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Dimensional crossover of thermal transport in few-layer graphene

Abstract

Graphene1, in addition to its unique electronic2,3 and optical properties4, reveals unusually high thermal conductivity5,6. The fact that the thermal conductivity of large enough graphene sheets should be higher than that of basal planes of bulk graphite was predicted theoretically by Klemens7. However, the exact mechanisms behind the drastic alteration of a material’s intrinsic ability to conduct heat as its dimensionality changes from two to three dimensions remain elusive. The recent availability of high-quality few-layer graphene (FLG) materials allowed us to study dimensional crossover experimentally. Here we show that the room-temperature thermal conductivity changes from 2,800 to 1,300 W m−1 K−1 as the number of atomic planes in FLG increases from 2 to 4. We explained the observed evolution from two dimensions to bulk by the cross-plane coupling of the low-energy phonons and changes in the phonon Umklapp scattering. The obtained results shed light on heat conduction in low-dimensional materials and may open up FLG applications in thermal management of nanoelectronics.

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Figure 1: Samples and measurement procedure.
Figure 2: Experimental data.
Figure 3: Theoretical interpretation.

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References

  1. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

    CAS  Google Scholar 

  2. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    CAS  Google Scholar 

  3. Zhang, Y. B., Tan, Y. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

    CAS  Google Scholar 

  4. Nair, R. R. et al. Fine structure constant defines visual transparency of graphene. Science 320, 1308 (2008).

    Article  CAS  Google Scholar 

  5. Balandin, A. A. et al. Superior thermal conductivity of single-layer graphene. Nano Lett. 8, 902–907 (2008).

    Article  CAS  Google Scholar 

  6. Ghosh, S. et al. Extremely high thermal conductivity of graphene: Prospects for thermal management applications in nanoelectronic circuits. Appl. Phys. Lett. 92, 151911 (2008).

    Article  Google Scholar 

  7. Klemens, P. G. Theory of the a-plane thermal conductivity of graphite. J. Wide Bandgap Mater. 7, 332–339 (2000).

    Article  CAS  Google Scholar 

  8. Lepri, S., Livi, R. & Politi, A. Thermal conduction in classical low-dimensional lattices. Phys. Rep. 377, 1–80 (2003).

    Article  CAS  Google Scholar 

  9. Balandin, A. A. Chill out: New materials and designs can keep chips cool. IEEE Spectr. 35–39 (2009).

  10. Narayan, O. & Ramaswamy, S. Anomalous heat conduction in one-dimensional momentum-conserving systems. Phys. Rev. Lett. 89, 200601 (2002).

    Article  Google Scholar 

  11. Chang, C. W., Okawa, D., Garcia, H., Majumdar, A. & Zettl, A. Breakdown of Fourier’s law in nanotube thermal conductors. Phys. Rev. Lett. 101, 075903 (2008).

    Article  CAS  Google Scholar 

  12. Basile, G., Bernardin, C. & Olla, S. Momentum conserving model with anomalous thermal conductivity in low dimensional systems. Phys. Rev. Lett. 96, 204303 (2006).

    Article  Google Scholar 

  13. Yang, L., Grassberger, P. & Hu, B. Dimensional crossover of heat conduction in low dimensions. Phys. Rev. E 74, 062101 (2006).

    Article  CAS  Google Scholar 

  14. Che, J., Çağin, T. & Goddard, W. A. III Thermal conductivity of carbon nanotubes. Nanotechnology 11, 65–69 (2000).

    Article  CAS  Google Scholar 

  15. Mingo, N. & Broido, D. A. Carbon nanotube ballistic thermal conductance and its limits. Phys. Rev. Lett. 95, 096105 (2005).

    Article  CAS  Google Scholar 

  16. Kim, P., Shi, L., Majumdar, A. & McEuen, P. L. Thermal transport measurements of individual multiwalled nanotubes. Phys. Rev. Lett. 87, 215502 (2001).

    Article  CAS  Google Scholar 

  17. Srivastava, G. P. The Physics of Phonons (IOP Publishing Ltd, 1990).

    Google Scholar 

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

    Article  CAS  Google Scholar 

  19. Nika, D. L., Ghosh, S., Pokatilov, E. P. & Balandin, A. A. Lattice thermal conductivity of graphene flakes: Comparison with bulk graphite. Appl. Phys. Lett. 94, 203103 (2009).

    Article  Google Scholar 

  20. Bao, W. Z. et al. Controlled ripple texturing of suspended graphene and ultrathin graphene membranes. Nature Nanotech. 4, 562–566 (2009).

    Article  CAS  Google Scholar 

  21. Ferrari, A. C. et al. Raman spectrum of graphene and graphene layers. Phys. Rev. Lett. 97, 187401 (2006).

    Article  CAS  Google Scholar 

  22. Calizo, I., Balandin, A. A., Bao, W., Miao, F. & Lau, C. N. Temperature dependence of the Raman spectra of graphene and graphene multi-layers. Nano Lett. 7, 2645–2649 (2007).

    Article  CAS  Google Scholar 

  23. Nika, D. L., Pokatilov, E. P., Askerov, A. S. & Balandin, A. A. Phonon thermal conduction in graphene: Role of Umklapp and edge roughness scattering. Phys. Rev. B 79, 155413 (2009).

    Article  Google Scholar 

  24. Hu, J., Ruan, X. & Chen, Y. P. Thermal conductivity and thermal rectification in graphene nanoribbons: A molecular dynamics study. Nano Lett. 9, 2730–2735 (2009).

    Article  CAS  Google Scholar 

  25. Mounet, N. & Marzari, N. First-principles determination of the structural, vibrational and thermodynamic properties of diamond, graphite, and derivatives. Phys. Rev. B 71, 205214 (2005).

    Article  Google Scholar 

  26. Berber, S., Kwon, Y-K. & Tomanek, D. Unusually high thermal conductivity of carbon nanotubes. Phys. Rev. Lett. 84, 4613–4616 (2000).

    Article  CAS  Google Scholar 

  27. Dawlaty, J. M., Shivaraman, S., Chandrashekhar, M., Rana, F. & Spencer, M. G. Measurement of ultrafast carrier dynamics in epitaxial graphene. Appl. Phys. Lett. 92, 042116 (2008).

    Article  Google Scholar 

  28. Bistritzer, R. & MacDonald, A. H. Electronic cooling in graphene. Phys. Rev. Lett. 102, 206410 (2009).

    Article  CAS  Google Scholar 

  29. Mohiuddin, T. M. G. et al. Uniaxial strain in graphene by Raman spectroscopy: G peak splitting, Grüneisen parameters, and sample orientation. Phys. Rev. B 79, 205433 (2009).

    Article  Google Scholar 

  30. Berciaud, S., Ryu, S., Brus, L. E. & Heinz, T. F. Probing the intrinsic properties of exfoliated graphene: Raman spectroscopy of free-standing monolayers. Nano Lett. 9, 346–352 (2009).

    Article  CAS  Google Scholar 

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Acknowledgements

A.A.B. acknowledges support from ONR through award N00014-10-1-0224, ARL/AFOSR through award FA9550-08-1-0100 and SRC - DARPA through the FCRP Center on Functional Engineered Nano Architectonics (FENA) and the Interconnect Focus Center (IFC). C.N.L. and W.B. acknowledge support from ONR/DMEA H94003-09-2-0901, NSF/CBET 0854554 and GRC.

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Contributions

A.A.B. conceived the experiment, led the data analysis, proposed theoretical interpretation and wrote the manuscript; S.G. carried out Raman measurements; S.S. carried out finite-element modelling for thermal data extraction; W.B. prepared most of the samples; C.N.L. supervised the sample fabrication; D.L.N. and E.P.P. assisted with theory development and carried out computer simulations of thermal conductivity.

Corresponding author

Correspondence to Alexander A. Balandin.

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The authors declare no competing financial interests.

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Ghosh, S., Bao, W., Nika, D. et al. Dimensional crossover of thermal transport in few-layer graphene. Nature Mater 9, 555–558 (2010). https://doi.org/10.1038/nmat2753

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