Skip to main content


Log in

Some remarks on the Peltier heat in the thermoelectric phenomena

  • Feature Article
  • Published:
Journal of Solid State Electrochemistry Aims and scope Submit manuscript


In the present article, we conceptually develop some understanding of the Peltier heat resulting at the rectifying junction between a metal and an n-type semiconductor with a depleted space charge layer (“the Schottky barrier”) as well as two Ohmic contacts between a metal and an n-type semiconductor with an enriched space charge layer, and two dissimilar metals chosen as three instructive examples via “the thought experiment,” based upon the energy band diagram of metal and semiconductor. Additionally, we briefly discussed on the difference between the contact potential and diffusion potential, both of which proved to be a thermodynamic reversible potential as well that influences greatly the Peltier coefficient. We concluded that the reduction in the kinetic energy of more energetic electrons passing through the rectifying junction as well as the two Ohmic contacts is accompanied by the Peltier heat evolution. By contrast, the enhancement in the kinetic energy of less energetic electrons passing through the rectifying junction as well as the two Ohmic contacts is associated with the Peltier heat absorption. The Peltier heat evolution and absorption resulting at the rectifying junction as well as the two Ohmic contacts can be well understood in terms of reduction/enhancement in the kinetic energy of electrons crossing the junction, respectively, under the isothermal constraint of a couple of junctions. The rectifying junctions provide Peltier effects more markedly than the two Ohmic contacts. This idea provides in particular a basis for the thermoelectric generator (batteries) and it can be extended to other rectifying junctions such as a p-n junction and another Ohmic contact between metal and p-type semiconductor with an enriched space charge layer.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others


  1. Note that strictly treating, [particle] has no physical dimension in its character. For the sake of clarity, it is introduced here in comparison with the Faraday constant.

  2. The terms “positive and negative biasing voltages” with respect to the Fermi energy level E_F of conduction electrons and holes used by semiconductor people are comparable with those terms “applying anodic and cathodic over-voltages” with respect to that Fermi energy level E_F of redox electrons used by electrochemists, respectively.

  3. Note that according to the Max Planck’s thermodynamic sign convention on heat Q, the sign of heat evolved is negative, while the sign of heat absorbed is positive, as viewed from the thermodynamic system, which is just opposite to the Anglo-American sign convention. The thermodynamic system of the Peltier effect is just electron crossing the junctions M/S and S/M or the Ohmic contacts. This concept is reflected on Figs. 6 and 7.


  1. Pyun SI (2021) Thermodynamic aspects of energy conversion systems with focus on osmotic membrane and selective-permeable membrane (Donnan) systems including two applications of the Donnan potential. Chem-Texts 7:20 (pp 1–29).

  2. Crow DR (1974) Principles and application of electrochemistry. Chapter 6, Blackie Academic & Professional London, pp 88–128

  3. Haensel H, Neumann W (1978) Physik, Bd VII Festkoerper. Chapter 40.4 VEB Deutscher Verlag der Wissenschaft, Berlin, pp 167–202

  4. Pyun SI (2020) Thermodynamic and electro-kinetic analyses of direct electron transfer (DET) and mediator-involved electron transfer (MET) with the help of a redox electron mediator. J Solid State Electrochem 24:2685–2693

    Article  CAS  Google Scholar 

  5. Dekker AJ (1962) Solid state physics. Chapter 14 Prentice-Hall, Inc Englewood Cliffs, NJ pp. 348–365

  6. Hummel RE (1985) Electronic properties of materials. Chapter 8.7 Springer-Verlag, Berlin, pp 101–119

  7. Zemansky MW (1951) Heat and thermodynamics. Chapter 14, McGraw-Hill Book Company, Inc., New York, pp 279–309

  8. Zemansky MW (1957) Heat and thermodynamics. Chapter 13, McGraw-Hill Book Company, Inc., New York, pp 396–441

  9. Schulze GER (1974) Metallphysik. Chapter M22, Springer-Verlag, Berlin, pp 350–354

  10. Vogel H (1974) Gerthsen Kneser Vogel Physik. Chapter 6.6, Springer-Verlag, Berlin, pp 346–354

  11. Weissmantel Ch, Hamann C (1979) Grundlagen der Festkoerperphysik. Chapter 6.5.7, Springer-Verlag, Berlin, pp 420–423

Download references


This contribution is dedicated to Professor George Inzelt in memory of editorial collaboration on the occasion of his 75th birthday. The authors cordially wish him further good health and success in research. The authors are also indebted to Professor Fritz Scholz for his continuous suggestion and interest in this work.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Su-Il Pyun.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

A feature article as a contribution to “the Professor George Inzelt birthday Festschrift issue”

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shin, HC., Pyun, SI. Some remarks on the Peltier heat in the thermoelectric phenomena. J Solid State Electrochem 25, 2737–2746 (2021).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: