Wafer Failure Pattern Analysis

1. Wafer Failure Pattern Analysis 張智星 (Roger Jang) jang@mirlab.org http://mirlab.org/jang 清華大學 資訊系 MIR實驗室

2. Types of Analysis • Clustering • Given failure patterns, find their natural grouping • Ranking • Given a wafer failure pattern, find similar patterns (returned in a ranking list) • Classification • Given a failure pattern, find patterns by its cause by using a set of training data

3. A Typical Wafer Failure Pattern

4. Flowchart for Clustering • Steps for clustering wafer failure patterns • Import failure patterns from external files • Normalize the pattern if necessary • Define a distance metrics (with rotation-invariance or not) • Cluster wafer failure patterns • K-means clustering • Hierarchical clustering • Fuzzy c-means clustering

5. Original Patterns

6. Binary Patterns

7. Round Binary Patterns

8. K-means Clustering • 20 trials of k-means clustering, with no. of clusters = 5

9. Results of K-means Clustering • Use background colors to indicate clusters.

10. Hierarchical Clustering • A typical result of hierarchical clustering

11. Ranking of Wafer Patterns • Data at a glance:

12. Flowchart for Ranking • Steps for ranking wafer failure patterns • Import wafer patterns from external files • Define a distance metrics (with rotation-invariance or not) • Rank all wafer patterns based on a given pattern • Plot the ranking results • Adapt parameters to approximate human’s ranking (relevancy feedback)

13. All Wafer Patterns

14. Distance with Rotation-Invariance

15. Ranked Results w/o Rotation Query pattern No. 1 No. 2 No. 3

16. Ranking Results with Rotation Query pattern No. 1 No. 2 No. 3

17. Enhancement of Failure Patterns • To further improve the ranking, we can enhance the failure patterns in various ways • Apply median filter to eliminate salt-and-pepper noise (The results are shown in the next few slides.) • Extract objects/regions from connected components • Use statistics of extracted objects as features for further processing

18. All Wafer Patterns after Median Filter

19. Ranked Results w/o Rotation Query pattern No. 1 No. 2 No. 3

20. Ranked Results with Rotation Query pattern No. 1 No. 2 No. 3

21. Classification of Wafer Failure Patterns Ring Line Automatic classification Sector Center Localized Edge

22. Features based on Radon Transform Radon transform: Edge • CRT Center Ring

23. Features Based on Region Statistics Raw data Image segmentation Flowchart Noise reduction Red indicates failure dies Image segmentation Each region filled with different colors Region property measurement

24. Operators for Region Identification • Erosion (浸蝕) and Dilation (膨脹)

25. Available Classifiers • K-nearest-neighbor • Quadratic classifier • Naïve Bayes classifier • Sparse-representation classifier • Gaussian-mixture-model classifier • Neural networks • SVM: Support vector machine • CART: Classification and regression tree • LVQ: Learning vector quantization

26. Distance metrics Hamming distance L-1 norm L-2 norm … ROI extraction Median filter Hough transformation Projection … Invariant Operators Rotation Radial translation Expand or Contract … Adaptation Learning to rank Artificial neural networks … Other Enhancements