Skip to main content
SpringerLink
Log in

Mesoscopic hydro-thermodynamics of phonons in semiconductors: heat transport in III-nitrides

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

It is presented a generalized hydro-thermodynamics (called mesoscopic hydro-thermodynamics MHT) of phonons in semiconductors, driven away from equilibrium by external forces, derived by the method of moments from a generalized Peierls-Boltzmann kinetic equation built in the framework of a non-equilibrium statistical ensemble formalism. The resulting MHT involves the enormous set of coupled evolution equations for the densities of the quasi-particles (phonons) and their energy together with their fluxes of all orders. The handling of them requires the introduction of a contraction of description what defines MHT’s of different orders. We illustrate the matter analyzing heat transport by phonons in GaN within the framework of a MHT of first order to obtain a generalized Guyer-Krumhansl equation from which it is analyzed the effect of geometry on the heat transport. It is described the influence of size (from bulk to nanometric scales) on the reduction of the thermal conductivity and the improving of the figure of merit of thermoelectric devices.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Castelvecchi, G.P. Collins, M. Fischetti, S. Mirsky, M. Moyer, G. Musser, C. Soares, K. Wong, Scientific American 302, 68 (2010)

    Google Scholar 

  2. D.G. Cahill, W.K. Ford, K.E. Goodson, G.D. Mahan, A. Majumdar, H.J. Maris, R. Merlin, S.R. Phillpot, J. Appl. Phys. 93, 793 (2003)

    Article  ADS  Google Scholar 

  3. G.I. Meijer, Science 328, 318 (1991)

    Article  ADS  Google Scholar 

  4. Z.M. Zhang, Nano/Microscale Heat Transfer (McGraw Hill, New York, 2007)

  5. D.Y. Tzou, Macro to Micro Scale Heat Transport (Taylor and Francis, Washington, 1997)

  6. N. Li, J. Ren, L. Wang, G. Zhang, P. Hänggi, B. Li, Rev. Mod. Phys. 84, 1045 (2012)

    Article  ADS  Google Scholar 

  7. S. Liu, X.F. Xu, R.G. Xie, G. Zhang, B.W. Li, Eur. Phys. J. B 85, 337 (2012)

    Article  ADS  Google Scholar 

  8. I. Chowdhury, R. Prasher, K. Lofgreen, G. Chrysler, S. Narasimhan, R. Mahajan, D. Koester, R. Alley, R. Venkatasubramanian, Nature Nanotechnol. 4, 235 (2009)

    Article  ADS  Google Scholar 

  9. C. Dames, G. Chen, in Thermoelectrics Handbook: Macro to Nano, edited by D.M. Rowe (CRC Taylor and Francis, Boca Raton, 2006)

  10. R. Klein, Introduction to Phonon Hydrodynamic in: Nonequilibrium Phonon Dynamics, edited by W.E. Bron (Plenum, New York, 1985), Vol. 124

  11. R. Luzzi, A.R. Vasconcellos, J.G. Ramos, Predictive Statistical Mechanics: a Non-Equilibrium Ensemble Formalism (Kluwer Academic, Dordrecht, 2002)

  12. R. Luzzi, A.R. Vasconcellos, J.G. Ramos, Rivista Nuovo Cimento 29, 1 (2006)

    Google Scholar 

  13. R. Luzzi, A.R. Vasconcellos, J.G. Ramos, Statistical Foundations of Irreversible Thermodynamics (Teubner-Bertelsmann-Springer, Dordrecht, 2000)

  14. R. Luzzi, A.R. Vasconcellos, J.G. Ramos, Rivista Nuovo Cimento 24, 1 (2001)

    Google Scholar 

  15. D.N. Zubarev, V. Morozov, G. Röpke, Statistical Mechanics of Non Equilibrium Processes: Relaxation and Hydrodynamic Processes (Academie Verlag-Wiley VCH, Berlin, 1997), Vol. 2

  16. A.R. Vasconcellos, A.R.B. Castro, C.A.B. Silva, R. Luzzi, arXiv:1211.0342 and J. Appl. Phys., submitted

  17. L. Lauck, A.R. Vasconcellos, R. Luzzi, Physica A 168, 789 (1990)

    Article  ADS  Google Scholar 

  18. F.S. Vannucchi, A.R. Vasconcellos, R. Luzzi, Int. J. Mod. Phys. B 23, 5283 (2009)

    Article  ADS  MATH  Google Scholar 

  19. D.N. Zubarev, V. Morozov, G. Röpke, Statistical Mechanics of Non Equilibrium Processes: Basic Concepts, Kinetic Theory (Academie Verlag-Wiley VCH, Berlin, 1996), Vol. 1

  20. P. Coveney, R. Highfield, The Arrow of Time (Fawcett-Columbine, New York, 1990)

  21. T. Deuderwaerdere, J. Casas Vazquez, D. Jou, G. Lebon, Phys. Rev. E 53, 498 (1996)

    Article  ADS  Google Scholar 

  22. C.A.B. Silva, J.G. Ramos, A.R. Vasconcellos, R. Luzzi, Phys. Rev. E submitted (2012)

  23. D. Jou, J. Casas Vazquez, J.R. Madureira, A.R. Vasconcellos, R. Luzzi, J. Chem. Phys. 116, 1571 (2001)

    Article  ADS  Google Scholar 

  24. D. Jou, J. Casas Vazquez, J.R. Madureira, A.R. Vasconcellos, R. Luzzi, J. Mod. Phys. B 15, 4211 (2001)

    Article  ADS  Google Scholar 

  25. F.X. Alvarez, D. Jou, A. Sellito, J. Appl. Phys. 105, 014317 (2009)

    Article  ADS  Google Scholar 

  26. U. Fano, Rev. Mod. Phys. 29, 74 (1957)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. N.N. Bogoliubov, Lectures in Quantum Statistics I (Gordon and Breach, New York, 1967)

  28. J.R. Klauder, B.S. Skagerstam, Coherent States (World Scientific, Singapore, 1984)

  29. D. Pines, The Many-Body Problem (Benjamin, New York, 1961)

  30. J.R. Madureira, A.R. Vasconcellos, R. Luzzi, L. Lauck, Phys. Rev. E 57, 3637 (1998)

    Article  ADS  Google Scholar 

  31. J.G. Ramos, A.R. Vasconcellos, R. Luzzi, J. Chem. Phys. 112, 2692 (2000)

    Article  ADS  Google Scholar 

  32. J.C. Maxwell, Philos. Trans. Roy. Soc. Lond. 157, 49 (1867)

    Article  Google Scholar 

  33. S.P. Heims, E.T. Jaynes, Rev. Mod. Phys. 34, 143 (1962): see Appendix B in p. 164

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. R.A. Guyer, J.A. Krumhansl, Phys. Rev. 148, 766 (1966)

    Article  ADS  Google Scholar 

  35. R.A. Guyer, J.A. Krumhansl, Phys. Rev. 148, 778 (1966)

    Article  ADS  Google Scholar 

  36. J.M. Ziman, Electrons and Phonons (Clarendon, Oxford, 1960)

  37. Dynamical of Fractal Surfaces, edited by F. Family, T. Viazek (World Scientific, Singapore, 1991)

  38. C. Guthy, C-Y. Nam, J.E. Fischer, J. Appl. Phys. 103, 064319 (2008)

    Article  ADS  Google Scholar 

  39. D. Burnett, Proc. Lond. Math. Soc. 40, 382 (1935)

    Article  MathSciNet  Google Scholar 

  40. C.G. Rodrigues, A.A.P. Silva, C.A.B. Silva, A.R. Vasconcellos, J.G. Ramos, R. Luzzi, Braz. J. Phys. 40, 63 (2010)

    Article  ADS  Google Scholar 

  41. R. Luzzi, A.R. Vasconcellos, J. Casas-Vazquez, D. Jou, J. Chem. Phys. 107, 7383 (1997)

    Article  ADS  Google Scholar 

  42. R. Luzzi, A.R. Vasconcellos, J. Casas-Vazquez, D. Jou, Physica A 248, 111 (1998)

    Article  ADS  Google Scholar 

  43. A.C. Algarte, A.R. Vasconcellos, R. Luzzi, Phys. Stat. Sol. b 173, 487 (1992)

    Article  ADS  Google Scholar 

  44. A.C. Algarte, A.R. Vasconcellos, R. Luzzi, Phys. Rev. B 54, 11311 (1996)

    Article  ADS  Google Scholar 

  45. J. Casas-Vazquez, D. Jou, Rep. Prog. Phys. 66, 1937 (2003)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, Pontifícia Universidade Católica de Goiás, 74605-010, Goiânia, Goiás, Brazil

    Clóves G. Rodrigues

  2. Condensed Matter Physics Department, Institute of Physics “Gleb Wataghin”, University of Campinas-Unicamp, 13083-859, Campinas, SP, Brazil

    Áurea R. Vasconcellos & Roberto Luzzi

Authors
  1. Clóves G. Rodrigues
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Áurea R. Vasconcellos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roberto Luzzi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Clóves G. Rodrigues.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rodrigues, C.G., Vasconcellos, Á.R. & Luzzi, R. Mesoscopic hydro-thermodynamics of phonons in semiconductors: heat transport in III-nitrides. Eur. Phys. J. B 86, 200 (2013). https://doi.org/10.1140/epjb/e2013-40109-1

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2013-40109-1

Keywords

Search

Navigation