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

2025-07-13

AI Summary

Conventional floating random walk (FRW) capacitance extraction suffers from bias when applied to complex, non-hierarchical dielectric structures. Method: This paper proposes MicroWalk—an algorithm that achieves the first unbiased FRW transition computation for arbitrary dielectric distributions. Its transition probabilities are mathematically equivalent to those derived from finite-difference method (FDM) solutions, yet computed significantly faster. MicroWalk integrates stochastic finite differencing, a hybrid sampling strategy, special analytical treatment of first-step transitions within cubic cells, and a hierarchical cubic cell analytical solver—balancing accuracy and efficiency. Contribution/Results: Evaluated on realistic 3D advanced-process structures, MicroWalk outperforms existing FRW solvers by delivering substantially higher capacitance extraction accuracy while maintaining high computational efficiency. With up to 802× speedup over standard FDM-based solvers, it establishes a scalable, high-fidelity paradigm for parasitic capacitance modeling in very-large-scale integrated circuits.

Technology Category

• Machine Learning: Hardware-aware ML
• Search and Optimization: Sampling/Simulation-based Search
• Natural Language Processing: Information Extraction

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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$ imes$ 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.

Problem

• Handling non-stratified dielectrics in FRW transitions
• Improving accuracy of capacitance extraction algorithms
• Reducing computational cost of FRW transition schemes

Innovation

• MicroWalk enables accurate FRW transitions
• Hybrid strategy combines MicroWalk with special treatments
• Provably unbiased with finite difference equivalence