Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures

Huynh Van Cong

doi:doi:10.11648/j.ajmp.20180704.13

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Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures

Huynh Van Cong

Published in American Journal of Modern Physics (Volume 7, Issue 4)

Received: 1 July 2018 Accepted: 13 July 2018 Published: 8 August 2018

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Abstract

In various degenerate donor-silicon systems, taking into account the effects of donor size and heavy doping and using an effective autocorrelation function for the potential fluctuations expressed in terms of the Heisenberg uncertainty relation and also an expression for the Gaussian average of , a ≥ 1 being the kinetic energy of the electron, calculated by the Kane integration method (KIM), we investigated the density of states, the optical absorption coefficient and the electrical conductivity, noting that this average expression calculated by the KIM was found to be equivalent to that obtained by the Feynman path-integral method. Then, those results were expressed in terms of for total electron energy , vanished at the conduction-band edge: , and for exhibited their exponential tails, going to zero as , and presenting the maxima, in good accordance with an asymptotic form for exponential conduction-band tail obtained by Halperin and Lax, using the minimum counting methods. Further, in degenerate d-Si systems at low temperatures, using an expression for the average of , p ≥ 3/2, calculated using the Fermi-Dirac distribution function, we determined the mobility, electrical conductivity, resistivity, Hall factor, Hall coefficient, Hall mobility, thermal conductivity, diffusion coefficient, absolute thermoelectric power, Thomson coefficient, Peltier coefficient, Seebeck thermoelectric potential, and finally dimensionless figure of merit, which were also compared with experimental and theoretical results, suggesting a satisfactory description given for our obtained results.

Published in	American Journal of Modern Physics (Volume 7, Issue 4)
DOI	10.11648/j.ajmp.20180704.13
Page(s)	136-165
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

Donor Size, Heavy Doping, Electrical Conductivity, Hall Effect, Diffusion Coefficient

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Huynh Van Cong. (2018). Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures. American Journal of Modern Physics, 7(4), 136-165. https://doi.org/10.11648/j.ajmp.20180704.13

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ACS Style

Huynh Van Cong. Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures. Am. J. Mod. Phys. 2018, 7(4), 136-165. doi: 10.11648/j.ajmp.20180704.13

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AMA Style

Huynh Van Cong. Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures. Am J Mod Phys. 2018;7(4):136-165. doi: 10.11648/j.ajmp.20180704.13

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@article{10.11648/j.ajmp.20180704.13,
  author = {Huynh Van Cong},
  title = {Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures},
  journal = {American Journal of Modern Physics},
  volume = {7},
  number = {4},
  pages = {136-165},
  doi = {10.11648/j.ajmp.20180704.13},
  url = {https://doi.org/10.11648/j.ajmp.20180704.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20180704.13},
  abstract = {In various degenerate donor-silicon systems, taking into account the effects of donor size and heavy doping and using an effective autocorrelation function for the potential fluctuations expressed in terms of the Heisenberg uncertainty relation and also an expression for the Gaussian average of , a ≥ 1  being the kinetic energy of the electron, calculated by the Kane integration method (KIM), we investigated the density of states, the optical absorption coefficient and the electrical conductivity, noting that this average expression calculated by the KIM was found to be equivalent to that obtained by the Feynman path-integral method. Then, those results were expressed in terms of  for total electron energy , vanished at the conduction-band edge: , and for  exhibited their exponential tails, going to zero as , and presenting the maxima, in good accordance with an asymptotic form for exponential conduction-band tail obtained by Halperin and Lax, using the minimum counting methods. Further, in degenerate d-Si systems at low temperatures, using an expression for the average of , p ≥ 3/2, calculated using the Fermi-Dirac distribution function, we determined the mobility, electrical conductivity, resistivity, Hall factor, Hall coefficient, Hall mobility, thermal conductivity, diffusion coefficient, absolute thermoelectric power, Thomson coefficient, Peltier coefficient, Seebeck thermoelectric potential, and finally dimensionless figure of merit, which were also compared with experimental and theoretical results, suggesting a satisfactory description given for our obtained results.},
 year = {2018}
}

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TY  - JOUR
T1  - Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures
AU  - Huynh Van Cong
Y1  - 2018/08/08
PY  - 2018
N1  - https://doi.org/10.11648/j.ajmp.20180704.13
DO  - 10.11648/j.ajmp.20180704.13
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 136
EP  - 165
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20180704.13
AB  - In various degenerate donor-silicon systems, taking into account the effects of donor size and heavy doping and using an effective autocorrelation function for the potential fluctuations expressed in terms of the Heisenberg uncertainty relation and also an expression for the Gaussian average of , a ≥ 1  being the kinetic energy of the electron, calculated by the Kane integration method (KIM), we investigated the density of states, the optical absorption coefficient and the electrical conductivity, noting that this average expression calculated by the KIM was found to be equivalent to that obtained by the Feynman path-integral method. Then, those results were expressed in terms of  for total electron energy , vanished at the conduction-band edge: , and for  exhibited their exponential tails, going to zero as , and presenting the maxima, in good accordance with an asymptotic form for exponential conduction-band tail obtained by Halperin and Lax, using the minimum counting methods. Further, in degenerate d-Si systems at low temperatures, using an expression for the average of , p ≥ 3/2, calculated using the Fermi-Dirac distribution function, we determined the mobility, electrical conductivity, resistivity, Hall factor, Hall coefficient, Hall mobility, thermal conductivity, diffusion coefficient, absolute thermoelectric power, Thomson coefficient, Peltier coefficient, Seebeck thermoelectric potential, and finally dimensionless figure of merit, which were also compared with experimental and theoretical results, suggesting a satisfactory description given for our obtained results.
VL  - 7
IS  - 4
ER  -

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Huynh Van Cong

Department of Physics, Laboratory of Mathematics and Physics, University of Perpignan, Perpignan, France

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APA Style

Huynh Van Cong. (2018). Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures. American Journal of Modern Physics, 7(4), 136-165. https://doi.org/10.11648/j.ajmp.20180704.13

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ACS Style

Huynh Van Cong. Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures. Am. J. Mod. Phys. 2018, 7(4), 136-165. doi: 10.11648/j.ajmp.20180704.13

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AMA Style

Huynh Van Cong. Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures. Am J Mod Phys. 2018;7(4):136-165. doi: 10.11648/j.ajmp.20180704.13

Copy | Download

@article{10.11648/j.ajmp.20180704.13,
  author = {Huynh Van Cong},
  title = {Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures},
  journal = {American Journal of Modern Physics},
  volume = {7},
  number = {4},
  pages = {136-165},
  doi = {10.11648/j.ajmp.20180704.13},
  url = {https://doi.org/10.11648/j.ajmp.20180704.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20180704.13},
  abstract = {In various degenerate donor-silicon systems, taking into account the effects of donor size and heavy doping and using an effective autocorrelation function for the potential fluctuations expressed in terms of the Heisenberg uncertainty relation and also an expression for the Gaussian average of , a ≥ 1  being the kinetic energy of the electron, calculated by the Kane integration method (KIM), we investigated the density of states, the optical absorption coefficient and the electrical conductivity, noting that this average expression calculated by the KIM was found to be equivalent to that obtained by the Feynman path-integral method. Then, those results were expressed in terms of  for total electron energy , vanished at the conduction-band edge: , and for  exhibited their exponential tails, going to zero as , and presenting the maxima, in good accordance with an asymptotic form for exponential conduction-band tail obtained by Halperin and Lax, using the minimum counting methods. Further, in degenerate d-Si systems at low temperatures, using an expression for the average of , p ≥ 3/2, calculated using the Fermi-Dirac distribution function, we determined the mobility, electrical conductivity, resistivity, Hall factor, Hall coefficient, Hall mobility, thermal conductivity, diffusion coefficient, absolute thermoelectric power, Thomson coefficient, Peltier coefficient, Seebeck thermoelectric potential, and finally dimensionless figure of merit, which were also compared with experimental and theoretical results, suggesting a satisfactory description given for our obtained results.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures
AU  - Huynh Van Cong
Y1  - 2018/08/08
PY  - 2018
N1  - https://doi.org/10.11648/j.ajmp.20180704.13
DO  - 10.11648/j.ajmp.20180704.13
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 136
EP  - 165
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20180704.13
AB  - In various degenerate donor-silicon systems, taking into account the effects of donor size and heavy doping and using an effective autocorrelation function for the potential fluctuations expressed in terms of the Heisenberg uncertainty relation and also an expression for the Gaussian average of , a ≥ 1  being the kinetic energy of the electron, calculated by the Kane integration method (KIM), we investigated the density of states, the optical absorption coefficient and the electrical conductivity, noting that this average expression calculated by the KIM was found to be equivalent to that obtained by the Feynman path-integral method. Then, those results were expressed in terms of  for total electron energy , vanished at the conduction-band edge: , and for  exhibited their exponential tails, going to zero as , and presenting the maxima, in good accordance with an asymptotic form for exponential conduction-band tail obtained by Halperin and Lax, using the minimum counting methods. Further, in degenerate d-Si systems at low temperatures, using an expression for the average of , p ≥ 3/2, calculated using the Fermi-Dirac distribution function, we determined the mobility, electrical conductivity, resistivity, Hall factor, Hall coefficient, Hall mobility, thermal conductivity, diffusion coefficient, absolute thermoelectric power, Thomson coefficient, Peltier coefficient, Seebeck thermoelectric potential, and finally dimensionless figure of merit, which were also compared with experimental and theoretical results, suggesting a satisfactory description given for our obtained results.
VL  - 7
IS  - 4
ER  -

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