Measurement of Specific Capacitance for Nb/Al–AlO $_{x}$/Nb Josephson Junctions in Single-Flux Quantum Circuit Applications

In this study, we investigate different technologies to measure the specific capacitances C
₈
of Nb/Al-AlO
_x
/Nb Josephson junctions. They involve measuring Fiske mode resonance in long Josephson junctions, superconducting quantum interference device (SQUID) resonance, and Josephson plasma resonance. We find a logarithmic relationship between the junction C
₈
and its critical current density J
_c
in the range 0.1-2 kA/cm
²
using the Fiske mode resonance method. Our measured C
₈
values using SQUID resonance and Josephson plasma resonance are compared with the results obtained by other groups via analyzing the major errors in the C
₈
calculation. We discuss the accuracy in evaluating C
₈
for all three techniques and suggest using Fiske mode resonance as a relatively stable method for C
₈
extraction for the future design of our single-flux quantum circuit.