Phonon Mechanisms for Excess Heat Capacity in Membrane Isolated Superconducting Transition Edge Sensors

The mechanics of phonon transport in membrane-isolated superconducting transition edge sensors is discussed. Surveys of the literature on this type of sensor reveal a number of designs with excess heat capacity and a smaller subset that exhibit decoupling of the superconducting film from the underlying dielectric. A simple model is addressed in which the membrane, despite its thermal isolation, fails to fully thermalize to the temperature of the metal film heating it. A population of phonons exists which is emitted by the metal film, partially thermalizes the dielectric and is then reabsorbed in the metal film without escaping from the device structure to the thermal bath. The size of this population and its contribution to the heat capacity are estimated for several device scenarios.