University of California, Berkeley PLASMA

MODELING PLASMA PROCESSING DISCHARGES

M.A. Lieberman

Department of Electrical Engineering and Computer SciencesUniversity of California

Berkeley, CA 94720

Collaborators:E. Kawamura, D.B. Graves, and A.J. Lichtenberg, UC BerkeleyC. Lazzaroni and P. Chabert, Ecole Polytechnique, FranceJ. Gudmundsson, Shanghai Jiao Tong U; Science Institute, U. IcelandA. Leblanc, ENS Cachan, FranceJing Zhang, Donghua U, Shanghai, China

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http://www.eecs.berkeley.edu/∼lieber

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OUTLINE

• Fast computation of atmospheric pressure rf capacitive discharges

• Fluid model of E-H transition instability in electronegativeinductive discharge

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ATMOSPHERIC PRESSURE

CAPACITIVE RF DISCHARGE

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MOTIVATION

• Biomedical — example of reactive oxygen species(Review article: H.W. Lee et al, J. Phys. D 44, 053001, 2011)

— Applications to sterilization, cancer cell treatment, bloodcoagulation, wound healing

• Unique materials — example of anatase crystalline TiO2

(Review article: D. Mariotti and R.M. Sankaran, J. Phys. D, 323001, 2010)

(Anatase TiO2: H.G. Yang et al, Nature 453, 638, 2008)

— Applications to photonics crystals, photo/electrochromic devices,gas sensors, spintronic devices, anticancer or gene therapies,solar cells for electric energy or hydrogen production

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DISCHARGE CONFIGURATION

• Atmospheric pressure

• He or Ar with trace reactive gases

• 1D plane-parallel geometry (∼0.2–2 mm gap)

• RF-driven (nominal 13.56 MHz)

He or Ar+

Trace gas

~

Reactivespecies

~0.1–1 mm

13.56 MHz

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University of California, Berkeley PLASMA

EEPF TIME VARIATIONS

• He/N2 fluid simulation with kinetic (Bolsig+) EEPF calculation

Lowtemperaturetail

Timevariation

(J. Waskoenig, PhD Thesis, Queens U Belfast, 2010)

• Conclusions used in modeling— The EEPF oscillates in time with the rf electron power absorbed— The EEPF is Maxwellian below a break energy Eb ≈ 20 V

(metastable He excitation energy)— The EEPF has a low temperature tail above the break energy

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HYBRID DISCHARGE MODEL

• Numerical solution of particle balances for each speciesdnj

dt= Gj − Lj

Gj = volume creation rate (2-body, 3-body and surfaces)Lj = volume loss rate (2-body, 3-body, and surfaces)

• Analytical solutions of— the discharge dynamics (homogeneous model)— the time-varying Te(t)— the effective rate coefficients 〈K〉

• Coupling the analytical and numerical solutions

=⇒ fast solution of the discharge equilibrium

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COMPARISON TO FLUID SIMULATION

• He/0.5%O2 (16 species), 1mm gap, 13.56 MHz

• Neutral (left) and charged (right) densities versus power

(open symbols — global model; solid symbols — fluid results, Waskoenig, 2010)

• ⇒ Reasonable agreement of model and fluid simulations40 sec simulation time on fast laptop

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E/H (CAPACITIVE/INDUCTIVE) MODE TRANSITION

INSTABILITY IN ELECTRONEGATIVE DISCHARGE

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MOTIVATION

• Low pressure inductive reactors for thin film processing

— Example: fabrication of CMOS transistors formicroprocessors/memory

— Inductive reactors often operate near the E/H transitionwith electronegative feedstock gases

— Macroscopic instabilities observed in both commercialand research reactors

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University of California, Berkeley PLASMA

E/H MODE TRANSITION

• Plasma resistance Re ver-sus ne as Irf is varied

• A “gap” occurs betweenIrf = 7.5 and 8 A

• Measurements at 10 mTorrCl2 show “gap region”

• Previous measurements (many)and global models (many)indicate instability

• First calculation of E/Hinstability in fluid simu-lations

1e+14 1e+15 1e+16 1e+17

Center n (m )

0

1

2

3

4

5

6

R (o

hm

s)

e-3

Capacitive(E-mode)

e

Inductive(H-mode)

I =7.5A

Gap

I =8Arf rf

15 mTorr Cl2 fluid simulation

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) measurements

abs

e-3

Gapregion

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BULK-FLUID/ANALYTIC-SHEATH MODEL

• 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

0.21 m

0.18 m

— Electromagnetic field solve— Fluid bulk plasma model— Analytical sheath model— Flow model of reactive gas— Commercial software (COMSOL)

(Kawamura et al, PSST 2011)LiebermanPSC12 12

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E/H TRANSITION INSTABILITY

• Example: 2.2 kHz instability in 15mTorr Cl2 at Irf = 7.75 A, show-ing (a) nCl−(t), (b) ne(t), and (c)Te(t)

• At time t1 the discharge enters ca-pacitive mode

• From t1–t2 the discharge is in ca-pacitive mode

• From t2–t3 the discharge makes atransition to inductive mode

• From t3–t4 the discharge is in in-ductive mode

• From t4–t1 the discharge makes atransition back into capacitive mode

0 0.0005 0.001 0.00156e+16

7e+16

8e+16

9e+16

1e+17

1.1e+17

n

(m

)

(a)

Cl–

-3

0 0.0005 0.001 0.00150

2e+15

4e+15

6e+15

8e+15

1e+16

n

(m

)

(b)

e-3

0 0.0005 0.001 0.0015t (s)2

2.1

2.2

2.3

2.4

2.5

T

(V)

(c)

e

t

t

t

t1

2

3

4

t

tt

t

12

3

4

t

t

t t

1

2

3 4

.

.

..

.

.

.

.

.

. . .

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Te(r, z) VERSUS t

• Te strongly lo-calized near coil

• t1 (enter E-mode):Te jumps to high-est value

• t2–t4 (E-modefollowed by tran-sition to H-mode):Te decays in time

t = t1 t = t2

t = t3 t = t4

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ne(r, z)/nemax VERSUS t

• ne weakly local-ized near coil

• t1 (enter E-mode):ne rapidly de-cays with time

• t3 (enter H-mode):ne rapidly in-creases with time

nemax = 1.29× 1015 m−3 at t1 nemax = 5.73× 1015 m−3 at t2

nemax = 15.6× 1015 m−3 at t3 nemax = 5.86× 1015 m−3 at t4

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FLUID AND GLOBAL MODEL COMPARISON

• Intersection of dne/dt = 0 and dn−

/dt = 0 curves ⇒ equilibrium

• Slope dn−

/dne of dne/dt = 0 curve positive ⇒ unstable

1014

1015

1016

1016

1017

n– (

m–3)

ne (m–3)

dne/dt = 0

dn− /dt = 0

Globalmodeltheory

Fluidsimulation.

• Good agreement of fluid calculation and analytical global model

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NEUTRAL TIME AVERAGES OVER INSTABILITY

• Neutral species time variations are very small

• Time averages:

Gas Temperature (K) Molar Cl Fraction

• Tg rises to 530 K inside discharge

• Chlorine density varies significantly with radiusLiebermanPSC12 17

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SUMMARY

• A one-dimensional hybrid analytical-numerical global model ofatmospheric pressure, rf-driven capacitive discharges was developed

• Coupling analytical solutions of the time-varying discharge andEEPF dynamics, and numerical solutions of the discharge chemistry,allows for a fast solution of the discharge equilibrium

(Lazzaroni et al, to appear in PSST, 2012)

• The E/H transition instability has been found and studied in2D fluid simulations

• The fluid instability dynamics is in good agreement with ananalytical global model

(Kawamura et al, submitted to PSST, 2012)

Download this talk:

http://www.eecs.berkeley.edu/∼lieber

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