study on expansion of electron sheath and breakdown in...

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

[email protected]

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.


PYS_LSP_GEC-Oct2010

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)


PYS_LSP_GEC-Oct2010

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


PYS_LSP_GEC-Oct2010

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


PYS_LSP_GEC-Oct2010

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


PYS_LSP_GEC-Oct2010

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


PYS_LSP_GEC-Oct2010

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.


PYS_LSP_GEC-Oct2010

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.


PYS_LSP_GEC-Oct2010

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.


PYS_LSP_GEC-Oct2010

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


PYS_LSP_GEC-Oct2010

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


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.


PYS_LSP_GEC-Oct2010

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.


PYS_LSP_GEC-Oct2010

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


PYS_LSP_GEC-Oct2010

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.


PYS_LSP_GEC-Oct2010

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


PYS_LSP_GEC-Oct2010

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

[email protected],

Yeong-Shin Park

NUPLEX, Dept. of Nuclear, Seoul National University,

Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742, Korea


PYS_LSP_GEC-Oct2010

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.

study on expansion of electron sheath and breakdown in...

Documents