Fast Monte Carlo method via reduced sample number and node filtering

Abstract

Monte Carlo (MC) method is convenient and robust to estimate timing yield of circuits under the influence of process variations. The important question in MC method is the number of samples while we assure a desired accuracy of yield estimate, which is often addressed using a rule of thumb. Minimum number of samples can be estimated via approximation by a normal distribution, but the provided number may be too small to be used in practice considering that target yield, which is used to derive the number, is unknown. Chebyshev's inequality has been used to derive a sample number, but the number is too large this time. We develop a new expression, which provides the sample number that is much closer to the minimum (3× to 8×) compared to the number provided by Chebyshev's inequality (5× to 15×). We also propose a simple node filtering algorithm, where we identify the nodes that are likely to affect timing yield; the simulation with each MC sample can handle only a fraction of circuit elements as a result. Reducing the number of MC samples and simulating only selected nodes together yield 27× to 125× speedup over standard MC method.