Determining the depairing current in superconducting nanowire single-photon detectors

We estimate the depairing current of superconducting nanowire single-photon detectors (SNSPDs) by studying the dependence of the nanowires' kinetic inductance on their bias current. The kinetic inductance is determined by measuring the resonance frequency of resonator-style nanowire coplanar waveguides both in transmission and reflection configurations. Bias current dependent shifts in the measured resonant frequency correspond to the change in the kinetic inductance, which can be compared with theoretical predictions. We demonstrate that the fast relaxation model described in the literature accurately matches our experimental data and provides a valuable tool for determination of the depairing current. Accurate measurement of the depairing current is critical for nanowire quality analysis, as well as modeling efforts aimed at understanding the detection mechanism in SNSPDs.

Figure 1

Scanning electron micrographs of a NbN CPW resonator used in experiment. (a) The narrow, meandered nanowire CPW is placed between two wide, 50 $\mathrm{\Omega }$ leads (also in CPW configuration), forming a transmission-line resonator. (b) Transition from the 50 $\mathrm{\Omega }$ lead to the $\mathrm{k}\mathrm{\Omega }$ nanowire. (c) Zoomed-in view of the nanowire CPW.

Figure 2

Schematics for the setup for both the (a) reflection and (b) transmission type measurements. The THRU devices were 50 $\mathrm{\Omega }$ superconducting CPW fabricated on the same chip used for calibration purposes.

Figure 3

The measured and the fitting functions for the resonance (a) magnitude and (b) phase responses at zero and near the switching bias current for the 120-nm-wide NbN device. Fitting of the kinetic inductance ratio of the nanowire (c) using the fast (in blue) and the slow (in red) relaxation approximation models for the 120-nm-wide NbN device. The shaded area represents the model's accuracy of 1% and 0.5% for the fast and slow relaxation approximation models, respectively, according to Clem and Kogan [23]. In black, the numerical simulation of the kinetic inductance change using the fast relaxation model. It can be shown by the enlarged window that the numerical simulation fits the sample points better than the fast relax approximation model. The estimated depairing current from the models is 38.19 $\mu \mathrm{A}$ for the fast relaxation approximation, 38.78 $\mu \mathrm{A}$ for the fast relaxation numerical simulation, and 27.05 $\mu \mathrm{A}$ for the slow relaxation.

Figure 4

(a) Estimated depairing current using the fast relax model as a function of the operating temperature for both NbN and WSi devices and (b) the switching to depairing current ratio (constriction factor) for all the tested devices as a function of the fraction of superconductor transition temperature.

Figure 5

Depairing current at different temperatures with respect to increasing resonator width for NbN and WSi devices. The linear fit for the WSi devices shows the presence of an offset.