Relative Position Determination Using Masked Optimization Functions
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Solution Overview
Problem
Existing methods for determining the relative position of closely juxtaposed structures or pattern elements, such as those with spacings less than λ/NA, introduce instabilities due to weighting, leading to inaccurate measurements and limitations in metrological applications like linewidth measurement, as they fail to ensure homogeneity in intensity across edge trajectories.
Innovation Solution
A method involving the formation of an optimization function with displacement as a parameter, where masking is used to focus on the region of interest, allowing for subpixel accuracy in determining the relative position by summing the squared difference of pixel values in a weighted manner, and using cyclic displacement to account for image information across edges.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If weighting is applied to amplify pattern elements for determining relative displacement, then measurement sensitivity is improved, but instabilities are introduced that prevent accurate determination of relative displacement
Solution Approach 1:
The patent extracts only the relevant information (relative displacement) from the cross-correlation function without being affected by the instabilities introduced by weighting. By using the derivative of the cross-correlation function with respect to displacement, the method obtains the relative displacement directly at the maximum point, bypassing the instability problem while maintaining measurement sensitivity.
Solution Approach 2:
The patent changes the parameter being measured from the cross-correlation value itself to the derivative of the cross-correlation function with respect to displacement. This parameter transformation allows the method to determine relative displacement accurately even when weighting introduces instabilities, as the derivative method focuses on the slope at the maximum point rather than the absolute correlation value.
2Adaptability or versatility
If masking is applied to focus on specific regions for measurement, then measurement selectivity is improved, but the Fourier spectrum bandwidth is no longer limited, preventing accurate position determination
Solution Approach 1:
The patent extracts the relative displacement information from the cross-correlation function's derivative at the maximum point, which remains valid even when masking is applied. This extraction method allows selective measurement of specific regions while maintaining position determination accuracy, as the derivative approach is robust to the bandwidth expansion caused by masking.
3Measurement precision
If edge regions are masked for linewidth measurement, then measurement focus is improved, but light/dark transitions are introduced that cause intensity inhomogeneity and prevent accurate measurement
Solution Approach 1:
The patent replaces the direct intensity comparison method with a cross-correlation-based method that uses the derivative of the correlation function. This substitution allows accurate linewidth measurement even in the presence of light/dark transitions at masked edges, as the method relies on the shape and position of the correlation peak rather than absolute intensity values.
Solution Approach 2:
The patent changes from measuring absolute intensity values to measuring the relative position of the correlation maximum. This parameter transformation eliminates the problem of intensity inhomogeneity caused by light/dark transitions, as the method determines linewidth based on the displacement that maximizes the correlation function rather than on absolute intensity levels.
Data Source
AI summary
A method is provided for determining the position of a first structure (8a) relative to a second structure (8b) or a part thereof, said method having the steps of: a) providing a first picture (F1) having a multiplicity of pixels and which contains the first structure, b) providing a second picture (F2) having a multiplicity of pixels and which contains the second structure, c) forming an optimization function with the displacement of the two pictures relative to one another as parameter, the optimization function overlying the two pictures and masking the overlay such that in a determination of an extreme value of the optimization function a contribution is made only by the region of the overlay that corresponds to the second structure or the part thereof, d) ascertaining the extreme value of the optimization function and determining the optimal value of the displacement based on the extreme value of the optimization function, and e) determining the position of the first structure relative to the second structure or a part thereof with the optimal displacement value ascertained in step d).