Three-dimensional multi-physics simulation of dual-frequency capacitively coupled Ar/CF<sub>4</sub> plasma source

LI Jingze; ZHAO Mingliang; ZHANG Yuru; GAO Fei; WANG Younian

doi:10.7498/aps.74.20251121

Abstract

Capacitively coupled plasma sources, which are widely used in the etching and deposition processes of semiconductor manufacturing, have the advantages of simple structure, low cost, and the ability to generate large-area uniform plasma. To meet the requirements of advanced processes, fluid models are usually required to simulate plasma sources and optimize their important plasma parameters, such as density and uniformity. In this work, an independently-developed capacitively coupled plasma fast simulation program is employed to conduct three-dimensional fluid simulations of a dual-frequency capacitively coupled Ar/CF₄ plasma source, with the aims of verifying the effectiveness of the program and investigating the influence of discharge parameters such as gas pressure, high and low-frequency voltages, low frequency, and background component ratios. The simulation results show that the program has an extremely high simulation speed. As the low-frequency voltage increases, the plasma density initially remains approximately constant and then significantly increases, while the plasma uniformity initially rises and then significantly decreases. In this process, the γ-mode heating of the low-frequency source increases and becomes the dominant mode in replace of the α-mode of high-frequency source. As the lower frequency increases, plasma density initially remains approximately constant and then slightly increases, while the plasma uniformity does not change much. this is because the γ-mode heating is frequency independent, while the α-mode heating is much lower than high-frequency source. As the high-frequency voltage increases, the plasma density significantly increases, while the plasma uniformity initially rises and then significantly decreases, the α-mode heating of high-frequency source is significantly enhanced in this process. As the pressure increases, the plasma density significantly increases, and the plasma uniformity also rises significantly, the reason is the more complete collision between particles and background gases. As the Ar ratio in background gases increases, the plasma density changes slightly, the density of Ar-related particles generally increases and the density of CF₄-related particles generally decreases, although there are some non-monotonic changes in particle densities, which reflects the mutual promotion between some ionization and dissociation reactions.

Keywords:

Authors and contacts

Key Laboratory of Materials Modification by Laser, Ion, and Electron Beams (Ministry of Education), School of Physics, Dalian University of Technology, Dalian 116024, China

Corresponding author: ZHAO Mingliang, mlzhao@dlut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11935005).

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References

[1]	Lieberman M A, Lichtenberg A J 2005 Principles of Plasma Discharges and Materials Processing (New York: Wiley) pp387−457
[2]	王友年, 宋远红, 张钰如 2024 射频等离子体物理基础(北京: 科学出版社) 第236页 Wang Y N, Song Y H, Zhang Y R 2024 Fundamentals of Radio-frequency Plasma Physics (Beijing: Science Press) p236
[3]	Zorat R, Goss J, Boilson D, Vender D 2000 Plasma Sources Sci. Technol. 9 161 Google Scholar
[4]	Kimura T, Kasugai H 2010 J. Appl. Phys. 107 083308 Google Scholar
[5]	Saikia P, Bhuyan H, Escalona M, Favre M, Rawat R S, Wyndham E 2018 AIP Adv. 8 045113 Google Scholar
[6]	Donkó Z, Derzsi A, Vass M, Horváth B, Wilczek S, Hartmann B, Hartmann P 2021 Plasma Sources Sci. Technol. 30 095017 Google Scholar
[7]	Vahedi V, DiPeso G, Birdsall C K, Lieberman M A, Rognlien T D 1993 Plasma Sources Sci. Technol. 2 261 Google Scholar
[8]	Wünderlich D, Gutser R, Fantz U 2009 Plasma Sources Sci. Technol. 18 045031 Google Scholar
[9]	Passchier J D P, Goedheer W J 1993 J. Appl. Phys. 74 3744 Google Scholar
[10]	Alves L L, Marques L 2012 Plasma Phys. Controlled Fusion 54 124012 Google Scholar
[11]	Graves D B 1987 J. Appl. Phys. 62 88 Google Scholar
[12]	Kushner M J 2009 J. Phys. D: Appl. Phys. 42 194013 Google Scholar
[13]	Kushner M J 2007 IEEE Trans. Plasma Sci. 14 188
[14]	Yang Y, Kushner M J 2010 Plasma Sources Sci. Technol. 19 055011 Google Scholar
[15]	Model Low-Temperature Plasma Sources with the Plasma Module https://www.comsol.com/plasma-module [2025-8-16]
[16]	Benchmark Model of a Capacitively Coupled Plasma https://www.comsol.com/model/benchmark-model-of-a-capacitively-coupled-plasma-11745 [2025-8-16]
[17]	Model of an Argon/Chlorine Inductively Coupled Plasma Reactor with RF Bias https://www.comsol.com/model/model-of-an-argonchlorine-inductively-coupled-plasma-reactor-with-rf-bias-110171 [2025-8-16]
[18]	Model of an Argon/Oxygen Capacitively Coupled Plasma Reactor https://www.comsol.com/model/model-of-an-argonoxygen-capacitively-coupled-plasma-reactor-108931 [2025-8-16]
[19]	Li J Z, Zhao M L, Zhang Y R, Gao F, Wang Y N 2025 Comput. Phys. Commun. 307 109392 Google Scholar
[20]	Wen Y Y, Li X Y, Zhang Y R, Song Y H, Wang Y N 2022 J. Phys. D: Appl. Phys. 55 200001 Google Scholar
[21]	Vasenkov A V, Li X, Oehrlein G S, Kushner M J 2004 J. Vac. Sci. Technol. , A 22 511-530 Google Scholar
[22]	Zhang Y R, Bogaerts A, Wang Y N 2012 J. Phys. D: Appl. Phys. 45 485204 Google Scholar

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图 1 腔室结构示意图(r-z平面)

Figure 1. Diagram of chamber structure (r-z plane).

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图 2 模拟区域的网格划分

Figure 2. Discrete mesh of the simulation area.

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图 3 双频容性耦合Ar/CF₄等离子体中代表性的组分收敛曲线, 其纵坐标表示相应粒子密度的空间平均值

Figure 3. The representative convergence curves of species in dual frequency capacitively-coupled Ar/CF₄ plasma, where the y-axis represents the spatially averaged density.

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图 4 双频容性耦合Ar/CF₄等离子体中(a)电子密度、(b)电子温度、(c)电势和(d)—(j)离子密度的三维模拟结果

Figure 4. The three-dimensional simulation results of (a) electron density, (b) electron temperature, (c) potential and (d)–(j) ion densities in the dual frequency capacitively-coupled Ar/CF₄ plasma.

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图 5 双频容性耦合Ar/CF₄等离子体中(a)—(f)背景气体的密度、流速、温度以及(g)—(l)活性中性粒子密度的三维模拟结果

Figure 5. The three-dimensional simulation results of (a)–(f) densities, velocities and temperatures of background gases and (g)–(l) densities of active neutral particles in the dual frequency capacitively-coupled Ar/CF₄ plasma.

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图 6 不同低频电压下(a)电子密度、(b)电子温度、(c) Ar⁺离子密度、(d) $\rm CF_3^+ $离子密度、(e) F^–离子密度和(f) F原子密度的r方向空间分布

Figure 6. The radial spatial distribution of (a) electron density, (b) electron temperature, (c) Ar⁺ density, (d) $\rm CF_3^+ $ density, (e) F^– density, and (f) F density under different low-frequency voltages.

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图 7 不同低频频率下(a)电子密度、(b)电子温度、(c) Ar⁺离子密度、(d) $\rm CF_3^+ $离子密度、(e) F^–离子密度、(f) F原子密度的r方向空间分布

Figure 7. The radial spatial distribution of (a) electron density, (b) electron temperature, (c) Ar⁺ density, (d) $\rm CF_3^+$ density, (e) F^– density, and (f) F density under different lower frequencies.

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图 8 不同高频电压下(a)电子密度、(b)电子温度、(c) Ar⁺离子密度、(d) $\rm CF_3^+$离子密度、(e) F^–离子密度、(f) F原子密度的r方向空间分布

Figure 8. The radial spatial distribution of (a) electron density, (b) electron temperature, (c) Ar⁺ density, (d) $\rm CF_3^+ $ density, (e) F^– density, and (f) F density under different high-frequency voltages.

DownLoad: Full-Size Img PowerPoint

图 9 不同气压下(a)电子密度、(b)电子温度、(c) Ar⁺离子密度、(d) $\rm CF_3^+ $离子密度、(e) F^–离子密度、(f) F原子密度的r方向空间分布

Figure 9. The radial spatial distribution of (a) electron density, (b) electron temperature, (c) Ar⁺ density, (d) $\rm CF_3^+ $ density, (e) F^– density, and (f) F density under different pressures.

DownLoad: Full-Size Img PowerPoint

图 10 不同组分比例下(a)电子密度、(b)电子温度、(c) Ar⁺离子密度、(d) $\rm CF_3^+ $离子密度、(e) F^–离子密度、(f) F原子密度的r方向空间分布

Figure 10. The radial spatial distribution of (a) electron density, (b) electron temperature, (c) Ar⁺ density, (d) $\rm CF_3^+ $ density, (e) F^– density, and (f) F density under different component ratios.

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表 1 模型中考虑的碰撞反应

Table 1. Collision reactions considered in the model.

编号	反应表达式	文献	编号	反应表达式	文献
1	e + Ar → e + Ar	[19]	39	e + CF₄ → CF₃ + F^–	[19]
2	Ar⁺ + Ar → Ar⁺ + Ar	[19]	40	$\rm e + CF_4 \to CF_3^- + F $	[19]
3	$\rm CF_3^+ + Ar \to CF_3^+ + Ar $	[19]	41	F^– + CF₃ → e + CF₄	[19]
4	$\rm CF_2^+ + Ar \to CF_2^+ + Ar $	[19]	42	F^– + CF₂ → e + CF₃	[19]
5	CF⁺ + Ar → CF⁺ + Ar	[19]	43	F^– + CF → e + CF₂	[19]
6	F⁺ + Ar → F⁺ + Ar	[19]	44	F^– + F → e + F₂	[19]
7	F^– + Ar → F^– + Ar	[19]	45	$\rm CF_3^- + CF_3^+ \to 2CF_3 $	[19]
8	$\rm CF_3^- + Ar \to CF_3^- + Ar $	[19]	46	$\rm F^- + CF_3^+ \to CF_3 + F $	[19]
9	Ar^* + Ar → Ar^* + Ar	[19]	47	$\rm F^ + CF_3^+ \to CF_2 + F_2 $	[19]
10	CF₃ + Ar → CF₃ + Ar	[19]	48	$\rm F^- + CF_2^+ \to CF_2 + F $	[19]
11	CF₂ + Ar → CF₂ + Ar	[19]	49	$\rm F^- + CF_2^+ \to CF + F_2 $	[19]
12	CF + Ar → CF + Ar	[19]	50	F^– + CF⁺ → CF + F	[19]
13	F₂ + Ar → F₂ + Ar	[19]	51	F^– + F⁺ → 2F	[19]
14	F + Ar → F + Ar	[19]	52	$\rm CF_3^- + CF_2^+ \to CF_3 + CF_2 $	[19]
15	e + CF₄ → e + CF₄	[19]	53	$\rm CF_3^- + CF^+ \to CF_3 + CF $	[19]
16	Ar⁺ + CF₄ → Ar⁺ + CF₄	[19]	54	$\rm CF_3^- + F^+ \to CF_3 + F $	[19]
17	$\rm CF_3^+ + CF_4 \to CF_3^+ + CF_4 $	[19]	55	$\rm CF_2^+ + CF_3 \to CF_3^+ + CF_2 $	[19]
18	$\rm CF_2^+ + CF_4 \to CF_2^+ + CF_4 $	[19]	56	$\rm CF^+ + CF_3 \to CF_3^+ + CF $	[19]
19	CF⁺ + CF₄ → CF⁺ + CF₄	[19]	57	$\rm CF^+ + CF_2 \to CF_2^+ + CF $	[19]
20	F⁺ + CF₄ → F⁺ + CF₄	[19]	58	F + CF₃ → CF₄	[19]
21	F^– + CF₄ → F^– + CF₄	[19]	59	F + CF₂ → CF₃	[19]
22	$\rm CF_3^- + CF_4 \to CF_3^- + CF_4 $	[19]	60	F + CF → CF₂	[19]
23	Ar^* + CF₄ → Ar^* + CF₄	[19]	61	F₂ + CF₃ → CF₄ + F	[19]
24	CF₃ + CF₄ → CF₃ + CF₄	[19]	62	F₂ + CF₂ → CF₃ + F	[19]
25	CF₂ + CF₄ → CF₂ + CF₄	[19]	63	$\rm CF_3^- + F\to CF_3 + F^- $	[19]
26	CF + CF₄ → CF + CF₄	[19]	64	e + Ar → 2e + Ar⁺	[20]
27	F₂ + CF₄ → F₂ + CF₄	[19]	65	e + Ar → e + Ar^*	[20]
28	F + CF₄ → F + CF₄	[19]	66	e + Ar^* → 2e + Ar⁺	[20]
29	Ar + Ar → Ar + Ar	[19]	67	Ar^* + Ar^* → e + Ar + Ar⁺	[20]
30	CF₄ + CF₄ → CF₄ + CF₄	[19]	68	Ar^* + CF₂ → Ar + CF + F	[21]
31	Ar + CF₄ → Ar + CF₄	[19]	69	Ar^* + CF₃ → Ar + CF₂ + F	[21]
32	e + CF₄ → e + CF₃ + F	[19]	70	Ar^* + CF₄ → Ar + CF₂ + F₂	[21]
33	e + CF₄ → e + CF₂ + 2F	[19]	71	Ar⁺ + CF₂ → Ar + CF⁺ + F	[21]
34	e + CF₄ → e + CF + 3F	[19]	72	$\rm Ar^+ + CF_3 \to Ar + CF_2^+ + F $	[21]
35	$\rm e + CF_4 \to 2e + CF_3^+ + F $	[19]	73	$\rm Ar^+ + CF_4 \to Ar + CF_3^+ + F $	[22]
36	$\rm e + CF_4 \to 2e + CF_2^+ + 2F $	[19]	74	$\rm Ar^+ + CF_3^- \to Ar + CF_3 $	[21]
37	e + CF₄ → 2e + CF⁺ + 3F	[19]	75	Ar⁺ + F^– → Ar + F	[21]
38	e + CF₄ → 2e + CF₃ + F⁺	[19]	76	$\rm CF_3^+ + Ar\to CF_3 + Ar^+ $	[21]

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[1]	Lieberman M A, Lichtenberg A J 2005 Principles of Plasma Discharges and Materials Processing (New York: Wiley) pp387−457
[2]	王友年, 宋远红, 张钰如 2024 射频等离子体物理基础(北京: 科学出版社) 第236页 Wang Y N, Song Y H, Zhang Y R 2024 Fundamentals of Radio-frequency Plasma Physics (Beijing: Science Press) p236
[3]	Zorat R, Goss J, Boilson D, Vender D 2000 Plasma Sources Sci. Technol. 9 161 Google Scholar
[4]	Kimura T, Kasugai H 2010 J. Appl. Phys. 107 083308 Google Scholar
[5]	Saikia P, Bhuyan H, Escalona M, Favre M, Rawat R S, Wyndham E 2018 AIP Adv. 8 045113 Google Scholar
[6]	Donkó Z, Derzsi A, Vass M, Horváth B, Wilczek S, Hartmann B, Hartmann P 2021 Plasma Sources Sci. Technol. 30 095017 Google Scholar
[7]	Vahedi V, DiPeso G, Birdsall C K, Lieberman M A, Rognlien T D 1993 Plasma Sources Sci. Technol. 2 261 Google Scholar
[8]	Wünderlich D, Gutser R, Fantz U 2009 Plasma Sources Sci. Technol. 18 045031 Google Scholar
[9]	Passchier J D P, Goedheer W J 1993 J. Appl. Phys. 74 3744 Google Scholar
[10]	Alves L L, Marques L 2012 Plasma Phys. Controlled Fusion 54 124012 Google Scholar
[11]	Graves D B 1987 J. Appl. Phys. 62 88 Google Scholar
[12]	Kushner M J 2009 J. Phys. D: Appl. Phys. 42 194013 Google Scholar
[13]	Kushner M J 2007 IEEE Trans. Plasma Sci. 14 188
[14]	Yang Y, Kushner M J 2010 Plasma Sources Sci. Technol. 19 055011 Google Scholar
[15]	Model Low-Temperature Plasma Sources with the Plasma Module https://www.comsol.com/plasma-module [2025-8-16]
[16]	Benchmark Model of a Capacitively Coupled Plasma https://www.comsol.com/model/benchmark-model-of-a-capacitively-coupled-plasma-11745 [2025-8-16]
[17]	Model of an Argon/Chlorine Inductively Coupled Plasma Reactor with RF Bias https://www.comsol.com/model/model-of-an-argonchlorine-inductively-coupled-plasma-reactor-with-rf-bias-110171 [2025-8-16]
[18]	Model of an Argon/Oxygen Capacitively Coupled Plasma Reactor https://www.comsol.com/model/model-of-an-argonoxygen-capacitively-coupled-plasma-reactor-108931 [2025-8-16]
[19]	Li J Z, Zhao M L, Zhang Y R, Gao F, Wang Y N 2025 Comput. Phys. Commun. 307 109392 Google Scholar
[20]	Wen Y Y, Li X Y, Zhang Y R, Song Y H, Wang Y N 2022 J. Phys. D: Appl. Phys. 55 200001 Google Scholar
[21]	Vasenkov A V, Li X, Oehrlein G S, Kushner M J 2004 J. Vac. Sci. Technol. , A 22 511-530 Google Scholar
[22]	Zhang Y R, Bogaerts A, Wang Y N 2012 J. Phys. D: Appl. Phys. 45 485204 Google Scholar

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Three-dimensional multi-physics simulation of dual-frequency capacitively coupled Ar/CF₄ plasma source

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Three-dimensional multi-physics simulation of dual-frequency capacitively coupled Ar/CF4 plasma source

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Corresponding author: ZHAO Mingliang, mlzhao@dlut.edu.cn

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Three-dimensional multi-physics simulation of dual-frequency capacitively coupled Ar/CF₄ plasma source