DeepRWCap: Neural-Guided Random-Walk Capacitance Solver for IC Design
This work addresses a critical bottleneck in IC design by improving the efficiency and accuracy of capacitance extraction for modern semiconductor technologies, though it is incremental as it builds on existing random walk methods with machine learning enhancements.
The paper tackles the challenge of unbiased sampling in Monte Carlo random walk methods for capacitance extraction in densely packed semiconductor structures by introducing DeepRWCap, a neural-guided solver that predicts transition quantities to guide walk steps, achieving a mean relative error of 1.24±0.53% and speedups of up to 49% compared to state-of-the-art methods.
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 $1.24\pm0.53$\% 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.