Optimisation of QCL Structures Modelling by Polynomial Approximation.

Area of Science:

• Semiconductor Nanodevices
• Quantum Engineering
• Computational Physics

Background:

• Modeling quantum cascade laser (QCL) structures presents significant analytical and numerical challenges.
• Existing simulation methods for these nanodevices demand substantial computational resources.
• Complex quantum well systems in contemporary QCLs require specialized approaches for accurate modeling.

Purpose of the Study:

• To investigate the applicability of the semi-analytical polynomial approximation method for solving the Schrödinger equation in QCLs.
• To develop and optimize a novel algorithm for determining self-energies and polynomial coefficients in QCL modeling.
• To enhance the computational efficiency and accuracy of QCL simulations.

Main Methods:

• Application of a semi-analytical polynomial approximation method to compute potential, wave functions, and electron charge distribution.
• Development of a new algorithm for calculating self-energies.
• Optimization of polynomial approximation for complex quantum well systems.
• Implementation of a new module for the finite model of the superlattice (FMSL).

Main Results:

• The polynomial approximation method achieves accurate results and rapid convergence for self-consistent solutions of Schrödinger and Poisson equations.
• The proposed algorithm and optimized method demonstrate effectiveness for contemporary QCL structures.
• The developed FMSL module successfully simulated a mid-infrared emitting QCL.

Conclusions:

• The semi-analytical polynomial approximation method is a viable and effective approach for modeling QCL structures.
• The new algorithm and optimized methods provide a computationally efficient alternative for QCL simulations.
• This work contributes to advancing the design and analysis of quantum cascade lasers.