simulation of transients in plasma processing … · introduction gec00_pramod_2 university of...

53rd Annual Gaseous Electronics ConferenceOct. 24 - 27, 2000Houston, Texas

SIMULATION OF TRANSIENTS IN PLASMA PROCESSINGREACTORS USING MODERATE PARALLELISM*

Pramod Subramonium** and Mark J. Kushner*****Department of Chemical Engineering

***Department of Electrical and Computer EngineeringUniversity of Illinois

Urbana, IL 61801

email: [email protected]@uiuc.edu

*Work supported by SRC, NSF and AFOSR/DARPA

AGENDA

GEC00_PRAMOD_1

University of Illinois Optical and Discharge Physics

• Introduction

• Description of the model

• Validation

• Properties of pulsed plasmas

• Argon

• Ar/Cl2

• Conclusions

INTRODUCTION

GEC00_PRAMOD_2


• Transient phenomena are often encountered in plasma processing

• Pulsed operation of plasmas

• Study startup and shutdown

• Recipe changes

• Pulsed plasmas

• Damage free plasma etching with better uniformity and anisotropy

• Additional control knobs : Duty cycle and Pulse repetition frequency

• Reduce charge buildup on wafer and suppress notching

• Difficult to resolve in multi-dimensional plasma equipment models

• Moderately parallel algorithms for hybrid models were developed toinvestigate the long-term transients.

HYBRID PLASMA EQUIPMENT MODEL (HPEM)

GEC00_PRAMOD_3


• HPEM iterates modules to converged solution.

• Electromagnetics Module• Maxwell's equations are solved in frequency domain

• Electron-Energy Transport Module• Electron impact source functions and transport coefficients• Monte Carlo Simulation is used to generate spatially dependent EEDs

• Fluid Kinetics Module• Fluid transport equations for species densities, fluxes and

temperature• Poisson's equation for time dependent electric potential• Ions and Neutrals : Continuity, Momentum and Energy equation• Electrons : Drift-diffusion equation

• Modeling truly time dependent phenomena is difficult using an modulariterative scheme

DESCRIPTION OF THE PARALLEL HYBRID MODEL

GEC00_PRAMOD_4


• The HPEM, a modular simulator,was parallelized by employing ashared memory programmingparadigm on a Symmetric Multi-Processor (SMP) machine.

• The Electromagnetics, ElectronMonte Carlo and Fluid-kineticsModules are simultaneouslyexecuted on three processors.

• The variables which are updated indifferent modules are immediatelymade available through sharedmemory for use by other modules.

• Dynamic load balancing isimplemented to equal the taskson different processors.

EMM EMCS FKME,B K

E,N,σσσσ ΝΝ

VALIDATION OF THE MODEL : NUMERICS

GEC00_PRAMOD_5


• Parallel and serial execution gives similar results for steady stateconditions in Ar plasma.

• Electron Density

• 3-5% difference in the estimatedelectron density

Serial Parallel

0.550.531.3421.301 8.958.53

8 x 1011 cm-35 x 1010 cm-3

• Ar, 20 mTorr, 300 W, GECRC

• Electron Temperature (Te)

• The steady state Te is same inparallel and serial execution.

0

1

2

3

4

5

6

Ele

ctro

n Te

mpe

ratu

re (e

V)

SERIAL

PARALLEL

0 10 20 4030 50Time ( µs)

VALIDATION OF THE MODEL : PHYSICS

GEC00_PRAMOD_6


• Model results compare well with experiments*

• Simulations (1 and 2) showsimilar trends as in experiments

• Rates of avalanche and decay atleading edge and interpulseperiods are well captured

• Quantitative agreement incolumn densities depends onphysics model ("1" and "2")• "1" : Low degree of radiation

trapping of Ar (4s) and Ar (4p)• "2" : High degree of radiation

trapping of Ar (4s) and Ar (4p)

• Ar, 20 mTorr, 300 W, 10kHz/50%

0 50 100 150 200

5

0

10

15

20

Time ( µs)E

lect

ron

Den

sity

(10

12 c

m-2

) Experiment

2 2

1 1

* G. A. Hebner and C. B. Fleddermann, J. Appl. Phys. 82, 2814 (1997)

2-D DYNAMICS IN ARGON : ELECTRON DENSITY [e]

GEC00_PRAMOD_7


• The peak [e] migrates to below thecoils during "power-on" where thesource is maximum

• At steady state , [e] becomes moreuniform.

• As the power is turned off, in theearly afterglow ambipolar lossesdominate over generation ofelectrons.

• Rate of electron decay decreasesin the late afterglow.

• Faster decay of [e] in the centerthan at the walls due to shorterdiffusion length

• Ar, 20 mTorr, 300 W, 10kHz/50%

0 µs OFF (a)

20 ON (b)

40 ON (c)

60 OFF (d)

80 OFF (e)

100 OFF (f)

9 x 1011 cm-31 x 109 cm-3

EFFECT OF DUTY CYCLE AND PULSE REPETITIONFREQUENCY (PRF)

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• EFFECT OF DUTY CYCLE• Decay time for electron density ([e])

was longer than the off-period• Rise time is about 25 µµs• Higher duty cycle resulted in a

constant [e]

0

2

4

6

8

10

12

0 50 100 150 200

Ele

ctro

n D

ensi

ty (1

011

cm-3

)

70%

50%

30%

10% 10%

30%

50%

70%

Time (µs)

• EFFECT OF PRF• Peak [e] is same for all cases• Higher PRF resulted in higher

time averaged [e]• Lower PRF resulted in lower [e]

in the late afterglow

0

2

4

6

8

10

12

Ele

ctro

n D

ensi

ty (1

011

cm-3

)

10 10

5

20 20 20 20

0 50 100 150 200Time (µs)

2-D DYNAMICS IN Ar/Cl2 : Cl- DENSITY [Cl-]

GEC00_PRAMOD_9


• When the pulse begins, the plasmapotential peaks thereby"compressing" the [Cl-]

• At steady state, [Cl-] "rebounds" asthe plasma potential decreases.

• Due to inertia, [Cl-] does notrespond to changes in plasmapotential immediately.

• When the plasma is turned off, the[Cl-] increases due to a higher rateof dissociative attachment at lowTe.

• Later, the plasma potential fallsand [Cl-] spreads.

0 µs OFF (a)

9 ON (b)

20 ON (c)

40 ON (d)

60 OFF (e)

90 OFF (f)

6 x 1011 cm-31 x 109 cm-3

• Ar/Cl2 = 80/20, 20 mTorr, 300 W, 10 kHz/50%

Ar/Cl2 : PLASMA POTENTIAL AND Cl- FLUX VECTORS

GEC00_PRAMOD_10


• As the pulse begins, the peakplasma potential migrates to underthe coils.

• As the steady state is reached, thepeak plasma potential movestowards the center.

• Cl- flux vectors point towards thepeak plasma potential whenplasma potential is large.

• It takes about 25 µµs for the ions tomove from periphery to the center.

• When the plasma is turned off, Cl-

flux vectors reverse, pointingtowards boundaries.

0 µs ON (a) 20 ON (d)

60 OFF (e)

90 OFF (f)10 ON (c)

5 ON (b)

35 V-3 V

• Ar/Cl2 = 80/20, 20 mTorr, 300 W, 10 kHz/50%

EFFECT OF PULSE REPETITION FREQUENCY (PRF)

GEC00_PRAMOD_11


• Electron density (at center)

• Non-monotonic behavior in peak[e] is also observed in experiments.

• Lower PRF results in higher rate ofdissociation due to higher Te

• Decay rate is similar for all PRFs

Time (µs)0 50 100 150 200

2

4

6

8

10

0

Ele

ctro

n D

ensi

ty (1

011

cm

-3)

5 kHz

5

20 20 20 20

10 10

• Cl- density [Cl-] (at center)

• During plasma turn on, Cl- ionsmove to the center

• [Cl-] then decreases due to ion-ion recombination.

• When power is removed, [Cl-]increases and then decreases.

0 50 100 150 200

0.5

1

1.5

2

0

Time (µs)

Cl-

Den

sity

(10

11 c

m-3

)5 kHz

1010

20 20

20

EFFECT OF DUTY CYCLE ON FLUXES TO SUBSTRATE

GEC00_PRAMOD_12


• Flux to substrate can be controlled by varying duty cycle.• As duty cycle increases, the flux to the substrate increases• For 10%, plasma potential decays away in 40 µµs after the turn off.• For 50%, plasma potential decays away in 25 µµs after the turn off.

0 50 100 150 200Time (µs)

0

5

10

15

20

Pos

itive

ion

and

el

ectro

n flu

x (1

015

cm-2

s-1

)

Cl-

flux(

1014

cm

-2 s

-1)

0

2

4

6

8

Cl-Cl-

Electron and Positive ion flux

+ +e e

• DUTY CYCLE : 10%

0 50 100 150 200Time (µs)

0

10

20

30

40

Pos

itive

ion

and

el

ectro

n flu

x (1

015

cm-2

s-1

)

Cl-

flux(

1014

cm

-2 s

-1)

0

2

4

6

8

10

Cl-Cl-

+ +

e e

Electron and Positive ion flux

• DUTY CYCLE : 50%• Ar/Cl2 = 80/20, 20 mTorr, 300 W, 10 kHz

CONCLUSIONS

GEC00_PRAMOD_13


• A new 2-D hybrid model was proposed to address transients based onmoderate parallelism.

• Plasma transport, neutral fluid transport, and electromagnetics aresimultaneously computed on separate processors.

• Computational studies were performed for pulsed operation of Ar andAr/Cl2 ICPs.

• In argon plasmas, the peak in electron temperature during the turn-onphase is nearly twice the steady state value.

• In electronegative plasmas, electron-ion plasma in the activeglowbecomes ion-ion plasma in the afterglow.

• Negative ions do not respond immediately to plasma potential changes.

• Present study can be extended to investigate the effect of pulsed ECRsand charge buildup in fine features during etching.

simulation of transients in plasma processing … · introduction gec00_pramod_2 university of...

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