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IEEE Transactions on Applied Superconductivity

Measurement of the error rate of single flux quantum circuits with high temperature superconductors

Ben J. Ruck, Yonuk Chong, Regina Dittmann, A. Engelhardt, B. Oelze, Erik Sodtke, M. Siegel, W.E. Booij, Mark G. Blamire

Published Jun 1, 1999• 15 citations
Publisher

Abstract

The determination of bit error rates in single flux quantum logic circuits operating at temperatures well above the temperature of liquid helium is essential since the question of stability against thermal noise arises. We determined experimentally the static and for the first time the dynamic error rate at temperatures of about 40 K with the help of simple test circuits. The static error rate has been investigated using two different circuits with bicrystal junctions in either single-layer or multilayer configuration. In both cases the internal state of a storage loop was observed by a dc-SQUID. A ring oscillator based on a Josephson transmission line allowed us to measure the dynamic error rate of a Josephson comparator at high frequencies. This circuit has been fabricated using junctions by focused-electron-beam irradiation. It is specially suited for the detection of seldom occurring switching errors.

DOI
10.1109/77.783867

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The determination of bit error rates in single flux quantum logic circuits operating at temperatures well above the temperature of liquid helium is essential since the question of stability against thermal noise arises. We determined experimentally the static and for the first time the dynamic error rate at temperatures of about 40 K with the help of simple test circuits. The static error rate has been investigated using two different circuits with bicrystal junctions in either single-layer or multilayer configuration. In both cases the internal state of a storage loop was observed by a dc-SQUID. A ring oscillator based on a Josephson transmission line allowed us to measure the dynamic error rate of a Josephson comparator at high frequencies. This circuit has been fabricated using junctions by focused-electron-beam irradiation. It is specially suited for the detection of seldom occurring switching errors.
The application of high temperature superconductor (HTS) Josephson junctions in digital rapid single flux quantum circuits requires a careful study of the influence of thermal noise on the bit error rate (BER). We have determined experimentally, for the first time, the BER of a HTS rapid single flux quantum circuit. A comparator, formed by two Josephson junctions, was integrated in a Josephson transmission line ring oscillator, allowing us to perform high speed testing of the comparator at GHz frequencies. For fabrication, focused-electron-beam-irradiated junctions have been used because of their small parameter spread and excellent alignment possibilities. A BER of less than 10−11 was obtained at 39 K.
We have designed and simulated a circuit for the experimental determination of the rate of dynamic switching errors in high-temperature superconductor RSFQ circuits. The proposal is that a series-connected pair of Josephson junctions is read out by SFQ pulses circulating in a ring-shaped Josephson transmission line at high frequency. Suitable bias currents determine the switching thresholds of the junction pair. By measuring the voltage across the transmission line, it is proposed that the occurrence of a switching error can be detected. The bit error rate can be determined from the mean time before false switching together with the SFQ circulation frequency. The circuit design allows measurements over a wide temperature range.
We measured the static error rate of a high-Tc superconductor dc superconducting quantum interference device (SQUID), which, in the form as a storage loop for single flux quanta, is a basic element of rapid single flux quantum circuits. Using high-Tc multilayer bicrystal technology, we fabricated a stacked dc SQUID pair, one SQUID serving as the storage loop, the other one as the readout device. The escape rate of a stored flux quantum was measured as a function of the bias current at a temperature of 28 K. The measured error rates were in good agreement with a model calculation based on thermally activated barrier crossing.
We report the fabrication and measurement of quantum flux parametron logic from high-transition-temperature Josephson junctions operating at 25 K, above the temperature of liquid helium. The circuits are written directly into the plane of a single-layer thin film of YBa2Cu3O7 using a focused helium ion beam. A single-cell quantum flux parametron was constructed and correct logic operation was verified by using an on-chip superconducting quantum interference device for readout. A three-cell shift register was also fabricated and tested using a three-phase clock cycle. We estimate the average bit energy to be about 1×10−20 J at 1 GHz.
A major restriction in the development of a working Rapid Single Flux Quantum (RSFQ) logic circuit with high-Tc superconductors is given by the influence of thermal noise. This gives reason to ask for a general determination of the digital bit error rate. As other approaches, our method of calculating the switching probability is based on the Fokker-Planck equation. In the past few years the bit error rates for a single Josephson junction, SQUIDs and the comparator were calculated by using this theory. We demonstrate numerical solution of the multidimensional Fokker-Planck equation to calculate bit error rates due to thermal noise for a Toggle Flip Flop circuit. In the present work, we combine thermal noise analysis with the effects of process variations in order to derive rules for designing high-Tc RSFQ logic circuits.
The influence of thermal noise gives a major restriction in the development of Rapid Single Flux Quantum (RSFQ) logic circuits with high-T/sub c/ superconductors. In the past, we have demonstrated a general way for determining the digital bit error rate and for predicting operation ranges with good noise immunity. The method is based on a single Fokker-Planck equation which includes the full system dynamics. However, the complexity of this equation increases dramatically with the number of Josephson junctions. Our new approach describes a method to divide an RSFQ logic cell into several basic primitives. They can be characterized quickly in terms of switching probability for a lot of different parameters. From these analyses, look-up tables are built-up. We describe how to combine these data in order to achieve the bit-error rate for the whole cell. While saving more than 90% of computation time, the comparison with our previous results for full system analyses shows less than 4% difference. This approach provides for a powerful tool to include the influence of thermal noise into the optimization process of RSFQ logic circuits as well.