Semi-supervised rotation-invariant representation learning for wafer map pattern analysis

Recently, data-driven approaches have been widely employed to analyze the defect patterns in wafer maps, which are crucial for identifying the root causes of failures in the semiconductor fabrication process. Representation learning embeds wafer maps into compact vector representations of useful features, based on which various downstream tasks can be performed to efficiently analyze the patterns on a large scale. If wafer maps are annotated with their defect class labels, the learned representations of wafer maps will be more informative and discriminative in defect patterns. However, the manual labeling of all wafer maps by domain experts is difficult due to practical constraints. In this study, we present a semi-supervised representation learning method that fully utilizes the information from both unlabeled and labeled wafer maps to learn better representations of wafer maps with a lower labeling cost. Given a partially labeled dataset, rotation-invariant representations of wafer maps are learned using the following three objectives. First, each unlabeled wafer map is close to any wafer map of a certain class and far from those of other classes. Second, each pair of labeled wafer maps are close to each other if they belong to the same class and are far from each other otherwise. Third, the different rotations of each wafer map are close to each other for both the unlabeled and labeled wafer maps. The effectiveness of the proposed method is demonstrated for various downstream tasks related to wafer map pattern analysis: visualization, clustering, retrieval, and classifier training.