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IEEE International Midwest Symposium on Circuits and Systems (MWSCAS)

Inductive Noise Coupling in Superconductive Passive Transmission Lines

Gleb Krylov, Eby G. Friedman

Published Aug 9, 2021• 9 citations
Publisher

Abstract

Superconductive niobium-based circuits is a promising energy efficient beyond-CMOS technology that can supplement or replace existing large scale CMOS systems. Modern superconductive circuits utilize more than ten metal layers for gates and interconnect. Many sources of inductive coupling noise exist within this environment. Superconductive circuits are particularly vulnerable to inductive coupling, as the operation of the logic gates and flip flops depends on precise bias conditions, and the signal magnitude is relatively small. These inductive coupling sources are characterized, and the effects of inductive coupling noise in different circuit structures are described. Guidelines to mitigate the deleterious effects of coupling noise are presented.

DOI
10.1109/mwscas47672.2021.9531837

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Superconductive niobium-based circuits is a promising energy efficient beyond-CMOS technology that can supplement or replace existing large scale CMOS systems. Modern superconductive circuits utilize more than ten metal layers for gates and interconnect. Many sources of inductive coupling noise exist within this environment. Superconductive circuits are particularly vulnerable to inductive coupling, as the operation of the logic gates and flip flops depends on precise bias conditions, and the signal magnitude is relatively small. These inductive coupling sources are characterized, and the effects of inductive coupling noise in different circuit structures are described. Guidelines to mitigate the deleterious effects of coupling noise are presented.
The increasing complexity of modern superconductive circuits, and single flux quantum (SFQ) circuits in particular, has made the issue of coupling noise of growing importance. Limited metal resources within superconductive circuits have exacerbated this issue. In this article, the different sources of coupling noise within SFQ circuits are described. Coupling noise among inductors, routing striplines, and bias microstriplines within SFQ circuits degrade performance while decreasing margins. In this article, inductive and capacitive coupling between the different layers are characterized. Inductive coupling models between different layers in the MIT LL SFQ5ee process match experimental data within 3%. The dependence of inductive coupling on the thickness of the oxide and metal layer is also discussed. An understanding of inductive and capacitive coupling can determine the minimum physical distance between lines. In addition, tradeoffs exist among inductive coupling, capacitive coupling, layout complexity, and the vias between ground layers. The different coupling sources are characterized, and guidelines are provided to enhance the automated routing process.
Superconductive electronics based on Josephson junctions (JJ) is a promising cryogenic alternative technology to complementary metal oxide semiconductor (CMOS) technology for ultra-low energy, high speed stationary applications. For complex superconductive systems, the automated routing process determines the topology and methodology to connect cells while satisfying design constraints. On-chip signal routing has become an issue of growing importance in modern superconductive technologies; particularly, single flux quantum (SFQ) systems. Specialized routing methods for these systems are required. These routing methods include passive transmission lines (PTLs) and Josephson transmission lines (JTLs) behaving as interconnects. A primary issue within a long SFQ interconnect is the effects of resonance due to the imperfect match between the PTLs and Josephson junctions. A repeater insertion methodology to reduce and manage these resonance effects is required for driving long and short interconnect in VLSI complexity SFQ systems. Permissible interconnect lengths are suggested to ensure the reflections do not affect the returning signals. The microwave behavior of the interconnect striplines is also considered to accurately estimate the surface inductance of the lines. A closed-form expression describing the dependence of the surface inductance of a stripline on the line thickness, magnetic field, and current density is discussed. Another primary issue within SFQ circuits is coupling noise between transmission striplines, degrading performance and decreasing margins. Inductive and capacitive coupling noise between the routing layers, for the MIT LL SFQ5ee process, is described. An analysis of inductive and capacitive coupling noise can determine the minimum physical spacing between lines to enhance the automated routing process in large scale systems. The increasing complexity of modern SFQ circuits has also made the issue of flux trapping of growing importance. The use of wide striplines for signal routing has exacerbated this issue. Trapped residual magnetic fields within the striplines damage the operability of superconductive circuits. Area efficient topologies for striplines are introduced to manage flux trapping in large scale SFQ circuits. These topologies are composed of several narrow lines rather than a single wide stripline. The first approach is a narrow parallel line topology in series with small resistors where each narrow line is connected to a single small resistor and via. The resistors in the parallel line topology remove any trapped fluxons and break any loops while requiring additional vias. The second topology is a fingered narrow line topology. The fingered narrow line topology enhances the scalability of SFQ systems while not requiring additional area and vias. These proposed topologies require significantly less area while preventing flux from being trapped within wide superconductive striplines and reducing coupling noise between striplines. These methodologies and techniques are intended as guidelines to enable robust routing with superconductive interconnects. With these and other advances in design methodologies for superconductive electronics, the complexity of SFQ circuits is expected to greatly increase.
By measuring forward and backward coupling between superconducting coplanar transmission lines at various temperatures, we determined the dependence of inductive coupling on the London penetration depth. If the transmission lines are separated by a shielding ground line, inductive coupling increases with increasing penetration depth. If the shielding line is damaged or absent, there is a slight decrease. Since both effects are in the percentage range, they can only be observed in the forward-coupled noise signal. The backward coupled noise is nearly temperature independent. We measured inductive coupling factors between 6 and 8% on 10- and 5-/spl mu/m-wide transmission lines, which are separated by a shielding ground line. Excellent agreement was obtained between measurements and FEM simulations.
An increase in bias currents supplied to single-flux-quantum (SFQ) circuits is a rising problem in building large-scale integrated SFQ circuits, because the magnetic fields generated by bias currents and ground return currents affect the circuit operation. Current recycling technique, which can drastically reduce the total bias current of SFQ circuits, is expected to be a very effective solution for large-scale SFQ circuits. To realize the current recycling technique, signal transmission between SFQ logic circuits located on different ground planes is required. Two types of inductively coupled pulse transfer circuits were examined in this study. One is composed of a simple JTL driver and a DC-SQUID receiver whose junctions are slightly under-damped to enhance the magnetic sensitivity of the SQUID. The other circuit is composed of an SFQ driver based on a delay flip-flop (DFF) and a SQUID receiver. The advantage of the DFF-based circuit is that the coupling time between the driver and the receiver can be increased to ensure appropriate switching in the receiver junction. Two types of transfer circuits were implemented using the SRL 2.5 kA/cm2Nb process and their correct operation was experimentally confirmed. Circuit structures for effective coupling of the SFQ pulse transfer were also investigated. It was shown that a ground plane boundary should be separated from a ground plane hole underneath coupling inductors to obtain high coupling factors.
There is widespread interest in transferring Single Flux Quantum (SFQ) logic from niobium technology to a suitable HTS technology. The higher operating temperature results in increased noise and associated errors. We have developed numerical methods to study noise induced errors and how they depend on circuit parameters. A simple picture holds for all the circuits studied to date. The error probability shows an error function (integrated Gaussian) distribution. The width of the distribution is circuit dependent, but is 1 to 4 times the noise contribution of a single junction, and the noise free (deterministic) margin corresponds to the point where the error probability is 0.5. The distributions are frequently asymmetric, and minimum error rate does not occur for a design centered between the deterministic margins. A stochastic optimizer has been developed that allows us reoptimize circuits for conditions when noise induced margin narrowing is important. We have used this to study the influence of layout induced stray inductance on the feasibility of HTS circuits using the T flip-flop as an example. Stray inductance appears to be as important as junction reproducibility, and significant improvements are needed to allow high operating temperatures.
We address the problem of reducing the noise of an RSFQ circuit, which may significantly decohere a Josephson qubit in the case of integration of these circuits. The main sources of such noise in traditional RSFQ circuits are low-ohmic shunting resistors ensuring sufficiently high damping. We developed the toggle flip-flop (TFF) cells with weakly-damped individual junctions due to high-ohmic shunts. The dominant part of necessary damping in this circuit was realized by applying an additional, so-called 'perpendicular', low-ohmic resistor connecting the centre of the storing TFF inductance to ground. The TFF circuits with junctions shunted by 50 Ω resistors and perpendicular resistor of 1.5 Ω, ensuring suppression of noise by more than one order, have been fabricated and demonstrated an operation range of ±20%. In order to make the circuit compact and, therefore, less sensitive to external noise, the passive frozen-flux-based phase shifting elements, replacing large quantizing inductances, were also included. The circuits were fabricated using PTB Nb trilayer process with critical current density j c = 100 A/cm 2 .