Journal of Electronic Materials

, Volume 48, Issue 5, pp 3399–3404 | Cite as

Fermi Level and Electrostatic Screening Factor in Degenerate Semiconductors and Metal Alloys

  • John S. CetnarEmail author
  • D. L. Rode
Topical Collection: 60th Electronic Materials Conference 2018
Part of the following topical collections:
  1. 60th Electronic Materials Conference 2018


An analytical solution has been found for the calculation of the Fermi level and the electrostatic screening factor for semiconductors and metal alloys in the degenerate limit using non-parabolic energy bands and Fermi statistics. The solution yields a more accurate determination of Fermi levels than methods that assume parabolic energy bands and a more accurate determination of screening factors than the Thomas–Fermi formula, which also assumes parabolic bands and thus predicts screening that is too weak relative to self-consistent field screening in highly degenerate systems, including metal alloys. Mobility and resistivity calculations using this analytical solution yield results that are closer to experimental data than traditional formulas derived assuming parabolic bands.


Degenerate semiconductors non-parabolic bands Fermi statistics ionized impurity screening ionized impurity scattering metal alloy resistivity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work is supported by the Air Force Office of Scientific Research through Project FA9550-17RYCOR490. The authors wish to thank D. C. Look for enlightening and useful discussions. In addition, we wish to thank Tim Cooper for performing the Hall-effect measurements. Finally, we express our gratitude to John D. Wiley for pointing out the existence of this problem 43 years ago; we are sorry it took this long to repair.


  1. 1.
    N.F. Mott, Proc. Camb. Philos. Soc. 32, 281 (1936).CrossRefGoogle Scholar
  2. 2.
    R. Resta, Phys. Rev. B 16, 2717 (1977).CrossRefGoogle Scholar
  3. 3.
    P. Csavinszky, Phys. Rev. B 21, 632 (1980).CrossRefGoogle Scholar
  4. 4.
    R.B. Dingle, Lond. Edinb. Dubl. Philos. Mag. 46, 831 (1955).CrossRefGoogle Scholar
  5. 5.
    E. Burstein, Phys. Rev. 93, 632 (1954).CrossRefGoogle Scholar
  6. 6.
    T.S. Moss, Proc. Phys. Soc. Lond. Sect. B 67, 775 (1954).CrossRefGoogle Scholar
  7. 7.
    A.A. Ziabari, S.M. Rozati, Physica B 407, 4512 (2012).CrossRefGoogle Scholar
  8. 8.
    A. Walsh, J.L.F. Da Silva, S.-H. Wei, Phys. Rev. B 78, 075211 (2008).CrossRefGoogle Scholar
  9. 9.
    L. Falicov, M. Cuevas, Phys. Rev. 164, 1025 (1967).CrossRefGoogle Scholar
  10. 10.
    D.L. Rode, in Semiconductors and Semimetals, Chap. 1, Vol. 10, edited by R.K. Willardson and A.C. Beer (Amsterdam: Elsevier, 1975), pp. 1–89Google Scholar
  11. 11.
    C. Pozrikidis, Numerical Computation in Science and Engineering, 2nd edn. (New York: Oxford University Press, 1998), p. 522.Google Scholar
  12. 12.
    E.O. Kane, J. Phys. Chem. Solids 1, 249 (1957).CrossRefGoogle Scholar
  13. 13.
    E.O. Kane, in Semiconductors and Semimetals, Chap. 3, Vol. 1, edited by R.K. Willardson and A.C. Beer (Amsterdam: Elsevier, 1966), pp. 75–100Google Scholar
  14. 14.
    K.W. Böer, Survey of Semiconductor Physics, vol. 1, (New York: Wiley, 2002), pp. 382–384Google Scholar
  15. 15.
    D.C. Look, K.D. Leedy, in Oxide-Based Materials and Devices III (Bellingham: International Society for Optics and Photonics, 2012), p. 826302.Google Scholar
  16. 16.
    N.W. Ashcroft, N.D. Mermin, Solid State Physics (Boston: Brooks/Cole Thomson Learning, 1976), pp. 340–342.Google Scholar
  17. 17.
    D.C. Look, K. Leedy, L. Vines, B. Svensson, A. Zubiaga, F. Tuomisto, D.R. Doutt, L. Brillson, Phys. Rev. B 84, 115202 (2011).CrossRefGoogle Scholar

Copyright information

© This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2019

Authors and Affiliations

  1. 1.Air Force Research Laboratory, Sensors Directorate, Wright-Patterson Air Force BaseDaytonUSA
  2. 2.Department of Electrical and Systems EngineeringWashington University in St. LouisSt. LouisUSA

Personalised recommendations