### 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 |
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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 |

### 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