Optimizing the operating temperature of a transition edge sensor

We discuss the theory for optimizing the operating temperature of a voltage biased superconducting transition edge sensor (TES) in terms of energy resolution and speed, considering only internal detector noise sources. The noise processes included in the modeling are the unavoidable Johnson and phonon noise. The phonon noise is calculated for the case of ballistic transport. If other external and excess internal noise sources are not dominant, an optimal operating temperature can be found to minimize the energy resolution. The detector slows down by approximately a factor of two at the optimal energy resolution point.