Radial phononic thermal conductance in thin membranes in the Casimir limit: Design guidelines for devices

Abstract

In a previous publication 1 , we discussed the formalism and some computational results for phononic thermal conduction in the suspended membrane geometry for radial heat flow from a central source, which is a common geometry for some lowtemperature detectors, for example. We studied the case where only diffusive surface scattering is present, the so called Casimir limit, which can be experimentally relevant at temperatures below ∼ 10 K in typical materials, and even higher for ultrathin samples. Here, we extend our studies to much thinner membranes, obtaining numerical results for geometries which are more typical in experiments. In addition, we interpret the results in terms of a small signal and differential thermal conductance, so that guidelines for designing devices, such as low-temperature bolometric detectors, are more easily obtained. Scaling with membrane dimensions is shown to differ significantly from the bulk scattering, and, in particular, thinning the membrane is shown to lead to a much stronger reduction in thermal conductance than what one would envision from the simplest bulk formulas.

A macroscopic object passively cooled into its quantum ground state of motion: beyond single-mode cooling

“…Noting that the dominant phonon wavelength λ dom. ≈ 2.23 v s /(k B T ) is of the order of e p around 1 K, we can treat the problem as pure 2D transport, leading to the simple result [77]:…”

Preface to Special Topic: Selected Articles from Phononics 2013: The Second International Conference on Phononic Crystals/Metamaterials, Phonon Transport and Optomechanics, 2-7 June 2013, Sharm El-Sheikh, Egypt

“…20 And radial thermal transport in a thin membrane is computationally investigated considering the limiting regime of diffuse surface scattering. 21 Finally, returning to the notion of property enhancement, the previously mentioned study of phonon transport for thermoelectric cooling utilizes materials with inhomogeneous thermal conductivity. 6 We are grateful to Executive Editor Professor A. T. Charlie Johnson, Jr., Grace Chik and Christine Urso and the staff at the American Institute of Physics for their support on this special edition.…”