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Study on Expansion of Electron Sheath and Breakdown in it
Yeong-Shin Park,
Da-Hye Choi,
Kyoung-Jae Chung
and Y. S. Hwang
NUPLEX, Dept. of Nuclear, Seoul National University,
Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742, Korea
bluer@snu.ac.kr
63rd Gaseous Electronics Conference
October 5th 2010
Maison de la Chimie, Paris, France
1/17 Study on expansion of electron sheath and breakdown in it
PYS_LSP_GEC-Oct2010
Abstract
Electron sheath forms in front of a small electrode biased positively with respect to the potential of
surrounding plasma. Based on the collisionless Child-Langmuir model for ion sheath in low
pressure plasma, electron sheath model has been suggested. Equation of electron sheath
thickness derived from the model describes that the thickness is determined by plasma density,
electron temperature and sheath voltage as the ion sheath is. However, electron sheath is about
1.6 times thicker than ion sheath at same conditions. The calculated sheath thicknesses are
verified by probe diagnostics as well as particle simulation. Using the 1D particle-in cell code,
thickness of electron sheath are investigated, as well. Outbreak voltages of the breakdown in the
electron sheath are gauged at various pressures and powers. Regarding the plasma as a cathode,
biased electrode as an anode and electron sheath thickness as a discharge gap respectively, one-
dimensional breakdown model is suggested. Applying Townsend’s criteria of DC discharge to this
breakdown model, a nonlinear equation for breakdown voltages is derived. Comparison of model-
based numerical calculations to experimental results shows a good agreement between them.
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Introduction:Electron Sheath and an Additional Plasma in front of + biased electrode
An additional plasma as well as electron sheath
generates with positive voltages biased on a small electrode immersed in plasma.
PlasmaBubblePlasmaBubble
(+) Bias Electrode
Ambient Plasma
(+) Bias Electrode
Ambient Plasma
Electron Sheath
(+) Bias Electrode
Ambient Plasma
Evolution of Electron Sheath
Breakdown
e
e
e
Electron Sheath is formed in
front of the positively biased
electrode having small area
relative to entire plasma reference
wall.
An additional plasma with
high density generates in front
of the biased electrode.
The additional plasmas are
called fireball[1], anode spot[2],
and so on.
Electron Sheath expands as the
bias voltage increases.
Breakdown occurs due to
ionization collisions between
neutrals and accelerated electrons
in electron sheath.
Additional Plasma
Double Layer
[1] M. Sanduloviciu et al., Phys. Lett. A 208, 136 (1995)
[2] B. Song et al., J. Phys. D: Appl. Phys. 24, 1789 (1991)
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Introduction: Objectives of the Research
Motivation of the research
The generation of an additional plasma in front of positively biased electrode are well known phenomenon.
Electrons accelerated inside electron sheath make ionization collisions with neutrals and make a breakdown.
However, the additional plasma is generally used in order to make and study double layer easily rather than
the additional plasma itself.
Also, there is a lack of study on electron sheath since the sheath is a rare phenomenon in plasmas, different
from ion sheath which is widely studied so far.
For the reason, electron sheath and breakdown mechanism inside the electron sheath are investigated.
Contribution of the Research
1. Introduction of electron sheath thickness with sheath voltages and the ambient plasma properties
2. Present simple understanding of breakdown inside electron sheath and expectation of breakdown voltage
under a practical operating condition.
Research outline
1. Introduction of model for electron sheath thickness
2. Verification of the electron sheath model by measuring and simulating electron sheath thickness
3. Introduction of electron sheath breakdown model based on simple DC Townsend’s discharge model
4. Verification the breakdown model by experiments
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LP
Matching Network
RF Source RF Antenna
Quartz Tube
Vacuum Pump
S/S Cap
Pyrex Tube
VB
RM
BM
LP
RMVB
VB
RM
BM : Bias Module
LP : Langmuir Probe
◈ Overview of the experimental system
◈ Bias electrode
Inductively Coupled Plasma
Bias Module
Positively Biased Electrode
Electrode Material : S/S, Al, Cu, Mo
Hole Diameter : 1 ~ 5 mm
Hole Depth : 1 ~ 6 mm
Sweeping Voltage : -100 ~ 300 V
Measuring Resistance : 5~100 ohm
Ambient Plasma using diffused plasma
Single-turn RF antenna / L-type matching network
13.56 MHz RF Power : 100 ~ 600 W
Gas : Argon / Pressure : 1 ~ 30 mTorr /
Experimental Set-up
Insulator (Al203)
Positively
biased
Electrode
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0 2 4 6 8 10 12 14 16
0
20
40
60
Bia
s V
olt
ag
e [
V]
Bias Current [mA]
77.6mTorr
139.5mTorr
201.1mTorr
Ar
300W, 1mm
Macroscopic observation
Direct evidence of breakdown within the sheath
- the most reliable proof of breakdown
Observation of the plasma bubble itself
- shape, size of the plasma bubble
- growth and decline of the plasma bubble
Can not catch up the exact breakdown point
◈ Figure of the additional plasma near bias electrode
(bias module having double holes)
◈ Bias voltage and corresponding current of the additional plasma
(measured at another device)
When the additional plasma occurs,
- sudden current jump, voltage drop
Similar characteristics of DC glow discharge
- analogous voltage-current characteristic curve
Hysteresis is shown
- existence of self-consistent plasma
Self-sustaining DC-glow like plasma
ambient
plasma
Additional
Plasma
Additional Plasma generates within Electron Sheath
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Determination of Breakdown Voltage inside Electron Sheath
0 50 100 150 200
0.00
0.01
0.02
0.03
0.04
Bia
s C
urr
en
t [a
.u.]
Bias Voltage [V]
1st knee
Plasma
Properties
Breakdown
Current Jump
Voltage Drop
Signal Distortion
due to suddencurrent jump
2nd knee
Breakdown
Condition
Electron Sheath
Expansion
Hysteresis
Vbreakdown (VB)Vplasma
Characteristic curve of current–voltage on bias electrode
1. First knee [ V ≤ Vplasma ]
properties of ambient plasma
ion sheath
act as planar type Langmuir probe
- plasma potential
- electron temperature
- electron density
2. Electron sheath expansion
[ Vplasma < V ≪ Vbreakdown ]
gradual increment of current due to
electron sheath expansion
3. Second knee [Vplasma ≪ V < Vbreakdown ]
hysteresis
- evidence of self-consistent plasma
4. Breakdown [ V ≥ Vbreakdown ]
Breakdown voltage
current jump, voltage drop
Breakdown voltage (VB) : voltage just before current jump or maximum voltage before voltage drop
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30 35 40 45 50100
150
200
250
300Gas: Ar, Bias Module: 3mm-t1mm-s/s, Voltage Sweep : ~300V
200w
300w
400w
500w
Bre
ak
do
wn
Vo
lta
ge
[V
]
Mass Flow [sccm]
◈ Plot of breakdown voltage as a function of gas flow rate
Pressure effect on breakdown
As raising the operating pressure, the
breakdown voltage decreases. The result shows
that the breakdown voltages decrease with
operating pressure.
t is shown that the neutral particles contribute to
discharge. Therefore, the operating regime would
be correlated to the left side of Paschen’s curve.
0 100 200 300 400 500 600100
150
200
250
300
Low Density
Gas: Ar, Bias Module: 3mm-t1mm-s/s, Voltage Sweep : ~300V
Bre
ak
do
wn
Vo
lta
ge
[V
]
RF Power [W]
50sccm
45sccm
40sccm
High Density
◈ Breakdown voltage according to RF power variation
Effect of RF power for ambient plasma
Under the condition of low electron density,
breakdown voltages decrease steeply as the RF
power increases. On the other hands, breakdown
voltages are raised with the increase of RF
power in high density plasma.
It is shown that the properties of ambient plasma
such as electron density, electron temperature and
plasma potential affect on breakdown condition.
Measured Breakdown Voltages at different operating conditions.
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Breakdown Voltages with Ambient Plasma Properties
100 200 300 400 5000
20
40
60
80
0
5
10
15
20
25
0
20
40
60
80
0
2
4
6
8
10
12Pressure : 10 mTorr
Electron Temperature
Plasma Potential
Net Voltage
Bre
ak
do
wn
Vo
lta
ge
[V
]
Power for Ambient Plasma [W]
Bias Voltage
Bre
ak
do
wn
Cu
rre
nt
[mA
]
P
las
ma
Po
ten
tia
l [V
]
Ele
ctr
on
Te
mp
era
ture
[e
V]
Ele
ctr
on
De
ns
ity
[X
10
10 c
m-3]
◈ Breakdown conditions and plasma properties with RF power
- Gas : Argon, Hole Thickness : 1 mm, Hole Diameter : 3 mm
Effect of ambient plasma properties
1. Plasma potential does not affect breakdown
voltage directly but acts as a reference potential
for the bias voltage.
2. Strictly, the breakdown potentials are acquired by
subtracting plasma potential from bias voltage.
3. Over 200 W, Breakdown currents show linear
dependency on the power for ambient plasma as
electron density does.
4. Lower plasma density is preferable to makes
the breakdown in electron sheath.
However, breakdown voltage is raised rapidly as
RF power decreases below 200 W. It seems that
the plasma density is not enough to provide
sufficient electron toward electron sheath to make
the additional plasma. Also, plasma cannot
touch/penetrate with/toward the bias electrode
without depletion of plasma density. In this
manner, it is needed to take plasma density
depletion into accounts when experimental result
acquired in low density plasma are analyzed.
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Comparison with DC glow discharge
1. Electron-avalanche from cascading ionization collisions
between accelerated electrons and neutrals is the key
of discharge.
2. Electrons are supplied from plasma.
3. Discharge gap is determined by length of electron
sheath between anode and plasma.
4. Potential difference is fixed with sheath voltage.
5. Electrons entering into the sheath have thermal velocity
and are accelerated by sheath voltage
Characteristics of electron sheath breakdown
Breakdown voltages are characterized by operating
pressure, properties of bulk plasma, and length
of the electron sheath.
Sheath size is decided by ambient plasma and bias
voltage.
Electron Sheath
BreakdownDC Glow Discharge
Ambient Plasma = Cathode
Sheath Voltage = Voltage across electrodes
Electron Sheath = Distance btw. electrodes
Breakdown Model for breakdown inside Electron Sheath
Electron sheath as a discharge gap
Decreasing tendency of breakdown voltage as rising
pressure indicates that more collisions are needed to
generate the additional plasma more easily.
Therefore, long discharge gap (thick electron sheath) is
more favorable than short one for easy breakdown in
consideration of Pachen’s curve.
As aforementioned, breakdown occurs more easily at
low density plasma. It seems because the electron
sheath becomes longer at low density plasma.
The result has a correlation with left side of the
Paschen’s curve in DC discharge.
Different from DC glow discharge, the gap distance,
electron sheath thickness, varies with sheath
voltage.
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Assumptions (based on collisionless Child-Langmuir sheath for ions as Schiesko’s work[1] )
1. Collisionless sheath with relatively high potential drop compared to electron temperature.
2. Electron impinging to the sheath has the 1-directional thermal velocity.
Equation for Electron Sheath Thickness
21( ) ( )
2e em u x e x 1. Electron energy conservation :
2. Electron flux conservation : 0( ) ( )e e een x u x J
3. Electron flux at sheath edge :0
81 1
4 4
ee s th s
e
eTJ en v en
m
( )eu x
em
( )en x
0eJ
1
4thv
: electron mass,
: electron velocity,
: incident electron current,
: electron density,
: 1-D electron thermal velocity
Electron Sheath Thickness ∝ V03/4, ne
-1/2, Te-1/4
: 1.58 times thicker than ion sheath3/ 4 1/ 2 3/ 4
1/ 4 1/ 40 0 02 2 2 2
3 3
eDS
e e e
V T Vs
T en T
3/ 4
022
3ion DS
e
Vs
T
[1] L. Schiesko et al, Phys. Plasmas 15, 073507 (2008)
(for ion)
Governing Equations
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Measurement of Electron Sheath Thickness
0 25 50 75 100 1250
1
2
30.5X10
16m
-3, 2eV
10.0X1016
m-3, 2eV
0.1X1016
m-3, 2eV
5.0X1016
m-3, 2eV
1X1016
m-3, 3eV
Ele
ctr
on
Sh
ea
th S
ize
[m
m]
Potential Difference btw. Plasma and Bias Electrode [V]
1X1016
m-3, 2eV
Line : Calculated Result
Dot : Experimental Data
-10 V
-150 V ~ 150 V
Iis
Probe Position
pla
sm
a
ele
ctro
n
sh
eath
Measured sheath size and calculated one shows relatively good agreement with each other at higher sheath potentials.
At lower sheath voltages, differences between them are quite large due to difficulties in measurement and violating the assumption that the electron temperature is much lower than sheath voltage.
◈ Comparison between measured(red square) and calculated(blue
line) electron sheath thickness with sheath potential
Measuring electron sheath edge
: Ion saturation current varies with electron
sheath expansion
Ion saturation currents are monitored as varying
Langmuir probe location and bias voltage.
Electron sheath expands with bias voltage.
When the probe is immersed in plasma, ion
saturation currents are almost constant. However,
the ion saturation current is reduced as the probe
is located inside the electron sheath.
or Sheath Voltage
Biased
Electrode
Langmuir
Probe
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PYS_LSP_GEC-Oct2010
Simulation of Electron Sheath Thickness
1.57 1.59 1.61 1.63 1.65
8.1
8.2
8.3
8.4
8.5
Cu
rre
nt
[a.u
.]
Length [mm]
0.0 0.2 0.4 0.6 0.8 1.02
3
4
5
6
7
8
9
10
Simulation
Theory
Ele
ctr
on
sh
ea
th t
hic
kn
es
s [
mm
]
Electron density [x1016
m-3]
Ambient Plasma
ElectronSheath
Simulation region
V
Sheath edge
Positiveelectrode
Electron sheath simulation using Particle-in-cell code[1]
1D Particle-in-cell code, xpdp1[2], is used.
To estimate electron sheath thickness at fixed sheath voltage
and fixed ambient plasma, electron currents arriving anode
are measured as varying sheath length.
Sheath size is determined as the length at which the current
reaching anode starts to decrease.
Result from theoretical model and the simulation results are
well matched.
1.61 mm ≤ Sheath size < 1.62 mm
◈ schematic diagram of simulation domain for electron sheath
[1] D.H. Choi et al., “Study on bipolar flow in plasma electron sheath using particle-
in-cell(PIC) code simulation”, presented at KISTEP, (2009)
[2] J. Verboncoeur et al., Electron. Res. Lab. Tech. Memo. No. UCBERL M90/67,
Aug. 7, 1990.
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1. Electron sheath is dominant before breakdown.
1. There are no initial ions in the sheath.
2. Electrons impinging into sheath from plasma have only 1-directional thermal velocity.
3. Charged particle distribution in electron sheath is not considered in this model.
4. Uniform Electric Field
1. The energy gained by particles is proportional to the flight distance.
2. Sheath expansion
1. Sheath size is determined by electron sheath model.
2. Voltage rules the length of the sheath, d (distance between ambient plasma and biased electrode).
3. Density and electron temperature of ambient plasma influence on sheath expansion as well.
3. Corresponding/bipolar electron current coefficient, γco
1. Ion flux generated by ionization can enhance the electron flux (bipolar flow) [1].
electronco
ion
dI
dI
Assumptions for the Breakdown Model in Electron Sheath
[1] I. Langmuir, Physical Review 33, 954 (1929)1/2
electron ion
ion electron
dI mk
dI m
0.378k at 0ionI
2. In case of argon, γco is 102 when the ion current is zero.
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Nonlinear Equation for Breakdown Voltages
◈ Breakdown mechanism in electron sheath
: DC discharge with plasma cathode and electron sheath gap
A
N
O
D
E
PLASMA
CATHODE
-
-
--
-
-
-
+
+
+
N
N
N
d x
Γea Γe(x)=Γeceαx Γec=Γeo+Γes
Γes=γeqΓic
Γeo
Γic
------
-
ln ln ln(1 1/ )b
se
BpdV
Apd
0. Based on Townsend discharge
1. Electron sheath = Discharging gap
2. Produced ions contribute to enhance
electron Current
1/21/ 4
3/ 4003/ 4
2 2
3
e
e e
Ts V d
T en
1/ 2
1 ico se
e
m
m
1/ 2 1/ 21/ 4 1/ 4
3/ 4 1/ 40 0
3/ 4 3/ 4
2 2 1 2 2ln 1 exp 0
3 3
e eb b
e e co e e
T TAp V Bp V
T en T en
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Verification of the Breakdown Model by Comparison with Exp.
Verification of the electron sheath model
1 2 3 4 5 6 7 8 9 10 11
0
50
100
150
200
250
300
RF power 300 W, 3 mm, t1 mm
Bre
ak
do
wn
Vo
lta
ge
[V
]
Pressure [mTorr]
calculation
experiment
10-4
10-3
10-2
10-1
100
101
102
10-1
100
101
102
103
104
Bre
ak
do
wn
Vo
lta
ge
[V
]
Pressure [Torr]
Collisionless
Available
Regime
Collisional
Unavailable
◈ Calculated breakdown voltages with pressure at
fixed plasma density and electron temperature
Breakdown voltages with respect to operating pressures are analogous to the Paschen’s curve for DC discharge.
The electron sheath model is valid for collisionless sheath. Thus, the breakdown model is available in low pressure regime.
In this manner, it is characterized as a breakdown model inside electron sheath in low temperature and low pressure plasma.
◈ Comparison between calculated and measured breakdown voltages
Measured breakdown voltages are well matched with theoretical results which are calculated with measured ambient plasma operating conditions such as gas pressure, electron density, electron temperature and plasma potential.
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Breakdown Voltage with Ambient Plasma Properties
2 3 4 5 6100
150
200
250
300
350
400
ne = 6.0× 10
10cm
-3
ne = 4.0× 10
10cm
-3
ne = 2.0× 10
10cm
-3
exp. data
Gas : Ar
Te = 3 eV
co
= 117, α = 2.3
Bre
ak
do
wn
Vo
lta
ge
[V
]
Pressure [mTorr]
2 3 4 5 6100
200
300
400Gas : Ar
ne = 4.0×10
10cm
-3
co
= 117, α = 2.3
Te = 1eV
Te = 3eV
Te = 5eV
exp. data
Bre
ak
do
wn
Vo
lta
ge
[V
]
Pressure [mTorr]
Electron density in ambient plasma ↑
→ Electron sheath thickness ↓
→ Breakdown voltage inside electron sheath ↑
Electron Temperature ↑
→ Electron sheath thickness ↓
→ Breakdown voltage inside electron sheath ↑
◈ Breakdown voltages with ambient plasma density
Ambient plasma density Electron Temperature
◈ Breakdown voltages with plasma density
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Conclusion
1. Electron sheath expands and breaks down electrically with sheath voltage.
2. Breakdown inside electron sheath can be regarded as a DC discharge having plasma cathode.
3. Electron sheath plays a role of discharge gap, which varies with sheath voltage, not fixed.
4. Electron sheath thickness is larger at lower plasma density and lower electron temperature.
5. Based on Townsend’s criteria, equation for breakdown voltage inside electron sheath is derived.
6. The breakdown model is valid in low pressure regime ensuring collisionless sheath.
7. The breakdown inside electron sheath occurs at lower voltage as the larger electron sheath forms
at lower ambient plasma density and lower electron temperature.
1/ 2 3/ 41/ 4 0 0
1/ 2 1/ 4
2 2
3 e e
Vs
e n T
1/ 2 1/ 21/ 4 1/ 4
3/ 4 1/ 40 0
3/ 4 3/ 4
2 2 1 2 2ln 1 exp 0
3 3
e eb b
e e co e e
T TAp V Bp V
T en T en
Thank you.
If you have any question, please contact to
bluer@snu.ac.kr,
Yeong-Shin Park
NUPLEX, Dept. of Nuclear, Seoul National University,
Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742, Korea
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2 3 4 5 6 7 8 9 10
0
50
100
150
200
250
300
350
B
rea
kd
ow
n V
olt
ag
e [
V]
Pressure [mTorr]
200W cal.
300W cal.
400W cal.
200W exp.
300W exp.
400W exp.
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