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IEEE Transactions on Magnetics

Josephson device with well-defined and low critical points

H. Beha

Published May 1, 1983• 1 citation
Publisher

Abstract

Two different basic types of switching behavior of Josephson interferometers are possible: a vortex-to-vortex and a vortex-to-voltage transition. Both transition types are separated by the so-called critical points on the threshold curve of the device. For critical points, in general, no analytic expression is available. Therefore, the position of the critical points can only be determined by numerical solutions. In the designs known, the critical points are very sensitlve with respect to parameter variations, which makes LSI design very difficult. In this paper, the design and the experimental results of an asymmetric Josephson interferometer with one well-defined and low critical point are described. This well-defined critical point corresponds to the tip point of the threshold characteristic, which is defined by an analytical expression. The practical consequence for the design of Josephson circuits will be indicated. The dynamic switching behavior of the asymmetric interferometer with respect to the critical points will be discussed extensively in the phase plane, together with the potential energy.

DOI
10.1109/tmag.1983.1062321

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Two different basic types of switching behavior of Josephson interferometers are possible: a vortex-to-vortex and a vortex-to-voltage transition. Both transition types are separated by the so-called critical points on the threshold curve of the device. For critical points, in general, no analytic expression is available. Therefore, the position of the critical points can only be determined by numerical solutions. In the designs known, the critical points are very sensitlve with respect to parameter variations, which makes LSI design very difficult. In this paper, the design and the experimental results of an asymmetric Josephson interferometer with one well-defined and low critical point are described. This well-defined critical point corresponds to the tip point of the threshold characteristic, which is defined by an analytical expression. The practical consequence for the design of Josephson circuits will be indicated. The dynamic switching behavior of the asymmetric interferometer with respect to the critical points will be discussed extensively in the phase plane, together with the potential energy.
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This paper describes the dynamic threshold characteristics of Josephson switching gates. When high speed input signals are applied to the Josephson logic gate, the threshold characteristics of the gate are not always in accord with the well-known static threshold curves. This is because the static threshold curves are affected by quantum flux change in Josephson junctions under the high speed operation. The dynamic threshold characteristics of two typical logic gates, one is the CIL gate and the other the interferometer, are described in detail.
A new type of logic gate that can be designed using a nonhysteretic Josephson weak link is proposed. The basic component of the proposed device is a one-junction interferometer, and a logic state is represented by either a zero or a single-flux-quantum. In contrast to the "Parametric Quantron," this device is designed to operate without a three-phase clock and the dependence of the junction critical current on magnetic field is not used. The switching behavior of the device was simulated by computer and an analytical expression for the switching delay has been obtained.
Thin-film Josephson-junction quantum-interference devices require only a small amount of magnetic flux to switch them between the voltage state and the superconducting state. They are sensitive to any spurious magnetic flux present at the device. The magnetic flux may be trapped in the superconducting ground plane, particularly in ground plane holes. This paper analyzes the effects of the trapped magnetic flux on the threshold curves of three-junction Josephson interferometers. The threshold curves of the interferometer are calculated automatically by using a circuit optimization program. The automatic procedure of calculating the threshold curves of an interferometer can be applied to any Josephson-junction interferometer device. The threshold curves of both symmetric and asymmetric interferometers are calculated. We find that the threshold curves of a symmetric three-junction interferometer changes periodically as a function of the effective coupled trapped magnetic flux with a period of Φ0. The threshold curves are shifted and severely distorted in shape by the presence of the coupled trapped magnetic flux. The degeneracy of the threshold curves of a symmetric interferometer makes the unique quantitative determination of the trapped magnetic flux difficult. However, the degeneracy is removed in an asymmetric interferometer. The presence of the unbalanced trapped magnetic flux greatly shifts the entire threshold curve of an asymmetric interferometer.
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).