Numerical investigation of low pressure inductively coupled plasma sources: A review

Zhang Yu-Ru; Gao Fei; Wang You-Nian

doi:10.7498/aps.70.20202247

Abstract

Inductively coupled plasmas have been widely used in the etch process due to the high plasma density, simple reactor geometry, etc. Since the plasma characteristics are difficult to understand only via experiments, the numerical study seems to be a valuable and effective tool, which could help us to gain an in-depth insight into the plasma properties and the underlying mechanisms. During the past few years, various models have been employed to investigate inductive discharges, such as global model, fluid model, fluid/Monte Carlo collision hybrid model, biased sheath model, particle-in-cell/Monte Carlo collision hybrid model, etc. Since the plasma parameters are volume averaged in the global model, which effectively reduces the computational burden, it is usually used to study the reactive gas discharges with a complex chemistry set. In order to obtain the spatial distribution, a two-dimensional or three-dimensional fluid model is necessary. However, in the fluid model, the electron energy distribution function is assumed to be Maxwellian, which is invalid under special discharge conditions. For instance, strong electric field and low pressure may result in non-Maxwellian distributions, such as bi-Maxwellian distribution, two-temperature distribution, etc. Therefore, a fluid/Monte Carlo collision hybrid model is adopted to take the electron kinetics into account. Besides, a separate biased sheath model is necessary to study the influence of the sheath on the plasma properties self-consistently. The particle-in-cell/Monte Carlo collision hybrid model is a fully kinetic method based on the first-principles, which could be used to investigate the non-local and non-thermal equilibrium phenomena. In conclusion, the numerical investigation of inductively coupled plasmas has a significant importance for plasma process optimization.

Keywords:

Authors and contacts

Key Laboratory of Materials Modification by Laser, Ion, and Electron Beams, Ministry of Education, School of Physics, Dalian University of Technology, Dalian 116024, China

Corresponding author: Wang You-Nian, ynwang@dlut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11875101, 11935005), the Natural Science Foundation of Liaoning Province, China (Grant No. 2020-MS-114), and the Fundamental Research Fund for the Central Universities, China (Grant Nos. DUT20LAB201, DUT21LAB110)

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References

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Cited By

图 1 多时间尺度和多空间尺度变化示意图

Figure 1. Schematic diagram of multi-scale variations.

DownLoad: Full-Size Img PowerPoint

图 2 (a)气压为20 mTorr (1 mTorr ≈ 0.133 Pa)时Ar/H₂放电^[21]和(b)气压为30 mTorr时Ar/N₂放电^[22]中的正离子密度

Figure 2. Positive ion densities calculated in (a) Ar/H₂ discharges at 20 mTorr and (b) Ar/N₂ discharges at 30 mTorr. Reprinted from Ref. [21, 22], with the permission of AIP Publishing.

DownLoad: Full-Size Img PowerPoint

图 3 SF₆/Ar放电中, 当Ar含量为30%时, F原子的(a)产生和(b)损失速率^[25]

Figure 3. Relative (a) creation and (b) loss reaction rates of F atoms, as a function of pressure, for Ar fraction of 30% in the SF₆/Ar plasma. Reprinted with permission from Ref. [25]. Copyright [2016], American Vacuum Society.

DownLoad: Full-Size Img PowerPoint

图 4 当气压分别为(a) 50 mTorr和(b) 5 mTorr时, 双腔室ICP中的电子密度分布^[31]

Figure 4. Two dimensional distribution of the electron density in the considered two-chamber ICP source for 50 mTorr (a) and 5 mTorr (b). Reprinted from Ref. [31], with the permission of AIP Publishing.

DownLoad: Full-Size Img PowerPoint

图 5 不同低频频率下的离子密度分布　(a) 6.78 MHz; (b) 4.52 MHz; (c) 3.39 MHz; (d) 2.26 MHz^[32]

Figure 5. Distributions of the ion density at different LFs: (a) 6.78 MHz; (b) 4.52 MHz; (c) 3.39 MHz; (d) 2.26 MHz. Reprinted from Ref. [32], with the permission of AIP Publishing.

DownLoad: Full-Size Img PowerPoint

图 6 (a)分布式多线圈ICP; (b)集成式多线圈ICP^[33]

Figure 6. (a) DM-ICP and (b) IMC-ICP source configurations. Reprinted with permission from Ref. [33]. Copyright (2016) The Japan Society of Applied Physics.

DownLoad: Full-Size Img PowerPoint

图 7 螺线管线圈示意图^[34]

Figure 7. Schematic diagram of the solenoid coil. Reprinted from Ref. [34], with the permission of AIP Publishing.

DownLoad: Full-Size Img PowerPoint

图 8 气压为50 mTorr时, 不同轴向位置处周期平均的EEDF^[43]

Figure 8. Pulse averaged $f\left( \varepsilon \right)$ at different heights at 50 mTorr. Reprinted from Ref. [43], with the permission of AIP Publishing.

DownLoad: Full-Size Img PowerPoint

图 9 不同气压下, 电子密度随串联电容的演化^[48]

Figure 9. Electron density ${n_{\rm{e}}}$ versus the matching capacitance ${C_1}$. Reprinted with permission from Ref. [48].

DownLoad: Full-Size Img PowerPoint

图 10 不同偏压幅值下, r = 7 cm处电离率的时空分布^[50]

Figure 10. Spatiotemporal distributions of the ionization rate at r = 7 cm at different bias voltages. Reprinted with permission from Ref. [50]. Copyright [2015], American Vacuum Society.

DownLoad: Full-Size Img PowerPoint

图 11 不同偏压频率及幅值下的离子能量角度分布^[51]

Figure 11. IEADFs versus RF bias frequencies and amplitudes. Reprinted from Ref. [51], with the permission of IOP Publishing.

DownLoad: Full-Size Img PowerPoint

[1]	Hittorf W 1884 Wiedemanns Ann. Phys. 21 90
[2]	Lieberman M A, Lichtenberg A J 2005 Principles of Plasma Discharges and Materials Processing (New York: Wiley) pp462, 463
[3]	Czerwiec T, Graves D B 2004 J. Phys. D: Appl. Phys. 37 2827 Google Scholar
[4]	Xu H J, Zhao S X, Zhang Y R, Gao F, Li X C, Wang Y N 2015 Phys. Plasmas 22 043508 Google Scholar
[5]	Wegner Th, Kullig C, Meichsner J 2017 Plasma Sources Sci. Technol. 26 025006 Google Scholar
[6]	Kim J H, Chung C W 2020 Phys. Plasmas 27 023503 Google Scholar
[7]	Lee M H, Lee K H, Hyun D S, Chung C W 2007 Appl. Phys. Lett. 90 191502 Google Scholar
[8]	Gao F, Zhao S X, Li X S, Wang Y N 2010 Phys. Plasmas 17 103507 Google Scholar
[9]	Moon J H, Kim K H, Hong Y H, Lee M Y, Chung C W 2020 Phys. Plasmas 27 033511 Google Scholar
[10]	Wegner Th, Kullig C, Meichsner J 2016 Phys. Plasmas 23 023503 Google Scholar
[11]	Lee H C, Lee M H, Chung C W 2010 Appl. Phys. Lett. 96 071501 Google Scholar
[12]	Schulze J, Schungel E, Czarnetzki U 2012 Appl. Phys. Lett. 100 024102 Google Scholar
[13]	Lanham S J, Kushner M J 2017 J. Appl. Phys. 122 083301 Google Scholar
[14]	Lee H W, Kim K H, Seo J I, Chung C W 2020 Phys. Plasmas 27 093508 Google Scholar
[15]	王建伟, 宋亦旭, 任天令, 李进春, 褚国亮 2013 物理学报 62 245202 Google Scholar Wang J W, Song Y X, Ren T L, Li J C, Chu G L 2013 Acta Phys. Sin. 62 245202 Google Scholar
[16]	张改玲, 滑跃, 郝泽宇, 任春生 2019 物理学报 68 105202 Google Scholar Zhang G L, Hua Y, Gao Z Y, Ren C S 2019 Acta Phys. Sin. 68 105202 Google Scholar
[17]	Gudmundsson J T 2001 Plasma Sources Sci. Technol. 10 76 Google Scholar
[18]	Thorsteinsson E G, Gudmundsson J T 2010 Plasma Sources Sci. Technol. 19 015001 Google Scholar
[19]	Thorsteinsson E G, Gudmundsson J T 2010 J. Phys. D: Appl. Phys. 43 115201 Google Scholar
[20]	Toneli D A, Pessoa R S, Roberto M, Gudmundsson J T 2015 J. Phys. D: Appl. Phys. 48 325202 Google Scholar
[21]	Kimura T, Kasugai H 2010 J. Appl. Phys. 107 083308 Google Scholar
[22]	Kimura T, Kasugai H 2010 J. Appl. Phys. 108 033305 Google Scholar
[23]	Thorsteinsson E G, Gudmundsson J T 2010 J. Phys. D: Appl. Phys. 43 115202 Google Scholar
[24]	Chanson R, Rhallabi A, Fernandez M C, Cardinaud C, Landesman J P 2013 J. Vac. Sci. Technol., A 31 011301 Google Scholar
[25]	Yang W, Zhao S X, Wen D Q, Liu W, Liu Y X, Li X C, Wang Y N 2016 J. Vac. Sci. Technol., A 34 031305 Google Scholar
[26]	Pateau A, Rhallabi A, Fernandez M C, Boufnichel M, Roqueta F 2014 J. Vac. Sci. Technol., A 32 021303 Google Scholar
[27]	Annusova A, Marinov D, Booth J P, Sirse N, Lino da Silva M, Lopez B, Guerra V 2018 Plasma Sources Sci. Technol. 27 045006 Google Scholar
[28]	Le Dain G, Rhallabi A, Girard A, Cardinaud C, Roqueta F, Boufnichel M 2019 Plasma Sources Sci. Technol. 28 085002 Google Scholar
[29]	Bukowski J D, Graves D B, Vitello P 1996 J. Appl. Phys. 80 2614 Google Scholar
[30]	Xu X, Rauf S, Kushner M J 2000 J. Vac. Sci. Technol., A 18 213 Google Scholar
[31]	Kudryavtsev A A, Serditov K Yu 2012 Phys. Plasmas 19 073504 Google Scholar
[32]	Sun X Y, Zhang Y R, Li X C, Wang Y N 2015 Phys. Plasmas 22 053508 Google Scholar
[33]	Brcka J 2016 Jpn. J. Appl. Phys. 55 07LD08 Google Scholar
[34]	Zheng B, Shrestha M, Wang K, Schuelke T, Shun’ko E, Belkin V, Fan Q H 2019 J. Appl. Phys. 126 123302 Google Scholar
[35]	Jeong Y D, Lee, Y J, Kwon D C, Choe H H 2017 Curr. Appl. Phys. 17 403 Google Scholar
[36]	Agarwal A, Bera K, Kenney J, Likhanskii A, Rauf S 2017 J. Phys. D: Appl. Phys. 50 424001 Google Scholar
[37]	Zhang A, Kim K H, Kwon D C, Chung C W 2019 Phys. Plasmas 26 083509 Google Scholar
[38]	Vahedi V, Surendra M 1995 Comput. Phys. Commun. 87 179 Google Scholar
[39]	Nanbu K 2000 IEEE Trans. Plasma Sci. 28 971 Google Scholar
[40]	Georgieva V 2006 Ph. D. Dissertation (Antwerp: University of Antwerp)
[41]	Sommerer T J, Kushner M J 1992 J. Appl. Phys. 71 1654 Google Scholar
[42]	Ventzek P L G, Hoekstra R J, Kushner M J 1994 J. Vac. Sci. Technol., B 12 461 Google Scholar
[43]	Logue M D, Kushner M J 2015 J. Appl. Phys. 117 043301 Google Scholar
[44]	Tinck S, Bogaerts A 2016 J. Phys. D: Appl. Phys. 49 195203 Google Scholar
[45]	Qu C, Nam S K, Kushner M J 2020 Plasma Sources Sci. Technol. 29 085006 Google Scholar
[46]	Tian P, Kushner M J 2017 Plasma Sources Sci. Technol. 26 024005 Google Scholar
[47]	Zhao S X, Wang Y N 2010 J. Phys. D: Appl. Phys. 43 275203 Google Scholar
[48]	Xu H J, Zhao S X, Gao F, Zhang Y R, Li X C, Wang Y N 2015 Chin. Phys. B 24 115201 Google Scholar
[49]	Kwon D C, Chang W S, Park M, You D H, Song M Y, You S J, Im Y H, Yoon J S 2011 J. Appl. Phys. 109 073311 Google Scholar
[50]	Zhang Y R, Gao F, Li X C, Bogaerts A, Wang Y N 2015 J. Vac. Sci. Technol., A 33 061303 Google Scholar
[51]	Wen D Q, Liu W, Gao F, Lieberman M A, Wang Y N 2016 Plasma Sources Sci. Technol. 25 045009 Google Scholar
[52]	Vahedi V, DiPeso G, Birdsall C K, Lieberman M A, Rognlien T D 1993 Plasma Sources Sci. Technol. 2 261 Google Scholar
[53]	Kawamura E, Birdsall C K, Vahedi V 2000 Plasma Sources Sci. Technol. 9 413 Google Scholar
[54]	Birdsall C K 1991 IEEE Trans. Plasma Sci. 19 65 Google Scholar
[55]	Takao Y, Kusaba N, Eriguchi K, Ono K 2010 J. Appl. Phys. 108 093309 Google Scholar
[56]	Takao Y, Eriguchi K, Ono K 2012 J. Appl. Phys. 112 093306 Google Scholar
[57]	Mattei S, Nishida K, Onai M, Lettry J, Tran M Q, Hatayama A 2017 J. Comput. Phys. 350 891 Google Scholar
[58]	Nishida K, Mattei S, Mochizuki S, Lettry J, Hatayama A 2016 J. Appl. Phys. 119 233302 Google Scholar
[59]	Nishida K, Mattei S, Lettry J, Hatayama A 2018 J. Appl. Phys. 123 043305 Google Scholar

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