SNSPDs#
A biasing current, denoted as \(i_{d}\), typically in the microampere (\(\mu A\)) range, needs to be applied across the SNSPD detector in its superconducting state.
WWhen the SNSPD is superconducting, \(R_{SNSPD} = 0\), meaning no photons are detected. According to Ohm’s law \(V=iR_{SNSPD}\), there is a short circuit across the SNSPD. The currents in each node of the interconnected SNSPD circuit model in Figure [1] are derived from Kirchhoff’s current law in Equation [2]. The total biasing current applied to the detection component subsystem, \(i_b\), is divided across the parallel terminator resistor current \(i_{TERM}\) and the SNSPD detector biasing current \(i_b\).
When a photon with energy \(E_p(T) = \frac{\hbar c}{\lambda}\) is absorbed, it creates a resistive hotspot in the SNSPD, making \(R_{SNSPD} \approx k \Omega\). A high-speed voltage pulse is generated from the energy stored in the SNSPD-meander inductor \(E_{L_k}\), as described in Equation [3], flowing across the increasing thermal hotspot due to inductive current \(i_{L_k}\) resistive dissipation. For a fast cooldown of the SNSPD back to the superconducting state, minimizing the inductive current dissipation is essential [1], and no further SNSPD biasing current \(i_d\) is required in its resistive state.
The lowest impedance path for the system-biasing current \(i_b\) in the circuit in Figure [1] is through the parallel terminator resistor \(R_{TERM} \approx 50 \Omega\), designed to match the impedance of the high-speed tapered coplanar waveguide \(R_{TAPER,CPW}\). While the SNSPD is in its non-superconducting state and needs to cool down to reset, the rest of the system biasing current \(i_b\) flows through the terminator resistor to prevent electro-thermal dissipation latching.
The output voltage pulse \(V_{pulse}\) rise time \(\tau_{rise}\) in Equation [4] is related to the shunt combined complex impedance of the coplanar waveguide and the terminator \(Z_{load}\), with the RF interconnection standard 50 \(\Omega\) impedance. The reset time of the detector is also related to the shunt load impedance and the inductive energy dissipation in Equation [5] [2, 1].
The energy dissipated at the SNSPD hotspot immediately during photon absorption \(E_p(T) = \frac{\hbar c}{\lambda}\) can be expressed in relation to the superconducting-biasing current \(i_s\).
References
Annunziata, A. J., Santavicca, D. F., Frunzio, L., Catelani, G., Rooks, M. J., Frye, D., … & Prober, D. E. (2010). Reset dynamics and latching in niobium superconducting nanowire single-photon detectors. Journal of Applied Physics, 108(8), 084507.
Kerman, A. J., Dauler, E. A., Keicher, W. E., Yang, J. K. W., Rosfjord, K. M., & Berggren, K. K. (2006). Kinetic-inductance-limited reset time of superconducting nanowire photon counters. Applied Physics Letters, 88(11), 111116.