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极紫外光刻是目前新一代超高集成度半导体芯片制造流程中重要的一环, 激光诱导放电等离子体是极紫外光源产生的重要技术手段之一. 本文基于全局状态方程、原子结构计算程序、碰撞辐射模型建立了一个辐射磁流体力学模型, 对激光诱导放电等离子体的动力学特性及极紫外的辐射特性进行模拟, 模拟复现了放电过程中的箍缩现象, 得到的极紫外光的转化效率与实验符合. 研究发现放电电流的上升速率对极紫外光的产生有极大的影响, 该结果对后续极紫外光输出功率、转化效率以及光谱纯度的提升有重要的指导意义.
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关键词:
- 辐射磁流体力学 /
- 激光诱导放电等离子体 /
- 碰撞辐射模型 /
- 极紫外光
Extreme ultraviolet (EUV) light source is an important part of EUV lithography system in semiconductor manufacturing. The EUV light source requires that the 4p64dn-4p54dn+1 + 4dn–14f transitions of Sn8+~13+ ions emit thousands of lines which form unresolved transition arrays near 13.5 nm. Laser-induced discharge plasma is one of the important technical means to excite target into an appropriate plasma condition. Laser-induced discharge plasma has a simple structure and a low cost. It also has important applications in mask inspection, microscopic imaging, and spectral metrology. In the design and production process, there are many factors that can influence the conversion efficiency, such as current, electrode shape, and laser power density. The simulation method is a convenient way to provide guidance for optimizing the parameters. In this paper, a completed radiation magneto-hydrodynamic model is used to explore the dynamic characteristics of laser-induced discharge plasma and its EUV radiation characteristics. To improve the accuracy, a more detailed global equation of state model, an atomic structure calculation model including relativistic effect and a collision radiation model are proposed simultaneously. The simulation reconstructs the discharge process effectively, which is divided into five stages in the first half cycle of current, including expansion of laser plasma, column formation of discharge plasma, diffusion of discharge plasma, contraction of discharge plasma, and re-diffusion of discharge plasma. It is revealed that the pinch effect during the current rising time exerts a significant influence on the generation of EUV radiation. The conversion efficiency of EUV radiation is still low under our existing conditions, and hopefully a higher rising rate of current can improve the conversion efficiency in the future work.-
Keywords:
- radiation magneto-hydrodynamic /
- laser induced discharge plasma /
- collisional-radiative model /
- extreme ultraviolet
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图 1 激光诱导放电等离子体及其极紫外辐射磁流体模拟流程图
Fig. 1. Flow chart of radiative magneto-hydrodynamic simulation of LDP and its EUV radiation.
图 2 电子密度为1020 cm–3时, 不同电子温度条件下锡的离子组分以及平均电离度
Fig. 2. Charge state distributions, average ionization degrees of tin plasma at different electron temperatures when ne = 1020 cm–3.
图 3 电子温度为20 eV时, 不同电子密度下锡离子的电离态分布以及平均电离度
Fig. 3. Charge state distributions, average ionization degrees of tin plasma at different electron densities when Te = 20 eV.
图 4 激光诱导放电模拟过程中电流波形
Fig. 4. Simulation of current waveform during laser induced discharge.
图 5 放电过程中等离子密度模拟 (a) 320 ns; (b) 480 ns; (c) 720 ns; (d) 960 ns; (e) 1200 ns; (f) 1840 ns; (g) 2400 ns; (h) 2700 ns
Fig. 5. Simulation of plasma density during discharge: (a) 320 ns; (b) 480 ns; (c) 720 ns; (d) 960 ns; (e) 1200 ns; (f) 1840 ns; (g) 2400 ns; (h) 2700 ns.
图 6 放电过程中极紫外辐射功率密度模拟 (a) 480 ns; (b) 704 ns; (c) 382 ns; (d) 1008 ns; (e) 1152 ns; (f) 1328 ns; (g) 1504 ns; (h) 1712 ns
Fig. 6. Simulation of EUV radiation power during discharge: (a) 480 ns; (b) 704 ns; (c) 382 ns; (d) 1008 ns; (e) 1152 ns; (f) 1328 ns; (g) 1504 ns; (h) 1712 ns.
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[1] Wagner C, Harned N 2010 Nat. Photonics 4 24
Google Scholar
[2] Tallents G, Wagenaars E, Pert G 2010 Nat. Photonics 4 809
Google Scholar
[3] Schriever G, Semprez O R, Jonkers J, Yoshioka M, Apetz R 2012 J. Microlithogr. Microfabr. Microsyst. 11 021104
Google Scholar
[4] Pankert J, Bergmann K, Klein J, Neff W, Rosier O, Seiwert S, Smith C, Probst S, Vaudrevange D, Siemons G, et al. 2004 Emerging Lithographic Technologies VIII Santa Clara, California, May 20, 2004 p152
[5] Sayan S, Chakravorty K, Teramoto Y, Shirai T, Morimoto S, Watanabe H, Sato Y, Aoki K, Liang T, Tezuka Y, et al. 2021 Extreme Ultraviolet (EUV) Lithography XII San Jose, California, United States, March 23, 2021 p116090L
[6] Teramoto Y, Santos B, et al. 2014 Extreme Ultraviolet (EUV) Lithography V San Jose, California, United States, April 17, 2014 p904813
[7] Sayan S, Chakravorty K, Teramoto Y, Santos B, Nagano A, Ashizawa N, Shirai T, Morimoto S, Watanabe H, Aoki K, Sato Y 2023 Optical and EUV Nanolithography XXXVI San Jose, California, United States, May 26, 2023 pPC124940E
[8] Kruecken T 2007 AIP Conf. Proc. 901 181
Google Scholar
[9] Hassanein A, Sizyuk V A, Tolkach V I, Morozov V A, Rice B J 2004 J. Micro/Nanolithgr. MEMS MOEMS 3 130
Google Scholar
[10] Hassanein A, Sizyuk V, Sizyuk T 2008 Emerging Lithographic Technologies XII, San Jose, California, United States, March 20, 2008 p692113
[11] Zakharov V S, Juschkin L, Zakharov S V, O’Sullivan G, Sokel E, Tobin I 2012 International Workshop on EUV and Soft X-Ray Sources Dublin, Ireland, October 8–11, 2012 pS26
[12] Sasaki A, Nishihara K, Sunahara A, Furukawa H, Nishikawa T, Koike F 2010 Extreme Ultraviolet (EUV) Lithography San Jose, California, United States, March 22, 2010 p76363D
[13] Masnavi M, Nakajima M, Hotta E, Horioka K, Niimi G, Sasaki A 2007 J. Appl. Phys. 101 033306
Google Scholar
[14] Tsygvintsev I P, Krukovskiy A Y, Gasilov V A, Novikov V G, Romanov I V, Paperny V L, Rupasov A A 2016 Mathematical Models and Computer Simulations 8 595
Google Scholar
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Google Scholar
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Google Scholar
[17] 陈忠旺, 宁成 2017 物理学报 66 215202
Google Scholar
Cheng Z W, Ning C 2017 Acta Phys. Sin. 66 215202
Google Scholar
[18] Zakharov S V, Zakharov V S, Choi P, Krukovskiy A Y, Novikov V G, Solomyannaya A D, Berezin A V, Vorontsov A S, Markov M B, Parot’kin S V 2011 Extreme Ultraviolet (EUV) Lithography II San Jose, California, United States, April 8, 2011 p796932
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[20] Sasaki A, Sunahara A, Furukawa H, Nishihara K, Nishikawa T, Koike F 2016 J. Phys. Conf. 688 012099
Google Scholar
[21] Wang L J, Qian Z H, Huang X L, Jia S L 2013 IEEE T. Plasma Sci. 41 2015
Google Scholar
[22] Vovchenko E D, Melekhov A P V 2016 International Conference of Photonics and Information Optics Moscow, Russia, February 3–5, 2016 p012013
[23] More R M, Warren K H, Young D A, Zimmerman G B 1988 Phys. Fluids 31 3059
Google Scholar
[24] Sasaki A 2013 High Energ. Dens. Phys. 9 325
Google Scholar
[25] 汤文辉, 徐彬彬, 冉宪文, 徐志宏 2017 物理学报 66 030505
Google Scholar
Tang W H, Xu B B, Ran X W, Xu Z H 2017 Acta Phys. Sin. 66 030505
Google Scholar
[26] 段耀勇, 郭永辉, 邱爱慈 2011 核聚变与等离子体物理 31 2
Google Scholar
Duan Y Y, Guo Y H, Qiu A C 2011 Nucl. Fusion Plasma Phys. 31 2
Google Scholar
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Google Scholar
Duan Y Y, Guo Y H, Qiu A C, Wu G 2010 Acta Phys. Sin. 59 5588
Google Scholar
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Google Scholar
Han X Y, Li L X, Dai Z S, Zheng W D, Gu P J, Wu Z Q 2021 Acta Phys. Sin. 70 115202
Google Scholar
[30] Vichev I Y, Solomyannaya A D, Grushin A S, Kim D A 2019 High Energ. Dens. Phys. 33 100713
Google Scholar
[31] Gu M F 2004 AIP Conf. Proc. 730 127
Google Scholar
[32] Han B, Wang F, Salzmann D, Zhao G 2015 Publ. Astron. Soc. Jpn. 67 29
Google Scholar
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Google Scholar
[34] 王均武, 王新兵, 左都罗 2020 激光技术 44 173
Google Scholar
Wang J W, Wang X B, Zuo D L 2020 Laser Technology 44 173
Google Scholar
[35] Xie Z, Wu J, Dou Y P, Lin J Q, Tomie T 2019 AIP Adv. 9 085029
Google Scholar
[36] Wang J W, Wang X B, Zuo D L, Zakharov V S 2021 Chin. Phys. B 30 095207
Google Scholar
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