Abstract

A finite-element method for the analysis of eigenstates in a quantum well, which is based on the Galerkin procedure, is discussed. A general boundary condition of the envelope function at the heterointerface is introduced by using the transfer matrix. The validity of the method is confirmed by calculating the eigenstates of GaAs/AlGaAs and InAs/GaSb rectangular quantum wells. Numerical examples of voltage-applied quantum wells are presented.

Keywords

Quantum wellEigenvalues and eigenvectorsFinite element methodGalerkin methodBoundary value problemEnvelope (radar)PhysicsQuantumMatrix (chemical analysis)Wave functionQuantum mechanicsTransfer-matrix method (optics)Condensed matter physicsMaterials scienceComputer scienceTelecommunications

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Numerically stable secular equation for superlattices via transfer-matrix formalism and application to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">I</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">A</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">I</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mrow><mml:mn>0.23</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ga</mml:mi></mml:mrow><mml:mrow><mml:mn>0.77</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="normal">Sb</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">I</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">A</mml:mi><mml:mi mathvariant="normal">s</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">I</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mrow><mml:mn>0.3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ga</mml:mi></mml:mrow><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="normal">S</mml:mi><mml:mi mathvariant="normal">b</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">G</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">S</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:math>superlattices

Frank Szmulowicz

The numerically stable, Hermitian secular equation for superlattices within the envelope-function approximation [F. Szmulowicz, Phys. Rev. B 54, 11 539 (1996)] is derived via th...

1998 Physical review. B, Condensed matter 16 citations

Publication Info

Year
1989
Type
article
Volume
25
Issue
5
Pages
889-895
Citations
99
Access
Closed

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Kentaro Nakamura, Akira Shimizu, M. Koshiba et al. (1989). Finite-element analysis of quantum wells of arbitrary semiconductors with arbitrary potential profiles. IEEE Journal of Quantum Electronics , 25 (5) , 889-895. https://doi.org/10.1109/3.27977

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DOI
10.1109/3.27977