(251g) Statistics Pattern Analysis and Its Application to Semiconductor Process Monitoring

In the semiconductor industry, statistical process monitoring (SPM) has been recognized as a critical component of the manufacturing system [1-3]. Traditional multivariate SPM techniques, such as principal component analysis (PCA) and partial least squares (PLS) that were developed for chemical and petrochemical processes monitoring, have been extended to monitor semiconductor processes. However, the unique challenges associated with semiconductor processes cannot be readily addressed by these methods. To achieve acceptable performance, the traditional SPM methods require extensive, often off-line data preprocessing such as data unfolding, trajectory alignment and warping, as well as trajectory mean shift. These requirements make model building and maintenance extremely labor intensive, and result in suboptimal performance of many SPM applications. To address these challenges, several pattern classification based monitoring (PCM) methods have been developed recently such as fault detection methods using Mahalanobis distance [4], k-nearest-neighbor rule (FD-kNN) [5], and principal component based k-nearest-neighbor rule (PC-kNN) [6]. However, some limitations still remain as data preprocessing is needed to handle unequal batch/step length and misaligned batch trajectory.

Recently we proposed a novel statistics pattern analysis (SPA) approach to address these challenges [7, 8]. Its flow diagram is illustrated in Fig. 1. In SPA, we monitor batch statistics of different variables to perform fault detection instead of monitoring process variables as in multivariate SPM and PCM methods. It has been shown that by monitoring batch statistics, the proposed SPA method not only eliminate all data pre-processing steps required by existing SPM and PCM methods but also provides superior fault detection performance.

Fig. 1 The proposed SPA method for fault detection: (a) original 3-D batch records with unequal length; (b) batch statistics generated by time and frequency domain statistical analysis; (c) fault detection based on the dissimilarity between the test sample and the training samples

In this work, we investigate the underlying reasons for the limitations associated with the traditional multivariate SPM methods. In addition, we study the fundamental properties of the proposed SPA method and compared them with those of other existing SPM methods using an industrial example. For instance, one example of variable histogram is shown in Fig. 2 where it is seen clearly that despite the non-Gaussian distribution of  the original variables (See Fig. 2a ? the case of MPCA), the batch statistics, including higher order statistics (HOS), follows a multivariate Gaussian distribution to a much better degree due to the central limit theorem (See Fig. 2b). The comprehensive study provides theoretical perspectives that explain SPA's superior performance in semiconductor process monitoring.

Key words: semiconductor manufacturing, fault detection, statistical process monitoring, pattern recognition, higher-order statistics, statistics pattern analysis

(a)                                                              (b)

Fig. 2 One example of variable histogram: (a) MPCA where original variables do not comply with Gaussian distribution; (b) SPA where batch statistics comply with Gaussian distribution

References:

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