Two-dimensional simulation of inductively coupled plasma based on COMSOL and comparison with experimental data

Jia Cheng; Linhong Ji; Kesheng Wang; Chuankun Han; Yixiang Shi

doi:10.1088/1674-4926/34/6/066004

J. Semicond. > 2013, Volume 34 > Issue 6 > 066004

SEMICONDUCTOR TECHNOLOGY

Two-dimensional simulation of inductively coupled plasma based on COMSOL and comparison with experimental data

Jia Cheng^{1, 2,}, Linhong Ji^{1, 2}, Kesheng Wang^{1, 2}, Chuankun Han³ and Yixiang Shi⁴

+ Author Affiliations

Corresponding author: Cheng Jia, Email:chengjia@tsinghua.edu.cn

DOI: 10.1088/1674-4926/34/6/066004

Abstract: A two-dimensional axisymmetric inductively coupled plasma (ICP) model, and its implementation in the COMSOL multiphysical software, is described. The simulations are compared with the experimental results of argon discharge from the gaseous electronics conference RF reference cell in the inductively coupled plasma mode. The general trends of the number density and temperature of electrons with radial scanning are approximately correct. Finally, we discuss the reasons why the comparisons are not in agreement, and then propose an improvement in the assumptions of the Maxwellian electron energy distribution function and reaction rate.

Key words: inductively coupled plasma, simulation, COMSOL

References

[1]	Lymberopoulos D P, Economou D J. 2-dimensional self-consistent radio-frequency plasma simulations relevant to the gaseous electronics conference RF reference cell. J Res Natl Inst Stand Technol, 1995, 100(4):473 doi: 10.6028/jres
[2]	Kim H C, Iza F, Yang S S, et al. Particle and fluid simulations of low-temperature plasma discharges:benchmarks and kinetic effects. J Phys D:Appl Phys, 2005, 38:R283
[3]	Surendra M. Radio frequency discharge benchmark model comparison. Plasma Sources Sci Technol, 1995, 4:56 doi: 10.1088/0963-0252/4/1/007
[4]	Miller P A, Hebner G A, Greenberg K E, et al. An inductively-coupled plasma source for the gaseous electronics conference RF reference cell. J Res Natl Inst Stand Technol, 1995, 100(4):427 doi: 10.6028/jres
[5]	COMSOL 3. 2, Userbook.
[6]	Lymberopoulos D P, Economou D J. Fluid simulations of glow-discharges-effect of metastable atoms in argon. J Appl Phys, 1993, 73(8):3668 doi: 10.1063/1.352926
[7]	Panagopoulos T, Kim D, Midha V, et al. Three-dimensional simulation of an inductively coupled plasma reactor. J Appl Phys, 2002, 91(5):2687 doi: 10.1063/1.1448673
[8]	Brcka J. Modeling remote H₂ plasma in semiconductor processing tool. Proceedings of the COMSOL Users Conference, Boston, 2006
[9]	Lymberopoulos D P, Economou D J. 2-dimensional simulation of polysilicon etching with chlorine in a high-density plasma reactor. IEEE Trans Plasma Sci, 1995, 23(4):573 doi: 10.1109/27.467977
[10]	Novikova T, Kalache B, Bulkin P. Numerical modeling of capacitively coupled hydrogen plasmas:effects of frequency and pressure. J Appl Phys, 2003, 93(6):3198 doi: 10.1063/1.1555678
[11]	Lymberopoulos D P, Economou D J. Modeling and simulation of glow-discharge plasma reactors. J Vac Sci Technol A, 1994, 12(4):1229 doi: 10.1116/1.579300
[12]	Bukowski J D, Graves D B, Vitello P. Two-dimensional fluid model of an inductively coupled plasma with comparison to experimental spatial profiles. J Appl Phys, 1996, 80(5):2614 doi: 10.1063/1.363169
[13]	Jaeger E F, Berry L A, Tolliver J S, et al. Power deposition in high-density inductively-coupled plasma tools for semiconductor processing. Phys Plasmas, 1995, 2(6):2597 doi: 10.1063/1.871222
[14]	Lee M H, Chung C W. On the E to H and H to E transition mechanisms in inductively coupled plasma. Phys Plasmas, 2006, 13:063510 doi: 10.1063/1.2212387
[15]	Rauf S, Kushner M J. Model for noncollisional heating in inductively coupled plasma processing sources. J Appl Phys, 1997, 81(9):5966 doi: 10.1063/1.364385
[16]	Sakiyama Y, Graves D B. Corona-glow transition in the atmospheric pressure RF-excited plasma needle. J Phys D:Appl Phys, 2006, 39:3644 doi: 10.1088/0022-3727/39/16/018
[17]	Cheng Jia, Zhu Yu, Wang Jinsong. Two-dimensional discharge simulation of inductively coupled plasma etcher. Chinese Journal of Semiconductors, 2007, 28(6):989

Fig. 1. Simulation geometry of GECRC/ICP

DownLoad: Full-Size Img PowerPoint

Fig. 2. GECRC/ICP (a) electron number density and (b) electron temperature distribution

DownLoad: Full-Size Img PowerPoint

Fig. 3. GECRC/ICP (a) power density and (b) azimuthal electric field distribution

DownLoad: Full-Size Img PowerPoint

Fig. 4. Comparison of simulation and experiment for electron number density along radial scanning 1.5 cm above the lower electrode. (a) Original reaction rate coefficient. (b) 1.1 times reaction rate coefficient

DownLoad: Full-Size Img PowerPoint

Fig. 5. Comparison of simulation and experiment for electron temperature along radial scanning 1.5 cm above the lower electrode

DownLoad: Full-Size Img PowerPoint

Table 1. Important collision parameters in argon discharge

Table 2. The coefficients of PDE in Eq. (21)

[1]	Lymberopoulos D P, Economou D J. 2-dimensional self-consistent radio-frequency plasma simulations relevant to the gaseous electronics conference RF reference cell. J Res Natl Inst Stand Technol, 1995, 100(4):473 doi: 10.6028/jres
[2]	Kim H C, Iza F, Yang S S, et al. Particle and fluid simulations of low-temperature plasma discharges:benchmarks and kinetic effects. J Phys D:Appl Phys, 2005, 38:R283
[3]	Surendra M. Radio frequency discharge benchmark model comparison. Plasma Sources Sci Technol, 1995, 4:56 doi: 10.1088/0963-0252/4/1/007
[4]	Miller P A, Hebner G A, Greenberg K E, et al. An inductively-coupled plasma source for the gaseous electronics conference RF reference cell. J Res Natl Inst Stand Technol, 1995, 100(4):427 doi: 10.6028/jres
[5]	COMSOL 3. 2, Userbook.
[6]	Lymberopoulos D P, Economou D J. Fluid simulations of glow-discharges-effect of metastable atoms in argon. J Appl Phys, 1993, 73(8):3668 doi: 10.1063/1.352926
[7]	Panagopoulos T, Kim D, Midha V, et al. Three-dimensional simulation of an inductively coupled plasma reactor. J Appl Phys, 2002, 91(5):2687 doi: 10.1063/1.1448673
[8]	Brcka J. Modeling remote H₂ plasma in semiconductor processing tool. Proceedings of the COMSOL Users Conference, Boston, 2006
[9]	Lymberopoulos D P, Economou D J. 2-dimensional simulation of polysilicon etching with chlorine in a high-density plasma reactor. IEEE Trans Plasma Sci, 1995, 23(4):573 doi: 10.1109/27.467977
[10]	Novikova T, Kalache B, Bulkin P. Numerical modeling of capacitively coupled hydrogen plasmas:effects of frequency and pressure. J Appl Phys, 2003, 93(6):3198 doi: 10.1063/1.1555678
[11]	Lymberopoulos D P, Economou D J. Modeling and simulation of glow-discharge plasma reactors. J Vac Sci Technol A, 1994, 12(4):1229 doi: 10.1116/1.579300
[12]	Bukowski J D, Graves D B, Vitello P. Two-dimensional fluid model of an inductively coupled plasma with comparison to experimental spatial profiles. J Appl Phys, 1996, 80(5):2614 doi: 10.1063/1.363169
[13]	Jaeger E F, Berry L A, Tolliver J S, et al. Power deposition in high-density inductively-coupled plasma tools for semiconductor processing. Phys Plasmas, 1995, 2(6):2597 doi: 10.1063/1.871222
[14]	Lee M H, Chung C W. On the E to H and H to E transition mechanisms in inductively coupled plasma. Phys Plasmas, 2006, 13:063510 doi: 10.1063/1.2212387
[15]	Rauf S, Kushner M J. Model for noncollisional heating in inductively coupled plasma processing sources. J Appl Phys, 1997, 81(9):5966 doi: 10.1063/1.364385
[16]	Sakiyama Y, Graves D B. Corona-glow transition in the atmospheric pressure RF-excited plasma needle. J Phys D:Appl Phys, 2006, 39:3644 doi: 10.1088/0022-3727/39/16/018
[17]	Cheng Jia, Zhu Yu, Wang Jinsong. Two-dimensional discharge simulation of inductively coupled plasma etcher. Chinese Journal of Semiconductors, 2007, 28(6):989

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Received: 11 October 2012 Revised: 23 December 2012 Online: Published: 01 June 2013

Article Navigation > Journal of Semiconductors > 2013 > 34(6): 066004

Jia Cheng, Linhong Ji, Kesheng Wang, Chuankun Han, Yixiang Shi. Two-dimensional simulation of inductively coupled plasma based on COMSOL and comparison with experimental data[J]. Journal of Semiconductors, 2013, 34(6): 066004. doi: 10.1088/1674-4926/34/6/066004 ****J Cheng, L H Ji, K S Wang, C K Han, Y X Shi. Two-dimensional simulation of inductively coupled plasma based on COMSOL and comparison with experimental data[J]. J. Semicond., 2013, 34(6): 066004. doi: 10.1088/1674-4926/34/6/066004.

Citation:

J Cheng, L H Ji, K S Wang, C K Han, Y X Shi. Two-dimensional simulation of inductively coupled plasma based on COMSOL and comparison with experimental data[J]. J. Semicond., 2013, 34(6): 066004. doi: 10.1088/1674-4926/34/6/066004.

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Two-dimensional simulation of inductively coupled plasma based on COMSOL and comparison with experimental data

DOI: 10.1088/1674-4926/34/6/066004

1.
Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
2.
State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
3.
School of Engineering Technology, China University of Geosciences, Beijing 100083, China
4.
Department of Thermal Engineering, Tsinghua University, Beijing 100084, China

Funds:

the Research Project from State Key Laboratory of Tribology in Tsinghua University SKLT11C2

Project supported by the National Science & Technology Major Project No. 02 (No. 2011ZX02403-004) and the Research Project from State Key Laboratory of Tribology in Tsinghua University (No. SKLT11C2)

the National Science & Technology Major Project No. 02 2011ZX02403-004

More Information

Corresponding author: Cheng Jia, Email:chengjia@tsinghua.edu.cn
Received Date: 2012-10-11
Revised Date: 2012-12-23
Published Date: 2013-06-01

Abstract

Abstract

A two-dimensional axisymmetric inductively coupled plasma (ICP) model, and its implementation in the COMSOL multiphysical software, is described. The simulations are compared with the experimental results of argon discharge from the gaseous electronics conference RF reference cell in the inductively coupled plasma mode. The general trends of the number density and temperature of electrons with radial scanning are approximately correct. Finally, we discuss the reasons why the comparisons are not in agreement, and then propose an improvement in the assumptions of the Maxwellian electron energy distribution function and reaction rate.
- inductively coupled plasma,
- simulation,
- COMSOL

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References(17)

References

[1]	Lymberopoulos D P, Economou D J. 2-dimensional self-consistent radio-frequency plasma simulations relevant to the gaseous electronics conference RF reference cell. J Res Natl Inst Stand Technol, 1995, 100(4):473 doi: 10.6028/jres
[2]	Kim H C, Iza F, Yang S S, et al. Particle and fluid simulations of low-temperature plasma discharges:benchmarks and kinetic effects. J Phys D:Appl Phys, 2005, 38:R283
[3]	Surendra M. Radio frequency discharge benchmark model comparison. Plasma Sources Sci Technol, 1995, 4:56 doi: 10.1088/0963-0252/4/1/007
[4]	Miller P A, Hebner G A, Greenberg K E, et al. An inductively-coupled plasma source for the gaseous electronics conference RF reference cell. J Res Natl Inst Stand Technol, 1995, 100(4):427 doi: 10.6028/jres
[5]	COMSOL 3. 2, Userbook.
[6]	Lymberopoulos D P, Economou D J. Fluid simulations of glow-discharges-effect of metastable atoms in argon. J Appl Phys, 1993, 73(8):3668 doi: 10.1063/1.352926
[7]	Panagopoulos T, Kim D, Midha V, et al. Three-dimensional simulation of an inductively coupled plasma reactor. J Appl Phys, 2002, 91(5):2687 doi: 10.1063/1.1448673
[8]	Brcka J. Modeling remote H₂ plasma in semiconductor processing tool. Proceedings of the COMSOL Users Conference, Boston, 2006
[9]	Lymberopoulos D P, Economou D J. 2-dimensional simulation of polysilicon etching with chlorine in a high-density plasma reactor. IEEE Trans Plasma Sci, 1995, 23(4):573 doi: 10.1109/27.467977
[10]	Novikova T, Kalache B, Bulkin P. Numerical modeling of capacitively coupled hydrogen plasmas:effects of frequency and pressure. J Appl Phys, 2003, 93(6):3198 doi: 10.1063/1.1555678
[11]	Lymberopoulos D P, Economou D J. Modeling and simulation of glow-discharge plasma reactors. J Vac Sci Technol A, 1994, 12(4):1229 doi: 10.1116/1.579300
[12]	Bukowski J D, Graves D B, Vitello P. Two-dimensional fluid model of an inductively coupled plasma with comparison to experimental spatial profiles. J Appl Phys, 1996, 80(5):2614 doi: 10.1063/1.363169
[13]	Jaeger E F, Berry L A, Tolliver J S, et al. Power deposition in high-density inductively-coupled plasma tools for semiconductor processing. Phys Plasmas, 1995, 2(6):2597 doi: 10.1063/1.871222
[14]	Lee M H, Chung C W. On the E to H and H to E transition mechanisms in inductively coupled plasma. Phys Plasmas, 2006, 13:063510 doi: 10.1063/1.2212387
[15]	Rauf S, Kushner M J. Model for noncollisional heating in inductively coupled plasma processing sources. J Appl Phys, 1997, 81(9):5966 doi: 10.1063/1.364385
[16]	Sakiyama Y, Graves D B. Corona-glow transition in the atmospheric pressure RF-excited plasma needle. J Phys D:Appl Phys, 2006, 39:3644 doi: 10.1088/0022-3727/39/16/018
[17]	Cheng Jia, Zhu Yu, Wang Jinsong. Two-dimensional discharge simulation of inductively coupled plasma etcher. Chinese Journal of Semiconductors, 2007, 28(6):989

Two-dimensional simulation of inductively coupled plasma based on COMSOL and comparison with experimental data

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