K-distance tree for nearest neighbor metrology
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Solution Overview
Problem
Metrology applications face inefficiencies when scaling to large numbers of measurements, particularly in determining nearest neighbor distances between structures in semiconductor devices, which is an O(N^2) problem.
Innovation Solution
Utilizing a k-distance (kd) data tree to store positional coordinates of shapes within an image, allowing for efficient identification of nearest neighbors with a reduced time complexity from O(N^2) to O(log(n)) by parsing the kd tree for nearest neighbor shapes and measuring distances between them.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional O(N^2) nearest neighbor search is used, then measurement accuracy is maintained, but computational time and resources increase significantly with large numbers of shapes
Solution Approach 1:
The patent pre-processes the image by extracting shapes and their positional coordinates, then stores them in a kd-tree data structure. This preliminary organization of data enables fast nearest neighbor search during the measurement phase, reducing computational time from O(N^2) to O(log N) while maintaining measurement accuracy.
Solution Approach 2:
The patent transforms the problem from a two-dimensional image space to a multi-dimensional feature space by extracting positional coordinates and storing them in a kd-tree. This dimensional transformation enables efficient spatial indexing and nearest neighbor search, significantly reducing computational complexity while maintaining measurement precision.
2Productivity
If k-distance tree is used for nearest neighbor search, then computational efficiency improves to O(log n), but device complexity increases due to data structure requirements
Solution Approach 1:
The patent introduces a kd-tree data structure as an intermediary between the image data and the nearest neighbor search process. This intermediate representation organizes shape positional coordinates in a way that enables efficient querying, reducing the computational complexity from O(N^2) to O(log N) while managing the added structural complexity through standardized algorithms.
3Measurement precision
If all shapes are processed to determine nearest neighbors, then measurement completeness is ensured, but processing time increases with the number of shapes
Solution Approach 1:
The patent performs preliminary extraction of all shapes and their positional coordinates from the image, storing them in a kd-tree. This pre-processing ensures that all shapes are accounted for in the measurement, maintaining completeness, while the structured storage enables fast nearest neighbor search that scales efficiently with the number of shapes.
Data Source
AI summary
Systems or techniques are provided for image metrology. In various embodiments, a system can comprise a memory that stores computer executable components and a processor that executes the computer executable components stored in the memory. The computer executable components can comprise a measurement component that accesses a k-distance data tree comprising positional coordinates of a plurality of shapes within an image; and measures distances between neighboring shapes of the plurality of shapes, wherein the measuring comprises parsing the k-distance data tree for nearest neighbor shapes within the plurality of shapes.