Resistive transition of niobium superconducting hot-electron bolometer mixers

We present a model for the description of the resistive transition in hot-electron bolometer mixers. We show that the transition is a property of a superconducting microbridge connected to normal conducting cooling pads. Using the concepts of the superconducting proximity effect, charge-imbalance generation, and Andreev reflection, we have calculated the resistance versus temperature of the device and demonstrate its dependence on the length of the microbridge, both theoretically and experimentally. The analysis reopens the question of the relationship between the resistive transition and the situation in which the device is optimally operated as a heterodyne mixer.