Differential Propagation Delay Measurement of RSFQ Library Cells Using Ring Oscillators

Performing comprehensive timing characterization of library cells and establishing their model-to-hardware correlation are essential for building robust integrated circuits and scaling circuit complexity. To measure the propagation delay of fabricated library cells, we have designed a differential delay measurement scheme using SFQ ring oscillators. The reference and design-under-test (DUT) rings are designed using circuit elements that are either common to both rings or are of nominally similar design, except for the DUT. By inserting a single pulse in the ring, the oscillation period is measured using two methods: (1) direct voltage measurement, and (2) frequency measurement using a frequency divider followed by an SFQ-to-DC converter. Subtracting delay of the two rings gives us the propagation delay of the DUT. A 1 cm by 1 cm chip and another 5 mm by 5 mm chip, incorporating stand-alone ring oscillator test structures for different library cells, have been fabricated in the MIT-LL SFQ5ee process. The chips also contain test circuits to validate two variants of the input/output multiplexing scheme that facilitate reducing the pads requirement. Two copies of a chip with fifteen DUTs were tested. The measured and simulated results for the voltage and frequency of the ring are compared. The simulations account for critical current density (
J_c
) and sheet resistance (Rs) fabrication parameters. In addition, we have used the
J_c
as a single free parameter to get a better matching with measurement results. For one of the chips, a 15% higher
J_c
in simulations results in better matching with measured frequency results for all the DUTs. For example, the discrepancy between simulated and measured DUT ring frequency for the NOT cell was reduced from 19% to 1% when the
J_c
was changed from nominal to 15% higher in simulations. Detailed measurement and simulation results for several DUTs are presented.