  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.
