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

TL;DR

This paper investigates phononic thermal conductance in thin membranes under the Casimir limit, providing design guidelines for low-temperature detectors by analyzing how membrane thinning affects thermal conductance.

Contribution

It extends previous models to thinner membranes and interprets results in terms of thermal conductance, offering practical design insights for low-temperature device applications.

Findings

Thinning membranes significantly reduces thermal conductance.

Scaling behavior differs from bulk scattering predictions.

Design guidelines for low-temperature detectors are derived.

Abstract

In a previous publication, 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 low-temperature 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 $\sim$ 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.