Importance of satisfying thermodynamic consistency in optoelectronic device simulations for high carrier densities

We show the importance of using a thermodynamically consistent flux discretization when describing drift–diffusion processes within light emitting diode simulations. Using the classical Scharfetter–Gummel scheme with Fermi–Dirac statistics is an example of such an inconsistent scheme. In this case, for an (In,Ga)N multi quantum well device, the Fermi levels show an unphysical hump within the quantum well regions. This result originates from neglecting diffusion enhancement associated with Fermi–Dirac statistics in the numerical flux approximation. For a thermodynamically consistent scheme, such as the SEDAN scheme, the humps in the Fermi levels disappear. We show that thermodynamic inconsistency has far reaching implications on the current–voltage curves and recombination rates.