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Thermal boundary conductance across metal-nonmetal interfaces: effects of electron-phonon coupling both in metal and at interface

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Abstract

We theoretically investigate the thermal boundary conductance across metal-nonmetal interfaces in the presence of the electron-phonon coupling not only in metal but also at interface. The thermal energy can be transferred from metal to nonmetal via three channels: (1) the phonon-phonon coupling at interface; (2) the electron-phonon coupling at interface; and (3) the electron-phonon coupling within metal and then subsequently the phonon-phonon coupling at interface. We find that these three channels can be described by an equivalent series-parallel thermal resistor network, based on which we derive out the analytic expression of the thermal boundary conductance. We then exemplify different contributions from each channel to the thermal boundary conductance in three typical interfaces: Pb-diamond, Ti-diamond, and TiN-MgO. Our results reveal that the competition among above channels determines the thermal boundary conductance.

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References

  1. P.L. Kapitza, J. Phys. USSR 4, 181 (1941)

    Google Scholar 

  2. D.G. Cahill et al., J. Appl. Phys. 93, 793 (2003)

    Article  ADS  Google Scholar 

  3. R.J. Stevens, A.N. Smith, P.M. Norris, J. Heat Transfer 127, 315 (2005)

    Article  Google Scholar 

  4. H. Lyeo, D.G. Cahill, Phys. Rev. B 73, 144301 (2006)

    Article  ADS  Google Scholar 

  5. L. Guo et al., J. Heat Transfer 134, 042402 (2012)

    Article  Google Scholar 

  6. P.E. Hopkins et al., Int. J. Thermophys. 28, 947 (2007)

    Article  ADS  Google Scholar 

  7. R.M. Costescu, M.A. Wall, D.G. Cahill, Phys. Rev. B 67, 054302 (2003)

    Article  ADS  Google Scholar 

  8. M. Battayal et al., Diamond Relat. Mater. 17, 1438 (2008)

    Article  ADS  Google Scholar 

  9. R.J. Stoner, H.J. Maris, Phys. Rev. B 48, 16373 (1993)

    Article  ADS  Google Scholar 

  10. R.J. Stoner et al., Phys. Rev. Lett. 68, 1563 (1992)

    Article  ADS  Google Scholar 

  11. E.T. Swartz, R.O. Pohl, Rev. Mod. Phys. 61, 605 (1989)

    Article  ADS  Google Scholar 

  12. D.A. Young, H.J. Maris, Phys. Rev. B 40, 3685 (1989)

    Article  ADS  Google Scholar 

  13. T.S. Basu et al., Appl. Phys. Lett. 103, 083115 (2013)

    Article  ADS  Google Scholar 

  14. K.V. Reich, Prog. Theor. Exp. Phys. 2013, 013I01 (2013)

    Article  Google Scholar 

  15. L. Zhang et al., J. Phys.: Condens. Matter 25, 445801 (2013)

    ADS  Google Scholar 

  16. P.E. Hopkins, P.M. Norris, J. Heat Transfer 131, 043208 (2009)

    Article  Google Scholar 

  17. M.L. Huberman, A.W. Overhauser, Phys. Rev. B 50, 2865 (1994)

    Article  ADS  Google Scholar 

  18. A.V. Sergeev, Phys. Rev. B 58, 10199(R) (1998)

    Article  ADS  Google Scholar 

  19. G.D. Mahan, Phys. Rev. B 79, 075408 (2009)

    Article  ADS  Google Scholar 

  20. J. Ren, J.X. Zhu, Phys. Rev. B 87, 241412(R) (2013)

    Article  ADS  Google Scholar 

  21. P.E. Hopkins, J.L. Kassebaum, P.M. Norris, J. Appl. Phys. 105, 023710 (2009)

    Article  ADS  Google Scholar 

  22. A. Majumdar, P. Reddy, Appl. Phys. Lett. 84, 4768 (2004)

    Article  ADS  Google Scholar 

  23. P. Singh, M. Seong, S. Singh, Appl. Phys. Lett. 102, 181906 (2013)

    Article  ADS  Google Scholar 

  24. J. Ordonez-Miranda, J.J. Alvarado-Gil, R. Yang, Int. J. Thermophys. 34, 1817 (2013)

    Article  ADS  Google Scholar 

  25. J. Ordonez-Miranda, R. Yang, J.J. Alvarado-Gil, J. Appl. Phys. 111, 044319 (2012)

    Article  ADS  Google Scholar 

  26. S. Giordano, F. Manca, Int. J. Heat Mass Transfer 78, 189 (2014)

    Article  Google Scholar 

  27. Y. Wang, X. Ruan, A.K. Roy, Phys. Rev. B 85, 205311 (2012)

    Article  ADS  Google Scholar 

  28. C.L. Phillips, P.S. Crozier, J. Chem. Phys. 131, 074701 (2009)

    Article  ADS  Google Scholar 

  29. Z. Li et al., Nano Lett. 12, 3121 (2012)

    Article  Google Scholar 

  30. J. Ordonez-Miranda, J.J. Alvarado-Gil, R. Yang, J. Appl. Phys. 109, 094310 (2011)

    Article  ADS  Google Scholar 

  31. J. Lombard, F. Detcheverry, S. Merabia, J. Phys.: Condens. Matter 27, 015007 (2015)

    ADS  Google Scholar 

  32. T.Q. Qiu, C.L. Tien, J. Heat Transfer 115, 835 (1993)

    Article  Google Scholar 

  33. J. Fujimoto et al., Phys. Rev. Lett. 53, 1837 (1984)

    Article  ADS  Google Scholar 

  34. H.E. Elsayed-Ali et al., Phys. Rev. Lett. 58, 1212 (1987)

    Article  ADS  Google Scholar 

  35. L. Wang, X. Wei, Int. J. Heat Mass Transfer 51, 1751 (2008)

    Article  MATH  Google Scholar 

  36. L. Wang, X. Zhou, X. Wei, Heat Conduction: Mathematical Models and Analytical Solutions (Springer-Verlag, Berlin, 2008)

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

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  40. P. Vadasz, Int. J. Heat Mass Transfer 50, 4131 (2007)

    Article  MATH  Google Scholar 

  41. M.A. Al-Nimr, Int. J. Thermophys. 18, 1257 (1997)

    Article  ADS  Google Scholar 

  42. U. Mizutani, Introduction to the Electron Theory of Metals (Cambridge University Press, Cambridge, 1995)

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

    Article  ADS  Google Scholar 

  44. V.E. Peletskii, High Temp. High Pressures 17, 111 (1985)

    Google Scholar 

  45. W. Weber, Phys. Rev. B 8, 5093 (1973)

    Article  ADS  Google Scholar 

  46. E.I. Isaev et al., J. Appl. Phys. 101, 123519 (2007)

    Article  ADS  Google Scholar 

  47. W. Spengler et al., Phys. Rev. B 17, 1095 (1978)

    Article  ADS  Google Scholar 

  48. W. Lengauer et al., J. Alloy Compd. 217, 137 (1995)

    Article  Google Scholar 

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Correspondence to Jun Zhou or Jie Ren.

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Li, M., Wang, Y., Zhou, J. et al. Thermal boundary conductance across metal-nonmetal interfaces: effects of electron-phonon coupling both in metal and at interface. Eur. Phys. J. B 88, 149 (2015). https://doi.org/10.1140/epjb/e2015-50771-8

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  • DOI: https://doi.org/10.1140/epjb/e2015-50771-8

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