EEDF F ti i PlEEDF Formation in Plasmas - ispc … · Plasma consists of bulk (()p (p )neutral)...

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

Kenichi NanbuProfessor Emerit s Tohok Uni ersit JAPANProfessor Emeritus, Tohoku University, JAPAN

1

OutlineOutline

1. Introduction

Definition of EEDF

Two-temperature Maxwellian

2 EEDF from PIC/MC2. EEDF from PIC/MC

3. EEDF of RF Ar Plasmas

Effect of pressure

Effect of frequency

Effect of secondary electron emission coefficient

ff f i iEffect of position

4. EEDF of RF CF4 Plasmas

Effect of pressureEffect of pressure

Effect of frequency

Effect of secondary electron emission coefficient

2Acknowledgements

辻野貴志

タイプライターテキスト

Copyright remains with the author(s).

1 Introduction1. Introduction

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

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

3

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

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

Definition of EEDF

N : electrons in volume element dVN : electrons in volume element dV: number of electrons inεεϕ dN )( ),( εεε d+

1)(∫∞

d 1)(0

=∫ εεϕ d

⎟⎞

⎜⎛2 εε

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

e2/3

eM exp

)(

2)(

kTkT

εεπ

εϕ (equilibrium)

4Te: electron temperature

)( εεϕ

e

const.)(

lnkT

εεεϕ

−= (equilibrium)

Measure EEDF(lhs) → obtain Te

Electron density : ne = N /dVy e

Do not confuse !

)eV(/)(:EEDF -3/2εεϕ

)eVm( / )(:EEPF

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

e 　　

　

εεϕ

εεϕ

n

Velocity space and VDFvv dNf )( : number of electrons in atvd vvv dNf )( : number of electrons in at

zyx dvdvdvd =v

vd v

∫∞

51)( =∫

∞

∞−vv df

Mean velocity (drift velocity)

df∫∞

)( vvvv df∫ ∞−= )(

Electron temperature:Te13

vvvv dfmkT ∫∞

∞−−= )()(

2

1

2

3 2e

11∫∞ 22 )(

2

1)(

2

1vvv mdfvm −= ∫

∞

∞−

( )m ( )22e )(

3v−= v

k

mT 　

Of i li ibl b f i2)(

⎞⎛⎞⎛ 22/3

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

2)(vv v

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛=

kT

vv

kT

mv

2exp

24)(

22

2/3

ππχ (equil.)

6)()(,2

1 2 εϕχε →= vmv

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

e- + Ar → e- + Ar+ + e-

εεϕεσε dk )()(2

∫∞

(ionization)

EEDF governs rate constant

εεϕεσε

dm

k )()(izizth∫= (ionization)

EEDF governs rate constant.

7

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

5

5

0

(-3/

2)]}

Raw Data

T1 = 1.840 eV

T2 = 0.8929 eV

-10

-5

EE

DF

[eV

^(

-15

ln{E

-20

0 10 20 30 40 50

Energy (eV)

8

EEDF is two-temperature Maxwellian.

⎧ f)( T

⎩⎨⎧

>≤

=c2M2

c1M1

for),(

for),()(

εεεϕεεεϕ

εϕ　　　

　　

Tc

Tc

T1=1.840eV, T2=0.8929eV, εc=13.0eV

⎩ c2M2 )(ϕ

9

Since εi =15 76eV > ε EEDF for ε> ε governs the rate kiSince εiz 15.76eV > εc , EEDF for ε> εc governs the rate kiz.

Coefficients c1, c2

1)()(cε

∫∫∞

dTdT 2M210 M1

at)()(

1),(),(c

εεεϕεϕ

εεϕεεϕε

==

=+ ∫∫TcTc

dTcdTc

c2M21M1 at　),(),( εεεϕεϕ == 　　TcTc

dttt f)(1

)( 222 π+∫

∞

c = 0 999094

xxxdtttx

erfc4

)exp(2

)exp( 222 +−=−∫c1 = 0.999094c2 = 607.048

{rate const. for equil. T1}

{rate const for two-temp}= 26.0

10

{rate const. for two-temp}

2. EEDF from PIC/MC

Energy 221 mv=ε

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

∂∂∂ q)()()()(

⎞⎛⎞⎛∂∂

⋅×++∂∂

⋅+∂∂

nfm

qnfnf

t vBvE

xv

inelel

)()(⎟⎠⎞

⎜⎝⎛

∂∂

+⎟⎠⎞

⎜⎝⎛

∂∂

=t

nf

t

nf　　　　　　　　　　　　　

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

inelel ⎠⎝⎠⎝

B eq shows : E-field, B-field, elastic coll., and inelastic coll. govern EEDF

PIC/MC : solution method of B equation

11

qRef : 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)

Main ideaGrades of N(=1000) students{x1, x2, ・・・ , xN}idea of distribution, e.g.

2 ⎤⎡ ⎞⎛)Maxwellian(

2

1exp

2

1)(

2

D σπσ　　

xxxf

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−=

deviation standard:

mean:

σ　　　　　　　

　　　　　　　　x

exact expression

∑ −= )(1

)(E xxN

xfN

iδ

∫ ∫

∑∞

∞−

∞

∞−

=

== 1)()(

)()(

ED

1E

dxxfdxxf

Nf

ii

Relation between fD and fE

High fD → {x1, x2, ・・・} is dense

∫ ∫∞ ∞

12

g fD { 1 2 }Low fD → {x1, x2,・・・} is sparse

f (v, x, t ) of B eq is like fD

fE for B eq is expressed as

n ∑=N

tttf 33 ))(())(()( xxvvxv δδn

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

∑=

−−=i

ii tttf1

E ))(())((),,( xxvvxv δδ

g g { i( ), i( ) , , }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 stochasticThe law is partly deterministic, partly stochastic.Let us consider electrons in E-field.Collision probability of electron in (t ，t +Δt ) isp y ( ， )

b d i d)/2(

tvNP Δ= )(Tgc εσ

13

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

)/2( mε=ε Tσ

In case of Pc=1/6, play dice.I f lli i (t +Δt ) d (t +Δt ) d t i dIn case of no collision, xi(t +Δt ) and vi(t +Δt ) are determined

by solving the equation of motion

)( td i E

v

The equation is coupled with the field equation

),( tqdt

m ii xE=

th h 0ερ

=⋅∇ E

throughspecies):( jnq

jjj 　　∑=ρ

where nj is a functional of sets {xi}j

If a collision occurs, we determine

j

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

These are the theoretical basis of PIC/MC14

These are the theoretical basis of PIC/MC.

3. EEDF of RF Ar Plasmas

General structure of Ar rf dischargeelectrode spacing = 25.4mm (fixed)p =25mTorrf =13 56MHzf =13.56MHzγ=0.1Vrf =200VVrf 00V

φ(z,t), Ez(z,t) ,ρ(z,t), ・・・

15

3.0E+02 6.0E+04

0.0E+00

1.0E+02

2.0E+02

ntia

l (V

)

0.0E+00

3.0E+04

(V/m

)

-2.0E+02

-1.0E+02

0.0E 00

Pot

en Time-ave.

0

π/2

π

3π/2

-3.0E+04

0.0E 00

Ez

(

0

π/2

π

3π/2

-3.0E+02

0 5 10 15 20 25

z (mm)

3π/2-6.0E+04

0 5 10 15 20 25

z (mm)

1.5E-04

2.0E-04

3 5 0E+05

1.0E+06

m3)

5.0E-05

1.0E-04

rge

Den

sity

(C

/m3

0

π/2

π

3π/2

0.0E+00

5.0E+05

rbed

Pow

er (

W/m

0

-5.0E-05

0.0E+00

0 5 10 15 20 25

Cha

r

-1.0E+06

-5.0E+05

0 5 10 15 20 25

Abs

or π/2

π

3π/2

16

0 5 10 15 20 25

z (mm)

0 5 10 15 20 25

z (mm)

1.0E+16 1.0E+16

6.0E+15

8.0E+15D

ensi

ty (

1/m

3

Time-ave.

6.0E+15

8.0E+15

sity

(1/

m3)

Time-ave.

2.0E+15

4.0E+15

Ele

ctro

n D Time ave.

0

π/2

π

3π/2

2.0E+15

4.0E+15

Ion

Den 0

π/2

π

3π/2

0.0E+00

0 5 10 15 20 25

z (mm)

0.0E+00

0 5 10 15 20 25

z (mm)

2.5

3.0

(eV

1 0E+01

1.0E+02

(eV

1 0

1.5

2.0

aver

aged

Val

ues

(

Te

2〈ε_e〉/3

1.0E+00

1.0E+01

aver

aged

Val

ues

(

Ti

2〈ε_i〉/3

0.0

0.5

1.0

0 5 10 15 20 25

Tim

e-a

1.0E-02

1.0E-01

0 5 10 15 20 25

Tim

e-a

17

0 5 10 15 20 25

z (mm)

0 5 10 15 20 25

z (mm)

6.0E+20 5

3.0E+20

4.0E+20

5.0E+20

Rat

e (1

/m3/

s)

Ionization

Excitation

Charge Exchange

-5

0

[eV

^(-3

/2)]

}

Raw Data

T1 = 0.5375 eV

T2 = 2.708 eV

1.0E+20

2.0E+20

3.0E 20

Rea

ctio

n R

-15

-10

ln{E

ED

F [

0.0E+00

0 5 10 15 20 25

z (mm)

-20

0 10 20 30 40 50

Energy (eV)

0.03

0 01

0.02

IED

F (

1/eV

)

0.00

0.01

0 20 40 60 80 100 120

18

0 20 40 60 80 100 120

Energy (eV)

Mechanism of electron heatingDrift velocity of electron at sheath edgeApplied voltage tV ωϕϕ == sinApplied voltage Sheath thickness Expanding sheath accelerates electrons.

tV ωϕϕ == 　,sinrf

)sin1(max21 ϕδ −≅

)( 23

21 ππϕ ～=Expanding sheath accelerates electrons.)( 22ϕ

19

Ar, 13.56 MHz, 25 mTorr, γi=0

6.0E 15

(1/m ← Sampling position of EEDF and

drift velocity W

4.0E+15

Den

sity

Time-ave.

drift velocity Wz

Forward

B k d

ctro

n D e ve.

0

π/2

Backward

2.0E+15Ele

c π/2

π

3 /2

0.0E+00

3π/2

0 5 10 15

z (mm)20

z (mm)


m) Forward

0.0E+00z

(V/m Backward

Ez

0

π/2-3.0E+04

π/2

π

-6 0E+04

3π/2

6.0E+04

0 5 10Sampling position of EEDF and

21z (mmSampling position of EEDF and drift velocity Wz


1.0E-02

1.0E-01

1.0E+00

2)]

Forward

Backward1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

ED

F [

eV^(

-3/2

)]

Forward

Backward

1.0E-07

1.0E-06

1.0E-05

1.0E-04

1.0E-03

EE

DF

[eV

^(-3

/2 Backward

1.0E-07

1.0E-06

1.0E-05

0 10 20 30 40

Energy (eV)

EE

2.0E+05

3.0E+05

)

.0 07

0 10 20 30 40

Energy (eV)

1.0E+05

|Wz|

(m

/s)

Forward

Backward

0.0E+00

0.00 0.25 0.50 0.75 1.00

Normalized Phase t/T

1 0E 01

1.0E+00 1.0E+00

π/2 π 3π/2

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

EE

DF

[eV

^(-3

/2)]

Forward

Backward

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

EE

DF

[eV

^(-3

/2)]

Forward

Backward

221.0E-07

1.0E-06

0 10 20 30 40

Energy (eV)

1.0E-07

1.0E-06

0 10 20 30 40

Energy (eV)

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

1.0E+01 3.0

1.0E-03

1.0E-01

V^(

-3/2

)]

25 mTorr

50 mTorr

100 mTorr

150 mTorr

200 mTorr

2.0

2.5

(eV

)

T1

T2

1.0E-07

1.0E-05

EE

DF

[eV 200 mTorr

0.5

1.0

1.5

T1,

T2

1.0E-09

0 10 20 30 40 50

Energy (eV)

0.0

0 50 100 150 200 250

Pressure (mTorr)

23

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

T1 governs overall temperature Te

As p→large, Te→large

4

V

25 mTorr

50 mTorr

2

3

empe

ratu

re (

eV

50 mTorr

100 mTorr

150 mTorr

200 mTorr

1

Ele

ctro

n T

e

0

0 5 10 15 20 25

z (mm)

24

Two regions for εεϕεφ )()( =)61(0R1:

R2:As p→large, →small

)eV76.15(0 th =<< 　εε　εε <th

)( 2RφAs p large, smallHence, ionization frequency per electron → small

But, as p→large, e--Ar collision frequency → largeO ll ff i

)( 2Rφ

Overall effect is:As p increases, ne→inc →dec →inc →inc

1.0E-01

1.0E+01

2)]

25 mTorr

50 mTorr

100 mTorr1.5E+16

2.0E+16

(1/m

3

25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr

1.0E-05

1.0E-03

EE

DF

[eV

^(-3

/2

150 mTorr

200 mTorr

5 0E+15

1.0E+16

Ele

ctro

n D

ensi

ty (

1.0E-09

1.0E-07

0 10 20 30 40 50

0.0E+00

5.0E+15

0 5 10 15 20 25

E

25

Energy (eV) z (mm)

Effect on IEDF at electrode

0.10

0.08

0.10

25 mTorr

50 mTorr

0.04

0.06

ED

F (

1/eV

) 100 mTorr

150 mTorr

200 mTorr

0.02

0.0IE

0.00

0 20 40 60 80 100 120

Energy (eV)

26

Energy (eV)

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

1 0E+01 3 0

1 0E-03

1.0E-01

1.0E+01

(-3/

2)]

13.56 MHz

20 MHz

40 MHz

60 MHz2.0

2.5

3.0

V)

1.0E-07

1.0E-05

1.0E-03

EE

DF

[eV

^(

60 MHz

0 5

1.0

1.5

T1,

T2

(eV

T1

T2

1.0E-09

1.0E 07

0 10 20 30 40 50

Energy (eV)

0.0

0.5

0 10 20 30 40 50 60 70

Frequency (MHz)

T2

27

gy ( ) q y ( )

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

As f→large, Te→large

4

3

pera

ture

(eV

13.56 MHz

20 MHz

40 MHz

60 MHz

1

2

Ele

ctro

n T

emp

0

0 5 10 15 20 25

E

z (mm)

28

Two energy regionsR1: R2:As f→large →large

)eV76.15(0 th =<< 　　εεεε <th

)(RφAs f→large, →largeHence, ionization rate → large

)( 2Rφ

29

Overall effectAs f →large, ne→large

1.2E+17

1.4E+17

8.0E+16

1.0E+17

ensi

ty (

1/m

3 13.56 MHz

20 MHz

40 MHz

4.0E+16

6.0E+16

Ele

ctro

n D

e

60 MHz

0.0E+00

2.0E+16

0 5 10 15 20 250 5 10 15 20 25

z (mm)

30

Effect of γ, secondary electron emission coefficientA 0 0 1Ar, γ=0， 0.1p =25mTorrV f =200VVrf 200Vz =L/2 (L=25.4mm)EEDF has a high energy tail of secondary electrons.Hence, ionization rate increases.Therefore, ne increases.

1.0E-01

1.0E+01

]

γi = 0

i 0 1 1 0E+20

1.2E+20

1.4E+20

m3/

s

1.0E-07

1.0E-05

1.0E-03

EE

DF

[eV

^(-3

/2) γi = 0.1

4 0E+19

6.0E+19

8.0E+19

1.0E+20

niza

tion

Rat

e (1

/m

γi = 0

i 0 1

1.0E-11

1.0E-09

0 50 100 150 200 250

E

0.0E+00

2.0E+19

4.0E+19

0 5 10 15 20 25

Ion γi = 0.1

31

0 50 100 150 200 250

Energy (eV) z (mm)

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

1.0E+02

1.0E-02

1.0E+00

V^(

-3/2

)]

Bulk

Sheath

1 0E 08

1.0E-06

1.0E-04

EE

DF

[eV

1.0E-10

1.0E-08

0 10 20 30 40 50

32

Energy (eV)


π → 3π/2 では2 < ε < 25 eV 電子数増加顕著

2 V 電子数減少顕著

1.0E-01

1.0E+00

0

π/2

ε < 2 eV 電子数減少顕著

加熱された！

1.0E-02

^(-3

/2)]

π/2

π

3π/2

1 0E-04

1.0E-03

ED

F [

eV^

1.0E-05

1.0E-04EE

π/2 → π では，高エネルギー領域側の電子数増加が顕著

1.0E-06

0 5 10 15 20 25 30

領域側の電子数増加が顕著

33Energy (eV)


6 0E+15

(

6.0E+15

Den

sity

04.0E+15

ctro

n D 0

π/2

2.0E+15Ele

c π

3π/2π/2 π において加熱される電子

0.0E+00

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．

0 5 10 15

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

34

z (mm)電子．電界が弱いので，加熱は比較的小さい．


m)

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，

0.0E+00z

(V/m

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．

Ez

0

π/2-3.0E+04

π/2

π

-6 0E+04

3π/2

6.0E+04

0 5 10π/2の位相でシース中に侵入した電子が今度は

35z (mm)π/2の位相でシ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．

4. EEDF of RF CF4 plasmas4 p

CF4 is used in plasma etchingS i i CF lSpecies in CF4 plasma

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

+, CF3+

Electron-CF4 collision cross section (by H. Ito)4 ( y )

101

102

2 )

Qm

Qv3

100

101

n (1

0-16 c

m2

Qv4

Qv3

Qv2×3

Qdn

Qi(CF3+)

Qi(C+)

10-1

ross

-Sec

tion

Qv2×3

Qi(CF2+)

Qi(C )

Qi(F+)

10-2

Cr

Q i(CF+)

Qa(F-)

Qa(CF3- )

3610-2 10-1 100 101 102 103

Electron Energy (eV)

10-3

Structure of rf CF4 plasmap(CF4) =25mTorrf =13.56MHzVrf =200VVrf 200Vγ=0.1z =L/2 (L=25.4mm) for EEDFSh h i hi kSheath is thick.

3.0E+04

6.0E+04

m)

3.0E+04

6.0E+04

m)

Ar CF4

-3.0E+04

0.0E+00

Ez

(V/m

0

π/2

π-3.0E+04

0.0E+00

Ez

(V/m

0

π/2

π

-6.0E+04

0 5 10 15 20 25

z (mm)

π

3π/2

-6.0E+04

0 5 10 15 20 25

z (mm)

π

3π/2

37

Electron density is strongly time-modulated.Order of densities

CF3+ > F- > CF3

- > e- > CF2+

4.0E+14

05.0E+15

CF3+

2.0E+14

3.0E+14

n D

ensi

ty (

1/m

3 π/2

π

3π/2

2 0E 15

3.0E+15

4.0E+15

nsity

(1/

m3)

CF2+

CF+

C+

F+

F

0.0E+00

1.0E+14Ele

ctro

n

0 0E+00

1.0E+15

2.0E+15

Den F-

CF3-

Electron

0 5 10 15 20 25

z (mm)

0.0E+00

0 5 10 15 20 25

z (mm)

38

EEDF has a long high-energy tail

1.0E+01

1.0E+02

V)

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

-5

0

2)]}

Raw Data

T1 =0.9236 eV

1 0E 01

1.0E+00

Tem

pera

ture

(eV

-10

{EE

DF

[eV

^(-3

/2

T2 = 4.543 eV

1.0E-02

1.0E-01

0 5 10 15 20 25-20

-15

0 10 20 30 40 50

ln{

z (mm) Energy (eV)

39

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

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

2.5E+16 4.0 4.0E+0425 mTorr50 mTorr

1.5E+16

2.0E+16

sity

(1/

m3)

2.0

3.0

empe

ratu

re (

eV

Electron0.0E+00

2.0E+04

Ez

(V/m

)

50 mTorr100 mTorr150 mTorr200 mTorr

5.0E+15

1.0E+16

Den

s

1.0

Ele

ctro

n TElectron

Positive Ion

Negative Ion

Te

-4 0E+04

-2.0E+04

E

ωt = 0

40

0.0E+00

0 50 100 150 200 250

Pressure (mTorr)

0.0 -4.0E+04

0 5 10 15 20 25

z (mm)

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

8.0E+15

1.0E+16

/m3

25 mTorr

50 mTorr

100 T15

20

(eV

25 mTorr

50 mTorr

4.0E+15

6.0E+15

ctro

n D

ensi

ty (

1/m

100 mTorr

150 mTorr

200 mTorr 10

tron

Tem

pera

ture

100 mTorr

150 mTorr

200 mTorr

0.0E+00

2.0E+15

0 5 10 15 20 25

Ele

0

5

0 5 10 15 20 25

Ele

ctz (mm) z (mm)

41

density(CF3+ , F- , CF3

- )→increase

2.5E+16

3.0E+16

m3)

25 mTorr

50 mTorr

100 mTorr

150 mTorr

1.0E+16

1.5E+16

2.0E+16

CF

3+ D

ensi

ty (

1/m

200 mTorr

0.0E+00

5.0E+15

0 5 10 15 20 25

C

z (mm)

3.0E+1625 mTorr

50 mTorr3.0E+16

25 mTorr

50 mTorr

1.5E+16

2.0E+16

2.5E+16

nsity

(1/

m3)

100 mTorr

150 mTorr

200 mTorr

1.5E+16

2.0E+16

2.5E+16

ensi

ty (

1/m

3)

100 mTorr

150 mTorr

200 mTorr

5.0E+15

1.0E+16F-

Den

5.0E+15

1.0E+16

CF

3- D

e

42

0.0E+00

0 5 10 15 20 25

z (mm)

0.0E+00

0 5 10 15 20 25

z (mm)

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

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

8

10

V)

25 mTorr

4

6

8

Tem

pera

ture

(eV 50 mTorr

100 mTorr

150 mTorr

200 mTorr

0

2CF

3+

0 5 10 15 20 25

z (mm)

825 T

8

4

6

atur

e (e

V)

25 mTorr

50 mTorr

100 mTorr

150 mTorr

200 mTorr4

6

erat

ure

(eV

)

25 mTorr

50 mTorr

100 mTorr

150 mTorr

200 mTorr

2

4

F-

Tem

pera

2

4

CF

3- T

empe 200 mTorr

430

0 5 10 15 20 25

z (mm)

0

0 5 10 15 20 25

z (mm)

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

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

1 0E 01

1.0E+01 25 mTorr

50 mTorr

100 mTorr 25.0

30.0

1 0E-05

1.0E-03

1.0E-01

DF

[eV

^(-3

/2)]

100 mTorr

150 mTorr

200 mTorr

15.0

20.0

25.0

1, T

2 (e

V)

1.0E-09

1.0E-07

1.0E 05

EE

D

0 0

5.0

10.0

T

T1

T2

0 10 20 30 40

Energy (eV)

0.0

0 50 100 150 200 250

Pressure (mTorr)

44

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

As f increases, plasma changes:sheath→thinner

6.0E+0413.56 MHz

20 MHz

0.0E+00

3.0E+04

Ez

(V/m

)

40 MHz

60 MHz

-6.0E+04

-3.0E+04

0 5 10 15 20 25

ωt = 0

45

0 5 10 15 20 25

z (mm)

As f increasesAs f increases, electronegative → electropositive plasmaOnly at 13.56MHz, plasma is electronegative!O y 3.56 , p s s e ec o eg ve!

1.0E+17

3.0

4.0

e (e

V

1.0E+16

Den

sity

(1/

m3)

2.0

n T

empe

ratu

re

Electron

1 0E+14

1.0E+15D

0 0

1.0

Ele

ctro

ElectronPositive IonNegative IonTe

1.0E+14

0 10 20 30 40 50 60 70

Frequency (MHz)

0.0

46

electronegative→electropositive at f=20MHzelectronegative→electropositive at f 20MHz

13.56 MHz 60 MHz

8.0E+16CF3+ CF2+ CF+C+ F+ F-CF3- Electron

4.0E+15

5.0E+15

CF3+

CF2+

4.0E+16

6.0E+16

Den

sity

(1/

m3)

2.0E+15

3.0E+15

Den

sity

(1/

m3)

CF2

CF+

C+

F+

F-

0.0E+00

2.0E+16

0 5 10 15 20 25

D

0.0E+00

1.0E+15

0 5 10 15 20 25

D CF3-

Electron

0 5 10 15 20 25

z (mm)

0 5 10 15 20 25

z (mm)

47

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

8.0E+16 13.56 MHz (×10)

20 MHz

40 MHz

8.0E+16

m3

13.56 MHz

20 MHz

40 MHz

4.0E+16

6.0E+16

on D

ensi

ty (

1/m

3

60 MHz

4.0E+16

6.0E+16

Ion

Den

sity

(1/

m

60 MHz

0.0E+00

2.0E+16Ele

ctro

0.0E+00

2.0E+16

Pos

itive

0 5 10 15 20 25

z (mm)

0 5 10 15 20 25

z (mm)

6.0E+15 13.56 MHz

20 MHz

3 0E+15

4.0E+15

5.0E+15

Den

sity

(1/

m3

20 MHz

40 MHz

60 MHz

1.0E+15

2.0E+15

3.0E+15

Neg

ativ

e Io

n

48

0.0E+00

0 5 10 15 20 25

z (mm)

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

5

V

13.56 MHz

20 MH

1.0E+01

13.56 MHz

2

3

4

Tem

pera

ture

(eV 20 MHz

40 MHz

60 MHz

1 0E 05

1.0E-03

1.0E-01

F [

eV^(

-3/2

)]

20 MHz

40 MHz

60 MHz

0

1

2

Ele

ctro

n

1 0E 09

1.0E-07

1.0E-05

EE

DF

0 5 10 15 20 25

z (mm)

1.0E-09

0 10 20 30 40 50

Energy (eV)

5.0

3.0

4.0

(eV

)

1.0

2.0T1,

T2

T1

T2

490.0

0 10 20 30 40 50 60 70

Frequency (MHz)

As f increases,time modulation of ne→small

13.56 MHz 60 MHz

4.0E+14

3

0

π/2

8.0E+16

3

2.0E+14

3.0E+14

ron

Den

sity

(1/

m3

π

3π/2

4.0E+16

6.0E+16

ron

Den

sity

(1/

m3

0

π/2

0.0E+00

1.0E+14

0 5 10 15 20 25

Ele

ctr

0.0E+00

2.0E+16

0 5 10 15 20 25

Ele

ctr

π

3π/2

0 5 10 15 20 25

z (mm)

0 5 10 15 20 25

z (mm)

50

Comparison with ArO ll T d d (CF )Overall Te → decrease one order (CF4)cf. → increase by 2.6 times (Ar)

4.0 4.0

13.56 MHz 60 MHz

2 0

3.0

ed V

alue

s (e

V

2 0

3.0

ed V

alue

s (e

V

1.0

2.0

Tim

e-av

erag

e

Te

2〈ε_e〉/31.0

2.0

Tim

e-av

erag

e

Te

2〈ε_e〉/3

0.0

0 5 10 15 20 25

z (mm)

0.0

0 5 10 15 20 25

z (mm)

51

Effect of γ, secondary electron emission coefficientCF4 0 0 1CF4γ=0， 0.1p(CF4) =25mTorrVrf =200Vz =L/2 (L=25.4mm)

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

2 0E+14

2.5E+14

3.0E+14

(1/m

3 1.0E-01

1.0E+01

2)]

γi = 0

γi = 0.1

1.0E+14

1.5E+14

2.0E+14

Ele

ctro

n D

ensi

ty (

γi = 0

γi 0 1

1.0E-05

1.0E-03

EE

DF

[eV

^(-3

/2

γ

0.0E+00

5.0E+13

0 5 10 15 20 25

E γi = 0.1

1.0E-09

1.0E-07

0 50 100 150 200 250

52

z (mm) Energy (eV)

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

1.0E+00

1 0E-04

1.0E-02

eV^(

-3/2

)]

γi = 0

γi = 0.1

1.0E-06

1.0E-04

EE

DF

[e

6 0 1 6 0E 15

1.0E-08

0 10 20 30 40 50 60

Energy (eV)

4.0E+15

5.0E+15

6.0E+15

nsity

(1/

m3 γi = 0

γi = 0.14.0E+15

5.0E+15

6.0E+15

ensi

ty (

1/m

3

γi = 0

γi = 0.1

1.0E+15

2.0E+15

3.0E+15

Pos

itive

Ion

Den

1.0E+15

2.0E+15

3.0E+15

Neg

ativ

e Io

n D

e

530.0E+00

0 5 10 15 20 25

z (mm)

0.0E+00

0 5 10 15 20 25

z (mm)

For larger γ,T1 becomes smaller and hence so does TT1 becomes smaller, and hence so does Te.

1.0E+00 5.0

1.0E-04

1.0E-02

F [

eV^(

-3/2

)]

γi = 0

γi = 0.1

2 0

3.0

4.0

, T2

(eV

)

T1

1 0E 08

1.0E-06

EE

DF

0 0

1.0

2.0T1

T2

1.0E-08

0 10 20 30 40 50 60

Energy (eV)

0.0

0.0 0.1

γi

5

3

4

mpe

ratu

re (

eV

1

2

Ele

ctro

n T

em

γi = 0

γi = 0.1

54

0

0 5 10 15 20 25

z (mm)

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

Ar CF4

1.0E-01

1.0E+01

3/2)

]

γi = 0

γi = 0.1

1.0E-01

1.0E+01

3/2)

]

γi = 0

γi = 0.1

1 0E 07

1.0E-05

1.0E-03

EE

DF

[eV

^(-3

1 0E 07

1.0E-05

1.0E-03

EE

DF

[eV

^(-3

1.0E-09

1.0E-07

0 10 20 30 40 50

E ( V)

1.0E-09

1.0E-07

0 10 20 30 40 50 60

E ( V)

55

Energy (eV) Energy (eV)

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.

56

Date post:	14-Sep-2018
Category:	Documents
Upload:	vucong
View:	217 times
Download:	0 times

EEDF F ti i PlEEDF Formation in Plasmas - ispc … · Plasma consists of bulk (()p (p )neutral)...

Documents