Analytical compact modeling for the electrical and optical simulation of quantum-well–based light-emitting diodes

We present a simplified model for the hole injection recombination current in multiple quantum-well (MQW) micro-light-emitting diodes (μLEDs) by representing the MQWs as a single equivalent quantum well (EQW). Building on our initial model, we have reformulated the fundamental equations, which were previously expressed using the complex analytical Lambert W0(x) function, in terms of applied forward voltage, material properties, and model parameters. The resulting model provides a simplified and concise expression for the hole injection recombination current, applicable within the forward operating region. It incorporates key factors such as the EQW position within the depletion region, the hole diffusion coefficient, the electrical series resistance, and the thermal resistance. This refined model forms the foundation for an explicit methodology to extract both the injection recombination current parameters and the thermal resistance of the μLED. Furthermore, we introduce an empirical analytical compact model for optical power density, which is linked to the injection recombination current density (J) as a power function of the Lambert W0(J) function, applicable across all injection recombination current regimes. We have also developed a methodology to extract the three relevant optical parameters involved. The proposed analytical electro-optical compact model, validated against experimental data from green and blue μLEDs, is well suited for the electrical and optical simulation of quantum-well-based μLEDs.