Monte Carlo Failure Rate Estimation via Regression Ordering
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Solution Overview
Problem
Current methods for estimating failure rates in high-yield semiconductor designs with low probability of failure are computationally intensive and often inaccurate, especially when dealing with a large number of random variables, as they require simulating millions of Monte Carlo samples, which is unreasonable with modern machines.
Innovation Solution
A method that draws a set of Monte Carlo samples, selects a subset for simulation, constructs a regression model using the simulated samples, orders the remaining candidates based on predicted performance values, and simulates them in ascending or descending order to efficiently find all failures, without requiring high model accuracy for feasibility decisions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Monte Carlo sampling with simulation is used to estimate failure rate, then the estimation can be obtained, but the computational cost becomes unreasonably high when failure probability is very low (e.g., 1e-6 or 1e-9)
Solution Approach 1:
The patent applies preliminary action by first drawing a large set of Monte Carlo samples and constructing a regression model before the actual failure detection phase. This preliminary modeling step enables efficient ordering and identification of failure-prone samples without requiring full simulation of all samples, thus resolving the contradiction between accurate failure rate estimation and computational efficiency.
Solution Approach 2:
The patent segments the Monte Carlo sampling process into distinct phases: (1) drawing samples and constructing regression model, (2) ordering samples based on predicted performance, and (3) selective simulation of ordered samples. This segmentation allows the method to handle low failure probability cases efficiently by focusing computational resources on the most critical samples rather than uniformly processing all samples.
2Measurement precision
If a large number of Monte Carlo samples are simulated to accurately estimate very low failure rates, then estimation accuracy improves, but the time required becomes prohibitively long
Solution Approach 1:
The patent performs preliminary regression model construction using a subset of samples before the main failure detection phase. This preliminary action creates a predictive framework that guides subsequent sampling and simulation, enabling accurate failure rate estimation without requiring exhaustive simulation of all possible samples, thereby reducing simulation time while maintaining accuracy.
Solution Approach 2:
The patent substitutes the traditional mechanical Monte Carlo simulation approach with a regression-based predictive system. Instead of relying solely on brute-force simulation of numerous samples, the method uses regression models to predict performance and identify failure-prone samples, replacing the mechanical simulation process with a more efficient computational approach that reduces time loss.
3Productivity
If regression modeling is used to order Monte Carlo samples by predicted performance, then computational burden is reduced, but the method becomes more complex
Solution Approach 1:
The patent introduces a regression model as an intermediary between the Monte Carlo samples and the failure detection process. This intermediary component predicts sample performance and enables efficient ordering without requiring full simulation of each sample. While this adds a modeling step, it significantly improves computational efficiency by reducing the number of expensive simulations needed, thus resolving the contradiction between efficiency and complexity.
Data Source
AI summary
A method and system to estimate failure rates in designs. N Monte Carlo samples are drawn from the random distribution that describes process variation in the design. A subset of these samples is selected, and that subset of Ninit samples are simulated (with a circuit simulator) to measure a performance value for each sample. A model is constructed, using the values of the Ninit process points as training inputs, and the corresponding Ninit performance values as training outputs. The candidate Monte Carlo samples are from the N Monte Carlo samples that have not yet been simulated. Each candidate is simulated on the model to get predicted performance values, and the samples are ordered in ascending (or descending) order of the predicted performance values. Simulation of candidates samples is then begun, in that order. The sampling and simulation will stops once there is sufficient confidence that all failures are found.