Phononic Thermal Conduction Engineering for Bolometers: From Phononic Crystals to Radial Casimir Limit

We discuss two alternative and complementary means of controlling radial phonon conduction for bolometers in two dimensions: by using phononic crystals or by roughening the surface of the membranes (Casimir limit). For phononic crystals, we present new experiments with a modified geometry and a larger hole periodicity than before, achieving a low thermal conductance ∼2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sim }2$$\end{document} pW/K at 150 mK. Calculations in the Casimir limit, on the other hand, show that for small detector dimensions thermal conductance below 1 fW/K seems achievable.