the spatiotemporal evolution of an rf dusty plasma: comparison of numerical simulations and...
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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 model
1D fluid model Aerosol general dynamic equation
Done in 0DChallenging 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
-10
+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