Photomask Flatness Measurement with Gravity Error Separation
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Solution Overview
Problem
The accuracy of pattern transfer in semiconductor material fabrication is compromised by deviations in the flatness of photomasks from the ideal plane, leading to errors in patterning.
Innovation Solution
A method and apparatus for measuring photomask flatness at various orientations, using interferometers and controllers to calculate true flatness by separating gravitational errors from actual flatness, and fitting measurements to orthogonal polynomials like Zernike polynomials.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If photomask flatness is measured at a single orientation, then the measurement process is simple and quick, but gravitational errors contaminate the flatness measurement
Solution Approach 1:
The flatness measurement is segmented into multiple orientation measurements (at least two different orientations) rather than a single measurement. This segmentation allows the gravitational error component to be separated from the true flatness by comparing measurements taken at different orientations, thereby improving measurement accuracy without requiring complex equipment modifications
Solution Approach 2:
The measurement process employs periodic action by repeatedly measuring the photomask at different orientations. The controller coordinates the positioning system to rotate the photomask to predetermined orientations and performs measurements at each orientation, creating a periodic measurement cycle that enables gravitational error separation through mathematical processing of multiple measurements
2Measurement precision
If multiple flatness measurements at different orientations are performed, then gravitational errors can be separated from true flatness, but the measurement time increases
Solution Approach 1:
The system performs preliminary actions by pre-calculating and storing the relationship between orientations and gravitational error components. The controller uses predetermined orientations and pre-established mathematical models to rapidly process the multiple measurements, reducing the time penalty associated with taking multiple measurements at different orientations
Solution Approach 2:
The patent replaces mechanical measurement adjustments with automated positioning and mathematical processing. Instead of mechanically adjusting the measurement system to compensate for gravity, the system uses automated positioning to change orientations and substitutes mathematical calculations (performed by the controller) to separate gravitational errors, reducing manual intervention and measurement time
3Measurement precision
If orthogonal polynomial fitting is applied to process measurements, then true flatness can be accurately determined, but computational complexity increases
Solution Approach 1:
The system applies parameter changes by transforming the raw flatness measurements into orthogonal polynomial coefficients through mathematical fitting. This transformation changes the parameter representation from direct measurement values to polynomial coefficients, which inherently separate different error components (including gravitational errors) from the true flatness signal, enabling accurate determination through standardized mathematical procedures
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables accurate determination of photomask flatness, reducing errors in semiconductor material patterning and ensuring precise transfer of patterns onto substrates.
Implementation Method 1
measuring a first flatness measurement of the substrate at a first orientation relative to a vertical direction, measuring a second flatness measurement of the substrate at a second orientation relative to the vertical direction
Data Source
AI summary
A method of determining a flatness of a substrate, the method including measuring a first flatness measurement of the substrate at a first orientation relative to a vertical direction, measuring a second flatness measurement of the substrate at a second orientation relative to the vertical direction, measuring a third flatness measurement of the substrate at a third orientation relative to a vertical direction, and measuring a fourth flatness measurement of the substrate at a fourth orientation relative to a vertical direction, each of the first orientation, the second orientation, the third orientation, and the fourth orientation being at a different orientation relative to the vertical direction. The method further including generating a first set of differences, fitting the first set of differences to respective orthogonal polynomials, and generating a true flatness of the substrate.