Metrology Recipe Training With Physical Regularization
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Solution Overview
Problem
Current metrology techniques for semiconductor manufacturing face challenges in achieving optimal measurement performance due to suboptimal model training methods that do not fully exploit domain knowledge and are sensitive to discrepancies between simulated and real data, leading to large modeling errors and suboptimal results, especially with increasing complexity and small resolution requirements.
Innovation Solution
The implementation of a physically regularized optimization process during measurement model training, utilizing specific domain knowledge and performance metrics such as measurement precision and tool-to-tool matching to control the optimization process, thereby improving measurement reliability and reducing errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional model training methods are used without physical regularization, then training computational effort is reduced, but measurement precision and reliability deteriorate due to large modeling errors and sensitivity to discrepancies between simulated and real data
Solution Approach 1:
The patent applies parameter changes by modifying the optimization objective function to include physical regularization terms. The loss function is transformed from a simple data-fitting term to a composite function that incorporates measurement precision metrics and physical consistency constraints, thereby improving measurement precision while managing complexity through structured parameter integration
Solution Approach 2:
The patent introduces physical regularization metrics as intermediary elements that mediate between the raw measurement data and the final model parameters. These intermediaries (precision metrics, physical constraints) act as bridges that guide the optimization process to produce more reliable measurements without directly complicating the core measurement mechanism
2Reliability
If physics-based measurement models with iterative regression are used, then measurement reliability improves, but loss of time increases due to iterative computation requirements
Solution Approach 1:
The patent applies preliminary action by pre-computing and incorporating physical regularization metrics and domain knowledge into the optimization framework before actual model training. By preparing these constraints and metrics in advance, the iterative regression process is guided more efficiently, reducing the number of iterations needed while maintaining reliability
Solution Approach 2:
The patent substitutes the traditional mechanical iterative regression process with an optimization approach that integrates physical constraints directly into the objective function. This replacement reduces reliance on extensive iterative computation by embedding domain knowledge and physical principles into the optimization landscape itself, thereby maintaining reliability while reducing training time
3Productivity
If machine learning based measurement models are used, then productivity increases through faster processing, but measurement precision deteriorates due to lack of physical constraints
Solution Approach 1:
The patent creates a composite measurement model that combines machine learning components with physics-based constraints. The model integrates the speed advantages of machine learning with the precision benefits of physical principles, forming a hybrid approach that achieves both high productivity and accurate parameter estimation through the synergistic combination of different methodological elements
4Reliability
If domain knowledge is not incorporated into optimization, then ease of operation is maintained, but measurement reliability deteriorates due to suboptimal performance on complex structures
Solution Approach 1:
The patent applies self-service by enabling the optimization process to automatically incorporate and utilize domain knowledge and physical constraints without requiring manual intervention. The system self-regulates by integrating measurement precision metrics and physical principles directly into the optimization objective function, improving reliability while maintaining operational simplicity through automated constraint enforcement
Data Source
AI summary
Methods and systems for training and implementing metrology recipes based on performance metrics employed to quantitatively characterize the measurement performance of a metrology system in a particular measurement application. Performance metrics are employed to regularize the optimization process employed during measurement model training, model-based regression, or both. For example, the known distributions associated with important measurement performance metrics such as measurement precision, wafer mean, etc., are specifically employed to regularize the optimization that drives measurement model training. In a further aspect, a trained measurement model is employed to estimate values of parameters of interest based on measurements of structures having unknown values of one or more parameters of interest. In a further aspect, trained measurement model performance is validated with test data using error budget analysis. In another aspect, a model-based regression on a measurement model is physically regularized by on one or more measurement performance metrics.