Article | Published:

Precise control of thermal conductivity at the nanoscale through individual phonon-scattering barriers

Nature Materials volume 9, pages 491495 (2010) | Download Citation

Abstract

The ability to precisely control the thermal conductivity (κ) of a material is fundamental in the development of on-chip heat management or energy conversion applications. Nanostructuring permits a marked reduction of κ of single-crystalline materials, as recently demonstrated for silicon nanowires. However, silicon-based nanostructured materials with extremely low κ are not limited to nanowires. By engineering a set of individual phonon-scattering nanodot barriers we have accurately tailored the thermal conductivity of a single-crystalline SiGe material in spatially defined regions as short as 15 nm. Single-barrier thermal resistances between 2 and 4×10−9 m2 K W−1 were attained, resulting in a room-temperature κ down to about 0.9 W m−1 K−1, in multilayered structures with as little as five barriers. Such low thermal conductivity is compatible with a totally diffuse mismatch model for the barriers, and it is well below the amorphous limit. The results are in agreement with atomistic Green’s function simulations.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    et al. Nanoscale thermal transport. J. Appl. Phys. 93, 793–818 (2003).

  2. 2.

    Nanoscale thermal transport and microrefrigerators on a chip. Proc. IEEE 94, 1613–1638 (2006).

  3. 3.

    et al. On-chip cooling by superlattice-based thin-film thermoelectrics. Nature Nanotech. 4, 235–238 (2008).

  4. 4.

    et al. Eras: InGaAs/InGaAlAs superlattice thin-film power generator array. Appl. Phys. Lett. 88, 113502 (2006).

  5. 5.

    et al. Thermal conductivity reduction and thermoelectric figure of merit increase by embedding nanoparticles in crystalline semiconductors. Phys. Rev. Lett. 96, 045901 (2006).

  6. 6.

    , & Thermal conductivity of Si–Ge superlattices. Appl. Phys. Lett. 70, 2957–2959 (1997).

  7. 7.

    & Effect of nanodot areal density and period on thermal conductivity in SiGe/Si nanodot superlattices. Appl. Phys. Lett. 92, 053112 (2008).

  8. 8.

    et al. Ultralow thermal conductivity in disordered, layered WSe2 crystals. Science 315, 351–353 (2007).

  9. 9.

    , & Lower limit to the thermal conductivity of disordered crystals. Phys. Rev. B 46, 6131–6140 (1992).

  10. 10.

    & Thermal boundary resistance. Rev. Mod. Phys. 61, 605–668 (1989).

  11. 11.

    et al. Ballistic-phonon heat conduction at the nanoscale as revealed by time-resolved X-ray diffraction and time-domain thermoreflectance. Phys. Rev. B 76, 075337 (2007).

  12. 12.

    , , & Composition of self-assembled Ge/Si islands in single and multiple layers. Appl. Phys. Lett. 81, 2614–2616 (2002).

  13. 13.

    et al. Cross-plane thermal conductivity of self-assembled Ge quantum dot superlattices. Phys. Rev. B 67, 165333 (2003).

  14. 14.

    et al. Electrical and thermal conductivity of Ge/Si quantum dot superlattices. J. Electrochem. Soc. 152, G432–G435 (2005).

  15. 15.

    et al. Cross-plane thermal conductivity reduction of vertically uncorrelated Ge/Si quantum dot superlattices. Appl. Phys. Lett. 93, 013112 (2008).

  16. 16.

    , , & Optical heterodyne sampling device. Patent WO/2007/045773 (2006).

  17. 17.

    et al. High thermal conductivity of a hydrogenated amorphous silicon film. Phys. Rev. Lett. 102, 035901 (2009).

  18. 18.

    et al. Coherent phonons in Si/SiGe superlattices. Phys. Rev. B 75, 195309 (2007).

  19. 19.

    , & Signal analysis and characterization of experimental setup for the transient thermoreflectance technique. Rev. Sci. Instrum. 77, 084901 (2006).

  20. 20.

    et al. Thermal conductivity imaging at micrometre-scale resolution for combinatorial studies of materials. Nature Mater. 3, 298–301 (2004).

  21. 21.

    Analysis of heat flow in layered structures for time-domain thermoreflectance. Rev. Sci. Instrum. 75, 5119–5122 (2004).

  22. 22.

    , & Pulse accumulation, radial heat conduction, and anisotropic thermal conductivity in pump–probe transient thermoreflectance. Rev. Sci. Instrum. 79, 114902 (2008).

  23. 23.

    et al. Cross-plan Si/SiGe superlattice acoustic and thermal properties measurement by picosecond ultrasonics. J. Appl. Phys. 101, 013705 (2007).

  24. 24.

    , , & Characterization of mechanical and thermal properties using ultrafast optical metrology. MRS Bull. 31, 607–613 (2006).

  25. 25.

    et al. Comparison of the 3 omega method and time-domain thermoreflectance for measurements of the cross-plane thermal conductivity of epitaxial semiconductors. J. Appl. Phys. 105, 054303 (2009).

  26. 26.

    Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices. Phys. Rev. B 57, 14958–14973 (1998).

  27. 27.

    Calculation of Si nanowire thermal conductivity using complete phonon dispersion relations. Phys. Rev. B 68, 113308 (2003).

  28. 28.

    , & Thermal conductivity of a-Si:H thin films. Phys. Rev. B 50, 6077–6081 (1994).

  29. 29.

    et al. Silicon nanowires as efficient thermoelectric materials. Nature 451, 168–171 (2008).

  30. 30.

    Desperately seeking silicon. Nature 451, 132–133 (2008).

  31. 31.

    et al. Enhanced thermoelectric performance of rough silicon nanowires. Nature 451, 163–167 (2008).

  32. 32.

    & Minimum thermal conductivity of superlattices. Phys. Rev. Lett. 84, 927–930 (2000).

  33. 33.

    Lattice thermal conductivity reduction and phonon localizationlike behaviour in superlattice structures. Phys. Rev. B 61, 3091–3097 (2000).

  34. 34.

    et al. Thermal conductivity in strain symmetrized Si/Ge superlattices on Si(111). Appl. Phys. Lett. 83, 4184–4186 (2003).

  35. 35.

    Lattice thermal conductivity of disordered semiconductor alloys at high temperatures. Phys. Rev. 131, 1906–1911 (1963).

  36. 36.

    et al. Nanoparticle-in-alloy approach to efficient thermoelectrics: Silicides in SiGe. Nano Lett. 9, 711–715 (2009).

  37. 37.

    & Thermal conductivity of amorphous solids above the plateau. Phys. Rev. B 35, 4067–4073 (1987).

  38. 38.

    & Phonon transport in nanowires coated with an amorphous material: An atomistic green’s function approach. Phys. Rev. B 68, 245406 (2003).

  39. 39.

    , & Simulation of phonon transport across a non-polar nanowire junction using an atomistic green’s function method. Phys. Rev. B 76, 195429 (2007).

  40. 40.

    , & Phonon transport in isotope-disordered carbon and boron-nitride nanotubes: Is localization observable? Phys. Rev. Lett. 101, 165502 (2008).

  41. 41.

    New empirical model for the structural properties of silicon. Phys. Rev. Lett. 56, 632–635 (1986).

  42. 42.

    & Thermal resistivity of Si–Ge alloys by molecular-dynamics simulation. J. Appl. Phys. 103, 113524 (2008).

Download references

Acknowledgements

This work was supported by the EU (Nano-thermoelectrics, IRG 39302), ANR (Thermaescape, ANR-06-NANO-054-01, Accatone), (EThNA, ANR-06-NANO-020), (OCTE, ANR-06-BLAN-129), the Conseil Régional d’Aquitaine (projet Photon et Phonons, 2007), the DFG (SPP1386, RA 1634/5-1), the European Regional Development Fund (n. 4212/09-13) and the State of Saxony. We acknowledge A. Hiess, Ch. Mickel, G. Scheider, T. Dienel, C. C. Bof Bufon, S. Harazim, D. Grimm, S. Baunack and B. Eichler for experimental assistance, B. Rellinghaus for access to the Tecnai T20 TEM and A. Rotondi (Univ. Pavia) for insightful discussions on error propagation in the 3ω method measurements.

Author information

Affiliations

  1. CPMOH, Université Bordeaux-CNRS, 351 cours de la Libération, 33405 Talence, France

    • G. Pernot
    • , J. M. Rampnoux
    •  & S. Dilhaire
  2. Institute for Integrative Nanosciences, IFW Dresden, Helmholtzstr. 20, 01069 Dresden, Germany

    • M. Stoffel
    • , F. Pezzoli
    • , P. Chen
    • , J. Schumann
    • , I. Mönch
    • , Ch. Deneke
    • , O. G. Schmidt
    •  & A. Rastelli
  3. LITEN, CEA-Grenoble, 17 rue des Martyrs, Grenoble 38054, France

    • I. Savic
    • , G. Savelli
    • , S. Wang
    • , M. Plissonnier
    •  & N. Mingo
  4. Fraunhofer-IPM, Heidenhostraße 8, 79110 Freiburg, Germany

    • A. Jacquot
  5. Max-Planck-Institut für Festkörperforschung, Heisenbergstr. 1, 70569 Stuttgart, Germany

    • U. Denker
  6. Jack Baskin School of Engineering, The University of California at Santa Cruz, 1156 High Street, Santa Cruz, California 95064, USA

    • N. Mingo

Authors

  1. Search for G. Pernot in:

  2. Search for M. Stoffel in:

  3. Search for I. Savic in:

  4. Search for F. Pezzoli in:

  5. Search for P. Chen in:

  6. Search for G. Savelli in:

  7. Search for A. Jacquot in:

  8. Search for J. Schumann in:

  9. Search for U. Denker in:

  10. Search for I. Mönch in:

  11. Search for Ch. Deneke in:

  12. Search for O. G. Schmidt in:

  13. Search for J. M. Rampnoux in:

  14. Search for S. Wang in:

  15. Search for M. Plissonnier in:

  16. Search for A. Rastelli in:

  17. Search for S. Dilhaire in:

  18. Search for N. Mingo in:

Contributions

G.P. and J.M.R. carried out the HPTR measurements and analysis; M.S., U.D. and O.G.S. were responsible for the sample growth; G.S. and M.P. metallized the samples for HPTR. F.P. and M.S. carried out AFM measurements; F.P., P.C. and A.R. carried out the 3ω measurements and analysis, on a set-up realized by A.J.; P.C., F.P., J.S. and I.M. processed and characterized the samples for 3ω measurements; C.D. carried out the TEM measurements; I.S. carried out the Green’s function calculation. I.S., S.W. and N.M. developed the theory. A.R., S.D. and N.M. coordinated the work and wrote the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to A. Rastelli or S. Dilhaire or N. Mingo.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    Supplementary Information

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nmat2752

Further reading