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 Frank Szmulowicz
1998 Physical review. B, Condensed matter 16 citations

Abstract

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 the transfer-matrix approach using Burt's boundary conditions. In the process, the tangents-only form of the secular equation is related to an earlier transfer matrix approach [L. R. Ram-Mohan, K. H. Yoo, and R. L. Aggarwal, Phys. Rev. B 38, 6151 (1988)] and extended to structures with an arbitrary number of layers per superlattice period. The formalism is applied to superlattices with two $({\mathrm{I}\mathrm{n}\mathrm{A}\mathrm{s}/\mathrm{I}\mathrm{n}}_{0.23}{\mathrm{Ga}}_{0.77}\mathrm{Sb})$ and three $({\mathrm{I}\mathrm{n}\mathrm{A}\mathrm{s}/\mathrm{I}\mathrm{n}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{S}\mathrm{b}/\mathrm{G}\mathrm{a}\mathrm{S}\mathrm{b})$ layers per superlattice period, which are of interest for infrared detector and infrared cascade-laser applications, respectively.

Keywords

SuperlatticePhysicsFormalism (music)Mathematical physicsQuantum mechanics

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Publication Info

Year
1998
Type
article
Volume
57
Issue
15
Pages
9081-9087
Citations
16
Access
Closed

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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
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Frank Szmulowicz (1998). 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. Physical review. B, Condensed matter , 57 (15) , 9081-9087. https://doi.org/10.1103/physrevb.57.9081

Identifiers

DOI
10.1103/physrevb.57.9081