Lithography Failure Causality Modeling via Transfer Entropy Networks
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Solution Overview
Problem
Current predictive maintenance methods for lithographic systems are inefficient due to the need for domain expertise, high false positive rates, and the inability to accurately trace causal relationships between events, leading to suboptimal alert validation and prolonged lead times in identifying root causes.
Innovation Solution
The method employs transfer entropy to determine causal relationships between parameter excursion events and failure events, constructing a process network to identify directed cycles and root causes, thereby improving predictive modeling and reducing diagnostic time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional predictive maintenance methods are used, then domain expertise is required and false positive rates are high, but diagnostic accuracy is reduced and lead time is prolonged
Solution Approach 1:
The patent introduces transfer entropy as an intermediary computational method that objectively quantifies causal relationships between system parameters. This mediator replaces subjective domain expertise with a mathematical framework that automatically identifies root causes by measuring information flow between events, thereby improving diagnostic accuracy while reducing the time required for analysis
Solution Approach 2:
The patent replaces the mechanical/expert-based diagnostic system with an information-theoretic system using transfer entropy calculations. This substitution transforms the diagnostic process from relying on human expertise and manual analysis to an automated computational approach that processes parameter data and identifies causal relationships objectively and rapidly
2Loss of information
If traditional event analysis methods are used, then causal relationships between events cannot be accurately traced, but system understanding is limited
Solution Approach 1:
The patent implements a feedback mechanism where transfer entropy calculations continuously evaluate the causal relationships between system events. By computing the information flow from one event to another and using this feedback to refine the causal model, the system accurately traces cause-and-effect relationships while maintaining a manageable analytical framework through iterative refinement
Data Source
AI summary
A method for determining a causal relationship between events in a plurality of parameter time series, the method including: identifying a first event associated with a parameter excursion event; identifying a second event associated with a failure event, wherein there are a plurality of events including the first events and second events; determining values of transfer entropy for pairs of the events to establish a causal relationship for each of the pairs of events; using the determined values of transfer entropy and identified causal relationships to determine a process network, wherein each of the events is a node in the process network, the edges between nodes being dependent upon the values of transfer entropy; identifying a directed cycle within the plurality of events and the causal relationships; classifying a directed cycle; and classifying one or more events having a causal relation to the classified directed cycle.