Scaled Sigma Sampling for IC Robustness Assessment
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Solution Overview
Problem
Current methods for evaluating integrated circuit (IC) robustness and yield require extensive computational time to estimate low-probability tails of statistical distributions, making it difficult to achieve high confidence in rare defect scenarios, especially for designs with many sensitive process parameters or long simulation times.
Innovation Solution
The use of scaled sigma sampling and Quantile-Quantile (Q-Q) plots allows for the estimation of circuit metrics and yield within specification limits by scaling the standard deviation of process parameters, providing visibility to low-probability failures without the need for a large number of simulations, and enabling assessment of IC design robustness even in unfinished simulations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If repeated Monte Carlo simulations are performed to evaluate low-probability tails of process parameter distributions, then measurement precision of defect rates is improved, but loss of time increases significantly
Solution Approach 1:
The patent performs preliminary simulations to collect data from the central region of the distribution (within 3 sigma) where sufficient data can be obtained quickly. This preliminary data establishes a baseline for the distribution characteristics, allowing subsequent extrapolation to tail regions without requiring exhaustive sampling of those rare events.
Solution Approach 2:
The patent introduces an intermediary statistical model that bridges the gap between easily-obtainable central region data and difficult-to-sample tail region data. By fitting a probability distribution to the central region data and using this model to extrapolate tail behavior, the method acts as a mediator that transfers information from high-probability regions to low-probability regions without requiring direct sampling of the tails.
2Measurement precision
If the number of simulations is increased to obtain high confidence estimates of low probabilities, then measurement precision improves, but productivity decreases
Solution Approach 1:
The patent performs simulations to a sufficient degree for the central region (obtaining data within 3 sigma with high confidence) but deliberately stops before performing the excessive number of simulations that would be required to directly sample tail regions. This partial action approach obtains enough information from the high-probability region to make reliable predictions about low-probability events through statistical extrapolation.
Data Source
AI summary
A method can include generating a first set of sample values for input variables in accordance with a prescribed set of probability distributions, running a set of simulations on an electronic component based upon the first set of sample values, multiplying the standard deviations of the original distributions by a scaling factor λ, generating a second set of sample values for the input variables based on the probability distributions thus generated, and running a set of simulations on the electronic component based on this second set of sample values. The method can also include the generation of Q-Q plots based on the data from the first and second set of simulations and data from a truly normal distribution or the distribution obeyed by the independently varying input parameters; and the use of these plots for assessment of the robustness and functionality of the electronic component.