在半導體製造流程中，清腔(chamber purging) 是很重要的一個步驟。
在積體電路的製作過程中，進入機台的各種化學原料常容易黏附於機台內，
進而在生產時造成晶圓表面的殘留微粒(particles)，此殘留微粒會與積體電
路相互反應，使產品產生缺陷，造成良率下降的問題。故不時進行清腔以
維持機台內的乾淨程度，是晶圓生產時必要之步驟。本文討論一清腔因子
實驗，在此實驗中，我們無法直接量測機台在清洗後的乾淨程度，而只能
由清洗後第一次製造之晶圓上的微粒顆數來評估機台的乾淨程度。而為了
確認每種清洗法的清潔能力，針對每一種清洗法，在本實驗中，將清洗後
再製造之程序多次重複執行，並量測每次製造時晶圓上微粒顆數。針對此
實驗，我們提出一套創新的分析方法。我們使用廣義線性模型(generalized
linear model,GLM) 及此實驗之背景知識，來建立一個合理的統計模型，並
定義出因子的各種效應。我們利用GLM 中的費雪得分法(Fisher scoring
method) 來提供一個此模型下的參數估計演算法。而對於參數的檢定問題，
我們則利用概似比檢定(likelihood ratio test) 來執行。我們利用電腦模擬
檢驗這些估計及檢定方法的功效，發現其可有效地估計及檢定參數。我們
並將這些估計及檢定方法，應用於清腔實驗的真實數據分析上，找到能影
響清潔效果之重要因子效應，以建議一個強力清洗法，來提昇晶圓製造之
良率。
i

One of the most important steps in the manufacturing of semiconductor
wafers is the purging process of chambers. In the manufacturing operations,
some chemicals inserted into chambers might remain in the chambers after
the operations, causing the appearance of contaminant particles on the
surface of the subsequently produced wafers. The particles can damage the
integrated circuits on the wafers, thereby reducing yields. It is necessary
to regularly purge chambers and remove residual chemicals to maintain the
cleanliness inside the chambers. In the thesis, we discuss an experiment
conducted to study the effects of some purging factors. In the experiment,
it was impossible to directly measure the degree of cleanliness inside the
chamber, so that the number of particles on a wafer produced by the chamber
was taken as a surrogate response to evaluate the cleanliness level inside
the chamber. To accurately determine the cleaning efficiency of the purging
methods, the process of purging-then-making-a-wafer was continuously
repeated several times for each purging method, and in each repetition,
the number of particles on the wafer was measured and recorded. For the
experiment, we propose an innovative analysis method. We adopt some
domain knowledge about purging and modify the generalized linear models
in statistics to build a reasonable statistical model with various factorial
effects for the data generated by the experiment. We follow the Fisher
scoring method to derive an algorithm for the estimation of the parameters
in the model. For the testing of effect significance, we present a method
based on the likelihood ratio. We use computer simulations to verify the
effectiveness of the methods, and find they can accurately estimate and test
the parameters. We demonstrate these methods on a real data of purging
experiment to identify the influential factorial effects, which are then used
to suggest a best purging method for improving the yield of wafers.

1 緒論1
1.1 清腔因子實驗 1
1.2 實驗數據 3
1.3 舊有分析手法 5
2 文獻回顧7
2.1 廣義線性模型 7
2.2 參數估計方法 8
2.3 概似比檢定 9
3 模型討論 10
3.1 統計建模 10
3.2 粗略分析法 18
4 參數估計與檢定 21
4.1 參數估計 21
4.2 檢定 23
5 模擬驗證 25
5.1 模擬設定 25
5.2 模擬結果 26
6 真實數據分析 33
7 結論 36
參考文獻 37
附錄A: 計分函數與費雪訊息矩陣之詳細推導 38

Cooper, D. W. (1986). “Particulate contamination and microelectronics manufacturing:
an introduction,” Aerosol Science and Technology, 5(3), 287-299.

Dobson A.J. and Barnett, A.G. (2008). An introduction to generalized linear
models, 3rd edition, CRC Press.

McCullagh, P., and Nelder, J. A. (1989). Generalized linear models, 2nd
edition, CRC press.

Nelder, J. A., and Wedderburn R. W. M. (1972). “Generalized Linear Models,”
Journal of the Royal Statistical Society, Series A, Vol. 135, No. 3, pp.
370-384.