Parametric Measurement Model Calibration Using Wafer Residuals
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Solution Overview
Problem
Parametric models in semiconductor metrology are becoming increasingly complex and error-prone due to the difficulty in accurately calibrating structural variations and system errors, leading to challenges in measurement recipe development and execution, especially for complex three-dimensional semiconductor structures.
Innovation Solution
A method for calibrating simulated measurement signals by incorporating residual fitting errors from real measurement signals, using regression and K-nearest neighbor search or statistical models to adjust simulated signals, ensuring they accurately represent real measurement variations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If parametric models are made more complex to accurately characterize three-dimensional semiconductor structures, then measurement capability and characterization accuracy are improved, but model error and calibration difficulty increase
Solution Approach 1:
The patent performs preliminary calibration of the parametric model using reference wafers with known structural parameters before actual measurements. This preliminary action establishes accurate baseline values for model parameters, reducing subsequent measurement errors. The calibration process includes determining reference values for critical dimensions and film thicknesses, then using these to adjust the parametric model predictions.
Solution Approach 2:
The patent implements a feedback mechanism where measurement residuals (differences between measured and predicted values) are continuously monitored and used to adjust model parameters. The system calculates residuals for each measurement, compares them against threshold values, and automatically adjusts the parametric model to minimize these residuals, thereby improving measurement precision while maintaining model reliability.
2Ease of manufacture
If traditional calibration methods using nominal wafers are used, then the process is simple and fast, but accuracy is insufficient for complex three-dimensional structures
Solution Approach 1:
The patent segments the calibration process into distinct stages: (1) initial calibration using nominal wafers for quick setup, (2) intermediate calibration using reference wafers with known three-dimensional structures to capture complex geometries, and (3) continuous validation using control wafers. This segmentation allows the system to maintain simplicity where possible while achieving high accuracy for complex structures through targeted reference measurements.
Solution Approach 2:
The patent introduces reference wafers with precisely known three-dimensional structural parameters as intermediaries between the calibration system and actual production measurements. These reference wafers serve as mediators that bridge the gap between simple nominal wafer calibration and complex structure measurement, providing accurate reference data for model adjustment without requiring direct measurement of every complex feature.
3Measurement precision
If system parameters are perturbed to minimize errors, then measurement accuracy is improved, but the time required for calibration increases
Solution Approach 1:
The patent performs preliminary determination of optimal parameter perturbation ranges using reference wafer data before actual calibration. By pre-calculating appropriate perturbation magnitudes based on known reference structures, the system avoids excessive trial-and-error iterations, significantly reducing calibration time while maintaining measurement accuracy.
Solution Approach 2:
The patent systematically varies model parameters within predetermined ranges and uses regression analysis to identify optimal values that minimize residuals. The system changes parameters such as critical dimensions, film thicknesses, and material optical properties in a controlled manner, using automated optimization algorithms to converge quickly on accurate values without requiring extensive manual adjustment.
Data Source
AI summary
Methods and systems for calibrating simulated measurement signals generated by a parametric measurement model are described herein. Regression on real measurement signals is performed using a parametric model. The residual fitting error between the real measurement signals and simulated measurement signals generated by the parametric model characterizes the error of the parametric model at each set of estimated values of the one or more floating parameters. Simulated measurement signals are generated by the parametric model at specified values of the floating parameters. A residual fitting error associated with the simulated measurement signals generated at the specified values of the floating parameters is derived from the residual fitting errors calculated by the regression on the real measurement signals. The simulated measurement signals are calibrated by adding the residual fitting error to the uncalibrated, simulated measurement signals. The calibrated, simulated measurement signals improve the accuracy of measurements and measurement recipe development.