本篇論文為以隨機晶圓為基礎使用統計檢定假說，找出不同晶圓尺寸間迴力棒圖的關係，在設計出模擬法方便使用者只須要給出尺寸就能快速取得隨機瑕疵所造成的晶圓圖特性分界，以達到快速判讀晶圓圖異常的目地。 首先，我們以最大尺寸的晶圓進行較縝密及精確的邊界模擬，對此尺寸以兩次線性回歸，最終取得較方便及優良的方法。並且藉由隨著晶圓尺寸調整迴力棒圖之中心線的偏移量，來校正在不同尺寸下的中心點，以防止在隨機性分析上的中心點偏差，且中心線之偏移量與晶圓尺寸有著特別的關係，另外也重新微調其標準差數值，以符合我們所期望的信賴區間百分比，並以這兩個部分為特點，擴展成由使用者決定晶圓尺寸後快速產生出高判別度且廣範圍、廣尺寸的迴力棒邊界。 接著，我們先使用隨機數產生的合成晶圓，將原本1.96倍的標準差(95%信賴區間)增加至2.58倍(99%信賴區間)及3.89倍(99.99%信賴區間)，在全域的分析之下，加強B-Score隨機性之驗證。其後再以正規化NBD做各區段的常態性分析，觀察同一區段所產生的B-Score之分布在我們所找的幾個臨界點上是否符合，驗證B-score為一個標準分數。 最後和先前論文的方法結果互相做比較，並且使用我們的誤差函數來量化兩者之間的差距，以用來顯示本論文所改善的程度。 ;In this thesis, we find the relationship between diesize and Boomerang Chart based on wafer map which random distribution of defects, build the model by the relationship that let user just provided diesize to get bound of wafer cause by random defects to achieve the aim of discrimination abnormal wafers fast. At first, we use the largest diesize to simulate bound accurately and carefully. We chose two linear regressions for this diesize. And by adjusting the offset of the center line of the bar graph with the wafer size, the center point at different sizes is corrected to prevent the center point deviation in the randomness analysis, and the offset of the center line for each diesize has a special relationship. Additionally, the standard deviation value is re-adjusted to meet the desired confidence interval percentage. Model based on the two factors to let user get bound of Boomerang Chart fast for full yield range, wider diesize and accurately has been provided. Then, we generate synthetic wafer by random number. Increasing the original standard deviation of 1.96 times (95% confidence interval) to 2.58 times (99% confidence interval) and 3.89 times (99.99% confidence interval). We use full-range analysis to enhance the verification of randomness. And then verify the normality of normalized NBD to observe whether distribution of B-score meets to our critical points. By these steps, verified B-score is a standard score. At last, the results of the previous thesis are compared with our method and our error function is used to quantify the difference between these to show the extent of improvement in this thesis.
