Quantitative evaluation of delay time in the single-flux-quantum circuit

We measured the delay times of several components of the rapid single-flux-quantum (RSFQ) circuit using ring oscillators so as to improve the precision in the timing design. The delay time deviates from the designed value because of wafer-to-wafer and on-wafer parameter spreads. In addition, three-dimensional structures of the actual circuits generate unpredictable parasitic inductances, which occasionally lead to the large timing deviation from the design. The 1-σ local spread of the delay time originating from the fabrication was found to be 5.2% for a Josephson transmission line (JTL) composed of two junctions. This result provides a quantitative indication of timing margins required between SFQ pluses. However, the delay times tended to be smaller than those in numerical simulation by approximately 20%. We think that this is because the timing parameters were extracted without any considerations of the parasitic inductance of shunt resistors in the simulation. To examine the influence of the parasitic inductance, we designed four JTLs having additional inductances in series with shunt resistors, and measured each delay time. The decreasing ratio of delay time to the parasitic inductance was found to be 0.32 ps per 1 pH. We estimated that the parasitic inductance connected in series with a shunt resistor was 1.6 pH for the JTL. This timing consideration is applicable to all the cells because the junctions used in the actual circuits have roughly the same geometry as that of the JTL.