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 nanoscale. 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 eigenstate-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 band gap 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 nonradiative recombination in realistic devices.
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All authors are grateful to Professor Douglas Arnold and Professor James Speck for invaluable discussions. The authors are also grateful to Mylène Sauty and Abel Thayil for regular and fruitful discussions. J.-P.B., P.P., and M.F. are supported by the Simons foundation Grant No. 601944. S.M. is supported by the NSF RAISE-TAQS Grant No. DMS-1839077 and the Simons foundation Grant No. 563916. C.W. is supported by the Simons foundation Grant No. 601954 and NSF Raise-TAQS Grant No. DMS-1839077.
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