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XIII International Conference on Gas Discharges and their Applications (GD2000) in Glasgow
Strathclyde University, 3-8 September 2000
Spatiotemporal Analysis of Plasma Kinetics of
Radio Frequency Glow Discharge in Nitrogen
K Satoh, H Itoh and H Tagashira
Department of Electrical & Electronic Engineering,
Muroran Institute of Technology, Muroran 050-8585, JAPAN
[email protected]
Agenda 1. Motivation & Objective
2. Experimental results
3. Simulation model & conditions
4. Simulation results
5. Conclusions
Introduction
Motivation
Radio
frequency glow discharge in nitrogen and its mixtures are used for
- plasma nitriding, thin film deposition, removal of pollutant gases
to control discharge plasmas
to improve efficiency of the processes
quality of devices
Spatiotemporal
understanding the
kinetics of the discharge
plasmas is essential
variation of excited molecule (C3Pu) density has been measured.
Objective
To
clarify the plasma kinetics of capacitively coupled rf discharge at 13.56
MHz in nitrogen by spatiotemporally resolved optical emission spectroscopy
and by the self-consistent Propagator method.
Particularly, mechanism of the double layer formation in nitrogen rf
discharge is interpreted with the modelling.
EXCITED MOLECULE DENSITY(N2) & EXCITATION RATE(H2)
hydrogen
nitrogen
Olivier Leroy et al, J.Phys.D: Appl.
Phys. 28, pp.500-7, (1995)
300
K
200
A
100
0
0.00
V0cosq
A
double
layer
A
0.25
tim
e(
0.50
cyc
le)
K
0.75
1.00
K
wave-ride
electron
3
0
P
ion
posit
(cm)
C3Pu density profile
p=1.5Torr, f=13.56MHz
Time (ns)
Excitation Rate [a.u.]
400
G
G
Powered electrode
Grounded electrode
0.0(cm)
3.0(cm)
Distance (mm)
P
Excitation rate H(n=3)
p=1Torr, f=13.56MHz
Two relative maxima of the excitation rate are observed near the both electrodes.
Similar profile is observed in hydrogen rf discharge.
Relative maxima are due to the double layer formation (Leroy et al.)
The double layer formation has been reported for the discharges in electro-negative
gases, but only in hydrogen rf discharge in electropositive gases.
SIMULATION MODEL
One dimensional model in the field direction
E
Discharge space is divided into 40 thick slabs and
the velocity distributions of electrons and ions f(e,q)
are defined in the slabs.
The behaviour of the charged particles is calculated
using Propagator method.
Each of the thick slabs is divided into 20 thin slabs
in order to calculate the diffusion of the particles
accurately.
External circuit
Cb=20pF
Cg=10pF
Vg
ig
Vrf=Vs sinwt
where
e
ne , n+
we , w+
S
1
d
e 0 x
  x dx 
Vg t 
1 d


x

x
dx

e 0 d 0
d
x=d
q
position
q
eemax
energy
jg  x, t   eS nW  neWe  Vg t  
e=0
q=0
polar angle
x=0
t
Cb
1
Vs t  
ig t ' dt '

Cg  Cb
Cg  Cb 0
: the electronic charge
: densities of electrons & positive ion at x and at t
: velocities of electrons & positive ion at x and at t
: area of electrodes
Space charge field (1D Poisson’s eq.)
E  x, t   
f(e,q) at x=xi
e0
: the permittivity in vacuum
Vg(t) : gap voltage
(x, t) : net charge density
PROPAGATOR METHOD (one dimensional)
Velocity distribution f(e, q, x) is stored in the memory of computer using multidimension array. The balance of a volume cell in the distribution f(e, q, x) in unit time
t is calculated using Newton’s law and expectation values.
The Balance in unit time t
Velocity distribution f(e, q, x)
Acceleration
vx=vx0 + (eE/2m) t
Drift
x=x0 + vx0t + (eE/2m)t2
E
The expectation values of
–
momentum collision
f(ei,qj, xk)・ PT・qm/qT
–
excitation collision
f(ei,qj, xk)・ PT・qex/qT
–
ionisation collision
f(ei,qj, xk)・ PT・qion/qT
–
free flight (no collision)
f(ei,qj, xk) ・(1- PT )
–
the probability of collision PT=exp(-NqTvt)
f(e,q) at x=xi
x=d
q
position
q
eemax
q=0
energy
e=0
polar angle
x=0
Simulation conditions
second
coefficient
cross sections
collision frequency
(positive ion)
： d=3.0cm
： p=0.5, T=20.0 ℃
： Vs sin wt, f=13.56MHz
： fully absorbing walls
for charged particles
： i=0.05
： Ohmori et al.
： nT_ion=69.306×v×p (s-1)
v - ion speed (cm/s)
p - gas pressure (Torr)
electron collision cross section
-14
10
qm
-15
10
qi
2
length
gas pressure & temp.
applied voltage & freq.
electrodes
cross sections (cm )
gas
-16
10
qv (10)
qex (20)
-17
10
-18
10
10
step
： t =7.37x10-12 (s)
10
10
10
10
10
electron
energy
(eV)
mesh number of f (e, q, x )
Y Ohmori,et al, J. Phys. D: Appl.
energy e 0 ～ 40eV 40 meshes  e= 1.0eV (electron)
Phys., vol.21, pp.724-729 (1988)
0 ～ 10eV 40 meshes  e= 0.2eV (positive ion)
angle q
0 ～  rad 20 meshes  q= /20 (0.157) rad
position x 0 ～ 3 cm 40 meshes  x = 0.075 cm(thick), x’= 3.75×10-3 cm(thin)
initial density distribution of electrons & ions
： 1.0x107 (cm-3) uniformly distributed in a gap
time
-19
-1
0
1
2
3
Spatiotemporal profile of C3Pu density ―experiment―
p=0.5 Torr
p=1.5 Torr
400
2
2
Excitation Rate [a.u.]
6.0x10
3
density of C Pu (a.u.)
8.0x10
2
K
4.0x10
2
2.0x10
0.0
0.00
A
A
200
K
100
0.50
(c
yc
le
)
K
0.25
0.75
1.00
0
P
tio
posi
3
)
m
c
(
n
G
A
A
0
0.00
0.25
tim
e
300
tim
e(
0.50
cyc
le)
K
0.75
1.00
3
0
ion
posit
(cm)
G
P
 The large (first) maxima in front of the instantaneous cathode and the small (second) relative maxima
in front of the instantaneous anode are observed.
 These profiles are qualitatively good agreement with that of the excitation rate observed in
hydrogen rf discharge by Leroy et al, and this suggests that the double layer is formed in
nitrogen rf discharge
Excitation rate of C3Pu
Simulation result
1.0x10
18
8.0x10
17
6.0x10
17
4.0x10
17
2
6.0x10
2
4.0x10
3
density of C Pu (a.u.)
3
-3 -1
exitation rate of C Pu (cm s )
optical emission spectroscopy
2.0x10
K
17
0.0
3000.00
3000.25
)
cle
cy
e(
tim
3000.50
0.25
tim
e
K
3
3000.75
3001.00 0
1
2
)
n
o (cm
positi
G
A
A
0.0
0.00
A
A
K
2
2.0x10
0.50
(c
yc
le
)
K
3
0.75
1.00
0
P
posit
cm)
ion (
G
P
 The excitation profile obtained by this simulation qualitatively agrees well with that
obtained by the emission spectroscopy.
 Remarkable point is
– simplified model used here gives the spatiotemporally correct position of the
excitation maxima.
4x10
8
3x10
8
8
A
8
ion density (cm)
-3
3000.00
3000.25
time 3000.50
(cyc
le) 3000.75
3001.00
4x10
8
3x10
8
2x10
1x10
0
P
2
)
on (cm
positi
1.5x10
8
K
3
1
8
G
1.0x10
7
5.0x10
K
7
8
A
8
3000.00
3000.25
time 3000.50
3000.75
(cyc
le)
3001.00
0.0
-5.0x10
2999.00
0
0
3
1
0
P
2
)
on (cm
positi
G
P
1
positio
n
400
2999.25
2999.50
2999.75
(cm)
2
3
G
3000.00
(T/8)
K
300
electric field (V/cm)
1x10
2.0x10
8
-3
2x10
0
np
Electric field
net charge density
net charge density (cm )
ne
electron density (cm)
-3
Electron, Ion & net charge densities and electric field
200
A
100
0
-100
A
-200
2999.00
2999.25
2999.50
tim
e (c
ycl 2999.75
e)
3000.00 0.0
K
3.0
2.0
)
1.0
n (cm
o
positi
P
The net charge density immediately in front of the both electrodes is always positive during
one rf cycle, however, that two maxima of negative space charge appear near the
instantaneous anodes.
The maxima of the negative space charge and the relative maxima of the electric field are
seen at the spatiotemporally same position.
Spatiotemporal position of the second maxima of the excitation rate agrees well with
those of maxima of net charge density.
G
Spatial variations of ne, ni, vx, e & electric field at T/8
9
1.0x10
200
8
60
0.6
0.4
electric field (V/cm)
-3
density (cm )
100
0
4
mean energy
A
field
2
K
velocity
-100
-2
-4
ni
0.2
-6
ne
0.0
-200
0.0
P
0.5
1.0
1.5
2.0
position (cm)
2.5
-8
3.0
G
These electrons
– contribute to the double layer
formation
– have excitation collision with
nitrogen molecules.
Small peaks of C3Pu
0
40
electron mean energy (eV)
0.8
20
0
-20
-40
average velocity of electrons (cm/s)
6
Electric field in the plasma is
slightly positive.
This field accelerates electrons
towards the powered electrode
(x=0cm) . (velocity is negative)
6
-60x10
Net charge density in left hall of
the plasma is negative, so that
electric field increases towards
the powered electrode.
Electrons are accelerated further
by this field.
Fourier expansion of the electric field
Spatial variations of the amplitude of the first three
terms of Fourier expansion of the electric field
written as below
a0, a1, a2, b1 and b 2, (V/cm)
4
b1
2
a0 
E x  
  a n cos nx  bn sin nx 
2 n 1
a1
0
-2
b2
a2
a0
where an and bn are coefficients.
-4
0.0

0.5
1.0
1.5
2.0
position (cm)
2.5
3.0
Plasma : cosine component is dominant
/2(rad) leads against the phase of
applied voltage
Sheath : sine component is dominant
The electrons in the plasma are accelerated by the weak electric field.
The phase of the field leads /2 (rad) against that of the applied voltage.
 The electrons accelerated by this field contributes to the double layer
formation.

Conclusions
 Spatiotemporally resolved optical emission spectroscopy in nitrogen rf glow
discharge is performed and the spatiotemporal profile of the excitation rate of
C3Pu state is obtained.
 Self-consistent simulation of rf glow discharge in nitrogen using the
Propagator method has been carried out, and the spatiotemporal profile
of the excitation rate of C3Pu is obtained. This profile qualitatively agrees
well with that obtained by the emission spectroscopy.

From the simulation,
the double layer is formed in nitrogen rf discharge.
 The electrons accelerated by the weak electric field in the plasma, the
phase of which leads /2 (rad) against that of the applied voltage, make a
contribution to the double layer formation.