Efficient FRW Transitions via Stochastic Finite Differences for Handling Non-Stratified Dielectrics

TL;DR

This paper introduces MicroWalk, an efficient and unbiased algorithm for accurate floating-random-walk transitions in complex non-stratified dielectrics, significantly improving accuracy and speed in 3D capacitance extraction.

Contribution

MicroWalk provides a novel unbiased transition scheme for arbitrary dielectrics, combining finite difference equivalence with high efficiency, enabling more accurate capacitance extraction.

Findings

MicroWalk is 802 times faster than previous methods.

The hybrid solver improves accuracy over existing FRW solvers.

Experiments confirm significant accuracy and efficiency gains.

Abstract

The accuracy of floating-random-walk (FRW) based capacitance extraction stands only when the recursive FRW transitions are sampled unbiasedly according to surrounding dielectrics. Advanced technology profiles, featuring complicated non-stratified dielectrics, challenge the accuracy of existing FRW transition schemes that approximate dielectrics with stratified or eight-octant patterns. In this work, we propose an algorithm named MicroWalk, enabling accurate FRW transitions for arbitrary dielectrics while keeping high efficiency. It is provably unbiased and equivalent to using transition probabilities solved by finite difference method, but at orders of magnitude lower cost (802$\times$ faster). An enhanced 3-D capacitance solver is developed with a hybrid strategy for complicated dielectrics, combining MicroWalk with the special treatment for the first transition cube and the analytical algorithm for stratified cubes. Experiments on real-world structures show that our solver achieves a significant accuracy advantage over existing FRW solvers, while preserving high efficiency.