## 1 Introduction
It should be noted that the idea of uncorrelated (independent) carrier localization in polar InGaN QWs was suggested for the first time in earlier work by [PERSON] et al. [32], based on a universal non-exponential decay of time-resolved photoluminescence (PL) at low, <10 K, temperatures. A strong carrier localization assumed from the data analysis in [32] was attributed to fluctuations of either InGaN composition or QW width. Another earlier study [33] considered low-temperature PL from quasi-bulk (50-100 nm) very-diluted (0.4-2.0% of In) InGaN layers sandwiched between thick GaN claddings. Observation of distinct fine structures in the emission spectra enabled the authors of [33] to associate the observed peaks with clusters containing two or three neighboring In atoms capable of capturing holes. The localization energies of holes in the above clusters estimated from the emission peak positions were about 35-50 meV and about 65-80 meV, respectively, whereas no evidence for electron localization was found in [33]. These data demonstrated that (i) composition fluctuations in InGaN alloys are a factor largely responsible for hole localization and (ii) the hole localization has an atomistic character. The atomistic nature of hole localization has also been demonstrated theoretically in [34; 35]. Here, the electronic structure of cubic InGaN alloys was calculated by using the pseudopotential supercell technique. Despite the absence of electronic states in the energy gap, strong resonant localization of holes by the In-N-In-N-In atomic chains was predicted, so that the chains played a role of deep acceptors. The hole wave functions were found to be highly anisotropic with a specific size of about 0.7 nm obtained by averaging over all directions for In\({}_{0.2}\)Ga\({}_{0.8}\)N alloys. No electron localization was identified in the study. Additional simulations of spherical In\({}_{0.76}\)Ga\({}_{0.24}\)N/In\({}_{0.33}\)Ga\({}_{0.67}\)N quantum dots 2.8 nm in diameter have shown that hole localization is insensitive to the quantum-confining potential formed in the quantum dot, but occurs at a dot corner due to a local strain [35]. Important data on the hole localization by composition fluctuations in AlGaN alloys have been reported in [36]. In this paper, real composition fluctuations in bulk Al\({}_{0.25}\)Ga\({}_{0.75}\)N and a GaN/AlGaN QW grown by metalorganic vapor phase epitaxy were restored by atomic-probe tomography by making necessary statistical corrections. Then, the obtained composition profiles were used in quantum-mechanical simulations of the conduction and valence band profiles perturbed by fluctuations and, finally, the emission spectra of the Al\({}_{0.25}\)Ga\({}_{0.75}\)N alloy and GaN/AlGaN QW were calculated, providing good agreement with the measured spectra. Based on the above data, the localization radius of holes of about 0.9-1.5 nm and the respective localization energies of about 40-60 meV were estimated. Though these results are relevant to AlGaN alloys, they clearly indicate that the hole localization by composition fluctuations occurs on an atomic scale and provides rather high localization energies. The study reported in this paper is aimed at better understanding the role of QCSE, carrier localization, and other factors for efficiency limitation of the LEDs emitting in the \"green gap\" spectral range. For this purpose, the semi-empirical approach [31] is extended to polar and nonpolar InGaN QWs. RRC and ARC predicted by the extended model will be shown to agree quantitatively with the data of [20; 21] obtained for polar LEDs. Calculation of theoretical wavelength-dependent internal quantum efficiencies (IQEs) of polar and nonpolar LEDs based on these RCs and their comparison with each other enables an assessment of the roles of QCSE and carrier localization in the \"green gap\" efficiency decline. The results obtained by the new model are also compared with other theories suggested previously for RRC and ARC.