Random projection based k Nearest Neighbor rule for semiconductor process fault detection

Fault detection technique is essential for improving overall equipment efficiency of semiconductor manufacturing industry. It has been recognized that fault detection based on k nearest neighbor rule (kNN) can deal with some unique characteristics of semiconductor processes, such as multimode batch trajectories and nonlinearity. However, the computation complexity and storage space required in neighbors searching of kNN prevent it from online monitoring, especially for high dimensional cases. To deal with it, principal component based kNN is also presented in literature, in which dimension reduction by principal component analysis (PCA) is done before kNN rule applied to perform fault detection. However, the process of dimension reduction by PCA may distort the distances of pairwise samples (trajectories). Thus the performance of kNN for fault detection degenerates after projection by PCA. To overcome this drawback, we propose a new fault detection method based on random projection and kNN rule, which combines the advantages of random projection in distance preservation and kNN rule in dealing with the problems of multimodality and nonlinearity that often coexist in semiconductor processes. Industrial example illustrates the performance of the proposed method.