KINETIC EFFECTS IN PLASMA PROCESSING …lieber/PLSC100504crop.pdfUniversity of California, Berkeley...

University of California, Berkeley PLASMA

KINETIC EFFECTSIN PLASMA PROCESSING DISCHARGES

M.A. Lieberman and E. Kawamura

Dept. EECS, UC Berkeley

PLSC100501 1


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


II. BULK-FLUID/ANALYTIC-SHEATHHYBRID SIMULATIONS

(with D.B. Graves)

Motivation: fast computation of plasma reactor parameters

PLSC100501 7


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)

PLSC100501 8


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

PLSC100501 9


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

)


Model


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 )


Model


abs

gC

l2-3

gCl2 abs

PLSC100501 10


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

PLSC100501 11


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

PLSC100501 12


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

PLSC100501 13


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

PLSC100501 14


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

PLSC100501 15

KINETIC EFFECTS IN PLASMA PROCESSING …lieber/PLSC100504crop.pdfUniversity of California, Berkeley...

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