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表面波プラズマのトムソン散乱診断と
電子加熱機構
河野明廣
名古屋大学工学研究科
電子情報システム専攻
プラズマ科学のフロンティア 2008
Outline
・Motivation: electron heating mechanism in SWP
・Laser Thomson scattering measurement system
・Measurements for low-pressure SWP
・Fluid-Monte-Carlo hybrid modeling
・Conclusions
Planar surface wave plasma
・Planar Surface wave plasma source (SWP)
・easily scalable to a large area device
・low electron temperature
・How electrons are heated in low-pressure SWP is not well understood yet.
Microwave E field in SWP
Dielectric (quartz)
10 mm
E
Resonance layer
Plasma
ne=6.7×1011cm-3
Microwave 2.45 GHz (wpe=w at nc=7.4×1010cm-3)
Resonance layer and electron heating mechanism
ne  nc
Dielectric plate
ne
(w pe  1   d wwave )
Presheath
ne  nc
(w pe  wwave )
Sheath
p 0
p 0
Resonance layer
p 0
D
E

p
Is the following electron heating mechanism realistic?
Surface wave
Electrostatic wave
Landau damping
Reported probe measurement data
for 915MHz Ar SWP
Nagatsu et al. APL 2002
個々の電子によるトムソン散乱
Laser
2 =2 E2
I ∝ (E
E2 + E
E)-2 E)
= 4E
散乱光強度は電子数の揺らぎに
に比例する。
EE
-E
Scattered light
(Doppler shifted)
Non-collective scattering
k0
ks
+
- +-++
-+
-+
- +- +
-+
-+
- +- +
k
D
(Debye length)
Laser
N1  N  N1
(N1 )2  N
N 2  N  N 2
(N2 )2  N
Total scattering intensity
I  ( N1 - N2 )2  (N1 - N2 )2
 (N1 )2  (N2 )2  2N1N2  2N
k方向の速度成分
に比例した
ドップラーシフト
Condition for non-collective scattering
Direction of scattering
D 
1
k
i.e.,
  (kD )-1  1
Collective scattering
k0
k
k
s
+ + +
+
+ +
- - - - + + + +
+ +
- - - - -
Laser
Direction of
scattering
D
デバイ長より長い空間スケールでは，電子密度の揺らぎはイオ
ン密度の揺らぎを伴う必要がある。
Typical signal level in low-temperature plasma measurements
Total cross section
Plasma ne=1011cm-3

Laser 200mJ/pulse
5×1017 photon
8 re 2
36000 photon/cm
scattered
F4 lens
3
 6.65 10-25 cm2
×1/256 (solid angle loss)
Monochormator
×1/10
(transmittance)
Detector
1.4 photon
finally detected
×1/10
(quantum efficiency)
Requirements for efficient measurements
Rayleigh and stray scattering
Thomson spectrum

~10 nm
・Very low scattering intensity (photon counting level)
→ Need of multichannel spectrum recording
・Strong Rayleigh- and stray-light interference
→ Need of sharp and deep notch filtering
Triple grating spectrograph (TGS)
2D photon counting
ICCD camera
Spatial
filter
Intermediate
slit
The combination of a spatial filter and an intermediate slit
reduces the Rayleigh component by a factor of ~10-6
Rev. Sci. Instrum. 71(2000)2716
Stray light elimination by TGS
Entrance slit
Intermediate slit
Stray
Thomson
(Subtractive dispersion)
1st grating
2nd grating
3rd grating
Spatial filter
Rayleigh
Stray
Thomson
Thomson
Scattering position
Photon image
in the ICCD camera
Wavelength / electron velocity
Thomson spectrum (1D EEPF) for Ar ICP
1000
300
100
200
Photon count
Photon count
250
150
100
50
10
1
0
0.1
50
100
150
200
250
300
Channel number
200 W, 20 mTorr
20000 shot accumulation
350
0
5
10
15
Electron energy (eV)
ne=5.5×1011cm-3
Te=2.3 eV
20
25
Thomson spectrum for Ar SWP
880 W, 50 mTorr, Ar SWP
40 mm from the quartz plate
100240 shot accumulation
1.4 10 4
Improvements
Laser energy
×5
TGS
×1.8
QE of ICCD camera ×3.5
105
ne=3.0×1011cm-3
Te=1.6 eV
1.2 104
10 4
Photon count
1 10 4
8000
1000
6000
100
4000
2000
10
0
1
-15
-10
-5
0
5
Wavelength shift (nm)
10
15
0
5
10
15
Electron energy (eV)
20
N2ラマンスペクトルによる絶対強度校正
Thomson scattering measurement of the spatial profile
of EEDF near the dielectric plate of SWP
Quartz Plate
Thomson scattering measurement of the spatial profile
of EEDF near the dielectric plate of SWP
Side view
Top view
Microwave
2.45GHz
f400mm
z observation
Beam
x
y
Dielectric
plate
YAG
laser
532 nm, 330 mJ, 30 pps
z
z
Chamber is movable
horizontally ( x and y
direction) by 50 mm
x observation
Entrance slit of TGS
Eliminating Raman background from the quartz plate
in z-oboservation
(a)
(b)
(c)
Thomson spectra observed at different positions
x observation
Photon count
Photon count
z observation
Electron energy (eV)
Electron energy (eV)
Ar 10 mTorr, 800W
Observed spatial distribution of Te and ne
x observation
z observation
Ar 10 mTorr
800 W
Microwave E field in SWP
Dielectric (quartz)
10 mm
E
Resonance layer
Plasma
ne=6.7×1011cm-3
Microwave 2.45 GHz (wpe=w at nc=7.4×1010cm-3)
Estimation of E field near the dielectric plate
using fluid model
Electron momentum balance
Space charge field
Microwave field (assumed)
Field boundary condition
ne  (nev e )

0
t
x
v e
v e
kTe ne
e
ve
 - ( ESC  Ew ) - mv e
t
x
m
m n x
dESC
e
+ was fixed at the value of the static
 (n - ne ) nsolution
without microwave field
dx
0
x
Ew  E0 exp(- ) coswt
d
Esc  0 (deep in the plasma)
(d~10mm)
Dielectric plate
Electron continuity
E
x
E field near the resonance layer
E = Ew+Esc= Eaverage+E(t)
E(t)
1000
E(t)
500
0
E(t)
0
Eaverage
0
-500
2
2
ne=nc
(wpe=ww
)
ne(t)
1
ne=nc (wpe=ww)
1
1
0
0
Eaverage
Eaverage
-1000
Normalized density
Field intensity (V/cm)
Should apply to
the experimental condition
100
200
300
400
0
500 0
1
ne=nc (wpe=ww)
ne(t)
20
40
60
80
0
100 0
ne(t)
Distance from the dielectric plate (in D)
increasing ne
20
40
60
80
100
Collisionless electron motion in the resonance E filed
(Monte-Carlo simulation)
Dielectric plate
vx
3
2
1
0
-1
-2
-3
Phase space
x
2 eV
Electron bunch
5 eV
・Low energy electrons are not heated.
・High energy electron are heated by phase randomization caused by
・ sharp spatial change in the microwave field
・ electron reflection by the sheath field
Monte Carlo simulation
Ar 10 mTorr
Outer boundary
Dielectric plate
・Simulation space: 1D in space and 3D in velocity space
200 mm
・Electrons move in the E field given by the fluid-model
computation.
・At the outer boundary, electrons are reflected or annihilated by
setting a (variable) threshold energy, so that electron loss balances
with electron production.
・A simplified electron collision cross section set (Vahedi, 1993)
・Coulomb collisions taken into account (K. Nanbu,
IEEE Trans. Plasma Sci.
(2000))
Estimation of ionization frequency
via ne response to microwave power modulation
Microwav E field in the Monte-Carlo simulation was determined so that the
resulting ionization frequency agrees with the experimental value
Monte Carlo simulation of electron heating
Dielectric plate
vx
3
2
1
0
-1
-2
-3
x
Monte-Carlo simulation results
Electron temperature
in low energy part
EEPF
Ar 10 mTorr
Electron temperature (eV)
3
2
1
0
0
10
20
30
40
50
Distance from the dielectric plate (mm)
・EEDFs are nearly Maxwellian
・No beam-like component
Stochastic heating in ICP and SWP
RF ICP
Microwave SWP
e
e
E
E
No energy gain
Sheath
Skin
layer
Sheath
Skin
layer
Summary
・Thomson scattering measurement using
TGS + ICCD camera is a powerful method for
electron diagnostics of low-temperature plasmas
・In low pressure SWP, the main electron heating
mechanism appears to be the stochastic heating via
collision of electrons with the resonance layer
Probe in overdense plasma
ne
Overdense plamsa
cutoff density
Strong E field?
position
Negatively biased
probe
When a probe is put in an overdense plasma and negatively biased,
a layer is produced near the probe, where ne=ncut-off; microwave field
may be strengthened by this resonance layer and may have a large
effect on the probe characteristics.
Simulation space
Simulation space
r ~ 90D
Assume cylindrical symmetry
512 grid points
(1/6)D spacing
Probe
r=4D
ne  n  const.
Boundary conditions
Probe surface
v e v 

0
r
r
f 0
f  f0  f1 sin wt
Governing equations
ne
Electron continuity    (ne v e )  0
t
v e
kTe
e

(
v


)
v

n

f - col v e
Electron motion
e
e
e
t
m ne
m
Ion continuity
Ion motion
Poisson
Te=2eV
n
   (n v  )  0
t
2
v 
kT
e
v
 -( v    ) v  n - f t
Mn
M
 free
 f 2
T+=0.1eV
e
0
(n - ne )
vcol /(w pe / 2 )  0.016
 free / D  650
Probe current without microwave field
0.01
0.01
I
dI/dV
d2I/dV2
0.001
Electron current (A)
Electron current (A)
0.008
I
dI/dV
d2I/dV2
0.006
0.004
0.002
0.0001
10-5
10-6
0
-0.002
10-7
-20
-15
-10
-5
DC probe bias voltage (V)
0
-20
-15
-10
-5
DC probe bias voltage (V)
0
Probe current with microwave potential fluctuation
Vprobe=V0+V1sinwt,
V1=2.0 V,
0.01
0.01
I
dI/dV
d2I/dV2
I
dI/dV
d2I/dV2
0.001
Electron current (A)
0.008
Electron current (A)
wpe/w = 1.0
0.006
0.004
0.002
0.0001
10-5
10-6
0
10-7
-0.002
-20
-15
-10
-5
DC probe bias voltage (V)
0
-20
-15
-10
-5
0
DC probe bias voltage (V)
For underdense plasma, the result is almost identical with that without microwave field.
Probe current with microwave potential fluctuation
Vprobe=V0+V1sinwt,
0.01
0.01
I
dI/dV
d2I/dV2
I
dI/dV
d2I/dV2
0.001
Electron current (A)
0.008
Electron current (A)
wpe/w = 2.2
V1=0.05 V,
0.006
0.004
0.002
0.0001
10-5
10-6
0
10-7
-0.002
-20
-15
-10
-5
DC probe bias voltage (V)
0
-20
-15
-10
-5
DC probe bias voltage (V)
0
Probe current with microwave potential fluctuation
Vprobe=V0+V1sinwt,
V1=0.3 V,
0.01
0.01
I
dI/dV
d2I/dV2
I
dI/dV
d2I/dV2
0.001
Electron current (A)
0.008
Electron current (A)
wpe/w = 2.5
0.006
0.004
0.002
0.0001
10-5
10-6
0
10-7
-0.002
-20
-15
-10
-5
DC probe bias voltage (V)
0
-20
-15
-10
-5
DC probe bias voltage (V)
0
Probe current with microwave potential fluctuation
Vprobe=V0+V1sinwt,
V1=2.0 V,
0.01
0.01
I
dI/dV
d2I/dV2
I
dI/dV
d2I/dV2
0.001
Electron current (A)
0.008
Electron current (A)
wpe/w = 3.3
0.006
0.004
0.002
0.0001
10-5
10-6
0
10-7
-0.002
-20
-15
-10
-5
DC probe bias voltage (V)
0
-20
-15
-10
-5
DC probe bias voltage (V)
0
Field intensity near the probe surface
with 2.45 GHz potential fluctuation
Vprobe=V0+V1sinwt,
Probe
bias -15V
Vprobe = -15 + 0.7sin(ωt)
V1=0.7 V
Probe
bias -5V
Vprobe = -5 + 0.7sin(ωt)
Probe
bias -9V
Vprobe = -9 + 0.7sin(ωt)
Field intensity (V/cm)
Field Intensity (V/cm)
1000
0
-1000
-2000
-3000
-4000
Large filed fluctuation
-5000
0
50
100
Position (μm)
150
200
0
50
100
150
200
0
Position (μm)
Distance from the probe surface (m)
50
100
Position (μm)
150
200
2.45 GHz experiment
EEPF(Ar65mTorr_1kW)
V-I特性(Ar65mTorr_1kW)
1017
1.4 10 -1
1.2 10
z= 2.5
z= 5.0
z= 7.5
z=10.0
z=12.5
z=15.0
-1
EEPF
EEPF
8 10-2
1016
6 10-2
p
Probe Icurrent
(A) (A)
1 10-1
mm
mm
mm
mm
mm
mm
z= 2.5
z= 5.0
z= 7.5
z=10.0
z=12.5
z=15.0
mm
mm
mm
mm
mm
mm
1015
4 10-2
1014
2 10-2
0 10 0
-2 10 -2
-40
1013
-30
-20
-10
0
10
Volt(V)
DC probe
bias voltage (V)
20
30
0
5
10
15
20
25
Energy[ev]
Energy (eV)
30
35
40
Probe current with microwave potential fluctuation
Vprobe=V0+V1sinwt,
0.01
0.01
Electron current (A)
I
dI/dV
d2I/dV2
0.008
Electron current (A)
wpe/w = 3.3
V1=5.0 V,
0.006
0.004
0.002
I
dI/dV
d2I/dV2
0.001
0.0001
10-5
0
10-6
-0.002
-25
-20
-15
-10
-5
DC probe bias voltage (V)
Te=3eV
0
-25
-20
-15
-10
-5
DC probe bias voltage (V)
vcol /(w pe / 2 )  0.4
0
Summary
When the plasma potential oscillates at a microwave
frequency and the plasma is overdense, the probe current
is affected in a complicated manner. The distortion in the
V-I characteristics may result in false peaks in the second
derivative.

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