Monte Carlo Field Solver Parasitic Capacitance Extraction
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional random walk Monte Carlo field solvers exhibit poor performance in parasitic capacitance extraction due to inefficient allocation of random walks, leading to slow convergence and high computational runtime, particularly in complex integrated circuit designs.
Innovation Solution
The method involves partitioning a Gaussian surface into regions and dynamically reallocating random walks based on statistical variances, as well as employing antithetic random walks to reduce variance and improve convergence speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If random walks are uniformly allocated across all regions of the Gaussian surface, then the method is simple to implement, but the convergence speed is slow and computational runtime is high
Solution Approach 1:
The patent implements dynamic allocation of random walks by adjusting the number of walks per region based on statistical variance metrics calculated from previous iterations. The allocation formula nw_i = ceil(N_total * (sv_i / sum(sV))) dynamically reassigns computational resources to regions with higher variance, transforming the static uniform allocation into an adaptive dynamic system that optimizes convergence speed while maintaining implementation feasibility through automated variance-based adjustment
Solution Approach 2:
The patent incorporates feedback mechanisms by calculating statistical variance (sv_i) for each region from previous random walk results and using this feedback to adjust the allocation of subsequent random walks. The variance metric serves as a feedback signal that guides resource allocation, creating a closed-loop system where computational effort is continuously optimized based on observed convergence characteristics of different regions
2Measurement precision
If more random walks are performed to improve accuracy, then the extraction precision increases, but the computational runtime increases significantly
Solution Approach 1:
The patent applies local quality by treating different regions of the Gaussian surface differently based on their local statistical characteristics. Regions with higher variance receive more random walks while regions with lower variance receive fewer walks, optimizing the overall computational efficiency. This localized adaptation allows the system to achieve the required accuracy with fewer total random walks compared to uniform allocation, thereby reducing computational runtime while maintaining extraction precision
Solution Approach 2:
The patent changes the parameter of random walk allocation from a fixed uniform distribution to a variable distribution based on statistical variance. By dynamically adjusting the number of walks per region according to the variance parameter (sv_i), the system optimizes the balance between accuracy and computational time, achieving high precision extraction without the linear increase in runtime that would result from uniformly increasing the total number of walks
3Speed
If statistical variance is reduced through optimized allocation, then convergence speed improves, but the device complexity increases
Solution Approach 1:
The patent implements self-service by enabling the allocation algorithm to automatically adjust random walk distribution based on statistically computed variance metrics without requiring external intervention or complex manual configuration. The system computes variance from its own simulation results and uses this information to self-optimize the allocation of computational resources, achieving fast convergence while keeping the algorithm relatively simple and self-contained
Data Source
AI summary
A method for performing parasitic capacitance extraction of an integrated circuit (IC) design includes: defining a Gaussian surface around an origin net of the IC design; partitioning the Gaussian surface into a plurality of regions; performing an initial plurality of random walks from each region using a Monte Carlo field solver; and dynamically allocating an additional plurality of random walks among the plurality of regions, wherein the allocation is based on statistical errors associated with the initial plurality of random walks for each of the regions. Results from the random walks are averaged to estimate parasitic capacitance of the origin net. The method may include performing the random walks for each region in pairs, wherein a first random walk of the pair is selected in accordance with an anti-symmetric probability function, and a second random walk of the pair is antithetic to the first random walk of the pair.