X-Ray Diffraction Measurement of Complex Semiconductor Deep-Hole Profiles
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Solution Overview
Problem
Existing methods struggle to accurately model the three-dimensional shape of deep holes with complex cross-sections in semiconductor substrates, leading to inaccuracies in measurements due to the use of inappropriate initial values for shape parameters.
Innovation Solution
A measurement device and method utilizing X-ray diffraction scattering to reduce the number of shape parameters by extracting feature data, generating a regression model, and minimizing differences through iterative adjustments of shape parameters, thereby improving accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the number of shape parameters is increased to represent complex deep hole shapes, then measurement precision is improved, but device complexity and calculation burden increase
Solution Approach 1:
The patent extracts and eliminates redundant parameters from the shape parameter set. By analyzing the correlation between parameters and removing those that do not significantly contribute to shape representation, the patent reduces the number of parameters while maintaining measurement precision for complex deep hole shapes.
Solution Approach 2:
The patent transforms the shape parameter representation by changing from a large set of correlated parameters to a reduced set of independent parameters. This parameter transformation maintains the ability to represent complex shapes while reducing computational complexity and improving measurement efficiency.
2Measurement precision
If iterative adjustment of shape parameters is performed to minimize differences, then measurement precision is improved, but measurement time increases
Solution Approach 1:
The patent performs preliminary actions by pre-calculating and storing correlation information between shape parameters and scattering patterns. This preliminary processing enables faster iterative adjustments during actual measurement by avoiding redundant calculations and guiding the optimization process more efficiently.
Solution Approach 2:
The patent implements feedback mechanisms where measurement results are used to refine and update shape parameter estimates. The iterative process uses feedback from scattering intensity comparisons to progressively improve parameter accuracy, balancing measurement precision with acceptable measurement time through efficient feedback loops.
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
The method allows for precise modeling of complex deep hole shapes, reducing inaccuracies and enhancing the measurement precision of semiconductor features.
Implementation Method 1
a transmission small angle X-ray scattering (hereinafter referred to as T-SAXS) technique is generally used
Implementation Method 2
analyze a diffraction image obtained by photoelectric conversion of the scattered X-rays
Implementation Method 3
analyze a diffraction image obtained by photoelectric conversion of the scattered X-rays
Data Source
AI summary
A measurement device includes an analyzer configured to analyze a diffraction image of X-rays scattered from a subject; estimate a surface contour shape of a measurement area of the subject; extract feature data from shape information, and determine shape parameters for representing the surface contour shape; calculate a theoretical scattering intensity of each of the scattered X-rays when values of the shape parameters are changed; calculate a difference between a measured scattering intensity of each scattered X-ray and the corresponding theoretical scattering intensity, and generate a regression model of a relationship between a corresponding value of the shape parameter and the difference for each shape parameter; extract one shape parameter candidate value reducing the difference from the regression model, and calculate a theoretical scattering intensity of the shape parameter candidate value; and estimate the value of the shape parameter minimizing the difference while repeatedly changing the shape parameter candidate value.