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arXiv:2104.07371 · Superconductor Science and Technology

Propagation of picosecond pulses on superconducting transmission line interconnects *

Vladimir V. Talanov, Derek Knee, David C. Harms, Kieran Perkins, Andrew Urbanas, Jonathan Egan, Quentin Herr, Anna Herr

Published Feb 22, 2022• 8 citations
arXivHTMLPDF

Abstract

Abstract Interconnects are a major discriminator for superconducting digital technology, enabling energy-efficient data transfer and high-bandwidth heterogeneous integration. We report a method to simulate propagation of picosecond pulses in superconducting passive transmission lines (PTLs). A frequency-domain propagator model obtained from the Ansys high-frequency structure simulator (HFSS) field solver is incorporated in a Cadence Spectre circuit model, so that the particular PTL geometry can be simulated in the time-domain. The Mattis Bardeen complex conductivity of the superconductor is encoded in the HFSS field solver as a complex-conductivity insulator. Experimental and simulation results show that Nb 20 Ω microstrip PTLs with 200 nm interlayer dielectric thickness can support propagation of a single-flux-quantum pulse up to 7 mm and a double-flux-quantum pulse up to 28 mm.

DOI
10.1088/1361-6668/ac5783

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Abstract Interconnects are a major discriminator for superconducting digital technology, enabling energy-efficient data transfer and high-bandwidth heterogeneous integration. We report a method to simulate propagation of picosecond pulses in superconducting passive transmission lines (PTLs). A frequency-domain propagator model obtained from the Ansys high-frequency structure simulator (HFSS) field solver is incorporated in a Cadence Spectre circuit model, so that the particular PTL geometry can be simulated in the time-domain. The Mattis Bardeen complex conductivity of the superconductor is encoded in the HFSS field solver as a complex-conductivity insulator. Experimental and simulation results show that Nb 20 Ω microstrip PTLs with 200 nm interlayer dielectric thickness can support propagation of a single-flux-quantum pulse up to 7 mm and a double-flux-quantum pulse up to 28 mm.
Superconducting technologies are moving toward very large-scale integration (VLSI) of circuits. Passive transmission lines (PTLs) are used to quickly and efficiently propagate single flux quantum pulses between separated logic elements of these VLSI circuits. PTLs are often insufficiently modeled to correspond to reality. Therefore, the PTL needs to be thoroughly studied to determine realistic propagation characteristics. A quasi-transverse magnetic (TM) formulation is used to study superconducting passive transmission lines. The ambient temperature and changes in penetration depth with frequency are taken into account when solving the electromagnetic fields of a PTL. Per-frequency transmission line parameters are extracted from the quasi-TM field solutions. The results show a very close correlation to TetraHenry, an existing 3D solver, at significantly reduced computational cost. The results also clearly show that PTL propagation characteristics are sensitive to frequency and temperature.
The ballistic transport of picosecond digital signals along terminated microstrip lines is a key feature of single flux quantum (SFQ) logic. In this work, we have used fast photoconductors driven by a femtosecond laser to measure directly for the first time the propagation and termination of picosecond pulses along Nb microstrip lines. Electrical pulses as short as 0.8 ps full-width-at-half-maximum (FWHM) have been measured. After propagating distances of 200 /spl mu/m, 1 mm, and 6.5 mm, the pulses broadened to 1.0, 1.2, and 1.8 ps (FWHM), respectively. In the frequency domain, attenuation is found to be negligible up to the gap frequency of Nb(0.7 THz), beyond which attenuation increases rapidly. We have also measured the reflections of the picosecond pulses off different terminations: open circuit, short circuit, and various resistors. The effective suppression of reflections with matched resistive loads is demonstrated up to frequencies approaching 1 THz.>
Superconductive passive transmission lines (PTL) are widely used for signal routing in large-scale rapid single flux quantum (RSFQ) circuits. Due to the imperfect matching of the transmission lines between the driver and receiver, single flux quantum (SFQ) pulses are partially reflected. The round trip propagation time of these reflections can coincide with the following SFQ pulse, resulting in a decrease in bias margins or incorrect circuit behavior. This resonant effect depends upon the length of the PTL and the clock frequency of the signal. A methodology to reduce and manage this effect is the focus of this article. A closed-form expression describing the dependence of the resonance frequency on the length of the PTL is presented. This expression describes a set of forbidden lengths for PTL interconnect segments in RSFQ circuits. The proposed methodology and algorithm insert active PTL-based repeaters into long superconductive interconnect while ensuring the length of the line segment is outside the forbidden region and increasing bias margins.
We have studied single-flux-quantum (SFQ) propagation properties in passive transmission lines (PTLs) based on a 10-Nb-layer device structure (ADP2). In ADP2, we can use the PTLs with a line width about 5 mum, one seventh of conventional line width by adopting a strip line (SL) structure and increasing the characteristic impedance. The evaluation has been conducted on the PTL length and the via-hole structure by using ring oscillators. We found that the decrease in the operating region was larger for longer PTL, compared with that in a conventional device structure (STD2). The results would be caused by the increase in the surface resistance. The via-holes connecting the PTLs on different layers have more complicated structure than those of STD2. We have designed the via-hole structure using the electromagnetic wave simulator HFSS. As a result, we have demonstrated sufficiently large operating margins at any data rates up to 80 Gb/s even for the ring oscillator with 30 via-holes.
As the complexity of superconductor circuits grows, we envision a dense network of passive transmission lines (PTLs) being used to interconnect cells in rapid-single-flux-quantum (RSFQ) circuits. In our library approach, each cell has dedicated tracks as place holders for routing PTLs. Higher impedance PTLs are desirable due to their narrower width. However, at higher impedance, the margins for the PTL receiver degrade rapidly. We have designed, fabricated, tested, and simulated passive transmission lines (PTLs) for high-speed interconnects in the MIT-LL SFQ5ee 10 kA/cm2process. For the symmetric dual ground planes case, PTLs are in the M1 layer with M0 and M2 ground planes, or in the M3 layer with M2 and M4 ground planes. For the asymmetrical dual ground planes case, PTLs are in M2 or M3 layers with M1 and M4 ground planes. We report ±30% margins for these PTLs. We investigate the receiver margins for these PTLs and report impact of margins as a function of corners, interlayer transitions, variants of drivers, and receivers. We demonstrate 100 GHz PTL operation in ring oscillator measurements. We have also adopted multi-layer multi-conductor transmission line models for PTL simulation. We observe good model-to-hardware correlation for low- and high-frequency operation.
We have studied the propagation of subpicosecond electrical pulses on coplanar superconducting Nb transmission lines. Pulses with 0.6 ps full width at half maximum were generated by photoconductively shorting a\sim 10 \mum region between two charged 1 to 5 μm lines separated by a 2 to 10 μm gap. The propagating pulses were sampled by the delayed shorting of a fast phototconductive switch between a sampling probe and one of the transmission lines at variable distances away from the generation point. Silicon-on-sapphire wafers served as the transmission line substrate, with the 0.5 μm thick Si layer heavily damaged by an oxygen implant to provide the subpicosecond carrier life time for the excitation and probe switches. Measurements and analyses of pulses propagated up to 8 mm distance at temperatures from 2 K to 10 K showed a threshold for strong attenuation and dispersion at a frequency reflecting the onset of pair breaking in the superconducting transmission lines. The results at least qualitatively confirm the superconducting microstrip transmission line calculations of Kautz based on Mattis and Bardeen's formulae for the complex conductivity of superconductors.