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容性耦合硅烷等离子体尘埃颗粒空间分布的二维流体模拟

段蒙悦 贾文柱 张莹莹 张逸凡 宋远红

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容性耦合硅烷等离子体尘埃颗粒空间分布的二维流体模拟

段蒙悦, 贾文柱, 张莹莹, 张逸凡, 宋远红

Two-dimensional fluid simulation of spatial distribution of dust particles in a capacitively coupled silane plasma

Duan Meng-Yue, Jia Wen-Zhu, Zhang Ying-Ying, Zhang Yi-Fan, Song Yuan-Hong
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  • 基于自主研发的二维流体尘埃模型, 研究了射频容性耦合硅烷等离子体放电中不同腔室结构对尘埃颗粒密度空间分布的影响. 模拟发现, 有别于一维模型, 径向电场和作用在尘埃颗粒上的离子拖拽力径向分量是导致尘埃颗粒密度分布径向不均匀的主要因素, 使其在极板边缘处呈现两个局部峰值, 其中一个峰值表明尘埃颗粒有可能会克服电场力的支撑更接近极板. 在极板半径较小或极板间距较小的情况下, 径向离子拖拽力的作用增强, 使尘埃颗粒更易于在极板边缘处和腔室侧壁附近聚集, 出现环状尘埃颗粒分布带. 在放电极板有介质材料包裹的情况下, 尘埃颗粒密度径向分布的均匀性得到改善. 最后, 还模拟了单个尘埃颗粒在极板边缘处的涡旋运动规律.
    In this work, we develop a two-dimensional fluid model to study the spatial density distributions of dust particles in a radio frequency capacitively coupled silane plasma. Unlike those scenarios based on the one-dimensional fluid model, in this work, the nonuniformity of the radial density distributions of dust particles is attributed mainly to the radial components of the electric field force and the ion drag force acting on the dust particles, leading to the two local density peaks near the electrode edges. It seems that dust particles tend to overcome the support of the electric field force and move much closer to the electrodes, as one of the density peaks indicates. Moreover, with the decrease of the radii of the discharge electrodes or the distance between them, the radial component of the ion drag force is enhanced, resulting in more dust particles gathering near the electrode edge region, and forming a ring-shaped particle density distribution. In the case of the discharge electrodes wrapped with dielectric materials, the uniformity of the radial density distributions of dust particles between the two electrodes is improved. Finally, the vortex motion of a single dust particle near the electrode edge region is also simulated in this work.
      通信作者: 宋远红, songyh@dlut.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 12020101005, 11975067, 12005176, 12275039)资助的课题.
      Corresponding author: Song Yuan-Hong, songyh@dlut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12020101005, 11975067, 12005176, 12275039).
    [1]

    Selwyn G S, Singh J, Bennett R S 1989 J. Vac. Sci. Techool. A 7 2758Google Scholar

    [2]

    Fortov V E, Khrapak A G, Khrapak S A, Molotkov V I, Petrov O F 2004 Phys. Usp. 47 447Google Scholar

    [3]

    Melzer A, Nunomura S, Samsonov D, Ma Z W, Goree J 2000 Phys. Rev. E 62 4162Google Scholar

    [4]

    Thomas H, Morfill G E, Demmel V, Goree J, Feuerbacher B, Möhlmann D 1994 Phys. Rev. Lett. 73 652Google Scholar

    [5]

    Ivlev A V, Steinberg V, Kompaneets R, Höfner H, Sidorenko I, Morfill G E 2007 Phys. Rev. Lett. 98 145003Google Scholar

    [6]

    Samsonov D, Goree J, Ma Z W, Bhattacharjee A, Thomas H M, Morfill G E 1999 Phys. Rev. Lett. 83 3649Google Scholar

    [7]

    Goree J, Morfill G E, Tsytovieh V N, Vladimirov S V 1999 Phys. Rev. E 59 7055Google Scholar

    [8]

    Chai K B, Bellan P M 2016 Phys. Plasmas 23 023701Google Scholar

    [9]

    Morfill G E, Thomas H M, Konopka U, Rothermel H, Zuzic M, Ivlev A, Goree J 1999 Phys. Rev. Lett. 83 1598Google Scholar

    [10]

    Akdim M R, Goedheer W J 2003 Phys. Rev. E 67 056405Google Scholar

    [11]

    Rozsa K, Bano G, Gallagher A 2001 IEEE Trans. Plasma Sci. 29 256Google Scholar

    [12]

    De Bleecker K, Bogaerts A, Goedheer W 2004 Phys. Rev. E 70 056407Google Scholar

    [13]

    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 015206Google Scholar

    [14]

    Bleecker K D, Bogaerts A, Goedheer W 2006 New J. Phys. 8 178Google Scholar

    [15]

    Akdim M R, Goedheer W J 2003 J. Appl. Phys. 94 104Google Scholar

    [16]

    De Bleecker K, Bogaerts A, Goedheer W 2006 Phys. Rev. E 73 026405Google Scholar

    [17]

    Barnes M S, Keller J H, Forster J C, Neill J A, Coultas D K 1992 Phys. Rev. Lett. 68 313Google Scholar

    [18]

    Gallagher A, Howling A A, Hollenstein C 2002 J. Appl. Phys. 91 5571Google Scholar

    [19]

    Norberg S A, Johnsen E, Kushner M J 2015 Plasma Sources Sci. Technol. 24 035026Google Scholar

    [20]

    Boufendi L, Bouchoule A 1994 Plasma Sources Sci. Technol. 3 262Google Scholar

    [21]

    Lieberman M A, Lichtenberg A J 2005 Principles of Plasma Discharges and Materials Processing (Hoboken, NJ, USA: John Wiley & Sons, Inc. ) pp23–43

  • 图 1  放电腔室结构示意图

    Fig. 1.  Schematic diagram of the capacitive reactor.

    图 2  z0 = 3 cm, R0 = 9 cm时, 等离子体中的密度空间分布 (a)电子; (b) $ {\text{SiH}}_3^ + $正离子; (c) $ {\text{SiH}}_3^ - $负离子; (d)尘埃颗粒

    Fig. 2.  Spatial density distributions in plasma at z0 = 3 cm and R0 = 9 cm: (a) Electron; (b) $ {\text{SiH}}_3^ + $; (c) $ {\text{SiH}}_3^ - $; (d) dust particles.

    图 3  z0 = 3 cm, R0 = 9 cm时, 尘埃颗粒所受电场力(a)轴向分量、(b)径向分量, 以及离子拖拽力(c)轴向分量、(d)径向分量的二维空间分布

    Fig. 3.  Spatial distributions of (a) axial component and (b) radial component of the electric field force, (c) axial component and (d) radial component of the ion drag force at z0 = 3 cm and R0 = 9 cm.

    图 4  (a) z = 3.88 cm 时, 径向离子拖拽力随r的变化; (b) $ {\text{SiH}}_3^ + $正离子通量矢量图(极板间距z0 = 3 cm, 电极半径R0 = 9 cm)

    Fig. 4.  (a) Radial component of the ion drag force along r direction at z = 3.88 cm; (b) flux vector map of $ {\text{SiH}}_3^ + $ (Gap distance z0 = 3 cm and the electrode radius R0 = 9 cm).

    图 5  极板间距z0 = 3 cm, 极板半径不同时, $ {\text{SiH}}_3^ + $密度(a)—(c), 尘埃颗粒密度(d)—(f), 离子拖拽力径向分量(g)—(i)的二维空间分布情况 (a), (d), (g) R0 = 9 cm; (b), (e), (h) R0 = 8 cm; (c), (f), (i) R0 = 7 cm

    Fig. 5.  Spatial distributions of $ {\text{SiH}}_3^ + $ densities (a)–(c), dust particles densities (d)–(f) and radial component of the ion drag force (g)–(i) at the different electrode radius and z0 = 3 cm: (a), (d), (g) R0 = 9 cm; (b), (e), (h) R0 = 8 cm; (c), (f), (i) R0 = 7 cm.

    图 6  电极半径R0 = 8 cm, 极板间距不同时, $ {\text{SiH}}_3^ + $ 密度(a)—(c), 尘埃颗粒密度(d)—(f), 离子拖拽力径向分量(g)—(i)的二维空间分布情况 (a), (d), (g) z0 = 3.0 cm; (b), (e), (h) z0 = 2.0 cm; (c), (f), (i) z0 = 1.4 cm

    Fig. 6.  Spatial distributions of (a)–(c) $ {\text{SiH}}_3^ + $ densities, (d)–(f) dust particles densities and (g)–(i) radial component of the ion drag force at the different electrode spacing and R0 = 8 cm: (a), (d), (g) z0 = 3.0 cm; (b), (e), (h) z0 = 2.0 cm; (c), (f), (i) z0 = 1.4 cm.

    图 7  z0 = 3 cm, R0 = 9 cm时, 上下极板在无介质层包裹和有介质层包裹的情况下 $ {\text{SiH}}_3^ + $密度(a), (b)和尘埃颗粒密度(c), (d)

    Fig. 7.  Spatial distributions of $ {\text{SiH}}_3^ + $ densities (a), (b) and dust particles densities (c), (d) in the case of discharge electrode without or with dielectric materials at z0 = 3 cm and R0 = 9 cm.

    图 8  上极板边缘(a)和下极板边缘(b)位置处的尘埃颗粒涡旋运动轨迹; 尘埃颗粒轴向位置(c), (d)及径向位置(e), (f)随时间演化过程(极板间距z0 = 3 cm, 电极半径R0 = 9 cm)

    Fig. 8.  Vortex trajectory of dust particles at the edge of (a) the upper plate and (b) the lower plate; axial position (c), (d) and radial position (e), (f) of dust particles over time (Gap distance z0 = 3 cm and the electrode radius R0 = 9 cm).

    表 1  除电子外, 模型中包含的不同粒子情况

    Table 1.  Overview of the different species incorporated in the model, besides the electrons.

    MoleculesIonsRadicals
    SiH4, SiH4(2-4), SiH4(1-3)$ {\text{SiH}}_3^ + , {\text{ S}}{{\text{i}}_{2}}{\text{H}}_4^ + $SiH3, Si2H4
    H2$ {\text{H}}_2^ + $H
    Si2H6, Si3H8, Si4H10, Si5H12$ \begin{gathered} {\text{S}}{{\text{i}}_{5}}{\text{H}}_5^ - , {\text{ S}}{{\text{i}}_{3}}{\text{H}}_7^ - , {\text{ S}}{{\text{i}}_{4}}{\text{H}}_9^ - , {\text{ S}}{{\text{i}}_{5}}{\text{H}}_{11}^ - ,\end{gathered} $

    $ {\text{S} }{ {\text{i} }_{2} }{\text{H} }_4^ - , {\text{ S} }{ {\text{i} }_3}{\text{H} }_6^ - , {\text{ S} }{ {\text{i} }_{4} }{\text{H} }_8^ - , {\text{ S} }{ {\text{i} }_{5} }{\text{H} }_{10}^ - , $
    dust
    Si2H5, Si3H7, Si4H9, Si5H11 , Si2H4, Si3H6, Si4H8, Si5H10
    下载: 导出CSV
  • [1]

    Selwyn G S, Singh J, Bennett R S 1989 J. Vac. Sci. Techool. A 7 2758Google Scholar

    [2]

    Fortov V E, Khrapak A G, Khrapak S A, Molotkov V I, Petrov O F 2004 Phys. Usp. 47 447Google Scholar

    [3]

    Melzer A, Nunomura S, Samsonov D, Ma Z W, Goree J 2000 Phys. Rev. E 62 4162Google Scholar

    [4]

    Thomas H, Morfill G E, Demmel V, Goree J, Feuerbacher B, Möhlmann D 1994 Phys. Rev. Lett. 73 652Google Scholar

    [5]

    Ivlev A V, Steinberg V, Kompaneets R, Höfner H, Sidorenko I, Morfill G E 2007 Phys. Rev. Lett. 98 145003Google Scholar

    [6]

    Samsonov D, Goree J, Ma Z W, Bhattacharjee A, Thomas H M, Morfill G E 1999 Phys. Rev. Lett. 83 3649Google Scholar

    [7]

    Goree J, Morfill G E, Tsytovieh V N, Vladimirov S V 1999 Phys. Rev. E 59 7055Google Scholar

    [8]

    Chai K B, Bellan P M 2016 Phys. Plasmas 23 023701Google Scholar

    [9]

    Morfill G E, Thomas H M, Konopka U, Rothermel H, Zuzic M, Ivlev A, Goree J 1999 Phys. Rev. Lett. 83 1598Google Scholar

    [10]

    Akdim M R, Goedheer W J 2003 Phys. Rev. E 67 056405Google Scholar

    [11]

    Rozsa K, Bano G, Gallagher A 2001 IEEE Trans. Plasma Sci. 29 256Google Scholar

    [12]

    De Bleecker K, Bogaerts A, Goedheer W 2004 Phys. Rev. E 70 056407Google Scholar

    [13]

    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 015206Google Scholar

    [14]

    Bleecker K D, Bogaerts A, Goedheer W 2006 New J. Phys. 8 178Google Scholar

    [15]

    Akdim M R, Goedheer W J 2003 J. Appl. Phys. 94 104Google Scholar

    [16]

    De Bleecker K, Bogaerts A, Goedheer W 2006 Phys. Rev. E 73 026405Google Scholar

    [17]

    Barnes M S, Keller J H, Forster J C, Neill J A, Coultas D K 1992 Phys. Rev. Lett. 68 313Google Scholar

    [18]

    Gallagher A, Howling A A, Hollenstein C 2002 J. Appl. Phys. 91 5571Google Scholar

    [19]

    Norberg S A, Johnsen E, Kushner M J 2015 Plasma Sources Sci. Technol. 24 035026Google Scholar

    [20]

    Boufendi L, Bouchoule A 1994 Plasma Sources Sci. Technol. 3 262Google Scholar

    [21]

    Lieberman M A, Lichtenberg A J 2005 Principles of Plasma Discharges and Materials Processing (Hoboken, NJ, USA: John Wiley & Sons, Inc. ) pp23–43

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出版历程
  • 收稿日期:  2023-04-27
  • 修回日期:  2023-06-03
  • 上网日期:  2023-06-06
  • 刊出日期:  2023-08-20

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