Optimisation of QCL Structures Modelling by Polynomial Approximation

Abstract

Modelling of quantum cascade laser (QCL) structures, despite a regular progress in the field, still remains a complex task in both analytical and numerical aspects. Computer simulations of such nanodevices require large operating memories and effective algorithms to be applied. Promisingly, by applying semi-analytical polynomial approximation method to computing potential, wave functions and electron charge distribution, accurate results and quick convergence of the self-consistent solution for the Schrödinger and Poisson equations are reachable. Additionally, such an approach makes the respective numerical models competitively effective. For contemporary QCL structures, with quantum wells quite typically forming complex systems, a special approach to determining self energies and coefficients of approximating polynomials is required. Under this paper we have analysed whether the polynomial approximation method can be successfully applied to solving the Schrödinger equation in QCL. A new algorithm for determining self energies has been proposed and a new method has been optimised for the researched structures. The developed solutions have been implemented as a new module for the finite model of the superlattice (FMSL) and tested on the QCL emitting light in the mid-infrared range.