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Finite difference method for solving the Schrödinger equation with band nonparabolicity in mid-infrared quantum cascade lasers

Cooper, JD, Valavanis, A, Ikonic, Z, Harrison, P and Cunningham, JE (2010) Finite difference method for solving the Schrödinger equation with band nonparabolicity in mid-infrared quantum cascade lasers. Journal of Applied Physics, 108 (11). 113109 - 113109 . ISSN 0021-8979

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Abstract

The nonparabolic Schrödinger equation for electrons in quantum cascade lasers (QCLs) is a cubic eigenvalue problem (EVP) which cannot be solved directly. While a method for linearizing this cubic EVP has been proposed in principle for quantum dots [ Hwang et al., Math. Comput. Modell., 40, 519 (2004) ] it was deemed too computationally expensive because of the three-dimensional geometry under consideration. We adapt this linearization approach to the one-dimensional geometry of QCLs, and arrive at a direct and exact solution to the cubic EVP. The method is then compared with the well established shooting method, and it is shown to be more accurate and reliable for calculating the bandstructure of mid-infrared QCLs.

Item Type: Article
Copyright, Publisher and Additional Information: collaboration: eid: 113109 numpages: 5 keywords: eigenvalues and eigenfunctions; finite difference methods; quantum cascade lasers; Schrodinger equation
Keywords: eigenvalues and eigenfunctions, finite difference methods, quantum cascade lasers, Schrodinger equation
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Electronic & Electrical Engineering (Leeds) > Institute of Microwaves and Photonics (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 21 Dec 2010 12:32
Last Modified: 08 Jul 2014 05:07
Published Version: http://link.aip.org/link/?JAP/108/113109/1
Status: Published
Publisher: AIP
Identification Number: 10.1063/1.3512981
URI: http://eprints.whiterose.ac.uk/id/eprint/42712

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