A self-growing hidden Markov tree for wafer map inspection

This paper presents an automatic identification of the defect spatial wafer map using a growing wavelet-based hidden Markov tree (gHMT) statistical model. The hierarchical tree-based model, gHMT, utilizes the growing and learning procedure to increase successively the size of the wavelet tree. It can characterize image processing masks from the defect spatial patterns. Like the standard hidden Markov tree, gHMT cannot only capture the statistical behavior of the real-world measurements at multiple scales in space and frequency but also has the ability to accurately identify the locations of the defect regions using the smallest possible size. These regions provide essential information and intrinsic features of each pattern. When all the possible defect patterns are modeled by gHMT, the maximum likelihood classifier is applied to the wavelet energy features extracted from each trained models. Accordingly, defect spatial patterns are identified. The effectiveness of the proposed classifier based on gHMT is illustrated through the experimental data from a wafer foundry plant. It can identify different defect patterns on wafers to help readers delve into the matter.