錯誤偵測與分類為半導體製程中極為重要的分析工具。Lee, et al. (2011) 針對此目的提供一個簡單且有效的統計分析流程來分析製程剖面資料，進而可建構健康指標來衡量晶圓片的健康狀況。唯其模型中的位移量 (level shift) 容易造成批次間的效應與批次內的效應混淆。同時，在許多製程步驟之中，初期的觀測點出現 on-off action，為生產過程中在更換晶圓製造時，生產機台的量測機台會偵測到劇烈的變化，造成初期會不穩定的現象。針對上述問題，本研究先將剖面資料拆解成批次間與批次內的效應。其次，本文採用函數主成份 (functional principle components Analysis) 方法來監控批次內的晶圓片是否有異常，最後，並以Lee, et al. (2011) 所提出的監控製程方法相比較，結果顯示本研究總共發現有9個異常晶圓片，相較於 Lee et al. (2011) 所提出的方法只能偵測出3個屬於first wafer effect的異常晶圓片，本研究方法有明顯的改善效果。

Fault detection and classification (FDC) plays an important role in monitoring IC manufacturing process. Recently, Lee et al. (2011) proposed a simple and efficient model to analyze a typical profile data. One of main concerns in this model is that the “level shift” parameter may be completely confounding with the process lot-to-lot variation; which usually leads to make a wrong decision on FDC. To overcome this difficulty, this thesis first separates the deviations in profile data into within-lot variations and between-lot variations. Due to the fact that the intrinsic lot-to-lot variation is a natural phenomenon of IC manufacturing process, therefore between-lot-variation shall be removed completely before implementing FDC procedure. In this study, we apply the functional principle component analysis (FPCA) technique to investigate wafer-to-wafer (within-lot) variation. A modified health index (HI) has been constructed. Finally, we also compare the proposed method with that of Lee, et al. (2011). The results demonstrate that our method can efficiently overcome the weakness of Lee, et al. (2011).

[1] Akima, H. (1970). A new method of interpolation and smooth curve fitting based on local procedures. Journal of the ACM (JACM), 17(4), pp. 589-602.
[2] Box, G. E. , Jenkins, G. M. and Reinsel, G. C. (2008). Time series analysis : forecasting and control. Wiley.
[3] Box, G. E., and Tiao, G. C. (1975). Intervention Analysis with Applications to Economic and Environmental Problems. Journal of the American Statistical Association, 70(349), pp. 70-79.
[4] Ghanem, R. G. and Spanos, P. D. (1991). Stochastic finite elements: a spectral approach. Springer.
[5] Johnson, R. A. and Wichern, D. W. (2007). Applied Multivariate Statistical Analysis. Prentice Hall.
[6] Kincaid, D. and Cheney, W. (2002). Numerical Analysis: Mathematics of Scientific Computing, Third Edition. American Mathematical Society.
[7] Lee, S. P., Chao, A. K., Tsung, F., Wong, D. S. H., Tseng, S. T., and Jang, S. S. (2011). Monitoring Batch Processes with Multiple On–Off Steps in Semiconductor Manufacturing. Journal of Quality Technology, 43(2), pp. 142-157.
[8] Montgomery, D. C. (2013). Introduction to statistical quality control. Wiley.
[9] Nomikos, P. and MacGregor, J. F. (1995). Multivariate SPC Charts for Monitoring Batch Processes. Technometrics, 37(1), pp. 41-59.
[10] Ramsay, J. O. and Silverman, B. W. (2002). Applied Functional Data Analysis: Methods and Case Studies. Springer.
[11] Ramsay, J. O. and Silverman, B. W. (2005). Functional Data Analysis. Springer.
[12] Stark, H. and Woods, John W. (1986). Probability, Random Processes, and Estimation Theory for Engineers. Prentice-Hall, Inc.
[13] 張佳蓉. (2007). 半導體製程與設備之健康指標分析. 國立清華大學工業工程與工程管理學系碩士論文.
[14] 張慶宏. (2009). 利用 Hotelling T2 分解方法處理機台錯誤偵測與分類之研究. 國立清華大學統計學研究所碩士論文.
[15] 陳妍言. (2008). 機台重要指標之探討. 國立清華大學統計學研究所碩士論文.
[16] 曾國豪. (2009). 批次剖面資料之動態模型分析. 國立清華大學統計學研究所碩士論文.
[17] 趙安國. (2008). 批次剖面資料之錯誤分析. 國立清華大學統計學研究所碩士論文.
[18] 羅新廷. (2013). 剖面資料之錯誤偵測分析 時間序列與干預模式建構. 國立清華大學統計學研究所碩士論文.
[19] 吳侑峻. (2015). 函數資料的異常製程偵測與診斷及變異分析之研究. 國立交通大學統計學研究所博士論文.