Solving the Schrodinger equation in arbitrary quantum-well potential profiles using the transfer matrix method

Jonsson, Björn; Eng, S. T.

doi:10.1109/3.62122

Cited by 215 publications

(99 citation statements)

References 24 publications

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“…One may examine other absorbing potentials by using transfer matrices discussed [11,15,7]. For this potential the transmission, reflection and absorption coefficients may be found exactly giving [6] …”

Section: Numerical Examplesmentioning

confidence: 99%

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A semiclassical transport model for two-dimensional thin quantum barriers

Jin

Novak

2007

Journal of Computational Physics

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Section: Numerical Examplesmentioning

confidence: 99%

“…One may also solve the boundary value problem (27) by using the transfer matrix method [11,15,7]. Since the solution is constant in the y-direction, the semiclassical impulse force is normal to the barrier curve.…”

Section: Routine Initializationmentioning

confidence: 99%

A semiclassical transport model for two-dimensional thin quantum barriers

Jin

Novak

2007

Journal of Computational Physics

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“…We have employed the single band effective mass approximation to calculate the WL QW energy levels and wave functions by solving numerically the onedimensional Schrödinger equation with the use of the transfer matrix method and by including strains. 23,24 The material parameters have been taken from Ref. 25.…”

Section: Resultsmentioning

confidence: 99%

Wetting layer states of InAs∕GaAs self-assembled quantum dot structures: Effect of intermixing and capping layer

Sęk

Ryczko

Motyka

et al. 2007

Journal of Applied Physics

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Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publicationCitation for published version (APA): Sek, G., Ryczko, K., Motyka, M., Andrzejewski, J., Wysocka, K., Misiewicz, J., ... Patriarche, G. (2007). Wetting layer states of InAs/GaAs self-assembled quantum dot structures. Effect of intermixing and capping layer. Journal of Applied Physics, 101(6), 063539-1/7. [063539]. DOI: 10.1063/1.2711146 General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. The authors present a modulated reflectivity study of the wetting layer ͑WL͒ states in molecular beam epitaxy grown InAs/ GaAs quantum dot ͑QD͒ structures designed to emit light in the 1.3-1.5 m range. A high sensitivity of the technique has allowed the observation of all optical transitions in the QD system, including low oscillator strength transitions related to QD ground and excited states, and the ones connected with the WL quantum well ͑QW͒. The support of WL content profiles, determined by transmission electron microscopy, has made it possible to analyze in detail the real WL QW confinement potential which was then used for calculating the optical transition energies. We could conclude that in spite of a very effective WL QW intermixing, mainly due to the Ga-In exchange process ͑causing the reduction of the maximum indium content in the WL layer to about 35% from nominally deposited InAs͒, the transition energies remain almost unaffected. The latter effect could be explained in effective mass envelope function calculations taking into account the intermixing of the QW interfaces described within the diffusion model. We have followed the WL-...

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“…The wave function intensity has been calculated by squaring wave function amplitude for the varying number of wells from 3 to 7. Transfer matrix method (TMM) [16] is a simple and accurate numerical method that can be used for a wide range of problems dealing with second-order differential equations. Therefore, TMM has been used to obtain solutions of Schrodinger equation in well and barrier regions.…”

Section: Introductionmentioning

confidence: 99%

ANALYSIS OF WAVE FUNCTION, ENERGY AND TRANSMISSION COEFFICIENTS IN GaN/ALGaN SUPERLATTICE NANOSTRUCTURES

Talele¹,

Patil²

2008

PIER

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Abstract-Analysis of wave function intensity, eigen energy and transmission coefficients in GaN/AlGaN superlattice nanostructure has been carried out using Transfer Matrix Method (TMM). The effect of change in Aluminum mole fraction in Al x Ga 1−x N barrier region has been included through variable effective mass in the Schrödinger time independent equation. The behaviour of wave function intensity has been studied for superlattice structure by changing the barrier width. The effect of smaller barrier width on wave function intensity in case of superlattice is clearly observed due to interaction of wave functions in the adjacent wells and it provides a new insight in the nature of interacting wave functions for thin barriers in GaN/AlGaN superlattice structures. The barrier widths have been optimized for the varying number of wells leading to better quantum confinement. The iterative method (Secant Method) is used to determine value of electron energy E. The number of iterations need to converge the value of E has been simulated. Transmission coefficients have been determined as a function of energy E considering tunneling effect for three well structures using TMM. Analysis has been extended to show surface image of wave function intensity for 5 and 6 wells.

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Solving the Schrodinger equation in arbitrary quantum-well potential profiles using the transfer matrix method

Cited by 215 publications

References 24 publications

A semiclassical transport model for two-dimensional thin quantum barriers

A semiclassical transport model for two-dimensional thin quantum barriers

Wetting layer states of InAs∕GaAs self-assembled quantum dot structures: Effect of intermixing and capping layer

ANALYSIS OF WAVE FUNCTION, ENERGY AND TRANSMISSION COEFFICIENTS IN GaN/ALGaN SUPERLATTICE NANOSTRUCTURES

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