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IEEE Transactions on Applied Superconductivity

Temperature-dependent bit-error rate of a clocked superconducting digital circuit

Quentin Herr, M.W. Johnson, M. J. Feldman

Published Jun 1, 1999• 28 citations
Publisher

Abstract

We measured the bit-error rate (BER) of an RS latch, a clocked SFQ circuit. A digital error-detection circuit was used to detect BER in the range unity to 10/sup -13/; below 10/sup -7/, the circuit was operated with a 12 GHz on-chip clock. BER was measured as a function of control current; both positive and negative control current was applied, leading to two distinct modes of error incidence. The error function curves extrapolate to 10/sup -80/ for optimal control current at a temperature of 5.5 K. Measurements were repeated over the range 3-7 K. Comparison to theoretical error-function estimates of BER indicate that the noise is strictly thermal.

DOI
10.1109/77.783807

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We measured the bit-error rate (BER) of an RS latch, a clocked SFQ circuit. A digital error-detection circuit was used to detect BER in the range unity to 10/sup -13/; below 10/sup -7/, the circuit was operated with a 12 GHz on-chip clock. BER was measured as a function of control current; both positive and negative control current was applied, leading to two distinct modes of error incidence. The error function curves extrapolate to 10/sup -80/ for optimal control current at a temperature of 5.5 K. Measurements were repeated over the range 3-7 K. Comparison to theoretical error-function estimates of BER indicate that the noise is strictly thermal.
A new method of analyzing bit error rates (BERs) for SFQ circuits and their outputs at GHz speeds will be presented. This method was used to test four- and six-bit pseudorandom code generators. The code generators were operated in free-run mode, i.e., without a synchronization (Reset) pulse. This enabled us to conduct BER testing to much lower levels than when the code generator is operated in Reset mode. The SFQ circuit output was amplified with a superconducting output latch to give voltage levels suitable for display on a sampling scope. The GHz output data was analyzed by external computer software; this permitted extended tests without user supervision. With the code generators operating in free-run mode, they routinely gave bit error rates (BERs) in the 10/sup -11/ range; the best BER recorded was 1.1*10/sup -13/ (2 errors in /spl sim/2.5 hours) at 2 GHz. We have successfully tested these code generators at frequencies in excess of 3.5 GHz with BERs in the 10/sup -10/ range as well.
The discovery of the superconductive properties of magnesium diboride enables us to attempt to produce a rapid single flux quantum (RSFQ) logic device with an operation temperature of about 20 K which can be easily reached with cryocoolers. As elevated temperatures significantly increase the probability of noise-induced errors, we examine the situation in this particular temperature range. We calculate bit-error rates (BER) due to thermal noise for a toggle flip-flop as a typical RSFQ circuit with a clock frequency of 100 GHz. For this, we consider parameter spread and noise separately and observe a very low noise-induced BER. The critical margin diminishes by a small amount only.
We have carried out measurements of bit error rate (BER) of Rapid Single-Flux-Quantum (RSFQ) XOR gates with various nominal dc power supply voltages (from 0.1 V to 1.0 mV), operating at speeds up to 25 GHz. (For these gates, implemented using HYPRES' standard, 3.5-/spl mu/m, 10 /spl mu/A//spl mu/m/sup 2/ Nb-trilayer process, this speed is close to maximum.) A special on-chip RSFQ test circuit allowed high-speed measurements of BER in the range from 10/sup -9/ to 10/sup -13/ to be carried out. As a result of these experiments, a new type of thermal-fluctuation-induced digital errors in RSFQ circuits has been identified. These "timing" errors arise at high speed due to time jitter of data and clock pulses. We have developed a simple theory of these errors which allows a fair description of the experimental data. The theory shows that in some cases the timing errors may be an important factor limiting speed performance of RSFQ circuitry. Nevertheless, our XOR gates could operate at 25 GHz with BER below 10/sup -13/ at the standard temperature (4.2 K) at any dc power supply voltage in our range. For the lowest voltage (0.1 Volt) the calculated static power dissipation in the gate was as low as 23 nanowatts, lower than the unavoidable dynamic dissipation (43 nanowatts).
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.