Dynamic Parameter Correlation Removal in Optical Metrology
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
In optical metrology, highly correlated parameters in models of structures lead to unstable search directions during parameter measurement, as changes in one parameter can be largely compensated by changes in its correlated parameters, making conventional methods inadequate for dynamic parameterization, especially when parameter correlation varies significantly over the search space.
Innovation Solution
A method for dynamic removal of correlation between parameters during measurement, involving the generation of a Jacobian matrix, application of singular value decomposition, and selection of a subset of parameters to compute a search direction, with iterative refinement until convergence is achieved, allowing for stable parameter measurement without changing the model of the structure.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional parameter measurement methods are used, then the measurement process is simple, but the search direction becomes unstable when parameters are highly correlated
Solution Approach 1:
The patent applies dynamics by making the parameterization adaptive and dynamic rather than static. The system continuously monitors parameter correlations during the measurement process and adjusts the parameterization in real-time to maintain stability. This is achieved through iterative updates of the transformation matrix based on current correlation information, allowing the measurement system to adapt to changing correlation conditions throughout the search space.
Solution Approach 2:
The patent transforms the original correlated parameters into a new set of uncorrelated parameters through a linear transformation. By changing the parameter representation from the original correlated set to a transformed uncorrelated set, the system eliminates the instability caused by parameter correlations while maintaining the ability to fully describe the structure being measured.
2Adaptability or versatility
If static parameterization is used, then the method is simple to implement, but it cannot adequately handle parameters with varying correlation across the search space
Solution Approach 1:
The system transitions from static to dynamic parameterization by continuously updating the transformation based on local correlation information. During the measurement process, the system evaluates parameter correlations at different points in the search space and adjusts the parameter transformation accordingly, enabling adaptation to varying correlation conditions throughout the measurement process.
Solution Approach 2:
The patent segments the search space into multiple regions where parameter correlations can be considered relatively constant. By dividing the overall parameter space into smaller segments and applying appropriate local transformations to each segment, the system achieves adaptability to varying correlations without requiring a completely complex global solution.
3Reliability
If model re-parameterization is performed to address correlation, then parameter stability improves, but the process becomes more complex and time-consuming
Solution Approach 1:
The system performs preliminary computation of the transformation matrix using available prior information about parameter correlations. By pre-computing transformation matrices based on initial correlation assessments or historical data, the system reduces the computational burden during the actual measurement process, achieving stability without excessive time loss.
Solution Approach 2:
The patent creates a transformed copy of the parameter space that preserves the essential relationships while eliminating correlations. Instead of repeatedly re-parameterizing the original parameters, the system works with a transformed copy of the parameter set that inherently lacks the correlation problems, thereby reducing computational overhead while maintaining measurement stability.
Data Source
AI summary
Dynamic removal of correlation of highly-correlated parameters for optical metrology is described. An embodiment of a method includes determining a model of a structure, the model including a set of parameters; performing optical metrology measurement of the structure, including collecting spectra data on a hardware element; during the measurement of the structure, dynamically removing correlation of two or more parameters of the set of parameters, an iteration of the dynamic removal of correlation including: generating a Jacobian matrix of the set of parameters, applying a singular value decomposition of the Jacobian matrix, selecting a subset of the set of parameters, and computing a direction of the parameter search based on the subset of parameters. If the model does not converge, performing one or more additional iterations of the dynamic removal of correlation until the model converges; and if the model does converge, reporting the results of the measurement.