eedf formation in plasmas › ... › nanbu_ispc18_iupac_summer_school.pdf(ispc-18, iupac summer...
TRANSCRIPT
![Page 1: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/1.jpg)
1
EEDF Formation in Plasmas(ISPC-18, IUPAC Summer School, Aug. 23, 2007)
Kenichi NanbuProfessor Emeritus, Tohoku University, JAPAN
![Page 2: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/2.jpg)
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
![Page 3: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/3.jpg)
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)
![Page 4: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/4.jpg)
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)
![Page 5: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/5.jpg)
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
![Page 6: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/6.jpg)
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.)
![Page 7: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/7.jpg)
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)
![Page 8: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/8.jpg)
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
![Page 9: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/9.jpg)
9
EEDF is two-temperature Maxwellian.
T1=1.840eV, T2=0.8929eV, εc=13.0eV
⎩⎨⎧
>≤
=c2M2
c1M1
for),(for),(
)(εεεϕεεεϕ
εϕ
TcTc
![Page 10: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/10.jpg)
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
![Page 11: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/11.jpg)
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
![Page 12: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/12.jpg)
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
![Page 13: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/13.jpg)
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
![Page 14: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/14.jpg)
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
![Page 15: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/15.jpg)
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), ・・・
![Page 16: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/16.jpg)
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
![Page 17: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/17.jpg)
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
Time-ave.0π/2π3π/2
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)
Time-ave.0π/2π3π/2
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
![Page 18: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/18.jpg)
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
)
![Page 19: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/19.jpg)
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 ~=
![Page 20: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/20.jpg)
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
Time-ave.0π/2π3π/2
← Sampling position of EEDF and drift velocity Wz
Forward
Backward
![Page 21: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/21.jpg)
21
Ar, 13.56 MHz, 25 mTorr, γi=0
-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
![Page 22: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/22.jpg)
22
Ar, 13.56 MHz, 25 mTorr, γi=0
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
![Page 23: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/23.jpg)
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
![Page 24: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/24.jpg)
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 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
![Page 25: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/25.jpg)
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
)]
25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
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
25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
![Page 26: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/26.jpg)
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
)
25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
![Page 27: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/27.jpg)
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
![Page 28: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/28.jpg)
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
13.56 MHz20 MHz40 MHz60 MHz
![Page 29: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/29.jpg)
29
Two energy regionsR1: R2:As f→large, →largeHence, ionization rate → large
)eV76.15(0 th =<< εεεε <th
)( 2Rφ
![Page 30: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/30.jpg)
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
![Page 31: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/31.jpg)
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
![Page 32: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/32.jpg)
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
![Page 33: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/33.jpg)
33
Ar, 13.56 MHz, 25 mTorr, γi=0
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!
![Page 34: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/34.jpg)
34
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
(
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.
![Page 35: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/35.jpg)
35
Ar, 13.56 MHz, 25 mTorr, γi=0
-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.
![Page 36: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/36.jpg)
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- )
![Page 37: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/37.jpg)
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
![Page 38: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/38.jpg)
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
![Page 39: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/39.jpg)
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
![Page 40: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/40.jpg)
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)
25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
ωt = 0
![Page 41: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/41.jpg)
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
25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
0
5
10
15
20
0 5 10 15 20 25
z (mm)El
ectro
n Te
mpe
ratu
re (e
V
25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
![Page 42: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/42.jpg)
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)
25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
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)
25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
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)
25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
![Page 43: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/43.jpg)
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)
25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
0
2
4
6
8
0 5 10 15 20 25
z (mm)
CF3
- Tem
pera
ture
(eV
)
25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
![Page 44: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/44.jpg)
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
)]
25 mTorr50 mTorr100 mTorr150 mTorr200 mTorr
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
![Page 45: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/45.jpg)
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)
13.56 MHz20 MHz40 MHz60 MHz
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
![Page 46: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/46.jpg)
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
![Page 47: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/47.jpg)
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
![Page 48: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/48.jpg)
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
13.56 MHz20 MHz40 MHz60 MHz
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
13.56 MHz20 MHz40 MHz60 MHz
![Page 49: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/49.jpg)
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
13.56 MHz20 MHz40 MHz60 MHz
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
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
![Page 50: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/50.jpg)
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
![Page 51: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/51.jpg)
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
![Page 52: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/52.jpg)
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
![Page 53: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/53.jpg)
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
![Page 54: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/54.jpg)
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
![Page 55: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/55.jpg)
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
![Page 56: 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](https://reader033.vdocuments.site/reader033/viewer/2022042309/5ed70f0362136e72fb7bc1e8/html5/thumbnails/56.jpg)
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.