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IEEE Transactions on Applied Superconductivity

Switching Time Versus DC Current Overdrive of a Josephson Junction Sampler

Bart J. Van Zeghbroeck

Published Jan 19, 2024• 1 citation
Publisher

Abstract

The time resolution of a Josephson junction sampler depends on the switching time of the junction. This switching time depends on the junctions' plasma frequency and McCumber parameter, but also on the amount of overdrive current applied. An approximate closed form expression is derived for the switching time as a function of the overdrive, excluding damping or noise. A key result is that the switching time depends logarithmically on the overdrive. Numeric simulations are used to justify the approximations made and reveal the dependence on damping. Comparisons are made between the analytic expression and a numeric simulation of the switching time. Application of the results to a Josephson sampler is presented.

DOI
10.1109/tasc.2024.3353132

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The time resolution of a Josephson junction sampler depends on the switching time of the junction. This switching time depends on the junctions' plasma frequency and McCumber parameter, but also on the amount of overdrive current applied. An approximate closed form expression is derived for the switching time as a function of the overdrive, excluding damping or noise. A key result is that the switching time depends logarithmically on the overdrive. Numeric simulations are used to justify the approximations made and reveal the dependence on damping. Comparisons are made between the analytic expression and a numeric simulation of the switching time. Application of the results to a Josephson sampler is presented.
It has generally been assumed that the switching dynamics of Josephson logic devices can be well approximated by treating the Josephson device as a capacitatively-shunted switch which opens instantaneously when a control current crosses threshold. In this approximation, the switching delay is proportional to RC, where R = load resistance and C = device capacitance. However, we show here that the above approximation is quite incorrect in the technologically important case of logic interferometers in which resonances are suppressed by internal damping. We treat in detail the case of damped two-junction interferometers with step-function control current. Analysis of the equations of motion shows that in addition to the RC delay there is an initial turn-on delay during which the output voltage is very small, and which is most pronounced for heavy internal damping. It consists of the time required for the difference in phase between the two junctions to increase to a critical value, followed by approximately the first half-cycle of growth of the average of the junction phases. The turn-on delay is a strong function of overdrive, (i.e., the factor by which the control current amplitude exceeds threshold), being smallest at large overdrives, and scales as (C/i0)1/2, where i0= junction critical current. Hence it can be reduced by miniaturization and/or increased junction current density. For parameter values typical of 5μm Josephson circuit technology, the turn-on delay is on the order of 10pS at large overdrives (≃2).
For a given level of overdrive, there exists a minimum-width control-current pulse that must be applied to switch a Josephson logic gate. Determination of this minimum pulsewidth is useful in setting limits on the speed of various Josephson circuit configurations and also in finding the narrowest pulse that a Josephson-junction gate can detect when it is employed as a pulse detector. The minimum control-current pulsewidth is a strong function of the overdrive factor of the control current. It scales as(C/I_{m})^{1/2}, where Imis the junction critical current, andCis the capacitance, and is on the order of 10 ps for Josephson quantum interferometers in 5-µm technology. Computer simulations have been done to find the dependence of minimum control-current pulsewidths on overdrive magnitude for a single-junction gate and for two- and three-junction interferometers. Analytic expressions of the minimum control-current pulsewidth that are in good agreement with simulations have been obtained for these three types of Josephson logic gates.
A high-resolution Josephson sampler using a single fluxoid is fabricated. The sampling pulse generator comprised a two-junction interferometer (DC–SQUID) with a damping resistance resistively coupled to a single junction as the sampling gate to reduce a turn-on delay. An ultra-fast sampling pulse was generated at a vortex-to-vortex transition in this sampler. The fabricated sampler had less than a 5ps time resolution and about a 5 µA current sensitivity. The dynamic waveform associated with two kinds of transitions was observed by the use of this sampler: a vortex-to-vortex transition and a vortex-to-voltage transition. The results show that the pulse corresponding to a single fluxoid has a nearly constant pulse height that is independent of the bias current and that setting the bias current near the critical point results in the long rise time of a DC–SQUID.
The authors propose a new type of sampler design based on shunted junctions ( beta c =1). The sampler is to be used for the investigation of single flux quantum devices (RSFQ) employing similar junctions (Kaplunenko et al. 1989, Filippenko et al. 1991). They measure the time resolution of the sampler and delay time of the shunted Josephson junction array. The circuit was manufactured on a single chip and was DC powered. They employed Nb-AlO x -Nb tunnel junctions of 300 A m -2 critical current density and observed Josephson oscillations of the output junction at frequencies from 6 to 50 GHz. Despite a long plasma period of 20 ps the time resolution was 5 ps. The transmission line of 27 Josephson junctions (critical current 165 mu A each) demonstrated time delay of 0.5 ps mu A -1 .
For a current-driven Josephson junction shunted by an Ohmic resistance, the dc voltage response and impedance to external high-frequency currents is calculated with a second-order perturbation method based on the unperturbed solution for the time evolution of the voltage as given by Aslamazov and Larkin. The response is proportional to signal power and has three characteristic-frequency regions depending on whether the internal self-generated Josephson frequency, ω0, is larger than, equal to, or smaller than the signal frequency, ω. For ω0< or >ω the response could be expressed by easily observable parameters of the dc voltage-current characteristics. This permits comparison of the predictions with experimental results obtained on point-contact junctions whose dc characteristics were only approximately represented by the simple model chosen for analysis. For ω0≪ω the response is found to be proportional to (i) the slope of the dc characteristic, (ii) the inverse square of the applied frequency, (iii) the inverse battery current in terms of the critical current, and (iv) the voltage amplitude of the inherent Josephson oscillations. For ω0≫ω ``classical'' detection proportional to curvature is obtained. For ω0∼ω resonance detection occurs, which depends to a considerable degree on fluctuations of the average contact voltage. These predictions are in reasonable agreement with experiments in which point-contact junctions were illuminated with klystron radiation at 10 and 90 GHz. Evidence is presented that the voltage fluctuations limiting the resonance response are the result of noise generated in the junction. Comparison of the noise-equivalent power expected from the simple model with measured results suggests that parasitic elements, such as shunt capacity, are not negligible at 90 GHz.