Faster Random Walk-based Capacitance Extraction with Generalized Antithetic Sampling

Abstract

Floating random walk-based capacitance extraction has emerged in recent years as a tried and true approach for extracting parasitic capacitance in very large scale integrated circuits. Being a Monte Carlo method, its performance is dependent on the variance of sampled quantities and variance reduction methods are crucial for the challenges posed by ever denser process technologies and layout-dependent effects. In this work, we present a novel, universal variance reduction method for floating random walk-based capacitance extraction, which is conceptually simple, highly efficient and provably reduces variance in all extractions, especially when layout-dependent effects are present. It is complementary to existing mathematical formulations for variance reduction and its performance gains are experienced on top of theirs. Numerical experiments demonstrate substantial such gains of up to 50% in number of walks necessary as well as in actual extraction times compared to the best previously proposed variance reduction approaches for the floating random-walk.