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.
In: Computers and Mathematics with Applications, Vol. 49, No. 1, 01.01.2005, p. 39-51.Research output: Contribution to journal › Article
}
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
VL - 49
SP - 39
EP - 51
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
SN - 0898-1221
IS - 1
ER -