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Journal of Applied Physics

Josephson comparator with modified dynamic behavior for improved sensitivity

Thomas Ortlepp, Shigeyuki Miyajima, Hannes Toepfer, Akira Fujimaki

Published Jun 15, 2012• 10 citations
Publisher

Abstract

The decision of a Josephson comparator is influenced by thermal noise which is limiting the practical sensitivity in many applications of superconductor electronics. We analyzed the Gaussian state distribution theoretically and identified the most effective way to improve the practical sensitivity of a Josephson comparator. We suggest a modified damping concept and demonstrate a gray zone width as low as 840 nA experimentally. This value is about ten times smaller than for conventional Josephson comparators and very close to the theoretical limit at liquid helium temperature.

DOI
10.1063/1.4729075

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The decision of a Josephson comparator is influenced by thermal noise which is limiting the practical sensitivity in many applications of superconductor electronics. We analyzed the Gaussian state distribution theoretically and identified the most effective way to improve the practical sensitivity of a Josephson comparator. We suggest a modified damping concept and demonstrate a gray zone width as low as 840 nA experimentally. This value is about ten times smaller than for conventional Josephson comparators and very close to the theoretical limit at liquid helium temperature.
The Josephson comparator is one of the building blocks of superconductor electronics. It is used as a decision element in all analog and digital circuits. For fast high-bandwidth analog-to-digital converters as well as for digital circuits with reduced switching energy its high sensitivity is most important. Thermal noise limits its decision uncertainty. In this work we analyze the influence of the bias current on the gray zone of a Josephson comparator. Circuit simulations are compared against experimental data. The experimental analysis shows a characteristic dependence of the gray zone on the bias current. We can identify a clear minimum value. This point is related to a certain clock frequency. At low frequencies the simulated relationship between the gray zone and the bias current is in very good agreement with experimental results. The comparison confirmed the circuit model and enables to adjust the design to certain applications to realize the best trade-off between clock frequency and grey zone. The article describes the experimental validation procedure and a derived normalized dependency in detail.
The Josephson comparator is one of the fundamental building blocks of rapid single flux quantum (RSFQ) electronics. Within this circuit family it is the exclusive device which provides logical data processing. The Josephson comparator is also the basic decision element for very fast analog-to-digital converters and sampler circuits for low input power and high-bandwidth signals based on the RSFQ technique. The performance of those devices is fundamentally determined by the characteristics of the Josephson comparator. In this study the gray zone dependency on the clock frequency of a Josephson comparator is investigated by simulations concerning the influence of thermal noise. This investigation is performed for a series of operating points defined by the bias current and different noise levels defined by the operating temperature. In contrast to former investigations, we analyzed the comparator embedded in a realistic environment for output data processing. We identified a characteristic clock frequency f c for a comparator topology designed for a 1 kA cm − 2 niobium fabrication technology. The gray zone of 8 µA remains constant for clock frequencies below f c = 15 GHz and starts to increase for larger frequencies. We also found out that this characteristic frequency is independent of the intensity of thermal noise and therefore independent of temperature.
The Josephson balanced comparator, a decision-making circuit comprising two Josephson junctions (JJs) connected in series from a clocking perspective and in parallel for the current to be measured, is ubiquitous in single flux quantum (SFQ) logic. Its noise properties are crucial for the performance of logic devices. The characteristics of the balanced comparator can also be used to monitor fab process and design implementation as an indicator for excess noise, overheating, linearity, dynamic effects, etc. We designed several test structures to measure gray zone of various comparators fabricated in different nodes of process at MIT-LL. We used digital circuitry to measure comparator characteristics at low frequencies and an analog testbed to perform high frequency characterization. Experimental results for gray zone of comparators designed for fabrication nodes with different current densities, sheet resistances, critical damping are presented and studied as a function of clock frequency.
The Josephson balanced comparator is the key component of Single Flux Quantum logic devices because it is the decision making element. It is formed by two Josephson junctions (JJs) connected in series from a clocking perspective and in parallel for the current to be measured. Its noise properties are crucial for the performance of logic devices. The balanced comparator can also be used to monitor the fab process and design implementation as an indicator of excess noise, overheating, linearity, dynamic effects, etc. We designed several test structures to measure the comparator gray zone at different fabrication process nodes at MIT-LL. We used digital circuitry to measure comparator characteristics at low frequencies. An analog testbed was used to perform high-frequency characterization. Experimental results for different current densities, sheet resistances, damping and clock frequencies are presented.
We have developed a method for calculation of quantum fluctuation effects, in particular, of the uncertainty zone developing at the potential curvature sign inversion, for a damped harmonic oscillator with arbitrary time dependence of frequency and for arbitrary temperature, within the Caldeira-Leggett model. The method has been applied to the calculation of the gray zone width Delta Ix of Josephson-junction balanced comparators. The calculated temperature dependence of Delta Ix in the range 1.5 to 4.2 K is in virtually perfect agreement with experimental data for Nb-trilayer comparators with critical current densities of 1.0 and 5.5 kA/cm2, without any fitting parameters.
We developed a weak-linked Josephson junction time-domain simulation tool based on the Bardeen-Cooper-Schrieffer (BCS) theory to account for the electrodynamics of Cooper pairs and quasiparticles in the presence of thermal noise. The model, based on Werthamer and Harris formalisms, allows us to describe the behavior of Josephson junctions for various current and/or voltage input waveforms, analog or digital, and for any operating temperature below the critical temperature of the superconducting materials. We show a good agreement between experimental and simulated IV curves of Josephson junctions, as well as a relative increase of the grey zone width of an SFQ balanced comparator between 4 and 20% due to the presence of quasiparticles, for McCumber parameters comprised between 0.1 and 1, respectively.