Two-dimensional phononic thermal conductance in thin membranes in the Casimir limit

TL;DR

This paper investigates phononic thermal conductance in thin membranes within the Casimir limit, providing numerical solutions for temperature profiles that are useful for designing membrane-supported bolometric detectors.

Contribution

It offers the first numerical analysis of 2D phononic thermal conduction in the Casimir limit, where no analytic solutions are available.

Findings

Numerical temperature profiles for various membrane thicknesses.

No analytic solutions exist for 2D Casimir limit, unlike 1D case.

Results applicable to designing bolometric radiation detectors.

Abstract

We discuss computational analysis of phononic thermal conduction in the suspended membrane geometry, in the experimentally commonly appearing 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 phonon scattering 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. Our results can be applied, for example, in the design of membrane-supported bolometric radiation detectors.