The accurate determination of the compositional fluctuations is pivotal in understanding their role in the reduction of efficiency in high indium content $In_{x}Ga_{1-x}N$ light-emitting diodes, the origin of which is still poorly understood. Here we have combined electron energy loss spectroscopy (EELS) imaging at sub-nanometer resolution with multiscale computational models to obtain a statistical distribution of the compositional fluctuations in $In_{x}Ga_{1-x}N$ quantum wells (QWs). Employing a multiscale computational model, we show the tendency of intrinsic compositional fluctuation in $In_{x}Ga_{1-x}N$ QWs at different Indium concentration and in the presence of strain. We have developed a systematic formalism based on the autonomous detection of compositional fluctuation in observed and simulated EELS maps. We have shown a direct comparison between the computationally predicted and experimentally observed compositional fluctuations. We have found that although a random alloy model captures the distribution of compositional fluctuations in relatively low In ($\sim$ 18%) content $In_{x}Ga_{1-x}N$ QWs, there exists a striking deviation from the model in higher In content ($\geq$ 24%) QWs. Our results highlight a distinct behavior in carrier localization driven by compositional fluctuations in the low and high In-content InGaN QWs, which would ultimately affect the performance of LEDs. Furthermore, our robust computational and atomic characterization method can be widely applied to study materials in which nanoscale compositional fluctuations play a significant role on the material performance.

38 pages, 5 Figures