陳正剛臺灣大學：工業工程學研究所洪弘HUNG, HUNGHUNGHUNG2007-11-262018-06-292007-11-262018-06-292004http://ntur.lib.ntu.edu.tw//handle/246246/51219半導體製程的訊息不僅反映在平均值，也會反映在共變異矩陣之中。因此，對於共變異矩陣的錯誤偵測與鑑別(FDC)也越來越重要。然而，現今半導體製程中所關心的變數越來越多，所能蒐集到的樣本越來越少，以至於現有的釵h檢定方法無法使用，例如最常見的蓋似比檢定(LRT)。本研究提出了克服樣本數問題的檢定方法。此外，我們也證明了相關的定理，提出一套對於共變異矩陣的錯誤分類準則。 我們用模擬的方式和實際的製程資料來驗證我們所提出的檢定方法在樣本數很小時可以有效的偵測到錯誤，且所提出的分類準則也可以有效的鑑別出錯誤。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 classificationAbstract i 論文摘要 ii Table of Contents iii List of Tables iv List of Figures v Chapter 1. Introduction and Motivation 1 Chapter 2. Fault Detection and Classification by Sample Covariance Matrix 6 2.1. Test Procedure for Fault Detection 6 2.2. Fault Classification with T Pattern 12 Chapter 3. Validation with Simulation and Real Case Study 20 3.1. Validation with Simulation 20 3.1.1. Scenario-1: s1= 3.5 20 3.1.2. Scenario-2: s1= 3.5, s2= 8 21 3.1.3. Scenario-3: r42= -0.2 22 3.1.4. Scenario-4: r42= -0.2, r51= 0.5 23 3.1.5. Scenario-5: s1= 3.5, r42= -0.2 23 3.2. Validation with Real Case Study 24 3.2.1. Sample size is 16 24 3.2.2. Sample size is 40 30 Chapter 4. Concluding Remarks and Future Works 35 References 38 Appendix I: Trend Chart of tii’s 39 Appendix II: Matlab Code 44564408 bytesapplication/pdfen-USBartlett 分解Cholesky 分解Bartlett's decompositionCholesky's decompositionthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/51219/1/ntu-93-R91546010-1.pdf