Technique for Measuring the Conductance of Silicon-Nitride Membranes Using Johnson Noise Thermometry

We present a technique for measuring the thermal conductance of isolated Silicon-Nitride (SixNy) membranes using Johnson noise thermometry. The isolated SixNy membranes have thin film AuCu resistors deposited on the surface with superconducting tracks. These resistors were used either as heat loads, or as thermometers by reading their Johnson noise with a low noise ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\sim}4\mbox{ pA/}\sqrt{\mathrm{Hz}}$\end{document} ) Superconducting Quantum Interference Device (SQUID). This technique measures, in real time, the Temperature-Power (T-P) relationship of the membrane, from which details of the thermal conductance can be extracted. We present preliminary results for two geometrically different SixNy membranes across a temperature range of 250 mK to 1.2 K.