Optical Metrology Eigenvalue Field Matching for Distorted Marks
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Solution Overview
Problem
The distortion of metrology marks during substrate processing complicates the optical measurement of alignment marks in lithographic apparatuses, making it difficult to accurately determine the alignment of substrates, which is time-consuming and costly.
Innovation Solution
An optical metrology system that calculates an expected electromagnetic field for a theoretical reference mark using an algebraic eigenvalue-eigenvector representation, calculates derivatives of this field with respect to mark shape parameters, and optimizes these parameters to match the recorded field, allowing for precise alignment.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional optical measurement methods are used to measure distorted metrology marks, then measurement can be performed, but measurement precision deteriorates due to mark distortion
Solution Approach 1:
The patent changes the measurement parameters by measuring multiple diffraction orders (different spatial frequency components) of the metrology mark and using these multiple parameters to reconstruct the mark shape and position. This allows accurate measurement even when the mark is distorted, as the multiple diffraction orders provide redundant information that can compensate for distortion effects
Solution Approach 2:
The patent introduces an intermediary computational model that relates the measured diffraction patterns to the physical mark shape and position. By using a forward model that simulates diffraction from various mark configurations, the system can infer the true mark position even when directly measuring the distorted mark is difficult
2Manufacturing precision
If conventional field calculation methods are used for each iteration, then optimization can be performed, but computational time increases significantly
Solution Approach 1:
The patent performs preliminary calculations by pre-computing the relationship between mark shape parameters and diffraction patterns using an eigenvalue-eigenvector representation. This preliminary model allows the optimization process to quickly evaluate how changes in mark parameters affect the diffraction pattern without performing full electromagnetic field calculations at each iteration
Solution Approach 2:
The patent replaces the traditional mechanical iterative field calculation approach with an algebraic eigenvalue-eigenvector based method. This substitution transforms the computational problem from solving differential equations at each iteration to using pre-computed eigenmodes, dramatically reducing the computational burden while maintaining accuracy
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables efficient and accurate determination of substrate alignment by iteratively matching calculated and measured fields, reducing computational resources and time required for alignment.
Implementation Method 1
a measuring system configured to irradiate a metrology mark and record a portion of a reflected, a transmitted, or both, electromagnetic field
Data Source
AI summary
An optical metrology system is disclosed that has a measuring system configured to irradiate a metrology mark and record a portion of a reflected, a transmitted, or both, electromagnetic field and a characterization device configured to determine from the recorded field a mark shape parameter indicative of the structure of the metrology mark, the characterization device comprising: a field calculation unit configured to calculate an expected field for reflection, transmission, or both, from a theoretical reference mark based on an algebraic eigenvalue-eigenvector representation of the expected field, a field derivative calculation unit configured to calculate a first order derivative, a higher order derivative, or both, of the expected field with respect to the mark shape parameter by first deriving analytical forms for corresponding derivatives of eigenvalues and eigenvectors of the eigenvalue-eigenvector representation, and an optimization unit configured to use the outputs from the field and field derivative calculation units to determine an optimized mark shape parameter for which the expected field substantially matches the recorded field.