Real-time modeling of quantum cascade laser operation using linear combinations of intrawell properties

Description of multi-quantum well heterostructures based on localized properties of the constituent single well eigenstates permits invaluable insight into the relationships between structure design and device operation. Analytical descriptions of single well electronic states permits analytical evaluation of tight-binding parameters used to describe coupled well interactions. An expansion of Fermi's Golden Rule in the single well basis is presented under the assumption that transitions between delocalized states can be written as linear combinations of intrawell mean scattering rates. This assumption of localized transitions permits the construction of predetermined sets for the limited single well scattering events. Using a simplified density matrix description of transport, where incoherent scattering and coherent tunneling is restricted to intrawell and interwell transitions, respectively, allows for an easily accessible model of transport. The combination of these computational techniques produces a simulation tool requiring near zero computational time. Application of these techniques to a four-well and a three-well resonant phonon depopulation quantum cascade laser demonstrates this method as a valuable tool for fast approximation of device operation.