Scatterometry Model Parameterization for Stable Automated Regression
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Solution Overview
Problem
Current scatterometry methods rely heavily on expert engineers to select which model parameters to float and fix, leading to subjectivity and increased engineering time, hindering the widespread adoption of scatterometry in manufacturing processes.
Innovation Solution
An automated method using a Jacobian matrix and precision metrics to determine which model parameters should be fixed or floated, reducing reliance on expert users and stabilizing the regression process, allowing for a more efficient and precise parameterization of scatterometry models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If expert engineers manually select model parameters to float and fix during regression analysis, then the selection can be based on experience and judgment, but the process becomes time-consuming and subjective
Solution Approach 1:
The system performs automated selection of float and fix parameters using algorithmic criteria based on the Jacobian matrix and precision metrics, eliminating the need for manual expert intervention. The computer system automatically determines which parameters should be floated or fixed based on mathematical optimization criteria rather than human judgment.
Solution Approach 2:
The manual expert judgment process is replaced with an automated computational system that uses Jacobian matrix calculations and precision metrics to objectively determine parameter selection. This substitutes human cognitive processes with mathematical algorithms that can be executed rapidly by computer systems.
2Adaptability or versatility
If multiple model parameters are allowed to float during regression, then the model can capture more variations in the measured spectra, but the regression stability decreases and precision is reduced
Solution Approach 1:
The system dynamically determines which parameters should be floated or fixed based on calculated precision metrics from the Jacobian matrix. This automated parameter selection optimizes the balance between model flexibility and regression stability by using mathematical criteria to identify the optimal subset of parameters to float, rather than using fixed rules or expert judgment.
3Productivity
If automated parameter selection is implemented, then the process becomes faster and more objective, but complex calculations such as Jacobian matrix computation are required
Solution Approach 1:
The system calculates the Jacobian matrix and precision metrics before performing the regression analysis, so that the optimal parameter selection is determined in advance. This preliminary computational step enables the subsequent regression to proceed efficiently with the pre-determined float/fix configuration, improving overall process speed despite the initial calculation complexity.
Data Source
AI summary
Provided is an automated determination of an optimized parameterization of a scatterometry model for analysis of a sample diffracting structure having unknown parameters. A preprocessor determines from a plurality of floating model parameters, a reduced set of model parameters which can be reasonably floated in the scatterometry model based on a relative precision for each parameter determined from the Jacobian of measured spectral information with respect to each parameter. The relative precision for each parameter is determined in a manner which accounts for correlation between the parameters for a combination.