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IEEE Transactions on Applied Superconductivity

A Measurement Method of Critical Current of Un-Shunted Josephson Junction

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

Published Sep 13, 2023• 3 citations
Publisher

Abstract

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.

DOI
10.1109/tasc.2023.3314855

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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.
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.
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.
In the design of electronic applications (for example, rapid single flux quantum (RSFQ) circuits), the properties of Josephson junctions (JJs) provided by technology are the major requirement. The characteristic voltage IcRn an dt he dynamic parameter βc are non-negligibly important, bu tt he external shunted junctions are only completely described by including the parasitic inductance between the junction area and the shunt resistor. The first publications of the RSFQ circuit technique were closely followed by many studies on the dynamic influence of this inductance. It has been pointed out that no practical value of this parameter has to be taken into account in the circuit design and optimization process. The operation of RSFQ logic circuits made of high-temperature superconductors (HTS) are strongly influenced by thermal noise. Our paper contains the determination of the digital bit-error rate for all different types of JJs by using a Fokker–Planck equation for describing the influence of thermal fluctuations. Ou ra nalysis shows that the parasitic inductance cannot be neglected in terms of noise. The intrinsic shunted junctions like high current density-, SINIS- and all kinds of HTS-JJs provide the best noise immunity for a fixed temperature.
Josephson junctions (JJs) with non-hysteretic I-V characteristic and high critical parameters are required for many applications; in particular, they are needed to create tunable THz range oscillators. We fabricated and studied shunted superconductor-insulator-superconductor (SIS) Nb-AlOx-Nb tunnel junctions with an area of about 1μm2, estimated their parameters, and compared them with theoretical models. To assess the performance of shunted junctions in the terahertz range, their characteristics were studied under the influence of a high-frequency signal; the estimated value of the characteristic voltage for the shunted junction at a high frequency is about 1 mV. To improve the circuit parameters, a new type of the shunting based on application of NIS junctions was proposed, which reduces the influence of parasitic inductance, expands the frequency range of the generator, and decreases the size of the structure. The JJs with a new type of shunting have been fabricated and studied. The niobium integrated circuits intended for matching the superconducting oscillator and an SIS junction as a microwave detector were designed, fabricated, and tested. Such structures are required for studying the spectral characteristics and analyzing the operation of the oscillator. The developed circuits have demonstrated efficient operation at frequencies from 300 to 700 GHz; the experimental results are in good agreement with the simulated characteristics. The results obtained will be implemented for further development of the THz range oscillators.
We measured the low frequency critical current noise in Nb/AlOx/Nb Josephson junctions. Unshunted junctions biased above the gap voltage and resistively shunted junctions biased near the critical current Ic have been measured. For both, the spectral density of δIc/Ic, Sic(f), is proportional to 1/f, scales inversely as the area A and is independent of Jc≡Ic/A over a factor of nearly 20 in Jc. For all devices measured at 4.2 K, Sic(1 Hz)=2.0±0.4×10−12/Hz when scaled to A=1 μm2. We find that, from 4.2 to 0.46 K, Sic(f) decreases linearly with temperature.
For a study of the supercurrent–phase relationship, we have fabricated Nb/Al/AlOx/Al/AlOx/Al/Nb-based Josephson junctions of low critical current density. At 4.2 K, junctions of a nominal area of 10×10 μm2 showed a nonhysteretic dc current–voltage characteristic with a critical current of about 10 μA. Similar junctions were part of washer-type rf superconductor quantum interference devices. These samples were inductively coupled to high-quality tank circuits for measurements at 4.2 K or at higher temperatures up to values close to the critical temperature of niobium. In this range, the current–phase relation, as deduced from impedance measurements of the phase-biased junction, did not deviate significantly from the sinusoidal shape.