### Abstract

We have calculated the properties of electron states in an InAs/GaAs quantum dot system based on the effective mass approximation of a one-band Hamiltonian model. This semiconductor nanostructure system consisted of an InAs quantum dot embedded in a GaAs substrate. In this paper, the Schrödinger equation of an ideal cubic quantum dot with infinite barrier was solved using a finite difference approach. The sparse matrix of N ^{3} x N ^{3} for the Hamiltonian was diagonalized to calculate the lowest states of electrons in this nanostructure system. The calculation was performed for different dot size and the obtained energy levels are comparable to those calculated analytically. The finite difference method was relatively faster and applicable to quantum dots of any geometry or potential profile. This was proven by applying the developed computational procedure to quantum dots of cubic, spherical and pyramidal geometries for the InAs/GaAs nanostructure system.

Original language | English |
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Title of host publication | Advanced Materials Research |

Pages | 347-351 |

Number of pages | 5 |

Volume | 501 |

DOIs | |

Publication status | Published - 2012 |

Event | 26th Regional Conference on Solid State Science and Technology, RCSSST 2011 - Seremban, Negeri Sembilan Duration: 22 Nov 2011 → 24 Nov 2011 |

### Publication series

Name | Advanced Materials Research |
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Volume | 501 |

ISSN (Print) | 10226680 |

### Other

Other | 26th Regional Conference on Solid State Science and Technology, RCSSST 2011 |
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City | Seremban, Negeri Sembilan |

Period | 22/11/11 → 24/11/11 |

### Fingerprint

### Keywords

- Electronic properties
- Finite difference
- Nanostructure
- Quantum dot
- Sparse matrix

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Advanced Materials Research*(Vol. 501, pp. 347-351). (Advanced Materials Research; Vol. 501). https://doi.org/10.4028/www.scientific.net/AMR.501.347

**Calculation of electronic properties of InAs/GaAs cubic, spherical and pyramidal quantum dots with finite difference method.** / Yek, Woon Chin; Gopir, Geri Kibe; Othman, Ahmad Puaad.

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

*Advanced Materials Research.*vol. 501, Advanced Materials Research, vol. 501, pp. 347-351, 26th Regional Conference on Solid State Science and Technology, RCSSST 2011, Seremban, Negeri Sembilan, 22/11/11. https://doi.org/10.4028/www.scientific.net/AMR.501.347

}

TY - GEN

T1 - Calculation of electronic properties of InAs/GaAs cubic, spherical and pyramidal quantum dots with finite difference method

AU - Yek, Woon Chin

AU - Gopir, Geri Kibe

AU - Othman, Ahmad Puaad

PY - 2012

Y1 - 2012

N2 - We have calculated the properties of electron states in an InAs/GaAs quantum dot system based on the effective mass approximation of a one-band Hamiltonian model. This semiconductor nanostructure system consisted of an InAs quantum dot embedded in a GaAs substrate. In this paper, the Schrödinger equation of an ideal cubic quantum dot with infinite barrier was solved using a finite difference approach. The sparse matrix of N 3 x N 3 for the Hamiltonian was diagonalized to calculate the lowest states of electrons in this nanostructure system. The calculation was performed for different dot size and the obtained energy levels are comparable to those calculated analytically. The finite difference method was relatively faster and applicable to quantum dots of any geometry or potential profile. This was proven by applying the developed computational procedure to quantum dots of cubic, spherical and pyramidal geometries for the InAs/GaAs nanostructure system.

AB - We have calculated the properties of electron states in an InAs/GaAs quantum dot system based on the effective mass approximation of a one-band Hamiltonian model. This semiconductor nanostructure system consisted of an InAs quantum dot embedded in a GaAs substrate. In this paper, the Schrödinger equation of an ideal cubic quantum dot with infinite barrier was solved using a finite difference approach. The sparse matrix of N 3 x N 3 for the Hamiltonian was diagonalized to calculate the lowest states of electrons in this nanostructure system. The calculation was performed for different dot size and the obtained energy levels are comparable to those calculated analytically. The finite difference method was relatively faster and applicable to quantum dots of any geometry or potential profile. This was proven by applying the developed computational procedure to quantum dots of cubic, spherical and pyramidal geometries for the InAs/GaAs nanostructure system.

KW - Electronic properties

KW - Finite difference

KW - Nanostructure

KW - Quantum dot

KW - Sparse matrix

UR - http://www.scopus.com/inward/record.url?scp=84860729440&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860729440&partnerID=8YFLogxK

U2 - 10.4028/www.scientific.net/AMR.501.347

DO - 10.4028/www.scientific.net/AMR.501.347

M3 - Conference contribution

AN - SCOPUS:84860729440

SN - 9783037854020

VL - 501

T3 - Advanced Materials Research

SP - 347

EP - 351

BT - Advanced Materials Research

ER -