Computational Lithography Model Calibration via Weighted CD Data
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Solution Overview
Problem
Conventional computational lithography models that minimize root mean squared (RMS) error for imaging parameters result in 'over-fit' models, leading to high variability in critical dimension (CD) due to imaging tool differences, causing yield loss and requiring extensive modifications across different lithography tools.
Innovation Solution
The use of gratings with varying line width to space width ratios and a cost-weighted data weighting algorithm that assigns inverse proportional weights to CD data variance, reducing data collection intrusiveness and calibrating lithography models to process medians, improves signal-to-noise ratio and reduces fitting errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional RMS error minimization is used for model fitting, then model accuracy to training data is improved, but model portability across different lithography tools deteriorates
Solution Approach 1:
The patent applies local quality by assigning different weights to different data points based on their reliability and representativeness. The weighting algorithm gives higher weights to data points that are more representative of actual production conditions and lower weights to noisy or less relevant data, thereby improving model portability while maintaining accuracy on important features
Solution Approach 2:
The patent changes the parameter of data weighting from uniform (conventional) to variable (weighted). By introducing a weighting algorithm that modifies the contribution of different data points to the RMS error calculation, the model becomes more adaptable to different lithography tools while maintaining fitting accuracy for critical parameters
2Measurement precision
If extensive data collection is performed to improve model accuracy, then model accuracy is improved, but data collection intrusiveness and time increase
Solution Approach 1:
The patent extracts only the most relevant and representative data points for model training by applying a weighting algorithm that identifies and prioritizes high-value data. This extraction approach obtains sufficient model accuracy without requiring extensive data collection, thereby reducing data collection time and intrusiveness
Solution Approach 2:
The patent applies partial action by collecting and weighting only the necessary subset of data required for accurate model training, rather than collecting all possible data. The weighting algorithm identifies the critical data points that provide the most value, allowing the model to achieve high accuracy with reduced data collection effort
3Device complexity
If uniform weighting is applied to all CD data points, then simplicity is maintained, but noise from high-variance data points dominates resulting in high CD variability
Solution Approach 1:
The patent applies local quality by assigning different weights to different CD data points based on their variance and reliability. Data points with high variance (noise) receive lower weights, while data points with low variance (high reliability) receive higher weights. This differential weighting reduces the dominance of noisy data points and improves manufacturing precision without significantly increasing algorithmic complexity
Data Source
AI summary
A method of computational lithography includes collecting a critical dimension (CD) data set including CD data from printing a test structure including a set of gratings which provide a plurality of feature types including different ratios of line width to space width, where the printing includes a range of different focus values. The CD data is weighted to form a weighted CD data set using a weighting algorithm (WA) that assigns cost weights to the CD data based its feature type and its magnitude of CD variation with respect to a CD value for its feature type at a nominal focus (nominal CD). The WA algorithm reduces a value of the cost weight as the magnitude of variation increases. At least one imaging parameter is extracted from the weighted CD data set. A computational lithography model is automatically calibrated using the imaging parameter(s).