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Spatial defect patterns generated during integrated circuit (IC) manufacturing processes contain information about potential problems in the fabrication processes. The detection of these defect patterns is critical to improve the yield and reliability in IC manufacturing. The analysis of spatial defect patterns often contains multiple steps in order to analyzed the defect clustering at high accuracy:
         i) Defect denoising. This can be based on the K_th nearest-neighbor noise removal technique and determines the existence of any clustered local defects on a wafer. The denoising step separates local defects from global defects if local defects exist. (see page4257)
         ii) Defect clustering process. This applies a similarity-based clustering technique to group the local defects into clusters according to their spatial locations.
         iii) Pattern identification. This process identifies the pattern for each of the local defect clusters (i.e., linear, curvilinear, amorphous, or ring-shaped patterns) via various model selection criteria.
         iv) Fine tuning. This process is applied in order to improve the accuracy of the clustering performance. The fine tuning process is based on model-based clustering with a fixed number of clusters and known patterns for each cluster. The fine tuning process can be based on model-based clustering with a mixture distribution of different densities such as MVNs, PCs, and fuzzy spherical-shells (SSs).
         v) Comparisons. The results of both simulated and real wafer map data can be compared for better understanding and accuracy.

Spatial statistics techniques [1] have often been employed to detect nonrandom patterns.

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[1] Cressie N. Statistics for Spatial Data. Hoboken, NJ: John Wiley & Sons; 1993.