Establishment and validation of three-dimensional simulation model for magnetron sputtering of rotating cylindrical cathode

MA Ziqi; XU Qiang; XIAO Mengran; TANG Shiyi; TAO Zhiqun; YANG Dongjie; AN Xiaokai; LIU Liangliang; CUI Suihan; WU Zhongzhen

doi:10.7498/aps.74.20250570

Abstract

Rotating cylindrical cathodes possess high theoretical target utilization rates and have been widely used in thin film deposition in various industries. Regarding plasma research, the plasma discharge and transport processes of rotating cylindrical cathodes involve three-dimensional systems, unlike those of planar cathodes. Traditional plasma models applied to these systems require a large quantity of computational resources and have poor convergence, making simulation difficult. In this context, the plasma density and electric potential distributions are calculated by a two-dimensional particle-in-cell/Monte Carlo collision (PIC/MCC) model, and they are used as a self-consistent background field in this work. Furthermore, a three-dimensional electron Monte Carlo method is used to track electron motion, so that three-dimensional plasma discharge simulation can be performed. On this basis, using plasma density projection as the etching flux and the cellular automata method, the rotational etching process of the cylindrical cathode is decomposed into stepwise micro-element static etching, thereby achieving three-dimensional etching behavior simulation. Subsequently, the etched target morphology is equivalently treated as the emission flux of In and Sn atoms, and a three-dimensional test particle Monte Carlo method is employed to trace their motion, realizing three-dimensional particle deposition simulation. Thus, a comprehensive three-dimensional simulation system is constructed through incorporating the cathode magnetic field, plasma discharge, target etching, and thin-film deposition into a complete simulation chain. The results indicate that this three-dimensional simulation system can accurately predict the operating conditions of cylindrical cathodes. The plasma stably accumulates on the cylindrical cathode surface, forming a three-dimensional discharge race track. The simulated etching profile is consistent with experimental result, showing the precise matching of the feature points with the residual thickness of the target. The utilization rate of the target material is 85.81%, with an error of less than 2% compared with that of the measurement. The molar ratio of In/Sn on the substrate is 11.76, with an error of 6.6% compared with the results measured by energy dispersive spectroscopy. The particle distribution on the substrate matches the actual film thickness distribution, with a uniform deposition length of 1730 mm, representing an error of only 1.1% compared with corresponding actual value.

Keywords:

Authors and contacts

School of New Materials, Peking University Shenzhen Graduate School, Shenzhen 518055, China

Corresponding author: CUI Suihan, cuish@pku.edu.cn ; WU Zhongzhen, wuzz@pkusz.edu.cn

Funds: Project supported by the Science and Technology Planning Project of Shenzhen, China (Grant No. KJZD20231023100304009), the National Key R&D Program of China (Grant No. 2023YFA1608802), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 52305174), the Shenzhen Postdoctoral Research Fund Project After Outbound, China (Grant No. 6700200201), and the China Postdoctoral Science Foundation (Grant No. 2024M750089).

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References

[1]	Saenko A V, Tominov R V, Jityaev I L, Vakulov Z E, Avilov V I, Polupanov N V, Smirnov V A 2024 Nanomaterials 14 1901 Google Scholar
[2]	Dhage S R, Badgujar A C 2018 J. Alloys Compd. 763 504 Google Scholar
[3]	Chen J F, Ding X P, Wang J F, Xie Z Y, Wang S H 2024 J. Alloys Compd. 1002 175318 Google Scholar
[4]	Sarakinos K, Alami J, Konstantinidis S 2010 Surf. Coat. Technol. 204 1661 Google Scholar
[5]	Matthews S, De Bosscher W, Blondeel A, Van Holsbeke J, Delrue H 2008 Vacuum 83 518 Google Scholar
[6]	Park J H, Ahn K J, Na S I, Kim H K 2011 Sol. Energy Mater. Sol. Cells 95 657 Google Scholar
[7]	Park J H, Ahn K J, Park K I, Na S I, Kim H K 2010 J. Phys. D: Appl. Phys. 43 115101 Google Scholar
[8]	Van Aeken K, Maheude S, Depla D 2008 J. Phys. D: Appl. Phys. 41 205307 Google Scholar
[9]	Fan Q H, Grago J J, Zhou L Q 2004 J. Appl. Phys. 95 6017 Google Scholar
[10]	Teunissen J, Ebert U 2016 Plasma Sources Sci. Technol. 25 044005 Google Scholar
[11]	Bogaerts A, Bultinck E, Kolev I, Schwaederlé L, Van Aeken K, Buyle G, Depla D 2009 J. Phys. D: Appl. Phys. 42 194018 Google Scholar
[12]	Musschoot J, Depla D, Buyle G, Haemers J, De Gryse R 2006 J. Phys. D: Appl. Phys. 39 3989 Google Scholar
[13]	Fu Y, Ji P, He M, Huang P, Huang G, Huang W 2024 Plasma Chem. Plasma Process. 44 601 Google Scholar
[14]	Bogaerts A, Kolev I, Buyle G 2008 Modeling of the Magnetron Discharge (Berlin: Springer) pp61–130
[15]	Zhu G, Yang Y, Xiao B, Gan Z 2023 Molecules 28 7660 Google Scholar
[16]	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 2023 物理学报 72 085202 Google Scholar Cui S H, Zuo W, Huang J, Li X T, Chen Q H, Guo Y X, Yang C, Wu Z C, Ma Z Y, Fu J Y, Tian X B, Zhu J H, Wu Z Z 2023 Acta Phys. Sin. 72 085202 Google Scholar
[17]	Kapran A, Ballage C, Hubicka Z, Minea T 2025 Vaccum 238 114324 Google Scholar
[18]	Sabavath G K, Swaroop R, Singh J, Panda A B, Haldar S, Rao N, Mahapatra S K 2022 Plasma Phys. Rep. 48 548 Google Scholar
[19]	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, Fu R K Y, Tian X B, Chu P K, Chu W Z 2022 J. Phys. D: Appl. Phys. 55 325203 Google Scholar
[20]	Sirghi L, Aoki T, Hatanaka Y 2004 Surf. Coat. Technol. 187 358 Google Scholar
[21]	Bultinck E, Kolev I, Bogaerts A, Depla D 2008 J. Appl. Phys. 103 013309 Google Scholar
[22]	Cui S H, Wu Z Z, Lin H, Xiao S, Zheng B C, Liu L L, An X K, Fu R K Y, Tian X B, Tan W C, Chu P K 2019 J. Appl. Phys. 125 063302 Google Scholar
[23]	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
[24]	沈向前, 谢泉, 肖清泉, 陈茜, 丰云 2012 物理学报 61 165101 Google Scholar Shen X Q, Xie Q, Xiao Q Q, Chen Q, Feng Y 2012 Acta Phys. Sin. 61 165101 Google Scholar
[25]	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. Technol. 29 025016 Google Scholar
[26]	Nanbu K, Konodo S 1997 Jpn. J. Appl. Phys. 36 4808 Google Scholar
[27]	Shidoji E, Nemoto M, Nomura T 2000 J. Vac. Sci. Technol. A 18 2858 Google Scholar
[28]	Mikolaychuk M, Knyazeva A 2014 AIP Conf. Proc. 1623 419 Google Scholar
[29]	Liu H, Niu X, Yu D R 2019 J. Plasma Phys. 85 905850208 Google Scholar
[30]	Rumble J R 2024 CRC Handbook of Chemistry and Physics (Florida: CRC Press) pp10–113
[31]	Shon C H, Lee J K 2002 Appl. Surf. Sci. 192 258 Google Scholar

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图 1 ITO圆柱阴极的基本结构与磁场配置　(a) 三维模型; (b) 横截面图; (c) 磁铁配置俯视图, 其中蓝色矢量符号表示磁极方向; (d) 端头和(e) 直部的磁铁配置截面

Figure 1. Basic structure and magnetic field configuration of ITO cylindrical cathode: (a) Three-dimensional (3D) model; (b) cross-sectional view; (c) top view of the magnet configuration, where the blue vectors represent the direction of the magnetic poles; (d), (e) magnet configuration of (d) the end and (e) the straight section.

DownLoad: Full-Size Img PowerPoint

图 2 圆柱靶材表面各向磁场分布　(a1)仿真和(a2)实验的法向(r)磁感应强度; (b1)仿真和(b2)实验的环向(θ)磁感应强度; (c1)仿真和(c2)实验的轴向(z)磁感应强度

Figure 2. Distribution of magnetic field on the surface of the cylindrical target: (a1), (a2) Normal (r) magnetic flux density by (a1) simulation and (a2) experiment; (b1), (b2) azimuthal (θ) magnetic flux density by (b1) simulation and (b2) experiment; (c1), (c2) axial (z) magnetic flux density by (c1) simulation and (c2) experiment.

DownLoad: Full-Size Img PowerPoint

图 3 双圆柱阴极的PIC/MCC模型示意图

Figure 3. Schematic diagram of the PIC/MCC model for the double cylindrical cathodes.

DownLoad: Full-Size Img PowerPoint

图 4 放电电压250 V、气压0.6 Pa条件下, 双圆柱阴极放电的稳态　(a) 等离子体密度、(b) 电势和(c) 磁感线分布

Figure 4. Steady-state distribution of (a) plasma density, (b) electric potential, and (c) magnetic flux lines for the discharge of double cylindrical cathodes at 250 V, 0.6 Pa.

DownLoad: Full-Size Img PowerPoint

图 5 三维检验电子MC模型示意图　(a) 纵截面; (b) 横截面

Figure 5. Schematic diagram of the 3D test electron MC model: (a) Longitudinal section; (b) cross section.

DownLoad: Full-Size Img PowerPoint

图 6 (a)靶面和(b)不同截面上的检验电子密度分布

Figure 6. Electron density distribution (a) on the target surface and (b) at different cross-sections.

DownLoad: Full-Size Img PowerPoint

图 7 圆柱阴极CA模型　(a) 静态模型; (b) 耦合旋转效应; (c) 动态刻蚀模拟流程图

Figure 7. Schematic diagram of the CA model for the cylindrical cathode: (a) Static model; (b) model coupled with rotation; (c) flowchart of dynamic erosion simulation with the rotational CA model.

DownLoad: Full-Size Img PowerPoint

图 8 (a)仿真和(b)实验得到的阴极刻蚀形貌

Figure 8. Cathode erosion profile obtained by (a) simulation and (b) experiment.

DownLoad: Full-Size Img PowerPoint

图 9 靶材粒子(a)沿x方向上和(b)沿z方向上的沉积数量分布

Figure 9. Deposition distribution of target material particles along (a) the x direction and (b) the z direction.

DownLoad: Full-Size Img PowerPoint

表 1 Ar气放电反应参数表^[23]

Table 1. Table of Ar gas discharge reaction parameters^[23].

序号	反应方程式	反应速率系数 k _r/(m³⋅s^–1)	反应阈值/eV	反应类型
1	e+Ar → Ar+e	$ 2.336 \times {10^{ - 14}}{T_{\text{e}}}^{1.609} \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
2	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
3	e+Ar → Ar^m+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
4	e+Ar^m → Ar⁺+2e	$ 6.8 \times {10^{ - 15}}{T_{\text{e}}}^{0.67} \times \exp \left( { - 4.2/{T_{\text{e}}}} \right) $	4.2	激发态电离
5	e+Ar^m → Ar+e	$ 4.3 \times {10^{ - 16}}{T_{\text{e}}}^{0.74} $	–11.56	退激发碰撞
6	Ar⁺+Ar → Ar⁺+Ar	硬球碰撞	—	弹性碰撞
7	Ar⁺+Ar → Ar+Ar⁺	硬球碰撞	—	电荷交换

DownLoad: CSV

[1]	Saenko A V, Tominov R V, Jityaev I L, Vakulov Z E, Avilov V I, Polupanov N V, Smirnov V A 2024 Nanomaterials 14 1901 Google Scholar
[2]	Dhage S R, Badgujar A C 2018 J. Alloys Compd. 763 504 Google Scholar
[3]	Chen J F, Ding X P, Wang J F, Xie Z Y, Wang S H 2024 J. Alloys Compd. 1002 175318 Google Scholar
[4]	Sarakinos K, Alami J, Konstantinidis S 2010 Surf. Coat. Technol. 204 1661 Google Scholar
[5]	Matthews S, De Bosscher W, Blondeel A, Van Holsbeke J, Delrue H 2008 Vacuum 83 518 Google Scholar
[6]	Park J H, Ahn K J, Na S I, Kim H K 2011 Sol. Energy Mater. Sol. Cells 95 657 Google Scholar
[7]	Park J H, Ahn K J, Park K I, Na S I, Kim H K 2010 J. Phys. D: Appl. Phys. 43 115101 Google Scholar
[8]	Van Aeken K, Maheude S, Depla D 2008 J. Phys. D: Appl. Phys. 41 205307 Google Scholar
[9]	Fan Q H, Grago J J, Zhou L Q 2004 J. Appl. Phys. 95 6017 Google Scholar
[10]	Teunissen J, Ebert U 2016 Plasma Sources Sci. Technol. 25 044005 Google Scholar
[11]	Bogaerts A, Bultinck E, Kolev I, Schwaederlé L, Van Aeken K, Buyle G, Depla D 2009 J. Phys. D: Appl. Phys. 42 194018 Google Scholar
[12]	Musschoot J, Depla D, Buyle G, Haemers J, De Gryse R 2006 J. Phys. D: Appl. Phys. 39 3989 Google Scholar
[13]	Fu Y, Ji P, He M, Huang P, Huang G, Huang W 2024 Plasma Chem. Plasma Process. 44 601 Google Scholar
[14]	Bogaerts A, Kolev I, Buyle G 2008 Modeling of the Magnetron Discharge (Berlin: Springer) pp61–130
[15]	Zhu G, Yang Y, Xiao B, Gan Z 2023 Molecules 28 7660 Google Scholar
[16]	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 2023 物理学报 72 085202 Google Scholar Cui S H, Zuo W, Huang J, Li X T, Chen Q H, Guo Y X, Yang C, Wu Z C, Ma Z Y, Fu J Y, Tian X B, Zhu J H, Wu Z Z 2023 Acta Phys. Sin. 72 085202 Google Scholar
[17]	Kapran A, Ballage C, Hubicka Z, Minea T 2025 Vaccum 238 114324 Google Scholar
[18]	Sabavath G K, Swaroop R, Singh J, Panda A B, Haldar S, Rao N, Mahapatra S K 2022 Plasma Phys. Rep. 48 548 Google Scholar
[19]	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, Fu R K Y, Tian X B, Chu P K, Chu W Z 2022 J. Phys. D: Appl. Phys. 55 325203 Google Scholar
[20]	Sirghi L, Aoki T, Hatanaka Y 2004 Surf. Coat. Technol. 187 358 Google Scholar
[21]	Bultinck E, Kolev I, Bogaerts A, Depla D 2008 J. Appl. Phys. 103 013309 Google Scholar
[22]	Cui S H, Wu Z Z, Lin H, Xiao S, Zheng B C, Liu L L, An X K, Fu R K Y, Tian X B, Tan W C, Chu P K 2019 J. Appl. Phys. 125 063302 Google Scholar
[23]	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
[24]	沈向前, 谢泉, 肖清泉, 陈茜, 丰云 2012 物理学报 61 165101 Google Scholar Shen X Q, Xie Q, Xiao Q Q, Chen Q, Feng Y 2012 Acta Phys. Sin. 61 165101 Google Scholar
[25]	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. Technol. 29 025016 Google Scholar
[26]	Nanbu K, Konodo S 1997 Jpn. J. Appl. Phys. 36 4808 Google Scholar
[27]	Shidoji E, Nemoto M, Nomura T 2000 J. Vac. Sci. Technol. A 18 2858 Google Scholar
[28]	Mikolaychuk M, Knyazeva A 2014 AIP Conf. Proc. 1623 419 Google Scholar
[29]	Liu H, Niu X, Yu D R 2019 J. Plasma Phys. 85 905850208 Google Scholar
[30]	Rumble J R 2024 CRC Handbook of Chemistry and Physics (Florida: CRC Press) pp10–113
[31]	Shon C H, Lee J K 2002 Appl. Surf. Sci. 192 258 Google Scholar

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