A Graph-Theoretic Approach for Spatial Filtering and Its Impact on Mixed-Type Spatial Pattern Recognition in Wafer Bin Maps

Statistical quality control in semiconductor manufacturing hinges on effective diagnostics of wafer bin maps, wherein a key challenge is to detect how defective chips tend to spatially cluster on a wafer-a problem known as spatial pattern recognition. Recently, there has been a growing interest in mixed-type spatial pattern recognition-when multiple defect patterns, of different shapes, co-exist on the same wafer. Mixed-type spatial pattern recognition entails two central tasks: (1) spatial filtering, to distinguish systematic patterns from random noises; and (2) spatial clustering, to group filtered patterns into distinct defect types. Observing that spatial filtering is instrumental to high-quality mixed-type pattern recognition, we propose to use a graph-theoretic method, called adjacency-clustering, which leverages spatial dependence among adjacent defective chips to effectively filter the raw wafer maps. Tested on real-world data and compared against a state-of-the-art approach, our proposed method achieves at least 46% gain in terms of internal cluster validation quality (i.e., validation without external class labels), and about 5% gain in terms of Normalized Mutual Information-an external cluster validation metric based on external class labels. Interestingly, the margin of improvement appears to be a function of the pattern complexity, with larger gains achieved for more complex-shaped patterns.