Matrix Factorization With Fixed Basis Samples for Defect Trend Analysis
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Solution Overview
Problem
Existing data analysis methods, such as non-negative matrix factorization (NMF), fail to effectively analyze patterns of defective chips over time due to changes in the element dictionary and element weights, making it difficult to track the evolution of manufacturing process improvements in semiconductor factories.
Innovation Solution
A data analyzing apparatus and method that fixes part of the basis samples as specific element dictionaries in matrix factorization, iteratively updating the remaining samples until a stop condition is met, allowing for the generation of both known and unknown element dictionaries and weights, enabling long-term analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Duration of action of stationary object
If conventional NMF is used to factorize data into element dictionaries and weights, then the data can be analyzed at a single point in time, but the element dictionary changes when data values change, making long-term analysis impossible
Solution Approach 1:
The patent applies dynamics by making the element dictionary partially updateable. Specifically, the system divides the element dictionary into fixed portions (containing known defect patterns) and updateable portions (containing newly discovered patterns). This dynamic structure allows the dictionary to remain stable for known patterns while adapting to new patterns over time, resolving the contradiction between stability and duration.
Solution Approach 2:
The patent segments the element dictionary into multiple portions: a fixed portion that maintains stability for long-term analysis and an updateable portion that adapts to new data. This segmentation allows different parts of the system to serve different functions - the fixed portion ensures consistency for tracking known defect patterns, while the updateable portion enables the system to learn new patterns, thus resolving the contradiction between stability and adaptability over time.
2Adaptability or versatility
If the element dictionary is updated for each new data set, then new patterns can be discovered, but known patterns of interest are lost and cannot be tracked over time
Solution Approach 1:
The system dynamically manages the element dictionary by maintaining a fixed portion that preserves known defect patterns and an updateable portion that discovers new patterns. This dynamic approach allows the system to adapt to new data while preserving historical information, preventing the loss of known patterns while still enabling pattern discovery.
Solution Approach 2:
The patent applies local quality by assigning different properties to different portions of the element dictionary. The fixed portion maintains stability and preserves known patterns, while the updateable portion allows flexibility and new pattern discovery. This local differentiation resolves the contradiction between adaptability and information preservation.
3Stability of the object's composition
If the element dictionary is kept fixed for long-term analysis, then stability is achieved, but the system cannot discover new defect patterns that emerge over time
Solution Approach 1:
The patent segments the element dictionary into fixed and updateable portions. The fixed portion ensures stability for long-term analysis of known patterns, while the updateable portion enables discovery of new patterns. This segmentation resolves the contradiction between stability and adaptability by allowing both properties to coexist in different parts of the system.
Solution Approach 2:
The system dynamically balances stability and adaptability by maintaining a fixed portion for stability and an updateable portion for adaptability. This dynamic structure allows the system to achieve both long-term stability for known patterns and the ability to discover new patterns, resolving the contradiction between these two requirements.
4Measurement precision
If complete re-factorization is performed for each data set, then all patterns are re-discovered, but the analysis cannot be performed over long periods and computational resources are wasted
Solution Approach 1:
The patent applies partial action by performing factorization only on the updateable portion of the element dictionary rather than complete re-factorization. This partial approach maintains measurement precision for both fixed and new patterns while significantly reducing computation time and resources, resolving the contradiction between accuracy and time efficiency.
Solution Approach 2:
The system performs preliminary action by pre-establishing the fixed portion of the element dictionary containing known patterns. This preliminary setup avoids the need for repeated factorization of the entire dictionary, enabling efficient long-term analysis while maintaining accuracy through the preserved fixed patterns.
Data Source
AI summary
According to one embodiment, a data analyzing apparatus acquires data containing the number N of analysis target samples (where N is an integer larger than or equal to 2). The apparatus performs a matrix factorization upon the data to factorize the data into the number K of basis samples and the number K of weights corresponding to the number K of basis samples (where K is an integer larger than or equal to 2), and fixes part of the K basis samples to specific basis samples in the matrix factorization.