### 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

- Hardware and Architecture
- Physics and Astronomy(all)

### Cite this

*Computer Physics Communications*,

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