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Optimisation of QCL Structures Modelling by Polynomial Approximation.

Stanisław Pawłowski1, Mariusz Mączka2

  • 1Department of Electrodynamics and Electrical Machine Systems, Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, 35-959 Rzeszow, Poland.

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This study introduces a semi-analytical polynomial approximation method for modeling quantum cascade laser (QCL) structures, offering accurate and efficient solutions for complex nanodevice simulations. The new approach enhances computational effectiveness for QCL design.

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Schrödinger–Poisson equationspolynomials approximationsemiconductor superlatticestransfer matrix method

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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.