Influence of dust particles on non-local kinetic behavior in low-pressure radio frequency plasma

ZHAO Yueyue; MIAO Yang; YANG Wei; DU Chengran

doi:10.7498/aps.74.20251096

Abstract

Low-pressure radio-frequency inductively coupled discharges can produce uniformly distributed monodisperse particles and plasma, making them widely used in nanodevice fabrication. The manufacturing of nanodevices typically requires the generation of particles ranging from nanometer to submicron scales. These particles usually carry negative charges and can significantly influence the discharge characteristics of the plasma. This study investigates the effects of particle size and density on electron bounce resonance heating (BRH) and fundamental plasma properties in low-pressure inductively coupled plasmas (ICPs) by using a hybrid model. The hybrid model consists of kinetic equation, electromagnetic field equation, and global model equation. The simulation results show that as the dust radius or density increases, the BRH effect characterized by the formation of a plateau in the probability function of electron energy, is gradually suppressed and eventually disappears, accompanied by a decrease in electron temperature, an increase in electron density, and an increase in particle surface potential. The dust charge decreases with the increase of particle density, while exhibiting a nonmonotonic variation with particle radius. The results show that the loss of high-energy electrons caused by the dust particles may create a more favorable plasma environment for the growth of monodisperse nanoparticles with low defects. Such an improvement in particle quality is crucial for reducing trap densities and enhancing the electrical performance of nanoparticle-based electronic devices.

Keywords:

Authors and contacts

College of Physics, Donghua University, Shanghai 201620, China

Corresponding author: YANG Wei, weiyang@dhu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12035003).

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References

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[46]	Wen H, Schulze J, Fu Y, Sun J Y, Zhang Q Z 2025 Plasma Sources Sci. Technol. 34 03LT01 Google Scholar
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[52]	Yang W, Wang Y N 2021 Plasma Phys. Control. Fusion 63 035031 Google Scholar
[53]	DiPeso G, Vahedi V, Hewett D W, Rognlien T D 1994 J. Vac. Sci. Technol. A 12 1387 Google Scholar
[54]	Belenguer Ph, Blondeau J Ph, Boufendi L, Toogood M, Plain A, Bouchoule A, Laure C, Boeuf J P 1992 Phys. Rev. A 46 7923 Google Scholar
[55]	Yang W, Gao F, Wang Y N 2022 Plasma Sci. Technol. 24 055401 Google Scholar
[56]	Yang W, Gao F, Wang Y N 2022 Phys. Plasmas 29 063503 Google Scholar
[57]	Allen J E 1992 Phys. Scr. 45 497 Google Scholar
[58]	Wood B P, Lieberman M A, Lichtenberg A J 1995 IEEE Trans. Plasma Sci. 23 89 Google Scholar

Cited By

图 1 模拟的腔室结构图

Figure 1. Chamber structure in the simulation.

DownLoad: Full-Size Img PowerPoint

图 2 模拟计算程序流程图

Figure 2. The flowchart of simulation.

DownLoad: Full-Size Img PowerPoint

图 3 不同尘埃半径(a), (b)与不同尘埃密度(c), (d)情况下EEPF及放大图

Figure 3. EEPF and zoomed-in plots for different dust radii (a), (b) and different dust densities (c), (d).

DownLoad: Full-Size Img PowerPoint

图 4 电子密度和电子温度随尘埃半径(a)与尘埃密度(b)的变化

Figure 4. Variation of electron temperature, electron density, and ion density with different dust radii (a) and dust densities (b).

DownLoad: Full-Size Img PowerPoint

图 5 尘埃带电量和表面电势随尘埃半径(a)与尘埃密度(b)的变化

Figure 5. Variation of dust charge and surface potential with different dust radii (a) and dust densities (b).

DownLoad: Full-Size Img PowerPoint

图 6 尘埃收集的电子流、离子流随尘埃半径的变化

Figure 6. Dust collected electron and ion currents under different dust radii.

DownLoad: Full-Size Img PowerPoint

[1]	Fortov V E, Ivlev A V, Khrapak S A, Khrapak A G, Morfill G E 2005 Phys. Rep. 421 1 Google Scholar
[2]	Merlino R L, Goree J A 2004 Phys. Today 57 32
[3]	Beckers J, Berndt J, Block D, Bonitz M, Bruggeman P J, Couëdel L, Delzanno G L, Feng Y, Gopalakrishnan R, Greiner F, Hartmann P, Horányi M, Kersten H, Knapek C A, Konopka U, Kortshagen U, Kostadinova E G, Kovačević E, Krasheninnikov S I, Mann I, Mariotti D, Matthews L S, Melzer A, Mikikian M, Nosenko V, Pustylnik M Y, Ratynskaia S, Sankaran R M, Schneider V, Thimsen E J, Thomas E, Thomas H M, Tolias P, Van De Kerkhof M 2023 Phys. Plasmas 30 120601 Google Scholar
[4]	Morfill G E, Ivlev A V 2009 Rev. Mod. Phys. 81 1353 Google Scholar
[5]	De La Cal E, Martín A, Carralero D, De Pablos J L, Pedrosa M A, Shoji M, Hidalgo C, the TJ-II Team 2013 Phys. Control. Fusion 55 065001 Google Scholar
[6]	Boufendi L, Bouchoule A 2002 Plasma Sources Sci. Technol. 11 A211 Google Scholar
[7]	Vladimirov S V, Ostrikov K 2004 Phys. Rep. 393 175 Google Scholar
[8]	Shukla P K, Eliasson B 2009 Rev. Mod. Phys. 81 25 Google Scholar
[9]	Kersten H, Deutsch H, Stoffels E, Stoffels W W, Kroesen G M W, Hippler R 2001 Contrib. Plasma Phys. 41 598 Google Scholar
[10]	杜诚然, 冯岩, 王晓钢 2022 载人航天 28 323 Du C R, Feng Y, Wang X G 2022 Manned Spaceflight 28 323
[11]	杨唯, 王垚楠, 梁颖悦, 黄晓江, 周鸿颖, 郭颖, 张菁, 冯岩, 王晓钢, 张立宪, 杜诚然 2025 中国科学: 物理学力学天文学 55 105206 Google Scholar Yang W, Wang Y N, Liang Y Y, Huang X J, Zhou H Y, Guo Y, Zhang J, Feng Y, Wang X G, Zhang L X, Du C R 2025 Sci. Sin. Phys. Mech. Astron. 55 105206 Google Scholar
[12]	Chu J H, Lin I 1994 Phys. Rev. Lett. 72 4009 Google Scholar
[13]	Thomas H, Morfill G E, Demmel V, Goree J, Feuerbacher B, Möhlmann D 1994 Phys. Rev. Lett. 73 652 Google Scholar
[14]	Liu B, Goree J, Feng Y 2010 Phys. Rev. Lett. 105 085004 Google Scholar
[15]	Du C R, Nosenko V, Thomas H M, Lin Y F, Morfill G E, Ivlev A V 2019 Phys. Rev. Lett. 123 185002 Google Scholar
[16]	Nunomura S, Zhdanov S, Samsonov D, Morfill G 2005 Phys. Rev. Lett. 94 045001 Google Scholar
[17]	Teng L W, Chang M C, Tseng Y P, I L 2009 Phys. Rev. Lett. 103 245005 Google Scholar
[18]	Couëdel L, Nosenko V, Ivlev A V, Zhdanov S K, Thomas H M, Morfill G E 2010 Phys. Rev. Lett. 104 195001 Google Scholar
[19]	Huang H, Ivlev A V, Nosenko V, Yang W, Du C R 2023 Phys. Rev. E 107 045205 Google Scholar
[20]	Huang D, Baggioli M, Lu S Y, Ma Z, Feng Y 2023 Phys. Rev. Res. 5 013149 Google Scholar
[21]	Killer C, Bockwoldt T, Schütt S, Himpel M, Melzer A, Piel A 2016 Phys. Rev. Lett. 116 115002 Google Scholar
[22]	Wysocki A, Räth C, Ivlev A V, Sütterlin K R, Thomas H M, Khrapak S, Zhdanov S, Fortov V E, Lipaev A M, Molotkov V I, Petrov O F, Löwen H, Morfill G E 2010 Phys. Rev. Lett. 105 045001 Google Scholar
[23]	Ivlev A V, Zhdanov S K, Thomas H M, Morfill G E 2009 Europhys. Lett. 85 45001 Google Scholar
[24]	Winter J 2000 Phys. Plasmas 7 3862 Google Scholar
[25]	Pigarov A Yu, Krasheninnikov S I, Soboleva T K, Rognlien T D 2005 Phys. Plasmas 12 122508 Google Scholar
[26]	Smirnov R D, Pigarov A Y, Rosenberg M, Krasheninnikov S I, Mendis D A 2007 Plasma Phys. Control. Fusion 49 347 Google Scholar
[27]	Kokura H, Yoneda S, Nakamura K, Mitsuhira N, Nakamura M, Sugai H 1999 Jpn. J. Appl. Phys. 38 5256 Google Scholar
[28]	Raha D, Das D 2013 Appl. Surf. Sci. 276 249 Google Scholar
[29]	Cheng Q, Xu S, Long J D, Ni Z H, Rider A E, Ostrikov K 2008 J. Phys. D: Appl. Phys. 41 055406 Google Scholar
[30]	Bapat A, Perrey C R, Campbell S A, Barry Carter C, Kortshagen U 2003 J. Appl. Phys. 94 1969 Google Scholar
[31]	Shen Z, Kortshagen U, Campbell S A 2004 J. Appl. Phys. 96 2204 Google Scholar
[32]	Shen Z, Kim T, Kortshagen U, McMurry P H, Campbell S A 2003 J. Appl. Phys. 94 2277 Google Scholar
[33]	Denysenko I B, Kersten H, Azarenkov N A 2015 Phys. Rev. E 92 033102 Google Scholar
[34]	Wang D Z, Dong J Q 1997 J. Appl. Phys. 81 38 Google Scholar
[35]	Denysenko I, Yu M Y, Ostrikov K, Smolyakov A 2004 Phys. Rev. E 70 046403 Google Scholar
[36]	Czarnetzki U, Alves L L 2022 Mod. Plasma Phys. 6 31 Google Scholar
[37]	Gu S, Kang H J, Kwon D C, Kim Y S, Chang Y M, Chung C W 2016 Phys. Plasmas 23 063506 Google Scholar
[38]	Kolobov V, Godyak V 2019 Phys. Plasmas 26 060601 Google Scholar
[39]	Liu Y X, Zhang Q Z, Jiang W, Hou L J, Jiang X Z, Lu W Q, Wang Y N 2011 Phys. Rev. Lett. 107 055002 Google Scholar
[40]	Chung C W, You K I, Seo S H, Kim S S, Chang H Y 2001 Phys. Plasmas 8 2992 Google Scholar
[41]	张钰如, 高飞, 王友年 2021 物理学报 70 095206 Google Scholar Zhang Y R, Gao F, Wang Y N 2021 Acta Phys. Sin. 70 095206 Google Scholar
[42]	Jia W Z, Zhang Q Z, Wang X F, Song Y H, Zhang Y Y, Wang Y N 2019 J. Phys. D: Appl. Phys. 52 015206 Google Scholar
[43]	De Bleecker K, Bogaerts A, Goedheer W 2004 Phys. Rev. E 70 056407 Google Scholar
[44]	Boeuf J P 1992 Phys. Rev. A 46 7910 Google Scholar
[45]	Alexandrov A L, Schweigert I V, Peeters F M 2008 New J. Phys. 10 093025 Google Scholar
[46]	Wen H, Schulze J, Fu Y, Sun J Y, Zhang Q Z 2025 Plasma Sources Sci. Technol. 34 03LT01 Google Scholar
[47]	Fu C C, Dong Y C, Li Y F, Wang W Z, Wang Z H, Liu W 2024 J. Phys. D: Appl. Phys. 57 135201 Google Scholar
[48]	Liu Y X, Zhang Q Z, Zhao K, Zhang Y R, Gao F, Song Y H, Wang Y N 2022 Chin. Phys. B 31 085202 Google Scholar
[49]	Li S, Rabadanov K M, Bogdanov E A, Kudryavtsev A A, Ashurbekov N A, Yuan C, Zhou Z 2021 Plasma Sources Sci. Technol. 30 047001 Google Scholar
[50]	Liang Y G, Wang Y, Li H, Tian R H, Yuan C X, Kudryavtsev A A, Rabadanov K M, Wu J, Zhou Z X, Tian H 2018 Phys. Plasmas 25 053702 Google Scholar
[51]	Fedoseev A V, Demin N A, Salnikov M V, Sukhinin G I 2019 Contrib. Plasma Phys. 59 e201800181 Google Scholar
[52]	Yang W, Wang Y N 2021 Plasma Phys. Control. Fusion 63 035031 Google Scholar
[53]	DiPeso G, Vahedi V, Hewett D W, Rognlien T D 1994 J. Vac. Sci. Technol. A 12 1387 Google Scholar
[54]	Belenguer Ph, Blondeau J Ph, Boufendi L, Toogood M, Plain A, Bouchoule A, Laure C, Boeuf J P 1992 Phys. Rev. A 46 7923 Google Scholar
[55]	Yang W, Gao F, Wang Y N 2022 Plasma Sci. Technol. 24 055401 Google Scholar
[56]	Yang W, Gao F, Wang Y N 2022 Phys. Plasmas 29 063503 Google Scholar
[57]	Allen J E 1992 Phys. Scr. 45 497 Google Scholar
[58]	Wood B P, Lieberman M A, Lichtenberg A J 1995 IEEE Trans. Plasma Sci. 23 89 Google Scholar

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