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An electrohydrodynamics model for non-equilibrium electron and phonon transport in metal films after ultra-short pulse laser heating

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Abstract

The electrons and phonons in metal films after ultra-short pulse laser heating are in highly non-equilibrium states not only between the electrons and the phonons but also within the electrons. An electrohydrodynamics model consisting of the balance equations of electron density, energy density of electrons, and energy density of phonons is derived from the coupled non-equilibrium electron and phonon Boltzmann transport equations to study the nonlinear thermal transport by considering the electron density fluctuation and the transient electric current in metal films, after ultra-short pulse laser heating. The temperature evolution is calculated by the coupled electron and phonon Boltzmann transport equations, the electrohydrodynamics model derived in this work, and the two-temperature model. Different laser pulse durations, film thicknesses, and laser fluences are considered. We find that the two-temperature model overestimates the electron temperature at the front surface of the film and underestimates the damage threshold when the nonlinear thermal transport of electrons is important. The electrohydrodynamics model proposed in this work could be a more accurate prediction tool to study the non-equilibrium electron and phonon transport process than the two-temperature model and it is much easier to be solved than the Boltzmann transport equations.

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References

  1. P.B. Corkum, F. Brunel, N.K. Sherman, T. Srinivasan-Rao, Phys. Rev. Lett. 61, 2886 (1988)

    Article  ADS  Google Scholar 

  2. J.G. Fujimoto, J.M. Liu, E.P. Ippen, N. Bloembergen, Phys. Rev. Lett. 53, 1837 (1984)

    Article  ADS  Google Scholar 

  3. H.E. Elsayed-Ali, T.B. Norris, M.A. Pessot, G.A. Mourou, Phys. Rev. Lett. 58, 1212 (1987)

    Article  ADS  Google Scholar 

  4. G.L. Eesley, Phys. Rev. Lett. 51, 2140 (1983)

    Article  ADS  Google Scholar 

  5. C. Suárez, W.E. Bron, T. Juhasz, Phys. Rev. Lett. 75, 4536 (1995)

    Article  ADS  Google Scholar 

  6. W.S. Fann, R. Storz, H.W.K. Tom, J. Bokor, Phys. Rev. Lett. 68, 2834 (1992)

    Article  ADS  Google Scholar 

  7. R.W. Schoenlein, W.Z. Lin, J.G. Fujimoto, G.L. Eesley, Phys. Rev. Lett. 58, 1680 (1987)

    Article  ADS  Google Scholar 

  8. S.D. Brorson, J.G. Fujimoto, E.P. Ippen, Phys. Rev. Lett. 59, 1962 (1987)

    Article  ADS  Google Scholar 

  9. P.B. Allen, Phys. Rev. Lett. 59, 1460 (1987)

    Article  ADS  Google Scholar 

  10. S.D. Brorson, A. Kazeroonian, J.S. Moodera, D.W. Face, T.K. Cheng, E.P. Ippen, M.S. Dresselhaus, G. Dresselhaus, Phys. Rev. Lett. 64, 2172 (1990)

    Article  ADS  Google Scholar 

  11. M. Bass, Laser Materials Processing (North-Holland, Amsterdam, 1993)

  12. H. Häkkinen, U. Landman, Phys. Rev. Lett. 71, 1023 (1993)

    Article  ADS  Google Scholar 

  13. C.L. Cleveland, U. Landman, R.N. Barnett, Phys. Rev. Lett. 49, 790 (1982)

    Article  ADS  Google Scholar 

  14. C. Schäfer, H.M. Urbassek, L.V. Zhigilei, Phys. Rev. B 66, 115404 (2002)

    Article  ADS  Google Scholar 

  15. K. Sokolowski-Tinten, J. Bialkowski, A. Cavalleri, D. von der Linde, A. Oparin, J. Meyer-ter-Vehn, S.I. Anisimov, Phys. Rev. Lett. 81, 224 (1998)

    Article  ADS  Google Scholar 

  16. V. Schmidt, W. Husinsky, G. Betz, Phys. Rev. Lett. 85, 3516 (2000)

    Article  ADS  Google Scholar 

  17. M.I. Kaganov, I.M. Lifshitz, L.V. Tanatarov, Sov. Phys. J. Exp. Theor. Phys. 4, 173 (1957)

    MATH  Google Scholar 

  18. S.I. Anisimov, B.L. Kapeliovich, T.L. Perel’man, Sov. Phys. J. Exp. Theor. Phys. 39, 375 (1974)

    ADS  Google Scholar 

  19. T.Q. Qiu, C.L. Tien, Int. J. Heat Mass Transfer 35, 719 (1992)

    Article  ADS  Google Scholar 

  20. Z.C. Wang, Thermodynamics and Statistical Physics (Higher Education Press, Beijing, 1993)

  21. J.K. Chen, D.Y. Tzou, J.E. Beraun, Int. J. Heat Mass Transfer 49, 307 (2006)

    Article  MATH  Google Scholar 

  22. M. Lundstrom, Fundamentals of Carrier Transport (Cambridge University Press, Cambridge, 2000)

  23. L.D. Pietanza, G. Colonna, S. Longo, M. Capitelli, Eur. Phys. J. D 45, 369 (2007)

    Article  ADS  Google Scholar 

  24. W.L. McMillan, Phys. Rev. 167, 331 (1968)

    Article  ADS  Google Scholar 

  25. J.L. Cheng, M.W. Wu, J. Appl. Phys. 101, 073702 (2007)

    Article  ADS  Google Scholar 

  26. R. Bauer, A. Schmid, P. Pavone, D. Strauch, Phys. Rev. B 57, 11276 (1998)

    Article  ADS  Google Scholar 

  27. H.R. Schober, P.H. Dederichs, in Landolt-Börnstein, edited by K.-H. Hellwege, J.L. Olsen (Springer-Verlag, Berlin, 1981), Vol. III/13A

  28. J.M. Ziman, in Electrons and Phonons (Oxford University Press, London, 1962), p. 456

  29. L.D. Pietanza, G. Colonna, M. Capitelli, AIP Conf. Proc. 762, 1241 (2005)

    ADS  Google Scholar 

  30. N.W. Ashcroft, N.D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976)

  31. N.F. Mott, H. Jones, The Theory of the Properties of Metals and Alloys (Dover Publications, Inc., New York, 1958)

  32. S.I. Anisimov, B. Rethfeld, Proc. SPIE 3093, 192 (1997)

    ADS  Google Scholar 

  33. K. Ujihara, IEEE J. Quantum Electron. 8, 567 (1972)

    Article  ADS  Google Scholar 

  34. K. Venkatakrishnan, B. Tan, B.K.A. Ngoi, Opt. Laser Technol. 34, 199 (2002)

    Article  ADS  Google Scholar 

  35. A. Pattamata, C.K. Madnia, J. Heat Trans. 131, 082401 (2009)

    Article  Google Scholar 

  36. Z.B. Lin, L.V. Zhigilei, V. Celli, Phys. Rev. B 77, 075133 (2008)

    Article  ADS  Google Scholar 

  37. W. Wang, D.G. Cahill, Phys. Rev. Lett. 109, 175503 (2012)

    Article  ADS  Google Scholar 

  38. D.K.C. MacDonald, Thermoelectricity: an Introduction to the Principles (Dover Publication, Inc., New York, 2006)

  39. B.C. Stuart, M.D. Feit, S. Sherman, A.M. Rubenchik, B.W. Shore, M.D. Perry, J. Opt. Soc. Am. B 13, 459 (1996)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering and Materials Science and Engineering Program, University of Colorado, Boulder, CO, 80309, USA

    Jun Zhou & Ronggui Yang

  2. Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai, 200092, P.R. China

    Jun Zhou & Nianbei Li

Authors
  1. Jun Zhou
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  2. Nianbei Li
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  3. Ronggui Yang
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Correspondence to Ronggui Yang.

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Zhou, J., Li, N. & Yang, R. An electrohydrodynamics model for non-equilibrium electron and phonon transport in metal films after ultra-short pulse laser heating. Eur. Phys. J. B 88, 156 (2015). https://doi.org/10.1140/epjb/e2015-60354-4

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