半導體晶圓廠有非常複雜的製程步驟，以線上製程資訊對生產線終端測試數據建模為全廠製程監控(Fab-wide Process Control)以及製程良率提升非常重要的議題。生產線終端測試數據建模往往會碰到測試數據中存在著多重模式的挑戰，已經有研究提出以叢聚式迴歸(Clusterwise Linear Regression；CLR)建模的技術。然而，CLR演算法必須要預先得知資料的分群數目才能發揮其效能，且在多維度的資料型態很難呈現分群結果。本研究提出以叢聚迴歸為基之自組織映射圖網路(CLR-based Self-Organizing Map；CLR-SOM)針對多維度資料型態以視覺化的方式呈現分群結果，並提供良率工程師進行更精確分群建模所需要的相關資訊。

CLR-SOM網路主要有四個程序：(1)起始程序、(2)競爭程序、(3)合作程序以及(4)適應程序。並有三個加強CLR-SOM分群效能的方法：(1)重生、(2)軟性分群以及(3)模式間相似度調整。CLR-SOM演算法產生U-Matrix圖以視覺化的方式呈現分群結果，並可由分群結果得到分群數目、重要因子、模式的迴歸係數以及資料點對應各模式的歸屬機率。設計平行以及交叉的資料模式類型進行CLR-SOM模擬實驗，結果得到CLR-SOM的分群效能遠優於原始的SOM網路，特別是針對多重模式間距離很小的時候效能更優於原始SOM網路。實際半導體資料驗證顯示CLR-SOM偵測出此筆晶圓測試數據存在多重模式，並且尋找出隱藏因子進而將資料分群促進良率工程師診斷製程良率過低的根源。

In semiconductor manufacturing with hundreds of processing steps, modeling of end-of-line wafer test data with respect to in-line manufacturing data plays a key role to successful fab-wide process control and yield enhancement. In the past few years, Clusterwise Linear Regression (CLR) techniques have been applied to cope with the challenge that there are usually multiple models manifested on end-of-line wafer test data. However, the execution of CLR not only needs a pre-determined number of clusters but is also difficult to interpret the clusters in multi-dimensional space. This thesis proposes a visualized clustering technique, CLR-based Self-Organizing Map (CLR-SOM), to efficiently determine the number of clusters in multi-dimensional data and provides engineers the within-cluster information for detailed modeling.

The main procedure of CLR-SOM consists of four parts: Initialization, Competition, Cooperation and Adaptation. To further improve the CLR-SOM performance, three novel methods are developed: model reborn, soft clustering and the cluster-similarity adjustment. The outputs of CLR-SOM is a visualized clustering graph from U-Matrix, which is able to provide the number of clusters and within-cluster information such as the critical factors, regression coefficients and data membership. Simulation studies are conducted on parallel and cross models respectively. Results show that CLR-SOM has better performance than standard SOM, especially when the differences among individual models are small. Fab data validation demonstrates that CLR-SOM not only successfully detects multiple clusters manifested on wafer test data but also identifies a hidden variable to distinguish different clusters and facilitate engineers diagnose the root cause of low yield data.

第一章 緒論 1
1.1 研究動機與背景 1
1.2 研究目的 4
1.3 研究方法 6
1.4 研究架構 7
第二章 問題描述與文獻探討 8
2.1 問題描述 8
2.2 半導體製程之工程資料分析系統 10
2.2.1 晶圓允收測試資料 11
2.2.2 半導體全廠製程監控 12
2.2.3 晶圓測試數據建模 13
2.3 叢聚式迴歸 14
2.4 類神經網路 16
2.4.1 倒傳遞網路 18
2.4.2 群聚分析 20
2.4.3 倒傳遞網路分群法 22
2.5 自組織映射圖網路 23
2.6 文獻總結 25
第三章 CLR-SOM方法介紹 27
3.1自組織映射圖網路 27
3.1.1自組織映射圖網路演算法的流程 28
3.1.2自組織映射圖網路架構 29
3.1.3 自組織映射圖網路的重要概念 32
3.1.4 自組織映射圖網路學習的主要程序 34
3.2 以線性迴歸分群為基礎之自組織映射圖網路 37
3.2.1 CLR- SOM網路演算法的流程 37
3.2.2 CLR-SOM網路架構 38
3.2.3 CLR- SOM的主要程序 42
3.2.4 CLR-SOM網路圖形說明與解讀 52
3.2.5 CLR-SOM流程圖 56
第四章 模擬資料實驗分析 60
4.1模擬資料 60
4.2模擬案例分群結果 63
第五章 半導體實際資料驗證 71
5.1 半導體實際資料 71
5.2 以CLR-SOM進行實際案例視覺化分群 73
第六章 結論與未來研究 80
參考文獻 81

[1]呂學地(2009)，「應用資料探勘技術於半導體晶圓允收測詴參數預測之研究」，元智大學工業工程與管理研究所碩士論文。
[2]李宗霖(2010)，「叢聚式迴歸之收斂性質改善及其於晶圓允收測試資料建模的應用」，元智大學工業工程與管理研究所碩士論文。
[3]林瑞山(2004)，「類神經網路於預測晶圓測試良率之應用」，成功大學工程管理學系研究所碩士論文。
[4]周文賢，「多變量統計分析: SAS/STAT使用方法」，智勝出版，2002年。
[5]張中瀚(2010)，「結合主成分分析與叢聚式迴歸於晶圓允收測試資料之建模」，元智大學工業工程與管理研究所碩士論文。
[6]張其聖(2008)，「半導體產業研發設計階段以WAT參數資料建構黃金晶方分析模型」，國立清華大學工業工程與工程管理學系研究所碩士論文。
[7]陳昌榮，林育臣(2002)，「群聚演算法之比較及群聚參數的分析與探討」，朝揚科技學資訊管理研究所碩士論文。
[8]游淑敏(2008)，「以WAT參數資料建構半導體研發設計階段黃金晶方群聚分析」，國立清華大學工業工程與工程管理學系研究所碩士論文。
[9]黃賢文(2009)，「建立半導體晶圓允收測試參數之預測模型—以電容為例」，元智大學工業工程與管理研究所碩士論文。
[10]葉怡成，「類神經網路模式應用與實作」，儒林出版社，2003年。
[11]蕭博文(2006)，「台灣光電產業經營績效評估-結合DEA與DB-SCAN群聚分析」，國立交通大學管理學院碩士論文。
[12]DeSarbo, W. S., R. L. Oliver, and A. Rangaswamy (1989). “A simulated annealing methodology for clusterwise linear regression”, Psychometrika, 54, 70–736.
[13]DeSarbo,W. S. and D. Grisaffe (1998).“ Combinatorial optimization approaches to constrainedmarket segmentation: An application to industrial market segmentation”, Marketing Letters, 9, 115–134.
[14]Dempster, A. P., N. M. Laird and D. B. Rubin (1977). “Maximum likelihood from incomplete data via the E-M algorithm”, Journal of the Royal Statistical Society B, 39, 1–38.
[15]Fish, K. E., J. H. Barnes and M. W. Aiken(1995). “Artificial neural networks: a new methodology for industrial market segmentation,” Industrial Marketing Management, 24, 431-438.
[16]Harrison, C.A., R. Good, D. Kadosh and S.J. Qin (2003), “Multi-step supervisory control of flash memory device production via a simple first-principles model”, In: AEC/APC Symposium XV.
[17]Jeff Wu, C. F. (1983), “On the Convergence Properties of the EM Algorithm, The Annals of Statistics”, Vol. 11, No. 1, pp. 95-103.
[18]Kohonen, T. (1982), “Self-organized formation of topologically correct feature maps” , Biological Cybernetics, 43, pp. 59-69.
[19]Kohonen, T. (1990), “The self-organizing map”, Proceedings of the IEEE, 78, pp. 1464-1480.
[20]Lu,C.Y. and Fan,C.M. (2009), “Correlation analysis between wafer acceptance test and in-line data for process control”, In: AEC/APC Symposium
[21]Leisch, F. (2004). “FlexMix: A general framework for finite mixture models and latent class regression in R”, Journal of Statistical Software, 11, 1–18.
[22]Muller, C. H., and T. Garlipp (2005). “Simple consistent cluster methods based on redescending Mestimators with an application to edge identification in images”, Journal of Multivariate Analysis, 92, 359–385.
[23]Moyne, J. (2004). “Making the move to fab-wide apc”, Solid State Technology 47 (9), 47
[24]Qin, S.J., G. Cherry, R. Good, J. Wang and C. A. Harrison (2004). “Control and monitoring of semiconductor manufacturing processes: Challenges and opportunities”, In: IFAC symposium on dynamics and control of process systems.
[25]Qin, S.J., G. Cherry, R. Good, J. Wang and C.A. Harrison (2006). “Semiconductor manufacturing process control and monitoring: A fab-wide framework”, Journal of Process Control16 (3), 179-191.
[26]Schoene, C., Qin, S.J., Kutanoglu, E. and Stuber, J. (2007), “Electrical parameter control for semiconductor device manufacturing: a fabwide approach”, In: IFAC symposium on dynamics and control of process systems.
[27]Spath, H. (1979). “Algorithm 39: Clusterwise linear regression”, Computing, 22, 367–373
[28]Spath, H. (1982). “Algorithm 48: A fast algorithm for clusterwise linear regression”, Computing, 29,175–181.
[29]Vellido, A., P. J. G. Lisboa and J. Vaughan(1999). “Neural networks in business: a survey of applications,” Expert Systems with Applications, 17, 51-70.