Quantum Cascade Lasers (QCLs) offer a wide range of advantages making them a popular choice for coherent light sources. Its light emission is based on transitions between subbands formed by the muliple quantum well heterostructure. Due to the periodic nature of quantum cascade lasers, a single electron will contribute repeatedly to the photon emission process. The properties of the laser are mainly determined by the designer's choice of material and quantum well geometry. For this purpose, simulation tools can be a feasible approach to tune the QCL design to the desired optical and electrical characteristics. A design tool has rather stringent requirements with respect to computational resources and time but should still capture the relevant physics of the device.
In our approach we use the Pauli Master Equation (PME) to model current transport through the quantum cascade laser's semiconductor heterostructure. Based on the experiences with our MATLAB prototype developed earlier, a Monte Carlo (MC) simulator was implemented in C++ in our Vienna Schrödinger Poisson model framework. First the basis states for the PME solver are calculated either with a single-band effective mass model or k·p model. To consider the openness of the quantum system, perfectly matched layer boundary conditions can be applied to the discretized Schrödinger equation. To account for the periodic structure of a quantum cascade laser, three stages are considered in the model. The assignment of the wavefunctions to a single stage is done by an automated routine that requires no further user input. These eigenvalues and wavefunctions are then processed to calculate the relevant scattering rates for the quantum cascade laser. Currently, acoustic, longitudinal and polar optical phonon as well as intervalley scattering are included in the model. The software architecture is designed to allow for simple integration of new scattering mechanisms and therefore of additional physics. The tabulated scattering rates are used to efficiently pick a new random scattering event in the Monte Carlo loop. Whenever a transition between the central and the left or right stage occurs, it is considered as a contribution to the current. The electron is then re-injected into the central stage.