短時間低溫顯影之電子束微影與鄰近效應修正演算法

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doi:10.6342/NTU201704286

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短时间低温显影之电子束微影与邻近效应修正演算法

Short-Time and Low-Temperature Development for Electron-Beam Lithography and the Algorithms of Proximity Effect Correction

粘群 , 博士　　导师：管杰雄　　

英文 DOI： 10.6342/NTU201704286

电子束微影；邻近效应修正；显影模型；次十奈米微影；关键显影路径；群体智能；图形演算法； electron-beam lithography ； proximity effect correction ； development model ； sub-10 nm lithography ； critical-development path ； swarm intelligence ； graph algorithm

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摘要 │ 参考文献 (76) │ 国际计量

摘要〈TOP〉

并列摘要〈TOP〉

Electron-beam lithography (EBL) is one of the most popular and important techniques in manufacturing high-resolution nanopatterns without masks and enabling the fast development of electronic and photonic devices. The proximity effect is one of the most critical issue in EBL, as it can degrade the pattern quality and, thus, impact the performance of the applications greatly. Regarding the development as a static result of electron-beam exposure, most studies solving the proximity effect by focusing on the spatial distribution of electron intensity. In fact, the development is a dynamic process as a function of the development duration and temperature. The continually changing nature of development may lead to pattern deviation. This effect becomes more noticeable as the required feature size continually shrinks. Recently, some of the researches start to consider integrating the development simulation into the proximity effect correction (PEC). However, the EBL development is a complicated process, and the conventional methods are very computationally intensive and lengthy.

This dissertation focuses on solving the proximity effect of the high-voltage EBL using the positive-tone resist. We first use a set of single-spot experiments to categorize the development process and establish a comprehensive differential model of EBL to describe the relation among the incident electrons, resist, and the development conditions such as durations and temperatures. This model identifies the location of exposure point as a singular point of ultra-high development rate, which, thus, can be considered as the beginning point of the development. Further, we verify the characteristic region of each incident spot induced by the point spread function of the electron-beam system. Eliminating the proximity effect effectively, we further achieve the pattern of isolated line with the line width of 8 nm and dense line array with the line width of 9 nm with the pitch size of 30 nm by utilizing the results from single-spot experiments at low development temperatures.

The insights from the study of the single-spot experiments lead to the innovation of a novel short-range PEC method. Based on the 2-D development model, we propose a novel concept of the critical-development path and its usage in the evaluation of the fitness of EBL patterns. For the first time, we also transform the searching of the critical-development path into the shortest-path problem of graph theory, which enables the potential of using a more efficient algorithm in the simulation of the development path. We propose a Dijkstra-based algorithm with the data structure of priority queue to guarantee the correctness and to maintain the efficiency. Also, we investigate the optimization strategies in the PEC problems. The algorithm of swarm intelligence is introduced to the PEC and is compared with the simplex-based method. From the numerical analysis, we demonstrate that choosing of a suitable optimization scheme is important especially in minimizing a complicated function like the fitness function of EBL with pixel-based fine tuning. The PEC algorithm is applied to the fabrication of an U-shaped split-ring resonators and produces an optimized exposure pattern that shows excellent agreement with the targeted design objectives. Our work on the PEC strategy reduces the computational cost significantly and is particularly suitable for the design of complex pattern with various constraints.

参考文献 ( 76 ) 〈TOP〉

[1] J. Joo, B. Y. Chow, and J. M. Jacobson, “Nanoscale patterning on insulating substrates by critical energy electron beam lithography,” Nano Letters, vol. 6, no. 9, pp. 2021–2025, 2006.
连结：
[3] H. Duan, A. I. Fernández-Domínguez, M. Bosman, S. A. Maier, and J. K. W. Yang,“Nanoplasmonics: Classical down to the nanometer scale,” Nano Letters, vol. 12, no. 3, pp. 1683–1689, 2012.
连结：
[4] M. Ieong, B. Doris, J. Kedzierski, K. Rim, and M. Yang, “Silicon device scaling to the sub-10-nm regime,” Science, vol. 306, no. 5704, pp. 2057–2060, 2004.
连结：
[5] R. Near, C. Tabor, J. Duan, R. Pachter, and M. El-Sayed, “Pronounced effects of anisotropy on plasmonic properties of nanorings fabricated by electron beam lithography,”Nano Letters, vol. 12, no. 4, pp. 2158–64, 2012.
连结：
[6] D. R. Ward, F. Huser, F. Pauly, J. C. Cuevas, and D. Natelson, “Optical rectification and field enhancement in a plasmonic nanogap,” Nature nanotechnology, vol. 5, no. 10, pp. 732–736, 2010.
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使用DOI作为永久连结

引用含有DOI的文献

DOI可强化引用精确性、增强学术圈连结，并给予使用者跨平台的良好使用经验，目前在全世界已有超过五千万个对象申请DOI。 如想对DOI的使用与概念有进一步了解，请参考 （ ） 。

DOI可强化引用精确性、增强学术圈连结，并给予使用者跨平台的良好使用经验，目前在全世界已有超过五千万个对象申请DOI。如想对DOI的使用与概念有进一步了解，请参考（）。