Dimensional crossover of thermal transport in few-layer graphene

Dimensional crossover of thermal transport in few-layer graphene

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Thus, we have experimentally demonstrated 2D → 3D- dimensional crossover of heat conduction in FLG. We related the increased thermal conductivity of graphene to the fundamental properties of 2D systems and determined the physical mechanisms behind the thermal conductivity reduction in few-atom-thick crystals. The obtained results are important for the proposed graphene and FLG applications in nanoelectronics.

Methods

The trenches in the Si/SiO wafers were made using reactive ion etching (STS). The evaporated metal heat sinks ensured proper thermal contact with the flakes and a constant temperature during the measurements (Fig. 1b,c). FLG samples were heated with a 488nm laser (argon ion) in the middle of the suspended part (Fig. 1a). The size of the laser spot was determined to be 0.5–1µm. The diameter of the heated region on the flake was larger owing to the indirect nature of energy transfer from light to phonons. The laser light deposits its energy to electrons, which propagate with Fermi velocity v ≈ 10 ms . The characteristic time for energy transfer from electrons to phonons is of the order of τ ∼ 10 s (refs 27,28). The measurement time in our steady-state technique is a few minutes, which is much larger than τ but at the same time, much smaller than the time required to introduce any laser-induced damage to the sample. The correction to the hot-spot size is estimated as l – = v τ ∼ 1µm. Strain, stress and surface charges change the G-peak position in Raman spectra and may lead to its splitting . Strain and doping may also affect the thermal conductivity. To minimize these effects, we selected samples where a symmetric and narrow G peak was in its ‘standard’ location (∼1,579cm ) characteristic for the undoped unstrained graphene . No bias was applied to avoid charge accumulation . It was not possible to mechanically exfoliate FLG flakes with different numbers of atomic planes n and the same geometry. To avoid damage to the graphene, the obtained flakes were not cut to the same shape. Instead, we solved the heat diffusion equation numerically for each sample shape to extract its thermal conductivity (Fig. 1e). This was accomplished through an iteration procedure (Supplementary Information) for the Gaussian-distributed laser intensity and an effective spot size corrected to account for l – . The errors associated with the laser spot size and intensity variation were ∼8%, that is, smaller than the error associated with the local temperature measurement by Raman spectrometers (∼10–13%) determined by the spectral resolution of the instrument and random experimental data spread (see Fig. 2b). The effects of the thermal contact resistance were eliminated by using large-sized metallic heat sinks and ensuring a large FLG–sink contact area.

Received 2 October 2009; accepted 24 March 2010; published online 9 May 2010

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Acknowledgements

A.A.B.acknowledgessupportfromONRthroughawardN00014-10-1-0224,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.

Author contributions

A.A.B.conceivedtheexperiment,ledthedataanalysis,proposedtheoreticalinterpretation 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 developmentandcarriedoutcomputersimulationsofthermalconductivity.

Additional information

The authors declare no competing financial interests. Supplementary information accompanies this paper on w.nature.com/naturematerials. Reprints and permissions information is available online at http://npg.nature.com/reprintsandpermissions. CorrespondenceandrequestsformaterialsshouldbeaddressedtoA.A.B.

558 NATURE MATERIALS | VOL 9 | JULY 2010 | w.nature.com/naturematerials

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