Torsion Estimator for Lithographic Stage Positioning
Solution Overview
Problem
Lithographic apparatuses face challenges in accurately measuring the position of objects exhibiting non-rigid body mass behavior, such as torsion, which leads to position-dependent measurement errors and requires complex control solutions to mitigate the effects of torsion modes on closed-loop position control.
Innovation Solution
A measurement system that includes a torsion estimator to correct for torsion in position quantity measurements, using a position quantity calculator that processes signals from position sensors to derive accurate position, velocity, and acceleration data, thereby improving positioning accuracy by filtering out torsion frequency components.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a plurality of position sensors are used to measure stage position, then measurement precision is improved, but device complexity increases due to the need to handle multiple sensor signals and correct for torsion modes
Solution Approach 1:
The system uses feedback from multiple position sensors (encoders/interferometers) to detect stage position and torsion modes. The measured position signals are fed back through a model-based correction mechanism that estimates torsion effects and compensates the position measurement, enabling accurate position tracking despite stage flexibility
Solution Approach 2:
A torsion estimator acts as an intermediary between the raw position sensor signals and the final corrected position measurement. This estimator uses a mechanical model of the stage to separate the rigid body position from the torsional deformation components, providing a corrected position signal that accounts for stage flexibility
2Measurement precision
If notch filters are applied to reduce torsion mode effects, then measurement precision is improved, but device complexity increases due to complex calculations required for position-dependent notch filters
Solution Approach 1:
The patent replaces complex position-dependent notch filtering with a model-based torsion estimation approach. Instead of using frequency-domain filtering methods that require complex calculations, the system uses a mechanical model to directly estimate and compensate torsion effects in the time domain, significantly reducing computational complexity while maintaining accuracy
Solution Approach 2:
The system changes the approach from frequency-domain filtering (notch filters) to time-domain model-based compensation. By using a mechanical model that directly relates sensor measurements to stage position and torsion, the system avoids the computational burden of frequency analysis and position-dependent filter tuning
3Measurement precision
If bandwidth of the control loop is kept low to reduce torsion mode effects, then measurement precision is maintained, but productivity decreases due to slower positioning speed and accuracy
Solution Approach 1:
The system uses feedback from multiple position sensors to detect both rigid body position and torsion mode vibrations. By continuously monitoring position signals from sensors at different locations, the system can identify torsion vibrations and compensate them in real-time, enabling high-bandwidth control without being limited by torsion mode resonances
Solution Approach 2:
The torsion estimator serves as an intermediary that separates torsional vibrations from the desired position signal. By estimating the torsion component using a mechanical model and subtracting it from the raw sensor measurements, the system provides a clean position signal that enables high-bandwidth control while rejecting torsion mode interference
Data Source
AI summary
A measurement system is configured to derive a position quantity of an object, the measurement system includes at least one position quantity sensor configured to provide respective position quantity measurement signals; a position quantity calculator configured to determine a position quantity of the object from the position quantity measurement signal, wherein the position quantity calculator includes a torsion estimator configured to estimate a torsion of the object, the position quantity calculator being configured to correct the determined position quantity of the object for the estimated torsion.