Fundamentals of Plasma Physics IIIppst-2007.physik.uni-greifswald.de/fundamentals_3.pdf · • The...
Transcript of Fundamentals of Plasma Physics IIIppst-2007.physik.uni-greifswald.de/fundamentals_3.pdf · • The...
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Institute for Experimental and Applied Physics
Group Plasma Technology
Fundamentals of Plasma Physics IIIH. Kersten
Summer School on Plasma Physics, BNPTGreifswald, 11.09.2007
IEAP University of Kiel
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outline
3.1. Gas discharge plasmas
electric breakdown in gasesTownsend mechanismmicro discharges / streamersPaschen’s law
3.2. Stationary gas discharges
Townsend dischargeglow dischargestructures of a glow dischargehollow cathode effect, magnetron effectarc discharge
3.3. Plasma surface interaction
stationary plasma boundary sheathChild-Langmuir lawBohm criterion
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mechanical compression• gas is heated by shock waves (ballistic compression)electromagnetic compression• gas heating for short duration by high-current pulse discharges to very high temperatures• special form of electromagnetic compression at Pinch effect where a rapidly increasingmagnetic field compresses the plasma
plasma generation by electric fields
• plasmas are mostly generated by electrical discharges• in principle, a gas becomes ionized by an electric field (ignition) and a self-sustainingmechanism stabilizes the plasma at a certain current• time regime (frequency) of the field, gas pressure and electrode material are of greatimportance
plasma generation by waves / radiation
• for ionization of a gas also waves or particle beams can be used• e.g. microwave radiation, electron beams, laser, radioactive radiation
3.1. Gas Discharge Plasmas
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plasma generation(energy supply)
heating/compression
particle beam/external source
electric field
electromagneticfield
electromagneticwaves
glow discharge- positive column- low-pressure lamps- cathode sputtering- hollow cathode
arc discharge- high-pressure lamps- plasma welding
corona dischargedielectric barrier discharge (DBE)
- plasma display panel (PDP)capacitively coupled
plasma (CCP)
inductively coupledplasma (ICP)
- plasma torchmagnetron dischargeplasma focus
electron beam plasmaplasma jetmagnetohydrodynamicgenerator (MHD)
microvwave plasma- electron cyclotronresonance (ECR)
surface wave plasmahelicon wave plasma
3.1. Gas Discharge Plasmas
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atmospheric pressure dischargelow pressure rf discharge in argon
low pressure dc glow discharge in neon (positive column)
3.1. Gas Discharge Plasmas
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3.1. Gas Discharge Plasmas
plasma application:for example for illumination
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recipe(input)
pV, P
fgenerator
B
neutralsnn Tn
j+ jnE+ En
nn
electrons ne Te
ionsn+ n-T+ T-
substrate
chemical processing,deposition
products
physical processing,deposition
energy conversion : field, plasma, surface
plasmaspecies
3.1. Gas Discharge Plasmas
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P inelasticcollisions
optical emission
reactivespecies
new ions andelectrons
thermalizationof field energythrough elastic
collisions:hot electrons
Te↑
electrons gain energy
fromelectric field
~ eλe|E|
electrons and their collisions carry and distribute the energyfrom the matchbox to process gas (neutrals, ions) to the substrate
particle interaction: charge carriers in plasma
non-thermal plasmas
3.1. Gas Discharge Plasmas
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differentreactivespecieselectron
density ne
electron collision
rate νvoltage Ufree mean
path λ+
etch rate
selectivity
homogeneity
power loss (heat)
power
power loss (heat)
loss
plasma
Fundamental
energy conversion : field, plasma, surface
3.1. Gas Discharge Plasmas
plasma application:for example semiconductor etching
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collision processes innon-isothermal plasmas
electron-electroninteraction
heavyparticlereactions
no change ofparticlenumber
change ofparticlenumber
⇒e- + A 2e- + A+
e- + A+ 2e- + A++
e-+ A2 2e- + A + A+
⇒
⇒
e- + A + B A- + Be- + A2 A + A-
⇒⇒
ionization
attachment
dissociatione- + AB e- + A + Be- + AB e- + A+ + B-
elastic collisione- + A e- + A
electron collisions withheavy particles
excitatione- + A e- + A*e- + A* e- + A**(source of radiation:A* A + hv)
e- + A* e- + A⇒
deexcitation
recombinatione- + A+ A + hve- + A2
+ A + A⇒⇒
⇒
⇒
⇒
⇒
⇒⇒
collsion processes : generation
of charge carriers
3.1. Gas Discharge Plasmas
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collsion processes : generation of charge carriers
3.1. Gas Discharge Plasmas
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channels of ionization ( α)
• Direct electron impact ionization
• Ionization from excited levels
• Penning Ionization
** 2iKM e M e− + −+ ⎯⎯→ +
2iKM e M e− + −+ ⎯⎯→ +
* pKAr M M Ar e+ −+ ⎯⎯→ + +
dominant at high energy
dominant at low energy
collsion processes : generation of charge carriers
3.1. Gas Discharge Plasmas
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collsion processes : generation of charge carriers
3.1. Gas Discharge Plasmas
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Ar
ionization energyexcitation energy
ionization via ionization via excited states and excited states and
Penning effectPenning effect
ionization via ionization via impact impact
ionizationionization
collsion processes : generation of charge carriers
3.1. Gas Discharge Plasmas
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energy and momentum conservationcollision of an electron ( and ) and an atom ( and )
(ma >> me , va << ve)
elastic collision
ionizing collision
neon
neon
neon
exciting collision
ex
aaa
ee
aa
ee uv
mv
mv
mv
m++=+ 2222 '
2'
222
'' aaeeaaee vmvmvmvm +=+
io
aaa
eee
aa
ee uv
mvv
mv
mv
m+++=+ 22222 '
2)"'(
222
')"'( aaeeeaaeevmvvmvmvm ++=+
2222 '2
'222 a
ae
ea
ae
e vm
vm
vm
vm
+=+
'' aaeeaaee vmvmvmvm +=+
em evr
aam vr
typical total cross section :)2
( 2e
e vm
uQ =
3.1. Gas Discharge Plasmas
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collsion processes : generation of charge carriers
3.1. Gas Discharge Plasmas
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collsion processes : losses of charge carriers
3.1. Gas Discharge Plasmas
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multiplication of charge carriers
3.1. Gas Discharge Plasmas
drift
EmeEv
eed
τμ 0==
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Townsend‘s coefficient
3.1. Gas Discharge Plasmas
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Pieter van Musschenbroek (1692-1761)Leiden jar‘s
3.1. Gas Discharge Plasmas
Streamers
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FunkenentladungElektrischer Durchschlag
in Luft: E ~ 30 kV/cm
3.1. Gas Discharge Plasmas
streamers
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presence of at least one dielectric in the discharge space
3.1. Gas Discharge Plasmasmicro discharges : DBD
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• thin cylindrical weakly ionized plasma columns, ∅ ≈ 200 μm• electron densities: 1014 … 1015 cm-3
• duration: 1 .. 10 ns• non-equilibrium plasmas (Te >> Tgas) ⇒ well suited for initiation of
plasma-chemical reactions
Microdischarges of short duration
3.1. Gas Discharge Plasmas
micro discharges : DBD
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electric breakdown
3.1. Gas Discharge Plasmas
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multiplication of charge carriers
3.1. Gas Discharge Plasmas
ignition of discharge
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Paschen‘s law
3.1. Gas Discharge Plasmas
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Paschen‘s law
3.1. Gas Discharge Plasmas
surfacegas
breakdown voltage depends on pressure, distance and gas
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Paschen‘s law
3.1. Gas Discharge Plasmas
Johann W. Hittorf (1824-1914)
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3.2. Stationary Gas Discharges
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Townsend discharge
3.2. Stationary Gas Discharges
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3.2. Stationary Gas Discharges
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glow discharge
3.2. Stationary Gas Discharges
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glow discharge
3.2. Stationary Gas Discharges
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glow discharge
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3.2. Stationary Gas Discharges
hollow cathode discharge
• cylindric cathode,
ring shaped anode
(at positive potential)
• merging of of glow edge
• „ideal plasma“: only negative glow
• oscillation of electrons increase of
ionization and dissociation
• hollow cathode effect
E
x
E
r
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3.2. Stationary Gas Discharges
micro hollow cathode discharge
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glow discharge
3.2. Stationary Gas Discharges
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principle of dc cathode sputtering,diode system
a gas flowb pumpc cathoded targete anodef deposited layerg cathode fallh positive columnI screening, shield
diode system (E)
magnetron system (E X B)
influence of magnetic field
3.2. Stationary Gas Discharges
magnetron discharge
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capacitively-coupled plasma
~ rf
ωpi ωωpe
rf domainMHz GHz
13.56 MHz
• Capacitive discharges are used in etching and deposition
• Radiofrequency domain is such that electrons follow the rf field wile ions follow time-averaged field
• Ionization degree is small (<0.001)
• Gas pressure is low (a few Pa); collisionless heating is often dominant
rf discharge
3.2. Stationary Gas Discharges
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rf discharge : CCP, ICP
3.2. Stationary Gas Discharges
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rf discharge : CCP, ICP
3.2. Stationary Gas Discharges
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PPR
symmetric, asymmetric
plasma jet
rf discharge : CCP
3.2. Stationary Gas Discharges
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• plasma excitation by an electric fieldgenerated by the transformer principle
• changing magnetic field of the conductorinduces an electric field in which the electronsare accelerated
• high plasma density
rf discharge : ICP
3.2. Stationary Gas Discharges
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arc discharge
3.2. Stationary Gas Discharges
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plasma welding and cutting
arc discharge
3.2. Stationary Gas Discharges
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Coulomb-dominated
plasmas
„reactive“neutral-
dominatedplasmas
focus
torch
highpressure
lampsMHD
hollow cathode
pseudo sparksECR
heliconelectron beam arcs
ICP
arcs
DBE
PDP
corona
Magnetron
microwavesurfacewaveCCP
low-pressure lamps
positive column
dc cathode sputtering
1012 1014 1016 1018
0.01 1 100 10k pressure p0 (Pa)
gas density N0 (cm-3)
plasma sources at different gas and charge carrier densitiesnon-idealplasmas
thermal plasmas
108
1010
1012
1014
1016
1018
char
geca
rrier
dens
ities
n e, i(
cm-3
)
electron energydistribution:
non-maxwellian
ideal weaklyionized,
non-isothermalplasmas
n e, i= N 0
3.2. Stationary Gas Discharges
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3.3. Plasma Surface Interaction
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role of charge carriers in plasma :
• occurrence of electrical conductivity• screening of electric fields• occurrence of oscillations and waves, and corresponding instabilities• interaction with magnetic fields• formation of characteristic boundary sheaths due to contact with walls
characteristic dimensions / time constants :
Debye length λD is the shielding length for the long range Coulombinteraction. It is the distance over which thermal motion causessignificant deviations from quasi-neutrality
The plasma frequency ωP is critical for the propagation of electromagnetic waves in plasmas (supply of energy).
3.3. Plasma Surface Interactionplasma bulk
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plasma in contact with floating wall:
floating potential Vfl
µe >> µi
sheath formation:
sheath potential:
wall charges up until ion flux equals electron flux⇒
or for additional Vs, then : Vbias = Vs - Vpl
evnevn eejje
iij ===
4 4
)/)((exp TVVnn eflplie ke −−=
)/ln(2 mmkTVVV
eie
plflbias−=−=
gas flow
Plasma potential Vpl
plasma
pump out
V
3.3. Plasma Surface Interactionplasma boundary sheath
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potential and charge carrier density for a typical glow discharge
3.3. Plasma Surface Interaction
plasma boundary sheath
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Rp Rstoc
collisionless power dissipation in the sheath
3.3. Plasma Surface Interaction
plasma boundary sheath
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3.3. Plasma Surface Interaction
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3.3. Plasma Surface Interaction
plasma boundary sheath
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Uev2
m 2e ⋅=⋅+e-
h n
E
Rudolf SeeligerUniversität Greifswald1918 -1955
Gehrcke-Seeliger-Demo.exe
3.3. Plasma Surface Interaction
plasma boundary sheath
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3.3. Plasma Surface Interaction
plasma boundary sheath
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3.3. Plasma Surface Interaction
plasma boundary sheath
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3.3. Plasma Surface Interaction
plasma boundary sheath : Child-Langmuir
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• electrons are repelledion matrix sheath
• ions are attractedexpanding sheath
• energetic ions arrive at substrate• stationary sheath position may be reached if
ω pl,e−1 = ε0 me e2 ne( )1 2
ω pl,i−1 = ε0 mi e2 ni( )1 2
ion current in plasmaspace-charge limited current
(Child current for given voltage and actual sheath thickness)
=
Negative voltage pulse applied:
3.3. Plasma Surface Interaction
plasma boundary sheath : Child-Langmuir
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• The transition zone between bulk plasma and a surface, the the SHEATH, is fundamental in plasmaSHEATH, is fundamental in plasma--surface interaction, plasmasurface interaction, plasma--assisted deposition of films, and ion extraction in ion sources.assisted deposition of films, and ion extraction in ion sources.
• Child Law (1911):
• Can be interpreted as – limited current density, j, for given distance, d, or–– adjusting sheathadjusting sheath thickness for given current density and
voltage.
2
230
212
94
dmQej wall
ii
φε⎟⎟⎠
⎞⎜⎜⎝
⎛=
3.3. Plasma Surface Interaction
plasma boundary sheath : Child-Langmuir
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( )
2c c
2Ebeje
2e
j e
jn and e-
j e
jnth wi
21
002
01
00
e0
e
0
02
2
00
i
0
ii
0
e
0
ee
0
02
2
Vc
Ec
dxdE
emj
bj
dxdE
mVe
jdx
Vd
mVevEbv
nnedxdE
dxVd
ii
e
e
i
i
i
ieeie
+=
==−=
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛
+−=
====−=−=
εεε
ε
ε
( ) ( ) ( ) ( ) ( )
2
21
21
2122
)(
)(
21
21
)(
)(
2
21
21
221
21
2
dxdV
42xE
E
42
221 2
21
⎟⎠⎞
⎜⎝⎛
↑↑
⎟⎠⎞
⎜⎝⎛ −+−=−
↑
⎥⎦
⎤⎢⎣
⎡+=
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛+=
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛+=
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
∫ ∫∫
ccc
x
d
xV
dV
xE
dE
dVxVcdxcdE
VdcdxcdxdVd
VdcdxcdxdVdV
dxdcc
dxdV
dxd
c cc
≈ 0E(x) ... )E(d :E
V(x)... ) V(d:V
x ... d :x
c
c
c
X 0 dc
V(dc)
E(dc)
integration limits ?
plasma boundary sheath : Child-Langmuir
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( ) ( ) ( ) 4221
221
21 ⎟⎠⎞
⎜⎝⎛ +⎟
⎠⎞
⎜⎝⎛+−=⇒ cc dExVcdxc
dxdV
0j mm j 121e
i
ei ≈⇒<<⇒>> ccc
( ) ( )
( ) ( )
( ) 0dV
4
4
2
21
c
21
221
2
21
221
2
≈
↑
⎟⎠⎞
⎜⎝⎛ +⎟
⎠⎞
⎜⎝⎛=
⎟⎠⎞
⎜⎝⎛ +⎟
⎠⎞
⎜⎝⎛≈
c
c
c
d
dxdExVcdV
dExVcdxdV
if sheath determined by positive space charges, then :
( )( )
iicc
ccc
V
d
mje
Vd
Vc
ddccV
dxcxV
dVdxxVcdVc
c
0023
2
23
2
224
3
0
0
241
41
2
294
1942
34
2 2
ε=
=⇒−=
=≈ ∫ ∫
294 0
202
3
2
ii
cc m
ej
Vd ε=
( )
( )sh
ci
mpfc
dd
xVme
dPap
~d 29
4j
10
c2
23
21
00⎟⎟⎠
⎞⎜⎜⎝
⎛=
≥↔≤
ε
λ
plasma boundary sheath : Child-Langmuir
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V0 = Vc
S = dc
plasma boundary sheath : Child-Langmuir
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3.3. Plasma Surface Interaction
plasma boundary sheath
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trench-to-sheath size is crucial for conformal treatment
3.3. Plasma Surface Interaction
plasma boundary sheath
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not to scale
3.3. Plasma Surface Interaction
plasma boundary sheath : magnetron
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Argon, 0.005mbar, 10W 30W 50W
Argon, 50W 0.005mbar 0.01mbar
... andepends on discharge power and pressure
3.3. Plasma Surface Interactionplasma boundary sheath
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10Pa 3Pa
2 4 6 8 10 120
2
4
6
8
10
12
14
16
18
20
H2 0.25μm H2 1μm He 0.25μm He 1μm Ne 0.25μm Ne 1μm O2 0.25μm O2 1μm N2 0.25μm N2 1μm Ar 0.25μm Ar 1μm
h [m
m]
p [Pa]
3.3. Plasma Surface Interaction
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PlasmaVrf
Time-averaged potential Zsheath=1/(jcsω)
Zplasma=Rp+jLpω
Impedance depends on :• Voltage, Vrf• Electron density, ne• Sheath size, sm
To find a self-consistent solution:• Child law• Particle balance• Power balance
sb(t)
sa(t)
EzEz
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3.3. Plasma Surface Interactionplasma boundary sheath : Bohm
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( )Sdxx sh === ... 0
sheath
no ionization in the sheath
continuity equation of ions:
conservation of energy:
vi(x) between 0 and dsh:
Boltzmann :
Poisson-equation :
( ) ( ) ( ) ( )0,0 iiii vnxvxn =
( ) 0 x 210;
21
02 =+= plii VekTvm ( )
i
plipli m
VevVekT 0
0
20 =⇒<<
( ) ( )( )i
pli m
xVVexv
−= 02 ( ) ( )( )
( ) ( ) ( )xVVV
nxn
mVe
nm
xVVexn
pl
plii
i
pli
i
pli
−=
=−
0
2)0(
2 00
( ) ( )[ ] ( )( )
( )
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−⎟
⎟⎠
⎞⎜⎜⎝
⎛
−−=⇒−−= ekT
xVe
pl
pleei e
xVVVne
dxVdxnxne
dxVd 02
1
0
02
2
0
02
2 0εε
( ) ( )( )e
okT
xVe
ee enxn 0=
plasma boundary sheath : Bohm
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( ) ( ) ( ) ( )
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡−+
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡−⎟
⎟⎠
⎞⎜⎜⎝
⎛−= 111202 0
0
21
0
02 ekTxVe
e
plpl
e eekT
VxVVnexE
ε
( )
( ) ( ) ??? e and xV 2
1e and 81
2111
0
2x22
1
epl kTxVVfor
xxxxx
<<<<
++≈−−≈−
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
⇒≥
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
−≈
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
++−−≈
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛−+++⎟
⎟⎠
⎞⎜⎜⎝
⎛−−−≈
ple
ple
e
epl
e
ee
e
plplpl
e
VhTe
VkTexVnexE
kTxVexV
VxVxVnexE
TkxVe
kTxVe
ekT
VxV
VxVVnexE
21
210
2410
12
1181
211202
0
0
0
202
20
2
0
02
22
2200
02
2
0
02
ε
ε
ε
with
in order to have a real solution, it must
Bohm criterion
0 21 epl kTVe ≥
plasma boundary sheath : Bohm
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p = 2.4Pa
p = 0.5Pa
ion energy [eV]
inte
nsity
[cps
]
0 50 100 150 200 250 300
Ar, p=5Pa, Vrf=520Vpp
ArH+
Inte
nsity
(a.
u.)
Ion Energy (eV)ion energy [eV]
inte
nsity
[a.u
.]
Ar, p = 5Pa, Vrf= 520Vpp
Vpl
VS
VshIEDF
3.3. Plasma Surface Interactionplasma boundary sheath
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0 5 10 15 20 25 30
0,000
0,001
0,002
0,003
0,004
0,005
0,006
0,007
Ar, 0.7Pa
300W 200W 100W 50W
sign
al [A
/Vcm
2 ]
ion energy [eV]
0 5 10 15 20 25 30 35 40
0,000
0,002
0,004
0,006
0,008
0,010
0,012
0,014
Ar, 300W
sign
al [A
/Vcm
2 ]
ion energy [eV]
0.35Pa
0.7Pa
2Pa
4.7Pa
7Pa
IEDF : dependence on powerintensity
IEDF : dependence on pressureintensity, mean energy
3.3. Plasma Surface Interactionplasma boundary sheath
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chemistry in bulk plasma provides etch speciesphysics provides ions and e- chemical
etching
desorption of etch products
physical sputtering
etchspecies etch rate
selectivity
homogeneityphysics in space charge sheaths
activation energy
ionic current
ion energyand current
3.3. Plasma Surface Interactionplasma boundary sheath : etching
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References