Journal of University of Chinese Academy of Sciences >
Numerical simulation of PIC-drift-diffusion hybrid model for multi-pulse EUV-induced hydrogen plasma
Received date: 2024-04-12
Accepted date: 2024-05-14
Online published: 2024-06-04
Based on the PIC-drift-diffusion hybrid model, a two-dimensional cylindrical-coordinate hybrid model computational procedure suitable for EUV-induced plasma has been developed, which fully takes into account the characteristics of EUV-induced plasma, and adopts the PIC method to track the motion process of ions, and adopts the drift-diffusion model to deal with electrons rapidly entering the quasi-equilibrium state. Based on this hybrid model, the long-time dynamic evolution of multi-pulse EUV-induced H plasma is simulated. The results show that the hybrid model can accurately describe the dynamical behavior of the plasma, and also significantly improve the computational efficiency and expand the time scale. The plasma evolution shows a certain cumulative effect, with the increase of the number of EUV pulses, the average density of the H plasma gradually rises, the average kinetic energy of the electrons gradually decreases, and the flux of H ions reaching the wall gradually increases, all of these parameters tend to stabilize after the number of pulses reaches a certain value. In addition, the pressure of the background gas has a significant effect on the multi-pulse cumulative effect, and the plasma parameters require more pulses to reach a steady state as the background gas pressure increases.
Yuqiang ZHANG , Xingang YU . Numerical simulation of PIC-drift-diffusion hybrid model for multi-pulse EUV-induced hydrogen plasma[J]. Journal of University of Chinese Academy of Sciences, 2026 , 43(3) : 316 -325 . DOI: 10.7523/j.ucas.2024.049
| [1] | van de Kerkhof M A, Benschop J P H, Banine V Y. Lithography for now and the future[J]. Solid-State Electronics, 2019, 155: 20-26. DOI: 10.1016/j.sse.2019.03.006 . |
| [2] | Morgan C G, Naulleau P P, Rekawa S B, et al. Removal of surface contamination from EUV mirrors using low-power downstream plasma cleaning[C]// Extreme Ultraviolet (EUV) Lithography. SPIE, 2010, 7636:595-604. DOI: 10.1117/12.846386 . |
| [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]. Journal of Applied Physics, 2012, 111(9): 093304. DOI: 10.1063/1.4709408 . |
| [5] | Beckers J, van de Ven T, van de Horst R, et al. EUV-induced plasma: a peculiar phenomenon of a modern lithographic technology[J]. Applied Sciences, 2019, 9(14): 2827. DOI: 10.3390/app9142827 . |
| [6] | van der Velden M H L, Brok W J M, van der Mullen J J A M, et al. Particle-in-cell Monte Carlo simulations of an extreme ultraviolet radiation driven plasma[J]. Physical Review E, 2006, 73(3): 036406. DOI: 10.1103/physreve.73.036406 . |
| [7] | Astakhov D I, Goedheer W J, Lee C J, et al. Exploring the electron density in plasma induced by EUV radiation: Ⅱ. Numerical studies in argon and hydrogen[J]. Journal of Physics D: Applied Physics, 2016, 49(29): 295204. DOI: 10.1088/0022-3727/49/29/295204 . |
| [8] | van der Horst R M, Beckers J, Osorio E A, et al. Exploring the electron density in plasma induced by EUV radiation: Ⅰ. Experimental study in hydrogen[J]. Journal of Physics D: Applied Physics, 2016, 49(14): 145203. DOI: 10.1088/0022-3727/49/14/145203 . |
| [9] | Brandt D C, Fomenkov I V, Farrar N R, et al. LPP EUV source readiness for NXE 3300B[C]// Extreme Ultraviolet (EUV) Lithography V. SPIE, 2014, 9048: 69-76. DOI: 10.1117/12.2048184 . |
| [10] | van der Horst R M. Electron dynamics in EUV-induced plasmas[D]. Eindhoven University of Technology: Eindhoven, The Netherlands, 2015. |
| [11] | van de Kerkhof M, Yakunin A M, Astakhov D, et al. EUV-induced hydrogen plasma: pulsed mode operation and confinement in scanner[J]. Journal of Micro/Nanopatterning, Materials, and Metrology, 2021, 20(3): 033801. DOI: 10.1117/1.jmm.20.3.033801 . |
| [12] | van de Ven T H M. Ion fluxes towards surfaces exposed to EUV-induced plasmas[D]. Eindhoven University of Technology: Eindhoven, The Netherlands, 2018. |
| [13] | Yakshinskiy B V, Wasielewski R, Loginova E, et al. Carbon accumulation and mitigation processes, and secondary electron yields of ruthenium surfaces[C]// Emerging Lithographic Technologies XI. SPIE, 2007, 6517:875-885. DOI: 10.1117/12.711785 . |
| [14] | Henke B L, Smith J A, Attwood D T. 0.1-10 keV x-ray-induced electron emissions from solids: models and secondary electron measurements[J]. Journal of Applied Physics, 1977, 48(5): 1852-1866. DOI: 10.1063/1.323938 . |
| [15] | Birdsall C K, Langdon A B. Plasma physics via computer simulation[M]. Boca Raton, Florida, USA: CRC Press, 2018. DOI: 10.1201/9781315275048 . |
| [16] | Chung Y M, Lee E M, Masuoka T, et al. Dissociative photoionization of H2 from 18 to 124 eV[J]. The Journal of Chemical Physics, 1993, 99(2): 885-889. DOI: 10.1063/1.465352 . |
| [17] | Kossmann H, Schwarzkopf O, Kammerling B, et al. Photoionisation cross section of H2 [J]. Journal of Physics B: Atomic, Molecular and Optical Physics, 1989, 22(14): L411-L414. DOI: 10.1088/0953-4075/22/14/004 . |
| [18] | van der Velden M H L, Brok W J M, van der Mullen J J A M, et al. Kinetic simulation of an extreme ultraviolet radiation driven plasma near a multilayer mirror[J]. Journal of Applied Physics, 2006, 100(7): 073303. DOI: 10.1063/1.2356085 . |
| [19] | Yoon J S, Song M Y, Han J M, et al. Cross sections for electron collisions with hydrogen molecules[J]. Journal of Physical and Chemical Reference Data, 2008, 37(2): 913-931. DOI: 10.1063/1.2838023 . |
| [20] | Tabata T, Shirai T. Analytic cross sections for collisions of H+, H2 +, H3 +, H, H2, and H- with hydrogen molecules[J]. Atomic Data and Nuclear Data Tables, 2000, 76(1): 1-25. DOI: 10.1006/adnd.2000.0835 . |
| [21] | Nanbu K. Probability theory of electron-molecule, ion-molecule, molecule-molecule, and Coulomb collisions for particle modeling of materials processing plasmas and cases[J]. IEEE Transactions on Plasma Science, 2000, 28(3): 971-990. DOI: 10.1109/27.887765 . |
| [22] | Economou D J. Hybrid simulation of low temperature plasmas: a brief tutorial[J]. Plasma Processes and Polymers, 2017, 14(1/2): 1600152. DOI: 10.1002/ppap.201600152 . |
| [23] | Hagelaar G J M, Kroesen G M W. Speeding up fluid models for gas discharges by implicit treatment of the electron energy source term[J]. Journal of Computational Physics, 2000, 159(1): 1-12. DOI: 10.1006/jcph.2000.6445 . |
| [24] | Hagelaar G J M, Pitchford L C. Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models[J]. Plasma Sources Science Technology, 2005, 14(4): 722-733. DOI: 10.1088/0963-0252/14/4/011 . |
| [25] | Ellis H W, Pai R Y, McDaniel E W, et al. Transport properties of gaseous ions over a wide energy range[J]. Atomic Data and Nuclear Data Tables, 1976, 17(3): 177-210. DOI: 10.1016/0092-640X(76)90001-2 . |
/
| 〈 |
|
〉 |