kinetic effects in plasma processing...
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University of California, Berkeley PLASMA
KINETIC EFFECTSIN PLASMA PROCESSING DISCHARGES
M.A. Lieberman and E. Kawamura
Dept. EECS, UC Berkeley
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I. 2D PARTICLE-IN-CELL (PIC) SIMULATIONSOF UNSTABLE WAVES EXCITED BY DOUBLE LAYERS
(with A.J. Lichtenberg and J.P. Verboncoeur)
Motivations: remote plasma processing; plasma thrusters
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REACTOR CONFIGURATION
Upstream Chamber
z x
y
3.5 cm
3.5 cm
3.0 cm
Downstream Chamber
Electronegative(oxygen) plasma
10 cm 10 cm
E = E cos tz z0
DL
ω
Substrate
Time-averaged Potential (V)
0 0.04
0.08 0.12
0.16 0.2
x (m) 0
0.02 0.04
0.06 0.08
0.1
y (m)
5
10
15
20
25
30DL
(2D PIC 6 mTorr O2)
DL+
−
Chargedensity ρ
Upstreamedge 2
Downstreamedge 1
• DL’s observed over a wide range of pressures (1–24 mTorr)(Kawamura et al, Phys. Fluids, 2009)
• DL’s typically have time-varying (wave) structures
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ABOUT 2D PIC SIMULATIONS
• Self-consistent results from first principles with no assumptionsabout electron and ion velocity distributions
• Stability, speed and accuracy require low densities:ne ≈ 4 × 1014 m−3, λD ≈ 0.8 mm
• Rescaled oxygen cross sections are used to simulatehigher densities and other chemistries
• A typical simulation takes 1–2 weeks
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MOVIE SHOWS SLOW AND FAST WAVES
Red: 900 kHz fast waves averaged over 0.1475 µs intervalsBlue: 85 kHz slow waves averaged over 1.18 µs intervals
SlowFast
DL
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KINETIC THEORY OF UNSTABLE WAVES
• Waves produce 20% oscillations in DL potential and position
• Electron and ion kinetic effects are important
−2000 −1500 −1000 −500 0 500−1
−0.5
0
0.5
1
1.5
2x 10
6
kr, ki (/m)
om
eg
a (
rad
/s)
6 mTRe k
Im kUnstable
• Most unstable slow wave at λ = 0.7 cm at 173 kHz(PIC simulation gives λ = 1 cm at 85 kHz)
• Fast wave weakly damped at λ = 0.7 cm; excitation fromnonuniformities and nonlinearities?
(Kawamura et al, to appear in J. Appl. Phys.)PLSC100501 6
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II. BULK-FLUID/ANALYTIC-SHEATHHYBRID SIMULATIONS
(with D.B. Graves)
Motivation: fast computation of plasma reactor parameters
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BULK-FLUID/ANALYTIC-SHEATH MODEL
• Example of inductive reactor (Malyshev and Donnelly, 2000–01)
Wafer chuck
(κ = κ )Plasma
φ
spacer
Air
symmetry (r = 0)Center of
z
outer wallsconductingPerfectly
Axisymmetric cylindrical geometry
3 41
Coils
(κ = 1)Sheath
r
p
(κ = 4)
(κ = 1)
Quartz dielectric
2
(κ = 4)Quartz dielectric window
i i
I I I
v v
VV
1
211in
1
1
2
2
2
Generator
v v
i i
I I
V V43
3 4
3 4
3 4
Coil set 1, 2, 3 and 4
— Electromagnetic field solve (including wafer chuck rf bias)— Fluid bulk plasma model— Analytical sheath model— Flow model of reactive gas— Commercial software (COMSOL)
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CHLORINE REACTOR SIMULATIONS
• 100 sccm Cl2 gas flow, 10 mTorr at outlet, 740 W at 13.56 MHz
• Total simulation time ≈ 70 min ( 2.2 GHz CPU 4GB RAM)
• Inductive >> capacitive power, high gas T, high Cl2 dissociation
Inductive Coupling
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.05 0.1 0.15
Max: 4.924e6
Min: 4.973e4
x106
0.05
0.249
0.448
0.647
0.845
1.044
1.243
1.442
1.641
1.84
2.039
2.238
2.437
2.636
2.835
3.034
3.233
3.432
3.631
3.829
4.028
4.227
4.426
4.625
4.824
Capacitive Coupling
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.05 0.1 0.15
Max: 543.583
Min: 5.4935.493
27.456
49.418
71.381
93.344
115.307
137.27
159.233
181.196
203.159
225.122
247.084
269.047
291.01
312.973
334.936
356.899
378.862
400.825
422.787
444.75
466.713
488.676
510.639
532.602
Gas Temperature (K)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.05 0.1 0.15
Max: 784.801
Min: 304.897304.897
324.485
344.073
363.661
383.249
402.837
422.425
442.012
461.6
481.188
500.776
520.364
539.952
559.54
579.128
598.716
618.304
637.892
657.48
677.068
696.656
716.243
735.831
755.419
775.007
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MODEL VERSUS EXPERIMENT
0 100 200 300 400 500 600 700 800
P (W)
1e+14
1e+15
1e+16
1e+17
n (m
)
Malyshev & Donnelly (8/2001)
Model
n vs. P at Discharge Center
abs
e-3
e abs
100 200 300 400 500 600 700 800
P (W)
0
1
2
3
T (V
)
Malyshev & Donnelly LP (2/2000)
ModelMalyshev & Donnelly TRG-OES (2/2000)
T vs. P at Discharge Center
abs
e
e abs
0 100 200 300 400 500 600 700 800
P (W)
1e+18
1e+19
1e+20
n (m
)
Malyshev & Donnelly (12/2000)
Model
n vs. P at Discharge Center
abs
gC
l-3
gCl abs
0 100 200 300 400 500 600 700 800
P (W)
1e+18
1e+19
1e+20
n (
m )
Malyshev & Donnelly (12/2000)
Model
n vs. P at Discharge Center
abs
gC
l2-3
gCl2 abs
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USING 1D/2D PIC SIMULATIONS
• Benchmark/verify assumptions of hybrid model
• Example of dual frequency excitation
rf
Plasma
I
Plasmay−I
H = H = y+I2drf
x
z
l
y
1D Planar PIC
rf2d
2D Rectangular Fluid
(2/162 MHz)
⇒ 1D PIC confirms analytical sheath model
• PIC simulations yield— electron energy distribution in bulk plasma— ion and fast neutral distributions on the substrate
• Couple PIC to hybrid model
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III. OOPD1 — 1D PIC CODE DEVELOPMENT
(with J.P. Verboncoeur, J.T. Gudmundsson and A. Wu)
Motivation: Unified extensible code with easy-to-use interface
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ENERGETIC PARTICLES ON THE SUBSTRATE
(20 mTorr O2 capacitive discharge: 5 cm gap, 500 V at 13.56 MHz)
angle energy
0
1.57 250
00
1.4E+09
Main bi-modal peak
Charge transfer peaks
O2+ Distribution
angle energy
0
1.57 250
00
7.99E+08Main bi-modal peak O2+ fragmentation
in sheath
O+ Distribution
angle energy
0
1.57 100
00
6.36E+09Low energy,
highly isotropic
O2 Distribution
angle energy
0
1.57 100
00
4.7E+08High energies,
mainly isotropic
O Distribution
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ION LOSS VELOCITIES IN MULTI-ION PLASMAS
• OOPD1 model of an argon/xenon experiment(see Lee, Hershkowitz and Severn 2007)
• Model results:
0 0.1 0.2 0.3 0.4 0.510
13
1014
1015
1016
x [cm]
Density [cm
−3]
Sheath edge
Xe+ density
Ar+ density
electron density
0 0.1 0.2 0.3 0.4 0.5−30
−25
−20
−15
−10
−5
0
5
x [cm]φ
[V]
Sheath edge
• Model sheath width = 0.31 cm, experiment = 0.27 cm
• Model Te = 0.49 V, experiment = 0.69 V
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ION VELOCITY SIMULATION RESULTS
0 0.1 0.2 0.3 0.4 0.5
0
2000
4000
6000
8000
10000
12000
x [cm]
Ion velocity [m/s] Sheath edge
Xe+ velocity
Ar+ velocity
• Bohm velocities√
eTe/Mi = 592 m/s for Xe+ and 1073 m/s for Ar+
• Model velocities = 636 m/s for Xe+ and 1190 m/s for Ar+
• Experimental velocities = 940 m/s for Xe+ and 1100 m/s for Ar+
• This is work in progress
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