Flow simulation of tin plasma in the collection mirror chamber of EUV lithography machine

doi:10.7523/j.ucas.2026.027

Abstract

Abstract: Based on the multi-component Navier-Stokes (N-S) equations, a User-Defined Function (UDF) source term program compatible with the CFD simulation software FLUENT was developed. This program facilitated the incorporation of mass, momentum, and energy source terms into the N-S equations. Building upon this foundation, the dynamic diffusion process of tin plasma within the collecting mirror chamber of an EUV lithography machine was simulated, and the impact of background hydrogen pressure (20~150 Pa) and flow rate (100~300 m/s) on the spatial distribution of tin plasma was analyzed. The results indicate that during a single laser pulse cycle, the kinetic energy of tin plasma is swiftly transferred to the background hydrogen in the form of a compression wave, resulting in a limited diffusion distance for the tin plasma. Under multi-pulse conditions, the tin plasma gradually accumulates, and Kelvin-Helmholtz instability emerges, driven by the axial flow of the background gas. An increase in background hydrogen pressure reduces the radial (perpendicular to the flow direction) transport distance of tin plasma, while exerting a negligible effect on the axial transport distance. Conversely, an increase in background hydrogen flow rate decreases the radial transport distance and increases the axial transport distance of tin plasma. By integrating data from various operating conditions, this study establishes a quantitative relationship between the radial dimensionless transport distance of tin plasma and the Reynolds number.

Key words: EUV lithography, Sn plasma, multicomponent fluid, Fluent, UDF development

CLC Number:

O368

LI Jinming, YU Xingang. Flow simulation of tin plasma in the collection mirror chamber of EUV lithography machine[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2026.027.

References

[1] Versolato O O.Physics of laser-driven tin plasma sources of EUV radiation for nanolithography[J]. Plasma Sources Science and Technology, 2019, 28(8): 083001. DOI:10.1088/1361-6595/ab3302.
[2] Tomie T.Tin laser-produced plasma as the light source for extreme ultraviolet lithography high-volume manufacturing: History, ideal plasma, present status, and prospects[J]. Journal of Micro/Nanolithography, MEMS, and MOEMS, 2012, 11(2): 021109-1. DOI:10.1117/1.JMM.11.2.021109.
[3] DOLGOV A, LOPAEV D, RACHIMOVA T, et al.Comparison of H₂ and He carbon cleaning mechanisms in extreme ultraviolet induced and surface wave discharge plasmas[J]. Journal of Physics D: Applied Physics, 2014, 47(6): 065205. DOI:10.1088/0022-3727/47/6/065205.
[4] Braginsky O V, Kovalev A S, Lopaev D V, et al.Removal of amorphous C and Sn on Mo:Si multilayer mirror surface in Hydrogen plasma and afterglow[J/OL]. Journal of Applied Physics, 2012, 111(9): 093304. DOI:10.1063/1.4709408.
[5] Banine V Y, Koshelev K N, Swinkels G H P M. Physical processes in EUV sources for microlithography[J]. Journal of Physics D: Applied Physics, 2011, 44(25): 253001. DOI:10.1088/0022-3727/44/25/253001.
[6] 刘司. 脉冲光纤激光烧蚀液滴锡等离子体的模拟[D].武汉:华中科技大学,2022.DOI:10.27157/d.cnki.ghzku.2022.001452.
[7] 王均武, 玄洪文, 王新兵, 等. 激光诱导放电等离子体极紫外光源的研究[J]. 中国激光, 2024, 51(7): 0701012. DOI:10.3788/CJL231488
[8] Astakhov D.Numerical study of extreme-ultra-violet generated plasmas in hydrogen[D]. Enschede, The Netherlands: University of Twente, 2016. DOI:10.3990/1.9789036541114.
[9] Elg D T, Panici G A, Liu S M, et al.Removal of Tin from Extreme Ultraviolet Collector Optics by In-Situ Hydrogen Plasma Etching[J]. Plasma Chemistry and Plasma Processing, 2018, 38(1): 223-245. DOI:10.1007/s11090-017-9852-4.
[10] van de Kerkhof M A, Yakunin A, Kvon V, et al. Understanding EUV-induced plasma and application to particle contamination control in EUV scanners[C]//Extreme Ultraviolet (EUV) Lithography XI. February 23-27, 2020. San Jose, USA. SPIE, 2020: 29. DOI:10.1117/12.2551020.
[11] 张宇强, 余新刚. 多脉冲EUV诱导氢等离子体的PIC-漂移扩散混合模型数值模拟研究[J]. 中国科学院大学学报, DOI: 10.7523/j.ucas.2024.049.
[12] Meng W S, Zhao C B, Wu J Z, et al.Simulation of flow and debris migration in extreme ultraviolet source vessel[J]. Physics of Fluids, 2024, 36(2): 023322. DOI:10.1063/5.0190136.
[13] 冯宇轩, 罗坤, 樊建人. 静电除尘器中纳米颗粒运动与荷电特性[J]. 中国科学院大学学报, 2021, 38(3): 297-305. DOI:10.7523/j.issn.2095-6134.2021.03.002.
[14] Horr R, Rebhi R, Didi F, et al.Numerical simulation of dynamic and thermal behavior of plasma jet interacting with substrate[J]. Results in Engineering, 2025, 27: 106125. DOI:10.1016/j.rineng.2025.106125.
[15] Zhu H L, Li X Y, Tong H H.Three-dimensional numerical simulation of physical field distribution of radio frequency thermal plasma[J]. Acta Physica Sinica, 2021, 70(15): 155202. DOI:10.7498/aps.70.20202135.
[16] 谢文军, 陈文波, 陈伦江, 等. 不同工作气体下直流电弧等离子体特性的数值模拟研究[J]. 真空科学与技术学报, 2025, 45(4): 272-277. DOI:10.13922/j.cnki.cjvst.202409009.
[17] 陈文波, 陈伦江, 刘川东, 等. 直流电弧等离子体炬的数值模拟研究[J]. 真空, 2019, 56(1): 56-58. DOI:10.13385/j.cnki.vacuum.2019.01.12.
[18] Sakhraji M, Ramos A, Monteiro E, et al.Plasma gasification process using computational fluid dynamics modeling[J]. Energy Reports, 2022, 8: 1541-1549. DOI:10.1016/j.egyr.2022.08.069.
[19] Selezneva S E, Boulos M I, van de Sanden M M, et al. Stationary supersonic plasma expansion: Continuum fluid mechanics versus direct simulation Monte Carlo method[J]. Journal of Physics D: Applied Physics, 2002, 35(12): 1362-1372. DOI:10.1088/0022-3727/35/12/312.
[20] Fernando H J S. Turbulent mixing in stratified fluids[J]. Annual Review of Fluid Mechanics, 1991, 23: 455-493. DOI:10.1146/annurev.fl.23.010191.002323.
[21] Chapman S, Cowling T G.The mathematical theory of non-uniform gases: an account of the kinetic theory of viscosity, thermal conduction and diffusion in gases[M]. Cambridge university press, 1990.
[22] Assael M J, Mixafendi S, Wakeham W A.The Viscosity and Thermal Conductivity of Normal Hydrogen in the Limit of Zero Density[J]. Journal of Physical and Chemical Reference Data, 1986, 15(4): 1315-1322. DOI:10.1063/1.555764.
[23] Neufeld P D, Janzen A R, Aziz R A.Empirical equations to calculate 16 of the transport collision integrals Ω (l, s)* for the Lennard-Jones (12-6) potential[J]. The Journal of chemical physics, 1972, 57(3): 1100-1102. DOI:10.1063/1.1678363.
[24] Owuna F J, Chapoy A, Ahmadi P, et al.Viscosity of Hydrogen and Methane Blends: Experimental and Modelling Investigations[J]. International Journal of Thermophysics, 2024, 45(8): 119. DOI:10.1007/s10765-024-03394-4.
[25] Dorsman C, Onnes H K, Weber S.Investigation on the viscosity of gases at low temperatures. I. Hydrogen[C]//KNAW, Proceedings. 1913, 15: 1912-1913.
[26] 吴江涛, 周永. 标准氢的黏度方程[J]. 化工学报, 2011, 62(2): 301-306.
[27] Cussler E L.Diffusion: mass transfer in fluid systems [M]. 3rd ed. Cambridge, U.K.: Cambridge University Press, 2009.
[28] Versolato O O, Sheil J, Witte S, et al.Microdroplet-tin plasma sources of EUV radiation driven by solid-state-lasers (Topical Review)[J]. Journal of Optics, 2022, 24(5): 054014. DOI:10.1088/2040-8986/ac5a7e.
[29] 邓巍巍, 翟天琪, 高立豪, 等. 面向EUV光源的实验流体力学研究进展[J]. 力学进展, 2024, 54(1): 138-172. DOI:10.6052/1000-0992-23-044.
[30] Brandt D C, Fomenkov I V, Farrar N R, et al.LPP EUV source readiness for NXE 3300B[C]//Extreme Ultraviolet (EUV) Lithography V. San Jose, California, USA. SPIE, 2014: 90480C. DOI:10.1117/12.2048184.
[31] Pstruś J, Moser Z, Gąsior W, et al.Surface tension and density measurements of liquid Sn-Zn alloys. experiment vs. SURDATdatabase of Pb-free solders[J]. Archives of Metallurgy and Materials, 2006, 51: 335-343.
[32] Pstruś J.Surface tension and density of liquid In-Sn-Zn alloys[J]. Applied Surface Science, 2013, 265: 50-59. DOI:10.1016/j.apsusc.2012.10.098.
[33] Chen Y Y, Zhao C X, Pan Q K, et al.Experimental study on the temporal evolution parameters of laser-produced tin plasma under different laser pulse energies for LPP-EUV source[J]. Photonics, 2023, 10(12): 1339. DOI:10.3390/photonics10121339.