Boundary-Line Shape Modeling for Deep Hole Measurement Accuracy
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Solution Overview
Problem
Existing methods for modeling three-dimensional shapes, such as those in semiconductor memory devices, face challenges in maintaining measurement accuracy and reducing the number of parameters required for polynomial approximation, particularly in deep holes or grooves, which can lead to decreased accuracy and incorrect convergence.
Innovation Solution
A modeling method that approximates the shape measurement target using a boundary line, sets a predetermined tolerance for measurement values, and arranges a calculation boundary line to converge within this tolerance, allowing for the expression of the shape using polynomial approximation, with the ability to divide the approximation range into multiple regions based on material interfaces and adjust the degree of the polynomial equation to fit measurement data within a standard deviation tolerance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If polynomial approximation is used to model three-dimensional shapes in deep holes or grooves, then measurement accuracy can be improved, but the number of parameters required increases leading to incorrect convergence
Solution Approach 1:
The patent applies segmentation by dividing the three-dimensional shape into multiple cross-sectional regions at different depth intervals. Each cross-section is independently approximated using polynomial functions, which reduces the number of parameters needed compared to modeling the entire deep structure with a single high-degree polynomial. This segmentation approach prevents incorrect convergence while maintaining measurement accuracy for deep holes and grooves.
2Measurement precision
If the degree of polynomial equation is increased to fit complex shapes, then measurement accuracy improves, but calculation complexity and risk of incorrect convergence increase
Solution Approach 1:
Instead of using a single high-degree polynomial to fit the entire complex three-dimensional shape, the patent segments the shape into multiple cross-sectional regions and applies lower-degree polynomials to each segment. This reduces calculation complexity and the risk of incorrect convergence while achieving the same overall approximation accuracy through the combination of multiple simpler polynomial fits.
Data Source
AI summary
A modeling method of shape-approximating a shape measurement target provided in a structure having a stack structure by a boundary line, and a standard deviation is provided as a tolerance for a measurement value of the shape measurement target, and a calculation boundary line is arranged to converge within the tolerance, and thereby, a shape of the shape measurement target is expressed.