PARAMETRIC STUDY OF THE FORMATION OFCOULOMB CRYSTALS IN THE GEC REFERENCE

CELL*

Vivek Vyas** and Mark J. Kushner*****Materials Science and Engineering

***Electrical and Computer EngineeringUniversity of Illinois

Urbana, IL 61801

Gregory A. Hebner, Merle Riley, Pauline Ho and

Richard BussSandia National Laboratories

Albuquerque, NM 87185

*Work supported by Sandia National Laboratories

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AGENDA

• Introduction

• Description of the Dust Transport Simulation(DTS)

• Parametric trends in Plasma Crystal Formation

• Conclusions

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INTRODUCTION

• Particles in low temperature, partially ionized plasmasexhibit collective behavior and form coulomb solids undercertain conditions.

• The regimes of plasma operating conditions in which thesestructures are formed are of interest as an indication ofcrystal formation mechanisms.

• In this paper we discuss results from a parametric study ofthe formation of coulomb crystals in a GEC Reference cell.

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• A modular simulatoraddressing low temperature,low pressure plasmas.

• EMM produceselectromagnetic fields andmagneto-static fields.

• EETM produces electrontemperature, electron impactsources, and transportcoefficients.

• FKM produces densities,velocities, and temperature ofplasma species.

HYBRID PLASMA EQUIPMENT MODEL (HPEM)

ELECTRO-MAGNETIC MODULE (EMM)

E,B ELECTRON ENERGY TRANSPORT MODULE (EETM)

FLUID KINETICS MODULE (FKM)

V, N

S, T e

, µµ

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DUST TRANSPORT SIMULATION ( DTS )

• The fluxes and densities from the HPEM are used in theDust Transport Simulation (DTS) to compute dust particletrajectories and locations.

• The DTS is a three-dimensional dust particle transportmodel.

• Forces included in the DTS are electrostatic, ion drag ,thermophoretic, fluid drag by neutrals , brownian motion,self-diffusion, coulomb repulsion and gravity.

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DUST TRANSPORT SIMULATION ( DTS )

• The net force is:

• A particle’s potential is calculated by equating the electronand ion currents to the surface.

coulomb) ( r exp 11

Q

4

Q (brownian)

4

M

)( kT - drag) (fluid 24Re

(Re)C )v( )(

r6 -

retic)(thermopho 6 - drag)-(ion s ),r( )( atic)(electrost EQ (gravity) gM )r(F

j

ji2

gas

iDii

Iions

iiii

−−−−

++++

∆∆

∆∆++

−−∇∇

−−

∇∇ΦΦ++++==

∑∑

∑∑

L

ij

Lijijo

igas

i

i

TiI

aR

RR

dtvN

t

v

diffusionselfNN

uKnC

TT

vKrv

λλλλπεπε

ππ

πµπµ

πµπµεεσσ

ΦΦ==

ΦΦ−−==

ee

e

II

I

kTq

mkT

Nq

Eq

mE

Nq

exp 3

a I

,12

a I

2e

2I

ππππ

ππ

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DUST TRANSPORT SIMULATION ( DTS )

• The charge on the particle is determined from thecapacitance C of the particle, where C has the form

• The debye length λλLis obtained by linearizing the Poisson-Vlassov equation:

. 1 4 C o

++==

L

aa

λλπεπε

.2

e

1 2

++==

I

I

e

e

oL EN

kTN

εελλ

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DUST TRANSPORT SIMULATION ( DTS )

• The ion-dust momentum transfer cross-section iscalculated according to the semi-analytic formula byKilgore et al.

• Coulomb coupling parameter is calculated as follows:

. c

1ln c 2I

I2

++==

ββσσ b

.mv

21

ë

aRexp

R

Q

4ðQ

Ã2

i

j L

ij

ij

j

o

i

i

∑∑

−−−−

==εε

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DUST TRANSPORT SIMULATION ( DTS )

• Phases of the structuresformed are analysed usingthe pair correlationfunction (PCF) for particlesor g(r).

• Peaks in the PCFcorrespond to to the first,second, and other nearestneighbors for particles.

Ar, 95 mTorr, 150 V,

100 particles of radius 3.8 µµm.

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MODIFIED GEC REFERENCE CELL

• A modified GEC Referencecell was used for thesimulations.

• A focus ring was used toconfine the particles.

• Lower electrode ispowered at 10 MHz, upperelectrode is grounded.

• Dust particles aregenerated between theelectrodes.

• Simulation time is 8 s.

DARK SPACE SHIELD

PUMP PORT

POWERED ELECTRODE

RADIUS (cm)

HE

IGH

T (

cm)

GROUNDED ELECTRODE

FOCUS RING

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OPERATING CONDITIONS

• Ar at a pressure of 95mTorr

• Substrate bias: 125 - 250 V

• Radius of dust particles :0.01-10 µµm.

• Gas flow : 300 sccm.

• TGAS = 350 K.

ELECTRON TEMPERATURE

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PLASMA PROPERTIES

AR+ DENSITYELECTRON DENSITY PLASMA POTENTIAL

Ar, 95 mTorr , substrate bias 150 V

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SUBSTRATE BIAS DETERMINES MORPHOLOGY

• For Ar, 95 mTorr and a particle size of 3.8µµm splitting into 2lattices is observed at higher substrate biases

VIEW

A single lattice observed at lower substrate biasSplitting into 2 lattices observed with increase

of substrate bias to 250 V

SINGLE LATTICE

FOCUS RING

INNERLATTICE

OUTER LATTICE

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EFFECT OF SUBSTRATE BIAS ON THE COULOMBCRYSTAL

• For typical conditions(Ar, 95mTorr), thesubstrate bias was variedfrom 125 V to 250 V.

• At higher voltagesparticles are observed tosplit into 2 sub-lattices.

• Larger radial forces athigher voltages pushparticles into an outerlattice.

0

0.5

1

1.5

2

2.5

3

100 150 200 250 300

NUMBER OF LATTICES

VOLTAGE (V)

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EFFECT OF PARTICLE RADIUS ON THE COULOMBCRYSTAL

• Particle radius was varied from 0.1µµm to 10 µµm keeping thenumber of particles in the lattice constant at 150.

• For 0.1 µµm we observe two distinct and well-separatedlattices. The upper lattice is disk shaped and well above thecentral electrode.

• For 10 µµm particle radius we observe a single lattice nearthe bottom electrode.The effect of gravity becomesimportant for larger particles.

• For intermediate radii, the upper lattice is found to disperseand become sparsely populated.

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EFFECT OF PARTICLE RADIUS ON LATTICEMORPHOLOGY

• Splitting of lattice observed at smaller radii for Ar, 95mTorr and a substrate bias of 150 V.

UPPER LATTICE

LOWER LATTICE

0.1 µµm PARTICLES ARRANGING IN 2 LATTICES

SINGLE LATTICE

10 µµm PARTICLES ARRANGING IN A SINGLE LATTICE

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EFFECT OF PARTICLE RADIUS ON THE COULOMBCRYSTAL

Net Force in Z-direction Particle Trapping Locations

Ar, 95 mTorr, substrate bias 150 V

Particle radius 0.1µµm

UPPER LATTICE

LOWER LATTICE

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EFFECT OF PARTICLE RADIUS ON THE COULOMBCRYSTAL

Net Force in Z-direction

Particle radius 1µµm

Particle Trapping Locations

Ar, 95 mTorr, substrate bias 150 V

SINGLELATTICE

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EFFECT OF PLASMA DENSITY ON INTERPARTICLESPACING

• The ion and electrondensities were varied whilekeeping other conditionsconstant.

• At low plasma densities weobserve a slight increase ininterparticle spacing becauseof an increase in the particletemperature.

• A monotonic decrease isobserved at higher plasmadensities because of reducedshielding length.

0.05

0.06

0.07

0.08

0.09

0.1

0 10 20 30 40 50 60 70 80

INTERPARTICLE SPACING

PLASMA DENSITIES (ARBITRARY UNITS)

1

10

100

1000

0 20 40 60 80 100

COULOMB COUPLING FACTOR

PLASMA DENSITIES (ARBITRARY UNITS)

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EFFECT OF NUMBER OF PARTICLES ONINTERPARTICLE SPACING

• The effect of the number ofparticles on interparticlespacing was studied fordifferent voltages.

• Interparticle spacing is foundto be in good agreement withexperimentally observedtrends.

• Interparticle spacing is foundto decrease with increase innumber of particles.

INCREASE IN NUMBER OF PARTICLES DECREASES INTERPARTICLE SPACING

POTENTIAL WELL

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EFFECT OF NUMBER OF PARTICLES ONINTERPARTICLE SPACING

0.11 cm 0.075cm 0.065cm

Interparticle spacing for 3.8 µµm particles (Ar, 95 mTorr, substrate bias 150 V).

7 particles 100 particles 200 particles

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EFFECT OF NUMBER OF PARTICLES ONINTERPARTICLE SPACING

• Maximum spacing is observed for 225 V. However no clearcorrelation of spacing with voltage is observed.

Interparticle spacing for 3.8µµm particles as a function of number ofparticles for Ar, 95 mTorr

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0 50 100 150 200 250 300

125 V150 V175 V200 V225 V

NUMBER OF PARTICLES

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EFFECT OF NUMBER OF PARTICLES ON THECOULOMB COUPLING FACTOR

• Coulomb Coupling factor increases with increase innumber of particles.

0

1000

2000

3000

4000

5000

0 100 200 300 400 500

COULOMB COUPLING FACTOR

NUMBER OF PARTICLES

Coulomb coupling factor as a function of the number of particles for Ar, 95 mTorr and a substrate bias of 150V.

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EFFECT OF PRESSURE ON THE COULOMBCRYSTAL

• Pressure was varied from 95mTorr to 1 Torr .

• For Ar, 150 V and 3.8µmparticles,

• Increase in pressuredecreases coulombcoupling factor becausehigher ion fluxes lead tohigher particle velocitiesand temperatures.

• Increase in pressuredecreases interparticlespacing.

1

10

100

1000

104

0 20 40 60 80 100 120

95 mTORR0.5 TORR1 TORR

NUMBER OF PARTICLES

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 20 40 60 80 100 120

95 mTORR0.5 TORR1 TORR

NUMBER OF PARTICLES

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CONCLUSIONS

• Abrupt splitting into 2 lattices observed for higher voltage.

• Particles of smaller size prefer forming 2 sublattices.

• Interparticle spacing decreases and coulomb couplingfactor increases with increase in the number of particles inthe lattice.

• Interparticle spacing decreases monotonically for higherelectron and flux densities.

• Increase in pressure decreases the coulomb couplingfactor and interparticle spacing.