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Two-dimensional phononic thermal conductance in thin membranes in the Casimir limit
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Image of FIG. 1.

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FIG. 1.

[Color online] Calculated temperature profiles for 2D Casimir heat conduction (points) for R = 250 and d = 1, 3.16, 10, 31.6, 100, where R and d have arbitrary units in (a) linear scale, (b) log-log scale. Higher curves have lower d. Dashed line shows the bulk diffusive result, Eq. (4), and dotted line the value of bath temperature used. In (b), the solid lines are power law fits with exponents -1/9, -1/8, -1/6, -1/5 from top to bottom.

Image of FIG. 2.

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FIG. 2.

[Color online] Calculated temperature profiles for 2D Casimir heat conduction (points) for R = 250, d = 1, and r h =1, with varying heat input power density 2q/σ = 10−4, 10−3, 0.01, and 0.1 K4 in (a) linear scale, (b) log-log scale. Higher curves have higher q. The dotted line is the value of bath temperature 0.1 K used.

Image of FIG. 3.

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FIG. 3.

[Color online] Calculated temperature profiles for 2D Casimir heat conduction (points) for R = 250, d = 1, and constant total heating power K4(arb)2, but with varying heater radius r h =1,3,7,25,50,100,150 in (a) linear scale, (b) log-log scale. The dashed lines mark the values of the heater radii.

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/content/aip/journal/adva/1/4/10.1063/1.3675925
2011-12-29
2014-04-24

Abstract

We discuss computational analysis of phononic thermal conduction in the suspended membrane geometry, in the case where heat can flow out radially in two dimensions from a central source. As we are mostly interested in the low-temperature behavior where bulk scattering of phonons becomes irrelevant, we study the limit where all phononscattering takes place at the membrane surfaces. Moreover, we limit the discussion here to the case where this surface scattering is fully diffusive, the so called Casimir limit. Our analysis shows that in the two-dimensional case, no analytic results are available, in contrast to the well known 1D Casimir limit. Numerical solutions are presented for the temperature profiles in the membrane radial direction, for several different membrane thicknesses and heater diameters. Our results can be applied, for example, in the design of membrane-supported bolometric radiation detectors.

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Scitation: Two-dimensional phononic thermal conductance in thin membranes in the Casimir limit
http://aip.metastore.ingenta.com/content/aip/journal/adva/1/4/10.1063/1.3675925
10.1063/1.3675925
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