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IEEE Transactions on Magnetics

Turn-on delay of Josephson interferometer logic devices

E. P. Harris

Published Jan 1, 1979• 49 citations

Abstract

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).

DOI: 10.1109/tmag.1979.1060167

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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.

This paper describes the design, fabrication and characterization of damped three-junction interferometers suitable for LSI latching logic. The high speed and low power dissipation of Josephson interferometers make them ideal devices for logic applications. However, their inherent high Q gives rise to resonances which appear as current steps in the quasiparticle curve. If not controlled, these current steps can interfere with the proper operation of logic circuits. Studies have shown that these resonances can be effectively damped by shunting the interferometer inductance with a small resistance. In this work the interferometers were made by placing the interferometer loops parallel to the groundplane and clustering the Josephson junctions together. This minimized the loop inductance associated with the counterelectrode which in turn meant that adequate damping could be achieved with metallurgically compatible short resistors connected only to the base electrode. The resultant structure with two overlying control lines each 2.5μm wide had an area of 0.008mm2. The Josephson junctions were 5μm in diameter. The measured damped resonance characteristics and threshold characteristics (Ig(Vg) and Im(Ic) respectively) of these structures agreed very well with theory.

The gate delay of a single CIL AND gate is measured with a Josephson sampler. The CIL gate consists of a CIL interferometer preceded by a three-junction SQUID isolation stage. The smallest delay observed was 6 ps. Simulation results and sampling measurements of a gate designed to switch to 3Vgare also reported. Processing variations precluded successful operation of the higher-voltage gate. The simulations suggest that this failure is due to the large difference of the average critical current from the design value. Scaling arguments show that for small-scale circuits high-speed operation with gate delays of a few picoseconds can be achieved with junction dimensions approximately equal to the Josephson penetration depth.

Resonances in the current-voltage characteristics of interferometers with two Nb-NbOx-Pb window junctions have been experimentally investigated. The data are compared with the theoretical curves computed both for the voltage and for the magnetic field dependence of the resonance amplitudes. Very good agreement is found in all the range of values of the damping parameter Γ=I0 R/Vr, where Vr is the resonant voltage and I0 and R are the maximum Josephson current and the parallel resistance of each junction. New features that cannot be explained in terms of the existing theory have been observed in devices with larger values of the parameter β=2πLI0/Φ0, where L is the loop inductance, and Φ0 is the flux quantum.

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.