Machine Learning for High Sigma Analog Designs (Invited)

Monte Carlo simulations have been the gold standard for assessing parametric yields of analog, mixed signal, and RF circuits as they offer one of the most direct representations of the variation induced by semiconductor manufacturing. However, Monte Carlo analyses are often too expensive for understanding high sigma yields with fewer defects than 1000ppm. To quantify the impact of rare events on circuit yield, we need insights into their probability densities. All rare event sampling techniques that seek to provide this insight employ a machine learning flow of some kind. The various implementations of importance sampling and statistical blockade, for example, try to locate the rare event populations in parametric space through input domain mapping. Despite their popularity, they can sometimes pose a significant challenge, especially when the dimensionality of the input variation space is high, as both feature selection and machine learning can be non-trivial. A good alternative to machine learning in the input parametric domain is the innovative scaled sigma sampling technique that leverages machine learning of the probability density differences produced by scaling input standard deviations. This paper reviews these key approaches for determining the high sigma yields of analog circuits.