Resistivity of Ultrathin Superconducting NbN Films for Bolometer Mixers

Bolometer mixers based on ultrathin NbN films find their applications in far infrared heterodyne detection. They consist of a microbridge, which is brought to its transition temperature by radiation and current. It was recently proposed that the resistivity increase should be understood in terms of vortex-antivortex unbinding as described in the Berezinskii-Kosterlitz-Thouless theory, although finite size effects, material properties, granularity and pinning will complicate a description of real devices. We have measured, close to the transition temperature, the current-voltage characteristics of a variety of NbN film samples, sputtered on a silicon substrate. Four terminal measurements of patterned films with different sizes are analyzed. We report the effect of the geometrical size on the logarithmic dependence of the voltage on the current. Results will be related to the properties of the NbN bolometric mixers.