Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section

Winnie Otieno; Hannington Oyoko

doi:doi:10.11648/j.ajop.20180603.11

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Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section

Winnie Otieno, Hannington Oyoko

Published in American Journal of Optics and Photonics (Volume 6, Issue 3)

Received: 2 September 2018 Accepted: 6 October 2018 Published: 29 October 2018

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Abstract

In the present work, a theoretical study of the variation of the photoionization cross-section with the incident photon frequency and the axial position of a hydrogenic donor impurity in GaAs quantum well dot of square cross-section is carried out. In the calculation, a trial wave function in the effective mass approximation and a finite potential well is used. The wave function is constructed with an appropriate envelope wave function that satisfies the boundary conditions, i.e., the wave function vanishes at the boundary. A trial wave function is employed to calculate the total energy of the hydrogenic donor impurity in the ground state. The total energy is then minimized with respect to the variational parameter in the trial wave function to obtain the minimum energy. The minimized total energies are then used to determine the donor binding energies within the quantum dot. It is observed that for a quantum dot of constant cross-section, the binding energy increases with a decrease in dot length to a peak value; thereafter it decreases rapidly towards zero. The binding energies obtained are used to compute the photoionization cross-section of the hydrogenic donor impurity as a function of the incident photon frequency for different positions of the donor impurity. It is observed that the photoionization cross-sections rise steeply to their peaks from almost zero value then gradually decrease as the photon frequency increases until they become almost constant for very high photon frequencies. The photoionization cross-section peak is much higher for the hydrogenic donor impurity located closest to the centre of the quantum well dot than for donor impurity located farther away from the dot centre. This indicates that the photoionization cross-section is sensitive to the location of the donor impurity in the quantum dot and to the incident photon frequency.

Published in	American Journal of Optics and Photonics (Volume 6, Issue 3)
DOI	10.11648/j.ajop.20180603.11
Page(s)	25-30
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

GaAsQuantum Dot, Hydrogenic Donor Impurity, Photoionization Cross-Section

References

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APA Style

Winnie Otieno, Hannington Oyoko. (2018). Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section. American Journal of Optics and Photonics, 6(3), 25-30. https://doi.org/10.11648/j.ajop.20180603.11

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ACS Style

Winnie Otieno; Hannington Oyoko. Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section. Am. J. Opt. Photonics 2018, 6(3), 25-30. doi: 10.11648/j.ajop.20180603.11

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AMA Style

Winnie Otieno, Hannington Oyoko. Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section. Am J Opt Photonics. 2018;6(3):25-30. doi: 10.11648/j.ajop.20180603.11

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@article{10.11648/j.ajop.20180603.11,
  author = {Winnie Otieno and Hannington Oyoko},
  title = {Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section},
  journal = {American Journal of Optics and Photonics},
  volume = {6},
  number = {3},
  pages = {25-30},
  doi = {10.11648/j.ajop.20180603.11},
  url = {https://doi.org/10.11648/j.ajop.20180603.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajop.20180603.11},
  abstract = {In the present work, a theoretical study of the variation of the photoionization cross-section with the incident photon frequency and the axial position of a hydrogenic donor impurity in GaAs quantum well dot of square cross-section is carried out. In the calculation, a trial wave function in the effective mass approximation and a finite potential well is used. The wave function is constructed with an appropriate envelope wave function that satisfies the boundary conditions, i.e., the wave function vanishes at the boundary. A trial wave function is employed to calculate the total energy of the hydrogenic donor impurity in the ground state. The total energy is then minimized with respect to the variational parameter in the trial wave function to obtain the minimum energy. The minimized total energies are then used to determine the donor binding energies within the quantum dot. It is observed that for a quantum dot of constant cross-section, the binding energy increases with a decrease in dot length to a peak value; thereafter it decreases rapidly towards zero. The binding energies obtained are used to compute the photoionization cross-section of the hydrogenic donor impurity as a function of the incident photon frequency for different positions of the donor impurity. It is observed that the photoionization cross-sections rise steeply to their peaks from almost zero value then gradually decrease as the photon frequency increases until they become almost constant for very high photon frequencies. The photoionization cross-section peak is much higher for the hydrogenic donor impurity located closest to the centre of the quantum well dot than for donor impurity located farther away from the dot centre. This indicates that the photoionization cross-section is sensitive to the location of the donor impurity in the quantum dot and to the incident photon frequency.},
 year = {2018}
}

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TY  - JOUR
T1  - Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section
AU  - Winnie Otieno
AU  - Hannington Oyoko
Y1  - 2018/10/29
PY  - 2018
N1  - https://doi.org/10.11648/j.ajop.20180603.11
DO  - 10.11648/j.ajop.20180603.11
T2  - American Journal of Optics and Photonics
JF  - American Journal of Optics and Photonics
JO  - American Journal of Optics and Photonics
SP  - 25
EP  - 30
PB  - Science Publishing Group
SN  - 2330-8494
UR  - https://doi.org/10.11648/j.ajop.20180603.11
AB  - In the present work, a theoretical study of the variation of the photoionization cross-section with the incident photon frequency and the axial position of a hydrogenic donor impurity in GaAs quantum well dot of square cross-section is carried out. In the calculation, a trial wave function in the effective mass approximation and a finite potential well is used. The wave function is constructed with an appropriate envelope wave function that satisfies the boundary conditions, i.e., the wave function vanishes at the boundary. A trial wave function is employed to calculate the total energy of the hydrogenic donor impurity in the ground state. The total energy is then minimized with respect to the variational parameter in the trial wave function to obtain the minimum energy. The minimized total energies are then used to determine the donor binding energies within the quantum dot. It is observed that for a quantum dot of constant cross-section, the binding energy increases with a decrease in dot length to a peak value; thereafter it decreases rapidly towards zero. The binding energies obtained are used to compute the photoionization cross-section of the hydrogenic donor impurity as a function of the incident photon frequency for different positions of the donor impurity. It is observed that the photoionization cross-sections rise steeply to their peaks from almost zero value then gradually decrease as the photon frequency increases until they become almost constant for very high photon frequencies. The photoionization cross-section peak is much higher for the hydrogenic donor impurity located closest to the centre of the quantum well dot than for donor impurity located farther away from the dot centre. This indicates that the photoionization cross-section is sensitive to the location of the donor impurity in the quantum dot and to the incident photon frequency.
VL  - 6
IS  - 3
ER  -

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Author Information

Winnie Otieno

Department of Physics, Pwani University, Kilifi, Kenya
Hannington Oyoko

Department of Physics, Pwani University, Kilifi, Kenya

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APA Style

Winnie Otieno, Hannington Oyoko. (2018). Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section. American Journal of Optics and Photonics, 6(3), 25-30. https://doi.org/10.11648/j.ajop.20180603.11

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ACS Style

Winnie Otieno; Hannington Oyoko. Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section. Am. J. Opt. Photonics 2018, 6(3), 25-30. doi: 10.11648/j.ajop.20180603.11

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AMA Style

Winnie Otieno, Hannington Oyoko. Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section. Am J Opt Photonics. 2018;6(3):25-30. doi: 10.11648/j.ajop.20180603.11

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@article{10.11648/j.ajop.20180603.11,
  author = {Winnie Otieno and Hannington Oyoko},
  title = {Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section},
  journal = {American Journal of Optics and Photonics},
  volume = {6},
  number = {3},
  pages = {25-30},
  doi = {10.11648/j.ajop.20180603.11},
  url = {https://doi.org/10.11648/j.ajop.20180603.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajop.20180603.11},
  abstract = {In the present work, a theoretical study of the variation of the photoionization cross-section with the incident photon frequency and the axial position of a hydrogenic donor impurity in GaAs quantum well dot of square cross-section is carried out. In the calculation, a trial wave function in the effective mass approximation and a finite potential well is used. The wave function is constructed with an appropriate envelope wave function that satisfies the boundary conditions, i.e., the wave function vanishes at the boundary. A trial wave function is employed to calculate the total energy of the hydrogenic donor impurity in the ground state. The total energy is then minimized with respect to the variational parameter in the trial wave function to obtain the minimum energy. The minimized total energies are then used to determine the donor binding energies within the quantum dot. It is observed that for a quantum dot of constant cross-section, the binding energy increases with a decrease in dot length to a peak value; thereafter it decreases rapidly towards zero. The binding energies obtained are used to compute the photoionization cross-section of the hydrogenic donor impurity as a function of the incident photon frequency for different positions of the donor impurity. It is observed that the photoionization cross-sections rise steeply to their peaks from almost zero value then gradually decrease as the photon frequency increases until they become almost constant for very high photon frequencies. The photoionization cross-section peak is much higher for the hydrogenic donor impurity located closest to the centre of the quantum well dot than for donor impurity located farther away from the dot centre. This indicates that the photoionization cross-section is sensitive to the location of the donor impurity in the quantum dot and to the incident photon frequency.},
 year = {2018}
}

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TY  - JOUR
T1  - Variation of the Photoionization Cross-Section with the Position of a Hydrogenic Donor Impurity in a Gallium Arsenide Quantum Well Dot of Square Cross-Section
AU  - Winnie Otieno
AU  - Hannington Oyoko
Y1  - 2018/10/29
PY  - 2018
N1  - https://doi.org/10.11648/j.ajop.20180603.11
DO  - 10.11648/j.ajop.20180603.11
T2  - American Journal of Optics and Photonics
JF  - American Journal of Optics and Photonics
JO  - American Journal of Optics and Photonics
SP  - 25
EP  - 30
PB  - Science Publishing Group
SN  - 2330-8494
UR  - https://doi.org/10.11648/j.ajop.20180603.11
AB  - In the present work, a theoretical study of the variation of the photoionization cross-section with the incident photon frequency and the axial position of a hydrogenic donor impurity in GaAs quantum well dot of square cross-section is carried out. In the calculation, a trial wave function in the effective mass approximation and a finite potential well is used. The wave function is constructed with an appropriate envelope wave function that satisfies the boundary conditions, i.e., the wave function vanishes at the boundary. A trial wave function is employed to calculate the total energy of the hydrogenic donor impurity in the ground state. The total energy is then minimized with respect to the variational parameter in the trial wave function to obtain the minimum energy. The minimized total energies are then used to determine the donor binding energies within the quantum dot. It is observed that for a quantum dot of constant cross-section, the binding energy increases with a decrease in dot length to a peak value; thereafter it decreases rapidly towards zero. The binding energies obtained are used to compute the photoionization cross-section of the hydrogenic donor impurity as a function of the incident photon frequency for different positions of the donor impurity. It is observed that the photoionization cross-sections rise steeply to their peaks from almost zero value then gradually decrease as the photon frequency increases until they become almost constant for very high photon frequencies. The photoionization cross-section peak is much higher for the hydrogenic donor impurity located closest to the centre of the quantum well dot than for donor impurity located farther away from the dot centre. This indicates that the photoionization cross-section is sensitive to the location of the donor impurity in the quantum dot and to the incident photon frequency.
VL  - 6
IS  - 3
ER  -

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