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A note on the electrochemical nature of the thermoelectric power

  • Y. Apertet
  • H. Ouerdane
  • C. Goupil
  • Ph. Lecoeur
Regular Article

Abstract.

While thermoelectric transport theory is well established and widely applied, it is not always clear in the literature whether the Seebeck coefficient, which is a measure of the strength of the mutual interaction between electric charge transport and heat transport, is to be related to the gradient of the system’s chemical potential or to the gradient of its electrochemical potential. The present article aims to clarify the thermodynamic definition of the thermoelectric coupling. First, we recall how the Seebeck coefficient is experimentally determined. We then turn to the analysis of the relationship between the thermoelectric power and the relevant potentials in the thermoelectric system: As the definitions of the chemical and electrochemical potentials are clarified, we show that, with a proper consideration of each potential, one may derive the Seebeck coefficient of a non-degenerate semiconductor without the need to introduce a contact potential as seen sometimes in the literature. Furthermore, we demonstrate that the phenomenological expression of the electrical current resulting from thermoelectric effects may be directly obtained from the drift-diffusion equation.

Keywords

Conduction Band Fermi Level Fermi Energy Seebeck Coefficient Thermoelectric Power 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    S.R. de Groot, Thermodynamics of Irreversible Processes (Interscience Publishers Inc., New York, 1958)Google Scholar
  2. 2.
    Y. Apertet, H. Ouerdane, C. Goupil, Ph. Lecoeur, Phys. Rev. E 85, 031116 (2012)ADSCrossRefGoogle Scholar
  3. 3.
    T.J. Seebeck, Abh. K. Akad. Wiss. Berlin 21, 289 (1821)Google Scholar
  4. 4.
    H.C. Oersted, Ann. Chim. Phys. 22, 199 (1823)Google Scholar
  5. 5.
    H.B. Callen, Phys. Rev. 73, 1349 (1948)ADSCrossRefGoogle Scholar
  6. 6.
    C. Herring, Phys. Rev. 96, 1163 (1954)ADSCrossRefGoogle Scholar
  7. 7.
    P.J. Price, Phys. Rev. 104, 1223 (1956)ADSCrossRefGoogle Scholar
  8. 8.
    R.R. Heikes, R.W. Ure, Thermoelectricity: Science and Engineering (Interscience Publishers, New York, 1961)Google Scholar
  9. 9.
    C. Wood, Rep. Prog. Phys. 51, 459 (1988)ADSCrossRefGoogle Scholar
  10. 10.
    C. Kittel, Introduction to Solid State Physics, 8th edition (John Wiley & Sons, New York, 2005)Google Scholar
  11. 11.
    G.D. Mahan, J. Appl. Phys. 87, 7326 (2000)ADSCrossRefGoogle Scholar
  12. 12.
    J. Cai, G.D. Mahan, Phys. Rev. B 74, 075201 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    M.R. Peterson, B.S. Shastry, Phys. Rev. B 82, 195105 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    A.A. Varlamov, K.V. Kavokin, EPL 103, 47005 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    H. Ouerdane, A.A. Varlamov, A.V. Kavokin, C. Goupil, C.B. Vining, Phys. Rev. B 91, 100501(R) (2015)ADSCrossRefGoogle Scholar
  16. 16.
    K. Behnia, Fundamentals of Thermoelectricity (Oxford University Press, Oxford, 2015)Google Scholar
  17. 17.
    H.B. Callen, Thermodynamics and an Introduction to Thermostatistics (John Wiley & Sons, New York, 1985)Google Scholar
  18. 18.
    Z. Zhou, C. Uher, Rev. Sci. Instrum. 76, 023901 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    I. Riess, Solid State Ionics 95, 327 (1997)CrossRefGoogle Scholar
  20. 20.
    J. Martin, T. Tritt, C. Uher, J. Appl. Phys. 108, 121101 (2010) and references thereinADSCrossRefGoogle Scholar
  21. 21.
    R.G. Chambers, Phys. Educ. 12, 374 (1977)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    M. Lundstrom, Fundamentals of Carrier Transport, second edition (Cambridge University Press, Cambridge, 2009)Google Scholar
  23. 23.
    A.F. Ioffe, Physics of Semiconductors (Infosearch, Ltd., London, 1960)Google Scholar
  24. 24.
    F.W.G. Rose, E. Billig, J.E. Parrott, J. Electron. Control 3, 481 (1957)CrossRefGoogle Scholar
  25. 25.
    C. Goupil, W. Seifert, K. Zabrocki, E. Muller, G.J. Snyder, Entropy 13, 1481 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    B.S. Shastry, Thermopower in Correlated Systems, in New Materials for Thermoelectric Applications: Theory and Experiment (Springer Netherlands, Dordrecht, 2013)Google Scholar
  27. 27.
    P. Sun, B. Wei, J. Zhang, J.M. Tomczak, A.M. Strydom, M. Sondergaard, B.B. Iversen, F. Steglich, Nat. Commun. 6, 7475 (2015)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Y. Apertet
    • 1
  • H. Ouerdane
    • 2
    • 3
  • C. Goupil
    • 4
  • Ph. Lecoeur
    • 5
  1. 1.Lycée Jacques PrévertPont-AudemerFrance
  2. 2.Russian Quantum CenterMoscow regionRussian Federation
  3. 3.UFR Langues Vivantes EtrangèresUniversité de Caen NormandieCaenFrance
  4. 4.Laboratoire Interdisciplinaire des Energies de Demain (LIED)UMR 8236 Université Paris Diderot, CNRSParisFrance
  5. 5.Institut d’Electronique FondamentaleUniversité Paris-Sud, CNRS, UMR 8622OrsayFrance

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