Simulation of extreme ultraviolet radiation of laser induced discharge plasma

Wang Jun-Wu; Xuan Hong-Wen; Yu Hang-Hang; Wang Xin-Bing; Vassily S. Zakharov

doi:10.7498/aps.73.20231158

Abstract

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 + 4d^n–14f transitions of Sn^8+~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:

Authors and contacts

1.
GBA Research Institute of AIRCAS, Guangzhou 510700, China
2.
Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
3.
Keldysh Institute of Applied Mathematics, Moscow 125047, Russia
4.
University of Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: Xuan Hong-Wen, xuanhw@aircas.ac.cn

Funds: Project supported by the Basic and Applied Basic Research Project of Guangzhou, China (Grant No. 2023A04J0024), the Talent Introduction Program of Chinese Academy of Sciences, China (Grant No. E33310030D), and the Aerospace Information Innovation Research Institute, Chinese Academy of Sciences, China (Grant Nos. E1Z1D101, E2Z2D101).

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References

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[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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[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

Cited By

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

Figure 1. Flow chart of radiative magneto-hydrodynamic simulation of LDP and its EUV radiation.

DownLoad: Full-Size Img PowerPoint

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

Figure 2. Charge state distributions, average ionization degrees of tin plasma at different electron temperatures when n_e = 10²⁰ cm^–3.

DownLoad: Full-Size Img PowerPoint

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

Figure 3. Charge state distributions, average ionization degrees of tin plasma at different electron densities when T_e = 20 eV.

DownLoad: Full-Size Img PowerPoint

图 4 激光诱导放电模拟过程中电流波形

Figure 4. Simulation of current waveform during laser induced discharge.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 7 放电等离子体羽辉图像^[34]　(a) 300 ns; (b) 450 ns; (c) 600 ns; (d) 750 ns; (e) 900 ns; (f) 1050 ns; (g) 1200 ns; (h) 1350 ns; (i) 1500 ns

Figure 7. Discharge plasma plume images^[34]: (a) 300 ns; (b) 450 ns; (c) 600 ns; (d) 750 ns; (e) 900 ns; (f) 1050 ns; (g) 1200 ns; (h) 1350 ns; (i) 1500 ns.

DownLoad: Full-Size Img PowerPoint

图 8 放电过程中光辐射总功率及极紫外辐射功率时域波形

Figure 8. Waveforms of total optical radiation power and EUV power during discharge.

DownLoad: Full-Size Img PowerPoint

map

[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
[15]	Beyene G A, Tobin I, Juschkin L, Hayden P, O’Sullivan G, Sokell E, Zakharov V S, Zakharov S V, O’Reilly F 2016 J. Phys. D: Appl. Phys. 49 225201 Google Scholar
[16]	吴福源, 禇衍运, 叶繁, 李正宏, 杨建伦, Ramis R, 王真, 祁建敏, 周林, 梁川 2017 66 215201 Google Scholar Wu F Y, Chu Y Y, Ye F, Li Z H, Yang J L, Ramis R, Wang Z, Qi J M, Zhou L, Liang C 2017 Acta Phys. Sin. 66 215201 Google Scholar
[17]	陈忠旺, 宁成 2017 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
[19]	Zakharov V S 2017 The International Photonics and Optoelectronics Meeting, Wuhan, China, November 3–5, 2017 pASu4A.1
[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 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
[27]	段耀勇, 郭永辉, 邱爱慈, 吴刚 2010 59 5588 Google Scholar Duan Y Y, Guo Y H, Qiu A C, Wu G 2010 Acta Phys. Sin. 59 5588 Google Scholar
[28]	Dunning F B, Hulet R G 1997 Atomic, Molecular, and Optical Physics: Charged Particles (San Diego: Academic Press) p169
[29]	韩小英, 李凌霄, 戴振生, 郑无敌, 谷培俊, 吴泽清 2021 70 115202 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
[33]	Zeng J L, Gao C, Yuan J M 2010 Phys. Rev. E 82 026409 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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