The Spatiotemporal Evolution of an RF Dusty

Plasma:Comparison of Numerical

Simulations and Experimental Measurements

Steven Girshick, Adam Boies and Pulkit AgarwalUniversity of Minnesota, Minneapolis, MN, USA

Johannes Berndt, Eva Kovacevic and Laïfa BoufendiGREMI, CNRS/Université d’Orléans, France

Acknowledgments: U.S.: NSF, DOE Plasma Science Center, Minnesota Supercomputing Institute; France: ANR-09-BLAN-023-03

OverviewTwo decades of experiments on RF plasmas in which nanoparticles nucleate and grow

Less development of numerical models for evolution of plasma-nanoparticle system in space & time

Almost no comparison of modeling & experiment

This work: Minnesota-GREMI collaboration (in progress) to compare modeling & experiment

Model overview

Plasma Chem. Plasma Process. 27, 292 (2007)IEEE Trans. Plasma Sci. 36, 1022 (2008) Phys. Rev. E 79, 026408 (2009)

Plasma model Aerosol model Chemistry model1D fluid model Aerosol general

dynamic equationDone in 0D

Challenging for 1D

Sectional model for particle size & charge distributions

Parameterizednucleation & growth rates

(no chemistry)

Electrode gap

Grounded electrode

RF powered electrode (showerhead)

Pure argon plasma containing Si nanoparticles

Parallel-plate capacitive RF plasma (1D)

Infinite parallel plates

• Nucleation occurs in void (particle-free) regions outside sheaths

• Surface growth occurs where nucleation is quenched

Nucleation zone

Transport (electrostatic, neutral drag, ion drag, diffusion, gravity, thermophoresis)

CoagulationDp = 0.75 nm

Aerosol sectional model

Nucleation

Surface growth

Size

-2-1

0+1

+2

Charging

Aerosol model

Replaces chemistry

Particle size distribution & average charge

Early times: negative particles trapped in center, neutral particles diffuse to walls

Later times: particle cloud spreads due to ion drag

Neutral drag pushes particles toward lower electrode

Spreading of particle cloud quenches nucleation

Charge carriersAppearance of particles causes rapid increase in ion density

Ion density profile follows nanoparticle charge density profile

> 90% of negative charge resides on nanoparticles

Electron density profile moves oppositely to nanoparticle density profile

Kink in electron density profile at lower sheath edge due to sharp drop in nanoparticle density

Predicted light scattering & plasma emission

Profiles of particle light scattering and plasma emission behave oppositely

Experimental setup

Measurements:plasma emission & laser light scattering

V = Vrf Sin (ωt + φ) + λ

RF VOLTAGE SUPPLY

Vrf = 150 V, ω =13.56 MHz

V = 0 Ground level

Gas (Argon) flow at 31 sccmE

lect

rode

gap

= 4

cm

Argon plasmawith particles

Pressure = 0.1275 Torr (17 Pa)

Porous electrode with radius = 6 cm

CCD Camera

Laser

Vacuum Chamber

Plasma

Viewport

Light scattering: model vs experiment

Reasonable qualitative agreement for scattering profiles

Discrepancy in location of scattering peak easily explained by difference in gas flow profile

Local peak in scattering near top electrode not predicted by model—might be due to un-modeled silane chemistry near showerhead

Emission: model vs experiment

Qualitative agreement on some main features

Model correctly predicts kink in profile near lower electrode

Poor agreement for location of maxima near top & bottom electrodes—may be due to experimental difficulty measuring emission close to electrodes

5 s 1

Summary

Discrepancies may be caused by experimental difficulties, or by inadequate model treatment of chemistry, particle charging and/or electron kinetics

Reasonable qualitative agreement for main features of spatiotemporal evolution

Developed 1D model for evolution of RF plasma in which nanoparticles nucleate & grow

Compared model predictions to experimental measure-ments of particle light scattering & plasma emission