在高數值孔徑微影系統中之成像模型建立

Image Modeling for a High Numerical Aperture Microlithography System

朱冠儒(Kuan-Ju Chu)

指導教授 ： 陳永耀

國立臺灣大學/電機資訊學院/電機工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.10564

摘要

微電子元件的發展，以矽晶為主的電子元件隨著摩爾定律(Moore’s law)所預測的，尺寸不斷地縮小，所以必須要有更好的透鏡解析度，傳統的微影術模型建立在純量的夫涅爾近似(Fresnel approximations)，這個近似只有在低數值孔徑的系統中成立，一旦在高數值孔徑的環境中，此夫涅爾近似將不再成立。
我們成功地整理出在高數值孔徑的微影系統中的影像模型方程式，此方程式是以向量模式推導，不再是傳統的純量模式推導，我們從和這相關的文獻中，重新整理這些文獻中有用的方程式，清楚地呈現在這篇論文中，我們設計各種不同的光罩，來比較在純量模式和向量模式中，不同條件下的差異，我們可以很清楚地發現，隨著數值孔徑不斷地增加，純量模式和向量模式的結果差異，將會越來越大，這即意味著，當我們在高數值孔徑微影系統中計算空間影像(aerial image)，我們必須採用向量模式。
在本篇論文中，我們將在第ㄧ章中介紹ㄧ些微影術的基礎知識，並在第二章中介紹純量繞射理論，在第三章中講解在同調和部份同調的光源條件下，純量模式的影像模型建立，在第四章推導向量模式的影像模型公式，第五章將比較純量模式和向量模式的空間影像差異，並在最後的第六章中，做一個本篇論文的結論。

關鍵字

微影術 ； 高數值孔徑 ； 空間影像 ； 影像模型

並列摘要

In the field of microlithography the demand for highly integrated electronic circuits has motivated investigation into better lens resolution. Traditional models used in microlithography are based on scalar image formation under the Fresnel approximations. This approximation holds in the low system but it breaks down when the exit pupil diameter is of the same order as the distance from pupil to image (high ), i.e. .
We successfully find vector imaging model in a high numerical aperture microlithography system. We survey papers about image modeling, and clearly reorganize the useful formulates from these papers. And we design different kinds of photo masks to compare the aerial image of the scalar imaging model and of the vector imaging model. We can clearly find that the intensity of the scalar model is much different from the intensity of the vector model when (high NA). So we should adopt the vector model when we need to calculate the aerial image in a high microlithography projection system.
In this thesis, we introduce some basic knowledge of optical lithography in chapter 1 and foundations of scalar diffraction theory in chapter 2. Then, scalar imaging with coherent illumination and partially coherent illumination is introduced in chapter3. The formulation about vector imaging model in a high numerical aperture microlithography system is derived in chapter 4. Simulation result and some comparisons will be shown in chapter 5. Finally conclusion will be made in chapter 6.

並列關鍵字

microlithography ； high NA ； aerial image ； image modeling

參考文獻

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