Adjustment of self-heating in long superconducting thin film NbN microbridges

The self-heating in long superconducting microbridges made from thin NbN films deposited on top of high silicon mesa structures was studied by analyzing the hysteresis current density jH. We observed a more than twofold decrease of jH with increase in the ratio of the height of the Si mesa, h, to the width of the microbridge, W, from 0 to 24. We describe our experimental results using one-dimensional thermal balance equations taking into account disordered matter in our thin NbN films and limitations imposed on the phonon mean free path by the width of the Si mesa. In the framework of this model we obtain a good agreement between theory and experiment over a wide temperature range from 4.2 K up to the critical temperature TC for all h/W ratios.