本篇論文提出統計分割群聚演算法量化晶圓圖的瑕疵圖樣，並提出均勻分佈之瑕疵圖樣的特性為一迴力棒圖(Boomerang-Chart)。 在兩種晶圓圖格式比較上，瑕疵圖樣利用均勻分佈亂數模擬隨機故障導致”雜訊”群聚集。本論文提出Boomerang Equivalence，是一種新的統計分割群聚演算法來預估晶圓圖的平均瑕疵數，利用此演算法可驗證瑕疵圖樣具有可加性。比較亂數模擬法與Boomerang Equivalence法預估的平均瑕疵數，在0.2、0.5與1的平均瑕疵數下，可約有15%、1%與3%的差異。由平均瑕疵數為0.2或為0.5的數片晶圓圖組成平均瑕疵數為1的單一晶圓圖的可加性分析中，亂數模擬法與Boomerang Equivalence法預估的平均瑕疵數差異皆小於2%。 經過驗證，Boomerang Equivalence法可用來判別晶圓圖的瑕疵圖樣是否為均勻分佈，其可加性的特性可於將來探討晶圓圖瑕疵源由並分解成不同瑕疵來源的子晶圓圖樣，提供數理上的可行性。 In this thesis proposes a “statistical partitioning clustering algorithms” to “quantize” the cluster pattern of Wafer Map. The characteristic of cluster pattern in Uniform distribution (simulation) is a Boomerang-Chart. Comparisons on two dataset Wafer Map, the cluster pattern utilizes the uniform random distribution to simulate the random defect induced by the “noise” dataset. In this thesis proposes Boomerang-Equivalence, a new statistical partitioning clustering algorithm, to evaluate the average defect number of Wafer Map. The Boomerang-Equivalence can verify the Additivity property of cluster pattern. Evaluated comparisons of average defect number with random defect simulation and Boomerang-Equivalence, the average defect number in 0.2、0.5 and 1 have the difference of 15%、1% and 3%。 In analysis of additivity property, the single wafer map in average defect number is 1 composed by multi-wafer maps that the average defect number are 0.2 or 0.5, the evaluation difference of average defect number is smaller than 2% compared with random defect simulation and Boomerang-Equivalence. After above verifications, Boomerang-Equivalence can check that a cluster pattern of wafer map is uniform distribution or not. The additivity property can support the reliability of Mathematic theory in finding defect source and decompose the sub-wafer maps in different sources.
