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Quantized thermal transport across contacts of rough surfaces

Nature Materials volume 12, pages 59–65 (2013)Cite this article

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Abstract

Heat transport across interfaces is often discussed in terms of the transmission probability of the heat-carrying phonons through the contact zone. Although interface roughness influences the true contact area and affects phonon scattering within the contact zone, its effect on nanoscale heat transport remains poorly understood. Here, we report experimental data on the pressure dependence of thermal transport across polished nanoscale contacts. The data can be quantitatively explained by a model of thermal conductance across interfaces that incorporates the effect of nanoscale roughness through the quantized thermal conductance across individual atomic-scale contacts within the contact zone.

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Figure 1: Pressure dependence of the contact between two bodies.
Figure 2: Typical experimental data for loading and unloading a contact.
Figure 3: Pressure dependence of the thermal interface conductance for various tips.

References

  1. Schwartz, E. & Pohl, R. Thermal boundary resistance. Rev. Mod. Phys. 61, 605–668 (1989).

    Article  Google Scholar 

  2. Dames, C. & Chen, G. Theoretical phonon thermal conductivity of Si–Ge superlattice nanowires. J. Appl. Phys. 95, 682–693 (2004).

    Article  CAS  Google Scholar 

  3. Kechrakos, D. The role of interface disorder in the thermal boundary conductivity between two crystals. J. Phys. Condens. Matter 3, 1443–1452 (1991).

    Article  Google Scholar 

  4. Stevens, R. J., Zhigilei, L. V. & Norris, P. M. Effects of temperature and disorder on thermal boundary conductance at solid–solid interfaces: Nonequilibrium molecular dynamics simulations. Int. J. Heat Mass Trans. 50, 3977–3989 (2007).

    Article  Google Scholar 

  5. Patton, K. R. & Geller, M. R. Thermal transport through a mesoscopic weak link. Phys. Rev. B 64, 155320 (2001).

    Article  Google Scholar 

  6. Prasher, R. Acoustic mismatch model for thermal contact resistance of van der Waals contacts. Appl. Phys. Lett. 94, 041905 (2009).

    Article  Google Scholar 

  7. Persson, B. N. J., Volokitin, A. I. & Ueba, H. Phononic heat transfer across an interface: thermal boundary resistance. J. Phys. Condens. Matter 23, 045009 (2011).

    Article  CAS  Google Scholar 

  8. Greenwood, J. A. & Williamson, J. B. P. Contact of nominally flat surfaces. Proc. R. Soc. A 295, 300–319 (1966).

    Article  CAS  Google Scholar 

  9. Persson, B. N. J. Elastoplastic contact between randomly rough surfaces. Phys. Rev. Lett. 87, 116101 (2001).

    Article  CAS  Google Scholar 

  10. Bhushan, B. Introduction to Tribology (Wiley, 2002).

    Google Scholar 

  11. Gmelin, E., Asen-Palmer, M., Reuther, M. & Villar, R. Thermal boundary resistance of mechanical contacts between solids at sub-ambient temperatures. J. Phys. D 32, R19–R43 (1999).

    Article  CAS  Google Scholar 

  12. Persson, B., Lorenz, B. & Volokitin, A. Heat transfer between elastic solids with randomly rough surfaces. Eur. Phys. J. E 31, 3–24 (2010).

    Article  CAS  Google Scholar 

  13. Luan, B. & Robbins, M. O. The breakdown of continuum models for mechanical contacts. Nature 435, 929–932 (2005).

    Article  CAS  Google Scholar 

  14. Knippenberg, M. T., Mikulski, P. T., Dunlap, B. I. & Harrison, J. A. Atomic contributions to friction and load for tip self-assembled monolayers interactions. Phys. Rev. B 78, 235409 (2008).

    Article  Google Scholar 

  15. Mo, Y., Turner, K. T. & Szlufarska, I. Friction laws at the nanoscale. Nature 457, 1116–1119 (2009).

    Article  CAS  Google Scholar 

  16. Cheng, S. & Robbins, M. Defining contact at the atomic scale. Tribol. Lett. 39, 329–348 (2010).

    Article  Google Scholar 

  17. Carpick, R. W. & Salmeron, M. Scratching the surface: Fundamental investigations of tribology with atomic force microscopy. Chem. Rev. 97, 1163–1194 (1997).

    Article  CAS  Google Scholar 

  18. Gao, G., Cannara, R. J., Carpick, R. W. & Harrison, J. Atomic-scale friction on diamond: A comparison of different sliding directions on (001) and (111) surfaces using MD and AFM. Langmuir 23, 5394–5405 (2007).

    Article  CAS  Google Scholar 

  19. Mo, Y. & Szlufarska, I. Roughness picture of friction in dry nanoscale contacts. Phys. Rev. B 81, 035405 (2010).

    Article  Google Scholar 

  20. Gao, J., Luedtke, W. D., Gourdon, D., Ruths, M., Israelachvili, J. N. & Landman, U. Frictional forces and Amontons law: From the molecular to the macroscopic scale. J. Phys. Chem. B 108, 3410–3427 (2004).

    Article  CAS  Google Scholar 

  21. Pendry, J. B. Quantum limits to the flow of information and entropy. J. Phys. A 16, 2161–2171 (1983).

    Article  Google Scholar 

  22. Maynard, R. & Akkermans, E. Thermal conductance and giant fluctuations in one-dimensional disordered systems. Phys. Rev. B 32, 5440–5442 (1985).

    Article  CAS  Google Scholar 

  23. Rego, L. G. C. & Kirczenow, G. Quantized thermal conductance of dielectric quantum wires. Phys. Rev. Lett. 81, 232–235 (1998).

    Article  CAS  Google Scholar 

  24. Schwab, K., Henriksen, E. A., Worlock, J. M. & Roukes, M. L. Measurement of the quantum of thermal conductance. Nature 404, 974–977 (2000).

    Article  CAS  Google Scholar 

  25. Hinz, M., Marti, O., Gotsmann, B., Lantz, M. A. & Dürig, U. High resolution vacuum scanning thermal microscopy of HfO2 and SiO2 . Appl. Phys. Lett. 92, 043122 (2008).

    Article  Google Scholar 

  26. Chapuis, P-O., Greffet, J-J., Joulain, K. & Volz, S. Heat transfer between a nano-tip and a surface. Nanotechnology 17, 2978–2981 (2006).

    Article  CAS  Google Scholar 

  27. Gotsmann, B. & Lantz, M. A. Atomistic wear in a single asperity sliding contact. Phys. Rev. Lett. 101, 125501 (2008).

    Article  Google Scholar 

  28. Bhaskaran, H. et al. Ultra-low nanoscale wear through atom-by-atom attrition in silicon-containing diamond-like-carbon. Nature Nanotech. 5, 181–185 (2010).

    Article  CAS  Google Scholar 

  29. Friedmann, T. A. et al. Thick stress-free amorphous-tetrahedral carbon films with hardness near that of diamond. Appl. Phys. Lett. 71, 3820–3822 (1997).

    Article  CAS  Google Scholar 

  30. Moseler, M., Gumbsch, P., Casiraghi, C., Ferrari, A. C. & Robertson, J. The ultrasmoothness of diamond-like carbon surfaces. Science 309, 1545–1548 (2005).

    Article  CAS  Google Scholar 

  31. Schwarz, U. D. A generalized analytical model for the elastic deformation of an adhesive contact between a sphere and a flat surface. J. Colloid Interface Sci. 261, 99–106 (2003).

    Article  CAS  Google Scholar 

  32. Andersson, S. & Backstrom, G. The thermal conductivity and heat capacity of single-crystal Si under hydrostatic pressure. J. Phys. Condens. Matter 21, 3727–3735 (1988).

    CAS  Google Scholar 

  33. Andersson, S. & Dzhavadov, L. Thermal conductivity and heat capacity of amorphous SiO2: Pressure and volume dependence. J. Phys. Condens. Matter 4, 6209–6216 (1992).

    Article  CAS  Google Scholar 

  34. Balandin, A. A., Shamsa, M., Liu, W. L., Casiraghi, C. & Ferrari, A. C. Thermal conductivity of ultrathin tetrahedral amorphous carbon films. Appl. Phys. Lett. 93, 043115 (2008).

    Article  Google Scholar 

  35. Grierson, D. S. et al. Thermal stability and rehybridization of carbon bonding in tetrahedral amorphous carbon. J. Appl. Phys. 107, 033523 (2010).

    Article  Google Scholar 

  36. Chen, G. Nanoscale Energy Transport and Conversion (Oxford Univ. Press, 2005).

    Google Scholar 

  37. Dames, C. & Chen, G. in Thermoelectrics Handbook: Macro to Nano (ed. Rowe, D. M.) (CRC, 2006).

    Google Scholar 

  38. Venkatesh, R., Amrit, J., Chalopin, Y. & Volz, S. Thermal resistance of metal nanowire junctions in the ballistic regime. Phys. Rev. B 83, 115425 (2011).

    Article  Google Scholar 

  39. Diao, J., Srivastava, D. & Menon, M. Molecular dynamics simulations of carbon nanotube/silicon interfacial thermal conductance. J. Chem. Phys. 128, 164708 (2008).

    Article  Google Scholar 

  40. Hsieh, W-P., Lyons, A. S., Pop, E., Keblinski, P. & Cahill, D. G. Pressure tuning of the thermal conductance of weak interfaces. Phys. Rev. B 84, 184107 (2012).

    Article  Google Scholar 

  41. Menges, F., Riel, H., Stemmer, A. & Gotsmann, B. Quantitative thermometry of nanoscale hot spots. Nano Lett. 12, 596–601 (2012).

    Article  CAS  Google Scholar 

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Acknowledgements

We thank T. A. Friedmann and R. W. Carpick for the taC sample and background information on the material. We are grateful to U. Drechsler and M. Despont for fabricating the heatable silicon tips. Furthermore, continuous support from E. Eleftheriou, H. Riel and W. Riess is gratefully acknowledged. We thank C. Bolliger for proofreading the manuscript, D. Cahill for sharing a manuscript before publication and C. Dames for stimulating discussions.

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Authors and Affiliations

  1. IBM Research—Zurich, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland

    B. Gotsmann & M. A. Lantz

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  1. B. Gotsmann
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  2. M. A. Lantz
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Contributions

B.G. and M.L. designed and ran the experiments and analysed the data. B.G. developed the model and performed the calculations. B.G. and M.L. wrote the manuscript.

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Correspondence to B. Gotsmann.

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The authors declare no competing financial interests.

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Gotsmann, B., Lantz, M. Quantized thermal transport across contacts of rough surfaces. Nature Mater 12, 59–65 (2013). https://doi.org/10.1038/nmat3460

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