Electrical transport in a superconducting niobium nitride ultrathin granular film: A disordered two-dimensional Josephson-junction array

A granular ultrathin niobium nitride (NbN) film, 10 nm thick, was patterned into long narrow lines ranging from 1 to 20 {μ}m wide. The film can be modeled as a two-dimensional array of Josephson junctions, with junctions on the scale of 30 nm, as supported by dc and rf electrical measurements (resistance, inductance, and critical current) in the absence of an applied magnetic field, both above and below the superconducting critical temperature Tc~6.5K. The analysis confirms the standard model of vortex unbinding in a regular two-dimensional junction array, with no free parameters. However, atomic-force-microscopy topographic images show substantial inhomogeneity, and this is also evident in reduced values of critical current density Jc in the narrowest lines. These are consistent with a simple model of film variations up to the 1 {μ}m scale. Finally, observations are reported of an anomalous decrease in the rf kinetic inductance of the films with increasing dc current, which may also be a consequence of the Josephson-junction array.