  The presence of disorder in semiconductors can dramatically change their
physical properties. Yet, models faithfully accounting for it are still scarce
and computationally inefficient. We present a mathematical and computational
model able to simulate the optoelectronic response of semiconductor alloys of
several tens of nanometer sidelength, while at the same time accounting for the
quantum localization effects induced by the compositional disorder at the
nano-scale. The model is based on a Wigner-Weyl analysis of the structure of
electron and hole eigenstates in phase space made possible by the localization
landscape theory. After validation against eigenstates-based computations in 1D
and 2D, our model is applied to the computation of light absorption in 3D InGaN
alloys of different compositions. We obtain the detailed structures of the
absorption tail below the average bandgap and the Urbach energies of all
simulated compositions. Moreover, the Wigner-Weyl formalism allows us to define
and compute 3D maps of the effective locally absorbed power at all frequencies.
Finally the proposed approach opens the way to generalize this method to all
energy-exchange processes such as radiative and non-radiative recombination in
realistic devices.
