American Journal of Modern Physics

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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

Received: 01 July 2018    Accepted: 13 July 2018    Published: 08 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.

DOI 10.11648/j.ajmp.20180704.13
Published in American Journal of Modern Physics (Volume 7, Issue 4, July 2018)
Page(s) 136-165
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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

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

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Author Information
  • 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

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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://download.sciencepg.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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    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
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    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
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    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
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