Computing parametric yield accurately and efficiently

An algorithm for computing parametric yield is presented. The algorithm uses statistical modeling techniques and takes advantage of incremental knowledge of the problem to reduce significantly the number of simulations needed. Polynomial regression is used to construct simple equations mapping parameters to measurements. These simple polynomial equations can then replace circuit simulations in the Monte Carlo algorithm for computing parametric yield. The algorithm differs from previous statistical modeling algorithms using polynomial regression for three major reasons: first, the random error that is postulated in polynomial regression equations is taken into account when computing parametric yield; second, the variance of the yield is computed; and third, the algorithm is fully automated. Therefore a direct comparison with Monte Carlo methods can be made. Examples indicate that significant speed-ups can be attained over Monte Carlo methods for a large class of problems.<>