Equivalent Circuit-Level Model of Quantum Cascade Lasers: Influence of Doping Density on Steady State and Dynamic Responses

Abstract

An equivalent circuit model of quantum cascade lasers (QCLs) is introduced by virtue of revised three-level rate equations. This model accounts for the influence of injector doping on electron dynamics of QCLs. Both the photon gain coefficient and the injection current efficiency depend on the injector doping density in this model. The nonradiative scattering times, radiative spontaneous relaxation time, and electron escape time are obtained by a fully nonequilibrium self-consistent Schrodinger-Poisson analysis of the scattering rate and energy balance equations. A general diode subcircuit is adopted to model the current-voltage relationship. Based on this new model, the steady and dynamic characteristics of devices with injector sheet doping densities in the range of $4\times 10^{11}\sim 6.5\times 10^{11}~{\rm cm}^{-2}$ are investigated by using a circuit simulator. Results indicate that doping density variations play an important role on threshold current and delay time of QCL devices.