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

TL;DR

This paper introduces a graph-theoretic spatial filtering method for wafer bin maps, significantly improving mixed-type spatial pattern recognition accuracy in semiconductor quality control.

Contribution

The paper proposes a novel adjacency-clustering approach that leverages spatial dependence for effective filtering, enhancing pattern recognition in wafer maps with complex defect shapes.

Findings

Achieves at least 46% improvement in internal cluster validation quality.

Gains about 5% in external cluster validation metric (Normalized Mutual Information).

Larger improvements observed for more complex defect patterns.

Abstract

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.