Sub-barrier and Above-barrier Electron Transport Through Multilayer Semiconductors

Voxob Rustamovich Rasulov; Rustam Yavkachovich Rasulov; Iqboljon Mamirjonovich Eshboltayev; Ravshan Rustamovich Sultanov

doi:doi:10.11648/j.ajpa.20200804.12

Sub-barrier and Above-barrier Electron Transport Through Multilayer Semiconductors

Voxob Rustamovich Rasulov, Rustam Yavkachovich Rasulov, Iqboljon Mamirjonovich Eshboltayev, Ravshan Rustamovich Sultanov

Published in American Journal of Physics and Applications (Volume 8, Issue 4)

Received: 24 July 2019 Accepted: 13 December 2019 Published: 16 September 2020

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Abstract

The transparency coefficients of the semiconductor structure consisting of alternating asymmetric potential barriers and wells are calculated, where taken into account the Bastard condition. It is shown that both in the above-barrier and over barrier passage of electrons, tunneling oscillations arise. The amplitude, in this case, is determined not only by the values of the wave vectors, but from the values of the effective masses of the current carriers. This oscillation does not disappear even in symmetric structures if they have a difference in the effective masses of current carriers located in two neighboring regions. In symmetrical structures, an oscillation of the coefficient of the above-barrier passage of a particle depending on its energy should be observed without taking into account the Bastard condition. Calculations show that for equal values of the width of the well and the potential barrier, as well as jumps in the potential of the barrier or well, the amplitude of the oscillations of the coefficient of over-barrier passage of particles is greater than the coefficient of passage above the well. In the case of an asymmetric structure, these considerations remain valed, but the physical nature of the parameters, for example, the number of oscillations, reflection and transmission coefficients, strongly depends on the ratio of the effective masses of electrons in neighboring layers and from the ratio of the height of the left and right potential barrier (regarding to the well). In an asymmetric (and in a symmetric, but with different effective masses of electrons in different layers) semiconductor structure, oscillation should be observed depending on the coefficient of transmission through the potential barrier on the energy of electron. This oscillation is caused by the interference of waves going to the barrier and reflected from the potential barrier. Such an interference phenomenon in the structure does not disappear even in a symmetric structure due to the difference in the effective masses of electrons located in different regions of the structure. The electronic states of a multilayer semiconductor structure consisting of alternating potential wells and barriers are analyzed.

Published in	American Journal of Physics and Applications (Volume 8, Issue 4)
DOI	10.11648/j.ajpa.20200804.12
Page(s)	56-63
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), 2020. Published by Science Publishing Group

Keywords

Semiconductor, Multilayer Structure, Barrier, Well, Electron, Transparency Coefficient

References

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[2]	G. M. Mladenov, V. M. Spivak, E. G. Koleva, A. V. Bogdan. Nanoelectronics. Introduction to nanoelectronic technology. Kiev-Sofia. 1 book. Technosphere. 2009. -327 p.
[3]	D. A. Usanov, A. V. Skripal. Physical foundations of nanoelectronics. –Saratov. 2013. -128 p.
[4]	V. R. Rasulov. To the Theory of Electron Passage in a Semiconductor Structure Consisting of Alternating Asymmetric Rectangular Potential Wells and Barriers. Russian Physics Journal (Russ Phys J), vol. 59, no. 10, p. 1699-1702, 2017.
[5]	G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructure, Editions de Physique. -Les Ulis, France. 1988. -317 p.
[6]	E. L. Ivchenko, G. E. Picus. Superlattices and Other Heterostructures: Symmetry and Optical Phenomena, Springer Series in Solid-State Sciences. -Springer-Verlag, Berlin, Heidelberg. 1995; second edition 1997. -657 p.
[7]	I. V. Belyaev, E. I. Golant, A. B. Pashkovsky. Particular properties of resonant interaction of electrons with a high–frequency electric field in two–barrier structures Fizika i texnika poluprovodnilov (FTP) (in russian), vol. 31, no 2, p. 137-144, 1997.
[8]	E. I. Golant, A. B. Pashkovsky. A resonant interaction between electrons and high-frequency electric fields in asymmetric double-barrier heterostructures. Fizika i texnika poluprovodnilov (FTP) (in russian), vol. 31, no 9, p. 1077-1082, 1997.
[9]	E. I. Golant, A. B. Pashkovsky. Resonant transitions between splitting energy levels of triple-barrier nanostructures and their application perspectives in submillimeter-wave devices. Fizika i texnika poluprovodnilov (FTP) (in russian), vol. 36, no 3, p. 334-337, 2002
[10]	E. I. Golant, A. B. Pashkovsky. Two level electron wave functions in the double-barrier quantum-size structures in a finite amplitude electric field. Fizika i texnika poluprovodnilov (FTP) (in russian), vol. 34, no 3, p. 330-337, 2002.
[11]	A. B. Pashkovsky. Resonant transmission of electrons through a three-barrier structure in the two-frequency electric field. Fizika i texnika poluprovodnilov (FTP) (in russian), vol. 45, no 6, p. 759-764, 2011.
[12]	V. F. Elesin. High-frequency response of double-barrier nanostructures/ Journal of Experimental and Theoretical Physics (JETP) (in russian), vol. 121, no. 4, p. 925-932, 2002.
[13]	V. F. Elesin. Resonance tunneling of electrons interacting with phones. / Journal of Experimental and Theoretical Physics (JETP) (in russian), vol. 123, no. 5, p. 1096-1105, 2003.
[14]	V. F. Elesin. Resonant tunneling and nonlinear response in a high frequency field. Journal of Experimental and Theoretical Physics (JETP) (in russian), vol. 124, no. 2, p. 379-393, 2003. -2003. -T. 124. -№2. -C. 379-393.
[15]	V. F. Elesin, I. Yu. Kateev. High-frequency properties of double-well nanostructures. Fizika i texnika poluprovodnilov (FTP) (in russian), vol. 42, no 5, p. 586-591, 2008.
[16]	V. F. Elesin. High-frequency properties of double-well nanostructures. Journal of Experimental and Theoretical Physics (JETP) (in russian), vol. 145, no. 6, p. 1078-1086, 2014.
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Voxob Rustamovich Rasulov, Rustam Yavkachovich Rasulov, Iqboljon Mamirjonovich Eshboltayev, Ravshan Rustamovich Sultanov. (2020). Sub-barrier and Above-barrier Electron Transport Through Multilayer Semiconductors. American Journal of Physics and Applications, 8(4), 56-63. https://doi.org/10.11648/j.ajpa.20200804.12

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ACS Style

Voxob Rustamovich Rasulov; Rustam Yavkachovich Rasulov; Iqboljon Mamirjonovich Eshboltayev; Ravshan Rustamovich Sultanov. Sub-barrier and Above-barrier Electron Transport Through Multilayer Semiconductors. Am. J. Phys. Appl. 2020, 8(4), 56-63. doi: 10.11648/j.ajpa.20200804.12

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AMA Style

Voxob Rustamovich Rasulov, Rustam Yavkachovich Rasulov, Iqboljon Mamirjonovich Eshboltayev, Ravshan Rustamovich Sultanov. Sub-barrier and Above-barrier Electron Transport Through Multilayer Semiconductors. Am J Phys Appl. 2020;8(4):56-63. doi: 10.11648/j.ajpa.20200804.12

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@article{10.11648/j.ajpa.20200804.12,
  author = {Voxob Rustamovich Rasulov and Rustam Yavkachovich Rasulov and Iqboljon Mamirjonovich Eshboltayev and Ravshan Rustamovich Sultanov},
  title = {Sub-barrier and Above-barrier Electron Transport Through Multilayer Semiconductors},
  journal = {American Journal of Physics and Applications},
  volume = {8},
  number = {4},
  pages = {56-63},
  doi = {10.11648/j.ajpa.20200804.12},
  url = {https://doi.org/10.11648/j.ajpa.20200804.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20200804.12},
  abstract = {The transparency coefficients of the semiconductor structure consisting of alternating asymmetric potential barriers and wells are calculated, where taken into account the Bastard condition. It is shown that both in the above-barrier and over barrier passage of electrons, tunneling oscillations arise. The amplitude, in this case, is determined not only by the values of the wave vectors, but from the values of the effective masses of the current carriers. This oscillation does not disappear even in symmetric structures if they have a difference in the effective masses of current carriers located in two neighboring regions. In symmetrical structures, an oscillation of the coefficient of the above-barrier passage of a particle depending on its energy should be observed without taking into account the Bastard condition. Calculations show that for equal values of the width of the well and the potential barrier, as well as jumps in the potential of the barrier or well, the amplitude of the oscillations of the coefficient of over-barrier passage of particles is greater than the coefficient of passage above the well. In the case of an asymmetric structure, these considerations remain valed, but the physical nature of the parameters, for example, the number of oscillations, reflection and transmission coefficients, strongly depends on the ratio of the effective masses of electrons in neighboring layers and from the ratio of the height of the left and right potential barrier (regarding to the well). In an asymmetric (and in a symmetric, but with different effective masses of electrons in different layers) semiconductor structure, oscillation should be observed depending on the coefficient of transmission through the potential barrier on the energy of electron. This oscillation is caused by the interference of waves going to the barrier and reflected from the potential barrier. Such an interference phenomenon in the structure does not disappear even in a symmetric structure due to the difference in the effective masses of electrons located in different regions of the structure. The electronic states of a multilayer semiconductor structure consisting of alternating potential wells and barriers are analyzed.},
 year = {2020}
}

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TY  - JOUR
T1  - Sub-barrier and Above-barrier Electron Transport Through Multilayer Semiconductors
AU  - Voxob Rustamovich Rasulov
AU  - Rustam Yavkachovich Rasulov
AU  - Iqboljon Mamirjonovich Eshboltayev
AU  - Ravshan Rustamovich Sultanov
Y1  - 2020/09/16
PY  - 2020
N1  - https://doi.org/10.11648/j.ajpa.20200804.12
DO  - 10.11648/j.ajpa.20200804.12
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 56
EP  - 63
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20200804.12
AB  - The transparency coefficients of the semiconductor structure consisting of alternating asymmetric potential barriers and wells are calculated, where taken into account the Bastard condition. It is shown that both in the above-barrier and over barrier passage of electrons, tunneling oscillations arise. The amplitude, in this case, is determined not only by the values of the wave vectors, but from the values of the effective masses of the current carriers. This oscillation does not disappear even in symmetric structures if they have a difference in the effective masses of current carriers located in two neighboring regions. In symmetrical structures, an oscillation of the coefficient of the above-barrier passage of a particle depending on its energy should be observed without taking into account the Bastard condition. Calculations show that for equal values of the width of the well and the potential barrier, as well as jumps in the potential of the barrier or well, the amplitude of the oscillations of the coefficient of over-barrier passage of particles is greater than the coefficient of passage above the well. In the case of an asymmetric structure, these considerations remain valed, but the physical nature of the parameters, for example, the number of oscillations, reflection and transmission coefficients, strongly depends on the ratio of the effective masses of electrons in neighboring layers and from the ratio of the height of the left and right potential barrier (regarding to the well). In an asymmetric (and in a symmetric, but with different effective masses of electrons in different layers) semiconductor structure, oscillation should be observed depending on the coefficient of transmission through the potential barrier on the energy of electron. This oscillation is caused by the interference of waves going to the barrier and reflected from the potential barrier. Such an interference phenomenon in the structure does not disappear even in a symmetric structure due to the difference in the effective masses of electrons located in different regions of the structure. The electronic states of a multilayer semiconductor structure consisting of alternating potential wells and barriers are analyzed.
VL  - 8
IS  - 4
ER  -

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Author Information

Voxob Rustamovich Rasulov

Department of Physics, Faculty of Physics and Mathematics, Fergana State University, Fergana, Uzbekistan
Rustam Yavkachovich Rasulov

Department of Physics, Faculty of Physics and Mathematics, Fergana State University, Fergana, Uzbekistan
Iqboljon Mamirjonovich Eshboltayev

Department of Physics, Faculty of Physics and Mathematics, Fergana State University, Fergana, Uzbekistan
Ravshan Rustamovich Sultanov

Department of Physics, Faculty of Physics and Mathematics, Fergana State University, Fergana, Uzbekistan

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APA Style

Voxob Rustamovich Rasulov, Rustam Yavkachovich Rasulov, Iqboljon Mamirjonovich Eshboltayev, Ravshan Rustamovich Sultanov. (2020). Sub-barrier and Above-barrier Electron Transport Through Multilayer Semiconductors. American Journal of Physics and Applications, 8(4), 56-63. https://doi.org/10.11648/j.ajpa.20200804.12

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ACS Style

Voxob Rustamovich Rasulov; Rustam Yavkachovich Rasulov; Iqboljon Mamirjonovich Eshboltayev; Ravshan Rustamovich Sultanov. Sub-barrier and Above-barrier Electron Transport Through Multilayer Semiconductors. Am. J. Phys. Appl. 2020, 8(4), 56-63. doi: 10.11648/j.ajpa.20200804.12

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AMA Style

Voxob Rustamovich Rasulov, Rustam Yavkachovich Rasulov, Iqboljon Mamirjonovich Eshboltayev, Ravshan Rustamovich Sultanov. Sub-barrier and Above-barrier Electron Transport Through Multilayer Semiconductors. Am J Phys Appl. 2020;8(4):56-63. doi: 10.11648/j.ajpa.20200804.12

Copy | Download

@article{10.11648/j.ajpa.20200804.12,
  author = {Voxob Rustamovich Rasulov and Rustam Yavkachovich Rasulov and Iqboljon Mamirjonovich Eshboltayev and Ravshan Rustamovich Sultanov},
  title = {Sub-barrier and Above-barrier Electron Transport Through Multilayer Semiconductors},
  journal = {American Journal of Physics and Applications},
  volume = {8},
  number = {4},
  pages = {56-63},
  doi = {10.11648/j.ajpa.20200804.12},
  url = {https://doi.org/10.11648/j.ajpa.20200804.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20200804.12},
  abstract = {The transparency coefficients of the semiconductor structure consisting of alternating asymmetric potential barriers and wells are calculated, where taken into account the Bastard condition. It is shown that both in the above-barrier and over barrier passage of electrons, tunneling oscillations arise. The amplitude, in this case, is determined not only by the values of the wave vectors, but from the values of the effective masses of the current carriers. This oscillation does not disappear even in symmetric structures if they have a difference in the effective masses of current carriers located in two neighboring regions. In symmetrical structures, an oscillation of the coefficient of the above-barrier passage of a particle depending on its energy should be observed without taking into account the Bastard condition. Calculations show that for equal values of the width of the well and the potential barrier, as well as jumps in the potential of the barrier or well, the amplitude of the oscillations of the coefficient of over-barrier passage of particles is greater than the coefficient of passage above the well. In the case of an asymmetric structure, these considerations remain valed, but the physical nature of the parameters, for example, the number of oscillations, reflection and transmission coefficients, strongly depends on the ratio of the effective masses of electrons in neighboring layers and from the ratio of the height of the left and right potential barrier (regarding to the well). In an asymmetric (and in a symmetric, but with different effective masses of electrons in different layers) semiconductor structure, oscillation should be observed depending on the coefficient of transmission through the potential barrier on the energy of electron. This oscillation is caused by the interference of waves going to the barrier and reflected from the potential barrier. Such an interference phenomenon in the structure does not disappear even in a symmetric structure due to the difference in the effective masses of electrons located in different regions of the structure. The electronic states of a multilayer semiconductor structure consisting of alternating potential wells and barriers are analyzed.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Sub-barrier and Above-barrier Electron Transport Through Multilayer Semiconductors
AU  - Voxob Rustamovich Rasulov
AU  - Rustam Yavkachovich Rasulov
AU  - Iqboljon Mamirjonovich Eshboltayev
AU  - Ravshan Rustamovich Sultanov
Y1  - 2020/09/16
PY  - 2020
N1  - https://doi.org/10.11648/j.ajpa.20200804.12
DO  - 10.11648/j.ajpa.20200804.12
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 56
EP  - 63
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20200804.12
AB  - The transparency coefficients of the semiconductor structure consisting of alternating asymmetric potential barriers and wells are calculated, where taken into account the Bastard condition. It is shown that both in the above-barrier and over barrier passage of electrons, tunneling oscillations arise. The amplitude, in this case, is determined not only by the values of the wave vectors, but from the values of the effective masses of the current carriers. This oscillation does not disappear even in symmetric structures if they have a difference in the effective masses of current carriers located in two neighboring regions. In symmetrical structures, an oscillation of the coefficient of the above-barrier passage of a particle depending on its energy should be observed without taking into account the Bastard condition. Calculations show that for equal values of the width of the well and the potential barrier, as well as jumps in the potential of the barrier or well, the amplitude of the oscillations of the coefficient of over-barrier passage of particles is greater than the coefficient of passage above the well. In the case of an asymmetric structure, these considerations remain valed, but the physical nature of the parameters, for example, the number of oscillations, reflection and transmission coefficients, strongly depends on the ratio of the effective masses of electrons in neighboring layers and from the ratio of the height of the left and right potential barrier (regarding to the well). In an asymmetric (and in a symmetric, but with different effective masses of electrons in different layers) semiconductor structure, oscillation should be observed depending on the coefficient of transmission through the potential barrier on the energy of electron. This oscillation is caused by the interference of waves going to the barrier and reflected from the potential barrier. Such an interference phenomenon in the structure does not disappear even in a symmetric structure due to the difference in the effective masses of electrons located in different regions of the structure. The electronic states of a multilayer semiconductor structure consisting of alternating potential wells and barriers are analyzed.
VL  - 8
IS  - 4
ER  -

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