## 3 Results and Discussion
### Model Limitations and Outlook for Future Studies  
The results presented in Section 3.1 show that the suggested semi-empirical model reproduces the wavelength dependence of both RRC and ARC from [20; 21] quantitatively well, if the only adjustable parameter of the model \(E_{t}\) is properly fitted. The model has, however, some intrinsic limitations originating from the fact that the most important parameter of the model, localization energy or localization radius, is fitted rather than derived theoretically and calculated. Since the composition fluctuations in InGaN alloys produce a variety of localized holes distributed inside the energy gap with a certain density of states (DOS), \(g(E)\), the localization radius in Equations (4) and (5) should be regarded as a parameter averaged over the ensemble of localized holes [22]. If \(g(E)\) is known, the averaging accounted for the Fermi distribution function of holes would enable a prediction of the  
Figure 4: Maximum IQE versus emission wavelength. Balls are experimental points summarized in [10]. Solid lines are theoretical estimates for [0001]-polar and nonpolar SQW LED structures, whereas the dotted line indicates the experimental trend in IQE variation at wavelengths longer than 540 nm. Dash-dotted line shows the IQE decrease caused by variation of the intrinsic material properties with the wavelength. dependences of the RCs on temperature and carrier concentration. However, it is impossible with the current model based on fitting to the data obtained at room temperature. Thus, the evaluation of DOS of localized holes becomes a key point for gaining a deeper insight into localization phenomenon. The asymptotic (far from the valence band edge) behavior of DOS has been provided by the optimal-fluctuation method but it is found to be inapplicable directly to InGaN alloys (see Section 2.3). Generally, DOS can be obtained by ab initio calculations. Those closest to an evaluation of DOS were the authors of [47], who investigated the energy distribution and spatial localization of a large number of ground and excited hole states in nonpolar InGaN QWs. However, the cluster of 82,000 atoms considered in [47] was insufficiently large to avoid the dependence of the obtained energy distribution on a particular configuration of In atoms in the cluster. Therefore, the evaluation of localized hole DOS and its dependence on the InGaN composition still remains problematic. Knowledge of \(g(E)\) for the correct estimation of the temperature-dependent localization radius is quite important in view of the anomalous behavior (increasing with temperature) of experimental RRC in blue and green LEDs revealed recently in [22]. In that study, such a behavior was explained qualitatively by assuming an exponential decrease of \(g(E)\) inside the InGaN energy gap. Leaving aside a discussion on the correctness of this assumption, I will show below how the data from [22] can be used for additional validation of the current semi-empirical model. According to Equations (4) and (5), the \(C_{sh}/B_{sh}\) ratio does not include the localization radius \(a\) and is proportional to the mean electron energy \(E_{e}\) nearly equal to thermal energy \(kT\) in the case of non-degenerate electrons. Figure 5 shows the experimental \(C_{sh}/B_{sh}\) ratios versus temperature estimated from the data of [22; 52]. The bars at the data points corresponding to green LED indicate the errors originating from an evaluation of the \(Q\)-factor from the current dependence of LED efficiency; the errors are especially pronounced at low temperatures, 50-100 K, where the efficiency is hardly approximated by the ABC-model (see [22] for more details on the experimental method). Similar bars for blue LEDs do not exceed the size of symbols.