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Free electron laser (FEL) is a high-quality laser source with wavelengths ranging from short-wave X-ray to long-wave infrared ray. Extreme ultra-violet (EUV) radiation at λ = 13.5 nm emitted by FEL can be used in manufacturing integrated circuit, such as EUV lithography exposure and mask defect inspection. However, the high spatial coherence characteristics and similar Gauss intensity profile distribution of FEL source has a negative effect on imaging, and cannot meet the requirements of imaging applications in EUV lithography. In this work, a newly light pipe for decoherence and intensity uniformity in an EUV spectral range is designed through the simulation calculations. The new light pipe consists of two pairs of tilted elements which are symmetrically distributed in the y-z plane and x-z plane, respectively. In this way, the beam transmission divergence in two dimensions can be widened at the same time, and the disturbance of the ray transmission track and spatial phase distribution is increased, so as to achieve the uniformization of light intensity and the reduction of spatial coherence. The simulation results show that for an EUV Gaussian beam at λ = 13.5nm, with a diameter of 200 μm, and a divergence of 20 mrad, the newly designed light pipe has more significant decoherence and illumination field uniformity than the conventional light pipe structure. When the new light pipe has an inner diameter of 1mm, a total length of not less than 600 mm, and a tilt angle of 10mrad , a basically uniform illumination field can be obtained, the coherence is completely disordered, and the non-uniformity of light intensity distribution in the illumination field decreases to 0.97 from 28.38 achieved by conventional cylindrical light pipe. At the same time, the light power transmission efficiency is about 37.6% and the maximum transmission efficiency is about 44.58%. The uniformity can be further improved by increasing the number of reflections. When the inner diameter and tilted angle of the light pipe are unchanged, the length of the light pipe increases to 1m, the non-uniformity of intensity distribution at the illumination field further decreases to 0.90, and the light power transmission efficiency is about 22.35%. The results show that the newly designed light pipe structure can meet the application requirements of decoherence and improve the uniformity of illumination field at EUV wavelength range, and it has great application prospects in EUV lithography and other imaging applications. 
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Keywords:
- extreme ultraviolet source /
- free electron laser /
- light pipe /
- phase /
- intensity uniformity
[1] 赵振堂, 戴志敏, 张文志, 刘波, 邓海啸, 张满洲, 田顺强 2023 复旦学报 62 293
Zhao Z T, Dai Z M, Zhang W Z, Liu B, Deng H X, Zhang M Z, Tian S Q 2023 J. Fudan Univ. 62 293
[2] 杨家岳, 董文锐, 江凌, 袁开军, 王方军, 吴国荣, 乔德志, 张未卿, 杨学明 2023 中国科学: 化学 53 2103
Yang J Y, Dong W R, Jiang L, Yuan K J, Wang F J, Wu G R, Qiao D Z, Zhang W Q, Yang X M 2023 Sci. Sin. Chim. 53 2103
[3] 吴嘉程, 蔡萌, 陆宇杰, 黄楠顺, 冯超, 赵振堂 2023 光学学报 43 2114002
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Wu J C, Cai M, Lu Z J, Huang N S, Feng C, Zhao Z T 2023 Acta Opt. Sin. 43 2114002
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Zhang S J, Guo Z, Cheng J M, Wang Y, Chen J H, Liu Z 2023 Acta Phys. Sin. 72 105203
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[10] Han-Kwang N, Rilpho L D, Gosse C D V 2020 US Paten 20 200 152 345
[11] Christopher N A, Ryan H M, Patrick P N 2011 SPIE 7969 796938
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[13] 班尼恩 V, 巴特瑞 P, 范格尔库姆 R, 阿门特 L, 彼得 D, 德维里斯 G, 栋克尔 R, 恩格尔伦 W, 弗里基恩斯 O, 格瑞米克 L, 卡塔伦尼克 A, 鲁普斯特拉 E, 尼恩惠斯 H K, 尼基帕罗夫 A, 瑞肯斯 M, 詹森 F, 克鲁兹卡 B 2019 CN Patent 110083019
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[18] Hsiao Y N, Wu H P, Chen C H, Lin Y C, Lee M K, Liu S H 2014 Opt. Rev. 21 715
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图 1 新型匀光管的结构模型
Figure 1. Structural model of the newly designed light pipe.
图 2 光线在匀光管内的传输轨迹示意图 (a) 常规圆柱型水平匀光管; (b)带有倾斜单元的匀光管
Figure 2. Schematic diagram of ray transmission in the light pipe: (a) Conventional cylindrical light pipe; (b) light pipe with tilted elements.
图 3 通过两个具有高空间相干性的高斯光源建立干涉场 (a) 示意图; (b)软件模拟仿真的光场分布
Figure 3. Two Gaussian sources with high spatial coherence are used to obtain the interference field: (a) Schematic diagram; (b) optical field distribution simulated by software.
图 4 四种不同匀光管结构 (a) 常规圆柱型匀光管(结构一); (b) 单倾斜单元匀光管(结构二); (c) 具有在一个平面内一对呈对称分布的倾斜单元的匀光管(结构三); (d) 具有在两正交平面内分别具有一对呈对称分布的倾斜单元的新型匀光管(结构四)
Figure 4. Four light pipes with different structures: (a) Conventional cylindrical light pipe (first structure); (b) light pipe with single tilted element (second structure); (c) light pipe with a pair of tilted elements are symmetrically distributed in the y-z plane (third structure); (d) newly designed light pipe with a two pairs of tilted elements are symmetrically distributed in the y-z plane and x-z plane (fourth structure).
图 5 不同L值时4种匀光管出口处相位分布 (a) 结构一; (b) 结构二; (c) 结构三; (d) 结构四, 新型匀光管
Figure 5. Phase distribution at the outlet of four light pipes when different L values: (a) First structure; (b) second structure; (c) third structure; (d) newly designed light pipe (fourth structure).
图 6 匀光管内光路传输示意图 (a) 高斯光束振幅分布特征; (b) 光线经过新型匀光管的掠入射角变化
Figure 6. Schematic diagram of light transmission in the light pipe: (a) Gaussian beam amplitude distribution; (b) variation of the grazing incidence angle of ray in the newly designed light pipe.
图 7 具有不同长度的4种匀光管在出口处的光场分布 (a)结构一; (b) 结构二; (c) 结构三; (d) 新型匀光管(结构四)
Figure 7. Optical field distribution at the outlet of four light pipes with different length: (a) First structure; (b) second structure; (c) third structure; (d) newly designed light pipe (fourth structure)
图 8 反射效率随匀光管长度的变化曲线
Figure 8. Reflection efficiency curve with the different length of the light pipe.
图 9 分别改变L, D和α时匀光管出口光场分布
Figure 9. Optical field distribution at the outlet of light pipe when L, D and α are variables.
图 10 分别改变L, D和α时匀光管的反射效率
Figure 10. Reflection efficiency of light pipe when L, D and α are variables.
表 1 模拟参数
Table 1. Simulation parameters.
模拟参数 参数值 模拟参数 参数值 光源波长/nm 13.5 光源特征 高斯光源 光源数量/个 2 每个光源功率/W 1 每个光源分析光线数/条 1 × 106 光源发散角 2θ/mrad 20 匀光管总长度 L/mm 200—1000 匀光管内径 D/mm 1 匀光管倾斜单元倾斜角度 α/mrad 10 探测器尺寸/mm 1 × 1 探测器像素数 800 × 800 
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[1] 赵振堂, 戴志敏, 张文志, 刘波, 邓海啸, 张满洲, 田顺强 2023 复旦学报 62 293
Zhao Z T, Dai Z M, Zhang W Z, Liu B, Deng H X, Zhang M Z, Tian S Q 2023 J. Fudan Univ. 62 293
[2] 杨家岳, 董文锐, 江凌, 袁开军, 王方军, 吴国荣, 乔德志, 张未卿, 杨学明 2023 中国科学: 化学 53 2103
Yang J Y, Dong W R, Jiang L, Yuan K J, Wang F J, Wu G R, Qiao D Z, Zhang W Q, Yang X M 2023 Sci. Sin. Chim. 53 2103
[3] 吴嘉程, 蔡萌, 陆宇杰, 黄楠顺, 冯超, 赵振堂 2023 光学学报 43 2114002
Google Scholar
Wu J C, Cai M, Lu Z J, Huang N S, Feng C, Zhao Z T 2023 Acta Opt. Sin. 43 2114002
Google Scholar
[4] 张少军, 郭智, 成加皿, 王勇, 陈家华, 刘志 2023 72 105203
Google Scholar
Zhang S J, Guo Z, Cheng J M, Wang Y, Chen J H, Liu Z 2023 Acta Phys. Sin. 72 105203
Google Scholar
[5] 林宏翔, 魏晓慧, 廖天发, 王文辕, 杜鹃, 杨明亮 2022 光子学报 51 1014008
Google Scholar
Lin Z X, Wei X H, Liao T F, Wang W Y, Du J, Yang M L 2022 Acta Photon. Sin. 51 1014008
Google Scholar
[6] Norio N, Ryukou K, Hiroshi S, Kimichika T, Yasunori T, Yosuke H, Tsukasa M, Miho S, Takanori T, Olga A T, Takashi O, Hiroshi K 2023 Jap. J. Appl. Phys. 62 SG0809
Google Scholar
[7] 马晓喆, 张方, 黄惠杰 2021 中国激光 48 2005001
Google Scholar
Ma X Z, Zhang F, Huang H J 2021 Chin. J. Lasers 48 2005001
Google Scholar
[8] 刘佳红, 张方, 黄惠杰 2022 激光与光电子学进展 59 0922011
Google Scholar
Liu J H, Zhang F, Huang H J 2022 Laser Optoelectron. Prog. 59 0922011
Google Scholar
[9] Kenneth A G, Markus P B, Antoine W, Iacopo M, Senajith B R, Arnaud P A, Michael R D, Carl W C, Chao W L, Daniel J Z, James B M, Patrick P N, Anne R 2014 SPIE 9048 90480Y
[10] Han-Kwang N, Rilpho L D, Gosse C D V 2020 US Paten 20 200 152 345
[11] Christopher N A, Ryan H M, Patrick P N 2011 SPIE 7969 796938
[12] 袁天语, 邵尚坤, 孙学鹏, 李惠泉, 华陆, 孙天希 2023 72 034203
Google Scholar
Yuan T Y, Shao S K, Sun X P, Li H Q, Hua L, Sun T X 2023 Acta Phys. Sin. 72 034203
Google Scholar
[13] 班尼恩 V, 巴特瑞 P, 范格尔库姆 R, 阿门特 L, 彼得 D, 德维里斯 G, 栋克尔 R, 恩格尔伦 W, 弗里基恩斯 O, 格瑞米克 L, 卡塔伦尼克 A, 鲁普斯特拉 E, 尼恩惠斯 H K, 尼基帕罗夫 A, 瑞肯斯 M, 詹森 F, 克鲁兹卡 B 2019 CN Patent 110083019
[14] 肖艳芬, 朱菁, 杨宝喜, 胡中华, 曾爱军, 黄惠杰 2013 中国激光 40 0216001
Google Scholar
Xiao Y F, Zhu J, Yang B X, Hu Z H, Zeng A J, Huang H J 2013 Chin. J. Lasers 40 0216001
Google Scholar
[15] 李慧, 马钺洋, 尹皓玉, 韩晓泉, 黄宇峰, 吴晓斌 2024 激光与光电子进展 61 已录用
Google Scholar
Li H, Ma Y Y, Yin H Y, Han X Q, Huang Y F, Wu X B 2024 Laser Optoelectron. Prog. 61 in press
Google Scholar
[16] Akram M N, Tong Z M, Ouyang G M, Chen X Y, Kartashov V 2010 Appl. Opt. 49 3297
Google Scholar
[17] Li D Y, Kelly D P, Sheridan J T 2013 Appl. Opt. 52 8617
Google Scholar
[18] Hsiao Y N, Wu H P, Chen C H, Lin Y C, Lee M K, Liu S H 2014 Opt. Rev. 21 715
Google Scholar
[19] Sun M J, Lu Z K 2010 Opt. Eng. 49 024202
Google Scholar
[20] 李丽, 韩学勤, 赵士伟, 包鸿音, 王兴宾 2014 激光与光电子学进展 51 011401
Google Scholar
Li L, Han X Q, Zhao S W, Bao H Y, Wang X B 2014 Laser Optoelectron. Prog. 51 011401
Google Scholar
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