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Application of PARAFAC2 to fault detection and diagnosis in semiconductor etch
Author(s) -
Wise Barry M.,
Gallagher Neal B.,
Martin Elaine B.
Publication year - 2001
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.689
Subject(s) - fault detection and isolation , dimensionality reduction , matrix (chemical analysis) , principal component analysis , dimension (graph theory) , batch processing , fault (geology) , chemometrics , biological system , sensitivity (control systems) , chemistry , computer science , analytical chemistry (journal) , chromatography , artificial intelligence , mathematics , electronic engineering , engineering , seismology , pure mathematics , actuator , biology , programming language , geology
Monitoring and fault detection of batch chemical processes are complicated by stretching of the time axis, resulting in batches of different length. This paper offers an approach to the unequal time axis problem using the parallel factor analysis 2 (PARAFAC2) model. Unlike PARAFAC, the PARAFAC2 model does not assume parallel proportional profiles, but only that the matrix of profiles preserves its ‘inner product structure’ from sample to sample. PARAFAC2 also allows each matrix in the multiway array to have a different number of rows. It has previously been demonstrated how the PARAFAC2 model can be used to model chromatographic data with retention time shifts. Fault detection and, to a lesser extent, diagnosis in a semiconductor etch process are considered in this paper. It is demonstrated that PARAFAC2 can effectively model batch process data from semiconductor manufacture with unequal dimension in one of the orders, such as the unequal batch length problem. It is shown that the PARAFAC2 model has approximately the same sensitivity to faults as other competing methods, including principal component analysis (PCA), unfold PCA (often referred to as multiway PCA), trilinear decomposition (TLD) and conventional PARAFAC. The advantage of PARAFAC2 is that it is easier to apply than MPCA, TLD and PARAFAC, because unequal batch lengths can be handled directly rather than through preprocessing methods. It also provides additional diagnostic information: the recovered batch profiles. It is likely, however, that it is less sensitive to faults than conventional PARAFAC. Copyright © 2001 John Wiley & Sons, Ltd.