Importance Sampling for Circuit Yield Analysis
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Solution Overview
Problem
Current Monte Carlo simulations for integrated circuit yield analysis are resource-intensive and inefficient, particularly when detecting rare failures in circuit blocks like SRAM bitcells, due to the high number of system variables and low failure rates, making them impractically time-consuming.
Innovation Solution
A computer-implemented method using importance sampling, where initial sampling sets are generated from distributions related to physical properties, transformed into importance sampling distributions with three sub-distributions to focus on rare failure regions, and dynamically updated to optimize computational resources and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Monte Carlo simulations are used for circuit yield analysis, then accuracy in detecting rare failures is improved, but computational time and resource consumption increase unreasonably
Solution Approach 1:
The method performs preliminary action by generating initial sampling sets and running initial simulations to identify failure regions before the main simulation phase. This preliminary exploration allows the importance sampling distribution to be constructed based on actual failure patterns observed in the initial phase, making the subsequent main simulation much more efficient at detecting rare failures without requiring exhaustive sampling.
Solution Approach 2:
The method changes parameters by transforming the original provided distributions into importance sampling distributions with different characteristics. The transformation process modifies the sampling distributions to concentrate samples in regions where failures are more likely to occur, based on patterns learned from initial simulations. This parameter transformation enables the main simulation to detect rare failures much more efficiently.
2Measurement precision
If the number of samples is increased to detect rare failures, then detection accuracy is improved, but computational resources required increase significantly
Solution Approach 1:
The method applies local quality by creating different sampling strategies for different regions of the parameter space. The importance sampling distribution is constructed to provide local focus on regions where failures are more likely to occur, rather than uniformly sampling across all possible parameter combinations. This localized sampling approach detects rare failures more accurately while using fewer computational resources overall.
Solution Approach 2:
The preliminary simulation phase performs essential exploration to identify which regions of the parameter space are relevant for failure detection. By using this preliminary information to guide the main simulation, the method avoids wasting computational resources on regions that would not contribute to detecting rare failures, thereby reducing the total quantity of computational resources needed.
3Productivity
If importance sampling distribution is transformed based on initial sampling distribution, then efficiency in identifying failure regions is improved, but complexity of the simulation method increases
Solution Approach 1:
The method segments the simulation process into distinct phases: initial sampling phase, distribution transformation phase, and main simulation phase. This segmentation allows each phase to have a specific, manageable function. The transformation of the importance sampling distribution is performed as a separate step based on statistical parameters from the initial phase, making the complexity modular and manageable rather than embedded throughout the entire simulation.
Solution Approach 2:
The method uses feedback by utilizing results from the initial sampling phase to inform and adjust the importance sampling distribution for the main simulation phase. The transformation parameters are determined based on feedback from observed failure patterns in the initial phase, creating a closed-loop system that adapts the sampling strategy based on actual system behavior rather than relying on predetermined assumptions.
Data Source
AI summary
A computer-implemented method for simulation of an integrated circuit for yield analysis includes: a) for plurality of variables, generating initial sampling sets by sampling from provided distributions related to physical properties of circuits; b) selecting at least one sample from each initial set randomly and combining into initial simulation set; c) running initial simulation of operation of circuit, applying initial simulation set, the operation having passing/failing criterion; d) if fails: storing samples of initial set into initial sampling distributions for each variable; e) repeating steps b)-d) until sufficient failures obtained; f) building importance sampling distribution based on each initial sampling distribution, the importance distribution having lower, center, upper portions; g) generating secondary simulation set by drawing samples from importance sampling distribution for each variable; h) simulating circuit by applying the secondary set; i) repeating steps g)-h); j) mapping resulting yields to provided distributions, to obtain a yield.