Monte Carlo Yield Prediction via Clustered Sampling
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Solution Overview
Problem
Conventional methods for determining the yield of a circuit in semiconductor manufacturing, such as Monte Carlo SPICE simulations, face challenges with high-dimensional parameter variations, leading to inefficient resource utilization and prolonged simulation times due to the need for large numbers of samples, especially in high sigma regions.
Innovation Solution
A method involving a first pass of Monte Carlo simulations to identify failed sampling points in the high sigma region, partitioning these points into clusters based on angular separation, determining cluster boundaries, performing sensitivity analysis to identify closest failed sampling points, and a second pass of simulations using these points to estimate circuit yield, thereby optimizing resource allocation and reducing simulation time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional Monte Carlo SPICE simulations are performed to determine circuit yield, then prediction accuracy is improved, but simulation time and computational resources increase significantly
Solution Approach 1:
The patent segments the Monte Carlo simulation process into two distinct passes: a first pass that identifies failed sampling points in the high sigma region, and a second pass that performs detailed simulations only on critical samples near the decision boundary. This segmentation allows the method to maintain prediction accuracy while dramatically reducing the total number of simulations required.
Solution Approach 2:
The first pass of Monte Carlo simulations serves as a preliminary action that identifies and clusters failed sampling points before the main yield prediction. By pre-identifying critical regions and estimating decision boundaries, the method prepares the simulation framework to focus computational resources only where they are most needed, avoiding unnecessary simulations in non-critical areas.
2Reliability
If the number of Monte Carlo samples is increased to cover high sigma regions, then yield prediction coverage is improved, but resource utilization deteriorates
Solution Approach 1:
The patent applies local quality by performing detailed simulations only in specific high-value regions (near the decision boundary and in high sigma failed samples) while using coarser sampling elsewhere. The method adaptively allocates computational resources to regions where they provide the most value for yield prediction, rather than uniformly distributing samples across the entire parameter space.
Solution Approach 2:
The method changes the sampling strategy parameter dynamically: using a coarser sampling approach in the first pass to identify failed samples, then transitioning to a finer, more focused sampling approach in the second pass for critical regions. This parameter change allows the system to achieve high prediction coverage without proportionally increasing computational resources.
3Measurement precision
If detailed circuit simulation is performed for the entire parameter space, then simulation accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent applies partial action by performing detailed circuit simulations only for a selected subset of samples that are most critical to yield prediction (those near the decision boundary and in high sigma regions). Instead of simulating the entire parameter space with fine granularity, the method performs partial simulations on strategically selected samples, achieving adequate accuracy with reduced computational complexity.
Data Source
AI summary
Methods and systems are disclosed for determining a yield of a circuit in semiconductor manufacturing. In one embodiment, a computer implemented method includes performing a first pass of Monte Carlo simulations of the circuit to identify a plurality of failed sampling points in a high sigma region of a statistical distribution, partitioning the plurality of failed sampling points into a plurality of clusters based on angular separation of the plurality of failed sampling points, determining a boundary of each cluster in the plurality of clusters, performing sensitivity analysis from the boundary of the each cluster to identify an estimated closest failed sampling point associated with the each cluster, and performing a second pass of Monte Carlo simulations of the circuit to determine the yield of the circuit using the estimated closest failed sampling point associated with the each cluster and the boundary of each cluster in the plurality of clusters.