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We present a detailed theoretical analysis of the electronic structure of$c$-plane InGaN/GaN quantum wells with indium contents varying between 10\% and25\%. The electronic structure of the quantum wells is treated by means of anatomistic tight-binding model, accounting for variations in strain and built-infield due to random alloy fluctuations. Our analysis reveals stronglocalisation effects in the hole states. These effects are found not only inthe ground states, but also the excited states. We conclude that localisationeffects persist to of order 100~meV into the valence band, for as little as10\% indium in the quantum well, giving rise to a significant density oflocalised states. We find, from an examination of the modulus overlap of thewave functions, that the hole states can be divided into three regimes oflocalisation. Our results also show that localisation effects due to randomalloy fluctuations are far less pronounced for electron states. However, thecombination of electrostatic built-in field, alloy fluctuations and structuralinhomogeneities, such as well-width fluctuations, can nevertheless lead tosignificant localisation effects in the electron states, especially at higherindium contents. Overall, our results are indicative of individually localisedelectron and hole states, consistent with the experimentally proposedexplanation of time-dependent photoluminescence results in $c$-plane InGaN/GaNQWs.

Random alloy fluctuations and structural inhomogeneities in $c$-plane  In$_{x}$Ga$_{1-x}$N quantum wells: theory of ground and excited electron and  hole states