Fault Detection and Classification by Sample Covariance Matrix and Its Applications to Plasma Etcher
Date Issued
2004
Date
2004
Author(s)
HUNG, HUNG
DOI
en-US
Abstract
The variabilities and complex relationships of semiconductor equipment variables can be characterized by the sample covariance matrix. Fault detection and classification (FDC) via sample covariance matrix is thus very important. However, the modern high-mix low-volume semiconductor manufacturing environment has made the sample size an issue diminishing the applicability of existing methods, such as the well-known likelihood-ratio test (LRT). This thesis proposes some testing methods independent of the sample size to detect faults causing changes in the covariance matrix. We apply Bartlett’s decomposition theorem and Cholesky’s decomposition theorem to the sample covariance matrix S to obtain a matrix T with nice distribution properties. We then propose test based on test statistics aggregating the elements of T. In addition, theorems are developed based on the matrix T to provide rules for fault classification. Data collected from an actual semiconductor tool and simulations will be used to demonstrate the proposed covariance fault detection and classification
Subjects
Bartlett 分解
Cholesky 分解
Bartlett's decomposition
Cholesky's decomposition
Type
thesis
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