隨著半導體製程的不斷進步，線幅的關鍵尺寸（Critical Dimension, CD）不斷地縮小，使得製程中所產生的製程變異之影響也愈加的重要。製程變異又可分為隨機變異（random variation）以及系統性變異（systematic variation），然而當中隨機變異是無法預測及避免的，了解系統性變異的發生原因及探討其對電路效能的影響，對於提高製程良率和改善電路設計將有很大的幫助。
光學微影製程是半導體製程中最主要的製程步驟，影響關鍵尺寸大小的最關鍵技術，而當中所產生的系統性變異也將更直接的影響到線幅寬度的大小，產生所謂的關鍵尺寸變異（CD variation）。由於光學微影系統的不斷演進，使用越來越高的數值口徑（numerical aperture, NA），來增加影像的解析度，並且使用大面積的照射，使得透鏡中所存在的透鏡像差之影響不能在被忽略，在這篇論文中，我們將介紹光學微影製程中幾個較為重要的系統性變異，例如：光阻劑塗佈（resist coating）、耀光（flare）、光罩偏差（mask error）、透鏡像差（lens aberration），並且探討透鏡像差對於整個關鍵尺寸變異的影響，因為，不同的透鏡像差對於不同的光罩圖形（layout pattern）會有不同的影響 [1]，我們利用Silvaco公司所提供的Athena軟體來模擬關鍵尺寸受到透鏡像差的微影結果，進而萃取出系統性變異的模型，最後，我們將利用它來估測出電路關鍵電路延遲的變化及其對於電路效能的影響。

As the developments of semiconductor process technology continue to improve, process variations
affect the circuit performance significantly. The problem of lens aberrations in lithography system
cannot be neglected, and especially today’s lithography systems use high NA to push the technology
node to 90nm or smaller one. It means that light travels the large portion of lens, so lens
aberration effect is more significant [1]. Systematic Variations in optical lithography have many
sources, such as mask error, flare and lens aberration, and the lens aberrations effect become more
and more important among them in recent years. In this thesis, we introduce various systematic
variations in optical lithography and focus on the phenomenon of lens aberrations effect. We use
the lithography simulator, Athena, to simulate the results that lens aberrations affect the different
test structures and then extract the CD contour maps. We model these systematic variations by
the statistic multiple regression and use these models to estimate the path delay. We propose a
framework to estimate the critical path delay of circuit affected by lens aberrations and observe the
impact of lens aberration on circuit performance.

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