Research ArticleMATERIALS SCIENCE

Heat conduction tuning by wave nature of phonons

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Science Advances  04 Aug 2017:
Vol. 3, no. 8, e1700027
DOI: 10.1126/sciadv.1700027
  • Fig. 1 Samples and experimental setup.

    Schematic and SEM images show fabricated samples of 1D (A) and 2D (B) phononic crystals (PnC) with ordered (δ = 0%) and disordered (δ = 15%) arrays of holes. Scale bars, 300 nm. (C) Schematic of the micro-TDTR setup, with inset showing a typical thermal decay curve with an exponential fitting.

  • Fig. 2 Thermal decay rate measurements with varying disorder.

    Measured thermal decay rates in both (A) 1D and (B) 2D ordered phononic crystals deviate from those in disordered structures at 4 K, whereas at 300 K (insets) heat dissipates through ordered and disordered structures at an equal rate. Error bars show an SD during the measurements (also included in the points at 300 K). Solid lines show results of the FEM simulations based on the Fourier heat transport equation. (C and D) Theoretically expected disorder dependence alongside the experimentally measured difference between thermal decay rates [Δδ = (γdisordered – γδ)/γdisordered] for 1D and 2D phononic crystals, respectively. The values of effective surface roughness used in the theoretical model are displayed on the corresponding fits. Disorder dependence of the difference Δδ in the Monte Carlo simulations (blue scatters). The inaccuracy of Monte Carlo simulation data was estimated as an SD in multiple simulations of the same structure and is equal to 1 and 2.5% for (C) and (D), respectively.

  • Fig. 3 Comparison between experiment and theories.

    Temperature dependence of the difference between thermal decay rates, calculated as Δ0 = (γdisordered – γordered)/γdisordered, obtained experimentally and predicted by Monte Carlo simulations and the theory of cutoff frequency for different values of effective surface roughness. Error bars show an upper bound of the signal deviation during the measurement. The inaccuracy of the Monte Carlo simulation data is lower than 2% for all points.

  • Fig. 4 Hole surface roughness.

    High-resolution top-view SEM images of two different holes. The surface roughness is contained within a 2.5-nm region. Scale bars, 20 nm.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/8/e1700027/DC1

    section S1. Micro-TDTR analysis

    section S2. Hole dimensions

    section S3. Side wall verticality

    section S4. Disorder dependence of thermal conductivity

    section S5. FEM simulations

    section S6. Monte Carlo simulations

    section S7. Calculation of the cutoff frequency for heat flux reduction calculation

    fig. S1. Measurement method.

    fig. S2. Hole dimensions.

    fig. S3. Tilted SEM image of a hole on the side of a membrane.

    fig. S4. Thermal conductivities with varying disorder.

    fig. S5. FEM simulations.

    fig. S6. 2D Monte Carlo map.

    fig. S7. Monte Carlo simulation of 1D and 2D disordered structures.

    fig. S8. Energy transmission.

    fig. S9. Energy density spectra.

    fig. S10. Phonon dispersion and heat flux spectra.

    fig. S11. Theoretical model: Impact of the specularity parameter.

    fig. S12. Theoretical model: Impact of the temperature increase.

    table S1. Ranges of hole dimensions for different set of 1D phononic crystals.

    References (4052)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Micro-TDTR analysis
    • section S2. Hole dimensions
    • section S3. Side wall verticality
    • section S4. Disorder dependence of thermal conductivity
    • section S5. FEM simulations
    • section S6. Monte Carlo simulations
    • section S7. Calculation of the cutoff frequency for heat flux reduction calculation
    • fig. S1. Measurement method.
    • fig. S2. Hole dimension.
    • fig. S3. Tilted SEM image of a hole on the side of a membrane.
    • fig. S4. Thermal conductivities with varying disorder.
    • fig. S5. FEM simulations.
    • fig. S6. 2D Monte Carlo map.
    • fig. S7. Monte Carlo simulation of 1D and 2D disordered structures.
    • fig. S8. Energy transmission.
    • fig. S9. Energy density spectra.
    • fig. S10. Phonon dispersion and heat flux spectra.
    • fig. S11. Theoretical model: Impact of the specularity parameter.
    • fig. S12. Theoretical model: Impact of the temperature increase.
    • table S1. Ranges of hole dimensions for different set of 1D phononic crystals.
    • References (40–52)

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