Optical Metrology Differential Fitting Reduces Model Bias
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Solution Overview
Problem
Existing optical metrology techniques face significant challenges in reducing measurement uncertainty due to model bias and tool-to-tool mismatch, which affect the accuracy of parameters such as critical dimension, sidewall angle, and thickness measurements in semiconductor processing.
Innovation Solution
The method involves using a differential fitting approach that compares the difference between experimental spectra from a target sample and anchor spectra from reference samples, utilizing anchor parameters determined from reference optical metrology tools to generate a differential experimental spectrum, which is then compared to a differential simulated spectrum to determine sample parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional model-based optical metrology is used to measure sample parameters, then the measurement process is straightforward, but model bias and tool-to-tool mismatch increase measurement uncertainty and reduce accuracy
Solution Approach 1:
The patent introduces an intermediary differential spectrum (the difference between experimental and anchor spectra) as a mediator in the measurement process. This differential spectrum serves as a bridge that eliminates the need for absolute model matching, thereby removing model bias and tool-to-tool mismatch effects while improving measurement accuracy and reliability
Solution Approach 2:
The patent transforms the measurement approach by changing from measuring absolute spectra to measuring differential spectra (parameter change in the spectral domain). This parameter transformation eliminates systematic errors associated with absolute measurements and enables more reliable parameter extraction through differential analysis
2Measurement precision
If anchor parameters from reference tools are used to generate differential simulated spectra, then tool-to-tool mismatch is reduced, but the complexity of the measurement process increases
Solution Approach 1:
The patent performs preliminary actions by measuring anchor spectra from reference samples and determining anchor parameters using reference tools before measuring the actual sample. This preliminary characterization enables the generation of differential simulated spectra that account for tool-specific characteristics, reducing tool-to-tool mismatch while maintaining process efficiency through pre-characterization
3Measurement precision
If differential fitting is applied to reduce model bias impact, then measurement accuracy improves, but the computational complexity of spectrum analysis increases
Solution Approach 1:
The patent extracts and removes the problematic components (model bias and tool-to-tool mismatch) from the measurement equation by working with differential spectra rather than absolute spectra. This extraction approach isolates the sample-specific information from systematic errors, improving accuracy while keeping computational complexity manageable through focused differential analysis
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 improves the accuracy of measurements by reducing the impact of model bias and tool-to-tool mismatch, leading to more precise determination of parameters like critical dimension, sidewall angle, and thickness, thereby enhancing the overall precision of optical metrology.
Implementation Method 1
Optical metrology techniques, such as ellipsometry and reflectometry, typically operate by illuminating a sample with a probe beam of electromagnetic radiation and then detecting and analyzing the reflected and/or transmitted energy
Implementation Method 2
an optical system that focuses the illumination, into incident light on a sample
Data Source
Figure 1A~1B
Figure 2~4
Figure 3
AI summary
Parameters of a sample are measured using a model-based approach that utilizes the difference between experimental spectra acquired from the sample and experimental anchor spectra acquired from one or more reference samples at the same optical metrology tool. Anchor parameters of the one or more reference samples are determined using one or more reference optical metrology tools. The anchor spectrum is obtained and the target spectrum for the sample is acquired using the optical metrology tool. A differential experimental spectrum is generated based on a difference between the target spectrum and the anchor spectrum. The parameters for the sample are determined using the differential experimental spectrum and the anchor parameters, e.g., by comparing the differential experimental spectrum to a differential simulated spectrum, which is based on a difference between spectra simulated using a model having the parameters and a spectrum simulated using a model having the anchor parameters.