The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section

Leonard Machuka; Hannigton Odhiambo Oyoko

doi:doi:10.11648/j.ijamtp.20180403.12

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The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section

Leonard Machuka, Hannigton Odhiambo Oyoko

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 4, Issue 3)

Received: 19 August 2018 Accepted: 17 September 2018 Published: 17 October 2018

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Abstract

We have carried out a theoretical study of the effect of Hermanson’s spatial dielectric function on the density of impurity states (DOIS) for a shallow hydrogenic donor impurity located in the center of a Gallium Arsenide (GaAs) Quantum Well Dot (QWD) of rectangular cross-section. The density of impurity states (DOIS) of an unscreened (hydrogenic) donor impurity was calculated and compared with that of the screened (non-hydrogenic) donor impurity for the same system. Our calculations were carried out using a trial wave function within the effective mass approximation. Our calculations have been carried out with finite barriers. In this study, we first calculated the ground state binding energies of both hydrogenic and non-hydrogenic donor impurity for different dot sizes. The donor binding energies in the two regimes are then used to compute the DOIS. The results show that for both hydrogenic and non-hydrogenic donor impurities, the DOIS sharply rises to a peak, and then decreases almost exponentially with increase in binding energy. The results also show that the DOIS obtained for the non-hydrogenic donor impurities is markedly enhanced over that for purely hydrogenic donor impurities in which a dielectric constant is employed in the potential. In fact, the enhanced DOIS is observed throughout the range of values for binding energy considered. To a good extend there is good agreement between our results and those reported in the literature. It is therefore, important that the effect of the spatial dielectric function should be considered when designing optoelectronic devices.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 4, Issue 3)
DOI	10.11648/j.ijamtp.20180403.12
Page(s)	73-77
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), 2024. Published by Science Publishing Group

Keywords

Density of Impurity States, Hydrogenic Donor, Non Hydrogenic Donor, Effective Mass Approximation, Spatial Dielectric Function, Quantum Dot, Donor Impurity

References

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[2]	Khordad, R., Sedehi, H. R., & Bahramiyan, H. (2018). Effects of impurity and cross-sectional shape on entropy of quantum wires. Journal of Computational Electronics, 17(2), 551-561.
[3]	Bugajski, M., & Nakwaski, W. (2017). Physics of semiconductor lasers. Elsevier.
[4]	Harrison, P., & Valavanis, A. (2016). Quantum wells, wires and dots: theoretical and computational physics of semiconductor nanostructures. John Wiley & Sons Mroziewicz, B.
[5]	Oyoko, H. O., Porras-Montenegro, N., López, S. Y., & Duque, C. A. (2007, December). Physica Status Solidi (C) Current Topics in Solid State Physics. In conference.
[6]	Tiutiunnyk, A., Akimov, V., Tulupenko, V., Mora-Ramos, M. E., Kasapoglu, E., Ungan, F.... & Duque, C. A. (2016). Electronic structure and optical properties of triangular GaAs/AlGaAs quantum dots: Exciton and impurity states. Physica B: Condensed Matter, 484, 95-108.
[7]	Masselink, W. T., Chang, Y. C., & Morkoc, H. (1984). Binding energies of acceptors in GaAs–Al x Ga1− x As quantum wells. Journal of Vacuum Science & Technology B: Microelectronics Processing and Phenomena, 2(3), 376-382.
[8]	Csavinszky, P., & Elabsy, A. M. (1985). Dielectric response to a donor ion in a Ga 1− x Al x As-GaAs-Ga 1− x Al x As quantum well of infinite depth. Physical Review B, 32(10), 6498.
[9]	Brown, J. W., & Spector, H. N. (1986). Hydrogen impurities in quantum well wires. Journal of applied physics, 59(4), 1179-1186.
[10]	Csavinszky, P., & Oyoko, H. (1991). Binding energy of on-axis hydrogenic and non hydrogenic donors in a GaAs/Ga 1− x Al x As quantum-well wire of circular cross section. Physical Review B, 43(11), 9262.
[11]	Elabsy, A. M. (1993). Hydrostatic pressure dependence of binding energies for donors in quantum well heterostructures. Physica Scripta, 48(3), 376.
[12]	Montes, A., Duque, C. A., & Porras-Montenegro, N. (1998). Density of shallow-donor impurity states in rectangular cross section GaAs quantum-well wires under applied electric field. Journal of Physics: Condensed Matter, 10(24), 5351.
[13]	Oyoko, H. O., Duque, C. A., & Porras-Montenegro, N. (2001). Uniaxial stress dependence of the binding energy of shallow donor impurities in GaAs–(Ga, Al) As quantum dots. Journal of Applied Physics, 90(2), 819-823.
[14]	Duque, C. A., Porras-Montenegro, N., Barticevic, Z., Pacheco, M., & Oliveira, L. E. (2006). Effects of applied magnetic fields and hydrostatic pressure on the optical transitions in self-assembled InAs/GaAs quantum dots. Journal of Physics: Condensed Matter, 18(6), 1877.
[15]	Abarna, R., Anitha, A., & Arulmozhi, M. (2017). Effects of Dielectric Screening Function and Image Charges on Hydrogenic Donor Binding Energy in a Surface Quantum Well. Journal of Physical Science, 28(1), 73.
[16]	J. Hermanson, Phys. Rev. 150, 660 (1996).
[17]	P. Csavinszky and H. Oyoko. Phys. Rev. B 43, 9262 – Published 15 April 1991.
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Leonard Machuka, Hannigton Odhiambo Oyoko. (2018). The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section. International Journal of Applied Mathematics and Theoretical Physics, 4(3), 73-77. https://doi.org/10.11648/j.ijamtp.20180403.12

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ACS Style

Leonard Machuka; Hannigton Odhiambo Oyoko. The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section. Int. J. Appl. Math. Theor. Phys. 2018, 4(3), 73-77. doi: 10.11648/j.ijamtp.20180403.12

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AMA Style

Leonard Machuka, Hannigton Odhiambo Oyoko. The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section. Int J Appl Math Theor Phys. 2018;4(3):73-77. doi: 10.11648/j.ijamtp.20180403.12

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@article{10.11648/j.ijamtp.20180403.12,
  author = {Leonard Machuka and Hannigton Odhiambo Oyoko},
  title = {The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {4},
  number = {3},
  pages = {73-77},
  doi = {10.11648/j.ijamtp.20180403.12},
  url = {https://doi.org/10.11648/j.ijamtp.20180403.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20180403.12},
  abstract = {We have carried out a theoretical study of the effect of Hermanson’s spatial dielectric function on the density of impurity states (DOIS) for a shallow hydrogenic donor impurity located in the center of a Gallium Arsenide (GaAs) Quantum Well Dot (QWD) of rectangular cross-section. The density of impurity states (DOIS) of an unscreened (hydrogenic) donor impurity was calculated and compared with that of the screened (non-hydrogenic) donor impurity for the same system. Our calculations were carried out using a trial wave function within the effective mass approximation. Our calculations have been carried out with finite barriers. In this study, we first calculated the ground state binding energies of both hydrogenic and non-hydrogenic donor impurity for different dot sizes. The donor binding energies in the two regimes are then used to compute the DOIS. The results show that for both hydrogenic and non-hydrogenic donor impurities, the DOIS sharply rises to a peak, and then decreases almost exponentially with increase in binding energy. The results also show that the DOIS obtained for the non-hydrogenic donor impurities is markedly enhanced over that for purely hydrogenic donor impurities in which a dielectric constant is employed in the potential. In fact, the enhanced DOIS is observed throughout the range of values for binding energy considered. To a good extend there is good agreement between our results and those reported in the literature. It is therefore, important that the effect of the spatial dielectric function should be considered when designing optoelectronic devices.},
 year = {2018}
}

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TY  - JOUR
T1  - The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section
AU  - Leonard Machuka
AU  - Hannigton Odhiambo Oyoko
Y1  - 2018/10/17
PY  - 2018
N1  - https://doi.org/10.11648/j.ijamtp.20180403.12
DO  - 10.11648/j.ijamtp.20180403.12
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 73
EP  - 77
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20180403.12
AB  - We have carried out a theoretical study of the effect of Hermanson’s spatial dielectric function on the density of impurity states (DOIS) for a shallow hydrogenic donor impurity located in the center of a Gallium Arsenide (GaAs) Quantum Well Dot (QWD) of rectangular cross-section. The density of impurity states (DOIS) of an unscreened (hydrogenic) donor impurity was calculated and compared with that of the screened (non-hydrogenic) donor impurity for the same system. Our calculations were carried out using a trial wave function within the effective mass approximation. Our calculations have been carried out with finite barriers. In this study, we first calculated the ground state binding energies of both hydrogenic and non-hydrogenic donor impurity for different dot sizes. The donor binding energies in the two regimes are then used to compute the DOIS. The results show that for both hydrogenic and non-hydrogenic donor impurities, the DOIS sharply rises to a peak, and then decreases almost exponentially with increase in binding energy. The results also show that the DOIS obtained for the non-hydrogenic donor impurities is markedly enhanced over that for purely hydrogenic donor impurities in which a dielectric constant is employed in the potential. In fact, the enhanced DOIS is observed throughout the range of values for binding energy considered. To a good extend there is good agreement between our results and those reported in the literature. It is therefore, important that the effect of the spatial dielectric function should be considered when designing optoelectronic devices.
VL  - 4
IS  - 3
ER  -

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Author Information

Leonard Machuka

Department of Physics, Pwani University, Kilifi, Kenya
Hannigton Odhiambo Oyoko

Department of Physics, Pwani University, Kilifi, Kenya

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APA Style

Leonard Machuka, Hannigton Odhiambo Oyoko. (2018). The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section. International Journal of Applied Mathematics and Theoretical Physics, 4(3), 73-77. https://doi.org/10.11648/j.ijamtp.20180403.12

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ACS Style

Leonard Machuka; Hannigton Odhiambo Oyoko. The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section. Int. J. Appl. Math. Theor. Phys. 2018, 4(3), 73-77. doi: 10.11648/j.ijamtp.20180403.12

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AMA Style

Leonard Machuka, Hannigton Odhiambo Oyoko. The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section. Int J Appl Math Theor Phys. 2018;4(3):73-77. doi: 10.11648/j.ijamtp.20180403.12

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@article{10.11648/j.ijamtp.20180403.12,
  author = {Leonard Machuka and Hannigton Odhiambo Oyoko},
  title = {The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {4},
  number = {3},
  pages = {73-77},
  doi = {10.11648/j.ijamtp.20180403.12},
  url = {https://doi.org/10.11648/j.ijamtp.20180403.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20180403.12},
  abstract = {We have carried out a theoretical study of the effect of Hermanson’s spatial dielectric function on the density of impurity states (DOIS) for a shallow hydrogenic donor impurity located in the center of a Gallium Arsenide (GaAs) Quantum Well Dot (QWD) of rectangular cross-section. The density of impurity states (DOIS) of an unscreened (hydrogenic) donor impurity was calculated and compared with that of the screened (non-hydrogenic) donor impurity for the same system. Our calculations were carried out using a trial wave function within the effective mass approximation. Our calculations have been carried out with finite barriers. In this study, we first calculated the ground state binding energies of both hydrogenic and non-hydrogenic donor impurity for different dot sizes. The donor binding energies in the two regimes are then used to compute the DOIS. The results show that for both hydrogenic and non-hydrogenic donor impurities, the DOIS sharply rises to a peak, and then decreases almost exponentially with increase in binding energy. The results also show that the DOIS obtained for the non-hydrogenic donor impurities is markedly enhanced over that for purely hydrogenic donor impurities in which a dielectric constant is employed in the potential. In fact, the enhanced DOIS is observed throughout the range of values for binding energy considered. To a good extend there is good agreement between our results and those reported in the literature. It is therefore, important that the effect of the spatial dielectric function should be considered when designing optoelectronic devices.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - The Effect of Hermanson’s Spatial Dielectric Function on the Density of Impurity States in a Gallium Arsenide Quantum Dot of Rectangular Cross-Section
AU  - Leonard Machuka
AU  - Hannigton Odhiambo Oyoko
Y1  - 2018/10/17
PY  - 2018
N1  - https://doi.org/10.11648/j.ijamtp.20180403.12
DO  - 10.11648/j.ijamtp.20180403.12
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 73
EP  - 77
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20180403.12
AB  - We have carried out a theoretical study of the effect of Hermanson’s spatial dielectric function on the density of impurity states (DOIS) for a shallow hydrogenic donor impurity located in the center of a Gallium Arsenide (GaAs) Quantum Well Dot (QWD) of rectangular cross-section. The density of impurity states (DOIS) of an unscreened (hydrogenic) donor impurity was calculated and compared with that of the screened (non-hydrogenic) donor impurity for the same system. Our calculations were carried out using a trial wave function within the effective mass approximation. Our calculations have been carried out with finite barriers. In this study, we first calculated the ground state binding energies of both hydrogenic and non-hydrogenic donor impurity for different dot sizes. The donor binding energies in the two regimes are then used to compute the DOIS. The results show that for both hydrogenic and non-hydrogenic donor impurities, the DOIS sharply rises to a peak, and then decreases almost exponentially with increase in binding energy. The results also show that the DOIS obtained for the non-hydrogenic donor impurities is markedly enhanced over that for purely hydrogenic donor impurities in which a dielectric constant is employed in the potential. In fact, the enhanced DOIS is observed throughout the range of values for binding energy considered. To a good extend there is good agreement between our results and those reported in the literature. It is therefore, important that the effect of the spatial dielectric function should be considered when designing optoelectronic devices.
VL  - 4
IS  - 3
ER  -

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