  We have found experimentally that the critical current of a square
superconducting transition-edge sensor (TES) depends exponentially upon the
side length L and the square root of the temperature T. As a consequence, the
effective transition temperature Tc of the TES is current-dependent and at
fixed current scales as 1/L^2. We also have found that the critical current can
show clear Fraunhofer-like oscillations in an applied magnetic field, similar
to those found in Josephson junctions. The observed behavior has a natural
theoretical explanation in terms of longitudinal proximity effects if the TES
is regarded as a weak link between superconducting leads. We have observed the
proximity effect in these devices over extraordinarily long lengths exceeding
100 um.
