DeepRWCap: Neural-Guided Random-Walk Capacitance Solver for IC Design

2025-11-10

AI Summary

Conventional Monte Carlo random-walk methods suffer from low efficiency and poor accuracy in capacitance extraction for integrated circuits with high dielectric contrast. Method: This paper proposes a neural-network-guided Monte Carlo random-walk solver. It employs a two-stage neural architecture: the first stage learns surface charge distributions, while the second models the spatial kernel function. To ensure physical consistency, cubic symmetry constraints and positional encoding are incorporated; the network jointly leverages 3D convolutions (to capture volumetric hierarchical features) and 2D depthwise separable convolutions (to model local kernel behavior). Results: Evaluated on ten industrial-scale designs, the method achieves a mean relative error of 1.24±0.53% and accelerates computation by 23% over Microwalk on average—up to 49% for complex structures—demonstrating substantial improvements in accuracy, efficiency, and generalization for high-contrast capacitive structures.

Technology Category

• Machine Learning: Kernel Methods
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work

Abstract

Monte Carlo random walk methods are widely used in capacitance extraction for their mesh-free formulation and inherent parallelism. However, modern semiconductor technologies with densely packed structures present significant challenges in unbiasedly sampling transition domains in walk steps with multiple high-contrast dielectric materials. We present DeepRWCap, a machine learning-guided random walk solver that predicts the transition quantities required to guide each step of the walk. These include Poisson kernels, gradient kernels, signs and magnitudes of weights. DeepRWCap employs a two-stage neural architecture that decomposes structured outputs into face-wise distributions and spatial kernels on cube faces. It uses 3D convolutional networks to capture volumetric dielectric interactions and 2D depthwise separable convolutions to model localized kernel behavior. The design incorporates grid-based positional encodings and structural design choices informed by cube symmetries to reduce learning redundancy and improve generalization. Trained on 100,000 procedurally generated dielectric configurations, DeepRWCap achieves a mean relative error of $1.24pm0.53$% when benchmarked against the commercial Raphael solver on the self-capacitance estimation of 10 industrial designs spanning 12 to 55 nm nodes. Compared to the state-of-the-art stochastic difference method Microwalk, DeepRWCap achieves an average 23% speedup. On complex designs with runtimes over 10 s, it reaches an average 49% acceleration.

Problem

• Solving capacitance extraction challenges in densely packed semiconductor structures
• Guiding random walk steps with machine learning for transition quantities
• Accelerating capacitance estimation while maintaining accuracy in IC design

Innovation

• Neural-guided random walk for capacitance solving
• Two-stage neural architecture with volumetric interactions
• Grid encodings and cube symmetries improve generalization