Skip to main content
Log in

Electron–phonon energy relaxation in bismuth excited by ultrashort laser pulse: temperature and fluence dependence

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

We present analysis of the experiments on excitation of bismuth by ultrafast laser pulses and compare with heating bismuth in equilibrium conditions. The analysis shows that the electron–phonon relaxation time is a strong function of the lattice temperature. We developed a kinetic theory, which predicts well the experimental results. We demonstrate that lattice heating and re-structuring with the temperature-dependent energy exchange rates occurs much faster than what follows from the two-temperature model with constant relaxation factor. The analytic formulae corrected by equilibrium and non-equilibrium data allowed the interpretation of various experiments without controversy. We demonstrate that all observed ultrafast transformation of bismuth are purely thermal in nature, thus excluding the conjectures about non-thermal melting.

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

Access this article

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

Similar content being viewed by others

References

  1. M.I. Kaganov, I.M. Lifshitz, L.V. Tanatarov, Zh. Eksp. Teor. Fiz. 31, 232 (1956) [Sov. Phys. JETP 4, 173 (1957)]

    Google Scholar 

  2. S.I. Anisimov, B.L. Kapeliovich, T.L. Perel’man, Zh. Eksp. Teor. Fiz. 66, 776–781 (1974) [Sov. Phys. JETP 39, 375–377 (1974)]

    ADS  Google Scholar 

  3. B. Rethfeld, A. Kaiser, M. Vicanek, G. Simon, Phys. Rev. B 65, 214303 (2002)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. J. Hohlfeld, S.-S. Wellershoff, J. Güdde, U. Conrad, V. Jähnke, E. Matthias, Chem. Phys. 251, 237 (2000)

    Article  Google Scholar 

  6. E. Beaurepaire, J.-C. Merle, A. Daunois, J.-Y. Bigot, Phys. Rev. Lett. 76, 4250 (1996)

    Article  ADS  Google Scholar 

  7. H.E. Elsayed-Ali, T. Juhasz, G.O. Smith, W.E. Bron, Phys. Rev. B 43, 4488 (1991)

    Article  ADS  Google Scholar 

  8. J.L. Hostetler, A.N. Smith, D.M. Czajkowsky, P.M. Norris, Appl. Opt. 38, 3614 (1999)

    Article  ADS  Google Scholar 

  9. Y. Giret, A. Gelle, B. Arnaud, Entropy driven atomic motion in laser-excited bismuth. Phys. Rev. Lett. 106, 155503 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. B.I. Cho, K. Engelhorn, A.A. Correa, T. Ogitsu, C.P. Weber, H.J. Lee, J. Feng, P.A. Ni, Y. Ping, A.J. Nelson, D. Prendergast, R.W. Lee, R.W. Falcone, P.A. Heimann, Phys. Rev. Lett. 106, 167601 (2011)

    Article  ADS  Google Scholar 

  12. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1996)

    Google Scholar 

  13. E. Gamaly, The physics of ultra-short laser interaction with solids at non-relativistic intensities. Phys. Rep. 508, 91–243 (2011)

    Article  ADS  Google Scholar 

  14. K. Sokolowski-Tinten, C. Blome, J. Blums, A. Cavalleri, C. Dietrich, A. Tarasevitch, I. Uschmann, E. Foerster, M. Kammler, M. Horn-von-Hoegen, D. von der Linde, Nature 422, 287 (2003)

    Article  ADS  Google Scholar 

  15. G. Sciaini, M. Harb, S.G. Kruglik, T. Payer, C.T. Hebeisen, F.-J. Meyer zu Heringdorf, M. Yamaguchi, M. Horn-von Hoegen, R. Ernstorfer, R.J.D. Miller, Nature 458, 56–59 (2009)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  17. L.D. Landau, Kinetic equation for the Coulomb effect. Phys. Z. Sowietjunion 10, 154 (1936) [Sov Phys. JETP 7, 203–209 (1937)]

    MATH  Google Scholar 

  18. E.G. Gamaly, A.V. Rode, V.T. Tikhonchuk, B. Luther-Davies, Phys. Plasmas 9, 949 (2002)

    Article  ADS  Google Scholar 

  19. E.D. Palik, Handbook of Optical Constants of Solids (Academic Press, San Diego, 1998)

    Google Scholar 

  20. E.G. Gamaly, A.V. Rode, Is the ultrafast melting of bismuth non-thermal? arXiv:0910.2150 (2009) (unpublished)

  21. S.L. Johnson, P. Beaud, C.J. Milne, F.S. Krasniqi, E.S. Zijlstra, M.E. Garcia, M. Kaiser, D. Grolimund, R. Abela, G. Ingold, Phys. Rev. Lett. 100, 155501 (2008)

    Article  ADS  Google Scholar 

  22. T. Garl, Ultrafast dynamics of coherent optical phonons in bismuth. Ph.D. thesis, Ecole Polytechnique, Palaiseau, France (2008)

  23. N.R. Comins, Philos. Mag. 25, 817 (1972)

    Article  ADS  Google Scholar 

  24. J.N. Hodgson, Philos. Mag. 7, 229 (1962)

    Article  ADS  Google Scholar 

  25. O. Landolt-Börnstein, in Numerical Data and Functional Relationships in Science and Technology, Group III, ed. by O. Madelung, M. Schulz, H. Weiss, Semiconductors, vol. 17 (Springer, Berlin, 1983)

    Google Scholar 

  26. L.D. Lide, CRC Handbook of Chemistry and Physics, 88th edn. (CRC Press, Taylor and Francis Group, Boca Raton, 2008)

    Google Scholar 

  27. D. Boschetto, E.G. Gamaly, A.V. Rode, B. Luther-Davies, D. Glijer, T. Garl, O. Albert, A. Rousse, J. Etchepare, Phys. Rev. Lett. 100, 027404 (2008)

    Article  ADS  Google Scholar 

  28. T. Garl, E.G. Gamaly, D. Boschetto, A.V. Rode, B. Luther-Davies, A. Rousse, Phys. Rev. B 78, 134302 (2008)

    Article  ADS  Google Scholar 

  29. A.V. Rode, D. Boschetto, T. Garl, A. Rousse, Transient dielectric function of fs-laser excited bismuth, in Ultrafast Phenomena XVI, ed. by P. Corkum, S. de Silvestri, K.A. Nelson, E. Riedle, R.W. Schoenlein (Springer, New York, 2009)

    Google Scholar 

  30. D. Boschetto, T. Garl, A. Rousse, J. Mod. Opt. 57, 953–958 (2010)

    Article  ADS  Google Scholar 

  31. D. Boschetto, T. Garl, A. Rousse, E.G. Gamaly, A.V. Rode, Appl. Phys. A 92, 873–876 (2008)

    Article  ADS  Google Scholar 

  32. D.M. Fritz, D.A. Reis, B. Adams, R.A. Akre, J. Arthur, C. Blome, P.H. Bucksbaum, A.L. Cavalieri, S. Engemann, S. Fahy, R.W. Falcone, P.H. Fuoss, K.J. Gaffney, M.J. George, J. Hajdu, M.P. Hertlein, P.B. Hillyard, M. Horn-von Hoegen, M. Kammler, J. Kaspar, R. Kienberger, P. Krejcik, S.H. Lee, A.M. Lindenberg, B. McFarland, D. Meyer, T. Montagne, É.D. Murray, A.J. Nelson, M. Nicoul, R. Pahl, D. von der Linde, J.B. Hastings, Ultra-fast bond softening in bismuth: mapping a solid’s interatomic potential with x-rays. Science 315, 633–636 (2007)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge numerous fruitful discussions with D. Boschetto and T. Garl, and helpful comments from B. Luk’yanchuk, K. Sokolowski-Tinten, and L. Zhigilei. This work was supported by the Australian Research Council through a Discovery Scheme, grant #DP0988054, and by a travel grant from the Australian Academy of Science.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. G. Gamaly.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gamaly, E.G., Rode, A.V. Electron–phonon energy relaxation in bismuth excited by ultrashort laser pulse: temperature and fluence dependence. Appl. Phys. A 110, 529–535 (2013). https://doi.org/10.1007/s00339-012-7126-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00339-012-7126-9

Keywords

Navigation