an important role in light emission in GaN and related alloys [28; 29; 30]. Compared to the blue LEDs, larger potential fluctuations, and thus deeper band tails in the green LEDs, cause easier caption of the excitons by defect states. At low temperatures, the recombination of the donor-bound excitons (DX) may be the main source of light emission. As the exciton localization energy of DX is low, the DX escape the trap states as the temperature increases,  
Figure 8: Fitting curves of [PERSON]’s formula for (**a**) blue LED and (**b**) green LED at 80 mA. transforming into free excitons (FX), and the amount of free excitons A (FXA) increases rapidly [31]. Therefore, FXA start to play an increasingly important role in the luminescence at high temperatures. Due to its large exciton binding energy, FXA is dominant even at room temperature [30]. To fit the data for the green LED in Figure 8b, we used two groups of parameters for the data near the left extreme value and in the low temperature region, and for the data near the right extreme value and in the high temperature region, respectively. Since the exciton localization energy of DX was previously reported to be approximately 6 meV [31], the band width difference between the two fitting curves was set to 6 meV in our curve fitting. The fitting curves of the green LED are shown in Figure 8b and agree well with the experimental data, except that due to the transition of the main luminescence mechanism from DX-based to FXA-based, the data in the intermediate temperature region are not fitted very well.