### Abstract

Three dimensional truncated pyramidal quantum dots are simulated numerically to compute the energy states and the wave functions. The simulation of the hetero-structures is realized by using a novel finite volume scheme to solve the Schrödinger equation. The simulation benefits greatly from the finite volume scheme in threefold. Firstly, the BenDaniel-Duke hetero-junction interface condition is ingeniously embedded into the scheme. Secondly, the scheme uses uniform meshes in discretization and leads to simple computer implementation. Thirdly, the scheme is efficient as it achieves second-order convergence rates over varied mesh sizes. The scheme has successfully computed all the confined energy states and visualized the corresponding wave functions. The results further predict the relation of the energy states and wave functions versus the height of the truncated pyramidal quantum dots.

Original language | English |
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Pages (from-to) | 371-385 |

Number of pages | 15 |

Journal | Computer Physics Communications |

Volume | 174 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2006 Mar 1 |

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### Keywords

- Energy levels
- Finite volume scheme
- Numerical simulations
- Schrödinger equation
- Second-order convergence
- Three dimensional truncated pyramidal quantum dot
- Wave functions

### ASJC Scopus subject areas

- Computer Science Applications
- Physics and Astronomy(all)

### Cite this

*Computer Physics Communications*,

*174*(5), 371-385. https://doi.org/10.1016/j.cpc.2005.10.012

**A second-order finite volume scheme for three dimensional truncated pyramidal quantum dot.** / Wang, Weichung; Hwang, Tsung-Min; Jang, Jia Chuan.

Research output: Contribution to journal › Article

*Computer Physics Communications*, vol. 174, no. 5, pp. 371-385. https://doi.org/10.1016/j.cpc.2005.10.012

}

TY - JOUR

T1 - A second-order finite volume scheme for three dimensional truncated pyramidal quantum dot

AU - Wang, Weichung

AU - Hwang, Tsung-Min

AU - Jang, Jia Chuan

PY - 2006/3/1

Y1 - 2006/3/1

N2 - Three dimensional truncated pyramidal quantum dots are simulated numerically to compute the energy states and the wave functions. The simulation of the hetero-structures is realized by using a novel finite volume scheme to solve the Schrödinger equation. The simulation benefits greatly from the finite volume scheme in threefold. Firstly, the BenDaniel-Duke hetero-junction interface condition is ingeniously embedded into the scheme. Secondly, the scheme uses uniform meshes in discretization and leads to simple computer implementation. Thirdly, the scheme is efficient as it achieves second-order convergence rates over varied mesh sizes. The scheme has successfully computed all the confined energy states and visualized the corresponding wave functions. The results further predict the relation of the energy states and wave functions versus the height of the truncated pyramidal quantum dots.

AB - Three dimensional truncated pyramidal quantum dots are simulated numerically to compute the energy states and the wave functions. The simulation of the hetero-structures is realized by using a novel finite volume scheme to solve the Schrödinger equation. The simulation benefits greatly from the finite volume scheme in threefold. Firstly, the BenDaniel-Duke hetero-junction interface condition is ingeniously embedded into the scheme. Secondly, the scheme uses uniform meshes in discretization and leads to simple computer implementation. Thirdly, the scheme is efficient as it achieves second-order convergence rates over varied mesh sizes. The scheme has successfully computed all the confined energy states and visualized the corresponding wave functions. The results further predict the relation of the energy states and wave functions versus the height of the truncated pyramidal quantum dots.

KW - Energy levels

KW - Finite volume scheme

KW - Numerical simulations

KW - Schrödinger equation

KW - Second-order convergence

KW - Three dimensional truncated pyramidal quantum dot

KW - Wave functions

UR - http://www.scopus.com/inward/record.url?scp=31544453868&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=31544453868&partnerID=8YFLogxK

U2 - 10.1016/j.cpc.2005.10.012

DO - 10.1016/j.cpc.2005.10.012

M3 - Article

AN - SCOPUS:31544453868

VL - 174

SP - 371

EP - 385

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

IS - 5

ER -