Penalty Function Optimization for Patterned Structure Metrology
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Solution Overview
Problem
Conventional optical metrology techniques for measuring patterned semiconductor structures face challenges in accuracy due to instability and insensitivity to certain parameters, leading to noisy and unrealistic results, especially when dealing with concurrent variations of multiple parameters.
Innovation Solution
The method employs a penalty function-based optimization approach that utilizes global parameters to stabilize the fitting process, allowing for the variation of more parameters and enhancing the reliability of measurements by incorporating knowledge about the expected behavior of these parameters across multiple measurement sites.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional fitting procedure is used to measure parameters of patterned structures, then measurement process is simple, but measurement precision and reliability deteriorate due to instability and insensitivity to certain parameters
Solution Approach 1:
The patent applies preliminary action by performing a global fit analysis across multiple measurement sites before conducting individual local fits. This preliminary global analysis establishes expected parameter behavior and constraints that guide subsequent local measurements, preventing instability and insensitivity issues in the fitting process while maintaining systematic simplicity.
Solution Approach 2:
The patent implements feedback by using results from global fit analysis to inform and constrain local fit procedures. The global fit provides expected parameter ranges and relationships that serve as feedback to guide local measurements, improving measurement precision by preventing unrealistic parameter values while maintaining a structured approach.
2Adaptability or versatility
If more parameters are allowed to vary in the fitting model, then measurement comprehensiveness improves, but measurement stability deteriorates due to parameter instability
Solution Approach 1:
The patent performs a preliminary global fit analysis that establishes stable baseline values and expected relationships for multiple parameters before allowing them to vary in local fits. This preliminary step ensures that even when many parameters are allowed to vary, they do so within stable, physically meaningful ranges constrained by global behavior.
Solution Approach 2:
The patent uses global fit results as feedback to constrain local parameter variations. By comparing local measurements against globally established expectations, the system allows comprehensive parameter variation while maintaining stability through continuous reference to global behavior patterns.
3Productivity
If individual measurement sites are analyzed independently, then measurement speed is high, but measurement reliability deteriorates due to lack of global context
Solution Approach 1:
The patent performs a preliminary global fit analysis across all measurement sites before conducting individual local fits. This preliminary global context establishment enables rapid local measurements to proceed with pre-established constraints, maintaining high speed while ensuring reliability through globally informed parameter expectations.
Solution Approach 2:
The patent implements feedback by using global fit results to guide and validate local measurements. Individual sites are analyzed quickly with the benefit of global context, where global parameter relationships serve as feedback to verify local measurement reliability without sacrificing measurement speed.
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
This approach results in more consistent and reliable measurements by penalizing deviations from expected global behavior, improving the accuracy and trustworthiness of the reported results.
Implementation Method 1
Reflectometry based tools typically measure changes in the magnitude of radiation returned/transmitted from/through the sample
Implementation Method 2
Optical Critical Dimension (OCD) measurement technique (known also as Scatterometry)
Implementation Method 3
ellipsometry based tools typically measure changes of the polarization state of radiation after interacting with the sample
Data Source
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AI summary
A method and system are provided for use in measurement of at least one parameter of a patterned structure. The method comprises: providing input data comprising: measured data including multiple measured signals corresponding to measurements on different sites of the structure; and data indicative of theoretical signals, a relation between the theoretical and measured signals being indicative of at least one parameter of the structure; providing a penalty function based on at least one selected global parameter characterizing at least one property of the structure; and performing a fitting procedure between the theoretical and measured signals, said performing of the fitting procedure comprising using said penalty function for determining an optimized relation between the theoretical and measured signals, and using the optimized relation to determine said at least one parameter of the structure.