Impact of random alloy fluctuations on the carrier distribution in multicolor (In,Ga)N/GaN quantum well systems

The efficiency of ($\mathrm{In}$,$\mathrm{Ga}$)$\mathrm{N}$-based light-emitting diodes (LEDs) is limited by the failure of holes to evenly distribute across the ($\mathrm{In}$,$\mathrm{Ga}$)$\mathrm{N}$/$\mathrm{Ga}\mathrm{N}$ multiquantum well stack that forms the active region. To tackle this problem, it is important to understand carrier transport in these alloys. In this work, we study the impact that random alloy fluctuations have on the distribution of electrons and holes in such devices. To do so, an atomistic tight-binding model is employed to account for alloy fluctuations on a microscopic level and the resulting tight-binding energy landscape forms input to a quantum corrected drift-diffusion model. Here, quantum corrections are introduced via localization-landscape theory. Similar to experimental studies in the literature, we have focused on a multiquantum well system in which two of the three wells have the same $\mathrm{In}$ content, while the third well differs in $\mathrm{In}$ content. By changing the order of wells in this ``multicolor'' quantum well structure and looking at the relative radiative-recombination rates of the different emitted wavelengths, we (i) gain insight into the distribution of carriers in such a system and (ii) can compare our findings to trends observed in experiment. We focus on three factors and evaluate the impact that each have on carrier distribution: an electron blocking layer, quantum corrections, and random alloy fluctuations. We find that the electron blocking layer is of secondary importance. However, in order to recover experimentally observed features---namely, that the $p$-side quantum well dominates the light emission---both quantum corrections and random alloy fluctuations should be considered. The widely assumed homogeneous virtual-crystal approximation fails to capture the characteristic light emission distribution across a multiquantum well stack.