The Spatiotemporal Evolution of an RF Dusty Plasma:

1. The Spatiotemporal Evolution of an RF Dusty Plasma: Comparison of Numerical Simulations and Experimental Measurements Steven Girshick, Adam Boies and Pulkit Agarwal University of Minnesota, Minneapolis, MN, USA Johannes Berndt, Eva Kovacevic and Laïfa Boufendi GREMI, CNRS/Université d’Orléans, France Acknowledgments: U.S.: NSF, DOE Plasma Science Center, Minnesota Supercomputing Institute; France: ANR-09-BLAN-023-03

2. Overview Two 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

3. Model overview Plasma model Aerosol model Chemistry model 1D fluid model Aerosol general dynamic equation Done in 0D Challenging for 1D Sectional model for particle size & charge distributions Parameterized nucleation & growth rates (no chemistry) Plasma Chem. Plasma Process. 27, 292 (2007) IEEE Trans. Plasma Sci. 36, 1022 (2008) Phys. Rev. E 79, 026408 (2009)

4. RF powered electrode (showerhead) Grounded electrode Electrode gap Parallel-plate capacitive RF plasma (1D) Infinite parallel plates Pure argon plasma containing Si nanoparticles

5. Surface growth Nucleation zone Charging -2 -1 0 +1 +2 Size Aerosol sectional model Nucleation Coagulation Dp = 0.75 nm Aerosol model Transport (electrostatic, neutral drag, ion drag, diffusion, gravity, thermophoresis) • Nucleation occurs in void (particle-free) regions outside sheaths • Surface growth occurs where nucleation is quenched Replaces chemistry

6. 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

7. Charge carriers Appearance 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

8. Predicted light scattering & plasma emission Profiles of particle light scattering and plasma emission behave oppositely

9. Gas (Argon) flow at 31 sccm • V = Vrf Sin (ωt + φ) + λ RF VOLTAGE SUPPLY Vrf = 150 V, • ω =13.56 MHz Argon plasma with particles Pressure = 0.1275 Torr (17 Pa) Electrode gap = 4 cm V = 0 Ground level Porous electrode with radius = 6 cm Experimental setup Vacuum Chamber Viewport Laser Measurements: plasma emission & laser light scattering Plasma CCD Camera

10. 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

11. 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

12. Summary 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 Reasonable qualitative agreement for main features of spatiotemporal evolution Discrepancies may be caused by experimental difficulties, or by inadequate model treatment of chemistry, particle charging and/or electron kinetics