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IEEE Transactions on Applied Superconductivity

Multiparameter optimization of RSFQ circuits using the method of inscribed hyperspheres

Q.P. Kerr, M. J. Feldman

Published Jun 1, 1995• 59 citations
Publisher

Abstract

Rapid Single Flux Quantum (RSFQ) circuits must be designed with large operating margins because of variations in the fabrication process. We describe a routine to optimize the yield, rather than the critical margin, of RSFQ circuits, based on the method of inscribed hyperspheres. The operating region is mapped out with a minimum of circuit simulations taking into account the relative size of the process variations. The method is effective for as many as nine parameters. We show that the standard optimization of critical margin will often give a seriously wrong result for multidimensional parameter space.>

DOI
10.1109/77.403306

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Rapid Single Flux Quantum (RSFQ) circuits must be designed with large operating margins because of variations in the fabrication process. We describe a routine to optimize the yield, rather than the critical margin, of RSFQ circuits, based on the method of inscribed hyperspheres. The operating region is mapped out with a minimum of circuit simulations taking into account the relative size of the process variations. The method is effective for as many as nine parameters. We show that the standard optimization of critical margin will often give a seriously wrong result for multidimensional parameter space.>
Simulations are used to optimize the design of simple rapid single flux quantum (RSFQ) logic gates and to determine their margins. Optimizations based on maximizing the smallest (critical) margin result in critical margins in the range of 19-50%. A Monte Carlo approach is used to illustrate the relationship between margins and process yield. Based on single gate simulations, the results show that 1 sigma parameter spreads of less than about +or-5% will be required to make medium- or large-scale integrated RSFQ logic circuits. A single-bit full adder using five RSFQ gates and a local self-timing network are simulated with discrete components. The full adder used 2000-A/cm/sup 2/ junctions with a specific capacitance of 0.04 pF/ mu /sup 2/ and had a logic delay of 87 ps and a worst-case margin of +or-19%. A small margin reduction which is not present in the individual gate simulations results from loading.>
Successful fabrication and demonstration of complex Rapid Single Flux Quantum (RSFQ) circuits depend heavily on the reliability of the cell library that is used for the design. In large-scale RSFQ integrated circuits, delay fluctuations (jitter) of each cell may occur due to fabrication tolerances. The fabrication-induced jitter of each cell might accumulate at each stage and bring out larger variations comparable with the designed delay. If such jitter is not considered while arranging timing of the circuit, it may cause the circuit to malfunction due to the shifting of SFQ pulses. Therefore, it is important to optimize and determine the delay fluctuations of each cell well before designing a large-scale integrated circuit. There are quite a number of parameters that affect the functioning and the performance of a logic gate; hence, an optimization tool is required. In this study, the progress on development of an optimization tool for a digital RSFQ cell library composed of fundamental logic gates, such as Josephson transmission lines, D-flip-flops, T-Flip-flops, splitters, and mergers are presented. Particle swarm optimization is used for an optimization algorithm, which determines the circuit parameters with minimum delay and/or jitter satisfying the required critical margin conditions.
Rapid Single flux quantum (RSFQ) confluence buffer is widely used in complex superconductive digital circuits. In this work, we have improved the currently used confluence buffer and obtained a more soundly designed confluence buffer. In simulations, improvements in the bias margins of 11 % and the global margins of 10%, compared to the previously used confluence buffer, were achieved. Global margins are very important in estimating a process error range allowed in fabrications. We used two circuit simulation tools, WRspice and Julia, to design and optimize the confluence buffer. We used Xic to obtain a mask layout. We fabricated the improved circuits by using Nb technology. The test results at low frequency showed that the improved confluence buffer operated correctly and had a very wide main bias margin of +/-43% enhanced from +/-26% of the previously used confluence buffer.
Rapid Single-Flux-Quantum Circuits Fabricated Using 20-kA/cm2\hbox{20}\hbox{-}\hbox{kA}/\hbox{cm}^{2}20-kA/cm2 Nb/AlOx/Nb\hbox{Nb}/\hbox{AlO}_{x}/\hbox{Nb}Nb/AlOx​/Nb Process
We designed and fabricated rapid single-flux-quantum (RSFQ) circuits using a new 20-kA/cm2process based on conventional Nb/AlOx/Nb Josephson junction (JJ) technology. Circular JJs were fabricated to improve their uniformity. They had sufficiently low spread of the critical currents for large-scale RSFQ circuits. We selected the circuit design parameters carefully, including the bias voltage and McCumber-Stewart parameter, balancing the energy consumption, switching speeds, margins, and integration density. We demonstrated several logic gates and shift registers at a clock frequency of 154 GHz with the designed bias voltage of 2.5 mV, and demonstrated energy-efficient shift registers using the low-voltage RSFQ (LV-RSFQ) technique at 83 GHz.
Rapid single flux quantum (RSFQ) digital circuits have reached the level of medium- to large-scale of integration. At this level, existing design methodologies, developed specifically for RSFQ circuits, have become computationally inefficient. Applying mature semiconductor methodologies to the design of RSFQ circuits, one encounters substantial difficulties originating from the differences between both technologies. In this paper, a new design methodology aimed at large-scale RSFQ circuits is proposed. This methodology is based on a semiconductor semicustom design approach. An established design methodology for small-stale RSFQ digital circuits, based on circuit (junction-level) simulation and device parameter optimization, is used for the design of basic RSFQ cells. A library composed of about 20 basic RSFQ cells has been developed based on this approach. A novel design methodology for large-scale circuits, presented in this paper, is based on logic (gate-level) simulation and timing optimization. This methodology has been implemented around the Cadence integrated design environment and used successfully at the University of Rochester for the design of two large-scale digital circuits.
In contrast to transistor-based semiconductor circuits, there is currently no widely accepted formalized circuit theory or design methodology for superconductor rapid single flux quantum (RSFQ) logic circuits. Experienced designers intuitively consider flux loops, nodal phase, and branch currents when making design choices, but the lack of a formalized design process makes it difficult for inexperienced RSFQ circuit designers to construct a functioning logic cell without a reference. This results in new circuit designers, mostly recycling templates from published circuit designs without fully understanding why the circuits function as they do. Inexperienced RSFQ circuit designers often follow an iterative process where cell parameter values are adjusted, and the cell is run through electronic simulation engines until the desired functionality is reached. We propose the development of a formalized circuit design theory for RSFQ logic from first principles using phase-based circuit analysis. The circuit is designed using dc analysis to establish the dc operating point of the circuit. Phase-based analysis and simulation are then used to verify the dynamic circuit functionality. To demonstrate this method, we discuss examples for well-known RSFQ cells. We analyze the initial operating margins of these designs and discuss design accuracy and efficiency. Methods for current regulation to minimize current leakage between cells are discussed. We also present how this design methodology can be used to design new circuits such as an RSFQ XNOR cell. We investigate how an inverting (NOT) cell can be combined with other logic cells to minimize cell latency.