Statistical Leakage Analysis Using Gaussian Mixture Model

Abstract

In the design process of advanced semiconductor devices, statistical leakage analysis has emerged as a major step due to uncertainties in the leakage current caused by the process variations. In this paper, a novel statistical leakage analysis which uses Gaussian mixture model (GMM) as the density function of leakage current is proposed. To estimate the probability density function, our proposed method clusters the rapidly converged leakage data using the GMM. The GMM can represent any distributions, soit is suitable to estimate the leakage distribution, which varies as the technology node or operating condition changes. In addition, our proposed method (SLA-GMM) defines a terminating condition that guarantees the convergence of the leakage data and prevents the underfitting or overfitting in the GMM modeling process. With sequential addition, SLA-GMM significantly reduced the error that can occur during the addition process. In studies with a goodness-of-fit test, SLA-GMM achieved up to 98% and 94% improvements in the Chi-square static and the K-S static compared with the previous method based on an analytic model.

Keywords

• Expectation-maximization algorithm
• Gaussian mixture model
• machine learning
• statistical leakage analysis