24B03
Numerical Analysis of Discharging Characteristics in Microwave-excited
Surface Wave Plasma Apparatus with Self-consistent Simulation Method
Self-consistentシミュレーションによるマイクロ波励起表面波プラズマ装置の放電特性解析
Dongmin Kim and Hiroyuki Ohsaki
キム ドンミン, 大崎 博之
The University of Tokyo
5-1-5 Kashiwanoha, Kashiwa, Chiba, 277-8516, Japan東京大学大学院 〒277-8516 千葉県柏市柏の葉5-1-5
A self-consistent simulation tool for the microwave excited plasma was developed. In this simulation tool,
microwave propagation in plasma is analyzed by combining the electron oscillation to the finite-differencetime-domain (FDTD) method. And the plasma parameters such as electron temperature, electron density
and space potential are simulated by the ambipolar diffusion model that is described by the fluid
conservation equations. Using this simulation tool, we simulated microwave propagation characteristics
and the distributions of plasma parameters in the surface wave driven plasma (SWP) apparatus.

1. Introduction
The microwave-excited SWP is one of the mostimportant methods to generate uniform and dense
plasma in a large area. However, the design ofmicrowave-excited SWP apparatus is not facile,
because the plasma parameters and the microwave
propagation characteristics are coupled verystrongly. In order to overcome this difficulty, many
simulation techniques have been developed andperformed. Toba et al. has developed self-consistent
simulation code in two-dimensional (2D) modeland simulated in planar-type dielectric SWP
apparatus[1]. And applying this simulation code, athree-dimensional (3D) simulation has been
performed by Nakagawa in Ring Dielectric Line
typed Surface Wave Plasma (RDL-SWP)
apparatus[2]. In this study, we have developed afeasible simulation tool for applying to design amicrowave- excited plasma apparatus. In this paper,
we will indicate the simulation method and resultand discuss about the validity of this simulation toolwith comparing the experimental result.
2. Simulation Method
The microwave propagation is governed by a very
shorter time scale than the plasma evolution such as
electron and ion’s drift and diffusion in bulk plasma.
This makes it possible to decompose theelectromagnetic fields and the plasma parameters
into separated calculations of microwave
propagation and plasma evolution in simulation.
Maxwell’s equation, which governs thepropagation of electromagnetic wave in plasma, aregiven as~H1~(1)  Et~
E 1~ ~(2) H  Jt ~
J e 2 ne ~~(3)E   en J
tme~~
where E and H are the electric and magnetic field

intensities with permittivity ε and permeability μ,~respectively. And J is the local plasma current
density by electron oscillation, e is the unsigned
charge on an electron, ne is the electron density, meis the electron mass and en is the electron-neutralelastic collision frequency. The power absorbing
distribution by incident microwave in plasma iscalculated by Poynting vector. And it was averaged
through several time periods of the microwave
source as follows.
1 t T~ ~(4)Pabs     E  J dv dt
tv
T
where Pabs is the power absorption, and T is thetime period taken into count.
In this simulation, we considered the chemical
reactions as shown in table 1. And it is assumed thatthe velocity distribution is satisfied the Maxwellian
distribution at everywhere. Thus, we can determine
the rate coefficient k in j process with integration asshown in equation (5) from the known cross section
as referred in table 1.

 k j   j v   f   j  v d0(5)At the plasma model, the governing equations forelectron’s ambipolar diffusion, metastable atoms,
and neutral atoms are as follows.

ne   Γ 0  Setnm,n
   Γ m, n  S m, n
t

(6)
(7)

Se  ki nn ne  ksi nm ne  kmpn 2(8)S m  kexnn ne  k si nm ne  k sc nm ne
 kr nm ne  2kmp nm2(9)Sn  ki nn ne  kexnn nek n TPe
Γ0   b e e  vin mivin miΓm,n   Dm,nnm,n(10)3. Simulation Result
The microwave propagation mode is shown infigure 2. A standing wave formed in a wide area ofplasma boundary and has synchronous phase withincident microwave. At this propagation mode, thepower absorbing distribution by plasma is as shownin figure 2. This distribution is normalized with themaximum power value.
(11)Figure. 1 Microwave propagation in plasma boundary(12) 3 
55 kbTepe
 pe     kbTe Γ 0    t  2 
22 me en(13)
 Pabs  eΓ e  E  Ploss
PE eene
3mPloss   kennn e pe mi enn  exkex   gi k gi   si k si

Figure. 2 Power absorbing distributions in plasma

(14)

(15)

where nm and nn are metastable and neutral atoms
density, Γ0 is the flux by ambipolar diffusion, Γm is
the metastables flux and Γn is the neutrals flux. And
Se is the electron generation rate, Sm is themetastables generation rate and Sn is the generation
rate of neutral atoms. Pe is the thermal energy
density and E is the ambipolar electric field in bulk
plasma, α is a normalization factor to fix the totalabsorbed power amount in plasma. gi is thethreshold energy for ionization from the groundstate, si is the threshold energy for ionization fromthe metastable state, and ex is the excitation energy.
At the wall boundary in plasma, the electron flux
is limited with Bohm sheath criterion and thethermal flux is assumed as lost as the averagekinetic energy by electron.
Table. 1 Chemical reactions taken into count in simulation

No Process
1Ar  e  Ar  e*

kjRef.

kex

[3]

ki

[4]

2

Ar  e  Ar  2e3

Ar  e  Ar  2e

ksi

[3]

4Ar  e  Ar  e

ksc

[5]

5Ar  e  Ar  e

kr[6]

6

Ar  Ar  Ar  Ar  e

kmp

[7]

7Ar  Ar  2Ar

k2q

[7]

8Ar  2Ar  Ar2  Ar

k3q[7]

****r***The distributions of electron temperature andelectron density are shown in figure 3. The electrontemperature is distributed widely ~3 eV in thecenter of discharging box but ~6 eV at the power
absorption concentrated area. And the electrondensity is highest as ~2.7×1017 m-3 at the place of 5
cm off from dielectric window.

(a) electron temperature(b) electron density
Figure. 3 Simulation result at 10 mTorr of argon gas
pressure and 1.5 kW of incident microwave power

4. Summary
We have performed a self-consistent simulationin RDL-SWP apparatus. And the validity of thissimulation tool was confirmed with comparing theexperimental results in reference [2]. The plasma
parameter distributions are well matched but theSW propagated more deeply into the center ofplasma boundary in experimental result.
References
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[2]
[3]
[4]
[5]
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[7]

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