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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.
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Keywords:
- plasma simulation /
- anode layer ion source /
- discharge structure /
- plasma properties
[1] Harper J M E, Cuomo J J, Kaufman H R 1982 J. Vac. Sci. Technol. A 21 737
Google 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 5
Google Scholar
Zhao J, Tang D L, Cheng C M, Geng S F 2009 Nucl. Fusion. Plasma. Phys. 29 5
Google Scholar
[3] Lee S, Kim J K, Kim D G 2012 Rev. Sci. Instrum. 83 02B703
Google Scholar
[4] Lieberman M A 1989 J. Appl. Phys. 66 2926
Google Scholar
[5] Gudmundsson J T 2020 Plasma Sources Sci. Technol. 29 113001
Google Scholar
[6] Birdsall C K 1991 IEEE Trans Plasma Sci. 19 65
Google Scholar
[7] Costin C, Marques L, Popa G, Gousset G 2005 Plasma Sources Sci. Technol. 14 168
Google Scholar
[8] Wood B P 1993 J. Appl. Phys. 73 4770
Google Scholar
[9] Zheng B C, Meng D, Che H L, Lei M K 2015 J. Appl. Phys. 117 203302
Google Scholar
[10] Raadu M A, Axnas I, Gudmundsson J T, Huo C, Brenning N 2011 Plasma Sources Sci. Technol. 20 065007
Google Scholar
[11] Boeuf J P, Chaudhury B 2013 Phys. Rev. Lett. 111 155005
Google Scholar
[12] Shah M, Chaudhury B, Bandyopadhyay M, Chakraborty A 2020 Fusion Eng. Des. 151 111402
Google 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 194018
Google Scholar
[15] Kim H C, Iza F, Radmilovíc-Radjenovíc M, Lee J K 2005 J. Phys. D: Appl. Phys. 38 R283
Google Scholar
[16] Geng S F, Qiu X M, Cheng C M, Chu P K, Tang D L 2012 Phys. Plasmas 19 043507
Google Scholar
[17] Gui B, Yang L, Zhou H, Luo S, Xu J, Ma Z, Zhang Y 2022 Vacuum 200 111065
Google Scholar
[18] 冉彪, 李刘合 2018 真空 55 51
Google Scholar
Ran B, Li L H 2018 Vacuum 55 51
Google Scholar
[19] Jiang Y, Tang H, Ren J, Li M, Cao J 2018 J. Phys. D:Appl. Phys 51 035201
Google Scholar
[20] Yu D R, Zhang F K, Liu H, Li H, Yan G J, Liu J Y 2008 Phys. Plasmas. 15 104501
Google 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 2276
Google Scholar
[23] Rossnagel S M, Kaufman H R 1988 J. Vac. Sci. Technol. A:Vac. Surf. Films 6 223
Google 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 055203
Google 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 055203
Google Scholar
[26] Shidoji E, Ohtake H, Nakano N, Makabe T 1999 Jpn. J. Appl. Phys. 38 2131
Google 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 025016
Google 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 1285
Google Scholar
[29] Yu W, Zhang L Z, Wang J L, Han L, Fu G S 2001 J. Phys. D: Appl. Phys. 34 3349
Google Scholar
[30] Samuelsson M, Lundin D, Jensen J, Raadu M A, Gudmundsson J T, Helmersson U 2010 Surf. Coat. Tech. 205 591
Google Scholar
[31] Vahedi V, Surendra M 1995 Comput. Phys. Commun. 87 179
Google Scholar
[32] 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 325203
Google Scholar
[34] 王忆锋, 唐利斌 2010 红外技术 32 213
Google Scholar
Wang Y F, Tang L B 2010 Infrared Tech. 32 213
Google Scholar
[35] Olesik J, Całusiński B 1994 Thin Solid Films 238 271
Google Scholar
[36] 汪礼胜, 唐德礼, 程昌明 2006 核聚变与等离子体物理 26 54
Google Scholar
Wang L S, Tang D L, Cheng C M 2006 Nucl. Fusion. Plasma. Phys. 26 54
Google 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)
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图 1 磁镜模型及检验粒子MC模型示意图
Figure 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
Figure 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
Figure 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)
Figure 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
Figure 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
Figure 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)
Figure 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
Figure 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)
Figure 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
Figure 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
Figure 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
Figure 12. Corresponding density distribution and potential distribution of different dac: (a) Distribution of ion density; (b) distribution of electron density; (c) distribution of potential.
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 
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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
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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
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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 2 53.8 43.8 0.81 4.02 (31.1, 57.9) 209.3 6 51.8 47.0 0.91 3.06 (31.3, 55.8) 188.0 10 40.6 59.3 1.46 1.78 (31.6, 54.8) 155.0 14 34.4 65.6 1.90 0.68 (32.1, 53.6) 90.0 18 24.3 75.6 3.10 0.34 (32.8, 52.9) 38.4
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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 2 51.0 47.5 0.93 1.38 3.72 (31.3, 55.9) 208.4 6 48.1 50.9 1.06 1.19 3.26 (31.4, 55.4) 199.5 10 40.6 59.3 1.46 0.99 1.78 (31.6, 54.8) 155.0 14 32.8 67.2 2.05 0.74 0.72 (31.7, 53.8) 103.1 18 25.7 74.2 2.88 0.52 0.26 (33.4, 53.4) 14.2
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[1] Harper J M E, Cuomo J J, Kaufman H R 1982 J. Vac. Sci. Technol. A 21 737
Google 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 5
Google Scholar
Zhao J, Tang D L, Cheng C M, Geng S F 2009 Nucl. Fusion. Plasma. Phys. 29 5
Google Scholar
[3] Lee S, Kim J K, Kim D G 2012 Rev. Sci. Instrum. 83 02B703
Google Scholar
[4] Lieberman M A 1989 J. Appl. Phys. 66 2926
Google Scholar
[5] Gudmundsson J T 2020 Plasma Sources Sci. Technol. 29 113001
Google Scholar
[6] Birdsall C K 1991 IEEE Trans Plasma Sci. 19 65
Google Scholar
[7] Costin C, Marques L, Popa G, Gousset G 2005 Plasma Sources Sci. Technol. 14 168
Google Scholar
[8] Wood B P 1993 J. Appl. Phys. 73 4770
Google Scholar
[9] Zheng B C, Meng D, Che H L, Lei M K 2015 J. Appl. Phys. 117 203302
Google Scholar
[10] Raadu M A, Axnas I, Gudmundsson J T, Huo C, Brenning N 2011 Plasma Sources Sci. Technol. 20 065007
Google Scholar
[11] Boeuf J P, Chaudhury B 2013 Phys. Rev. Lett. 111 155005
Google Scholar
[12] Shah M, Chaudhury B, Bandyopadhyay M, Chakraborty A 2020 Fusion Eng. Des. 151 111402
Google 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 194018
Google Scholar
[15] Kim H C, Iza F, Radmilovíc-Radjenovíc M, Lee J K 2005 J. Phys. D: Appl. Phys. 38 R283
Google Scholar
[16] Geng S F, Qiu X M, Cheng C M, Chu P K, Tang D L 2012 Phys. Plasmas 19 043507
Google Scholar
[17] Gui B, Yang L, Zhou H, Luo S, Xu J, Ma Z, Zhang Y 2022 Vacuum 200 111065
Google Scholar
[18] 冉彪, 李刘合 2018 真空 55 51
Google Scholar
Ran B, Li L H 2018 Vacuum 55 51
Google Scholar
[19] Jiang Y, Tang H, Ren J, Li M, Cao J 2018 J. Phys. D:Appl. Phys 51 035201
Google Scholar
[20] Yu D R, Zhang F K, Liu H, Li H, Yan G J, Liu J Y 2008 Phys. Plasmas. 15 104501
Google 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 2276
Google Scholar
[23] Rossnagel S M, Kaufman H R 1988 J. Vac. Sci. Technol. A:Vac. Surf. Films 6 223
Google 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 055203
Google 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 055203
Google Scholar
[26] Shidoji E, Ohtake H, Nakano N, Makabe T 1999 Jpn. J. Appl. Phys. 38 2131
Google 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 025016
Google 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 1285
Google Scholar
[29] Yu W, Zhang L Z, Wang J L, Han L, Fu G S 2001 J. Phys. D: Appl. Phys. 34 3349
Google Scholar
[30] Samuelsson M, Lundin D, Jensen J, Raadu M A, Gudmundsson J T, Helmersson U 2010 Surf. Coat. Tech. 205 591
Google Scholar
[31] Vahedi V, Surendra M 1995 Comput. Phys. Commun. 87 179
Google Scholar
[32] 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 325203
Google Scholar
[34] 王忆锋, 唐利斌 2010 红外技术 32 213
Google Scholar
Wang Y F, Tang L B 2010 Infrared Tech. 32 213
Google Scholar
[35] Olesik J, Całusiński B 1994 Thin Solid Films 238 271
Google Scholar
[36] 汪礼胜, 唐德礼, 程昌明 2006 核聚变与等离子体物理 26 54
Google Scholar
Wang L S, Tang D L, Cheng C M 2006 Nucl. Fusion. Plasma. Phys. 26 54
Google 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)
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