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面向复杂求解域的高效粒子网格/蒙特卡罗模型与阳极层离子源仿真

崔岁寒 左伟 黄健 李熙腾 陈秋皓 郭宇翔 杨超 吴忠灿 马正永 傅劲裕 田修波 朱剑豪 吴忠振

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面向复杂求解域的高效粒子网格/蒙特卡罗模型与阳极层离子源仿真

崔岁寒, 左伟, 黄健, 李熙腾, 陈秋皓, 郭宇翔, 杨超, 吴忠灿, 马正永, 傅劲裕, 田修波, 朱剑豪, 吴忠振

High-efficient particle-in-cell/Monte Carlo model for complex solution domain andsimulation of anode layer ion source

Cui Sui-Han, Zuo Wei, Huang Jian, Li Xi-Teng, Chen Qiu-Hao, Guo Yu-Xiang, Yang Chao, Wu Zhong-Can, Ma Zheng-Yong, Fu Jin-Yu, Tian Xiu-Bo, Zhu Jian-Hao, Wu Zhong-Zhen
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  • 等离子体仿真是研究等离子体放电特性的重要手段, 特别是阳极层离子源, 其放电结构的几何特性对等离子体特性的作用很难通过实验手段进行系统研究. 然而, 传统仿真模型一般是针对离子源进行整体建模, 离子源的阴阳极几何轮廓形成的复杂求解域, 导致模型的计算效率和收敛性较差. 鉴于此, 将离子源结构仿真与等离子体仿真分离, 首先利用磁镜原理将离子源内外阴极大小、形状和相对位置等一系列阴极几何参数简化为磁镜比Rm和磁镜中心磁感应强度 B 0两个磁镜参数, 并在此基础上, 建立了高效粒子网格/蒙特卡罗模型, 将收敛时间由1.00 μs缩短到0.45 μs, 大幅提升了计算效率和稳定性. 进一步利用该模型系统研究了阳极层离子源放电结构的几何特性对等离子体特性的影响规律, 发现Rm = 2.50, B 0 = 36 mT时磁镜对等离子体约束效果最佳, 当放电中心的位置与内外阴极间磁镜中心重合时, 不仅能够输出高密度离子束流, 同时可大幅减少阴极刻蚀, 并保证内外阴极的刻蚀平衡.
    Plasma simulation is important in studying the plasma discharge systematically, especially the anode layer ion source which has the complex geometrical characteristics of the discharge structure. However, owing to the complex solution domain formed by the geometric profile of the anode and cathode, the traditional simulation models show extremely small computational efficiency and poor convergence. This work presents a separate simulation for the ion source structure and the plasma discharge, separately, where the cathode geometric parameters (including the size, the shape and the relative position of the inner and outer cathodes) are simplified into two magnetic mirror parameters (the magnetic mirror ratio Rm and the magnetic induction intensity in the center of the magnetic mirror B 0), and then a high-efficient particle-in-cell/Monte Carlo collision (PIC/MCC) model is established to improve the computational efficiency and stability of the plasma simulation later. As a result, the convergence time of the plasma simulation is shortened significantly from 1.00 μs to 0.45 μs, and by which the influences of the geometrical characteristics of the discharge structure on the plasma properties are systematically studied. The simulation results reveal that magnetic mirror with Rm = 2.50 and B 0 = 36 mT can best confine the plasma in the central area between the inner cathode and outer cathode. When the discharge center of the plasmacoincides with the magnetic mirror center, the anode layer ion source presents both high density output of ion beam current and significantly reduced cathode etching, suggesting that the best balance is obtained between the output and cathode etching.
      通信作者: 吴忠振, wuzz@pku.edu.cn
    • 基金项目: 深圳市科技计划(批准号: SGDX20201103095406024, JSGG20191129112631389)、2022年深圳市高等院校稳定支持计划(批准号: 20220810143642004)、北京大学深圳研究生院新引进高端人才财政补助科研启动经费 (批准号: 1270110273) 和深圳市博士后出站科研资助经费 (批准号: 2129933651) 资助的课题.
      Corresponding author: Wu Zhong-Zhen, wuzz@pku.edu.cn
    • Funds: Project supported by the Science and Technology Research Plan of Shenzhen, China (Grant Nos. SGDX20201103095406024, JSGG20191129112631389), the Sustainable Supporting Funds for Colleges and Unversities in 2022, China (Grant No. 20220810143642004), the Research Start-up Fund of Introducing Talent of Peking University Shenzhen Graduate School, China (Grant No. 1270110273), and the Postdoctoral Research Fund Project after Outbound of Shenzhen, China (Grant No. 2129933651).
    [1]

    Harper J M E, Cuomo J J, Kaufman H R 1982 J. Vac. Sci. Technol. A 21 737Google Scholar

    [2]

    赵杰, 唐德礼, 程昌明, 耿少飞 2009 核聚变与等离子体物理 29 5Google Scholar

    Zhao J, Tang D L, Cheng C M, Geng S F 2009 Nucl. Fusion. Plasma. Phys. 29 5Google Scholar

    [3]

    Lee S, Kim J K, Kim D G 2012 Rev. Sci. Instrum. 83 02B703Google Scholar

    [4]

    Lieberman M A 1989 J. Appl. Phys. 66 2926Google Scholar

    [5]

    Gudmundsson J T 2020 Plasma Sources Sci. Technol. 29 113001Google Scholar

    [6]

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

    [7]

    Costin C, Marques L, Popa G, Gousset G 2005 Plasma Sources Sci. Technol. 14 168Google Scholar

    [8]

    Wood B P 1993 J. Appl. Phys. 73 4770Google Scholar

    [9]

    Zheng B C, Meng D, Che H L, Lei M K 2015 J. Appl. Phys. 117 203302Google Scholar

    [10]

    Raadu M A, Axnas I, Gudmundsson J T, Huo C, Brenning N 2011 Plasma Sources Sci. Technol. 20 065007Google Scholar

    [11]

    Boeuf J P, Chaudhury B 2013 Phys. Rev. Lett. 111 155005Google Scholar

    [12]

    Shah M, Chaudhury B, Bandyopadhyay M, Chakraborty A 2020 Fusion Eng. Des. 151 111402Google Scholar

    [13]

    Mattox D M 2001 Plat. Surf. Finish. 88 74

    [14]

    Bogaerts A, Bultinck E, Kolev I, Schwaederle L, Van Aeken K, Buyle G, Depla D 2009 J. Phys. D:Appl. Phys. 42 194018Google Scholar

    [15]

    Kim H C, Iza F, Radmilovíc-Radjenovíc M, Lee J K 2005 J. Phys. D: Appl. Phys. 38 R283Google Scholar

    [16]

    Geng S F, Qiu X M, Cheng C M, Chu P K, Tang D L 2012 Phys. Plasmas 19 043507Google Scholar

    [17]

    Gui B, Yang L, Zhou H, Luo S, Xu J, Ma Z, Zhang Y 2022 Vacuum 200 111065Google Scholar

    [18]

    冉彪, 李刘合 2018 真空 55 51Google Scholar

    Ran B, Li L H 2018 Vacuum 55 51Google Scholar

    [19]

    Jiang Y, Tang H, Ren J, Li M, Cao J 2018 J. Phys. D:Appl. Phys 51 035201Google Scholar

    [20]

    Yu D R, Zhang F K, Liu H, Li H, Yan G J, Liu J Y 2008 Phys. Plasmas. 15 104501Google Scholar

    [21]

    谢树艺 2012 工程数学矢量分析与场论 (第4卷) (北京: 高等教育出版社) 第29—35页

    Xie S Y 2012 Vector Analysis and Field Theory in Engineering Mathematics (Vol. 4) (Beijing: Higher Education Press) pp29–35 (in Chinese)

    [22]

    Rossnagel S M, Kaufman H R 1987 J. Vac. Sci. Technol. A:Vac. Surf. Films 5 2276Google Scholar

    [23]

    Rossnagel S M, Kaufman H R 1988 J. Vac. Sci. Technol. A:Vac. Surf. Films 6 223Google Scholar

    [24]

    弗朗西斯 F. 陈 著 (林光海 译) 1980 等离子体物理学导论(北京: 科学出版社) 第5—7页

    Francis F. Chen(translated by Lin G H)1980 Introduction to Plasma Physics (Beijing: Science Press) pp5–7 (in Chinese)

    [25]

    崔岁寒, 郭宇翔, 陈秋皓, 金正, 杨超, 吴忠灿, 苏雄宇, 马正永, 田修波, 吴忠振 2022 物理学报 71 055203Google Scholar

    Cui S H, Guo Y X, Chen Q H, Jin Z, Yang C, Wu Z C, Su X Y, Ma Z Y, Tian X B, Wu Z Z 2022 Acta Phys. Sin. 71 055203Google Scholar

    [26]

    Shidoji E, Ohtake H, Nakano N, Makabe T 1999 Jpn. J. Appl. Phys. 38 2131Google Scholar

    [27]

    Chen L, Cui S H, Tang W, Zhou L, Li T, Liu L, An X, Wu Z, Ma Z, Lin H 2020 Plasma. Sources. Sci. T. 29 025016Google Scholar

    [28]

    Lennon M A, Bell K L, Gilbody H B, Hughes J G, Kingston A E, Murray M J, Smith F J 1988 J. Phys. Chem. Ref. Data. 17 1285Google Scholar

    [29]

    Yu W, Zhang L Z, Wang J L, Han L, Fu G S 2001 J. Phys. D: Appl. Phys. 34 3349Google Scholar

    [30]

    Samuelsson M, Lundin D, Jensen J, Raadu M A, Gudmundsson J T, Helmersson U 2010 Surf. Coat. Tech. 205 591Google Scholar

    [31]

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

    [32]

    宮文英 2009 硕士学位论文 (成都: 电子科技大学)

    Gong W Y 2009 M. S. Thesis (Chengdu: University of Elecdtronic Science and Technology of China) (in Chinese)

    [33]

    Cui S H, Chen Q H, Guo Y X, Chen L, Jin Z, Li X T, Yang C, Wu Z C, Su X Y, Ma Z Y, Ricky K Y Fu, Tian X B, Paul K Chu, Wu Z Z 2022 J. Phys. D: Appl. Phys. 55 325203Google Scholar

    [34]

    王忆锋, 唐利斌 2010 红外技术 32 213Google Scholar

    Wang Y F, Tang L B 2010 Infrared Tech. 32 213Google Scholar

    [35]

    Olesik J, Całusiński B 1994 Thin Solid Films 238 271Google Scholar

    [36]

    汪礼胜, 唐德礼, 程昌明 2006 核聚变与等离子体物理 26 54Google Scholar

    Wang L S, Tang D L, Cheng C M 2006 Nucl. Fusion. Plasma. Phys. 26 54Google Scholar

    [37]

    陈志国 2021 硕士学位论文 (哈尔滨: 哈尔滨工业大学)

    Chen Z G 2021 M. S. Thesis (Harbin: Harbin Institute of Technology) (in Chinese)

  • 图 1  磁镜模型及检验粒子MC模型示意图

    Fig. 1.  Schematic diagram of the magnetic mirror model and test particle MC model.

    图 2  复杂求解域的高效PIC/MC模型示意图

    Fig. 2.  Schematic diagram high-efficient PIC/MC model for complex solution domain.

    图 3  B0 = 36 mT时, 不同dmag对应分析线α上磁感应强度

    Fig. 3.  Magnetic induction intensity on the analytical line α at different dmag with B0 = 36 mT.

    图 4  B0 = 36 mT时, 不同磁镜比Rm对应的磁场分布(a)和0.5 μs检验电子数密度分布(b)

    Fig. 4.  Distribution of magnetic field (a) and test-electron density of 0.5 μs (b) at different magnetic mirror ratio Rm with B0 = 36 mT

    图 5  电子逃逸率、检验电子数密度峰值、输出离子束流密度及输出离子数/阴极溅射离子数随Rm的变化

    Fig. 5.  Evolution tendency of the electron escape rate, the maximum test-electron density, the output ion beam density, and the ratio of the output ions to the sputtering ions with Rm.

    图 6  Rm = 2.50时, 不同Bm大小分析线α上磁感应强度

    Fig. 6.  Magnetic induction intensity on the analytical line α at different Bm with Rm = 2.50.

    图 7  Rm = 2.50时, 不同B0对应的磁场分布(a)和0.5 μs检验电子数密度分布(b)

    Fig. 7.  Distribution of magnetic field (a) and test-electron density of 0.5 μs (b) at different magnetic mirror ratio B0 with Rm = 2.50

    图 8  电子逃逸率、检验电子数密度峰值、输出离子束流密度及输出离子数/阴极溅射离子数随B0变化

    Fig. 8.  Evolution tendency of the electron escape rate, the maximum test-electron density, the output ion beam density, and the ratio of the output ions to the sputtering ions with B0.

    图 9  优化的阴极结构对应的磁场分布(a)及检验电子密度分布(b)

    Fig. 9.  Distribution of the magnetic field (a) and the test-electron density (b) under the optimized cathode structures.

    图 10  不同模型求出的等离子体密度分布演变过程 (a) 高效PIC/MC模型; (b) 传统PIC/MC模型

    Fig. 10.  Evolution process of the plasma density simulated by the different model: (a) High-efficient PIC/MC model; (b) traditional PIC/MC model.

    图 11  不同hac对应的密度分布及电势分布 (a)离子密度分布; (b)电子密度分布; (c)电势分布

    Fig. 11.  Corresponding density distribution and potential distribution of different hac: (a) Distribution of ion density; (b) distribution of electron density; (c) distribution of potential.

    图 12  不同dac对应的密度分布及电势分布 (a)离子密度分布; (b)电子密度分布; (c)电势分布

    Fig. 12.  Corresponding density distribution and potential distribution of different dac: (a) Distribution of ion density; (b) distribution of electron density; (c) distribution of potential.

    表 1  电子与背景Ar原子碰撞类型[28]

    Table 1.  Reactions of Ar discharge involving electrons[28].

    反应方程式反应速率系数kr/(m3⋅s–1 )反应能量阈值/eV反应类型
    e + Ar → Ar + e$2.336 \times {10^{ - 14} }{T_{\text{e} } }^{1.609} \times \exp \big[ {0.0618{ {\left( {\ln {T_{\text{e} } } } \right)}^2} - 0.1171{ {\left( {\ln {T_{\text{e} } } } \right)}^3} } \big]$弹性碰撞
    e + Ar → Ar+ + 2e$2.34 \times {10^{ - 14} }{T_{\text{e} } }^{0.59} \times \exp \left( { - 17.44/{T_{\text{e} } } } \right)$15.76电离碰撞
    下载: 导出CSV

    表 2  Ar+离子与背景Ar原子碰撞类型[28]

    Table 2.  Reactions of Ar discharge involving Ar+[28]

    反应方程式反应类型
    Ar+ + Ar → Ar+ + Ar弹性碰撞
    Ar+ + Ar → Ar + Ar+电荷交换
    下载: 导出CSV

    表 3  Ar气放电的主要反应表[28]

    Table 3.  Main reactions of Ar gas discharge[28].

    反应方程式反应速率系数 kr/(m3⋅s–1)反应能量阈值/eV反应类型
    e + Ar → Ar + e$ 2.336 \times {10^{ - 14}}{T_{\text{e}}}^{1.609} \times \exp \left[ {0.0618{{\left( {\ln {T_{\text{e}}}} \right)}^2} - 0.1171{{\left( {\ln {T_{\text{e}}}} \right)}^3}} \right] $弹性碰撞
    e + Ar → Ar+ + 2e$ 2.34 \times {10^{ - 14}}{T_{\text{e}}}^{0.59} \times \exp \left( { - 17.44/{T_{\text{e}}}} \right) $15.76电离碰撞
    e + Ar → Arm + e$ 2.5 \times {10^{ - 15}}{T_{\text{e}}}^{0.74} \times \exp \left( { - 11.56/{T_{\text{e}}}} \right) $11.56激发碰撞
    e + Arm → Ar+ + 2e$ 6.8 \times {10^{ - 15}}{T_{\text{e}}}^{0.67} \times \exp \left( { - 4.2/{T_{\text{e}}}} \right) $4.20激发态电离
    e + Arm → Ar + e$ 4.3 \times {10^{ - 16}}{T_{\text{e}}}^{0.74} $–11.56退激发碰撞
    Ar+ + Ar → Ar+ + Ar硬球模型弹性碰撞
    Ar+ + Ar → Ar + Ar+硬球模型电荷交换
    下载: 导出CSV

    表 4  不同hac对应的等离子体放电特性

    Table 4.  Plasma discharge characteristics at different hac.

    hac/mm阴极溅射离
    子占比/%
    输出离子
    占比/%
    输出离子数/阴
    极溅射离子数
    等离子体峰值
    密度/(1016 m–3)
    放电中心坐标/mm放电面积/mm2
    253.843.80.814.02(31.1, 57.9)209.3
    651.847.00.913.06(31.3, 55.8)188.0
    1040.659.31.461.78(31.6, 54.8)155.0
    1434.465.61.900.68(32.1, 53.6)90.0
    1824.375.63.100.34(32.8, 52.9)38.4
    下载: 导出CSV

    表 5  不同dac对应的等离子体特性

    Table 5.  Plasma properties at different dac.

    dac/mm阴极溅射离
    子占比/%
    输出离子
    占比/%
    输出离子数/阴
    极溅射离子数
    内外阴极溅
    射强度比
    等离子体峰值密
    度/(1016 m–3)
    放电中心
    坐标/mm
    放电面积/mm2
    251.047.50.931.383.72(31.3, 55.9)208.4
    648.150.91.061.193.26(31.4, 55.4)199.5
    1040.659.31.460.991.78(31.6, 54.8)155.0
    1432.867.22.050.740.72(31.7, 53.8)103.1
    1825.774.22.880.520.26(33.4, 53.4)14.2
    下载: 导出CSV
  • [1]

    Harper J M E, Cuomo J J, Kaufman H R 1982 J. Vac. Sci. Technol. A 21 737Google Scholar

    [2]

    赵杰, 唐德礼, 程昌明, 耿少飞 2009 核聚变与等离子体物理 29 5Google Scholar

    Zhao J, Tang D L, Cheng C M, Geng S F 2009 Nucl. Fusion. Plasma. Phys. 29 5Google Scholar

    [3]

    Lee S, Kim J K, Kim D G 2012 Rev. Sci. Instrum. 83 02B703Google Scholar

    [4]

    Lieberman M A 1989 J. Appl. Phys. 66 2926Google Scholar

    [5]

    Gudmundsson J T 2020 Plasma Sources Sci. Technol. 29 113001Google Scholar

    [6]

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

    [7]

    Costin C, Marques L, Popa G, Gousset G 2005 Plasma Sources Sci. Technol. 14 168Google Scholar

    [8]

    Wood B P 1993 J. Appl. Phys. 73 4770Google Scholar

    [9]

    Zheng B C, Meng D, Che H L, Lei M K 2015 J. Appl. Phys. 117 203302Google Scholar

    [10]

    Raadu M A, Axnas I, Gudmundsson J T, Huo C, Brenning N 2011 Plasma Sources Sci. Technol. 20 065007Google Scholar

    [11]

    Boeuf J P, Chaudhury B 2013 Phys. Rev. Lett. 111 155005Google Scholar

    [12]

    Shah M, Chaudhury B, Bandyopadhyay M, Chakraborty A 2020 Fusion Eng. Des. 151 111402Google Scholar

    [13]

    Mattox D M 2001 Plat. Surf. Finish. 88 74

    [14]

    Bogaerts A, Bultinck E, Kolev I, Schwaederle L, Van Aeken K, Buyle G, Depla D 2009 J. Phys. D:Appl. Phys. 42 194018Google Scholar

    [15]

    Kim H C, Iza F, Radmilovíc-Radjenovíc M, Lee J K 2005 J. Phys. D: Appl. Phys. 38 R283Google Scholar

    [16]

    Geng S F, Qiu X M, Cheng C M, Chu P K, Tang D L 2012 Phys. Plasmas 19 043507Google Scholar

    [17]

    Gui B, Yang L, Zhou H, Luo S, Xu J, Ma Z, Zhang Y 2022 Vacuum 200 111065Google Scholar

    [18]

    冉彪, 李刘合 2018 真空 55 51Google Scholar

    Ran B, Li L H 2018 Vacuum 55 51Google Scholar

    [19]

    Jiang Y, Tang H, Ren J, Li M, Cao J 2018 J. Phys. D:Appl. Phys 51 035201Google Scholar

    [20]

    Yu D R, Zhang F K, Liu H, Li H, Yan G J, Liu J Y 2008 Phys. Plasmas. 15 104501Google Scholar

    [21]

    谢树艺 2012 工程数学矢量分析与场论 (第4卷) (北京: 高等教育出版社) 第29—35页

    Xie S Y 2012 Vector Analysis and Field Theory in Engineering Mathematics (Vol. 4) (Beijing: Higher Education Press) pp29–35 (in Chinese)

    [22]

    Rossnagel S M, Kaufman H R 1987 J. Vac. Sci. Technol. A:Vac. Surf. Films 5 2276Google Scholar

    [23]

    Rossnagel S M, Kaufman H R 1988 J. Vac. Sci. Technol. A:Vac. Surf. Films 6 223Google Scholar

    [24]

    弗朗西斯 F. 陈 著 (林光海 译) 1980 等离子体物理学导论(北京: 科学出版社) 第5—7页

    Francis F. Chen(translated by Lin G H)1980 Introduction to Plasma Physics (Beijing: Science Press) pp5–7 (in Chinese)

    [25]

    崔岁寒, 郭宇翔, 陈秋皓, 金正, 杨超, 吴忠灿, 苏雄宇, 马正永, 田修波, 吴忠振 2022 物理学报 71 055203Google Scholar

    Cui S H, Guo Y X, Chen Q H, Jin Z, Yang C, Wu Z C, Su X Y, Ma Z Y, Tian X B, Wu Z Z 2022 Acta Phys. Sin. 71 055203Google Scholar

    [26]

    Shidoji E, Ohtake H, Nakano N, Makabe T 1999 Jpn. J. Appl. Phys. 38 2131Google Scholar

    [27]

    Chen L, Cui S H, Tang W, Zhou L, Li T, Liu L, An X, Wu Z, Ma Z, Lin H 2020 Plasma. Sources. Sci. T. 29 025016Google Scholar

    [28]

    Lennon M A, Bell K L, Gilbody H B, Hughes J G, Kingston A E, Murray M J, Smith F J 1988 J. Phys. Chem. Ref. Data. 17 1285Google Scholar

    [29]

    Yu W, Zhang L Z, Wang J L, Han L, Fu G S 2001 J. Phys. D: Appl. Phys. 34 3349Google Scholar

    [30]

    Samuelsson M, Lundin D, Jensen J, Raadu M A, Gudmundsson J T, Helmersson U 2010 Surf. Coat. Tech. 205 591Google Scholar

    [31]

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

    [32]

    宮文英 2009 硕士学位论文 (成都: 电子科技大学)

    Gong W Y 2009 M. S. Thesis (Chengdu: University of Elecdtronic Science and Technology of China) (in Chinese)

    [33]

    Cui S H, Chen Q H, Guo Y X, Chen L, Jin Z, Li X T, Yang C, Wu Z C, Su X Y, Ma Z Y, Ricky K Y Fu, Tian X B, Paul K Chu, Wu Z Z 2022 J. Phys. D: Appl. Phys. 55 325203Google Scholar

    [34]

    王忆锋, 唐利斌 2010 红外技术 32 213Google Scholar

    Wang Y F, Tang L B 2010 Infrared Tech. 32 213Google Scholar

    [35]

    Olesik J, Całusiński B 1994 Thin Solid Films 238 271Google Scholar

    [36]

    汪礼胜, 唐德礼, 程昌明 2006 核聚变与等离子体物理 26 54Google Scholar

    Wang L S, Tang D L, Cheng C M 2006 Nucl. Fusion. Plasma. Phys. 26 54Google Scholar

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    Chen Z G 2021 M. S. Thesis (Harbin: Harbin Institute of Technology) (in Chinese)

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出版历程
  • 收稿日期:  2022-12-15
  • 修回日期:  2023-01-26
  • 上网日期:  2023-02-14
  • 刊出日期:  2023-04-20

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