Overlay Measurement Error Correction Using High Order Regression
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Solution Overview
Problem
Conventional measurement systems for overlay alignment errors in semiconductor manufacturing struggle with optimizing the number and positions of shots to be measured, especially when using high order regression analysis models, leading to inaccurate corrections due to the impact of erroneous data and varying process conditions.
Innovation Solution
A measurement system that determines the optimal number and position of shots to be measured using a high order regression analysis model, detects and filters erroneous data, and restores missing data to achieve accurate overlay alignment error corrections by maximizing the determinant of the (XTX) matrix and employing robust regression analysis techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional first order regression analysis model is used for overlay alignment error measurement, then the measurement process is simple and fast, but the measurement precision is insufficient for fine line-width circuits
Solution Approach 1:
The patent transitions from a first order regression analysis model to a high order regression analysis model (second order or higher) to improve measurement precision. This parameter change in the model order enables accurate measurement of overlay alignment errors for fine line-width circuits while the system automatically handles the increased complexity through optimized shot selection and erroneous data filtering mechanisms
2Measurement precision
If the number and positions of shots to be measured are fixed in advance, then the measurement process is simple and fast, but the measurement precision and reliability are insufficient due to inability to optimize for high order regression analysis
Solution Approach 1:
The system performs preliminary optimization to determine the optimal number and positions of shots to be measured before actual measurement. This preliminary action includes selecting shots that maximize the determinant of the (XTX) matrix for high order regression analysis and pre-identifying potential erroneous data, thereby ensuring measurement precision without sacrificing productivity during the actual measurement process
Solution Approach 2:
The patent introduces dynamic selection of shots to be measured based on process conditions and regression analysis requirements. Instead of fixed shot selection, the system dynamically determines which shots to measure by evaluating the determinant of the (XTX) matrix and process variation, allowing optimization for high order regression analysis while maintaining measurement efficiency
3Measurement precision
If high order regression analysis model is used with optimized shot selection, then the measurement precision is improved, but the device complexity and data processing burden increase
Solution Approach 1:
The system extracts and removes erroneous data from the measurement dataset before performing high order regression analysis. By identifying and eliminating outliers and erroneous measurements through statistical analysis and process knowledge, the system reduces data processing complexity and prevents erroneous data from degrading the precision improvements gained from high order regression analysis
4Reliability
If erroneous data is not filtered, then the measurement process is simple and fast, but the reliability of overlay alignment error correction deteriorates due to impact on regression analysis
Solution Approach 1:
The system applies partial filtering by selectively removing only erroneous data points that fall outside acceptable statistical thresholds or process specifications, rather than filtering all data. This partial action approach maintains measurement and processing speed while improving reliability by eliminating only the harmful erroneous data that would degrade regression analysis results
Data Source
AI summary
A measurement system and a measurement method, which can obtain a measurement value close to a true value considering an overlay measurement error according to a higher order regression analysis model. The measurement system and the measurement method provide a technique for determining optimal positions of shots to be measured using an optimal experimental design. When the regression analysis model and the number of shots to be measured are determined in advance, a method is used for determining an optimal number of shots to be measured according to the regression analysis model and process dispersion using a confidence interval estimating method. A dynamic sampling method is used for dynamically changing the number and positions of shots to be measured according to a change in process features by combining the above two methods. And, when erroneous data is detected, or when measured data is missing, a robust regression analysis method and a technique for filtering the erroneous data and the missing data are used.