Quantum Cascade Lasers (QCLs) offer a wide range of advantages, which make them a popular choice for coherent light sources. Its light emission is based on transitions between subbands formed by the multiple 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 the quantum well geometry. 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. A Monte Carlo (MC) simulator has been 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 a 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 wave functions to a single stage is done by an automated routine, which requires no further user input. These eigenvalues and wave functions 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, alloy and interface roughness scattering are included in the model. To increase simulation speed the calculation of scattering rates is parallelized. Furthermore, we designed the software architecture to allow for simple integration of new scattering mechanisms and therefore of additional physics. The tabulated scattering rates are used to efficiently select 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.
The model gives insight into macroscopic and microscopic quantities such as current-voltage characteristics, scattering rates, carrier density spectrum, subband population, and optical gain.