“…It has also been making dramatic progress in high device performance at room temperature (300 K) [2,3]. As a complex quantum system, QCL can be modeled in various ways such as the rate equation model [4,5], Monte-Carlo (MC) simulation [6][7][8][9], and the nonequilibrium Green's function with the density matrix model [10,11]. The rate equation method in the design of mid-infrared QCLs cannot take fully into account of the complexity of temperature and density which mainly depend on the scattering time.…”