### Abstract

This paper investigates the mass discontinuity on the numerical solution of electron states in quantum dots. We consider quantum dot consists of material of InAs, electron effective mass 0.023 m_{e}, embedded in GaAs with electron effective mass 0.067 m_{e}, and conduction band offset 0.77 eV can be express into three dimensional effective mass Hamiltonian. Finite difference method has been used to solve one band electronic Schrödinger equation based on classic constant mass, position dependent effective mass and Ben Daniel-Duke Hamiltonian. The finite difference method calculated the energy levels and corresponding wavefunction of electron for basis quantum number n = 1 to 10 and size quantum dot from 100 to 1000 Å. A comparison between calculations of classic Hamiltonian with transcendental equation and finite difference has made to illustrate the mass discontinuity on the numerical and analytic solution. The calculation results show that the Ben Daniel and Duke always obtain smaller energy value than classic and position dependent Hamiltonian.

Original language | English |
---|---|

Title of host publication | Advanced Materials Research |

Pages | 415-419 |

Number of pages | 5 |

Volume | 895 |

DOIs | |

Publication status | Published - 2014 |

Event | 4th International Conference on Solid State Science and Technology, ICSSST 2012 - Melaka Duration: 18 Dec 2013 → 20 Dec 2013 |

### Publication series

Name | Advanced Materials Research |
---|---|

Volume | 895 |

ISSN (Print) | 10226680 |

### Other

Other | 4th International Conference on Solid State Science and Technology, ICSSST 2012 |
---|---|

City | Melaka |

Period | 18/12/13 → 20/12/13 |

### Fingerprint

### Keywords

- Discontinuity mass and finite difference
- Quantum dot

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Advanced Materials Research*(Vol. 895, pp. 415-419). (Advanced Materials Research; Vol. 895). https://doi.org/10.4028/www.scientific.net/AMR.895.415

**Discontinuity mass of finite difference calculation in InAs-GaAs quantum dots.** / Woon, C. Y.; Gopir, Geri Kibe; Othman, A. P.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Advanced Materials Research.*vol. 895, Advanced Materials Research, vol. 895, pp. 415-419, 4th International Conference on Solid State Science and Technology, ICSSST 2012, Melaka, 18/12/13. https://doi.org/10.4028/www.scientific.net/AMR.895.415

}

TY - GEN

T1 - Discontinuity mass of finite difference calculation in InAs-GaAs quantum dots

AU - Woon, C. Y.

AU - Gopir, Geri Kibe

AU - Othman, A. P.

PY - 2014

Y1 - 2014

N2 - This paper investigates the mass discontinuity on the numerical solution of electron states in quantum dots. We consider quantum dot consists of material of InAs, electron effective mass 0.023 me, embedded in GaAs with electron effective mass 0.067 me, and conduction band offset 0.77 eV can be express into three dimensional effective mass Hamiltonian. Finite difference method has been used to solve one band electronic Schrödinger equation based on classic constant mass, position dependent effective mass and Ben Daniel-Duke Hamiltonian. The finite difference method calculated the energy levels and corresponding wavefunction of electron for basis quantum number n = 1 to 10 and size quantum dot from 100 to 1000 Å. A comparison between calculations of classic Hamiltonian with transcendental equation and finite difference has made to illustrate the mass discontinuity on the numerical and analytic solution. The calculation results show that the Ben Daniel and Duke always obtain smaller energy value than classic and position dependent Hamiltonian.

AB - This paper investigates the mass discontinuity on the numerical solution of electron states in quantum dots. We consider quantum dot consists of material of InAs, electron effective mass 0.023 me, embedded in GaAs with electron effective mass 0.067 me, and conduction band offset 0.77 eV can be express into three dimensional effective mass Hamiltonian. Finite difference method has been used to solve one band electronic Schrödinger equation based on classic constant mass, position dependent effective mass and Ben Daniel-Duke Hamiltonian. The finite difference method calculated the energy levels and corresponding wavefunction of electron for basis quantum number n = 1 to 10 and size quantum dot from 100 to 1000 Å. A comparison between calculations of classic Hamiltonian with transcendental equation and finite difference has made to illustrate the mass discontinuity on the numerical and analytic solution. The calculation results show that the Ben Daniel and Duke always obtain smaller energy value than classic and position dependent Hamiltonian.

KW - Discontinuity mass and finite difference

KW - Quantum dot

UR - http://www.scopus.com/inward/record.url?scp=84896825222&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896825222&partnerID=8YFLogxK

U2 - 10.4028/www.scientific.net/AMR.895.415

DO - 10.4028/www.scientific.net/AMR.895.415

M3 - Conference contribution

SN - 9783038350330

VL - 895

T3 - Advanced Materials Research

SP - 415

EP - 419

BT - Advanced Materials Research

ER -