Abstract
Controlling thermal properties is central to many applications, such as thermoelectric energy conversion and the thermal management of integrated circuits. Progress has been made over the past decade by structuring materials at different length scales, but a clear relationship between structure size and thermal properties remains to be established. The main challenge comes from the unknown intrinsic spectral distribution of energy among heat carriers. Here, we experimentally measure this spectral distribution by probing quasi-ballistic transport near nanostructured heaters down to 30 nm using ultrafast optical spectroscopy. Our approach allows us to quantify up to 95% of the total spectral contribution to thermal conductivity from all phonon modes. The measurement agrees well with multiscale and first-principles-based simulations. We further demonstrate the direct construction of mean free path distributions. Our results provide a new fundamental understanding of thermal transport and will enable materials design in a rational way to achieve high performance.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fnnano.2015.109/MediaObjects/41565_2015_Article_BFnnano2015109_Fig1_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fnnano.2015.109/MediaObjects/41565_2015_Article_BFnnano2015109_Fig2_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fnnano.2015.109/MediaObjects/41565_2015_Article_BFnnano2015109_Fig3_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fnnano.2015.109/MediaObjects/41565_2015_Article_BFnnano2015109_Fig4_HTML.jpg)
Similar content being viewed by others
References
Chu, S. & Majumdar, A. Opportunities and challenges for a sustainable energy future. Nature 488, 294–303 (2012).
Quadrennial Technology Review (US Department of Energy, 2011); available at http://energy.gov/qtr
Majumdar, A. Materials science. Thermoelectricity in semiconductor nanostructures. Science 303, 777–778 (2004).
Bell, L. E. Cooling, heating, generating power, and recovering waste heat with thermoelectric systems. Science 321, 1457–1461 (2008).
Poudel, B. et al. High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys. Science 320, 634–638 (2008).
Biswas, K. et al. High-performance bulk thermoelectrics with all-scale hierarchical architectures. Nature 489, 414–418 (2012).
Lee, W. et al. Heat dissipation in atomic-scale junctions. Nature 498, 209–212 (2013).
Boukai, A. I. et al. Silicon nanowires as efficient thermoelectric materials. Nature 451, 168–171 (2008).
Seol, J. H. et al. Two-dimensional phonon transport in supported graphene. Science 328, 213–216 (2010).
Luckyanova, M. N. et al. Coherent phonon heat conduction in superlattices. Science 338, 936–939 (2012).
Dames, C. Thermal materials: pulling together to control heat flow. Nature Nanotech. 7, 82–83 (2012).
Singh, D. J. Nanostructuring and more. Nature Mater. 7, 616–617 (2008).
Dresselhaus, M. S. et al. New directions for low-dimensional thermoelectric materials. Adv. Mater. 19, 1043–1053 (2007).
Kraemer, D. et al. High-performance flat-panel solar thermoelectric generators with high thermal concentration. Nature Mater. 10, 532–538 (2011).
Yan, H. et al. Programmable nanowire circuits for nanoprocessors. Nature 470, 240–244 (2011).
Yin, X., Ye, Z., Rho, J., Wang, Y. & Zhang, X. Photonic spin Hall effect at metasurfaces. Science 339, 1405–1407 (2013).
Pop, E., Sinha, S. & Goodson, K. E. Heat generation and transport in nanometer-scale transistors. Proc. IEEE 94, 1587–1601 (2006).
Heremans, J. P., Dresselhaus, M. S., Bell, L. E. & Morelli, D. T. When thermoelectrics reached the nanoscale. Nature Nanotech. 8, 471–473 (2013).
Marconnet, A. M., Panzer, M. A. & Goodson, K. E. Thermal conduction phenomena in carbon nanotubes and related nanostructured materials. Rev. Mod. Phys. 85, 1295–1326 (2013).
Ziman, J. M. Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford Classic Texts in the Physical Sciences, 1960).
Yang, F. & Dames, C. Mean free path spectra as a tool to understand thermal conductivity in bulk and nanostructures. Phys. Rev. B 87, 035437 (2013).
Broido, D. A., Malorny, M., Birner, G., Mingo, N. & Stewart, D. A. Intrinsic lattice thermal conductivity of semiconductors from first principles. Appl. Phy. Lett. 91, 231922 (2007).
Esfarjani, K., Chen, G. & Stokes, H. T. Heat transport in silicon from first-principles calculations. Phys. Rev. B 84, 085204 (2011).
Garg, J., Bonini, N., Kozinsky, B. & Marzari, N. Role of disorder and anharmonicity in the thermal conductivity of silicon–germanium alloys: a first-principles study. Phys. Rev. Lett. 106, 045901 (2011).
Lindsay, L., Broido, D. A. & Reinecke, T. L. First-principles determination of ultrahigh thermal conductivity of boron arsenide: a competitor for diamond? Phys. Rev. Lett. 111, 025901 (2013).
Delaire, O. et al. Giant anharmonic phonon scattering in PbTe. Nature Mater. 10, 614–619 (2011).
Ma, J. et al. Glass-like phonon scattering from a spontaneous nanostructure in AgSbTe2 . Nature Nanotech. 8, 445–451 (2013).
Dames, C. & Chen, G. Thermoelectrics Handbook, Macro to Nano (ed. Rowe, D. M.) Ch. 42 (CRC Press, 2006).
Hochbaum, A. I. et al. Enhanced thermoelectric performance of rough silicon nanowires. Nature 451, 163–167 (2008).
Chen, G. Nonlocal and nonequilibrium heat conduction in the vicinity of nanoparticles. J. Heat Transfer 118, 539–545 (1996).
Sverdrup, P. G., Sinha, S., Asheghi, M., Uma, S. & Goodson, K. E. Measurement of ballistic phonon conduction near hotspots in silicon. Appl. Phys. Lett. 78, 3331 (2001).
Minnich, A. J. et al. Thermal conductivity spectroscopy technique to measure phonon mean free paths. Phys. Rev. Lett. 107, 095901 (2011).
Koh, Y. & Cahill, D. Frequency dependence of the thermal conductivity of semiconductor alloys. Phys. Rev. B 76, 075207 (2007).
Regner, K. T., Majumdar, S. & Malen, J. A. Instrumentation of broadband frequency domain thermoreflectance for measuring thermal conductivity accumulation functions. Rev. Sci. Instrum. 84, 064901 (2013).
Johnson, J. A. et al. Direct measurement of room-temperature nondiffusive thermal transport over micron distances in a silicon membrane. Phys. Rev. Lett. 110, 025901 (2013).
Siemens, M. E. et al. Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams. Nature Mater. 9, 26–30 (2009).
Schmidt, A. J., Chen, X. & Chen, G. Pulse accumulation, radial heat conduction, and anisotropic thermal conductivity in pump–probe transient thermoreflectance. Rev. Sci. Instrum. 79, 114902 (2008).
Cahill, D. G. Analysis of heat flow in layered structures for time-domain thermoreflectance. Rev. Sci. Instrum. 75, 5119 (2004).
He, Y., Donadio, D. & Galli, G. Heat transport in amorphous silicon: interplay between morphology and disorder. Appl. Phys. Lett. 98, 144101 (2011).
Chen, G. Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices. Phys. Rev. B 57, 14958–14973 (1998).
Péraud, J-P. M. & Hadjiconstantinou, N. G. Efficient simulation of multidimensional phonon transport using energy-based variance-reduced Monte Carlo formulations. Phys. Rev. B 84, 205331 (2011).
Maznev, A. A., Johnson, J. A. & Nelson, K. A. Onset of nondiffusive phonon transport in transient thermal grating decay. Phys. Rev. B 84, 195206 (2011).
Minnich, A. J. Determining phonon mean free paths from observations of quasiballistic thermal transport. Phys. Rev. Lett. 109, 205901 (2012).
Collins, K. C. et al. Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation. J. Appl. Phys. 114, 104302 (2013).
Ding, D., Chen, X. & Minnich, A. J. Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations. Appl. Phys. Lett. 104, 143104 (2014).
Zeng, L. & Chen, G. Disparate quasiballistic heat conduction regimes from periodic heat sources on a substrate. J. Appl. Phys. 116, 064307 (2014).
Wilson, R. B. & Cahill, D. G. Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments. Nature Commun. 5, 5075 (2014).
Goodson, K. E. & Ju, Y. S. Heat conduction in novel electronic films. Annu. Rev. Mater. Sci. 29, 261–293 (1999).
Cahill, D. G. et al. Nanoscale thermal transport. II. 2003–2012. Appl. Phys. Rev. 1, 011305 (2014).
Hu, Y., Kuemmeth, F., Lieber, C. M. & Marcus, C. M. Hole spin relaxation in Ge–Si core–shell nanowire qubits. Nature Nanotech. 7, 47–50 (2012).
Grant, M. & Boyd, S. in Recent Advances in Learning and Control (eds Blondel, V., Boyd, S. & Kimura, H.) (Lecture Notes in Control and Information Sciences, Springer-Verlag, 2008).
Grant, M. & Boyd, S. CVX: Matlab software for disciplined convex programming, version 2.0 beta (CVX Research, 2013); available at http://cvxr.com/cvx
Acknowledgements
The authors thank J. Garg for providing DFT data on Si0.992Ge0.008, and D. Broido, N.G. Hadjiconstantinou, A. Marconnet, J.K. Tong, J-P. Peraud, W. Dai, A. Maznev, K. Nelson, J. Cuffe, M. Luckyanova and K. Collins for discussions. This material is based on work supported as part of the ‘Solid State Solar-Thermal Energy Conversion Center (S3TEC)’, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences (grant no. DE-SC0001299/DE-FG02-09ER46577). Y.H. is partially supported by the Battelle/MIT Fellowship.
Author information
Authors and Affiliations
Contributions
Y.H. and G.C. developed the concept. Y.H. prepared the samples and performed the experiments. L.Z. performed the Monte Carlo simulation. Y.H. performed the numerical calculations on convex optimizations. All authors discussed the results and commented on the manuscript. G.C. directed the research.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary information
Supplementary information (PDF 960 kb)
Rights and permissions
About this article
Cite this article
Hu, Y., Zeng, L., Minnich, A. et al. Spectral mapping of thermal conductivity through nanoscale ballistic transport. Nature Nanotech 10, 701–706 (2015). https://doi.org/10.1038/nnano.2015.109
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nnano.2015.109
This article is cited by
-
Correlating activities and defects in (photo)electrocatalysts using in-situ multi-modal microscopic imaging
Nature Communications (2024)
-
Quantifying spectral thermal transport properties in framework of molecular dynamics simulations: a comprehensive review
Rare Metals (2023)
-
Effects of Chain Length, Stretching, and Molecular Groups on the Thermal Conductivity of Single Crosslinked Epoxy Resin Chains
Journal of Electronic Materials (2023)
-
Research progress of filled-type high-thermal-conductivity flexible polyimide composites: a review
Journal of Materials Science (2023)
-
Nanoscale imaging of phonon dynamics by electron microscopy
Nature (2022)