Abbe-SVD:一個使用奇異值分解法於Abbe’s Kernel所產生的全新快速微影成像模擬方法

Abbe-SVD: Compact Abbe’s Kernel Generation for Microlithography Aerial Image Simulation using Singular-Value Decomposition Method

江則佑(Tse-Yu Chiang)

指導教授 ： 陳中平

國立臺灣大學/電機資訊學院/電子工程學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.01570

摘要

目前在積體電路製造工業中最關鍵的製程是微影曝光製程，其利用曝光的過程將光罩上的設計樣式複製到晶圓上。然而，當光罩上的設計樣式越來越小至接近所用來曝光的波長時，在晶圓上的成像品質和解析度因為散射的效應而變糟。因此，採用有效的技巧和演算法來增加解析度的技術(RET)被提出，其需要利用模擬或是實驗結果來加以驗證。最直接和精確的模擬方式就是直接將成像曝光到晶圓上，而精確的電腦影像模擬可以計算出微影曝光後有曝光和沒有曝光的區域出來。目前的商用或是學校所研發出來利用Abbe成像方法在頻域做計算的部分同調光源OPC模擬軟體必須同時利用幾百台的電腦計算好幾天才能得到成像。因此，我們提出一個使用奇異值分解法於Abbe’s kernel所產生的全新快速微影成像模擬方法。這個方法的優點是：第一，因為不是所有的Abbe’s kernel對於成像都有著關鍵的影響，所以我們可以利用奇異值分解法將之消去產生精簡的kernel，使得我們可以加快模擬的時間，並維持使用者所要求的精確度。第二，我們提出了進階光源切割法，可以產生有著較高精確度的等效kernel。最後，我們使用LUT來加快模擬時間。
在這篇論文，我們在第一章中介紹基本光學微影曝光術的知識，第二章中推導出使用同調光源時的成像解析解。接著，部分同調光源的概念、進階的照射孔隙和Abbe成像方法會在第三章中說明，並推導出我們的Abbe-SVD演算法和進階光源切割法。第四章中會展示實驗的結果和相關的比較。第五章則是結論。

關鍵字

Abbe成像方法 ； 光學成像模擬 ； 微影曝光術 ； 光學鄰近修正術(OPC) ； 奇異值分解法

並列摘要

At the present days, the key and critical part of industrial IC manufacture is the optical lithography technology which can duplicate the design patterns on the mask onto wafer by light exposure. However, when the mask patterns are too small which are approaching light wave length, the image quality and resolution on the wafer are getting worse owing to diffraction effect. Therefore, some necessary resolution enhancement techniques are proposed with remarkable skills and algorithms, and need to be verified by simulations or experimental results. The most direct and accurate simulation is the imaging of patterns on wafer. Accurate imaging simulation can show exposed and unexposed regions after photolithography by computer. Existing commercial and academic OPC simulators which compute in frequency domain with Abbe's method applied on partial coherent light source take several days for computation with hundreds of computers working together at the same time. Hence, we propose to generate a compact Abbe's kernel for microlithography aerial image simulation using singular-value decomposition method. The advantages of this approach are as follows: First, since not all the Abbe's kernels have critical effects on aerial image, we can eliminate them to generate a compact one with SVD. Therefore, we can speed up simulation time, and furthermore keep the accuracy user specified. Second, with advanced concentric circles source discretization, equivalent kernels with higher precision is produced. Finally, we can use compact Abbe's kernel to build LUT to speed up simulation time.
In this thesis, we introduce some basic knowledge of optical lithography in chapter 1 and some coherent light in optics with analytical solution in chapter 2. Then, partially coherent light concept, advanced illumination aperture and Abbe's method are introduced in chapter 3 and our Abbe-SVD algorithm and advanced source discretization will also be derived. Experimental result and some comparisons will be shown in chapter 4 and finally conclusion will be made in chapter 5.

並列關鍵字

aerial image simulation ； microlithography ； optical proximity correction(OPC) ； singular-value decomposition

參考文獻

[1] Joseph W. Goodman. Introduction to Fourier Optics. McGraw Hill, 2 edition, 1996.

[3] Heinrich Kirchauer. Photolithography Simulation. Dissertationen der Technischen Universitat Wien, 1998.

[5] B. J. Lin. Microlithography theory and practice. Lectures in NTU, 2006.

[6] A. K.Wong. Resolution Enhancement Technique in Optical Lithography. SPIE Press, 2001.

[7] L. F. Thompson, C. G. Willson, and M. J. Bowden. Introduction to Microlighography. American Chemical Society, Washington, DC, 2 edition, 1994. pp.22-30.