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Figures

Image of FIG. 1.

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FIG. 1.

(a) and (b)The thermal conductivity versus carbon nanotube length in log-log scale for (5,5) SWCNT at 300 K and 800 K. The thermal conductivity of carbon nanotube diverged to the length, as κ∝Lβ. (c) and (d) Energy diffusion in a SWCNT at 2 K and room temperature.

Image of FIG. 2.

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FIG. 2.

The thermal conductivity of SiNWs (with fixed transverse boundary condition) vs length. The black solid lines are the best fitting ones. The harmonic (dash dotted) and 1/3 (dashed) laws are shown for reference.

Image of FIG. 3.

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FIG. 3.

(a) Thermal conductivity of SiNWs versus the percentage of randomly doping isotope atoms at 300 K. The results by Nose-Hoover method coincide with those by Langevin methods indicating that the results are independent of the heat bath used. The solid curve and the dash curve are the best fitting to the formula κ = A 1 e x/B + A 2 e −(1 − x)/B + C. (b) Thermal conductivity of the superlattice SiNWs versus the period length at 300 K.

Image of FIG. 4.

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FIG. 4.

(a) Room temperature thermal conductivity of SiNWs (red) and SiNTs (black) versus cross section area. (b) P-ratio of each eigen-mode for SiNTs (red) and SiNWs (blue) with the same cross section area. The p-ratio measures the fraction of atoms participating in a given mode, and effectively indicates the localized modes with O(1/N) and delocalized modes with O(1). (c) and (d) are normalized energy distribution on the cross section for SiNWs and SiNTs at 300 K, respectively. Positions of the circles denote the different locations on the plane, and intensity of the energy is depicted according to the color bar. P is participation ratio.

Image of FIG. 5.

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FIG. 5.

(a) Time dependence of normalized heat current autocorrelation function (HCACF) for SiNWs (dashed line), SiNTs (dottedline), and Ge/Si core-shell NWs with Lc/L = 0.65 (solid line). (b) Long-time region of (a). (c) Oscillation amplitude versus core-shell ratio Lc/L. (d) Amplitude of the fast Fourier transform of the long-time region of normalized HCACF of Ge/Si core-shell NWs.

Image of FIG. 6.

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FIG. 6.

(a) and (b) P-ratio for different phonon modes in GeNWs before and after coating. The black, red, and blue denote respectively p-ratio in GeNWs, Ge/Si core−shell NWs with perfect interface, and Ge/Si core−shell NWs with 10% interfacial roughness. (c) The polarization-resolved p-ratio for the longitudinal acoustic phonon near the Brillouin zone center in GeNWs (black) and Ge/Si core−shell NWs with perfect interface (red). (d) Normalized thermal conductivity versus coating thickness for different DGe. Thermal conductivity of GeNWs at each DGe is used as reference.

Image of FIG. 7.

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FIG. 7.

(a) The scaled thermal conductance, σ/S at 300 K vs width, W, for Zigzag graphene nanoribbon (ZGNR), armchair GNR (AGNR), zigzag carbon nanotube (ZCNT) and armchair CNT (ACNT). The inset shows σ/S for ZGNRs and AGNRs with the width varying from 0.5 to 35 nm. (b) Thermal conductivity of N-AGNR and N-ZGNR with variation of N, where the length of GNRs is fixed to be 11 nm. (c) Schematic illustration of the periodic T-shaped GNR. The left or right lead has perfect periodicity with uniform width W1 along the ribbon axis and the central region consists of constrictions with size LC × W2 and stubs with size L×W1. (d) Temperature dependence of thermal conductivity of ZGNRs and AGNRs for one and four layers atomic planes.

Image of FIG. 8.

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FIG. 8.

(a) and (b) are two localized edgemodes in the graphene sheet. (c) and (d) are two non-localized modes due to the broken of different boundary conditions in three directions.

Image of FIG. 9.

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FIG. 9.

(a) The side view of schematic picture of a folded GNR. Arrows correspond to eigenvectors of a ZA mode (ω = 50 cm-1) in the folded GNR with periodic boundary condition in z-axis. The ZA mode is a combination of out-of-plane mode and in-plane mode. (b) The transmission ratio at a given frequency is the transmission coefficient of the folded GNR over the transmission coefficient of the flat GNR. It shows the scattering effect on the GNR by the folds. (c) The spectra of phonon transmission coefficient of the flat GNR and the folded GNR calculated by NEGF. (d) Relative thermal conductivity modulation by compressing interlamellar space with different folds in GNRs. The value 1.0 of relative thermal conductivity corresponds to 111.5 W/m-K which is the thermal conductivity of the flat zigzag GNR.

Image of FIG. 10.

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FIG. 10.

Measured thermal conductance vs. temperature in an individual MWCNT with a diameter of 14 nm. The slopes of the fitted solid lines are 2.50 and 2.01, respectively. Upper insert: SEM image of the two suspended membranes, Rh and Rs, thermally connected by a MWCNT. The scale bar represents 1 μm. Lower insert: thermal conductivity of three individual MWCNTs with different diameters (14 nm, 80 nm and 200 nm from top).

Image of FIG. 11.

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FIG. 11.

Diameter dependence of thermal conductivity in ZnO nanowire at T = 80 K (solid circle) and 300 K (solid triangles). The thermal conductivity increases linearly with cross-section area (∼d2) of nanowires. Insert: An 8-inch Si/SiNx wafer containing more than 600 MEMS test devices and zoom in image of the optical picture of 4 × 5 devices.

Image of FIG. 12.

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FIG. 12.

(a) Measured thermal conductivity in double ribbons (coupled by van der Waals interaction) and single ribbon. The value in double ribbons is around 40% to 60% larger than that in single ribbon. (b) Switchable thermal conductivity of sample double ribbons with IPA, and reagent alcohol and DI water mixture wetting.

Image of FIG. 13.

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FIG. 13.

(a) and (b) SEM image of suspended and supported graphene samples. Scale bar represents 5 μm. (c) Thermal conductance per unit cross section area σ/A in suspended single layer graphene. The measured data is approaching the expected ballistic limit (black dashed line).

Image of FIG. 14.

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FIG. 14.

Thermal conductivity of multilayer graphene as a function of temperature. The length of the samples S1 (supported three layers), S2 (suspended five layers) and S3 (supported three layers) are 5 μm, 2 μm and 1 μm, respectively, and the width is 5 μm.

Image of FIG. 15.

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FIG. 15.

(a) Schematic of the local electron heating technique to measure the thermal contact resistance. (b) Spatially resolved thermal resistance of supported graphene with 1 μm in length. The sudden jump indicates thermal contact resistance in B-C and C-D interfaces.

Image of FIG. 16.

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FIG. 16.

Schematic pictures of thermal rectifier from different nanostructures. (a) The carbon nanocone. (b) The trapezia shaped GNR. (c) The two rectangular GNR with different widths. (d) The triangularly GNRs. (e) The asymmetric three-terminal GNR. Among the three terminals, the left and right terminals are energy-input or energy-output leads while the top terminal is a control lead. (f) The Möbius graphene strip with Zigzag edge and chiral index −1, where blue atoms are on the only edge. The red parts are heat bath regions. (g) The graphene Y junction. It consists of the stem section and branch sections, which have the same width. The symbol of diode with a red T represents a thermal diode.

Image of FIG. 17.

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FIG. 17.

(a) Heat flux J versus |Δ| for the homogenous mass and the graded mass carbon nanocones (CNCs). The temperature of top is Ttop = T0(1-Δ) and that of bottom as Tbottom = T0(1+Δ), where T0 is the average temperature, and Δ is the normalized temperature difference between the two ends. (b) Rectiffications versusΔ. (c) Temperature profile in CNCs at T0 = 300 K and Δ = ±0.5.

Image of FIG. 18.

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FIG. 18.

Phonon power spectra of top/bottom atoms in the carbon nanocones. (a) T0 = 300 K and Δ = 0.5, the bottom heat bath is at high temperature which corresponds to big flux; (b) T0 = 300 K,Δ = −0.5, corresponds to small flux. The values of overlap area were shown in each panel. The values of S+/− (overlaps of the power spectra of the two layers) are also shown.

Image of FIG. 19.

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FIG. 19.

(a) SEM image of a solid-state memory device with an individual VO2 nanobeam as a tunable thermal channel connecting the input terminal (Tin) and output terminal (Tout). (b) Tout as a function of Tin within a single temperature-sweeping loop of heating (red curve) and cooling (blue curve). (c) Tout as a function of Tin under different bias voltage on VO2 nanobeam. (d): Switching performance and repeatability test of the thermal memory within 150 cycles, each of which consists of a Write High-Read-Write Low-Read loop.

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2012-12-28
2014-04-25

Abstract

This review summarizes recent studies of thermal transport in nanoscaled semiconductors. Different from bulk materials, new physics and novel thermal properties arise in low dimensional nanostructures, such as the abnormal heat conduction, the size dependence of thermal conductivity,phonon boundary/edge scatterings. It is also demonstrated that phonons transport super-diffusively in low dimensional structures, in other words, Fourier's law is not applicable. Based on manipulating phonons, we also discuss envisioned applications of nanostructures in a broad area, ranging from thermoelectrics, heat dissipation to phononic devices.

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Scitation: Thermal transport in nanostructures
http://aip.metastore.ingenta.com/content/aip/journal/adva/2/4/10.1063/1.4773462
10.1063/1.4773462
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