Computational Lithography Model Calibration Using Information Matrix Test Pattern Selection
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Solution Overview
Problem
Current model calibration methods for lithographic processes are inefficient, relying on arbitrary and redundant test patterns, which fail to accurately predict imaging behavior across various geometric layouts and are computationally intensive, leading to resource wastage and inadequate representation of physical and chemical characteristics.
Innovation Solution
A method for selecting a subset of test patterns that effectively determines model parameter values by generating an information matrix and executing a selection algorithm to sample uniformly in parametric space, ensuring optimal coverage and reducing the number of necessary metrology measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If arbitrary and redundant test patterns are used for model calibration, then the calibration process can be performed, but the prediction accuracy for imaging behavior across various geometric layouts deteriorates and computational resources are wasted
Solution Approach 1:
The patent extracts and removes redundant test patterns from the calibration set by generating an information matrix that quantifies the contribution of each pattern to model parameter determination. Patterns that provide redundant information are identified and excluded, retaining only the essential subset that maximizes prediction accuracy while minimizing computational resource consumption.
Solution Approach 2:
The patent transforms the calibration approach by changing from using arbitrary test patterns to using a mathematically optimized subset selected based on information matrix analysis. This parameter change in pattern selection strategy improves the efficiency and accuracy of model calibration by systematically determining which patterns provide the most valuable information for each model parameter.
2Adaptability or versatility
If a large number of test patterns are used for comprehensive coverage, then representation of physical and chemical characteristics improves, but the number of metrology measurements and computational complexity increases
Solution Approach 1:
The patent extracts the essential test patterns that provide maximum representation of physical and chemical characteristics by analyzing the information matrix. This extraction process identifies the minimal subset of patterns that capture the essential variability needed for accurate model calibration, eliminating unnecessary measurements while maintaining comprehensive coverage of relevant characteristics.
Solution Approach 2:
The patent applies partial action by using only the necessary subset of test patterns rather than all possible patterns. The information matrix analysis determines the optimal partial set that provides sufficient coverage of physical and chemical characteristics without the excessive computational burden and measurement overhead of using all available patterns.
3Reliability
If redundant test patterns are used in calibration, then more data points are available for model fitting, but the calibration efficiency deteriorates and the number of required metrology measurements increases
Solution Approach 1:
The patent extracts and removes redundant test patterns from the calibration dataset by computing an information matrix that quantifies the information content of each pattern. This extraction process identifies and eliminates patterns that do not contribute unique information to model parameter determination, thereby improving calibration efficiency while maintaining or enhancing calibration accuracy with a reduced set of essential patterns.
Solution Approach 2:
The patent uses partial action by selecting only the necessary subset of test patterns for calibration based on information matrix analysis. This approach provides sufficient data points for accurate model fitting without the excessive redundancy that reduces calibration efficiency, achieving the optimal balance between reliability and productivity.
Data Source
AI summary
Embodiments of the present invention describe methods of selecting a subset of test patterns from an initial larger set of test patterns for calibrating a computational lithography model. An example method comprises: generating an information matrix for the initial larger set of test patterns, wherein the terms of the information matrix comprise one or more identified model parameters that represent a lithographic process response; and, executing a selection algorithm using terms of the information matrix to select the subset of test patterns that effectively determines values of the identified model parameters that contribute significantly in the lithographic process response, wherein the subset of test patterns characteristically represents the initial larger set of test patterns. The selection algorithm explores coverage relationships existing in the initial larger set of test patterns.