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

C. Y. Woon, Geri Kibe Gopir, A. P. Othman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 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.

Original languageEnglish
Title of host publicationAdvanced Materials Research
Pages415-419
Number of pages5
Volume895
DOIs
Publication statusPublished - 2014
Event4th International Conference on Solid State Science and Technology, ICSSST 2012 - Melaka
Duration: 18 Dec 201320 Dec 2013

Publication series

NameAdvanced Materials Research
Volume895
ISSN (Print)10226680

Other

Other4th International Conference on Solid State Science and Technology, ICSSST 2012
CityMelaka
Period18/12/1320/12/13

Fingerprint

Hamiltonians
Semiconductor quantum dots
Finite difference method
Electron energy levels
Electrons
Wave functions
Conduction bands

Keywords

  • Discontinuity mass and finite difference
  • Quantum dot

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Woon, C. Y., Gopir, G. K., & Othman, A. P. (2014). Discontinuity mass of finite difference calculation in InAs-GaAs quantum dots. In 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.

Advanced Materials Research. Vol. 895 2014. p. 415-419 (Advanced Materials Research; Vol. 895).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Woon, CY, Gopir, GK & Othman, AP 2014, Discontinuity mass of finite difference calculation in InAs-GaAs quantum dots. in 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
Woon CY, Gopir GK, Othman AP. Discontinuity mass of finite difference calculation in InAs-GaAs quantum dots. In Advanced Materials Research. Vol. 895. 2014. p. 415-419. (Advanced Materials Research). https://doi.org/10.4028/www.scientific.net/AMR.895.415
Woon, C. Y. ; Gopir, Geri Kibe ; Othman, A. P. / Discontinuity mass of finite difference calculation in InAs-GaAs quantum dots. Advanced Materials Research. Vol. 895 2014. pp. 415-419 (Advanced Materials Research).
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