Multivariate Modeling of Variability Supporting Non-Gaussian and Correlated Parameters

摘要

Process variations and atomic-level fluctuations increasingly pose challenges to the design and analysis of integrated circuits by introducing variability. Although several approaches have been proposed to deal with the inherent statistical nature of circuit design, we consider them incomplete with two important aspects often being insufficiently addressed: 1) non-Gaussian distributions and 2) highly correlated parameters. To address these points, we propose a fully multivariate and non-Gaussian approach based on an arbitrary model. A subset of the model parameters is treated as a multidimensional random variable, which is represented by a combination of generalized lambda distributions and Spearman rank correlation matrices—a very general approach with nearly arbitrary freedom in distribution shapes and parameter correlations. In our application scenarios, we show that such a model is able to fully and accurately capture variability in device compact models and standard cell performance models. Finally, we present adapted analysis methods making use of these models in circuit simulations and in efficient gate level analyses of digital circuits with high accuracy.