A scalable statistical static timing analyzer incorporating correlated non-Gaussian and Gaussian parameter variations
We propose a scalable efficient parameterized block-based statistical static timing analysis (SSTA) algorithm incorporating both Gaussian and non-Gaussian parameter distributions, capturing spatial correlations using a grid-based model. As a preprocessing step, we employ an independent component analysis to transform the set of correlated non-Gaussian parameters to a basis set of parameters that are statistically independent. Given the moments of the variational parameters, we use a Pade-approximation-based moment-matching scheme to generate the distributions of the random variables representing the signal arrival times and preserve correlation information by propagating arrival times in a canonical form. Our SSTA procedure is able to generate the circuit delay distributions with reasonably small prediction errors. For the ISCAS89 benchmark circuits, as compared to Monte Carlo simulations, we obtain average errors of 0.99%, 2.05%, 2.33%, and 2.36%, respectively, in the mean, standard deviation, and 5% and 95% quantile points of the circuit delay. Experimental results show that our procedure can handle as many as 256 correlated non-Gaussian variables in about 5 min of runtime. For a circuit with vertical bar G vertical bar gates and a layout with g spatial correlation grids, the complexity of our approach is O(g vertical bar G vertical bar).
timing design automation variational methods