Thermoelectric phenomena and devices in the generalized model of electron transport

Authors: Kruglyak Yu. А., Kostritskаya L. S.

Year: 2017

Issue: 22

Pages: 90-101


In the tutorial review article intended for researchers, university lecturers and students the thermoelectric Seebeck and Peltier phenomena are considered in the framework of a generalized transport model due to R. Landauer, S. Datta, and M. Lundstrom of modern nanoelectronics within the “bottom – up” approach. The Wiedemann – Franz law and Lorenz numbers as well as the four transport coefficients (specific resistivity, Seebeck and Peltier coefficients, and electronic thermal conductivity) are also qualitatively discussed. Referring to a 3D resistor in the diffusion regime the thermoelectric cooler and energy power generator are analyzed with an account of only electrons as real current carriers as well as with artificial but useful electron/hole conception. Coefficient of performance, power factor and figure of merit for thermoelectric devices are introduced and defined. How transport coefficients depend on the properties of electrotermics are also discussed. Qualitative dependence of the Seebeck coefficient and electronic conductivity from the position of the Fermi level relative to the bottom of the conduction band is demonstrated. Maximization of the power factor near the bottom of the conduction band is shown. As the Fermi level approaches to the bottom of the conduction band and then moves up, the Seebeck coefficient decreases. At the same time, the electronic conductivity increases due to the appearance of an increasing number of conductivity modes. Their product is the power factor, which is maximal in the vicinity of the bottom of the conduction band. The position of the maximum for a specific electrotermics is dependent on the band structure of the conductor and the physics of its scattering centers. It is shown why in practice we try by doping the semiconductor to shift the Fermi level closer to the bottom of the conduction band.

Tags: nanoelectronics; nanophysics; thermoelectric devices; thermoelectric phenomena; нанофизика; нанофизика; наноэлектроника; наноэлектроника; термоелектричні пристрої; термоелектричні пристрої; термоелектричні явища; термоелектричні явища


  1. Kruglyak Yu. S. Nanosystems, Nanomaterials, Nanotechnologies, 2013, vol. 11, no. 3, pp. 519 – 549. (In Russian)
  2. Kruglyak Yu. S. Nanosystems, Nanomaterials, Nanotechnologies, 2013 vol. 11, pp. 655 – 677. (In Russian)
  3. Ioffe A. F. Semiconductor Thermoelements and Thermoelectric Cooling. London: Infosearch, 1957.
  4. Anatychuk L. I. Termoelementy i termoelektricheskie us-troystva [Thermoelements and thermoelectric devices]. Kiev: Naukova dumka, 1979.
  5. Anatychuk L. I., Semenyuk V. A. Optimal’noe upravlenie svoystvami termoelektricheskikh materialov i priborov. [Optimum control of the properties of thermoelectric materials and devices]. Chernovtsy: Prut, 1992.
  6. Anatychuk L. I., Bulat L. P. Poluprovodniki v ekstremal’nykh temperaturnykh usloviyakh [Semiconductors under extreme temperature conditions]. Leningrad: Nauka, 2003.
  7. Anatychuk L. I. Termoelektrichestvo. T. 2. Termoelektricheskie preobrazovateli energii [Thermoelectricity. T. 2. Thermoelectric power converters]. Kiev – Chernovtsy: The Institute of Thermoelectricity, Bukrek, 2003.
  8. Anatychuk L. I., Termoelektrichestvo. T. 1. Fizika termoelektrichestva. [Thermoelectricity. T. 1. Physics of thermoelectricity]. Kiev – Chernovtsy: The Institute of Thermoelectricity, Bukrek, 2009.
  9. Ashkroft N., Mermin N. Fizika tverdogo tela [Solid State Physics]. Moscow: Mir, 1979.
  10. Mahan G. D, Bartkowiak M. Appl. Phys. Lett, 1999, vol. 74, no 7, pp. 953 – 954.
  11. Smith C., Janak J., Adler R. Electronic Conduction in Solids. New York: McGraw-Hill, 1965.
  12. Onsager L. Phys. Rev., 1931, vol. 37, no. 4, pp. 405 – 426.
  13. The Institute of Thermoelectricity of NASU / MES of Ukraine: (In Russian)
  14. Majumdar A. Science, 2004, no. 303, pp. 778 – 779.
  15. M. Dresselhaus, G. Chen, M. Tang, R. Yang, H. Lee, D. Wang, Z. Ren, J.-P. Fleureal, P. Gogna. Adv. Materials, 2007, vol. 19, no. 8, pp. 1043 – 1053.
  16. Minnich A. J., Dresselhaus M. S., Ren Z. F., G. Chen. Energy and Environmental Science, 2009, pp. 466 – 479.
  17. Hode M. IEEE Trans. Components Packaging Technologies, 2005, vol. 28, pp. 218 – 229.
  18. Hode M. IEEE Trans. Components Packaging Technologies, 2007, vol. 30, pp. 50 – 58.
  19. Hode M. IEEE Trans. Components Packaging Technologies, 2010, vol. 33, pp. 307 – 318.
  20. Lundstrom M., Jeong. Near-Equilibrium Transport: Fundamentals and Applications. Hackensack, New Jersey: World Scientific Publishing Company, 2013. (In Russian).
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