Energy states of vertically aligned quantum dot array with nonparabolic effective mass

Tsung Min Hwang; Weichung Wang

doi:10.1016/j.camwa.2005.01.004

Energy states of vertically aligned quantum dot array with nonparabolic effective mass

Tsung Min Hwang, Weichung Wang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

The electronic properties of a three-dimensional quantum dot array model formed by vertically aligned quantum dots are investigated numerically. The governing equation of the model is the Schrödinger equation which is incorporated with a nonparabolic effective mass approximation that depends on the energy and position. Several interior eigenvalues must be identified from a large-scale high-order matrix polynomial. In this paper, we propose numerical schemes that are capable of simulating the quantum dot array model with up to 12 quantum dots on a personal computer. The numerical experiments also lead to novel findings in the electronic properties of the quantum dot array model.

Original language	English
Pages (from-to)	39-51
Number of pages	13
Journal	Computers and Mathematics with Applications
Volume	49
Issue number	1
DOIs	https://doi.org/10.1016/j.camwa.2005.01.004
Publication status	Published - 2005 Jan

Keywords

Cubic Jacobi-Davidson method
Cubic large-scale eigenvalue problems
Energy levels
Matrix reduction
Semiconductor quantum dot array
The Schrödinger equation

ASJC Scopus subject areas

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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@article{a60908865a5c4bf88bd227e01face3c1,

title = "Energy states of vertically aligned quantum dot array with nonparabolic effective mass",

abstract = "The electronic properties of a three-dimensional quantum dot array model formed by vertically aligned quantum dots are investigated numerically. The governing equation of the model is the Schr{\"o}dinger equation which is incorporated with a nonparabolic effective mass approximation that depends on the energy and position. Several interior eigenvalues must be identified from a large-scale high-order matrix polynomial. In this paper, we propose numerical schemes that are capable of simulating the quantum dot array model with up to 12 quantum dots on a personal computer. The numerical experiments also lead to novel findings in the electronic properties of the quantum dot array model.",

keywords = "Cubic Jacobi-Davidson method, Cubic large-scale eigenvalue problems, Energy levels, Matrix reduction, Semiconductor quantum dot array, The Schr{\"o}dinger equation",

author = "Hwang, {Tsung Min} and Weichung Wang",

note = "Funding Information: This work is partially supported by the National Science Council and the National Center for Theoretical Sciences in Taiwan. *Author to whom all correspondence should be addressed. The authors thank Wen-Wei Lin for many helpful discussions and Chia-Chi Chung for assistance on some computational results. The authors are grateful to the referees for carefully reading the manuscript and their helpful comments. Our gratitude also goes to the Academic Paper Editing Clinic, National Taiwan Normal University.",

year = "2005",

month = jan,

doi = "10.1016/j.camwa.2005.01.004",

language = "English",

volume = "49",

pages = "39--51",

journal = "Computers and Mathematics with Applications",

issn = "0898-1221",

publisher = "Elsevier Limited",

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T1 - Energy states of vertically aligned quantum dot array with nonparabolic effective mass

AU - Hwang, Tsung Min

AU - Wang, Weichung

N1 - Funding Information: This work is partially supported by the National Science Council and the National Center for Theoretical Sciences in Taiwan. *Author to whom all correspondence should be addressed. The authors thank Wen-Wei Lin for many helpful discussions and Chia-Chi Chung for assistance on some computational results. The authors are grateful to the referees for carefully reading the manuscript and their helpful comments. Our gratitude also goes to the Academic Paper Editing Clinic, National Taiwan Normal University.

PY - 2005/1

Y1 - 2005/1

N2 - The electronic properties of a three-dimensional quantum dot array model formed by vertically aligned quantum dots are investigated numerically. The governing equation of the model is the Schrödinger equation which is incorporated with a nonparabolic effective mass approximation that depends on the energy and position. Several interior eigenvalues must be identified from a large-scale high-order matrix polynomial. In this paper, we propose numerical schemes that are capable of simulating the quantum dot array model with up to 12 quantum dots on a personal computer. The numerical experiments also lead to novel findings in the electronic properties of the quantum dot array model.

AB - The electronic properties of a three-dimensional quantum dot array model formed by vertically aligned quantum dots are investigated numerically. The governing equation of the model is the Schrödinger equation which is incorporated with a nonparabolic effective mass approximation that depends on the energy and position. Several interior eigenvalues must be identified from a large-scale high-order matrix polynomial. In this paper, we propose numerical schemes that are capable of simulating the quantum dot array model with up to 12 quantum dots on a personal computer. The numerical experiments also lead to novel findings in the electronic properties of the quantum dot array model.

KW - Cubic Jacobi-Davidson method

KW - Cubic large-scale eigenvalue problems

KW - Energy levels

KW - Matrix reduction

KW - Semiconductor quantum dot array

KW - The Schrödinger equation

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