## 3 Results and Discussion
The analyses of _I-V_, \(n_{\text{min}}\), the PHEMOS pattern, the \(S\) value, the EL spectrum, \(\lambda_{\text{P}}\), the ER, and the IQE indicated that as the sample's In composition, number of point defects, SRH recombination rate, carrier tunneling and overflow, and redshift all decreased; \(\Delta E_{C}\), crystal quality, and \(F_{\text{PZ}}\) all increased (as listed in Table 1). The improvement of the optoelectronic performances mentioned above increased the sample's radiative recombination rate. However, it needs to be clarified which factor dominantly increased the radiative recombination rate at low currents. In this work, we propose that the dominant factor was spatially localized carriers caused by in-plane potential-energy fluctuation in QWs [18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. The possible reason for the potential-energy fluctuation could be the combined effects of inhomogeneous distribution of point defects, which was strongly affected by \(F_{\text{PZ}}\), and In composition: Schematic diagrams depicted in Figure 7 systematically and interactively describe the situation. There were inhomogeneously distributed point defects [40] caused by Ga/N vacancies [14; 41] in QWs, which were not filled up by neighboring atoms with strong bonds between other atoms. This effect relaxed the neighboring atoms by increasing the lattice constant, which led to the bandgap energy near the point defect increasing [30; 33]. Thus, in a site with accumulated defects, the crystal relaxation occurs and the bandgap energy near this site increased like a potential barrier (PB). Thus, a relatively defect-free potential \"valley\" was created between the accumulated defective sites. In these potential valleys, carriers were localized as depicted in Figure 7 [30]. Note that the number of defects were much smaller in the potential valley, with better crystal quality that yielded higher strain [30]. Thus, \(F_{\text{PZ}}\) increases around the potential valley that seems to cause the PB height surrounding the defects to increase. Figure 7: Schematic illustration of the proposed local in-plane fluctuation of potential energy in the quantum wells (QWs) for (**a**) #1 and (**b**) #4, where PB represents the potential barrier. Regions I and II represent the radiative recombination and the SRH process or carrier tunneling via point defects, respectively. On the other hand, the strain near the defects was relaxed owing to the missing atoms. Hence, \(F_{\text{PZ}}\) would be smaller at the defective region. The point defects always changed the uniform distribution of In atoms over the QWs. Therefore, the In composition in the potential valley would be higher than in the defect sites. Since the effective bandgap energy decreased with In composition [27; 33] and \(F_{\text{PZ}}\), in the potential-valley area, the depth and PB height increased with the sample's In composition. The distribution of potential valleys broke the uniform potential and resulted in the phenomenon of potential-energy fluctuation in QWs. This potential-energy fluctuation in QWs increased with In composition, which led to increased carrier localization states in the QWs. Moreover, PB prevented carriers from diffusing into defects due to higher potential at the edge of the defects [13; 16; 25; 26; 30]. Consequently, carrier localization increased the local carrier density in the QWs [13]. Recent studies showed that the hole wavefunction is more localized compared to the electron wavefunction for the potential-energy fluctuation [20; 21]. These localized carriers increased the QW occupancy factor. As a result, these carriers radiatively recombined in Region I due to the decrease in the SRH process via point defects, which explains the improved radiative recombination (or the IQE) in these LEDs.