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旋转圆柱阴极具有较高的理论靶材利用率, 已经普遍应用于各行各业的薄膜制备中. 在其等离子体研究方面, 相对于平面阴极, 旋转圆柱阴极的等离子体放电输运过程涉及三维体系, 对此传统模型的计算量大且收敛性差, 导致仿真困难. 鉴于此, 本文利用二维粒子网格/蒙特卡罗模型计算得到的等离子体密度和电势分布作为自洽背景场, 再通过三维检验电子蒙特卡罗方法跟踪电子运动实现三维等离子体放电仿真. 在此基础上, 以等离子体密度投影作为刻蚀通量, 耦合元胞自动机方法和检验粒子蒙特卡罗方法分别实现三维靶材刻蚀和粒子沉积仿真, 从而构建了阴极磁场-等离子体放电-靶材刻蚀-薄膜沉积的全链条三维仿真体系. 结果表明, 该三维仿真体系能够精准预测圆柱阴极的工作状态, 其中靶材利用率为85.81%, 与实际误差低于2%, 沉积In/Sn摩尔比为11.76, 与实际相差6.6%, 载板上粒子分布与实际薄膜厚度分布吻合, 沉积均匀区长度为1730 mm, 与实际误差仅为1.1%.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.
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Keywords:
- rotating cylindrical magnetron /
- three-dimensional modeling /
- plasma discharge /
- plasma transport
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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
Fig. 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; magnet configuration of (d) the end and (e) the straight section.
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
Fig. 2. Distribution of magnetic field on the surface of the cylindrical target: Normal (r) magnetic flux density by (a1) simulation and (a2) experiment; azimuthal (θ) magnetic flux density by (b1) simulation and (b2) experiment; axial (z) magnetic flux density by (c1) simulation and (c2) experiment.
图 3 双圆柱阴极的PIC/MCC模型示意图
Fig. 3. Schematic diagram of the PIC/MCC model for the double cylindrical cathodes.
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
Fig. 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.
图 5 三维检验电子MC模型示意图 (a) 纵截面; (b) 横截面
Fig. 5. Schematic diagram of the 3D test electron MC model: (a) Longitudinal section; (b) cross section.
图 6 (a)靶面和(b)不同截面上的检验电子密度分布
Fig. 6. Electron density distribution (a) on the target surface and (b) at different cross-sections.
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
Fig. 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.
图 8 (a)仿真和(b)实验得到的阴极刻蚀形貌
Fig. 8. Cathode erosion profile obtained by (a) simulation and (b) experiment.
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
Fig. 9. Deposition distribution of target material particles along (a) the x direction and (b) the z direction.
序号 反应方程式 反应速率系数kr/(m3⋅s–1) 反应阈值/eV 反应类型 1 e+Ar→Ar+e $ \begin{aligned} &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] \end{aligned} $ — 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→ 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 4 e+Arm→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+Arm→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 
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