剖面資料分類方法應用在半導體製程上之研究

Abstract

在業界，工程師執行統計製程管制 (statistical process control，簡稱 SPC) 時，常使用管制圖監控製程參數是否發生改變。當失控資料產生時，可依此尋找可歸屬原因，對製程執行矯正。藉著失控資料所攜帶的訊息辨識失控類型，對於工程師後續的矯正作業將有莫大幫助。本篇論文的主旨即在於研究一筆失控剖面資料產生時該如何辨識此筆剖面資料的失控型態類型。 在本篇論文中，我們使用 KNN、LDA 和 QDA 三種常見的判別工具，來進行剖面資料分類 (classification) 的模擬研究，引用 Chiou and Li (2007) 中的例子，使用電腦模擬生成 8 組剖面資料做為訓練樣本，每組由兩種不同類型的資料所組成，觀測並比較三種分類法分類之正確率與標準誤，並且記錄三種分類方法的運算時間。整體來說 KNN 的表現最佳，所需的運算時間卻最多。 在實際應用上，我們將三種分類方法運用到兩個半導體製程的例子上進行模擬。實例一根據晶圓表面蝕刻 (etching) 剖面向下切入之角度可分成三類：正常、過度與不足；而我們利用剖面資料進行蝕刻型態種類分析；整體來說以 KNN表現最佳， LDA 也有不錯的正確率，QDA 之正確率則是略低於 LDA。實例二則是利用晶片 (chips) 良品與不良品之間於晶圓 (wafer) 上呈現的特殊排列方式進行晶圓資料的診斷；三種分類方法都能輕易的分辨出失控類型。

In the industry, engineers use control charts to monitor process variables for process stability. A point that plots outside of the control limits is interpreted as an evidence that the process is out of control, and investigations and corrective actions are required to find and eliminate the assignable cause or causes responsible for this behavior. It would be helpful for engineers to take right corrective actions if we can identify the type of the problems from the out-of-control data. In this research, we use three well-known classification methods, KNN, LDA and QDA to classify profile data and study the effectiveness of these methods via simulation. The simulation results indicate that the KNN method has the best performance in terms of the accurate classification rate, but takes the longest time in computation. For real-life examples, we simulate profile data for two potential applications in semiconductor manufacturing and apply the three classification methods on them. In the first example, the angle of wafer surface etching classifies the profile into three classes: normal, over-etching, and under-etching. Without knowing the angle, we apply the three classification methods to classify profile data. In this example, among the three methods, KNN performs the best, LDA the second, and QDA the worst. In the second example, the pattern of the defective chips on a wafer determines the class of a wafer. We first transform the 0-1 2-dimensional data into profile data, then apply the three classification methods to classify the wafers. The result shows that the performances of the three methods are fairly similar.