Wafermap Pattern Analysis Using Zernike Polynomials for Process Monitoring
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Solution Overview
Problem
The semiconductor manufacturing process generates vast amounts of data from discrete measurement sites on wafers, requiring efficient automated processing to ensure quality control and monitoring across numerous production steps, but existing methods lack effective tools for analyzing and classifying this data to detect anomalies and maintain process stability.
Innovation Solution
A computer-implemented method using Zernike polynomials to represent wafermap patterns, building a knowledgebase, grouping patterns, and employing machine learning to analyze new data for monitoring and control, identifying normal and abnormal conditions, and detecting anomalies to inform process adjustments.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If automated data processing is used to handle huge measurement data, then productivity is improved, but device complexity increases
Solution Approach 1:
Zernike polynomials serve as an intermediary mathematical tool that transforms complex wafermap measurement data into a standardized coefficient representation. This intermediary step enables automated processing of huge datasets by converting spatial patterns into comparable mathematical coefficients, improving productivity while managing system complexity through mathematical abstraction
Solution Approach 2:
The patent transforms wafermap patterns from spatial domain to coefficient domain by fitting Zernike polynomials. This parameter transformation converts complex 2D surface patterns into a set of scalar coefficients, enabling efficient automated comparison and analysis without directly processing the entire spatial dataset, thus improving processing efficiency while controlling complexity
2Measurement precision
If Zernike polynomials are used to represent wafermap patterns, then measurement precision is improved, but device complexity increases
Solution Approach 1:
Instead of directly analyzing the complex spatial wafermap data, the patent creates a mathematical copy using Zernike polynomial coefficients that represent the same pattern information. This coefficient representation serves as a simplified copy that preserves measurement precision while reducing processing complexity for comparison and classification tasks
Solution Approach 2:
The patent segments the continuous wafermap surface data into discrete Zernike polynomial coefficients through orthogonal decomposition. This segmentation transforms the complex continuous spatial pattern into separable coefficient components, improving measurement precision by isolating specific pattern features while reducing overall data processing complexity
3Manufacturing precision
If wafermap patterns are grouped into knowledgebase categories, then manufacturing precision is improved, but loss of information increases
Solution Approach 1:
The patent performs preliminary grouping of wafermap patterns into knowledgebase categories using Zernike coefficients before final quality assessment. This preliminary classification organizes data into meaningful groups (e.g., normal vs. abnormal patterns) while preserving the underlying coefficient data, enabling manufacturing precision through structured comparison without complete information loss
Solution Approach 2:
The Zernike polynomial coefficients serve multiple functions: they represent the complete wafermap pattern, enable pattern grouping into knowledgebase categories, and preserve detailed information for subsequent analysis. This multi-functionality allows manufacturing precision through categorization while minimizing information loss by maintaining the mathematical representation that can be reconstructed into full patterns
Data Source
AI summary
Monitoring of a semiconductor manufacturing process. Wafer measurement data is obtained (301); Zernike polynomials are fitted (302) to the wafer measurement data to obtain representation of respective wafermap patterns; a knowledgebase of wafermap patterns is built (303) based on the respective coefficients of the Zernike polynomials; the wafermap patterns of the knowledgebase are grouped (304) to wafermap pattern groups based on the respective coefficients of the Zernike polynomials; and at least some of the wafermap pattern groups of the knowledgebase and the respective coefficients of the Zernike polynomials are used (305) for analyzing new wafer measurement data for the purpose of monitoring the semiconductor manufacturing process.