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低气压感性耦合等离子体源模拟研究进展

张钰如 高飞 王友年

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低气压感性耦合等离子体源模拟研究进展

张钰如, 高飞, 王友年

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

Zhang Yu-Ru, Gao Fei, Wang You-Nian
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  • 感性耦合等离子体源具有放电气压低、等离子体密度高、装置结构简单等优点, 因此常被用于材料刻蚀及表面处理工艺中. 为了深入了解感性耦合等离子体的特性及其与表面的相互作用, 数值模拟成为了目前人们普遍采用的研究手段之一. 针对具体问题, 可以选择不同的模拟方法, 如整体模型、流体力学模型、流体力学/蒙特卡罗碰撞混合模型、偏压鞘层模型、粒子模拟/蒙特卡罗碰撞混合模型等. 其中, 整体模型计算效率最高, 常被用于模拟复杂的反应性气体放电. 但整体模型无法给出各物理量的空间分布, 因此二维及三维的流体力学模型, 也得到了人们的广泛关注. 在低气压等极端的放电条件下, 由于电子能量分布函数显著偏离麦氏分布, 则需要耦合蒙特卡罗碰撞模型, 来精确地描述等离子体内部的动理学行为. 此外, 通过耦合偏压鞘层模型, 还可以自洽地模拟鞘层的瞬时振荡行为对等离子体特性的影响. 对于等离子体中的非局域及非热平衡现象, 则需要采用基于第一性原理的粒子模拟方法来描述. 最后对目前感性耦合放电中的前沿问题进行了展望.
    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.
      通信作者: 王友年, ynwang@dlut.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11875101, 11935005)、辽宁省自然科学基金(批准号: 2020-MS-114)和中央高校基本科研业务费专项资金(批准号: DUT20LAB201, DUT21LAB110)资助的课题
      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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    Hittorf W 1884 Wiedemanns Ann. Phys. 21 90

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    Lieberman M A, Lichtenberg A J 2005 Principles of Plasma Discharges and Materials Processing (New York: Wiley) pp462, 463

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    Czerwiec T, Graves D B 2004 J. Phys. D: Appl. Phys. 37 2827Google Scholar

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    Xu H J, Zhao S X, Zhang Y R, Gao F, Li X C, Wang Y N 2015 Phys. Plasmas 22 043508Google Scholar

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    Wegner Th, Kullig C, Meichsner J 2017 Plasma Sources Sci. Technol. 26 025006Google Scholar

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    Kim J H, Chung C W 2020 Phys. Plasmas 27 023503Google Scholar

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    Lee M H, Lee K H, Hyun D S, Chung C W 2007 Appl. Phys. Lett. 90 191502Google Scholar

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    Gao F, Zhao S X, Li X S, Wang Y N 2010 Phys. Plasmas 17 103507Google Scholar

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    Moon J H, Kim K H, Hong Y H, Lee M Y, Chung C W 2020 Phys. Plasmas 27 033511Google Scholar

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    Wegner Th, Kullig C, Meichsner J 2016 Phys. Plasmas 23 023503Google Scholar

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    Lee H C, Lee M H, Chung C W 2010 Appl. Phys. Lett. 96 071501Google Scholar

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    Schulze J, Schungel E, Czarnetzki U 2012 Appl. Phys. Lett. 100 024102Google Scholar

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    Lanham S J, Kushner M J 2017 J. Appl. Phys. 122 083301Google Scholar

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    Lee H W, Kim K H, Seo J I, Chung C W 2020 Phys. Plasmas 27 093508Google Scholar

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    王建伟, 宋亦旭, 任天令, 李进春, 褚国亮 2013 物理学报 62 245202Google Scholar

    Wang J W, Song Y X, Ren T L, Li J C, Chu G L 2013 Acta Phys. Sin. 62 245202Google Scholar

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    张改玲, 滑跃, 郝泽宇, 任春生 2019 物理学报 68 105202Google Scholar

    Zhang G L, Hua Y, Gao Z Y, Ren C S 2019 Acta Phys. Sin. 68 105202Google Scholar

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    Gudmundsson J T 2001 Plasma Sources Sci. Technol. 10 76Google Scholar

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    Thorsteinsson E G, Gudmundsson J T 2010 Plasma Sources Sci. Technol. 19 015001Google Scholar

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    Toneli D A, Pessoa R S, Roberto M, Gudmundsson J T 2015 J. Phys. D: Appl. Phys. 48 325202Google Scholar

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    Kimura T, Kasugai H 2010 J. Appl. Phys. 107 083308Google Scholar

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    Kimura T, Kasugai H 2010 J. Appl. Phys. 108 033305Google Scholar

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    Thorsteinsson E G, Gudmundsson J T 2010 J. Phys. D: Appl. Phys. 43 115202Google Scholar

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    Chanson R, Rhallabi A, Fernandez M C, Cardinaud C, Landesman J P 2013 J. Vac. Sci. Technol., A 31 011301Google Scholar

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    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 031305Google Scholar

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    Pateau A, Rhallabi A, Fernandez M C, Boufnichel M, Roqueta F 2014 J. Vac. Sci. Technol., A 32 021303Google Scholar

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    Annusova A, Marinov D, Booth J P, Sirse N, Lino da Silva M, Lopez B, Guerra V 2018 Plasma Sources Sci. Technol. 27 045006Google Scholar

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    Le Dain G, Rhallabi A, Girard A, Cardinaud C, Roqueta F, Boufnichel M 2019 Plasma Sources Sci. Technol. 28 085002Google Scholar

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    Bukowski J D, Graves D B, Vitello P 1996 J. Appl. Phys. 80 2614Google Scholar

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    Xu X, Rauf S, Kushner M J 2000 J. Vac. Sci. Technol., A 18 213Google Scholar

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    Kudryavtsev A A, Serditov K Yu 2012 Phys. Plasmas 19 073504Google Scholar

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    Sun X Y, Zhang Y R, Li X C, Wang Y N 2015 Phys. Plasmas 22 053508Google Scholar

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    Brcka J 2016 Jpn. J. Appl. Phys. 55 07LD08Google Scholar

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    Zheng B, Shrestha M, Wang K, Schuelke T, Shun’ko E, Belkin V, Fan Q H 2019 J. Appl. Phys. 126 123302Google Scholar

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    Jeong Y D, Lee, Y J, Kwon D C, Choe H H 2017 Curr. Appl. Phys. 17 403Google Scholar

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    Agarwal A, Bera K, Kenney J, Likhanskii A, Rauf S 2017 J. Phys. D: Appl. Phys. 50 424001Google Scholar

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    Zhang A, Kim K H, Kwon D C, Chung C W 2019 Phys. Plasmas 26 083509Google Scholar

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    Vahedi V, Surendra M 1995 Comput. Phys. Commun. 87 179Google Scholar

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    Nanbu K 2000 IEEE Trans. Plasma Sci. 28 971Google Scholar

    [40]

    Georgieva V 2006 Ph. D. Dissertation (Antwerp: University of Antwerp)

    [41]

    Sommerer T J, Kushner M J 1992 J. Appl. Phys. 71 1654Google Scholar

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    Ventzek P L G, Hoekstra R J, Kushner M J 1994 J. Vac. Sci. Technol., B 12 461Google Scholar

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    Logue M D, Kushner M J 2015 J. Appl. Phys. 117 043301Google Scholar

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    Tinck S, Bogaerts A 2016 J. Phys. D: Appl. Phys. 49 195203Google Scholar

    [45]

    Qu C, Nam S K, Kushner M J 2020 Plasma Sources Sci. Technol. 29 085006Google Scholar

    [46]

    Tian P, Kushner M J 2017 Plasma Sources Sci. Technol. 26 024005Google Scholar

    [47]

    Zhao S X, Wang Y N 2010 J. Phys. D: Appl. Phys. 43 275203Google Scholar

    [48]

    Xu H J, Zhao S X, Gao F, Zhang Y R, Li X C, Wang Y N 2015 Chin. Phys. B 24 115201Google Scholar

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    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 073311Google Scholar

    [50]

    Zhang Y R, Gao F, Li X C, Bogaerts A, Wang Y N 2015 J. Vac. Sci. Technol., A 33 061303Google Scholar

    [51]

    Wen D Q, Liu W, Gao F, Lieberman M A, Wang Y N 2016 Plasma Sources Sci. Technol. 25 045009Google Scholar

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    Vahedi V, DiPeso G, Birdsall C K, Lieberman M A, Rognlien T D 1993 Plasma Sources Sci. Technol. 2 261Google Scholar

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    Kawamura E, Birdsall C K, Vahedi V 2000 Plasma Sources Sci. Technol. 9 413Google Scholar

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    Takao Y, Kusaba N, Eriguchi K, Ono K 2010 J. Appl. Phys. 108 093309Google Scholar

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    Takao Y, Eriguchi K, Ono K 2012 J. Appl. Phys. 112 093306Google Scholar

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    Mattei S, Nishida K, Onai M, Lettry J, Tran M Q, Hatayama A 2017 J. Comput. Phys. 350 891Google Scholar

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    Nishida K, Mattei S, Mochizuki S, Lettry J, Hatayama A 2016 J. Appl. Phys. 119 233302Google Scholar

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    Nishida K, Mattei S, Lettry J, Hatayama A 2018 J. Appl. Phys. 123 043305Google Scholar

  • 图 1  多时间尺度和多空间尺度变化示意图

    Fig. 1.  Schematic diagram of multi-scale variations.

    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

    Fig. 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.

    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]

    Fig. 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.

    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]

    Fig. 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.

    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]

    Fig. 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.

    图 6  (a)分布式多线圈ICP; (b)集成式多线圈ICP[33]

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

    图 7  螺线管线圈示意图[34]

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

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

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

    图 9  不同气压下, 电子密度随串联电容的演化[48]

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

    图 10  不同偏压幅值下, r = 7 cm处电离率的时空分布[50]

    Fig. 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.

    图 11  不同偏压频率及幅值下的离子能量角度分布[51]

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

  • [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 2827Google Scholar

    [4]

    Xu H J, Zhao S X, Zhang Y R, Gao F, Li X C, Wang Y N 2015 Phys. Plasmas 22 043508Google Scholar

    [5]

    Wegner Th, Kullig C, Meichsner J 2017 Plasma Sources Sci. Technol. 26 025006Google Scholar

    [6]

    Kim J H, Chung C W 2020 Phys. Plasmas 27 023503Google Scholar

    [7]

    Lee M H, Lee K H, Hyun D S, Chung C W 2007 Appl. Phys. Lett. 90 191502Google Scholar

    [8]

    Gao F, Zhao S X, Li X S, Wang Y N 2010 Phys. Plasmas 17 103507Google Scholar

    [9]

    Moon J H, Kim K H, Hong Y H, Lee M Y, Chung C W 2020 Phys. Plasmas 27 033511Google Scholar

    [10]

    Wegner Th, Kullig C, Meichsner J 2016 Phys. Plasmas 23 023503Google Scholar

    [11]

    Lee H C, Lee M H, Chung C W 2010 Appl. Phys. Lett. 96 071501Google Scholar

    [12]

    Schulze J, Schungel E, Czarnetzki U 2012 Appl. Phys. Lett. 100 024102Google Scholar

    [13]

    Lanham S J, Kushner M J 2017 J. Appl. Phys. 122 083301Google Scholar

    [14]

    Lee H W, Kim K H, Seo J I, Chung C W 2020 Phys. Plasmas 27 093508Google Scholar

    [15]

    王建伟, 宋亦旭, 任天令, 李进春, 褚国亮 2013 物理学报 62 245202Google Scholar

    Wang J W, Song Y X, Ren T L, Li J C, Chu G L 2013 Acta Phys. Sin. 62 245202Google Scholar

    [16]

    张改玲, 滑跃, 郝泽宇, 任春生 2019 物理学报 68 105202Google Scholar

    Zhang G L, Hua Y, Gao Z Y, Ren C S 2019 Acta Phys. Sin. 68 105202Google Scholar

    [17]

    Gudmundsson J T 2001 Plasma Sources Sci. Technol. 10 76Google Scholar

    [18]

    Thorsteinsson E G, Gudmundsson J T 2010 Plasma Sources Sci. Technol. 19 015001Google Scholar

    [19]

    Thorsteinsson E G, Gudmundsson J T 2010 J. Phys. D: Appl. Phys. 43 115201Google Scholar

    [20]

    Toneli D A, Pessoa R S, Roberto M, Gudmundsson J T 2015 J. Phys. D: Appl. Phys. 48 325202Google Scholar

    [21]

    Kimura T, Kasugai H 2010 J. Appl. Phys. 107 083308Google Scholar

    [22]

    Kimura T, Kasugai H 2010 J. Appl. Phys. 108 033305Google Scholar

    [23]

    Thorsteinsson E G, Gudmundsson J T 2010 J. Phys. D: Appl. Phys. 43 115202Google Scholar

    [24]

    Chanson R, Rhallabi A, Fernandez M C, Cardinaud C, Landesman J P 2013 J. Vac. Sci. Technol., A 31 011301Google 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 031305Google Scholar

    [26]

    Pateau A, Rhallabi A, Fernandez M C, Boufnichel M, Roqueta F 2014 J. Vac. Sci. Technol., A 32 021303Google 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 045006Google Scholar

    [28]

    Le Dain G, Rhallabi A, Girard A, Cardinaud C, Roqueta F, Boufnichel M 2019 Plasma Sources Sci. Technol. 28 085002Google Scholar

    [29]

    Bukowski J D, Graves D B, Vitello P 1996 J. Appl. Phys. 80 2614Google Scholar

    [30]

    Xu X, Rauf S, Kushner M J 2000 J. Vac. Sci. Technol., A 18 213Google Scholar

    [31]

    Kudryavtsev A A, Serditov K Yu 2012 Phys. Plasmas 19 073504Google Scholar

    [32]

    Sun X Y, Zhang Y R, Li X C, Wang Y N 2015 Phys. Plasmas 22 053508Google Scholar

    [33]

    Brcka J 2016 Jpn. J. Appl. Phys. 55 07LD08Google Scholar

    [34]

    Zheng B, Shrestha M, Wang K, Schuelke T, Shun’ko E, Belkin V, Fan Q H 2019 J. Appl. Phys. 126 123302Google Scholar

    [35]

    Jeong Y D, Lee, Y J, Kwon D C, Choe H H 2017 Curr. Appl. Phys. 17 403Google Scholar

    [36]

    Agarwal A, Bera K, Kenney J, Likhanskii A, Rauf S 2017 J. Phys. D: Appl. Phys. 50 424001Google Scholar

    [37]

    Zhang A, Kim K H, Kwon D C, Chung C W 2019 Phys. Plasmas 26 083509Google Scholar

    [38]

    Vahedi V, Surendra M 1995 Comput. Phys. Commun. 87 179Google Scholar

    [39]

    Nanbu K 2000 IEEE Trans. Plasma Sci. 28 971Google Scholar

    [40]

    Georgieva V 2006 Ph. D. Dissertation (Antwerp: University of Antwerp)

    [41]

    Sommerer T J, Kushner M J 1992 J. Appl. Phys. 71 1654Google Scholar

    [42]

    Ventzek P L G, Hoekstra R J, Kushner M J 1994 J. Vac. Sci. Technol., B 12 461Google Scholar

    [43]

    Logue M D, Kushner M J 2015 J. Appl. Phys. 117 043301Google Scholar

    [44]

    Tinck S, Bogaerts A 2016 J. Phys. D: Appl. Phys. 49 195203Google Scholar

    [45]

    Qu C, Nam S K, Kushner M J 2020 Plasma Sources Sci. Technol. 29 085006Google Scholar

    [46]

    Tian P, Kushner M J 2017 Plasma Sources Sci. Technol. 26 024005Google Scholar

    [47]

    Zhao S X, Wang Y N 2010 J. Phys. D: Appl. Phys. 43 275203Google Scholar

    [48]

    Xu H J, Zhao S X, Gao F, Zhang Y R, Li X C, Wang Y N 2015 Chin. Phys. B 24 115201Google 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 073311Google Scholar

    [50]

    Zhang Y R, Gao F, Li X C, Bogaerts A, Wang Y N 2015 J. Vac. Sci. Technol., A 33 061303Google Scholar

    [51]

    Wen D Q, Liu W, Gao F, Lieberman M A, Wang Y N 2016 Plasma Sources Sci. Technol. 25 045009Google Scholar

    [52]

    Vahedi V, DiPeso G, Birdsall C K, Lieberman M A, Rognlien T D 1993 Plasma Sources Sci. Technol. 2 261Google Scholar

    [53]

    Kawamura E, Birdsall C K, Vahedi V 2000 Plasma Sources Sci. Technol. 9 413Google Scholar

    [54]

    Birdsall C K 1991 IEEE Trans. Plasma Sci. 19 65Google Scholar

    [55]

    Takao Y, Kusaba N, Eriguchi K, Ono K 2010 J. Appl. Phys. 108 093309Google Scholar

    [56]

    Takao Y, Eriguchi K, Ono K 2012 J. Appl. Phys. 112 093306Google Scholar

    [57]

    Mattei S, Nishida K, Onai M, Lettry J, Tran M Q, Hatayama A 2017 J. Comput. Phys. 350 891Google Scholar

    [58]

    Nishida K, Mattei S, Mochizuki S, Lettry J, Hatayama A 2016 J. Appl. Phys. 119 233302Google Scholar

    [59]

    Nishida K, Mattei S, Lettry J, Hatayama A 2018 J. Appl. Phys. 123 043305Google Scholar

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出版历程
  • 收稿日期:  2020-12-31
  • 修回日期:  2021-01-27
  • 上网日期:  2021-04-28
  • 刊出日期:  2021-05-05

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