Bulletin of the American Physical Society
62nd Annual Gaseous Electronics Conference
Volume 54, Number 12
Tuesday–Friday, October 20–23, 2009; Saratoga Springs, New York
Session BM: Kinetics Workshop: General Kinetic Models |
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Chair: Mirko Vukovic, Tokyo Electron America Room: Saratoga Hilton Ballroom 1 |
Monday, October 19, 2009 10:00AM - 10:30AM |
BM.00001: Kinetic Modeling of Complex Plasma Equipment Invited Speaker: Vladimir Kolobov Kinetics of electrons, ions and neutrals play an important role in industrial plasma systems. These systems are often characterized by complex geometries and require 2D and 3D models of varying resolution for realistic simulations of relevant processes. We will describe hybrid approach to modeling such systems using kinetic models for electrons and hydrodynamic (fluid) models for ion and neutral components. Kinetic modeling of electrons involves numerical solution of the Boltzmann equation or its derivatives. Using two-term spherical harmonics expansion in velocity space, the 6D Boltzmann equation can be reduced to a 4D Fokker-Plank (F-P) equation for the Electron Energy Distribution Function (EEDF), which depends of electron energy and spatial position. This equation can be conveniently solved using total electron energy (kinetic + potential) for a wide range of discharge conditions. Further simplifications are possible in the two extremes. At high gas pressures one can solve local F-P equation for the EEDF as a function of local electric field and plasma composition, and generate Look-Up-Tables (LUTs) for electron transport coefficients and rates of electron induced chemical reactions to be used in fluid models for electrons. The other extreme corresponds to a ``nonlocal approach'' where the EEDF depend solely on the total energy and does to depend explicitly on spatial position. We will describe the architecture of the F-P solver for electrons in the CFD-ACE+ software package and its application to simulations of low-pressure ICP, CCP, and DC discharges, as well as high-pressure micro-plasmas. The peculiarities of the EEDF formation in these systems, and the importance of nonlocal kinetic effects for the formation of striations, electron heating and macro-plasma parameters will be discussed. We will also discuss the limitations of the F-P approach and our current efforts to develop a full Boltzmann solver for simulations of fast (runaway) electrons and nonlocal electromagnetic phenomena in low-pressure RF discharges. [Preview Abstract] |
Monday, October 19, 2009 10:30AM - 11:00AM |
BM.00002: Nonlocal collisionless and collisional electron transport in low temperature plasmas Invited Speaker: Igor Kaganovich The purpose of the talk is to describe recent advances in nonlocal electron kinetics in low-pressure plasmas. A distinctive property of partially ionized plasmas is that such plasmas are always in a non-equilibrium state: the electrons are not in thermal equilibrium with the neutral species and ions, and the electrons are also not in thermodynamic equilibrium within their own ensemble, which results in a significant departure of the electron velocity distribution function from a Maxwellian. These non-equilibrium conditions provide considerable freedom to choose optimal plasma parameters for applications, which make gas discharge plasmas remarkable tools for a variety of plasma applications, including plasma processing, discharge lighting, plasma propulsion, particle beam sources, and nanotechnology. Typical phenomena in such discharges include nonlocal electron kinetics, nonlocal electrodynamics with collisionless electron heating, and nonlinear processes in the sheaths and in the bounded plasmas. Significant progress in understanding the interaction of electromagnetic fields with real bounded plasma created by this field and the resulting changes in the structure of the applied electromagnetic field has been one of the major achievements of the last decade in this area of research [1-3]. We show on specific examples that this progress was made possible by synergy between full scale particle-in-cell simulations, analytical models, and experiments. In collaboration with Y. Raitses, A.V. Khrabrov, Princeton Plasma Physics Laboratory, Princeton, NJ, USA; V.I. Demidov, UES, Inc., 4401 Dayton-Xenia Rd., Beavercreek, OH 45322, USA and AFRL, Wright-Patterson AFB, OH 45433, USA; and D. Sydorenko, University of Alberta, Edmonton, Canada. \\[4pt] [1] D. Sydorenko, A. Smolyakov, I. Kaganovich, and Y. Raitses, IEEE Trans. Plasma Science \textbf{34}, 895 (2006); Phys. Plasmas \textbf{13}, 014501 (2006); \textbf{14} 013508 (2007); \textbf{15}, 053506 (2008). \\[0pt] [2] I. D. Kaganovich, Y. Raitses, D. Sydorenko, and A. Smolyakov, Phys. Plasmas \textbf{14}, 057104 (2007). \\[0pt] [3] V.I. Demidov, C.A. DeJoseph, and A.A. Kudryavtsev, Phys. Rev. Lett. \textbf{95}, 215002 (2005); V.I. Demidov, C.A. DeJoseph, J. Blessington, and M.E. Koepke, Europhysics News, \textbf{38}, 21 (2007). [Preview Abstract] |
Monday, October 19, 2009 11:00AM - 11:30AM |
BM.00003: Modeling of low-temperature plasmas: some case studies of different modeling approaches Invited Speaker: Annemie Bogaerts In this talk, some examples will be given of different modeling approaches, used in our group. Special attention will be put on input data, needed for the models. As an example of fluid modeling, we will illustrate the detailed plasma chemistry in a DBD used for gas conversion purposes. In this model, a large number of different species (various molecules, radicals and ions, besides the electrons) are included, which can all react with each other. For all these species, transport coefficients need to be defined, as well as reaction (sticking) probabilities at the walls. Moreover, energy-dependent cross sections and thermal rate coefficients have to be defined for all the electron reactions and the heavy particle reactions, respectively. These data are typically not available for the more exotic plasma species, so that certain assumptions have to be made. The second example is for particle-in-cell -- Monte Carlo collisions simulations, developed for magnetron discharges in argon/oxygen and argon/nitrogen gas mixtures, used for the reactive sputter-deposition of metal oxide and nitride layers. In this modeling approach, the behavior of the electrons, the various ions and energetic neutrals is described by Newton's laws, and their collisions are treated by the Monte Carlo procedure. Again, energy-dependent cross sections for the various collisions are required. The last example is for hybrid Monte Carlo -- fluid modeling, based on the HPEM code developed by Kushner and coworkers. It is applied to an ICP in Ar/Cl$_{2}$/O$_{2}$, used for Si etching. Besides the plasma behavior, also the etching (and deposition) process is described, for which a large number of data (etch and sticking probabilities and sputter yields) are required. We try to obtain accurate values for these data by molecular dynamics simulations. Results of the latter simulation method will also be presented. [Preview Abstract] |
Monday, October 19, 2009 11:30AM - 12:00PM |
BM.00004: The Linearized Kinetic Equation -- A Functional Analytic Approach Invited Speaker: Ralf Peter Brinkmann Kinetic models of plasma phenomena are difficult to address for two reasons. They i) are given as systems of nonlinear coupled integro-differential equations, and ii) involve generally six-dimensional distribution functions f(\textbf{r,v},t). In situations which can be addressed in a linear regime, the first difficulty disappears, but the second one still poses considerable practical problems. This contribution presents an abstract approach to linearized kinetic theory which employs the methods of functional analysis. A kinetic electron equation with elastic electron-neutral interaction is studied in the electrostatic approximation. Under certain boundary conditions, a nonlinear functional, the kinetic free energy, exists which has the properties of a Lyapunov functional. In the linear regime, the functional becomes a quadratic form which motivates the definition of a bilinear scalar product, turning the space of all distribution functions into a Hilbert space. The linearized kinetic equation can then be described in terms of dynamical operators with well-defined properties. Abstract solutions can be constructed which have mathematically plausible properties. As an example, the formalism is applied to the example of the multipole resonance probe (MRP). Under the assumption of a Maxwellian background distribution, the kinetic model of that diagnostics device is compared to a previously investigated fluid model. [Preview Abstract] |
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