An efficient algorithm for statistical timing yield optimization

Statistical timing yield optimization algorithms require computation of yield-gradient for gate resizing in every iteration. Numerical yield-gradients account for the effects of fan-in and fan-out gates, but are computationally expensive. In this paper, we formulate a more accurate analytical expression for the yield-gradient (termed effective yield-gradient) that includes these effects. Based on the statistical properties of the path delay variations, we derive a simplified expression for the effective yield gradient that is accurate and results in an improvement in the run-time. Using these simplified expressions, we also propose an algorithm for resizing multiple gates in an iteration. Results on ITC99 and ISCAS85 benchmarks show that the proposed multi-node resizing algorithm results in 83% improvement in the runtime with an average area penalty of 3% and no cost to the final yield achieved.