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Physica C Superconductivity

The impact of parameter spreads of Josephson junctions on the performance of quantum-based voltage standards

Guanghong Wen, Yi Zhu, Y. Zheng, Shuhe Cui, J. Wang, Hao Li, Lixing You

Published Aug 19, 2026• 0 citations
Publisher

Abstract

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 70 GHz on the parameter spread of 8,000 Josephson junctions with an average critical current (Ic) of 3.5 mA and an average normal state resistance (Rn) of 40 mΩ, using numerical simulations based on the resistively shunted junction (RSJ) model. The results indicate an upper limit spread of the Ic and Rn of the Josephson junctions. Specifically, to keep the maximum first Shapiro step above 0.9 mA, the Ic standard deviation, σ, should not exceed 25%, and for it to stay above 0.5 mA, the Rn deviation should not exceed 9%. This analysis specifically clarifies the required level of manufacturing process sophistication for superconducting devices to realize high-temperature superconducting (HTS) quantum-based voltage standards.

DOI
10.1016/j.physc.2026.1354930

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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 70 GHz on the parameter spread of 8,000 Josephson junctions with an average critical current (Ic) of 3.5 mA and an average normal state resistance (Rn) of 40 mΩ, using numerical simulations based on the resistively shunted junction (RSJ) model. The results indicate an upper limit spread of the Ic and Rn of the Josephson junctions. Specifically, to keep the maximum first Shapiro step above 0.9 mA, the Ic standard deviation, σ, should not exceed 25%, and for it to stay above 0.5 mA, the Rn deviation should not exceed 9%. This analysis specifically clarifies the required level of manufacturing process sophistication for superconducting devices to realize high-temperature superconducting (HTS) 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, σσσ, should not exceed 25%, and for it to stay above 0.6 mA, the resistance standard deviation should not exceed 1.5%.
Abstract The dynamics of overdamped Josephson junctions under varying microwave-driving conditions have been studied through numerical simulations using the resistively-shunted junction model, with a focus on primary voltage metrology applications, where a significantly high number of series-connected junctions and stringent uniformity of their electrical parameters are required. The aim is to determine the optimal junction characteristics and external microwave (rf) parameters that maximize the width of quantum voltage levels (Shapiro steps) from order n = 0 to n > 1. Both the rf and dc power requirements, along with the junction parameter spread and power attenuation, are analyzed as key factors that need to be optimized for improved performance of the quantum device. This work aims to advance the development of next-generation programmable Josephson voltage standards with logic architectures that surpass the conventional binary and ternary codifications used in present quantum voltage arrays, while significantly reducing the overall number of junctions as well as the number of sub-arrays and bias lines. Existing technologies exploiting n = 0 and n = ± 1 voltage steps are first discussed and analyzed to verify the validity of the simulation model. They are then further investigated to extend their usability with multi-order quantum steps for n up to 3. From the simulation results, it follows that present junction technologies may be employed with no modifications for the simultaneous operation of quantum steps up to n = 2, although optimal power efficiency would require a retrimming of the junction’s electrical parameters. On the contrary, extending the highest step order to n = 3 strictly requires the junction’s characteristic parameters to be properly adjusted to maintain sustainable power levels as well as acceptable quantum-locking ranges.
The application of high temperature superconductor Josephson junctions to voltage metrology is promising for many reasons, beyond the evident advantage of simplified cryogenics and reduced costs of the apparatus. Owing to their intrinsic non-hysteretic behavior, arrays of shunted bicrystal YBCO junctions are particularly interesting for the realization of an AC voltage standard with quantum accuracy. Moreover, shunted bicrystal YBCO junctions arrays are advantageous because of the reduced area of the junctions, the wide range of characteristic voltages, and large critical currents. However, some specific problems arise, like possible effects related to the higher operating temperature. Furthermore, fabrication technology sets tight constraints on the design of structures for the distribution of microwave currents along the array junctions. We investigated the step properties under millimeter wave irradiation at frequencies about 75 GHz of HTS junction and arrays prepared on bicrystal substrates having grain boundaries. High sensitivity techniques were adopted to evaluate the step flatness at nV level and assess the accuracy of the step voltage. A new method that makes use of an open resonator, was implemented to irradiate the array, providing synchronization of a large number of junctions.
We have studied the far infrared behavior of high -T/sub c/ superconductor-normal metal-superconductor (SNS) microbridges with T/sub c/>85 K and critical current-resistance products (I/sub c/R/sub N/) as high as 10 mV at 4 K. These are the highest I/sub c/R/sub N/ products reported to date for microfabricated Josephson junctions of any material. The junctions were integrated at the feeds of planar log-periodic antennas made from Au thin films. The junctions had dc normal state resistances R/sub N/ between 6 and 38 /spl Omega/, reasonably well matched to the antenna's estimated RF impedance of 53 /spl Omega/. Far infrared laser radiation at 404, 760, and 992 GHz induced distinct Shapiro steps (i.e. constant voltage steps at voltages n(hf/2e), n=1,2,...) in the current voltage characteristics as well as modulation of the critical current. Steps were observed at voltages up to 17 mV and 6 mV, at temperatures of 9 K and 57 K respectively. This corresponds to maximum Josephson oscillation frequencies of 8 and 3 THz at these temperatures. These are the first far infrared measurements performed on high T/sub c/ junctions. Measurements of the power, frequency, and temperature dependence of the Shapiro steps are presented and discussed in the context of a resistively and capacitively shunted junction (RCSJ) model. A value of 4.5 fF for the junction capacitance is inferred from the hysteresis of the slightly underdamped current-voltage characteristics.>
Analysis of the Josephson junction yield in the National Institute of Standards and Technology 10 V Programmable Josephson Voltage Standard (PJVS) has been performed by fabricating and measuring over 25 million Nb/NbxSi1-x/Nb junctions. Using the 265 116 junctions per PJVS device, it was possible to measure Shapiro steps on current voltage curves and then estimate the number of single-junction defects within these long arrays. By comparing the results of a quantum-based measurement to a model simulating junction defects, the quantity and magnitude of a small number of junction defects can be estimated from an array of many thousands of junctions. Understanding the source of junction defects in the fabrication process is important for maximizing yield and uniformity, both of which directly relate to the current margin of the quantized voltage step. We have recently fabricated 18 imperfect but usable PJVS devices and 16 that were free from defects, many with n = 1 Shapiro step margins approximately equal to 2 mA. The best of these wafers had a junction defect density of around 3 in a million.
Overdamped NbTiN Josephson junctions with Ti–TiN bilayered normal-metal barrier are proposed for metrological applications. Binary arrays consisting of 32 768 NbTiN/Ti–TiN/NbTiN junctions were fabricated for quantum voltage standards, and a Shapiro step at 1 V with the step height of about 0.5 mA was generated at around 8 K. The Ti layer was added to protect the base NbTiN electrode from nitrogen plasma during the deposition of the TiN layer. While the critical current Ic and the junction resistance Rn are mainly dominated by the thickness of the TiN barrier, Ic can be also adjusted by changing the thickness of the Ti barrier to maximize the operating margin for voltage standard circuits. An optimization of the NbTiN film in terms of film stress is also described for fabrication of circuits containing such a large number of junctions.