臺灣博碩士論文加值系統

隨著半導體產業不斷的進步，製程不斷的演進，製程線寬從180奈米一直進步到65 甚至45奈米。 當線寬尺寸逼近光波長時，光線穿過光罩後會產生繞射，這些繞射光疊加的結果會與光罩上的圖形跟我們所期望的結果相去甚遠，曝光後的圖形因而嚴重失真。所以有許多增加解析度的技術陸續被提出。而光學鄰近修正技術 (OPC) 就是其中一種增強解析度的方法，為了補償曝光後圖形失真的現象，我們可以經由修改光罩上的圖形，像是在邊緣多加一些襯線，讓繞射光在疊加後滿足我們實際的要求。但是在做完光學鄰近修正術 (OPC) 後，原本的形狀改變了，儲存這些形狀所需要的資料量也變高許多。
在本篇論文，我們提出一種以傅立葉描述元為基礎的表示法，用來表示做完光學鄰近修正術 (OPC) 後的結果。實驗結果顯示，相較於傳統的方法，我們可以節省約5倍的資料儲存量。

The geometry complexity of Optical Proximity Corrected (OPC) Mask and the aerial image are often overwhelming. To speed up the processing time of mask development, OPC quality assurance, and data storage, compact representation of the OPC mask and aerial image are of great importance.
In this thesis, we proposed a novel compact representation method based on the fourier descriptor (FD) method. FD is a widely used contour representation method for image processing. Our experimental result show that more than 5x reduction ratio of the data volume are observed with minor errors. To the best of authors knowledge, FD is applied
to OPC data representation in the first time.

1 Introduction 1
1.1 Lithography and Optical Systems . . . . . . . . . . . . . . . . . . . . . . . 1
2 Background 6
2.1 Lithography Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Principle of Lithography Imaging . . . . . . . . . . . . . . . . . . . 7
2.1.2 Photoresist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.3 Types of Photolithography . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Resolution Enhancement Technique . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Off-Axis Illumination . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Phase Shifting Mask . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.3 Optical Proximity Correction(OPC) . . . . . . . . . . . . . . . . . . 13
2.3 Photoresist Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Various Shape Representation Methods . . . . . . . . . . . . . . . . . . . . 14
2.4.1 Run-Length Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.2 Quadtree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.3 Chain Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Fourier Descriptor(FD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5.1 Properties of Fourier Descriptor . . . . . . . . . . . . . . . . . . . . 19
2.5.2 Sensitivity of Fourier Descriptor . . . . . . . . . . . . . . . . . . . . 22
3 Optical Simulation and OPC Algorithm 30
3.1 Optical Simulation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1.1 Jinc Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1.2 Jinc Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 OPC Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.1 Sampling and FD conversion . . . . . . . . . . . . . . . . . . . . . . 33
3.2.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.3 Sensitivity Calculation . . . . . . . . . . . . . . . . . . . . . . . . . 37
4 Simulation Results 40
4.1 Comparision With Some Shapes Using Different Number of Fourier De-
scriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1.1 Rectangular Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.1.2 Simulation of Various Other Shapes(non OPC) . . . . . . . . . . . 41
4.1.3 Simulation of a post OPC geometry . . . . . . . . . . . . . . . . . . 48
4.2 Adjustment of Fourier descriptors . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 Simulation of a post OPC geometry . . . . . . . . . . . . . . . . . . . . . . 50
4.4 An Example of FDOPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5 Conclusion 58
Bibliography 59

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[2] Amir Aalam Ghazanfarian Y.C. Pati and R. Fabian Pease. Exploiting Structure in Fast Aerial Image Computation for Integrated Circuit Patterns. IEEE Trans. on Semi-conductor Manufacturing, Feb. 1997. vol. 10, no. 1.
[3] B. J. Lin. Microlithography theory and practice. Lectures in NTU, 2006.
[4] A. K. Wong. Resolution Enhancement Technique in Optical Lithography. SPIE Press, 2001.
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[6] B. J. Lin. Phase-shifting masks gain an edge. Circuits and Devices, 1993.