(194a) Fault Detection Using Principal Component Based K-Nearest-Neighbor Rule

It has been recognized that effective fault detection techniques can help semiconductor manufacturers reduce scrap, increase equipment uptime, and reduce the usage of test wafers [1, 2]. Traditional univariate statistical process control charts have long been used for fault detection. Recently, multivariate statistical fault detection methods such as principal component analysis (PCA) based methods have drawn increasing interest in semiconductor manufacturing industry [3, 4]. However, the unique characteristics of the semiconductor processes, such as nonlinearity in most batch processes, multimodal batch trajectories due to product mix and process steps with variable durations, have posed some difficulties to the PCA based methods.

To explicitly account for these unique characteristics, a fault detection method using the k-nearest-neighbor rule (FD-kNN) is developed in our previous work [5, 6]. Because faults are usually not identified and characterized beforehand in fault detection, the traditional kNN algorithm [7] is adapted in [5] and [6] such that only normal operation data is needed to perform fault detection. Also, the developed method makes use of the kNN rule, which is a nonlinear classifier, it naturally handles possible nonlinearity in the data. In addition, the FD-kNN method makes decision based on the normal process behavior in a small neighborhood of a test sample, it is well suited for multimodal cases.

However, a disadvantage of the proposed FD-kNN method is that it requires considerable memory resources for large systems as all of the training data must be retained to compute the kNN distance for each test sample. Also, the computational complexity is directly proportional to the dimensionality of the data. Consequently, there is a practical upper limit to both the number of records and the data dimensionality that may be processed if the algorithm is implemented online. To reduce memory requirement and computation time of the proposed FD-kNN method while still keeping its advantage of handling nonlinear and multimode data, we propose an improved FD-kNN algorithm based on principal component analysis, denoted as PC-kNN. In PC-KNN, we first make use of the dimensionality reduction and information preserving property of principal component analysis (PCA) to extract principal components (PCs) that contain key information of the data set. Then, instead of applying kNN algorithm directly to the raw training data that usually has high dimensionality, we apply kNN algorithm to the low dimensional scores corresponding to the extracted PCs. By doing so, the improved PC-kNN method can significantly reduce the computation time and memory requirement without sacrificing fault detection capability. We demonstrate the superior performance of the proposed PC-kNN approach compared to the original FD-kNN approach using an industrial example.

Key words: semiconductor manufacturing, fault detection, k-nearest-neighbor rule, principal component analysis

References:

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5. Q.P. He & J. Wang (2006), A Multivariate Fault Detection Method Using k-Nearest-Neighbor Rule, AEC/APC Symposium XVIII, Sept. 30 ? Oct. 5, Westminster, CO

6. Q.P. He & J. Wang (2007), Fault detection using K-nearest neighbor rule for semiconductor manufacturing (invited), accepted by IEEE Transactions on Semiconductor Manufacturing.

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