EEDF Formation in Plasmas › ... › Nanbu_ISPC18_IUPAC_Summer_School.pdf(ISPC-18, IUPAC Summer School, Aug. 23, 2007) Kenichi Nanbu Professor Emeritus, Tohoku University, JAPAN 2

1

EEDF Formation in Plasmas(ISPC-18, IUPAC Summer School, Aug. 23, 2007)

Kenichi NanbuProfessor Emeritus, Tohoku University, JAPAN

2

Outline1. Introduction

Definition of EEDFTwo-temperature Maxwellian

2. EEDF from PIC/MC3. EEDF of RF Ar Plasmas

Effect of pressureEffect of frequencyEffect of secondary electron emission coefficientEffect of position

4. EEDF of RF CF4 PlasmasEffect of pressureEffect of frequencyEffect of secondary electron emission coefficient

Acknowledgements

3

1. Introduction

Homo sapiens－peaceBalance of male and femaleStop killing people by peace keeping

Plasma－sheathBalance of positive and negative species (bulk)Stop killing electrons by sheath formation (sheath)

4

Plasma consists of bulk(neutral) plus sheath(positive)

In DC, bulk has a potential hill with a flat top.Electrons cannot go down the hill.Discharge is self-sustained.

Definition of EEDFN : electrons in volume element dV

: number of electrons inεεϕ dN )( ),( εεε d+1)(

0=∫

∞εεϕ d

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

e2/3

eM exp

)(2)(

kTkTεε

πεϕ

Te: electron temperature

(equilibrium)

5

e

const.)(lnkTε

εεϕ

−= (equilibrium)

Measure EEDF(lhs) → obtain TeElectron density : ne = N /dVDo not confuse !

)eVm( / )(:EEPF

)eV( / )( :EEDF3/2-3-

e

-3/2

　　

　　

εεϕ

εεϕ

nVelocity space and VDF

vv dNf )( : number of electrons in at

zyx dvdvdvd =vvd v

1)( =∫∞

∞−vv df

6

Mean velocity (drift velocity)vvvv df∫

∞

∞−= )(

Electron temperature:Te

vvvv dfmkT ∫∞

∞−−= )()(

21

23 2

e

22 )(21)(

21 vvv mdfvm −= ∫

∞

∞−

( )22e )(

3v−= v

kmT 　

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛=

kTvv

kTmv

2exp

24)(

22

2/3

ππχ

Often, is negligible, but never so for ionDistribution of speed or

2)(vv v

)()(,21 2 εϕχε →= vmv

(equil.)

7

Why is EEDF important?Various reactions occur in processing plasma.Rate constant kr is obtained from EEDF.

e- + Ar → e- + Ar+ + e-

EEDF governs rate constant.

εεϕεσεε

dm

k )()(2iziz

th∫∞

= (ionization)

8

-20

-15

-10

-5

0

5

0 10 20 30 40 50

Energy (eV)

ln{E

EDF

[eV

^(-3

/2)]}

Raw DataT1 = 1.840 eVT2 = 0.8929 eV

If equilibrium is assumed, the rate obtained is far from true.Example : Ar, rf plasma, f =13.56MHz, p = 200mTorr, γ=0.1

9

EEDF is two-temperature Maxwellian.

T1=1.840eV, T2=0.8929eV, εc=13.0eV

⎩⎨⎧

>≤

=c2M2

c1M1

for),(for),(

)(εεεϕεεεϕ

εϕ　　　

　　　

TcTc

10

Since εiz=15.76eV > εc , EEDF for ε> εc governs the rate kiz. Coefficients c1, c2

c1 = 0.999094c2 = 607.048

c2M21M1

2M210 M1

at　),(),(

1),(),(c

c

εεεϕεϕ

εεϕεεϕε

ε

==

=+ ∫∫∞

　　　TcTc

dTcdTc

xxxdtttx

erfc4

)exp(21)exp( 222 π

+−=−∫∞

{rate const. for equil. T1}

{rate const. for two-temp}= 26.0

11

2. EEDF from PIC/MC

EnergyVelocity v is governed by the Boltzmann equation.Velocity distribution function f (v, x, t ) of electrons

Number of electrons in dv×dx is nf (v, x, t ) dvdxB eq shows :

E-field, B-field, elastic coll., and inelastic coll. govern EEDFPIC/MC : solution method of B equation

Ref : K. Nanbu, IEEE Trans, Plasma Science, Vol.28(2000)971-990.PIC/MC code:（株）計算力学研究センター(www.rccm.co.jp)

inelel

)()(

)()()()(

⎟⎠⎞

⎜⎝⎛

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

=

∂∂

⋅×++∂∂

⋅+∂∂

tnf

tnf

nfmqnfnf

t

　　　　　　　　　　　　　

vBvE

xv

221 mv=ε

12

Main ideaGrades of N(=1000) students{x1, x2, ・・・ , xN}

idea of distribution, e.g.

exact expression

Relation between fD and fEHigh fD → {x1, x2, ・・・} is denseLow fD → {x1, x2,・・・} is sparse

deviation standard:mean:

)Maxwellian(21exp

21)(

2

D

σ

σπσ

　　　　　　　

　　　　　　　　

　　

x

xxxf⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−=

∫ ∫

∑∞

∞−

∞

∞−

=

==

−=

1)()(

)(1)(

ED

1E

dxxfdxxf

xxN

xfN

iiδ

13

f (v, x, t ) of B eq is like fDfE for B eq is expressed as

n

We can derive the laws governing the set {xi(t ), vi(t ): i=1,2,・・・} from B eq.

The laws determine{xi(t +Δt ), vi(t +Δt )}

using a given {xi(t ), vi(t )}The law is partly deterministic, partly stochastic.Let us consider electrons in E-field.Collision probability of electron in (t ，t +Δt ) is

Ng:gas number density, v : speed at t:energy at t, :total collision cross section

∑=

−−=N

iii tttf

1

33E ))(())((),,( xxvvxv δδ

)/2( mε=ε Tσ

tvNP Δ= )(Tgc εσ

14

In case of Pc=1/6, play dice.In case of no collision, xi(t +Δt ) and vi(t +Δt ) are

determined by solving the equation of motion

The equation is coupled with the field equation

through

where nj is a functional of sets {xi}jIf a collision occurs, we determine

(1) type of collision(elastic, exciting, ionizing)(2) post-collision velocity

These are the theoretical basis of PIC/MC.

),( tqdt

dm ii xEv=

0ερ

=⋅∇ E

species):( jnqj

jj 　　∑=ρ

15

3. EEDF of RF Ar Plasmas

General structure of Ar rf dischargeelectrode spacing = 25.4mm (fixed)p =25mTorrf =13.56MHzγ=0.1Vrf =200V

φ(z,t), Ez(z,t) ,ρ(z,t), ・・・

16

-3.0E+02

-2.0E+02

-1.0E+02

0.0E+00

1.0E+02

2.0E+02

3.0E+02

0 5 10 15 20 25

z (mm)

Pote

ntia

l (V

)

Time-ave.0π/2π3π/2

-5.0E-05

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.0E-04

0 5 10 15 20 25

z (mm)

Cha

rge

Den

sity

(C/m

3

0π/2π3π/2

-6.0E+04

-3.0E+04

0.0E+00

3.0E+04

6.0E+04

0 5 10 15 20 25

z (mm)

Ez (V

/m)

0π/2π3π/2

-1.0E+06

-5.0E+05

0.0E+00

5.0E+05

1.0E+06

0 5 10 15 20 25

z (mm)

Abs

orbe

d Po

wer

(W/m

3)

0π/2π3π/2

17

0.0E+00

2.0E+15

4.0E+15

6.0E+15

8.0E+15

1.0E+16

0 5 10 15 20 25

z (mm)

Elec

tron

Den

sity

(1/m

3


0.0E+00

2.0E+15

4.0E+15

6.0E+15

8.0E+15

1.0E+16

0 5 10 15 20 25

z (mm)

Ion

Den

sity

(1/m

3)


0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 5 10 15 20 25

z (mm)

Tim

e-av

erag

ed V

alue

s (eV

Te

2〈ε_e〉/3

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

0 5 10 15 20 25

z (mm)

Tim

e-av

erag

ed V

alue

s (eV

Ti

2〈ε_i〉/3

18

0.0E+00

1.0E+20

2.0E+20

3.0E+20

4.0E+20

5.0E+20

6.0E+20

0 5 10 15 20 25

z (mm)

Rea

ctio

n R

ate

(1/m

3/s)

IonizationExcitationCharge Exchange

-20

-15

-10

-5

0

5

0 10 20 30 40 50

Energy (eV)

ln{E

EDF

[eV

^(-3

/2)]}

Raw DataT1 = 0.5375 eVT2 = 2.708 eV

0.00

0.01

0.02

0.03

0 20 40 60 80 100 120

Energy (eV)

IED

F (1

/eV

)

19

Mechanism of electron heatingDrift velocity of electron at sheath edgeApplied voltage Sheath thickness Expanding sheath accelerates electrons.

tV ωϕϕ == 　,sinrf

)sin1(max21 ϕδ −≅

)( 23

21 ππϕ ～=

20

Ar, 13.56 MHz, 25 mTorr, γi=0

0.0E+00

2.0E+15

4.0E+15

6.0E 15

0 5 10 15

z (mm)

Elec

tron

Den

sity

(1/m


← Sampling position of EEDF and drift velocity Wz

Forward

Backward

21


-6.0E+04

-3.0E+04

0.0E+00

0 5 10

z (mm

Ez (V

/m)

0π/2π3π/2

Forward

Backward

Sampling position of EEDF and drift velocity Wz

22


0.0E+00

1.0E+05

2.0E+05

3.0E+05

0.00 0.25 0.50 0.75 1.00

Normalized Phase t/T

|Wz|

(m/s)

ForwardBackward

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

0 10 20 30 40

Energy (eV)

EED

F [e

V^(

-3/2

)]

ForwardBackward

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

0 10 20 30 40

Energy (eV)

EED

F [e

V^(

-3/2

)]

ForwardBackward

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

0 10 20 30 40

Energy (eV)

EED

F [e

V^(

-3/2

)]

ForwardBackward

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

0 10 20 30 40

Energy (eV)EE

DF

[eV

^(-3

/2)]

ForwardBackward

π/2 π 3π/2

23

Effect of pressureAr, p =25, 50, 100, 150, 200mTorrf =13.56MHzVrf =200Vγ=0.1z =L/2 (L=25.4mm) for EEDF

1.0E-09

1.0E-07

1.0E-05

1.0E-03

1.0E-01

1.0E+01

0 10 20 30 40 50

Energy (eV)

EED

F [e

V^(

-3/2

)]

25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 50 100 150 200 250

Pressure (mTorr)

T1, T

2 (e

V)

T1T2

24

Consider two-temperature modelT1=low energy temperatureT2=high energy temperatureAs p→large, T1→large and T2→small

T1 governs overall temperature TeAs p→large, Te→large

0

1

2

3

4

0 5 10 15 20 25

z (mm)

Elec

tron

Tem

pera

ture

(eV


25

Two regions for R1: R2:As p→large, →smallHence, ionization frequency per electron → small

But, as p→large, e--Ar collision frequency → largeOverall effect is:

As p increases, ne→inc →dec →inc →inc

εεϕεφ )()( =)eV76.15(0 th =<< 　　εε

εε <th)( 2Rφ

1.0E-09

1.0E-07

1.0E-05

1.0E-03

1.0E-01

1.0E+01

0 10 20 30 40 50

Energy (eV)

EED

F [e

V^(

-3/2

)]


0.0E+00

5.0E+15

1.0E+16

1.5E+16

2.0E+16

0 5 10 15 20 25

z (mm)

Elec

tron

Den

sity

(1/m

3


26

Effect on IEDF at electrode

0.00

0.02

0.04

0.06

0.08

0.10

0 20 40 60 80 100 120

Energy (eV)

IED

F (1

/eV

)


27

Effect of frequencyAr, f=13.56, 20, 40, 60MHzp =25mTorrVrf =200Vγ= 0.1z =L/2 (L=25.4mm) for EEDF

1.0E-09

1.0E-07

1.0E-05

1.0E-03

1.0E-01

1.0E+01

0 10 20 30 40 50

Energy (eV)

EED

F [e

V^(

-3/2

)]

13.56 MHz20 MHz40 MHz60 MHz

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 10 20 30 40 50 60 70

Frequency (MHz)

T1, T

2 (e

V)

T1T2

28

As f→large, T1→large and T2→smallT1 governs overall temperature TeAs f→large, Te→large

0

1

2

3

4

0 5 10 15 20 25

z (mm)

Elec

tron

Tem

pera

ture

(eV


29

Two energy regionsR1: R2:As f→large, →largeHence, ionization rate → large

)eV76.15(0 th =<< 　　εεεε <th

)( 2Rφ

30

Overall effectAs f →large, ne→large

0.0E+00

2.0E+16

4.0E+16

6.0E+16

8.0E+16

1.0E+17

1.2E+17

1.4E+17

0 5 10 15 20 25

z (mm)

Elec

tron

Den

sity

(1/m

3 13.56 MHz20 MHz40 MHz60 MHz

31

Effect of γ, secondary electron emission coefficientAr, γ=0， 0.1p =25mTorrVrf =200Vz =L/2 (L=25.4mm)EEDF has a high energy tail of secondary electrons.Hence, ionization rate increases.Therefore, ne increases.

1.0E-11

1.0E-09

1.0E-07

1.0E-05

1.0E-03

1.0E-01

1.0E+01

0 50 100 150 200 250

Energy (eV)

EED

F [e

V^(

-3/2

)]

γi = 0γi = 0.1

0.0E+00

2.0E+19

4.0E+19

6.0E+19

8.0E+19

1.0E+20

1.2E+20

1.4E+20

0 5 10 15 20 25

z (mm)

Ioni

zatio

n R

ate

(1/m

3/s

γi = 0γi = 0.1

32

Effect of position z on EEDFγ=0z = 5.8mm (sheath edge) z =L/2 (center of bulk)Sheath oscillation gives energy to electrons.

1.0E-10

1.0E-08

1.0E-06

1.0E-04

1.0E-02

1.0E+00

1.0E+02

0 10 20 30 40 50

Energy (eV)

EED

F [e

V^(

-3/2

)]

BulkSheath

33


1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

0 5 10 15 20 25 30

Energy (eV)

EED

F [e

V^(

-3/2

)]

0π/2π3π/2

π/2 → π では，高エネルギー

領域側の電子数増加が顕著

π → 3π/2 では2 < ε < 25 eV 電子数増加顕著ε < 2 eV 電子数減少顕著

加熱された！

34


0.0E+00

2.0E+15

4.0E+15

6.0E+15

0 5 10 15

z (mm)

Elec

tron

Den

sity

(

0π/2π3π/2

π/2 → π において加熱される電子．

電界も強いので高エネルギーを有する．

π → 3π/2 において加熱される低エネルギー(<2eV)電子．電界が弱いので，加熱は比較的小さい．

35


-6.0E+04

-3.0E+04

0.0E+00

0 5 10

z (mm)

Ez (V

/m)

0π/2π3π/2

π/2の位相でシース中に侵入した電子が，今度はπ/2 → π でバルク側に，高電界で加速される

ために，高エネルギーを有する．

0 → πの位相では電界が無く，バルクと同等であるために2eV以下の低エネルギー電子が多い．π → 3π/2 では加熱されるが，電界が弱いので，

加熱は比較的小さい．

36

4. EEDF of RF CF4 plasmas

CF4 is used in plasma etchingSpecies in CF4 plasma

e-, F-, CF3-, F+, C+, CF+, CF2

+, CF3+

Electron-CF4 collision cross section (by H. Ito)

10-2 10-1 100 101 102 103

Electron Energy (eV)

10-3

10-2

10-1

100

101

102

Cros

s-Se

ctio

n (1

0-16 c

m2 )

Qm

Qv4

Qv3

Qv2×3

Qdn

Qi(CF3+)

Qi(CF2+)

Q i(CF+)

Qi(C+)

Qi(F+)

Qa(F-)

Qa(CF3- )

37

Structure of rf CF4 plasmap(CF4) =25mTorrf =13.56MHzVrf =200Vγ=0.1z =L/2 (L=25.4mm) for EEDFSheath is thick.

-6.0E+04

-3.0E+04

0.0E+00

3.0E+04

6.0E+04

0 5 10 15 20 25

z (mm)

Ez (V

/m)

0π/2π3π/2

-6.0E+04

-3.0E+04

0.0E+00

3.0E+04

6.0E+04

0 5 10 15 20 25

z (mm)

Ez (V

/m)

0π/2π3π/2

Ar CF4

38

Electron density is strongly time-modulated.Order of densities

CF3+ > F- > CF3

- > e- > CF2+

0.0E+00

1.0E+14

2.0E+14

3.0E+14

4.0E+14

0 5 10 15 20 25

z (mm)

Elec

tron

Den

sity

(1/m

3

0π/2π3π/2

0.0E+00

1.0E+15

2.0E+15

3.0E+15

4.0E+15

5.0E+15

0 5 10 15 20 25

z (mm)D

ensit

y (1

/m3)

CF3+CF2+CF+C+F+F-CF3-Electron

39

EEDF has a long high-energy tail

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

0 5 10 15 20 25

z (mm)

Tem

pera

ture

(eV

)

CF3+ CF2+ CF+C+ F+ F-CF3- Electron

-20

-15

-10

-5

0

0 10 20 30 40 50

Energy (eV)ln

{EED

F [e

V^(

-3/2

)]}

Raw DataT1 =0.9236 eVT2 = 4.543 eV

40

Effect of pressurep =25, 50, 100, 150, 200mTorrf =13.56MHzVrf =200Vγ=0.1z =L/2 (L=25.4mm) for EEDF

As p increases, plasma changes:electronegative→electropositive →electronegativeTe (bulk): decrease→stationary→increasesheath→thinner

0.0E+00

5.0E+15

1.0E+16

1.5E+16

2.0E+16

2.5E+16

0 50 100 150 200 250

Pressure (mTorr)

Den

sity

(1/m

3)

0.0

1.0

2.0

3.0

4.0

Elec

tron

Tem

pera

ture

(eV

ElectronPositive IonNegative IonTe

-4.0E+04

-2.0E+04

0.0E+00

2.0E+04

4.0E+04

0 5 10 15 20 25

z (mm)

Ez (V

/m)


ωt = 0

41

As p increases,electron density: increase→decreaseelectron temperature(sheath):opposite to bulk

0.0E+00

2.0E+15

4.0E+15

6.0E+15

8.0E+15

1.0E+16

0 5 10 15 20 25

z (mm)

Elec

tron

Den

sity

(1/m

3


0

5

10

15

20

0 5 10 15 20 25

z (mm)El

ectro

n Te

mpe

ratu

re (e

V


42

density(CF3+ , F- , CF3

- )→increase

0.0E+00

5.0E+15

1.0E+16

1.5E+16

2.0E+16

2.5E+16

3.0E+16

0 5 10 15 20 25

z (mm)

CF3

+ D

ensit

y (1

/m3)


0.0E+00

5.0E+15

1.0E+16

1.5E+16

2.0E+16

2.5E+16

3.0E+16

0 5 10 15 20 25

z (mm)

F- D

ensit

y (1

/m3)


0.0E+00

5.0E+15

1.0E+16

1.5E+16

2.0E+16

2.5E+16

3.0E+16

0 5 10 15 20 25

z (mm)

CF3

- Den

sity

(1/m

3)


43

temperature(CF3+)→increases near the electrode(E-field)

temperature(F- , CF3- )→decrease in the sheath(collisional loss)

0

2

4

6

8

10

0 5 10 15 20 25

z (mm)

CF3

+ Te

mpe

ratu

re (e

V) 25 mTorr

50 mTorr100 mTorr150 mTorr200 mTorr

0

2

4

6

8

0 5 10 15 20 25

z (mm)

F- T

empe

ratu

re (e

V)


0

2

4

6

8

0 5 10 15 20 25

z (mm)

CF3

- Tem

pera

ture

(eV

)


44

As p increases,two-temperature: T1→sudden increase at 150mTorr

(transition to electronegative)T2→small change, compared with T1

1.0E-09

1.0E-07

1.0E-05

1.0E-03

1.0E-01

1.0E+01

0 10 20 30 40

Energy (eV)

EED

F [e

V^(

-3/2

)]


0.0

5.0

10.0

15.0

20.0

25.0

30.0

0 50 100 150 200 250

Pressure (mTorr)

T1, T

2 (e

V)

T1T2

45

-6.0E+04

-3.0E+04

0.0E+00

3.0E+04

6.0E+04

0 5 10 15 20 25

z (mm)

Ez (V

/m)


Effect of frequencyf =13.56, 20, 40, 60MHzp =25mTorrVrf =200Vγ=0.1z =L/2 (L=25.4mm) for EEDF

As f increases, plasma changes:sheath→thinner

ωt = 0

46

As f increases, electronegative → electropositive plasmaOnly at 13.56MHz, plasma is electronegative!

1.0E+14

1.0E+15

1.0E+16

1.0E+17

0 10 20 30 40 50 60 70

Frequency (MHz)

Den

sity

(1/m

3)

0.0

1.0

2.0

3.0

4.0

Elec

tron

Tem

pera

ture

(eV

ElectronPositive IonNegative IonTe

47

electronegative→electropositive at f=20MHz

0.0E+00

2.0E+16

4.0E+16

6.0E+16

8.0E+16

0 5 10 15 20 25

z (mm)D

ensit

y (1

/m3)

CF3+ CF2+ CF+C+ F+ F-CF3- Electron

0.0E+00

1.0E+15

2.0E+15

3.0E+15

4.0E+15

5.0E+15

0 5 10 15 20 25

z (mm)

Den

sity

(1/m

3)

CF3+CF2+CF+C+F+F-CF3-Electron

13.56 MHz 60 MHz

48

As f increases,electron and positive ion increase,negative ion density slightly changes in bulk.

0.0E+00

2.0E+16

4.0E+16

6.0E+16

8.0E+16

0 5 10 15 20 25

z (mm)

Elec

tron

Den

sity

(1/m

313.56 MHz (×10)20 MHz40 MHz60 MHz

0.0E+00

2.0E+16

4.0E+16

6.0E+16

8.0E+16

0 5 10 15 20 25

z (mm)

Posit

ive

Ion

Den

sity

(1/m

3


0.0E+00

1.0E+15

2.0E+15

3.0E+15

4.0E+15

5.0E+15

6.0E+15

0 5 10 15 20 25

z (mm)

Neg

ativ

e Io

n D

ensit

y (1

/m3


49

As f increases,T1 suddenly decreases, and hence so does Te.Change of T2 is small.

0

1

2

3

4

5

0 5 10 15 20 25

z (mm)

Elec

tron

Tem

pera

ture

(eV


1.0E-09

1.0E-07

1.0E-05

1.0E-03

1.0E-01

1.0E+01

0 10 20 30 40 50

Energy (eV)

EED

F [e

V^(

-3/2

)]


0.0

1.0

2.0

3.0

4.0

5.0

0 10 20 30 40 50 60 70

Frequency (MHz)

T1, T

2 (e

V)

T1T2

50

As f increases,time modulation of ne→small

0.0E+00

1.0E+14

2.0E+14

3.0E+14

4.0E+14

0 5 10 15 20 25

z (mm)

Elec

tron

Den

sity

(1/m

3

0π/2π3π/2

13.56 MHz 60 MHz

0.0E+00

2.0E+16

4.0E+16

6.0E+16

8.0E+16

0 5 10 15 20 25

z (mm)El

ectro

n D

ensit

y (1

/m3

0π/2π3π/2

51

Comparison with ArOverall Te → decrease one order (CF4)cf. → increase by 2.6 times (Ar)

0.0

1.0

2.0

3.0

4.0

0 5 10 15 20 25

z (mm)

Tim

e-av

erag

ed V

alue

s (eV

Te

2〈ε_e〉/3

0.0

1.0

2.0

3.0

4.0

0 5 10 15 20 25

z (mm)

Tim

e-av

erag

ed V

alue

s (eV

Te

2〈ε_e〉/3

13.56 MHz 60 MHz

52

Effect of γ, secondary electron emission coefficientCF4γ=0， 0.1p(CF4) =25mTorrVrf =200Vz =L/2 (L=25.4mm)

EEDF has a high energy tail of secondary electrons.Hence, ionization rate increases,Therefore, ne increases.

0.0E+00

5.0E+13

1.0E+14

1.5E+14

2.0E+14

2.5E+14

3.0E+14

0 5 10 15 20 25

z (mm)

Elec

tron

Den

sity

(1/m

3

γi = 0γi = 0.1

1.0E-09

1.0E-07

1.0E-05

1.0E-03

1.0E-01

1.0E+01

0 50 100 150 200 250

Energy (eV)

EED

F [e

V^(

-3/2

)]

γi = 0γi = 0.1

53

As γ increases,electrons contributing to electron attachment (5－9 eV) decrease, and hence negative ion decreases, so does positive ion.

0.0E+00

1.0E+15

2.0E+15

3.0E+15

4.0E+15

5.0E+15

6.0E+15

0 5 10 15 20 25

z (mm)

Posit

ive

Ion

Den

sity

(1/m

3 γi = 0γi = 0.1

0.0E+00

1.0E+15

2.0E+15

3.0E+15

4.0E+15

5.0E+15

6.0E+15

0 5 10 15 20 25

z (mm)

Neg

ativ

e Io

n D

ensit

y (1

/m3 γi = 0

γi = 0.1

1.0E-08

1.0E-06

1.0E-04

1.0E-02

1.0E+00

0 10 20 30 40 50 60

Energy (eV)

EED

F [e

V^(

-3/2

)]

γi = 0γi = 0.1

54

For larger γ,T1 becomes smaller, and hence so does Te.

1.0E-08

1.0E-06

1.0E-04

1.0E-02

1.0E+00

0 10 20 30 40 50 60

Energy (eV)

EED

F [e

V^(

-3/2

)]

γi = 0γi = 0.1

0.0

1.0

2.0

3.0

4.0

5.0

0.0 0.1

γi

T1, T

2 (e

V)

T1T2

0

1

2

3

4

5

0 5 10 15 20 25

z (mm)

Elec

tron

Tem

pera

ture

(eV

γi = 0γi = 0.1

55

Effect of γ on EEDF is larger for electronegative plasma.Flux of emitted electrons are nearly the same for electropositive and electronegative plasmas.However, the flux has a stronger effect on EEDF in electronegative plasma because its electron density is much smaller than that ofelectropositive plasma.

Ar CF4

1.0E-09

1.0E-07

1.0E-05

1.0E-03

1.0E-01

1.0E+01

0 10 20 30 40 50

Energy (eV)

EED

F [e

V^(

-3/2

)]

γi = 0γi = 0.1

1.0E-09

1.0E-07

1.0E-05

1.0E-03

1.0E-01

1.0E+01

0 10 20 30 40 50 60

Energy (eV)

EED

F [e

V^(

-3/2

)]

γi = 0γi = 0.1

56

Acknowledgements

The speaker wishes to express his sincere thanks to

Dr. Kazuki Denpoh, Tokyo Electron AT Ltd.

for presenting the simulation data used in this lecture.Also the speaker expresses thanks to

Mr. Toshihiko Iwao, Graduate school, Tohoku Univ., Japan

for helping him with the preparation of this lecture.

Documents

EEDF Formation in Plasmas › ... › Nanbu_ISPC18_IUPAC_Summer_School.pdf(ISPC-18, IUPAC Summer School, Aug. 23, 2007) Kenichi Nanbu Professor Emeritus, Tohoku University, JAPAN 2