SRAM sign-off stops simulating every corner: transferred design points plus conformal calibration still deliver 99.88% yield on a 1-Mb macro
Synopsis
SRAM yield sign-off needs per-cell failure probabilities of 10⁻⁶ to 10⁻¹² at every PVT condition, and running importance sampling at each one is expensive. The method transfers each failure lobe's design point across PVT, corrects it with one SPICE run per lobe, and adds split-conformal margins computed from importance sampling on a random subset of sign-off conditions, escalating undecided conditions to importance sampling. Across all 242 unseen conditions of a SkyWater 130-nm cell and an ASAP7 7-nm cell, no calibrated decision was unsafe, the minimum operating voltage read from the conformal upper limit lay −1 to +34 mV from importance sampling, and a 1-Mb macro delivered at least 99.88% yield.
Interpretation
Cross-PVT sign-off no longer extrapolates the failure probability itself; it moves each failure lobe's design point and leaves the final decision to a conformal calibration with a stated risk bound. Earlier cross-corner and multi-corner yield methods extrapolate the remaining conditions with regression or Gaussian-process surrogates, and any uncertainty they state rests on the surrogate model. The evaluation covers read and write failures of a SkyWater 130-nm planar cell and an ASAP7 7-nm FinFET cell at 242 unseen conditions, all against importance-sampling truth cross-checked by plain Monte Carlo and a second importance-sampling proposal.
Carrying the design point to a new condition and spending one SPICE run per lobe removes the first-order part of the extrapolation error. Extrapolating per-lobe reliability indices is accurate for the FinFET cell but underestimates by up to 1.9 decades for the planar cell, whose failure direction rotates across PVT. After the anchored correction the worst SkyWater read error falls from 1.93 to 0.34 decades, yet the unguarded transfer is still unsafe by more than 0.1 decade at 33% of SkyWater conditions.
The direction error cannot be observed from the anchored run, so a 95th-percentile angle from block cross-validation inside the training box guards it, and conditions with a large residual escalate to a one-step estimate. With the guard, the SkyWater underestimate never exceeds 0.09 decade, at the price of up to 0.75 decade of pessimism and 5.5 runs per condition on average. Both ASAP7 studies stay within 0.07 decade at two runs per condition, and the calibrated θ95 is 15.3°, 4.5° and 0.8° for SkyWater read, ASAP7 read and ASAP7 write.
The sign-off decision itself is calibrated: importance sampling on randomly drawn calibration conditions yields split-conformal margins that bound the probability of an unsafe acceptance. A deterministic bound needs convexity that cannot be verified, and finite-sample importance-sampling bounds are uninformative at these probabilities, so the guarantee is coverage at a randomly selected condition. With 20 calibration conditions at nominal risk 0.15, no calibrated decision was unsafe and the minimum operating voltage lay −1 to +34 mV from importance sampling, whereas FORM, the unguarded transfer and moment surrogates were unsafe by up to −7, −10 and −219 mV.
Perspective
The conclusions rest on ngspice simulation, covering read and write static noise margins of a SkyWater 130-nm planar cell and an ASAP7 7-nm FinFET cell, with no silicon data; the conformal guarantee is marginal over randomly selected sign-off conditions, requires exchangeability between calibration and sign-off conditions, and does not extend to conditions outside the sign-off set.
The conformal guarantee is marginal rather than simultaneous over the grid, and one SkyWater split reached a 14% exceedance rate; its importance-sampling part relies on asymptotic confidence limits and needs the failure-weight effective sample size monitored; the minimum operating voltage read from the conformal upper limit is empirically, not formally, safe; the ASAP7 mismatch is an assumption, and the read study was repeated at 20 and 45 mV threshold-voltage spread.