Fault Detection Using Principal Components-Based Gaussian Mixture Model for Semiconductor Manufacturing Processes

Fault detection has been recognized in the semiconductor industry as an effective component of advanced process control framework in increasing yield and product quality. Recently, conventional process monitoring-based principal component analysis (PCA) has been applied to semiconductor manufacturing by quickly detecting when the process abnormalities have occurred. However, the unique characteristics of the semiconductor processes, nonlinearity in most batch processes, multimodal batch trajectories due to multiple operating conditions, significantly limit the applicability of PCA to the fault detection of semiconductor manufacturing. To explicitly address these unique issues in semiconductor processes, a principal components (PCs)-based Gaussian mixture model (GMM) (named PCGMM) has been proposed in this paper. GMM is capable to handle complicated data with nonlinearity or multimodal features by a mixture of multiple Gaussian components, which is very suitable to describe observations from semiconductor processes. Furthermore, two quantification indexes (negative Log likelihood probability and Mahalanobis distance) are proposed for assessing process states, and a Bayesian inference-based calculation method is further used to provide the process failure probability. The validity and effectiveness of PCGMM-based fault detection model are illustrated through two simulation processes and a semiconductor manufacturing process. The experimental results demonstrated that the proposed model is superior to PCA-based monitoring models and can achieve accurate and early detection of various types of faults in complicated manufacturing processes.