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Journal of Low Power Electronics and Applications

An Empirical Method for Predicting the Critical Current of Unshunted Josephson Junctions in a Shielded Room from Measurements in an Unshielded Room

Jian Zhou, Juan Wang, Yewen Yao, Yongliang Wang, Man Wang, Wei Peng

Published Oct 24, 2026• 0 citations
Publisher

Abstract

The critical current (Ic) of a Josephson junction (JJ) is a significant physical parameter that plays a crucial role in the design of subsequent devices and circuits, as well as in the optimization of manufacturing processes. To ensure accurate measurements, testing should ideally be conducted in a magnetically shielded room. However, due to laboratory constraints, tests are often performed in unshielded environments, where they are inevitably influenced by various environmental noises. This introduces significant uncertainty into the measured Ic values, thereby impacting the design of subsequent superconducting circuits. This study examines the impact of conductive, radiated, and flux noise on the repeatability of Ic measurements in an unshielded environment and establishes an empirical formula for predicting Ic values in shielded environments based on unshielded data. The deviation between the empirically predicted Ic and the experimentally measured value is less than 1%, verifying the effectiveness of the proposed formula. This approach offers a relatively accurate and cost-effective method for testing the critical current (Ic) of Josephson junctions (JJs) under unshielded conditions.

DOI
10.3390/jlpea16040049

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The critical current (Ic) of a Josephson junction (JJ) is a significant physical parameter that plays a crucial role in the design of subsequent devices and circuits, as well as in the optimization of manufacturing processes. To ensure accurate measurements, testing should ideally be conducted in a magnetically shielded room. However, due to laboratory constraints, tests are often performed in unshielded environments, where they are inevitably influenced by various environmental noises. This introduces significant uncertainty into the measured Ic values, thereby impacting the design of subsequent superconducting circuits. This study examines the impact of conductive, radiated, and flux noise on the repeatability of Ic measurements in an unshielded environment and establishes an empirical formula for predicting Ic values in shielded environments based on unshielded data. The deviation between the empirically predicted Ic and the experimentally measured value is less than 1%, verifying the effectiveness of the proposed formula. This approach offers a relatively accurate and cost-effective method for testing the critical current (Ic) of Josephson junctions (JJs) under unshielded conditions.
The measurement of critical currentIc, as an important parameter of un-shunted Josephson junctions (JJ), is critical for designing superconductor analog devices or digital circuits. However, precise measurement ofIcfrom current–voltage (I–V) characteristic curves often faces difficulties, such as the disturbance of environmental magnetic and electromagnetic waves (EM) noise, which significantly decreases theIcvalue from ideal critical currentIc0and increases the uncertainty ofIcmeasured value (>10 %). In this article, a test procedure is proposed for measuring theI–Vcurve of un-shunted JJ under a magnetic shielding environment, effectively avoiding deficiencies of conventional methods such as poor uncertainty and lowerIcmeasurement value. The uncertainty ofIcis investigated based on different superconducting JJs, and the results show that the combined uncertainty ofIcis less than 2% (the current stepμA). Also, a formula expressing the relationship ofIcwith the radius of JJ is proposed, which may provide a good way of predictingIcfor practical experimental measurements. The effectiveness of the procedure and the formula are both verified by experiments based on the Nb/Al-AlOx/Nb samples. The method is helpful for round-robin standard measurement onIcof un-shunted JJ and shortens the investigation process feedback time of the RSFQ integrated circuit.
Abstract Josephson superconducting qubits and parametric amplifiers are prominent examples of superconducting quantum circuits that have shown rapid progress in recent years. As such devices become more complex, the requirements for reproducibility of their electrical properties across a chip are being tightened. Critical current of the Josephson junction Ic is the essential electrical parameter in a chip. So, its variation is to be minimized. According to the Ambegaokar–Baratoff formula, critical current is related to normal-state resistance, which can be measured at room temperature. In this study, we focused on the dominant source of non-uniformity for the Josephson junction critical current–junction area variation. We optimized Josephson junction fabrication process and demonstrated resistance variation of 9.8–4.4% and 4.8–2.3% across 22 × 22 mm2 and 5 × 10 mm2 chip areas, respectively. For a wide range of junction areas from 0.008 to 0.12 μm2, we ensure a small linewidth standard deviation of 4 nm measured over 4500 junctions with linear dimensions from 80 to 680 nm. We found that the dominate source of junction area variation limiting Ic{\mathrm{I}}_{\mathrm{c}}Ic​ I c reproducibility is the imperfection of the evaporation system. The developed fabrication process was tested on superconducting highly coherent transmon qubits (T1 > 100 μs) and a nonlinear asymmetric inductive element parametric amplifier.
We investigated current-voltage characteristics of unshunted and externally shunted Josephson junctions (JJs) with high critical current densities Jcin order to extract their basic parameters and statistical characteristics for JJ modeling in superconducting integrated circuits as well as to assess their potential for future technology nodes. Nb/AlOx-Al/Nb junctions with diameters from 0.5 to 6 μm were fabricated using a fully planarized process with Mo or MoNxthin-film shunt resistors with sheet resistance Rsq= 2 Ω/sq and Rsq= 6 Ω/sq, respectively. We used our current standard MIT Lincoln Laboratory process node SFQ5ee to fabricate JJs with Jc= 0.1 mA/μm2and our new process node SFQ5hs (where “hs” stands for high speed) to make JJs with Jc= 0.2 mA/μm2and higher current densities up to about 1 mA/μm2. Using LRC resonance features on the I-V characteristics of shunted JJs, we extract the inductance associated with Mo shunt resistors of 1.4 pH/sq. The main part of this inductance, about 1.1 pH/sq, is the inductance of the 40-nm Mo resistor film, while the geometrical inductance of superconducting Nb wiring contributes the rest. We attribute this large inductance to “kinetic” inductance arising from the complex conductivity of a thin normal-metal film in an electromagnetic field with angular frequency ω, σ(ω) = σ0/(1 + iωτ), where σ0is the static conductivity and r the electron scattering time. Using a resonance in a large-area unshunted high-Jcjunction excited by a resistively coupled small-area shunted JJ, we extract the Josephson plasma frequency and specific capacitance of high-Jcjunctions in 0.1-1 mA/μm2Jcrange. We also present data on Jctargeting and JJ critical current spreads. We discuss the potential of using 0.2-mA/μm2JJs in very large scale integration single flux quantum circuits and 0.5-mA/μm2JJs in high-density integrated circuits without shunt resistors.
A method of accurately estimating the I/sub 0/ (critical current) of a Josephson junction (JJ) with thermal noise was developed by measuring the effective thermal noise temperature of a JJ. The effective thermal noise temperature of various JJ devices was measured and calculated. The JJ devices evaluated included inductively and resistively coupled logic devices and JJ devices in the presence of various noise sources. The noise sources included room-temperature resistors, switched JJ devices, and JJ devices in the linear I-V region beyond the gap. The R/sub NN/ compensator is shown to result in a noise temperature of about 6 K at an interferometer. The addition of a shunt junction lessens the noise penalty introduced by the compensator. A switched isolation interferometer in a two-input AND gate contributes negligible noise at the injection device. It is also shown that bandwidth connections to room-temperature equipment result in very large excess noise and require special input and output circuits on the chip.>
Experimental measurements on critical current noise in underdamped niobium based Josephson devices by a technique based on the switching current measurements is reported. By sweeping the junction with a current ramp we measure the critical current switching as a function of the time using the standard time of flight technique. In such a way it is possible to obtain the critical current fluctuations ΔIc=Ic(t)-<Ic(t)> and the relative standard deviations which corresponds to the root square of the current fluctuation power. Pointing at the white noise fluctuations (above few Hz) and taking into account the physical frequency of the device, it is possible to evaluate the power spectral density of the critical current. The analysis has involved high quality underdamped Josephson junctions having an area ranging from (4x4) μm2 to (40x40) μm2 in the temperature range from 4.2 K to few tenth of mK. These measurement provide very useful information about the intrinsic noise of Josephson devices involving SQUIDs and qubits.