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Numerical Study of Reactive Species Formation in Methane Plasma Discharge
1 2 1
Khawla MOKRANI , Ziane KECHIDI , and Abdelatif TAHRAOUI
1 Quantum Electronics Laboratory, Faculty of Physics, USTHB, Bp, 32 El Alia Bab Ezzouar.
2 Laboratory of Electrical Engineering and Automatics, University of Medea, Medea 26000.
I. Abstract
A unidimensional self-consistent fluid model is developed to gain insight into the homogeneous discharge behavior. Poisson’s equation for the electric
field is coupled to the first moments of the Boltzmann equation (continuity equation, drift-diffusion equation and energy equation). Transport and
reaction coefficients are obtained from the mean energy of the electrons. The model is applied to a reduced methane (CH4 ) kinetic with the main
ionization and excitation processes, which lead to species production such as CH4+ , CH3+ , H, CH3 and CH2 . The detailed discharge characteristics of the
plasma are simulated using COMSOL multiphysics software.
II. Theoretical Model III. Capacitive Coupled Plasma (CCP) discharge

To compute the electron energy distribution Upon the application of RF voltage to one of the symmetrically placed electrodes, electron impact ionization
function (EEDF), a range of electric field values and dissociation of CH4 occur, resulting in the generation of new species such as electrons, ions, and radicals.
is considered, given a specific density and com- The production of these new electrons and ions is crucial for sustaining the discharge. In RF discharges, elec-
position of the background gas. This results in tron impact reactions are primarily responsible for the increased formation of radicals. By increasing the RF
voltage applied across the electrodes while maintaining a fixed gas pressure and RF frequency, the plasma den-
combinations of average electron energies and
sity can be effectively increased. To comprehensively characterize the plasma chemistry within the discharge
their corresponding coefficients.
gap, a set of 367 gas-phase reactions involving 35 distinct species has been developed[1].
- The main governing equations of this dy-
namic plasma model are listed as follows:
The particle continuity equation describes the
continuity of each type species p:
∂n p
+ ∇ · ⃗Γ p = S p (1)
∂t
The flux ⃗Γ p of each type species p is given
by using the drift-diffusion approximation, in
terms of its the mobility and diffusion coeffi-
cient:
⃗Γ p = ±µ p ⃗En p − D p ∇n p (2)
For the electrons, its parameters are expressed
as a function of the average energy, a balance
equation is solved:
∂ne ε
+ ∇ · ⃗Γε = Sε (3)
∂t
IV. Species Included in the Model and Chemical reactions
The source term Sε is based on energy gain from
To characterize the chemical reactions occurring in a pure methane plasma, our model considers a compre-
the electric field and energy loss due to colli- hensive set of 35 species. [2, 3, 4]. These specific species are chosen because they are considered relevant and
sions, in the various reactions. It given by: significant in the observed chemistry of such systems. By including this wide range of species, our model aims
to provide a comprehensive representation of the complex chemical dynamics that occur within a methane
Sε = −e⃗Γe · ⃗E − Qel − Qinel (4) plasma.
The electron energy flux can be obtained from:
5 5
⃗Γε = − µe ⃗Ene ε − ne De ∇ε (5)
3 3
Where the first term is the hydrodynamic flux
of enthalpy, and the second term is the heat
conduction flux. These partial differential
equations are coupled to the Poisson equation,
to obtain the electric field distribution in the
plasma:
∇ · (ε 0 ∇ϕ) = −∇ · (ε 0 ⃗E) = − ∑ q p n p (6)

p
- The boundary conditions for the various V. Conclusions

species in the vicinity of the anode and cathode,
This work investigates the plasma chemistry of RF plasma discharges capacitively coupled in methane for
are given as follows (at x=0, d):
gas conversion. A one-dimensional fluid model is used to analyze plasma species densities and residence
time. The study reveals methane dissociation, formation of hydrocarbons (such as C2 H6 , C2 H4 , C2 H2 , C3 H8 ,
1
⃗e · ⃗n = ne vth,e − αs ∑ γi (Γ
⃗ i · ⃗n) + α′s ne µe E, C3 H6 ), and hydrogen production. It identifies dominant reaction pathways for methane consumption and end
Γ
4 product production. The study emphasizes the significance of hydrogen as a valuable outcome, highlighting
i
(7) its potential in gas conversion applications.
1
⃗ i · ⃗n = ni vth,i − α′s ni µi E,
Γ (8) VI. References
4
In the negative ion species, we have used the [1] C. De Bie, B. Verheyde, T. Martens, J. Van Dijk, S. Paulussen, and A. Bogaerts. Fluid modeling of the conversion of methane into higher hydrocarbons in an atmospheric pressure dielectric barrier
discharge. Plasma Process. Polym., 8(11), 2011.
Dirichlet boundary.
[2] D. Herrebout, A. Bogaerts, M. Yan, R. Gijbels, W. Goedheer, and E. Dekempeneer. One-dimensional fluid model for an rf methane plasma of interest in deposition of diamond-like carbon layers.
J. Appl. Phys., 90(2):570–579, 2001.

1, if ⃗E · ⃗n ≥ 0 0, if ⃗E · ⃗n ≥ 0 [3] T. Farouk, B. Farouk, A. Gutsol, and A. Fridman. Atmospheric pressure methane-hydrogen dc micro-glow discharge for thin film deposition. J. Phys. D. Appl. Phys., 41(17), 2008.
αs = , α′s =
0, if ⃗E · ⃗n < 0 1, if ⃗E · ⃗n < 0 [4] H. N. Varambhia, J. J. Munro, and J. Tennyson. R-matrix calculations of low-energy electron alkane collisions. Int. J. Mass Spectrom., 271(1-3):1–7, 2008.

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Numerical Study of Reactive Species Formation in Methane Plasma Discharge

II. Theoretical Model III. Capacitive Coupled Plasma (CCP) discharge

The electron energy flux can be obtained from:

∇ · (ε 0 ∇ϕ) = −∇ · (ε 0 ⃗E) = − ∑ q p n p (6)

- The boundary conditions for the various V. Conclusions

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