Quantum Cascade Lasers (QCLs) are based on a semiconductor heterostructure forming multiple quantum wells. The structure gives rise to the formation of subbands with properties that can be carefully designed by choice of material parameters and well widths. Photons are emitted by an intersubband transition from a higher to a lower state. Therefore, the laser wavelength can be tuned by adjusting the energy difference of these subbands. Many stages are cascaded to re-use electrons for another photon emission process.
To fulfill the inversion condition necessary for lasing, efficient population of the upper laser state and depopulation of the lower laser state need to be ensured. For this purpose, resonant tunneling between certain states can be introduced. Furthermore, phonon assisted electron transport can be used beneficially to move carriers from the lower laser states to the injector of the next stage. However, tunneling out of the upper laser state and scattering from the upper to the lower laser state are detrimental. Therefore, a design tool for QCLs needs to account for all these effects in an efficient but physically meaningful way to be useful. Thus, the numerical solution of the Schrödinger equation with QCL specific boundary conditions was investigated. The basis states are then used to calculate the subband transition rates. Relevant scattering processes for the quantum cascade lasers are due to acoustic, LO- and polar optical phonons. Current work is focused on developing algorithms within the Vienna Schrödinger Poisson (VSP) framework to efficiently calculate the matrix elements using fast Fourier transforms. The hereby obtained scattering rates will later be used to solve the transport problem based on the Pauli master equation.