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
Full text available as: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 |
| 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 Feb 2013 17:29 |
| 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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