Substrate Sample Matching Using CDFs to Decouple Process Variation
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Solution Overview
Problem
Conventional semiconductor device fabrication analyses provide whole substrate summaries that make it difficult to decouple the effects of wafer variations from process conditions, as they do not allow for point-by-point matching of pre-processed and post-processed substrate characteristics.
Innovation Solution
A system and method for matching pre-processing and post-processing substrate samples using probability distributions, specifically cumulative distribution functions, to identify monotonic relationships between dimensions, allowing for one-to-one matching and decoupling of wafer and process variations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If whole substrate summaries are used for fabrication analysis, then statistical representations of substrate characteristics are obtained, but it becomes difficult to decouple wafer variations from process conditions
Solution Approach 1:
The patent segments the substrate analysis by dividing it into multiple discrete sample locations across the substrate surface. Each location is treated as an independent measurement point with its own pre-processed and post-processed characteristics. This segmentation enables point-by-point matching and allows differentiation between variations inherent to specific substrate regions and variations introduced by processing conditions.
Solution Approach 2:
The patent introduces a spatial dimension to the analysis by mapping pre-processed substrate characteristics to post-processed characteristics at corresponding spatial locations. This dimensional approach transforms the analysis from aggregate statistical summaries to location-specific paired measurements, enabling the decoupling of substrate variations from process variations through spatial correlation.
2Loss of information
If point-by-point matching of pre-processed and post-processed substrates is implemented, then ability to decouple variations is improved, but complexity of analysis increases
Solution Approach 1:
The patent creates a virtual copy of the pre-processed substrate characteristics and maps them to corresponding locations on the post-processed substrate. This copying approach allows for direct comparison of paired measurements without requiring complex physical tracking or identification systems. The virtual mapping simplifies the analysis by establishing correspondence through coordinate transformation rather than physical tracking.
3Ease of operation
If conventional whole substrate analysis is used, then analysis simplicity is maintained, but precision in identifying individual feature impacts is reduced
Solution Approach 1:
The patent segments the substrate into multiple discrete sample locations, allowing individual feature impacts to be analyzed at each location. This segmentation enables precise identification of how specific pre-processed features affect post-processed outcomes without the averaging effect of whole-substrate summaries. Each segment can be independently analyzed while maintaining overall process context.
Data Source
AI summary
Various embodiments herein relate to systems, methods, and media for matching pre-processing and post-processing substrate samples. In some embodiments, a computer program product for matching pre-processing and post-processing substrate samples is provided, the computer program product comprising a non-transitory computer-readable on which is provided computer-executable instructions for: receiving a plurality of samples associated with a first set of dimensions characterizing a pre-processed substrate and a plurality of samples associated with a second set of dimensions characterizing a post-processed substrate; receiving an identification of one of the pre-processed dimensions and one of the post-processed dimensions that are to be matched; generating a first probability distribution of samples for the identified pre-processed dimension and a second probability distribution of samples for the identified post-processed dimension; and matching samples of the identified pre-processed dimension to samples of the identified post-processed dimension based on the first probability distribution and the second probability distribution.