### 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 | |

Publication status | Published - 2005 Jan 1 |

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### 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

### Cite this

**Energy states of vertically aligned quantum dot array with nonparabolic effective mass.** / Hwang, Tsung-Min; Wang, Weichung.

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 49, no. 1, pp. 39-51. https://doi.org/10.1016/j.camwa.2005.01.004

}

TY - JOUR

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

AU - Hwang, Tsung-Min

AU - Wang, Weichung

PY - 2005/1/1

Y1 - 2005/1/1

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

UR - http://www.scopus.com/inward/record.url?scp=17944382102&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17944382102&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2005.01.004

DO - 10.1016/j.camwa.2005.01.004

M3 - Article

AN - SCOPUS:17944382102

VL - 49

SP - 39

EP - 51

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 1

ER -