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Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams

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Abstract

Fourier theory of thermal transport considers heat transport as a diffusive process where energy flow is driven by a temperature gradient. However, this is not valid at length scales smaller than the mean free path for the energy carriers in a material, which can be hundreds of nanometres in crystalline materials at room temperature. In this case, heat flow will become ‘ballistic’—driven by direct point-to-point transport of energy quanta 1. Past experiments have demonstrated size-dependent ballistic thermal transport through nanostructures such as thin films, superlattices, nanowires and carbon nanotubes1,2,3,4,5,6,7,8. The Fourier law should also break down in the case of heat dissipation from a nanoscale heat source into the bulk. However, despite considerable theoretical discussion and direct application to thermal management in nanoelectronics2, nano-enabled energy systems9,10 and nanomedicine11, this non-Fourier heat dissipation has not been experimentally observed so far. Here, we report the first observation and quantitative measurements of this transition from diffusive to ballistic thermal transport from a nanoscale hotspot, finding a significant (as much as three times) decrease in energy transport away from the nanoscale heat source compared with Fourier-law predictions.

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Figure 1: Experimental set-up for measuring thermal transport across a nanoscale interface.
Figure 2: Analytical prediction of the Fourier and ballistic components of the resistivity for thermal transport away from a half-cylinder of diameter L.
Figure 3: Normalized dynamic soft X-ray diffraction signal for Ni lines on sapphire.
Figure 4: Measured effective thermal resistivity for nickel nanostructures of width L deposited on fused-silica and sapphire substrates.

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Acknowledgements

This work was financially supported by the DOE Division of Chemical Sciences, Geosciences, and Biosciences and the National Science Foundation Engineering Research Center for Extreme Ultraviolet Science and Technology. R.Y. acknowledges support from NSF/CAREER (#0846561) and AFOSR/DCT (#FA9550-08-1-0078) programmes.

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Authors and Affiliations

  1. JILA, University of Colorado at Boulder, Boulder, Colorado 80309, USA

    Mark E. Siemens, Qing Li, Margaret M. Murnane & Henry C. Kapteyn

  2. Department of Mechanical Engineering, University of Colorado, Boulder, Colorado 80309, USA

    Ronggui Yang

  3. Department of Chemistry, MIT, Cambridge, Massachusetts 02139, USA

    Keith A. Nelson

  4. Lawrence Berkeley Labs and Center for X-ray Optics, Berkeley, California 94720, USA

    Erik H. Anderson

Authors
  1. Mark E. Siemens
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  2. Qing Li
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  3. Ronggui Yang
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  4. Keith A. Nelson
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  5. Erik H. Anderson
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  6. Margaret M. Murnane
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  7. Henry C. Kapteyn
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Contributions

M.E.S., R.Y., Q.L., M.M.M. and H.C.K., planned the experiment. The samples were designed and fabricated by E.H.A. Experiments were carried out by M.E.S. and Q.L. All authors discussed the results, analysed the data and contributed to manuscript preparation.

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Correspondence to Mark E. Siemens.

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Siemens, M., Li, Q., Yang, R. et al. Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams. Nature Mater 9, 26–30 (2010). https://doi.org/10.1038/nmat2568

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