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In recent years, dual-frequency capacitively coupled plasma discharge technology has demonstrated remarkable advantages in the fields of material processing. In this paper, a one-dimensional PIC/MCC (particle-in-cell/Monte Carlocollision) simulation method is used to discuss the influence of low frequency on the discharge characteristics of capacitively coupled argon/methane plasma driven by dual-frequency (20/100 MHz) dipole, with an external magnetic field added. The simulation results show that when the high frequency is an integer multiple of the low frequency, the superposition of high and low frequencies is significant, and the sheath oscillation is more obvious. As low frequency increases, the electron density, charge density, high-energy electron density and electron heating rate all increase. Specifically, as low frequency increase, the electron density increases to 14%, the electron temperature near the sheath decreases by about 12%, the electron energy probability distribution (EEPF) shows a double Maxwellian distribution, the populations of both low-energy electrons and high-energy electrons increase, and at the same time, the densities of various ions and the angle and energy distributions of ${\text{CH}}_{4}^{+} $ and ${\text{CH}}_{3}^{+} $ particles reaching the electrode plates are influenced. In the Ar/CH4 plasma driven by dual-frequency, with external magnetic field added, the controlling of ion energy can effectively optimize the structure and performance of carbon-containing films. By regulating discharge parameters to control the incident angle of the ions on the substrate, carbon-containing atoms can be deposited in a specific direction, thereby achieving the directional growth of carbon-containing films. This is significant for the preparation of graphene films, carbon nanotube arrays, etc. Meanwhile, the regulation of the incident angle of ions is helpful to improve the binding force between the carbon film and the substrate. It is found in this study that when the incident angle of the ions is around 0.32, the average energy of the ions reaches its peak. This peak is most significant at a low frequency of 15 MHz. The results in this paper provide a theoretical reference for preparing carbon films. [1] Li Y M, Mann D, Rolandi M, Kim W 2004 Nano Lett. 4 317
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[2] Donnelly V M, Kornblit A 2013 J. Vac. Sci. Technol. A. 31 050825
Google Scholar
[3] Jung C O, Chi K K, Hwang B G, Moon J T, Lee M Y, Lee J G 1999 Thin Solid Films 341 112
Google Scholar
[4] Schulze J, Gans T, O'Connell D, Czarnetzki U, Ellingboe A R, Turner M M 2007 J. Phys. D: Appl. Phys. 40 7008
Google Scholar
[5] Boyle P C, Ellingboe A R, Turner M M 2004 J. Phys. D: Appl. Phys. 37 697
Google Scholar
[6] Robiche J , Boyle P C , Turner M M, Ellingboe A R 2003 J. Phys. D: Appl. Phys. 36 1810
[7] Goto H H, Löwe H D, Ohmi T 1992 J. Vac. Sci. Technol. A. 10 3048
Google Scholar
[8] Goto H H, Löwe H D, Ohmi T 1993 IEEE Trans. Semicond. Manuf. 6 58
Google Scholar
[9] Tsai W, Mueller G, Lindquist R, Frazier B, Vahedi V 1996 J. Vac. Sci. Technol. B 14 3276
Google Scholar
[10] Sharma S, Turner M M 2014 J. Phys. D: Appl. Phys. 47 285201
Google Scholar
[11] Kim H C, Lee J K, Shon J W 2003 Phys. Plasmas 10 4545
Google Scholar
[12] Yang S, Zhang W, Shen J F, Liu H, Tang C J, Xu Y H, Cheng J, Shao J R, Xiong J, Wang X Q, Liu H F, Huang J, Zhang X, Lan H, Li Y C 2024 AIP Adv. 14 065104
Google Scholar
[13] Sharma S, Sirse N, Turner M M, Ellingboe A R 2018 Phys. Plasmas 25 063501
Google Scholar
[14] Yin G Q, Gao S S, Liu Z H, Yuan Q H 2022 Phys. Lett. A 426 127910
Google Scholar
[15] 高闪闪2022 硕士学位论文(兰州: 西北师范大学)
Gao S S 2022 M. S. Thesis (Lanzhou: Northwest Normal University
[16] Yang S L, Zhang Y, Wang H Y, Cui J W, Jiang W 2017 Plasma Processes Polym. 14 1700087
Google Scholar
[17] Yang S L, Chang L, Zhang Y, Jiang W 2018 Plasma Sources Sci. Technol. 27 035008
Google Scholar
[18] Yan M H, Wu H H, Wu H, Peng Y L, Yang S L 2024 J. Vac. Sci. Technol. A 42 053007
Google Scholar
[19] Sharma S, Patil S, Sengupta S, Sen A, Khrabrov A, Kaganovich I 2022 Phys. Plasmas 29 063501
Google Scholar
[20] Sun J Y, Wen H, Zhang Q Z, Schulze J, Liu Y X, Wang Y N 2022 Plasma Sources Sci. Technol. 31 085012
Google Scholar
[21] Zheng B C, Wang K L, Grotjohn T, Schuelke T, Fan Q H 2019 Plasma Sources Sci. Technol. 28 09LT03
Google Scholar
[22] Yang S L, Zhang Y, Wang H Y, Wang S, Jiang W 2017 Phys. Plasmas 24 033504
Google Scholar
[23] Liu Y X, Liang Y S, Wen D Q, Bi Z H, Wang Y N 2015 Plasma Sources Sci. Technol. 24 025013
Google Scholar
[24] Yin G Q, Jiang Y B, Yuan Q H 2024 Mod. Phys. Lett. B 38 2450269
[25] Wang J-C, Tian P, Kenney J, Rauf S, Korolov I, Schulze J 2021 Plasma Sources Sci. Technol. 30 075031
Google Scholar
[26] Birdsall C K 1991 IEEE Trans. Plasma Sci. 19 65
Google Scholar
[27] Vahedi V, Surendra M 1995 Comput. Phys. Commun. 87 179
Google Scholar
[28] Verboncoeur J P 2001 J. Comput. Phys. 174 421
Google Scholar
[29] 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
[30] 金晓林, 杨中海 2006 物理学报 55 5930
Google Scholar
Jin X L, Yang Z H 2006 Acta Phys. Sin. 55 5930
Google Scholar
[31] Song M Y, Yoon J S, Cho H, Itikawa Y, Karwasz G P, Kokoouline V, Nakamura Y, Tennyson J 2015 J. Phys. Chem. Ref. Data. 44 023101
Google Scholar
[32] Sun J Y, Zhang Q Z, Liu J R, Song Y H, Wang Y N 2020 Plasma Sources Sci. Technol. 29 114002
Google Scholar
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图 1 模拟装置图
Figure 1. Simulation setup diagram.
图 2 固定磁场强度为20 G, Ar∶CH4 = 0.85∶0.15时, (a)电子密度; (b)电荷密度; (c)高能电子密度随低频频率变化的时空分布图
Figure 2. Spatiotemporal distribution diagram of the (a) electron density, (b) charge density, (c) high-energy electron density with low frequency at a fixed magnetic field strength of 20 G and Ar∶CH4 = 0.85∶0.15.
图 3 固定磁场强度为20 G, Ar∶CH4 = 0.85∶0.15, (a)电子温度 (eV), (b)电子加热率, (c)电场(V/m)随低频频率变化的时空分布图
Figure 3. Spatiotemporal distribution diagram of the (a) electron temperature (eV); (b) electron heating rate; (c) electric field (V/m) with low frequency at a fixed magnetic field strength of 20 G and Ar∶CH4 = 0.85∶0.15.
图 4 固定磁场强度为20 G, Ar∶CH4 = 0.85∶0.15, 电子能量概率分布函数随低频频率变化的分布图
Figure 4. Distribution of the electric energy probability function with low frequency at a fixed magnetic field strength of 20 G and Ar∶CH4 = 0.85∶0.15.
图 5 固定磁场强度为20 G, Ar∶CH4 = 0.85∶0.15, 电子、CH4+、CH3+、Ar+的离子密度随低频频率变化的分布图
Figure 5. The ion density distributions of electron、CH4+, CH3+, Ar+ with low frequency at a fixed magnetic field strength of 20 G and Ar∶CH4 = 0.85∶0.15.
图 6 固定磁场强度为20 G, Ar∶CH4 = 0.85∶0.15, 到达极板处的$ {\text{CH}}_{4}^{+} $, $ {\text{CH}}_{3}^{+} $粒子在每个速度方向与轴向的夹角处能量的平均值随低频频率变化的分布图
Figure 6. Distribution of the average value of the energy of $ {\text{CH}}_{4}^{+} $ and $ {\text{CH}}_{3}^{+} $ particles arriving at the pole plate at the angle between each velocity direction and the axial direction with low frequency at a fixed magnetic field strength of 20 G and Ar∶CH4 = 0.85∶0.15.
表 1 碰撞反应类型
Table 1. Collision reaction type in the simulation.
序号 反应式 碰撞类型 阈值/eV 1 $ {{\text{e}}^{{ - }}}{\text{ + Ar}} \to {{\text{e}}^{{ - }}}{\text{ + Ar}} $ 弹性碰撞 0 2 $ {{\text{e}}^{{ - }}}{\text{ + Ar}} \to {{\text{e}}^{{ - }}}{\text{ + Ar}} $ 激发碰撞 11.5 3 $ {{\text{e}}^{{ - }}}{\text{ + Ar}} \to 2{{\text{e}}^{{ - }}}{\text{ + A}}{{\text{r}}^{+}} $ 电离碰撞 15.80 4 $ {\text{A}}{{\text{r}}^{+}}{\text{ + Ar}} \to {\text{A}}{{\text{r}}^{+}}{\text{ + Ar}} $ 弹性碰撞 0.00 5 $ {\text{A}}{{\text{r}}^{+}}{\text{ + Ar}} \to {\text{Ar + A}}{{\text{r}}^ + } $ 电荷交换 0.00 6 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} $ 弹性碰撞 0 7 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_{4}}\left( {{{\text{V}}_{2}}} \right) $ 激发碰撞 0.162 8 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_{4}}\left( {{{\text{V}}_{1}}} \right) $ 激发碰撞 0.362 9 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_{3}}{\text{ + H}} $ 激发碰撞 7.5 10 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_{2}}{+}{{\text{H}}_2} $ 激发碰撞 9.1 11 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to {{\text{e}}^{{ - }}}{\text{ + C + 2}}{{\text{H}}_2} $ 激发碰撞 15.5 12 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to {{\text{e}}^{{ - }}}{\text{ + CH + }}{{\text{H}}_{2}}{\text{ + H}} $ 激发碰撞 15.5 13 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to {2}{{\text{e}}^{{ - }}}{\text{ + CH}}_4^ + $ 电离碰撞 12.63 14 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to {2}{{\text{e}}^{{ - }}}{\text{ + H + CH}}_3^ + $ 电离碰撞 12.63 15 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to {2}{{\text{e}}^{{ - }}}{+}{{\text{H}}_{2}}{\text{ + CH}}_2^ + $ 电离碰撞 16.2 16 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to 2{{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_{3}}{+}{{\text{H}}^ + } $ 电离碰撞 21.1 17 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to 2{{\text{e}}^{{ - }}}{\text{ + 2}}{{\text{H}}_{2}}{+}{{\text{C}}^ + } $ 电离碰撞 22 18 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to 2{{\text{e}}^{{ - }}}{\text{ + H + }}{{\text{H}}_{2}}{\text{ + C}}{{\text{H}}^ + } $ 电离碰撞 22.2 19 $ {{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_4} \to 2{{\text{e}}^{{ - }}}{\text{ + C}}{{\text{H}}_{2}}{+}{{\text{H}}_2^ +} $ 电离碰撞 22.3 
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[1] Li Y M, Mann D, Rolandi M, Kim W 2004 Nano Lett. 4 317
Google Scholar
[2] Donnelly V M, Kornblit A 2013 J. Vac. Sci. Technol. A. 31 050825
Google Scholar
[3] Jung C O, Chi K K, Hwang B G, Moon J T, Lee M Y, Lee J G 1999 Thin Solid Films 341 112
Google Scholar
[4] Schulze J, Gans T, O'Connell D, Czarnetzki U, Ellingboe A R, Turner M M 2007 J. Phys. D: Appl. Phys. 40 7008
Google Scholar
[5] Boyle P C, Ellingboe A R, Turner M M 2004 J. Phys. D: Appl. Phys. 37 697
Google Scholar
[6] Robiche J , Boyle P C , Turner M M, Ellingboe A R 2003 J. Phys. D: Appl. Phys. 36 1810
[7] Goto H H, Löwe H D, Ohmi T 1992 J. Vac. Sci. Technol. A. 10 3048
Google Scholar
[8] Goto H H, Löwe H D, Ohmi T 1993 IEEE Trans. Semicond. Manuf. 6 58
Google Scholar
[9] Tsai W, Mueller G, Lindquist R, Frazier B, Vahedi V 1996 J. Vac. Sci. Technol. B 14 3276
Google Scholar
[10] Sharma S, Turner M M 2014 J. Phys. D: Appl. Phys. 47 285201
Google Scholar
[11] Kim H C, Lee J K, Shon J W 2003 Phys. Plasmas 10 4545
Google Scholar
[12] Yang S, Zhang W, Shen J F, Liu H, Tang C J, Xu Y H, Cheng J, Shao J R, Xiong J, Wang X Q, Liu H F, Huang J, Zhang X, Lan H, Li Y C 2024 AIP Adv. 14 065104
Google Scholar
[13] Sharma S, Sirse N, Turner M M, Ellingboe A R 2018 Phys. Plasmas 25 063501
Google Scholar
[14] Yin G Q, Gao S S, Liu Z H, Yuan Q H 2022 Phys. Lett. A 426 127910
Google Scholar
[15] 高闪闪2022 硕士学位论文(兰州: 西北师范大学)
Gao S S 2022 M. S. Thesis (Lanzhou: Northwest Normal University
[16] Yang S L, Zhang Y, Wang H Y, Cui J W, Jiang W 2017 Plasma Processes Polym. 14 1700087
Google Scholar
[17] Yang S L, Chang L, Zhang Y, Jiang W 2018 Plasma Sources Sci. Technol. 27 035008
Google Scholar
[18] Yan M H, Wu H H, Wu H, Peng Y L, Yang S L 2024 J. Vac. Sci. Technol. A 42 053007
Google Scholar
[19] Sharma S, Patil S, Sengupta S, Sen A, Khrabrov A, Kaganovich I 2022 Phys. Plasmas 29 063501
Google Scholar
[20] Sun J Y, Wen H, Zhang Q Z, Schulze J, Liu Y X, Wang Y N 2022 Plasma Sources Sci. Technol. 31 085012
Google Scholar
[21] Zheng B C, Wang K L, Grotjohn T, Schuelke T, Fan Q H 2019 Plasma Sources Sci. Technol. 28 09LT03
Google Scholar
[22] Yang S L, Zhang Y, Wang H Y, Wang S, Jiang W 2017 Phys. Plasmas 24 033504
Google Scholar
[23] Liu Y X, Liang Y S, Wen D Q, Bi Z H, Wang Y N 2015 Plasma Sources Sci. Technol. 24 025013
Google Scholar
[24] Yin G Q, Jiang Y B, Yuan Q H 2024 Mod. Phys. Lett. B 38 2450269
[25] Wang J-C, Tian P, Kenney J, Rauf S, Korolov I, Schulze J 2021 Plasma Sources Sci. Technol. 30 075031
Google Scholar
[26] Birdsall C K 1991 IEEE Trans. Plasma Sci. 19 65
Google Scholar
[27] Vahedi V, Surendra M 1995 Comput. Phys. Commun. 87 179
Google Scholar
[28] Verboncoeur J P 2001 J. Comput. Phys. 174 421
Google Scholar
[29] 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
[30] 金晓林, 杨中海 2006 物理学报 55 5930
Google Scholar
Jin X L, Yang Z H 2006 Acta Phys. Sin. 55 5930
Google Scholar
[31] Song M Y, Yoon J S, Cho H, Itikawa Y, Karwasz G P, Kokoouline V, Nakamura Y, Tennyson J 2015 J. Phys. Chem. Ref. Data. 44 023101
Google Scholar
[32] Sun J Y, Zhang Q Z, Liu J R, Song Y H, Wang Y N 2020 Plasma Sources Sci. Technol. 29 114002
Google Scholar
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