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Some remarks on the Peltier heat in the thermoelectric phenomena

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Abstract

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.

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Notes

  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.

References

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Acknowledgements

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.

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Correspondence to Su-Il Pyun.

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

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Shin, HC., Pyun, SI. Some remarks on the Peltier heat in the thermoelectric phenomena. J Solid State Electrochem 25, 2737–2746 (2021). https://doi.org/10.1007/s10008-021-05019-4

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