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Closed magnetic field constructed by unbalanced magnetron sputtering (MS) cathodes has been a general means of developing the MS coating system. However, owing to the difficulties in characterizing the complex plasma behaviors, there are still no quantitative criteria or design bases for some critical points, such as the effective object, the working mechanism, the closure condition, the layout logic and the effectivity of the closed magnetic field. Here in this work, out of the movements of charged particles in magnetic field, the motion behaviors of electrons and ions in the vacuum chamber are studied and it is also revealed that the closed magnetic field can affect mainly the electrons and further control the distributions of ions. A Monte-Carlo collision (MCC) model of the closed magnetic field MS coating system is established by test-electron to characterize the plasma transport characteristics, and the electron constraint and coating deposition efficiency are studied by different layouts of the magnetron cathodes and the ion sources. The simulation results show that the cathode numbers and vacuum chamber size determine the constraint effect on electrons in closed magnetic field. By 8 MS cathodes and the chamber radius of 0.5 m, the proportion of the overflow electrons can decrease to 1.77%. To increase the proportion of the electrons in the coating region, four coupled magnetic fields are introduced in the center of vacuum chamber. The studies of cathode type, rotation angle and magnetic field direction reveal that the proportion of the overflow electrons is less than 3%. A local dense plasma distribution and a continuous uniform plasma distribution can be observed in the vacuum chamber, corresponding to the same and opposite layout in magnetic poles of the MS cathodes and the ion sources, and the proportion of the electrons in the coating region significantly increases to 53.41% and 42.25%, respectively.
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Keywords:
- closed magnetic field /
- electron motion /
- vacuum layout /
- deposition efficiency
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[3] Savvides N, Window B 1986 J. Vac. Sci. Technol. A 4 504
Google Scholar
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Google Scholar
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Google Scholar
[10] Rohde S L, Petrov I, Sproul W D, Barnett S A, Rudnik P J, Graham M E 1990 Thin Solid Films 193 117
[11] Sproul W D, Rudnik P J, Graham M E, Rohde S L 1990 Surf. Coat. Technol. 43 270
[12] 蒋百灵, 曹政, 鲁媛媛, 栾亚 2011 材料热处理学报 32 92
Jiang B L, Cao Z, Lu Y Y, Luan Y 2011 Transact. mater. heat treatment 32 92
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[15] 迈克尔·A. 力伯曼, 阿伦·J. 里登伯格著(浦以康 译) 2007 等离子体放电原理与材料处理 (北京: 科学出版社) 第18—30页
Lieberman M A, Lichtenberg A J (translated by Pu Y K) 2007 Principles of Plasma Discharges and Materials Processing (Beijing: Science Press) pp5–7 (in Chinese)
[16] 曹政, 蒋百灵, 鲁媛媛, 王陶 2011 材料研究学报 25 313
Cao Z, Jiang B L, Lu Y Y, Wang T 2011 Chin. J. Mater. Res. 25 313
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Google Scholar
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Google Scholar
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Google Scholar
Wang T L, Qiu Q Q, Jing L W, Zhang X B 2018 Acta Phys. Sin. 67 070703
Google Scholar
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Cui S H, Wu Z Z, Xiao S, Chen L, Li T J, Liu L L, Fu J Y, Tian X B, Zhu J H, Tan W C 2019 Acta Phys. Sin 68 195204
[24] Rossnagel S M, Kaufman H R 1987 J. Vac. Sci. Technol. A-Vac. Surf. Films 5 2276
Google Scholar
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Chen F F (translated by Lin G H) 1980 Introduction to Plasma Physics (Beijing: Science Press) pp5–7 (in Chinese)
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Google Scholar
[28] Chen L, Cui S H, Tang W, Zhou L, Li T J, Liu L L, An X K, Wu Z C, Ma Z Y, Lin H, Tian X B, Fu J Y, Chu P K, Wu Z Z 2020 Plasma Sources Sci. Technol. 29 025016
Google Scholar
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Google Scholar
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图 1 仿真区域示意图, el表示弹性碰撞, iz表示电离碰撞, ex表示激发碰撞
Figure 1. Schematic diagram of simulation region, el represents elastic collision, iz represents ionization collision, ex represents excitation collision.
图 2 真空室内磁感应强度分布
Figure 2. Distribution of magnetic induction intensity in vacuum chamber.
图 3 (a)闭合磁场; (b)非闭合磁场; (c) 10 μs闭合磁场电子分布; (d) 10 μs非闭合磁场电子分布
Figure 3. (a) Closed and (b) unclosed magnetic field; electron distribution in (c) closed and (d) unclosed magnetic field at 10 μs.
图 4 (a)实际磁感应强度与临界磁感应强度; (b)磁场闭合程度示意图
Figure 4. (a) The actual and limit magnetic induction intensity; (b) closure degree of magnetic field.
图 5 磁场分布和对应的30 μs的检验电子概率密度分布 (a)四阴极; (b)六阴极; (c)八阴极; (d)十阴极
Figure 5. Distribution of the magnetic field and the electronic probability density at 30 μs: (a) Four cathodes; (b) six cathodes; (c) eight cathodes; (d) ten cathodes.
图 6 磁场分布和对应的30 μs的检验电子概率密度分布 (a) 400 mm; (b) 500 mm; (c) 600 mm; (d) 700 mm
Figure 6. Distribution of the magnetic field and the electronic probability density at 30 μs: (a) 400 mm; (b) 500 mm; (c) 600 mm; (d) 700 mm.
图 7 磁场分布和对应的30 μs的检验电子概率密度分布 (a)正对相吸; (b)正对相斥
Figure 7. Distribution of the magnetic field and the electronic probability density at 30 μs: (a) Attract exactly; (b) repel exactly.
图 8 相吸模式下磁场分布和对应的30 μs的检验电子概率密度分布 (a) 0°; (b) 15°; (c) 30°; (d) 45°
Figure 8. Distribution of the magnetic field and the electronic probability density at 30 μs in attraction mode: (a) 0°; (b) 15°; (c) 30°; (d) 45°.
图 9 相斥模式下磁场分布和对应的30 μs的检验电子概率密度分布 (a) 0°; (b) 15°; (c) 30°; (d) 45°
Figure 9. Distribution of the magnetic field and the electronic probability density at 30 μs: (a) 0°; (b) 15°; (c) 30°; (d) 45°.
图 10 不同转角下镀膜区域电子占比(30 μs)
Figure 10. The proportion of the electron in the coating region with different angles at 30 μs.
表 1 电子参与的Ar放电主要反应表
Table 1. Reactions of Ar discharge involving electrons.
序号 反应方程式 反应类型 反应能量阈值/eV 1 e + Ar → Ar+ + 2e 电离碰撞 15.7 2 e + Ar → Arm + e 激发碰撞 11.5 3 e + Ar → Ar + e 弹性碰撞 — 
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表 2 不同数量阴极构成的闭合磁场中30 μs电子运动情况统计
Table 2. Statistics of electron motion in closed magnetic field composed of 4, 6, 8 and 10 cathodes at 30 μs.
阴极数量 电子溢出比例/% 镀膜区域电子占比/% 4 7.57 22.77 6 4.45 25.78 8 1.77 27.53 10 0.10 26.87
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表 3 不同真空室尺寸构成的闭合磁场中30 μs电子运动情况统计
Table 3. Statistics of electron motion in closed magnetic field with different sizes at 30 μs.
真空室尺寸/mm 电子溢出比例/% 镀膜区域电子占比/% 400 0.82 29.93 500 1.77 27.53 600 3.95 21.59 700 5.49 19.13
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[1] Window B, Savvides N 1986 J. Vac. Sci. Technol. A-Vac. Surf. Films 4 196
Google Scholar
[2] Window B 1986 J. Vac. Sci. Technol. A-Vac. Surf. Films 4 453
Google Scholar
[3] Savvides N, Window B 1986 J. Vac. Sci. Technol. A 4 504
Google Scholar
[4] Kelly P J, Arnell R D, Ahmed W, Afzal A 1996 Mater. Des. 17 215
Google Scholar
[5] Monaghan D P, Teer D G, Laing K C, Efeoglu I, Arnell R D 1993 Surf. Coat. Technol. 59 21
Google Scholar
[6] Arnell R D, Kelly P J 1999 Surf. Coat. Technol. 112 170
Google Scholar
[7] Zhou J, Wu Z, Liu Z H 2008 J. Univ. Sci. Technol. Beijing Miner. Metallurgy Mater. 15 775
[8] Kelly P J, Aenell R D 1998 Surf. Coat. Technol. 108 317
[9] Kelly P J, Arnell R D 1998 J. Vac. Sci. Technol. A-Vac. Surf. Films 16 2858
Google Scholar
[10] Rohde S L, Petrov I, Sproul W D, Barnett S A, Rudnik P J, Graham M E 1990 Thin Solid Films 193 117
[11] Sproul W D, Rudnik P J, Graham M E, Rohde S L 1990 Surf. Coat. Technol. 43 270
[12] 蒋百灵, 曹政, 鲁媛媛, 栾亚 2011 材料热处理学报 32 92
Jiang B L, Cao Z, Lu Y Y, Luan Y 2011 Transact. mater. heat treatment 32 92
[13] Kelly P J, Arnell R D 1996 Surf. Coat. Technol. 86–87 425
[14] Kelly P J, Arnell R D 1998 Vacuum 49 43
Google Scholar
[15] 迈克尔·A. 力伯曼, 阿伦·J. 里登伯格著(浦以康 译) 2007 等离子体放电原理与材料处理 (北京: 科学出版社) 第18—30页
Lieberman M A, Lichtenberg A J (translated by Pu Y K) 2007 Principles of Plasma Discharges and Materials Processing (Beijing: Science Press) pp5–7 (in Chinese)
[16] 曹政, 蒋百灵, 鲁媛媛, 王陶 2011 材料研究学报 25 313
Cao Z, Jiang B L, Lu Y Y, Wang T 2011 Chin. J. Mater. Res. 25 313
[17] 陈明, 周细应, 毛秀娟, 邵佳佳, 杨国良 2014 物理学报 63 098103
Google Scholar
Chen M, Zhou X Y, Mao X J, Shao J J, Yang G L 2014 Acta Phys. Sin. 63 098103
Google Scholar
[18] Yusupov M, Bultinck E, Depla D, Bogaerts 2011 New J. Phys. 13 033018
Google Scholar
[19] Bultinck E, Bogaerts A 2009 New J. Phys. 11 103010
Google Scholar
[20] 汪天龙, 邱清泉, 靖立伟, 张小波 2018 物理学报 67 070703
Google Scholar
Wang T L, Qiu Q Q, Jing L W, Zhang X B 2018 Acta Phys. Sin. 67 070703
Google Scholar
[21] Shidoji E, Ohtake H, Nakano N, Makabe T 1999 Jpn. J. Appl. Phys. Part 1 38 2131
[22] Kim J S, Liu C, Edgell D H, Pardo R 2006 Rev. Sci. Instrum. 77 03B106
Google Scholar
[23] 崔岁寒, 吴忠振, 肖舒, 陈磊, 李体军, 刘亮亮, 傅劲裕, 田修波, 朱剑豪, 谭文长 2019 物理学报 68 195204
Cui S H, Wu Z Z, Xiao S, Chen L, Li T J, Liu L L, Fu J Y, Tian X B, Zhu J H, Tan W C 2019 Acta Phys. Sin 68 195204
[24] Rossnagel S M, Kaufman H R 1987 J. Vac. Sci. Technol. A-Vac. Surf. Films 5 2276
Google Scholar
[25] Rossnagel S M, Kaufman H R 1988 J. Vac. Sci. Technol. A-Vac. Surf. Films 6 223
Google Scholar
[26] 弗朗西斯F. 陈(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
Chen F F (translated by Lin G H) 1980 Introduction to Plasma Physics (Beijing: Science Press) pp5–7 (in Chinese)
[27] Sirghi L, Aoki T, Hatanaka Y 2004 Surf. Coat. Technol. 187 358
Google Scholar
[28] Chen L, Cui S H, Tang W, Zhou L, Li T J, Liu L L, An X K, Wu Z C, Ma Z Y, Lin H, Tian X B, Fu J Y, Chu P K, Wu Z Z 2020 Plasma Sources Sci. Technol. 29 025016
Google Scholar
[29] Birdsall C K 1991 IEEE Trans. Plasma Sci. 19 65
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
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