K-sigma Corner Extraction for Monte Carlo Simulation
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Solution Overview
Problem
Current integrated circuit design methodologies require a large number of Monte Carlo simulation runs to verify yield, especially when the yield target is high, leading to significant computational expense and inefficiency, particularly during design iterations where designers need to quickly assess compliance with design specifications in worst-case scenarios.
Innovation Solution
The method involves calculating K-sigma target values by modeling circuit performance distributions, estimating K-sigma corners using a reduced number of Monte Carlo samples, and verifying these corners with additional simulations to minimize computational costs and efficiently identify design failures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a large number of Monte Carlo simulation runs are performed to verify yield with high confidence, then measurement precision and reliability are improved, but productivity and computational efficiency deteriorate
Solution Approach 1:
The patent performs preliminary actions by calculating K-sigma target values and estimating K-sigma corners before conducting full Monte Carlo simulations. This preliminary estimation identifies the most critical design corners that are likely to fail, allowing the simulation to focus computational resources on these specific cases rather than uniformly sampling the entire parameter space, thereby reducing the total number of simulations needed while maintaining verification accuracy
Solution Approach 2:
The patent segments the yield verification process into distinct phases: (1) calculating K-sigma target values from performance distributions, (2) estimating K-sigma corners using reduced Monte Carlo samples, and (3) verifying these corners with additional simulations. This segmentation allows each phase to be optimized independently, with the estimation phase using fewer samples to identify critical regions, thereby improving overall computational efficiency
2Productivity
If the number of Monte Carlo simulation samples is reduced to improve productivity, then design iteration speed is improved, but measurement precision and confidence level deteriorate
Solution Approach 1:
The patent changes the sampling parameters by using K-sigma corners as a transformation of the original parameter space. Instead of uniformly sampling according to the performance model, the method transforms parameters to identify corners that are K standard deviations from the mean, thereby concentrating samples in the most critical regions of the parameter space where failures are most likely to occur, which improves measurement precision with fewer samples
Solution Approach 2:
The patent performs preliminary calculation of K-sigma target values and estimation of K-sigma corners before the main verification simulation. This preliminary action identifies the critical parameter combinations that are most likely to cause failures, allowing the subsequent verification phase to focus computational resources on these specific corners rather than uniformly sampling the entire parameter space
3Loss of energy
If K-sigma corners are estimated using a small number of Monte Carlo samples, then computational expense is reduced, but manufacturing precision and accuracy of corner identification deteriorate
Solution Approach 1:
The patent applies parameter changes by transforming the original performance parameters into K-sigma corner parameters. This transformation concentrates the sampling effort on the most critical regions of the parameter space (those K standard deviations from the mean), thereby achieving accurate corner identification with fewer samples compared to uniform sampling methods
Solution Approach 2:
The patent substitutes the traditional mechanical Monte Carlo sampling approach with a model-based estimation approach. Instead of relying solely on brute-force sampling, the method uses calculated K-sigma target values and performance models to estimate corner parameters analytically or with reduced sampling, thereby reducing computational cost while maintaining accuracy
Data Source
AI summary
A system, method, and computer program product for efficiently finding the best Monte Carlo simulation samples for use as design corners for all design specifications to substitute for a full circuit design verification. Embodiments calculate a corner target value matching an input variation level by modeling the circuit performance with verified accuracy, estimate the corner based on a response surface model such that the corner has the highest probability density (or extrapolation from the worst sample if the model is inaccurate), and verify and/or adjust the corner by performing a small number of additional simulations. Embodiments also estimate the probability that a design already meets the design specifications at a specified variation level. Composite multimodal and non-Gaussian probability distribution functions enhance model accuracy. The extracted design corners may be of particular utility during circuit design iterations. A potential twenty-fold reduction in overall design specification verification time may be achieved.