Skip to main content
SpringerLink
Log in

Solutions to the Fermi-Dirac Integrals in Semiconductor Physics Using Polylogarithms

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

The value of polylogarithms for calculating Fermi-Dirac integrals has been recognized in the field of statistical physics. However, its value has not become widely recognized in condensed matter physics or semiconductor device modeling. The utility of the polylogarithms is that they are built into standard computer mathematical packages so that neither approximations nor numerical integrations of Fermi-Dirac integrals are necessary. The direct relationship between Fermi-Dirac integrals and polylogarithms is reviewed and several examples of Fermi-Dirac integrals in semiconductor physics are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abuelma'atti M.T. 1994. Solid-State Elec. 37: 1367.

  • Bednarczyk D. and Bednarczyk J. 1978. Phys. Lett. 64A: 409.

    Google Scholar 

  • Blakemore J.S. 1962. Semiconductor Statistics. Pergamon Press, New York, p. 364.

    Google Scholar 

  • Blakemore J.S. 1982. Solid-State Elec. 25: 1067.

    Google Scholar 

  • Blakemore J.S. 1985. Solid State Physics, 2nd ed. Cambridge University Press, New York, p. 308.

    Google Scholar 

  • Dingle R.B. 1957. Appl. Phys. Res. B 6: 255.

    Google Scholar 

  • Goldsmid H.J. 1986. Electronic Refrigeration. Pion Limited, London, p. 59.

    Google Scholar 

  • Jog S.D. 1979. Phys. Lett. 72A: 303.

    Google Scholar 

  • Joyce W.B. and Dixon R.W. 1977. Appl. Phys. Lett. 31: 354.

    Google Scholar 

  • Joyce W.B. 1978. Appl. Phys. Lett. 32: 680.

    Google Scholar 

  • Lee M.H. 1995. J. Math. Phys. 36: 1217.

    Google Scholar 

  • Lee M.H. 1996a. Phys. Rev. E 53: 548.

    Google Scholar 

  • Lee M.H. 1996b. Phys. Rev. E 54: 946.

    Google Scholar 

  • Lewin L. 1981a. Polylogarithms and Associated Functions. North Holland, New York, p. 1.

  • Lewin L. 1981b. Polylogarithms and Associated Functions. North Holland, New York, p. 189.

  • Lewin L. 1981c. Polylogarithms and Associated Functions. North Holland, New York, p. 236.

  • McDougall J.M. and Stoner E.C. 1938. Phil. Trans. Roy. Soc. London A 237: 67.

    Google Scholar 

  • Nag B.R. 1980. Electron Transport in Compound Semiconductors, in Springer Series in Solid-State Sciences, Vol. 11, Springer-Verlag, New York, p. 174.

    Google Scholar 

  • Nilsson N.G. 1973. Phys. Stat. Solidi A19: K75.

    Google Scholar 

  • Nilsson N.G. 1978. Appl. Phys. Lett. 33: 653.

    Google Scholar 

  • Reser B.I. 1996. J. Phys.: Cond. Matter 8: 3151.

    Google Scholar 

  • Rhodes P. 1950. Proc. Roy. Soc. London A 204: 396.

    Google Scholar 

  • Sommerfeld A. 1928. Z. Physik. 47: 1.

    Google Scholar 

  • Soonckindt L. and Lassabatere L. 1978. Revue de Phys. Appl. 13: 581.

    Google Scholar 

  • Spanier J. and Oldham K.B. 1987. An Atlas of Functions. Hemisphere Publishing Corporation, Washington, p. 231.

    Google Scholar 

  • Thompson W.J. 1997. Atlas for Computing Mathematical Functions. John Wiley and Sons, New York, p. 151.

    Google Scholar 

  • Unger K. 1988. Phys. Stat. Solidi B 149: K141.

    Google Scholar 

  • Visual Numerics, Inc. 5775 Flatiron Parkway, Ste. 220, Boulder, Colorado 80301, www.vni.com/products/imsl/index.html.

  • Waterloo Maple Inc., 57 Erb StreetWest,Waterloo, Ontario; Canada N2L 6C2, www.maplesoft.com.

  • Wolfram S. 1999. The Mathematica Book. Cambridge University, New York, p. 1.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, North Carolina State University, Raleigh, NC, 27695-7518, USA

    Marc D. Ulrich

  2. Extreme Devices, Inc, 3500 ComSouth Drive, Austin, TX, 78744, USA

    William F. Seng

  3. Department of Physics and Astronomy, Clemson University, 118 Kinard Laboratory of Physics, Clemson, SC, 29634, USA

    Peter A. Barnes

Authors
  1. Marc D. Ulrich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William F. Seng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peter A. Barnes
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ulrich, M.D., Seng, W.F. & Barnes, P.A. Solutions to the Fermi-Dirac Integrals in Semiconductor Physics Using Polylogarithms. Journal of Computational Electronics 1, 431–434 (2002). https://doi.org/10.1023/A:1020784532229

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020784532229

Search

Navigation