Angular Fourier Decomposition for Substrate Tilt Angle Determination
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Solution Overview
Problem
Conventional methods for determining the tilt angle of structures on a substrate are time-consuming and inefficient, requiring multiple scattering measurements and data collection from a large number of incidence angles, which increases measurement time and data load.
Innovation Solution
The method involves receiving a small angle scattering image of a substrate with structures oriented at a specific angle, performing angular Fourier decomposition to determine a first-order Fourier term, and calculating the tilt angle based on this term, using a reduced number of incidence angles to decrease measurement time and data load.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multiple scattering measurements are collected from a large number of incidence angles, then measurement precision is improved, but measurement time and data load increase
Solution Approach 1:
The patent extracts only the essential information needed for tilt angle determination by using a reduced set of incidence angles. Instead of collecting comprehensive scattering data from many angles, the method selectively measures at specific angles (including at least one angle different from the structure orientation angle) and processes this minimal sufficient data through Fourier decomposition to obtain the tilt angle, thereby reducing measurement time while maintaining accuracy.
Solution Approach 2:
The patent changes the measurement parameters by selecting specific incidence angles based on the structure orientation angle rather than using a fixed large set of angles. The method determines tilt angle by measuring scattering intensity at incidence angles that are strategically chosen (including angles different from the structure orientation angle) and applies Fourier decomposition, transforming the measurement approach to achieve both speed and accuracy.
2Measurement precision
If multiple scattering measurements are collected from a large number of incidence angles, then measurement precision is improved, but data load increases
Solution Approach 1:
The patent extracts only the essential scattering intensity data needed for tilt angle determination by measuring at a reduced set of incidence angles. The method collects scattering intensity at specific angles (including at least one angle different from the structure orientation angle) and processes this minimal sufficient data through Fourier decomposition, thereby reducing the quantity of data while maintaining measurement precision.
3Reliability
If conventional measurement methods are used, then comprehensive data is collected, but processing complexity and time increase
Solution Approach 1:
The patent replaces complex mechanical data collection procedures with a streamlined measurement approach. Instead of using conventional methods that require scanning through many incidence angles, the method substitutes this with targeted measurements at specific angles followed by Fourier decomposition processing, simplifying the overall measurement system while maintaining reliability.
Solution Approach 2:
The patent changes the measurement parameters by selecting specific incidence angles based on the structure orientation angle rather than using a fixed comprehensive set. The method determines tilt angle by measuring scattering intensity at strategically chosen angles (including angles different from the structure orientation angle) and applies Fourier decomposition, transforming the measurement approach to reduce processing complexity while maintaining measurement completeness.
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 significantly reduces measurement time and data load while maintaining accuracy in determining the tilt angle of substrate structures, thereby improving the efficiency and throughput of substrate processing systems.
Implementation Method 1
receiving, by a processing device, a first small angle scattering image of a substrate. The first small angle scattering image of the substrate is collected at a second angle of incidence of radiation
Data Source
AI summary
A method includes receiving, by a processing device, a first small angle scattering image of a substrate. The substrate includes a number of structures oriented at a first angle relative to a base of the substrate. The first small angle scattering image of the substrate is collected at a second angle of incidence of radiation relative to the base of the substrate, different than the first angle. The method further includes determining a first-order Fourier term associated with the first small angle scattering image by performing angular Fourier decomposition of the first small angle scattering image. The method further includes determining a value of the first angle based on the first-order Fourier term.