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Journal of Applied Physics

Transient analysis of low-hysteresis Josephson interferometer with feedback

S. E. G. Slusky, L. D. Jackel

Published Jan 1, 1982• 2 citations
Publisher

Abstract

We have performed a transient analysis of a Josephson interferometer in which feedback has been introduced to sharpen the transfer function. We examine the case for junctions with small, but finite, capacitance, so that the junction I-V characteristics have a small hysteresis. We find that no significant changes in switching times occur when feedback is introduced. The transfer function for the interferometer calculated in our ac analysis, which includes finite junction capacitance, is somewhat different from the one determined by a simple dc analysis that assumed zero capacitance.

DOI
10.1063/1.329939

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We have performed a transient analysis of a Josephson interferometer in which feedback has been introduced to sharpen the transfer function. We examine the case for junctions with small, but finite, capacitance, so that the junction I-V characteristics have a small hysteresis. We find that no significant changes in switching times occur when feedback is introduced. The transfer function for the interferometer calculated in our ac analysis, which includes finite junction capacitance, is somewhat different from the one determined by a simple dc analysis that assumed zero capacitance.
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).
A 1:2:1 Josephson interferometer has been fabricated with small-area, high–current-density tunnel junctions. The short intrinsic RC times of these junctions result in device I-V characteristics with reduced hysteresis suitable for use in nonlatching logic circuits. The control current for this interferometer was fed directly, and asymmetrically, into the base electrode. Critical current versus control current measurements indicate that this device has a current gain greater than unity. The interferometer described represents an exploratory study of circuit design incorporating low-hysteresis junctions.
The geometrical interelectrode capacitances of superconducting microbridges are too small to account for the observed hysteresis in their I-V characteristics. We propose a new model of microbridges in finite voltages, in which the relevant time constant is the supercurrent relaxation time τR. From an analysis of the experimental I-V curves it follows that τR can be identified with the pair relaxation time within a numerical factor. By equating τR/2π to the time constant C/G of the shunted Josephson junction model, we obtain values of C in reasonable agreement with those typically obtained from I-V characteristics.
We investigate the noise-affected I-V curves of small-area Josephson junctions through experiment, simulation, and theory. In particular, we consider I-V curves in which two different states of finite voltage coexist at the same dc bias: a high-voltage state that corresponds to the usual quasiparticle branch and a low-voltage state that is characterized by thermally activated phase diffusion. The observed hysteresis between the phase-diffusion and quasiparticle branches cannot be explained within the context of the simple resistively and capacitively shunted junction (RCSJ) model but is explained by extended models in which the damping increases with frequency. Frequency-dependent damping is shown to produce a qualitative change in the attractors of the noise-free system which allows the two voltage states to be simultaneously stable. This picture is confirmed by Monte Carlo simulations which accurately reproduce the experimental I-V curves of two different samples over a wide range of temperatures. In addition we develop analytic expressions for three key parameters of the I-V curve of junctions displaying hysteresis between the phase-diffusion and quasiparticle branches: the initial slope of the phase-diffusion branch, the bias level at which the junction switches from the phase-diffusion branch to the quasiparticle branch, and the bias level at which it returns to the phase-diffusion branch.
The effect of noise on the current-voltage characteristic of a Josephson junction is investigated (1) when the temperature is near the transition temperature of the superconductors and (2) when the junction is driven by an external signal. In case (1) the noise source is the quasiparticle tunneling current but in case (2) there is in addition the noise arising from the finite linewidth of the external signal. This latter noise source is shown to dominate when the junction is operating at high harmonics. We treat the problem in the limits of small and large capacitance and obtain a criterion to determine under what circumstances each limit applies. A solution that includes a first-order correction due to a finite capacitance is given. In the limit of large capacitance the existence and lifetime of hysteresis curves are discussed.