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IEEE Transactions on Electron Devices

Minimum-width control-current pulse for Josephson logic gates

S.H. Dhong, T. Van Duzer

Published Oct 1, 1980• 14 citations
Publisher

Abstract

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.

DOI
10.1109/t-ed.1980.20133

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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.
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 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.
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.
Switching speeds of experimental Josephson interferometer circuits are measured on chains of current injection logic (CIL) gates fabricated using 2.5-μm minimum features. Logic delay of 32 ps per gate is measured for a four-input OR gate with a fan-out of 2. The average power dissipation of the four-input OR gate is 4 μW and the corresponding power-delay product is 1.28×10−16 J. For four-input AND gates the measured logic delay is 60 ps, the power dissipation is 6 μW, and the power-delay product is 3.6×10−16 J. The results are found to be in excellent agreement with estimates based on computer simulations.
Devices of three types: magnetic pulse generators, read-out circuits, and digital circuits controlling them are needed to support scalable operation of quantum logic based on the Josephson junction qubits. The most natural framework for implementation of such a classical interface to quantum circuits is provided by the RSFQ technology . In this work, we argue, however, that specific qubit requirements can not be satisfied with the conventional RSFQ approach and describe the necessary modifications. We suggest a new structure of the pulse generator based on two long underdamped Josephson junctions which is characterized by the reduced power consumption and reduced output noise. We also show how to trade off power consumption and speed of the digital control circuits by using Josephson junctions with similar values of the shunt resistors but very different critical currents. Finally, we suggest a new read-out circuit which enables dynamic compensation of the backaction down to the level approaching fundamental quantum-mechanical limit.
A new type of single flux quantum logic gate is proposed, which can perform unilateral propagation of signal without using three-phase clock. This gate is designed to be built with bridge-type Josephson junctions. A basic logic gate consists of two one-junction interferometers coupled by superconducting interconnecting lines, and the logical states are represented by zero or one quantized fluxoid in one of one-junction interferometers. The bias current of the unequal magnitude to each of the two one-junction interferometers results in unilateral signal flow. By adjusting design parameters such as the ratio of the critical current of Josephson junctions and the inductances, circuits with the noise immunity of greater than 50% with respect to the bias current have been designed. Three cascaded gates were modeled and simulated on a computer, and the unilateral signal flow was confirmed. The simulation also shows that a switching delay about 2 picoseconds is feasible.