Patterned Substrate Metrology Using DEMRA Features for Small Data
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Solution Overview
Problem
Existing metrology techniques for patterned substrates face challenges in accurately determining characteristics due to complex light propagation and reliance on preconceived models, leading to poor performance on smaller data sets and the need for frequent model retraining.
Innovation Solution
Utilizing discrete effective medium refractive analysis (DEMRA) to generate features from spectral data, combined with machine learning models, to predict substrate characteristics by relating effective index of refraction to incident light wavelength, employing empirical models like Cauchy, Lorentz, Tauc-Lorentz, Forouhi-Bloomer, and Drude models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing metrology techniques use preconceived models to analyze patterned substrates, then the analysis can be performed with established methods, but the measurement precision deteriorates due to complex light propagation and poor performance on smaller data sets
Solution Approach 1:
The patent introduces DEMRA as an intermediary analysis method that simplifies complex light propagation by modeling the patterned substrate as discrete effective medium layers. This mediator translates complex optical interactions into manageable refractive index calculations, improving measurement precision without requiring full complexity of light propagation modeling.
Solution Approach 2:
The patent transforms the analysis approach by changing from direct light propagation modeling to effective medium refractive index parameter analysis. By measuring effective refractive indices at different wavelengths and comparing them to model predictions, the system achieves higher precision in substrate characteristic determination while avoiding the computational complexity of full wave optics.
2Reliability
If existing metrology techniques rely on frequent model retraining to maintain accuracy, then adaptability to different process recipes is reduced, but measurement precision can be maintained through continuous model updates
Solution Approach 1:
The patent creates a universal analysis framework based on DEMRA that can handle multiple process recipes and substrate types without requiring separate trained models for each. The effective medium refractive index approach provides a common language for analyzing diverse patterned substrates, making the system both reliable and adaptable simultaneously.
Solution Approach 2:
The patent performs preliminary DEMRA analysis to extract effective refractive index parameters before applying machine learning models. This preliminary processing creates standardized features that improve model generalization across different process recipes, reducing the need for frequent retraining while maintaining reliability.
3Measurement precision
If discrete effective medium refractive analysis is used to generate features from spectral data, then model performance on smaller data sets improves, but the complexity of the analysis process increases
Solution Approach 1:
The patent replaces complex mechanical/optical light propagation analysis with an effective medium refractive index model. This substitution simplifies the physical analysis by treating the patterned substrate as homogeneous layers with effective properties, achieving better model performance on small data sets while managing analytical complexity through mathematical abstraction.
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
Improves model performance on smaller data sets by incorporating physical properties, enabling accurate prediction of substrate characteristics and reducing the need for retraining across multiple process recipes.
Implementation Method 1
The set of features includes a set of fitted parameters corresponding to an empirical model that relates at least one effective index of refraction associated with the patterned substrate to a wavelength of light incident on the patterned substrate
Data Source
AI summary
A method includes obtaining, by at least one processing device, spectral data associated with a patterned substrate, generating, by the at least one processing device from the spectral data, a set of features using discrete effective medium refractive analysis (DEMRA) of the patterned substrate, and processing, by the at least one processing device, the set of features using a machine learning model to predict at least one characteristic of the patterned substrate from the set of features. The set of features includes a set of fitted parameters corresponding to an empirical model that relates at least one effective index of refraction associated with the patterned substrate to a wavelength of light incident on the patterned substrate.