The impact of parameter spread of high-temperature superconducting Josephson junctions on the performance of quantum-based voltage standards

Quantum metrology based on Josephson junction array reproduces the most accurate desired voltage by far, therefore being introduced to provide voltage standards worldwide. In this work, we quantitatively analyzed the dependence of the first Shapiro step height of the junction array at 50 GHz on the parameter spread of 10,000 Josephson junctions by numerical simulation with resistively shunted junction model. The results indicate an upper limit spread of the critical current and resistance of the Josephson junctions. Specifically, to keep the maximum first Shapiro step above 0.88 mA, the critical current standard deviation, $\sigma$, should not exceed 25%, and for it to stay above 0.6 mA, the resistance standard deviation should not exceed 1.5%.