Overlay Correction Using Polar Coordinate Functions
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Solution Overview
Problem
The reliability of the overlay measuring process in semiconductor device manufacturing is compromised due to the lack of uniformity in overlay measurement values, leading to inconsistent distortion corrections between different positions on a substrate.
Innovation Solution
A method involving the use of a polar coordinate function, specifically a Zernike polynomial, to calculate a correlation coefficient from overlay measurement values, which is then applied to correct the overlay values across the substrate, ensuring uniformity and improving the reliability of the overlay correction process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional overlay correction methods are used, then overlay measurement can be performed, but the uniformity of overlay measurement values deteriorates
Solution Approach 1:
The patent transforms overlay measurement values from a Cartesian coordinate system to a polar coordinate system, changing the parameter representation from (x, y) to (r, θ). This parameter transformation enables more effective modeling of distortion patterns using polar coordinate functions, improving the uniformity of correction across different substrate positions while maintaining measurement reliability
Solution Approach 2:
The patent introduces polar coordinate functions as an intermediary mathematical model between the raw overlay measurement data and the correction process. These functions serve as a mediator that captures the spatial distribution characteristics of overlay distortions, enabling more accurate and uniform correction across the substrate surface
2Measurement precision
If overlay measurement is performed at multiple positions, then comprehensive distortion detection is achieved, but the uniformity of measurement values deteriorates
Solution Approach 1:
By changing the coordinate parameter system from Cartesian to polar coordinates, the patent enables multiple position measurements to be represented in a unified polar framework. This allows the use of polar coordinate functions that naturally capture radial and angular distortion patterns, improving uniformity while maintaining comprehensive distortion detection capability across all measurement positions
Data Source
AI summary
A method of correcting an overlay includes setting a reference map having information relating to predetermined positions of a substrate. An overlay value is measured at each of the predetermined positions to obtain a plurality of overlay measurement values. The plurality of overlay measurement values is applied to a polar coordinate function to calculate a correlation coefficient of the polar coordinate function. The polar coordinate function uses coordinate values of the predetermined positions as parameters.