Non-Orthogonal Decomposition for Lithography Deformation Separation
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Solution Overview
Problem
Current methods struggle to accurately separate and determine substrate deformations from alignment mark deformations in lithographic processes, leading to measurement errors and incomplete correction of overlay penalties, as existing approaches like PCA fail to account for non-orthogonal physical processes causing these deformations.
Innovation Solution
A method involving the decomposition of mapping matrices between measurement datasets to separately determine mark and substrate deformations, using eigenvalue decomposition and non-orthogonal decomposition to identify scaling differences and separate deformation components, allowing for improved alignment, metrology, and process correction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If conventional PCA methods are used to separate deformation components, then dimensionality reduction is achieved, but the separation accuracy of mark and substrate deformations deteriorates because PCA assumes orthogonal processes while physical deformation processes are non-orthogonal
Solution Approach 1:
The patent changes the fundamental parameter of the decomposition approach from orthogonal (PCA) to non-orthogonal decomposition. This allows the method to accurately represent the non-orthogonal physical processes of mark and substrate deformations while still achieving dimensionality reduction. The non-orthogonal decomposition transforms the measurement data using a different mathematical framework that respects the actual physical relationships between deformation sources.
2Measurement precision
If multiple measurement colors are used to characterize deformation, then the ability to distinguish mark and substrate deformations improves, but the measurement complexity and data processing requirements increase
Solution Approach 1:
The patent segments the deformation characterization into distinct mark deformation and substrate deformation components through non-orthogonal decomposition. By using multiple measurement colors, the system captures different aspects of the deformations, and the decomposition method separates these into their source components. This segmentation allows accurate characterization while managing complexity through structured data organization and processing.
Solution Approach 2:
The patent adds the dimension of multiple measurement colors to the deformation characterization process. By measuring at different wavelengths or colors, the system obtains additional independent information about the deformations. The non-orthogonal decomposition then utilizes this multi-dimensional data to separate mark and substrate deformation components more effectively than single-color measurements could achieve.
3Manufacturing precision
If advanced alignment models are used to correct non-linear distortions, then overlay accuracy improves, but the ability to trace and eliminate root causes of distortions deteriorates because correction masks the underlying deformation sources
Solution Approach 1:
The patent performs preliminary decomposition of the measured distortions into mark and substrate deformation components before the alignment correction process. By separating the deformation sources in advance using non-orthogonal decomposition and multiple measurement colors, the system maintains traceability of the root causes. This preliminary action allows both accurate correction and continued ability to identify and eliminate specific deformation sources.
Solution Approach 2:
The patent establishes a feedback loop where the decomposed deformation information from multiple measurements is used to inform and refine the alignment correction process. The non-orthogonal decomposition provides detailed information about mark and substrate deformations that feeds back into the alignment model, allowing for more targeted corrections while maintaining awareness of the underlying causes. This feedback mechanism prevents loss of traceability information.
Data Source
AI summary
A method for determining substrate deformation includes obtaining first measurement data associated with mark positions, from measurements of a plurality of substrates; obtaining second measurement data associated with mark positions, from measurements of the plurality of substrates; determining a mapping between the first measurement data and the second measurement data; and decomposing the mapping, by calculating an eigenvalue decomposition for the mapping, to separately determine a first deformation (e.g. mark deformation) that scales differently from a second deformation (e.g. substrate deformation) in the mapping between the data. The steps of determining a mapping and decomposing the mapping may be performed together using non-linear optimization.