# Simulation of magnetized RF capacitively coupled plasma discharges using 3D sparse Particle-In-Cell algorithms

L Garrigues, G. Fubiani, M Lobet

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L Garrigues, G. Fubiani, M Lobet. Simulation of magnetized RF capacitively coupled plasma discharges using 3D sparse Particle-In-Cell algorithms. ICPIG 2025 - 36th International Conference on Phenomena in Ionized Gases, Jul 2025, Aix-en-Provence, France. hal-05361630

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https://hal.science/hal-05361630v1

Submitted on 12 Nov 2025

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# Simulation of magnetized RF capacitively coupled plasma discharges using 3D sparse Particle-In-Cell algorithms

L. Garrigues<fnref n="1" />, G. Fubiani<fnref n="1" /> and M. Lobet<fnref n="2" />

3D Particle-In-Cell (PIC) simulations in the context of low temperature plasma surveys are very time consuming. The combination of sparse methods with PIC algorithms can drastically reduce the computational time while maintaining a minimum error between standard and sparse PIC approaches. We illustrate a comparison between the two approaches in the context of magnetized radio-frequency (RF) capacitively coupled plasma (CCP) discharge.

## 1 Introduction

The radio-frequency (RF) capacitively coupled plasmas (CCP) are widely used in the semiconductor industry for etching and deposition [1]. The electrostatic Particle-In-Cell (PIC) method, which is based on the coupling between a Lagrangian description of the charged particles transport and a Eulerian approach to resolve the Poisson's equation on a prescribed computational grid, has been largely employed to study the effect of the voltage waveform and frequency applied on the RF electrode (see e.g.[2]), the plasma chemistry [3], etc.

The introduction of a magnetic field to enhance the plasma density has revealed the existence of instabilities that modify the plasma uniformity studied with 2D PIC simulations [4]. We have performed 3D PIC simulations of magnetized RF CCP using sparse PIC algorithms.

## 2 Sparse PIC approaches

In a standard discretization of a uniform square Cartesian grid of *M* meshes for a dimension *d*, the number of freedom is *M*^d. The objective of sparse algorithms is to compute a hierarchy of anisotropic grids with a coarser resolution, hence reducing the total number of degrees of freedom lower than *M*^d. Coupling sparse method with PIC algorithms leads to reduce the total number of cells and consequently the total number of particles for a same statistical error than the standard PIC algorithms [5]. This results in a faster calculation time.

Ricketson and Cerfon [6] have firstly demonstrated the interest of the sparse PIC method in the context of Landau damping and diocotron instability. More recently, the sparse PIC approach has been applied in the context of 2D simulations of low temperature plasmas, including collisions, ion motion, appropriated boundary conditions, for unmagnetized RF capacitively coupled plasma

discharge [7], and for partially magnetized plasmas [8].

## 3 Results

We will show at this conference the comparisons between standard and sparse PIC approaches in the context of 3D simulations of magnetized RF CCP discharges.

### Acknowledgments

This research was funded by l'Agence Nationale de la Recherche (ANR), project ANR-22-CE46-0012. This work was granted access to the HPC resources of TGCC/Joliot Curie under the allocation A0162B13923.

### References

[1] P. Chabert and N. Braithwaite, *Physics of Radio-Frequency Plasmas*, Cambridge University Press, Cambridge, UK, 2011.

[2] Z. Bi, Y. Liu, W. Jiang, X. Xu, and Y. Wang, *Curr. Appl. Phys.* **11**, S2–S8 (2011).

[3] Q. H. Yuan, C. Ye, Y. Xin, X. J. Huang, Z. Y. Ning, and G. Q. Yin, *Appl. Phys. Lett.* **93**, 071503 (2008).

[4] S. S. Ganta, K. Bera, S. Rauf, I. Kaganovich, A. Khrabov, A. T. Powis, D. Sydorenko, and L. Xu, *Phys. Plasmas* **31**, 102107 (2024).

[5] F. Deluzet, G. Fubiani, L. Garrigues, C. Guillet, and J. Narski, *ESAIM: Math. Model. Numer. Anal.* **56**, 1809 (2022).

[6] L. F. Rickeston and A. J. Cerfon, *Plasma Phys. Control. Fusion* **59**, 024002 (2017).

[7] L. Garrigues, M. Chung-To-Sang, G. Fubiani, C. Guillet, F. Deluzet, and J. Narski, *Phys. Plasmas* **31**, 073907 (2024).

[8] L. Garrigues, M. Chung-To-Sang, G. Fubiani, C. Guillet, F. Deluzet, and J. Narski, *Phys. Plasmas* **31**, 073908 (2024).

<footnote n="1">¹ LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France</footnote>

<footnote n="2">² Maison de la Simulation, CEA, CNRS, Université Paris-Sud, UVSQ, Université Paris-Saclay, Gif-sur-Yvette, France</footnote>