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Plasmas rf haute densité
Pascal ChabertLPTP, Ecole Polytechnique
©Pascal Chabert, 2006, All rights reserved
Programme
• Introduction – Généralité sur les plasmas
• Plasmas Capacitifs (CCP) – VHF – Multi-fréquence
• Plasmas inductifs (ICP)
• Plasmas hélicons
Industrial applications of plasmas
EtchingMicroelectronicSi, SiO2 and many others!
OptoelectronicMEMS, MOEMS, NEMS
DepollutionEnvironmental applicationsReactions with reactive
radicals created in the plasma
DepositionMicroelectronicSolar cellsFlat panel displaysCoatingsDiamond, silica
PlasmaProcessing
Surface treatmentNitridingPolymer films
Plasma1-100 mTorr
+
+ +
++
e-
sheath
Etching plasmas
Cl
Si
SiClyClx+
Cl
Cl
Cl
Cl
3x10-1 m
Cl2 Pump
• Ion flux (plasma density)
• Ion energy (sheath voltage)
• Reactive neutral flux
Need to control stabilityand uniformity of:
3x10-7 m
Plasma discharges
• Potential is maximum at the plasma center:
– Electrons are confined– Negative ions are confined– Positive ions are accelerated
toward the walls
Ji
Je JN
• Positive ion flux : directed• Electron flux : isotropic• Neutral flux : isotropic
Plasma
n+ = ne+ n-
<V>
~
Positive space charge: sheaths
0
Relative densities and energiesn (cm-3) n (cm-3)
Why sheaths?
• Without sheaths, currents at the wall are :
e
ee m
TkneJπ20=
+
++ =
mTkneJ
π20
• Since me << m+ and Te >> T+ :– Je >> J+ ⇒ loss of electrons
• The positive space charge builds up an E field directed to the walls which confines electrons and accelerate ions to the wall
Plasma
n+ = ne+ n-
<V>
~
Positive space charge: sheaths
0
E
Sheath thickness
• Positive ion current produced by the plasma (Bohm):
• Using current continuity and Child law,
we obtain the sheath thickness:
43
⎟⎟⎠
⎞⎜⎜⎝
⎛=
e
s
D TkVes
λ
++
+ =⎟⎟⎠
⎞⎜⎜⎝
⎛mTkneh
sV
mq e
l 02
23
21
0 29
4ε
++ =
mTknehj e
l 0
Plasma
Vs1
Vs2>Vs1
+-
Is
++
+
+ +
+
+
+
e-+ +
+e- e-
Particle and energy balance
Plasma (volume V)
Surrounded by a surface A
At low pressure…
Sheath
xxs
ns
n0
0
Plasma
n
d
at high pressure…
She
ath
xxs
ns
n0
0
Plasma
n
hl vs pressure
P (mTorr)100
0.5
0
hl
Plasma Dielectric constant and conductivity
Dielectric at high frequency (ω > ωp)Conductor at low frequency (ω < ωp)
ωpi ωωperf domain
MHz GHz
Skin depth
Dielectric at high frequency (ω > ωpe)Conductor at low frequency (ω < ωpe)
ωpi ωωperf domain
MHz GHz
Waves are absorbed in a skin depth Propagating waves (microwave diagnostics: interferometry, reflectometryetc.)
Inertial (low pressure)
Capacitively-coupled plasma
~ rf
Inductively-coupled plasma
~ rf
~ rf
Typical etching reactors: CCP’s, ICP’s
• Electrons follow the rf field
• Ions follow time-averaged fieldωpi ωωpe
rf domainMHz GHz
13.56 MHz or higher?
Magnetic confinement
mqB
c =ω
qBmRLv
=
Cyclotron frequency:
Larmor radius:
For typical conditions (B ≈ 50 Gauss):
• Non-magnetized ions: RL≈10-20cm
• Magnetized electrons: RL≈1-2 mm
Anisotropic dielectric constant
Waves in magnetized plasmas
N²
ω
helicons
Right-hand polarizedLeft-hand polarized
ωpeωci ωce
1
Alfven
Without B field, no propagation at ω < ωpe
Helicon reactors
Water cooling
rf13.56 MHz
Matching networkand source cooling
Helicon antenna
Wafer holder
Load lock and cartridge transfer
Sourcesolenoid
400l/sturbopump
150l/s turbo
Ar, SF6
Chambersolenoid
B0Helicons generate high density plasmas. Interesting for:
• Very deep etching
• Space plasma propulsion
A model of capacitive discharges
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
V.A. Godyak, “Soviet Radiofrequency Discharge Research”, Delphic Associates, Fall Church, 1996M.A. Lieberman, A.J. Lichtenberg, “Principles of Plasma Discharges and Materials Processing”, 2nd Edition 2005
sb(t)
sa(t)
EzEz
The homogeneous model
Ion density is constant between the electrodes
Plasma equivalent circuit
Plasmad
Surface A
Negligible since displacement current is smaller than conduction current in the plasma
Sheath model
Sheath motion
Voltage across one sheath
The voltage across one sheath is non-sinusoidal. Harmonics!
Combination of the two sheaths
The combination of the two sheath is sinusoidal
To summarize…
• Each sheath generates harmonics
• But the combination is sinusoidal
The combination of the two sheaths is described by a capacitor
Sheath equivalent circuit
What are these resistive terms?
Power dissipated by ions in the sheath
Collisionless electron heating in the sheath
Rp Rstoc
Collisionless power dissipation in the sheath
Open problem:
• Kinetic model « Hard wall »M.A. Lieberman, IEEE Plasma Sci. 16 (1988) 638I.D. Kaganovich, Phys. Rev. Lett. 89 (2002) 265006
• Fluid model « pressure heating »G. Gozadinos et al., Phys. Rev. Lett. 87 (2001) 135004
Equivalent circuit for the capacitive discharge
Scaling of absorbed power vs density
The inhomogeneous model
In the bulk, there are density gradients
In reality, the ion density is not homogeneous between the plates
Sheaths
The sheath is inhomogeneous
s(t)
Cs
2Rstoc + 2Rion + 2Rohm,sh
I0
• Ion density decreases towards the electrode due to acceleration
• But ion density is independent of time
Inhomogeneous circuit element values
Particle and energy balance in CCP’s
Plasma (volume V)
Since sm depends on I0
Strictly speaking, ne and Te are not decoupled
Results
1. The issue of multiple-frequency excitation2. Electromagnetic effects at high frequency
Contemporary capacitive discharges(Advanced issues)
0,0 0,1 0,2 0,3 0,4 0,510
100
1000
13.56 MHz
40.68 MHz
81.36 MHz
Ene
rgie
des
ions
(V)
Flux d'ions Ji (mA.cm-2)
15 mTorr
Frequency effect
■●▲ : Experiments----- : model
Eion < 100 V
Eion > 500 V
HF drive for high fluxLF bias for tunable ion energy
Dual Frequency Capacitive (DFC)
Vrf
A. Perret et al., Appl. Phys. Lett 86 ( 2005) 021501
New physics : multiple-frequency excitation
1. Collisionless heating in the dual frequency sheath
2. Electromagnetic regime: inductive heating at high frequency
M. Turner and P. Chabert, Phys. Rev. Lett. 96 (2006) 205001
P. Chabert, J.-L. Raimbault, P. Levif, J.-M. Rax and M. A. Lieberman, Phys. Rev. Lett. 95 (2005) 205001
~
z
r0
R
Hφ
Ez
Er
Collisionless heating in the DF sheath
S(t)
0n0
ns
Enhancement!
Collisionless heating in the DF sheath
Conclusions on heating in the DF sheath
• Heating in the dual frequency sheath (Collisionless and Ohmic) enhanced by low frequency
• This is because the low frequency voltage greatly increases thesheath size such that the high frequency produces heating over alarger volume
• Independent control of ion flux and ion energy is not achieved !
Let us now investigate electromagnetic effects at high frequency…
The capacitor at high frequency(Feynman “Lectures on Physics”, chapter 23-2)
r
z
Field line E
E0
r
z
Field line E Field line B
E0 B1
First order
The capacitor at high frequency(Feynman “Lectures on Physics”, chapter 23-2)
r
z
Field line E Field line B
E0 B1E1
First order
The capacitor at high frequency(Feynman “Lectures on Physics”, chapter 23-2)
r
z
Field line E Field line B
E0 B1E1
-0,4 -0,2 0,0 0,2 0,40,0
0,2
0,4
0,6
0,8
1,0
E0+E1 (100 MHz)
E (u
.a.)
r (m)
E0
• Standing wave profile
• The electric field is not radially uniform
The capacitor at high frequency(Feynman “Lectures on Physics”, chapter 23-2)
Electromagnetic regime: λ ∼ R and δ ∼ d
~
z
r0
R
Solve Maxwell’s equations for given s and ne (not self-consistent):
• λ ∼ R : Standing wave effect (Ez)• δ ∼ d : Skin effect (Er)• Edge effects
Hφ
Ez
Er
M.A. Lieberman et al., Plasma Sources Sci. Technol. 11 (2002) 283L. Sansonnens et al., Plasma Sources Sci. Technol. 15 (2006) 302
Fields are not radially uniform
Transmission line model
z
0 r
dr
TL elements depends on:• Local voltage and/or current (Vrf, Irf)• Electron density, ne• Sheath size, sm
Use:• Child law• Particle balance• Power balance
Self-consistent solutions for:• Vrf (r) and Irf (r)• ne(r)• sm(r)
C’R’cap
2R’i
L’R’ind
dr
P. Chabert et al., Physics of Plasmas 11 (2004) 1775P. Chabert et al., Physics of Plasmas 11 (2004) 4081 P. Chabert et al., Phys. Rev. Lett. 95 (2005) 205001
Experimental evidence of the effects
Top-grounded electrode
64 planar probesCartography of the ion flux
3 RFEARetarding Field Energy Analyser
Ion energy uniformity
Standing wave effect (1/2)
13.56 MHzJi max = 0.07 mA.cm-2
50 W, 200 mTorr (local heating)Ji/Jimax
Ji/Jimax
Ji/Jimax
60 MHzJi max = 0.15 mA.cm-2
81.36 MHzJi max = 0.17 mA.cm-2
A. Perret et al., Appl. Phys. Lett 83 ( 2003) 243
-20 -10 0 10 200,00
0,02
0,04
0,06
0,08
0,10
0,12
0,14
0,16
0,18 Experiments
J i(m
A.c
m-2)
X (cm)
TL Theory
81.36 MHz200 mTorr (local heating)50 W
Standing wave effect (2/2)
P. Chabert et al., Physics of Plasmas 11 (2004) 1775
Worsening factor
Fairly insensitive to the gas composition
Experiments
Skin effect, inductive heating
A. Perret et al., Appl. Phys. Lett 83 ( 2003) 243
TL Theory
Spatial E to H transitionsE mode at the centre, H mode at the edge
0 500 1000 1500 20000.0
0.5
1.0
1.5
2.0
Pin
d/Pca
p
V0 (V)
200 MHz
Global E to H transitions at low pressure
( ) eeeeeee nTKnPkTndtd )(
23
−=⎟⎠⎞
⎜⎝⎛
Uniform temperature plasma
Ploss : Inelastic collisions and energy flux at the wall E
H
Electrode radius = 0.15
1. Principles and equivalent circuit2. E to H transitions3. Instabilities at the E-H transition when electronegative
gases are being used
Inductive discharges (the issue of instabilities)
Inductive reactors (ICP or TCP)
• Inductive reactors are routinely being used for silicon and metal etching
• They allow independent control of ion flux and ion energy
• They may operate at higher density than capacitive
• They undertake E to H transitions
Inductive coupling
e
e
pp ne
mc
02μω
δ ==
Inertial skin depth (low-pressure)
Resistive skin depth (high pressure)
0
2μωσ
δp
p =
H~
E~ zk
cmp 31−≈δ
Dielectricwindow
Coil
Decaying wave
Electromagnetic model
Resistance of the plasma loop
Density (m-3) Density (m-3)
This can be explained in a much simpler way…
This is the high density regime (decaying dashed line on previous slide)
Inductance of the plasma loop
Note this L is not due to electron inertia ≠ from the L obtained in capacitive discharges
The transformer model
The transformer matrix
Equivalent circuit of ideal inductive discharges
Power balance in ideal inductive discharges
Real inductive discharges
ne
Pabs
Inductive (H)
Capacitive (E)H~
E~ zk
E
Ground
Increasing RF current leads to E → H transition
E→H Transitions
ne
Power
Pressure
Power
Inductive (H)
Capacitive (E)
Ploss
1rfI
12 rfrf II >
Instabilities at the transition…
0 5 10 15 20 25 300
50
100
150
200
250
300
Instabilities
Stable Inductive (H)
Stable Capacitive (E)
Effe
ctiv
e po
wer
(W)
Pressure (mTorr)
Experiment in CF4
…If electronegative gas is used !
2 4 6 8 10 12 14 160,0
0,2
0,4
Inte
nsity
(a. u
.)
Time (ms)
Light fluctuations
Global model of the instability
e
e
nnn +=
Γ+Γ=Γ
−+
−+
( )
i
e
T
Teee
iBi
eVn
eVn
Tunl
/
/
4141
2.015.1
Φ−−−−
Φ−
++
=Γ
=Γ
+=Γ
λ
Particle balance :
Power balance :
( ) −−−−=⎟⎠⎞
⎜⎝⎛ nKnKnPkTn
dtd
eeeabsee23
What is the formof this term ?
Loss term
VAKnnKnnKnn
dtdn
eattgegizgee Γ−−+= − det
*
VAKnnKnnKnn
dtdn
grecattge −−+−− Γ−−−= det
*
Typical model result
• Problems !• Experiment: 10 kHz• Model: 1.2 kHz• Model window is smaller• Model densities are
smaller
• More about this later…
SF6 For appropriate Icoil
0 1 2 3 40,01
0,1
1
10
n-n+
ne
Den
sitie
s (1
010 c
m-3)
Time (ms)
1. The wave mode and E-H-W transitions2. Instabilities, Double-layers3. Space propulsion using Double-layers?
Some aspects of helicon discharges
Experimental set-up (ANU-like)
Gas inlet
Pump
Pyrex tube
Double saddle antenna
Grid
Z (cm)
0
26
36
5456
Movable probesOr analyzer
Diff
usio
n ch
.S
ourc
e ch
ambe
r
B field
E → H → W Transitions (1)
• Capacitive (E) :– Low electron density– High voltage on the
antenna• Inductive (H) :
– Higher electron density– Ionization near the
antenna• Helicon (W) :
– Even higher electron density
– Ionization at the center; Wave propagation
0 400 800 1200 1600 20000
1
2
3
4
5
6
7
8SF6
Régime hélicon (W)Régimeinductif (H)
Transition H W
Transition E H
Rég
ime
capa
citif
(E)
Pres
sion
(mTo
rr)
Puissance rf (W)
E → H → W Transitions (2)
ns
PPloss
PAbsorbed
Equilibrium
P Ploss
PAbsorbed (Irf > Imin)(Irf < Imin)
ns
Eq.
Inductive H
Capacitive E
1
P
ns
2
3
E → H → W transitions
Lost power :
Absorbed power :( ) eecBeloss KnEEAunP ≈+=
StocOhmabs PPP +=
0ms 5ms 10ms0
1
2
3
4
5
6
7
z = 14 cm
z = 26 cm
z = 18 cm
z = 22 cm
I+ s
atur
atio
n (a
.u.)
Time
Instabilities with EN gases
0 5 10 15 20 250
200400600800
10001200140016001800
Pow
er (W
)
Pressure (mTorr)
Downstream instability
Source instability
E-H relaxation oscillationsChabert et al. Plasma Sources 10 478 (2001)Corr et al. Plasma Sources 12 265 (2003)
Downstream instability; looks similar to previous workTuszewski et al. Phys. Plasmas 10 539
0ms 1ms 2ms0
1
2
3
4
5
6
7
z = 16 cm
z = 20 cm
z = 23 cm
I+ s
atur
atio
n (a
.u.)
Time
z = 26 cm
0 5 10 15 20 25 300
5
10
15
20
25
30
Z (cm)
<Vp>
Diffusion chamber Sourcechamber
DOUBLE LAYER
18 cm
1mT, 600W, SF6:Ar (1:1) mixture Z axis
0 cm
26 cm
HIGHVp
LOWVp
18 cm+
+
+
+++
-- - -
- ---
-
In addition to downstream instabilities: Double-layers
t/Tinsta
Z (m
m)
Plasma Potential
0.5 1 1.5 2
50
100
150
200
250
300
350
400
450
500
10
15
20
25
30
35
Electronegative; Low Te
Ele
ctro
posi
tive
Hig
h Te
Plasma potential dynamics
26% SF6, Pressure = 1 mT, Power = 600 W Frequency = 850 Hz
Vp(z,t)
Propagating double layers
Propagating speed = 150 m/s
Static double layers
0 10 20 30 40 50 601015
1016
1017
E
lect
ron
dens
ity (m
-3)
Z (cm)
Diffusionchamber
source
0 10 20 30 40 50 600
1
2
3
4
5
6
Elec
tron
tem
pera
ture
(eV)
Z (cm)
Diffusionchamber source
4% SF68% SF6
4% SF68% SF6
0 7 13 % SF6
No DL Stable DL Propagating DL
HDLT Concept (Charles at ANU)
• Christine Charles and Rod Boswell at ANU have proposed to use a Double Layer for ion acceleration and produce thrust
• The Helicon Double Layer Thruster (HDLT) uses highly diverging B field to generate the DL
Charles and Boswell (2003) Appl. Phys. Lett. 82 1356Charles, 2005 Phys. Plamsas (2005) 12 044508
Xe Xe+ beam
DL
General conclusion
• Capacitive discharges have to be excited by more than one frequency to be used as efficient etching tools, which involves a lot of new fascinating issues (Academic point of view!)
• Inductive discharges produce high density plasmas with independent control of ion flux and ion energy, but are subject to instabilities at the E to H transition
• Helicon discharges produce even higher plasma densities which is interesting for plasma propulsion. They also have a lot of instabilities (which were not all discussed here) and seem to involve double-layers in some cases
