Exposure Apparatus Prediction Formula Determination Method
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Solution Overview
Problem
The existing methods for determining prediction formulas for fluctuations in optical characteristics of projection optical systems in exposure apparatuses require actual measurements each time exposure conditions change, which hinders throughput due to increased measurement frequency.
Innovation Solution
A method that determines a first prediction formula by obtaining a correlation coefficient between exposure conditions, allowing the formula to be derived from a second prediction formula without actual measurement when the correlation is within an allowable range, or by measuring when it falls outside this range.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If actual measurement is performed each time exposure condition changes to determine prediction formula, then prediction accuracy is improved, but throughput deteriorates due to increased measurement frequency
Solution Approach 1:
The patent creates a virtual copy of the measurement process through simulation. Instead of performing physical measurements for every exposure condition, the system simulates optical characteristic fluctuations based on previously measured data and exposure conditions, generating prediction formulas without actual measurements. This copying approach maintains prediction accuracy while eliminating the throughput penalty of frequent measurements.
Solution Approach 2:
The patent performs measurements in advance to build a database of optical characteristic fluctuations under various exposure conditions. These preliminary measurements enable the system to predict fluctuations for new exposure conditions using simulation, eliminating the need for real-time measurements and thus preserving throughput while maintaining prediction accuracy.
2Measurement precision
If prediction formula is determined for each exposure condition, then prediction accuracy is improved, but device complexity increases due to multiple formulas management
Solution Approach 1:
The patent creates a universal prediction framework that can handle multiple exposure conditions through a single simulation system. Instead of managing separate prediction formulas for each condition, the system uses one flexible simulation approach that adapts to different exposure conditions by adjusting input parameters, thus reducing management complexity while maintaining accuracy.
Solution Approach 2:
The patent manages different exposure conditions by changing simulation parameters rather than creating separate formulas. The system maintains a core prediction framework and adjusts input parameters (exposure amount, exposure period, optical system characteristics) based on the specific exposure condition, eliminating the need to manage multiple complex formulas while preserving prediction accuracy for each condition.
Data Source
AI summary
The present invention provides a determination method of determining a first prediction formula for predicting a fluctuation in optical characteristics of a projection optical system while a substrate is exposed on a first exposure condition, the method comprising obtaining a correlation coefficient between the first exposure condition and a second exposure condition corresponding to a second prediction formula for predicting the fluctuation in the optical characteristics, determining, when the correlation coefficient falls within an allowable range, the first prediction formula based on the second prediction formula without actually measuring the fluctuation in the optical characteristics, and determining, when the correlation coefficient falls outside the allowable range, the first prediction formula based on a result of actually measuring the fluctuation in the optical characteristics.