Cross-Corner Delay Variation Model for Standard Cell Libraries

For timing closure of logic circuits, circuit designers must perform sign-offs on a variety of
process, voltage, and temperature (PVT)
conditions. Designs of advanced logic circuits involve a multitude of voltage islands and operating modes, each of which requires delay characterizations at nearby PVT corners. Furthermore, advanced technologies nodes suffer from
corner explosion
: while the impact of PVT variations is being exacerbated, process variations are also diversifying, increasing the number of operating conditions exponentially. This paper revisits the importance of cross-corner timing estimations and proposes a delay variation model to mitigate such corner explosion. Our objective is to reduce PVT corner characterization effort for timely static timing analysis on an exploding number of operating conditions. Our proposed
Decomposed Propagation Vector Variation Model (DPVVM)
decomposes propagation delay and timing constraints into the driving by the receiver cell and its driver cell; by scaling them separately, delay characterization effort is reduced to a fraction of time while realizing accurate timing estimations. We also propose
Multi-Dimension Recomposition (MDR)
scheme, which exploits a multitude of pre-characterized corners to further improve the consistency of cross-corner timing estimations. As a result, with only 8.0% of a corner characterization effort compared to the full-characterization, DPVVM combined with MDR achieves overall cross-corner timing estimation errors of 4.8% and 5.6% for single cells and complex logic circuits—or improvements of 69% and 61% over the conventional derating method, respectively. Our proposed method’s characterization overhead is 11% over the conventional derating method; the overhead is marginal, accounting for only 0.76% of a full-characterization time.