## 4 Discussions
### Difference of the Influence of the Current at the High Temperature and the Low Temperature  
Figure 9a shows the relationship between the emission peak energies of the blue and green LEDs and the current for \(T_{j}\) of 250 K, derived from Figure 4a. It was observed that the emission peak energy has a linear relationship with the current and increases with increasing current. This relationship is attributed to the electric field formed by the increased carrier concentration that decreases the impact of the quantum-confined Stark effect (QCSE) [26; 34] and the energy band filling effect [35; 36]. The excitons' lifetime decreased in the high-temperature range, and therefore, as the current increased the excitons could not occupy the lower energy state prior to the recombination, leading to the blue shift of the emission peak [27]. Since many higher energy extended states may be present, this kind of recombination will be accompanied by the linewidth broadening, as shown in Figure 9c, which is derived from Figure 5a. The same reason can also cause increase of the radiation power, as can be figured out in Figure 6. The slope of the emission peak energy plotted versus the current of the green LED was \(1.59\times 10^{-4}\) eV/mA, and that of the blue LED was \(6.34\times 10^{-5}\) eV/mA. A higher slope implies a stronger potential fluctuation, indicating that the potential fluctuation of the green LED is much stronger than that of blue LED. Thus, compared to the blue LED, the potential valley of the green LED is deeper and contains more states, leading to a higher slope. Comparison of Figures 6 and 9a,c shows that in the high-temperature range (200 K or higher), the emission peak energy, FWHM, and radiation power of both the blue and green LEDs increased with increasing current density. The reason is discussed in the last paragraph. However, in the low-temperature range (below 150 K), the emission peak energy, FWHM, and the radiation power of the blue LED showed only a slight change with increasing current, while the corresponding values of the green LED still increased strongly with increasing current, as shown in Figures 6 and 9b,d. This difference can be explained by the band filling in real space of the LED at low temperatures, as will be discussed below. Compared to high temperatures, for current injection at low temperatures, the exciton lifetime is long enough for the excitons to relax to the potential minima [8; 37; 38]. Due to the strong spatial potential fluctuations and the low exciton mobility in the green LED, the excitons in the potential minima were restricted and bound. As mentioned above, the excitons play an important role in light emission in InGaN. Thus, exciton recombination mainly occurs at the position of the potential valley [28]. Figure 10 shows a two-dimensional diagram depicting the conduction band, motion of electrons in excitons, and radiative combination due to the potential fluctuation along the real space \(x\)-axis. It is a simplified version of the three-dimensional diagram depicting the potential fluctuation along the real space xy-plane [39]. The black solid dots represent excitons (electrons), the curved lines interpret the conduction band, and the dashed line stands for different filling levels of the excitons (electrons) at different currents (I\({}_{1}\), I\({}_{2}\) and I\({}_{3}\)). As shown in Figure 10a, when the current increased from I\({}_{1}\) to I\({}_{2}\) and I\({}_{3}\), the increased excitons were distributed among the higher-energy potential minima, leading to the existence of more radiative centers and more recombination excitons. Since potential minima are deep and mobility of excitons is relative low in the green LEDs (due to large potential fluctuation), excitons are inclined to be bound by potential minima with different positions and different energy levels. This leads to the greater FWHM and radiation power of the green LED with the increase of \(I_{F}\).