fundamentals of plasmas...school 2016 | fundamentals of plasmas | a. von keudell 22 what is a plasma...
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School 2016 | Fundamentals of Plasmas | A. von Keudell 1
Fundamentals of Plasmas Achim von Keudell Research Department Plasmas with Complex Interactions Ruhr-Universität Bochum
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School 2016 | Fundamentals of Plasmas | A. von Keudell 2
Gas
Plasma
+
+
+
+
-
-
-
-
-
- -
-
liquid Solid state
Plasma as the fourth state of matter
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School 2016 | Fundamentals of Plasmas | A. von Keudell 3
Definition Plasma is a (hot) ionized gas with reactive particles
like electrons, ions, and radicals.
More than 99% of visible matter is plasma.
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School 2016 | Fundamentals of Plasmas | A. von Keudell 4
spiral-galaxy NGC 1232
planetary nebula NGC 6853
young brown dwarf
Plasmas in the universe
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School 2016 | Fundamentals of Plasmas | A. von Keudell 5
polar light
lightning
Natural plasmas on earth
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School 2016 | Fundamentals of Plasmas | A. von Keudell 6
http://www.nap.edu/catalog/11960.html
Low temperature plasmas for our daily lifes
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School 2016 | Fundamentals of Plasmas | A. von Keudell 7
automotive
seat covers
colored plastic parts pasting
lamps ignition
soot removal
welding surface hardening
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School 2016 | Fundamentals of Plasmas | A. von Keudell 8
• Light generation (Plasmalamps) • Plasmaetching in Microelectronics (Computerchips) • Plasma based deposition (PECVD) • Plasma spraying • Surface modification (z.B. Hardening of metals, textiles and
polymers) • Surface sterilisation (z.B. inactivation of germs)
Plasma methods
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School 2016 | Fundamentals of Plasmas | A. von Keudell 9
• Artifical knee – plasma coated • Catheders – plasma coated • Stents – plasma coated • Artifical hips –plasmaspraying • Sterilisation in Hospitals • Drugs – plasma treated • Sterilisation of vials
Plasma in the biomedical sector
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School 2016 | Fundamentals of Plasmas | A. von Keudell 10
• Energy Storage (photocatalytic processes) • Plasma switches (power plants) • Solar panels • Nuclear fusion
• W 7-X, IPP Greifswald • ITER, Cadarache (Frankreich)
Plasma for energy research
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School 2016 | Fundamentals of Plasmas | A. von Keudell 11
• Waste treatment • Water and air cleaning • Plasma medicine
Envorinmental
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School 2016 | Fundamentals of Plasmas | A. von Keudell 12
Plasma vs. ne and Te
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School 2016 | Fundamentals of Plasmas | A. von Keudell 13
Plasma Fundamentals - Outline
1. What is a plasma ?
• Temperature • Debye shielding • Plasma frequency
2. The edge of a plasma
• Sheath physics 3. How to ignite a plasma
• Ignition, Paschen curve • Streamer • RF-ignition
4. Transport in a plasma
• Particle motion • Plasma as a fluid • Drift and diffusion
5. How to sustain a plasma
• DC plasma • Rf-plasmas • Plasma heating
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School 2016 | Fundamentals of Plasmas | A. von Keudell 14
|V|
Heating
Ionisation
ln f
What is a plasma ? Concept 1 - temperature
f
vz vD z
x
More details in the lecture on kinetics, see also master class
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School 2016 | Fundamentals of Plasmas | A. von Keudell 15
Te
Tg
T
p 1 atm
What is a plasma ? Concept 1 - temperature
However, the concept of temperature is only an approximation. Most plasmas are dominated by non-equilibrium. Distribution function are needed rather than temperatures. See also lectures on kinetics
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School 2016 | Fundamentals of Plasmas | A. von Keudell 16
What is a plasma ? - Concept 2 – Debye shielding, quasineutrality
-
-
-
-
-
-
- -
-
- -
( )rΦr
+
+
+
+
+
Example extra positive charge
0
-Φ0
Diffusion of e- due to ∇n
+ + + + + + + + + +
-
x=0
0
Φ0
ne
Diffusion of e- due to ∇n
e- e-
+ + + + + + + + + +
+
x=0
- - - - - - - - - -
- - - - - - - - - -
Example extra negative charge
Attraction of e-
Repelling of e-
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School 2016 | Fundamentals of Plasmas | A. von Keudell 17
What is a plasma ? - Concept 2 – Debye shielding (in formulas)
with
0
-Φ0
Diffusion of e- due to ∇n
+ + + + + + + + + +
-
x=0
- - - - - - - - - -
Example extra negative charge
Repelling of e-
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School 2016 | Fundamentals of Plasmas | A. von Keudell 18
What is a plasma ? - Concept 3 – Collective phenomena – the plasma parameter
-
-
-
-
-
-
- -
-
- -
( )rΦr
+
+
+
+
+
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School 2016 | Fundamentals of Plasmas | A. von Keudell 19
What is a plasma ? - Concept 4 – the plasma frequency
-
-
-
-
-
-
-
-
+
+
+
+
+
+
+ E
δ
+
-
- -
+
+
+
+
- - - -
- -
- -
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School 2016 | Fundamentals of Plasmas | A. von Keudell 20
What is a plasma ? - Concept 4 –the plasma frequency (formulas)
- - - - - - - -
+ + + + + + + +
E
δ
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School 2016 | Fundamentals of Plasmas | A. von Keudell 21
Assume: 100 MHz RF plasma in Ar
ne = 1016 m-3
Electrons can easily follow the RF cycle,
ions can NOT !!
electrons ions
What is a plasma ? - Concept 4 –the plasma frequency (numbers)
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School 2016 | Fundamentals of Plasmas | A. von Keudell 22
What is a plasma ? – Concept 5 – ideal and non-ideal plasmas
105 1010 1015 1020 1025 1030 1035 104010-2
10-1
100
101
102
103
104
105
106
107
T (e
V)
n (m-3)
2cmE eth >
2cmE eF >
ideal
non ideal
3/1n
Non-ideal plasma: Plasma crystal
thF EE =
relativistic
relativistic, degenerate
degenerate
3/2n
degenerate plasma: electrons in a metal
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School 2016 | Fundamentals of Plasmas | A. von Keudell 23
Ideal plasma - many electrons in Debye sphere: fluid approach possible
Ideal plasma – plasma larger than the Debye length:
What is a plasma ? – Concept 5 – ideal and non-ideal plasmas
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School 2016 | Fundamentals of Plasmas | A. von Keudell 24
Ideal plasma – thermal energy must be larger than the Coloumb energy
What is a plasma ? – Concept 5 – ideal and non-ideal plasmas
b0
Relation between collision parameter and Debye length
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School 2016 | Fundamentals of Plasmas | A. von Keudell 25
Parameter of a plasma – Nick Braithwaites Plasma Calculator
PLASMA CALCULATOR (N St J Braithwaite, European Summer School)
Physical Constants e/C k/J_K -̂1 me/kg Mp/kg epsi0/F_m -̂1 mu0/H_m -̂1 c0/m_s -̂1 1.60E-19 1.38E-23 9.00E-31 1.67E-27 8.85E-12 1.26E-06 3.00E+08
Gas data p/Pa Tg/K Mg/amu X-Sectn/m 2̂ 6.00E+00 3.00E+02 4.00E+01 1.00E-19
Plasma data Instructions
kTe/eV ne/m -̂3
Adjust gas, plasma and system data
2.00E+00 1.00E+16
(data boxes in this band are not protected)
Plasma parameters are immediately updated
System data
L/m RF/MHz B/T muwave/MHz rho_Cu/ohm_m 1.00E-01 1.36E+01 1.00E-01 2.45E+03 2.00E-08
Plasma System
Lengths/m inter-neutral inter-ch mfp Debye dskin dskin_Cu L 8.84E-08 4.64E-06 6.90E-03 1.05E-04 2.48E-01 1.93E-05 1.00E-01
Frequencies/rad_s^-1 wpe wpi wce wRF wm 5.67E+09 2.08E+07 1.78E+10 8.52E+07 1.54E+10
Frequencies/MHz fpe fpi fce nu RF muwave 9.03E+02 3.31E+00 2.83E+03 8.64E+01 1.36E+01 2.45E+03
Speeds/m_s^-1 ce ve cs cg 9.52E+05 5.96E+05 2.19E+03 3.97E+02
Fluxes/m^-2_s^-1 Gi Gg 2.19E+19 1.44E+23
Conductivity/ohm^-1_m^-1 sigDC Re[sigRF] Im[sigRF] 3.29E+00 1.67E+00 -1.65E+00
Densities/m^-3 ng ne % ionisation 1.45E+21 1E+16 0.00069 Comments to [email protected]
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School 2016 | Fundamentals of Plasmas | A. von Keudell 26
The edge of a plasma
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School 2016 | Fundamentals of Plasmas | A. von Keudell 27
0 x=s
ni
ne
E
Fe-
F∇n
n0
A plasma in front of a wall – sheath physics
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School 2016 | Fundamentals of Plasmas | A. von Keudell 28
A plasma in front of a wall – sheath physics (formula)
0 x=s
ni
ne
E
Fe-
F∇n
n0
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School 2016 | Fundamentals of Plasmas | A. von Keudell 29
0
Φp
ΦW
~λIonen ~λDebye
Φ
x
vth
vB
v(s)
s
pre-sheath sheath
A plasma in front of a wall – sheath physics – potential, ion velocity
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School 2016 | Fundamentals of Plasmas | A. von Keudell 30
A plasma in front of a wall – sheath physics - special cases
0
x=s
ni
ne
E
Fe-
F∇n
n0
Sheath edge, x=0
x=s
n+
ne
E
n0
n-
αb αs
Multiple ions
Electronegative plasmas
with
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School 2016 | Fundamentals of Plasmas | A. von Keudell 31
AC AA
Φ
Aa >> Ac
Aa << Ac
A plasma in front of a wall – sheath physics – plasma potential
Flux balance ions and electrons Plasma potential
Φ
Φ
Potential difference going from plasma to wall
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School 2016 | Fundamentals of Plasmas | A. von Keudell 32
ni
ne
+
+ +
n0
- V0
Φ
x s
E
Φ, E
ni
ne +
+
+
n0
x 0 s
A plasma in front of a wall – sheath physics – applying a voltage to an electrode
Matrix sheath Child Langmuir sheath
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School 2016 | Fundamentals of Plasmas | A. von Keudell 33
A plasma in front of a wall – sheath physics – ion energy distributions - collisions
Few collisions in the sheath many collisions in the sheath
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School 2016 | Fundamentals of Plasmas | A. von Keudell 34
sa sb
Ia Ib
A B
Irf cos ωt
~ rf
s s0
Va Vb
A plasma in front of a wall – sheath physics – ion energy distributions – rf-sheaths
t
E
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School 2016 | Fundamentals of Plasmas | A. von Keudell 35
N(E)
E
t
M<<
M>>
A plasma in front of a wall – sheath physics – ion energy distributions – rf-sheaths
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School 2016 | Fundamentals of Plasmas | A. von Keudell 36
A plasma in front of a wall – sheath physics – ion energy distributions - collisions
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School 2016 | Fundamentals of Plasmas | A. von Keudell 37
A plasma in front of a wall – sheath physics – applications in microelectronics
Neutrals (CFx, F) Ions (CFx+)
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School 2016 | Fundamentals of Plasmas | A. von Keudell 38
Working point of a Plasma – global model
E-Field ne, Te, f(E) n+,n-, n*
flux to surface
reactor geometry, Discharge type
Heating mechanisms
Atomic- and molecular physics
Transport, Diffusion Sheath physics
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School 2016 | Fundamentals of Plasmas | A. von Keudell 39
Te1 Te2
LHS RHS
Te
EIonisation
ionisation surface losses
Particle balance determines Electron temperature
Working point of a Plasma – global model
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School 2016 | Fundamentals of Plasmas | A. von Keudell 40
Power balance determines Electron density
ionisation Power loss to surfaces Absorbed power is a
complicated function of electon density
+ excitation, + electron loss to surfaces
Working point of a Plasma – global model
More on this in the lecture by M. Turner and L. Alves
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School 2016 | Fundamentals of Plasmas | A. von Keudell 41
Transport in a plasma
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School 2016 | Fundamentals of Plasmas | A. von Keudell 42
B
x
y
z
+ -
B
x
z
E
+ - y
Transport in a plasma – single particle motion
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School 2016 | Fundamentals of Plasmas | A. von Keudell 43
Transport in a plasma – single particle motion
electrons ions
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School 2016 | Fundamentals of Plasmas | A. von Keudell 44
N N N N
S S S S
S S S S
E plasma
e--gun
Ions
Electrons
Transport in a plasma – single particle motion – example hall thrusters
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School 2016 | Fundamentals of Plasmas | A. von Keudell 45
S N N S
x B B
E FExB
N N N
S S S S S S
S S S S S S
Transport in a plasma – single particle motion example magnetron
More on this in the lecture of A. Hecimovic
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School 2016 | Fundamentals of Plasmas | A. von Keudell 46
Transport in a plasma – motion as a fluid
Particle conservation
Momentum conservation
collisions
Energy conservation
convektion Compression/expansion Heat conduction Ohmic heating
RHS: plus source terms due to ionization or recombination
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School 2016 | Fundamentals of Plasmas | A. von Keudell 47
Transport in a plasma – motion as a fluid – the drift diffusion approximation
mobility diffusion
a typical solution
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School 2016 | Fundamentals of Plasmas | A. von Keudell 48
ni
ne
x
ni ne
Eambipolar n
∇n
Transport in a plasma – motion as a fluid – ambipolar diffusion
and Te>>Ti for
for
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School 2016 | Fundamentals of Plasmas | A. von Keudell 49
B
z
x
y
x
D||
D⊥
Transport in a plasma – magnetic confinement
x
y
without inertia
ExB-drift diamag. drift drift diffusion
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School 2016 | Fundamentals of Plasmas | A. von Keudell 50
B
z
x
y
x
D||
D⊥
Transport in a plasma – classical vs. Bohm diffusion
x
y
classical diffusion Bohm diffusion (empirical)
Idea: instabilities induce electric fields, which drive ExB drift for
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School 2016 | Fundamentals of Plasmas | A. von Keudell 51 ~
MHz ~ MHz
Transport in a plasma – magnetic confinement
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School 2016 | Fundamentals of Plasmas | A. von Keudell 52
Ignition of a plasma
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School 2016 | Fundamentals of Plasmas | A. von Keudell 53
0
- +
d
e-
Ionen
z
U
I
Ia
n
- + ne
n+
z
d 0
Ignition of a plasma – Townsend regime
1. Townsend coefficient gas amplification
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School 2016 | Fundamentals of Plasmas | A. von Keudell 54
- +
e-
ions
e-
e-
e-
e-
hν
ions Fast neutrals
e-
e-
metastables
Ionbombardment at the cathode
Secondary ion emission at the anode
photoeffect
fast neutrals
metastables
Ignition of a plasma – Townsend regime – Secondary effects
primary amplification secondary amplification
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School 2016 | Fundamentals of Plasmas | A. von Keudell 55
V
pd
Gas
+ metastables - +
1
2
1
2
long path breakdown
Ignition of a plasma – the Paschen curve
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School 2016 | Fundamentals of Plasmas | A. von Keudell 56
+
-
- - -
-
-
-
+
+
+ +
+
+
-
- -
-
-
-
hv
negative streamer positive streamer
neg. streamer
head
+
-
-
- -
- -
+
+
+
+
- -
pos. streamer
head +
+ +
photoionisation
-
- -
-
+
+
+
+
+ +
+
streamer channel
streamer channel
elec. drift
elec. avalanche
- -
Ignition of a plasma – High presssure - streamers
Meek criterion
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School 2016 | Fundamentals of Plasmas | A. von Keudell 57
Ignition of a plasma – High presssure - streamers
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School 2016 | Fundamentals of Plasmas | A. von Keudell 58
Emax
<E>
t
νm = 0
νm > 0
e-
E=E0 exp(iωt)
rf
Ignition of a plasma – rf-voltages
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School 2016 | Fundamentals of Plasmas | A. von Keudell 59
log p
log E Collision Rate too high
Diffusion- losses
Ignition of a plasma – Paschen curve for rf-voltages
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School 2016 | Fundamentals of Plasmas | A. von Keudell 60
Sustaining a plasma
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School 2016 | Fundamentals of Plasmas | A. von Keudell 61
normale glow
discharge
arc
abnormal glow-
discharge Townsend discharge
igni
tion
log I
V
10-4 A 10-1 A
1
2
3
4
5 6
7
8 I V
I < I >
Sustaining a plasma – current voltage characteristics of a DC plasma
6
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School 2016 | Fundamentals of Plasmas | A. von Keudell 62
Sustaining a plasma – instabilities at breakdown
I. Stefanovic et al.
4
5 6
7
+ -
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School 2016 | Fundamentals of Plasmas | A. von Keudell 63
Kaufmann, Handbuch der Experimentalphysik, 1929 Meyer, Berlin 1858
RUB
Sustaining a plasma – striations
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School 2016 | Fundamentals of Plasmas | A. von Keudell 64
S N
N S
N S
w
rL
B0
s
Rc
Θ
Sustaining a plasma – magnetron discharges
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School 2016 | Fundamentals of Plasmas | A. von Keudell 65
N S
N S
S N
N S
N S
S N
balanced unbalanced
Sustaining a plasma – balanced / unbalanced magnetrons
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School 2016 | Fundamentals of Plasmas | A. von Keudell 66
DC
Ar+
Cu+, Cu2+…
V
I
t
self- sputtering
Sustaining a plasma – High Power Pulsed Magnetron Sputtering (HPPMS)
N NS
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School 2016 | Fundamentals of Plasmas | A. von Keudell 67
J. Gudmundsson, N. Brenning, D. Lundin, U. Helmersson, JVSTA 30, 030801 (2012)
Sustaining a plasma – High Power Pulses Magnetron Sputtering (HPPMS)
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School 2016 | Fundamentals of Plasmas | A. von Keudell 68
1: ignition 2: plasma build-up 3: gas depletion 4: steady state or runaway self sputtering
J. Gudmundsson, N. Brenning, D. Lundin, U. Helmersson, JVSTA 30, 030801 (2012)
steady state
Sustaining a plasma – High Power Pulses Magnetron Sputtering (HPPMS)
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School 2016 | Fundamentals of Plasmas | A. von Keudell 69
sa sb
Ia Ib
A B
Irf cos ωt
~ rf
s s0
Va Vb
s
s s0
A=B
t
Sustaining a plasma – rf discharges – capacitive coupling
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School 2016 | Fundamentals of Plasmas | A. von Keudell 70
A B
0
Φ
A B
π/2
Φ
A B
π
Φ
A
B
Φ
A
B
Φ
A
B
Φ
-Vbias
-Vbias
-Vbias
~ ~ A=B A<<B
Sustaining a plasma – rf discharges – capacitive coupling/self bias
I=dQ/dt
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School 2016 | Fundamentals of Plasmas | A. von Keudell 71
Vbias
V
t
Vap
Ion currrent
electron current
2 π
Sustaining a plasma – rf discharges
sa sb
Ia Ib
A B
Irf cos ωt
~ rf
s s0
Va Vb
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School 2016 | Fundamentals of Plasmas | A. von Keudell 72
Vrf
Eind
Vrf
SiO2
jSpule
B
E
z
δ
R
d
Sustaining a plasma – rf discharges - inductive coupling ICP
Cylindrical configuration Planar configuration
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School 2016 | Fundamentals of Plasmas | A. von Keudell 73
Eind
Vrf
SiO2
jSpule
B
E
z
δ
R
d
Sustaining a plasma – ICP discharges – non linear power coupling
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School 2016 | Fundamentals of Plasmas | A. von Keudell 74
Sustaining a plasma – ICP discharges - hysteresis
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School 2016 | Fundamentals of Plasmas | A. von Keudell 75
x x
z
B
Resonance- zone
Φsource
Φsubstrate
Substrate
Sustaining a plasma – electron cyclotron discharges
B, ωce
ωµw
vres
∆z
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School 2016 | Fundamentals of Plasmas | A. von Keudell 76
ne
Tg
ng
δne
Sustaining a plasma – high pressure discharges - filamentation
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School 2016 | Fundamentals of Plasmas | A. von Keudell 77
-
+
- -
-
+
+ + + +
-
+
- -
+ + + +
- - - -
-
+
- -
+
- - - -
1. Townsend-Phase, electron avalanche
2. streamer
3. Charging up dielectricum
4. extinction
- -
Sustaining a plasma – barrier discharges
from L. Stollenwerk, New Journal of Physics 11, 103034 (2009)
Return stroke, ions move to cathode
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School 2016 | Fundamentals of Plasmas | A. von Keudell 78
Summary
1. What is a plasma ?
• Temperature • Debye shielding • Plasma frequency
2. The edge of a plasma
• Sheath physics
3. Transport on a plasma
• Particle motion • Plasma as a fluid • Drift and diffusion
4. How to ignite a plasma
• Ignition, Paschen curve • Streamer • RF-ignition
5. How to sustain a plasma
• DC plasma • Rf-plasmas • Plasma heating
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School 2016 | Fundamentals of Plasmas | A. von Keudell 79
Books: • Lieberman Lichtenberg, Principles of Plasma Discharges and Materials Processing • Alexander Piel An Introduction to Laboratory, Space, and Fusion Plasmas • F. Chen Plasma Physics and Controlled Fusion • Pascal Chabert und Nicholas Braithwaite Physics of Radio-Frequency Plasmas Scripts: (in German) http://reaktiveplasmen.rub.de/index.php?option=com_content&view=category&layout=blog&id=47&Itemid=112
• Introduction to Plasmaphysics I: Fundamentals
• Introduction to Plasmaphysics II: Low temperature plasmas
• Plasma Surface Interactions
Further reading: