Measurements of the current-phase relationship in SIS and SNS Josephson junctions

The current-phase relationship (CΦR) of Josephson junctions (JJs) is an important parameter for modeling the behavior of superconducting circuits such as those used for the voltage standard, SFQ digital logic, and quantum information. The CΦR for superconductor-insulator-superconductor (SIS) JJs is typically assumed to be perfectly sinusoidal although this can be inaccurate in certain cases. For JJs with normal-metal (N) barriers, called SNS junctions, the CΦR has been shown to have a ramp-like dependence, which can significantly affect the behavior of circuits using these JJs. For example, the use of SNS JJs with niobium-doped silicon barriers significantly alters the operating margins of NIST voltage standard circuits and can affect the timing and margins of SFQ digital circuits. We will show extracted CΦR data for both SIS and SNS junctions measured at 4 K using a microwave resonator technique. The measurement circuit consists of a ~ 5 GHz niobium resonator terminated with an RF-SQUID. Using an on-chip flux line to vary the SQUID JJ phase φ and the junction inductance, L_j (φ) ~ [ d(CΦR)/ dφ ]^-1, the resonator frequency shifts depending on the derivative of the CΦR and is measured by monitoring the transmission (S₂₁) of the coupled microwave circuit.