Accurate thermal conductance and impedance measurements of transition edge sensors

Past measurements of the thermal coupling of superconducting transition edge sensor (TES) calorimeters suspended on SiN membranes produced wide-ranging values for the exponent of the thermal coupling through the membranes. We present a measurement technique that is less susceptible to current dependence of the phase transition than the previous measurements. An initial measurement produced the expected exponent for a 2-D phonon gas: thermal conductance is proportional to T². In doing these measurements, we employ a modification to Lindeman's equivalent circuit technique for measuring TES complex impedance.