Fundamental limit of quantum device simulations
This pictures provides an atomistic view of an InGaN/GaN quantum well . Inside this quantum well (QW), 17% of the Gallium atoms are replaced by Indium atoms which are here randomly distributed (red dots). Such QWs are employed in many modern light-emitting devices, from full-color displays to LED lamps. The emission wavelength is controlled by the Indium concentration.
QW models and device simulations typically ignore this atomistic structure and assume a uniform QW alloy layer with uniform material properties. Such continuum models still deliver reasonable results in many cases. But some phenomena are hard to explain this way and require an atomistic approach. One example is the much discussed efficiency droop that seems to be mainly caused by strong Auger recombination. Recent studies link this effect to the non-uniformity of InGaN quantum wells (details).
Another example is the modeling of sub-nanometer alloy layers, as sometimes envisioned inside complex quantum wells (e.g., here and here). Considering the picture above, such structures are practically impossible to grow and a continuum model is clearly inappropriate, I think, especially with low alloy concentrations. For example, an Indium concentration of 10% corresponds to an average Indium atom distance of about 3nm, which is close to the thickness of a typical InGaN quantum well.
This issue is not restricted to III-nitride devices. Any kind of optoelectronic quantum structure simulation could face the same problem. Some groups have recognized this challenge but I think all of us should pay more attention to this fundamental limit of the continuum models commonly used in quantum device simulations.
 Courtesy of L. Lymperakis