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(a) Schematic for the reduction of bulk phonon mean free paths in nanowires and thin films. (b) Thermal conductivity κ for single-crystalline Si nanowires (left) and thin films (right) as a function of temperature T. Nanowire diameters are d = 115, 56, 37 nm, and thin film thicknesses are t = 20, 30, 50, 100 nm, 0.42, and 3 μm. Calculations are shown with solid lines and experiments [see Refs. 16–19 and 31] with symbols.
(a) Plots of the Casimir and reduced thermal conductivities for Si NW as a function of temperature T and diameters d = 10 nm–10 μm. (b), (c) Contour plots for the relative amount of Casimir ballistic transport (κ/κC ) and Fourier diffusive transport (κ/κF ), respectively. Left: boundary roughness η = 0.2 nm. Right: boundary scattering is totally diffuse (p = 0). At room temperature and d = 10 nm, the Casimir ratio is 77% and 74%, respectively.
The dependence of the Casimir ratio on the surface roughness η for nanowire diameters d = 10 nm, 100 nm, and 1 μm and temperatures 75 K (black) and 300 K (gray).
(a) Cumulative thermal conductivity in Si films with respect to the ballistic ratio RB = (1 − exp[−L/ℓ])/(1 − p) for temperatures (◼) T = 300 K, (◻) T = 100 K, and (●) T = 20 K and thicknesses t = 10 nm, 100 nm, and 1 μm. (b) Contour plots for the relative amount of Fourier diffusive transport (κ/κF ). Film boundary roughness is η = 0.2 nm.
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