Refined statistical static timing analysis through learning spatial delay correlations

Abstract

Statistical static timing analysis (SSTA) has been a popular research topic in recent years. A fundamental issue with applying SSTA in practice today is the lack of reliable and efficient statistical timing models (STM). Among many types of parameters required to be carefully modeled in an STM, spatial delay correlations are recognized as having significant impact on SSTA results. In this work, we assume that exact modeling of spatial delay correlations is quite difficult, and propose an experimental methodology to resolve this issue. The modeling accuracy requirement is relaxed by allowing SSTA to impose upper bounds and lower bounds on the delay correlations. These bounds can then be refined through learning the actual delay correlations from path delay testing on silicon. We utilize SSTA as the platform for learning and propose a Bayesian approach for learning spatial delay correlations. The effectiveness of the proposed methodology is illustrated through experiments on benchmark circuits