Challenges towards the simulation of GaN-based LEDs beyond the semiclassical framework

We discuss some of the key issues to be addressed along the way to complement, and possibly to replace, the standard semiclassical Boltzmann picture with genuine quantum approaches for the simulation of carrier transport and recombination in GaN-based LEDs, with the goal of gradually removing the fitting parameters presently required by semiempirical "quantum corrections" and to better understand the processes responsible for the efficiency droop. As examples of augmented semiclassical models, we present a three-step description of trap-assisted tunneling, especially relevant below the optical turn-on, and a carrier-density-dependent estimate of the phonon-assisted capture rate from bulk states to quantum wells (QWs). Moving to genuine quantum models, we solve the semiconductor Bloch equations to calculate the gain/absorption spectra of AlGaN/GaN QWs, and we discuss our first simulations of spatially and energetically resolved currents across the active region of a single-QW LED based on the nonequilibrium Green's function approach.