Defect Prediction Using Non-Probabilistic and Probabilistic Model Segmentation
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Solution Overview
Problem
Current device manufacturing processes, such as lithographic processes, face challenges in accurately predicting defects due to random variations, which existing non-probabilistic models fail to capture, leading to inefficiencies in defect identification and inspection strategies.
Innovation Solution
A method using a non-probabilistic model to obtain characteristics of patterns on a substrate, calculating attributes of their distributions, and determining defect probabilities by integrating probability density functions over specific ranges, thereby prioritizing inspection based on descending probabilities for efficient defect detection.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If non-probabilistic models are used to predict defects, then the model complexity is low and computation is fast, but the prediction accuracy is insufficient due to inability to capture random variations
Solution Approach 1:
The model is segmented into two distinct components: a non-probabilistic model for deterministic predictions and a separate probabilistic component for capturing random variations. This segmentation allows each component to specialize in what it does best while working together to provide comprehensive defect prediction with both accuracy and computational efficiency.
Solution Approach 2:
The patent creates a composite modeling approach by combining non-probabilistic and probabilistic models into a unified framework. The non-probabilistic model provides the base prediction while the probabilistic model adds a layer of uncertainty quantification, similar to how composite materials combine different materials to achieve superior properties.
2Productivity
If comprehensive defect prediction is performed on all patterns, then the prediction coverage is complete, but the inspection time and computational resources are excessively consumed
Solution Approach 1:
Instead of applying uniform inspection to all patterns, the patent applies different inspection depths and probabilities to different patterns based on their individual defect likelihoods. High-risk patterns receive more thorough inspection while low-risk patterns receive minimal inspection, optimizing the allocation of inspection resources.
Solution Approach 2:
The patent performs partial inspection by focusing computational resources on patterns with higher predicted defect probabilities. Rather than exhaustively analyzing all patterns equally, it applies inspection effort proportionally to the predicted risk, achieving sufficient defect detection with reduced overall inspection time.
3Reliability
If defect prediction accounts for random variations using probabilistic methods, then the prediction accuracy improves, but the computational complexity and processing time increase
Solution Approach 1:
The computational task is segmented into a deterministic phase using non-probabilistic models for quick baseline predictions and a probabilistic phase that only processes patterns above certain thresholds. This segmentation reduces the overall computational burden while maintaining reliability where it matters most.
Solution Approach 2:
The patent applies probabilistic analysis partially, only to patterns where the non-probabilistic model indicates potential defects or where uncertainty is highest. This partial application of probabilistic methods achieves improved reliability without the full computational cost of applying probabilistic models to all patterns.
Data Source
AI summary
A method including obtaining verified values of a characteristic of a plurality of patterns on a substrate produced by a device manufacturing process; obtaining computed values of the characteristic using a non-probabilistic model; obtaining values of a residue of the non-probabilistic model based on the verified values and the computed values; and obtaining an attribute of a distribution of the residue based on the values of the residue. Also disclosed herein are methods of computing a probability of defects on a substrate produced by the device manufacturing process, and of obtaining an attribute of a distribution of the residue of a non-probabilistic model.