Bulletin of the American Physical Society
65th Annual Gaseous Electronics Conference
Volume 57, Number 8
Monday–Friday, October 22–26, 2012; Austin, Texas
Session CT1: Plasma Sheaths I |
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Chair: Peter Ventzek, Tokyo Electron Limited Room: Amphitheatre 204 |
Tuesday, October 23, 2012 8:00AM - 8:30AM |
CT1.00001: Plasma-Sheath Revisited Invited Speaker: Natalia Sternberg The formulation of the plasma-wall problem goes back to Langmuir and Tonks, but up to this day has remained an intriguing and controversial problem. Its numerical solution shows a smooth transition from plasma to sheath and provides a limited understanding of the plasma-sheath interface. In many applications (such as plasma probe diagnostics, dc and rf discharges) the electrical properties of bounded plasma-sheath systems are controlled by the sheath. It is therefore common to study plasma and sheath separately using different mathematical models which provide an insight into each region. These models are quite simple, and often can be solved analytically, or by using simple numerical schemes. When plasma and sheath are studied separately, one has to decide how to join the solutions of the corresponding models. Two approaches are found in the literature to deal with this problem: one is the method of matched asymptotic expansions and the second one is patching. Application of asymptotic matching techniques to the plasma-wall problem has led to important theoretical results. However, the mathematical formalism and complexity associated with that method makes it difficult to use in applications. Moreover, the asymptotic plasma and the sheath solutions cannot be matched directly, and the modeling of an intermediate layer between the plasma and the sheath is required for a successful matching. Patching seems to be a more practical approach. Its idea is to join solutions of two different models by forcing their values and perhaps several derivatives to agree at some chosen point (the patching point). The main purpose of patching is to obtain continuity, but, in theory, smoothness is also possible. In contrast to asymptotic matching, it is possible to patch the plasma and the sheath solutions directly, eliminating the need for modeling an intermediate layer. The subject of this presentation is to discuss various fluid plasma and sheath models and their relationship to the corresponding plasma-wall problem. We will discuss the regions where the plasma and the sheath solutions are valid and develop discrete two-media plasma-sheath models which can be used to express the sheath characteristics through the plasma characteristics, or to find the integral characteristics of the sheath for given plasma parameters. [Preview Abstract] |
Tuesday, October 23, 2012 8:30AM - 8:45AM |
CT1.00002: Dust particle charge and screening in the collisional RF plasma sheath Job Beckers, Dirk Trienekens, Gerrit Kroesen Once immersed in plasma, a dust particle gathers a highly negative charge due to the net collection of free electrons. In most plasma's on earth and with particle sizes is in the micrometer range, the gravitational force is dominant and consequently the particle ends up within the plasma sheath region where it is confined due to balancing gravitational and electrical forces. In the plasma sheath region, the Orbital Motion Limited theory predicts charge values that significantly deviate from reality. This is due electron depletion and due the large directed drift velocity of ions, complexifying the prediction of the particle's charge dramatically. We have developed a novel method to measure the charge of a microparticle (10 $\mu $m in diameter and confined in a flat potential well above an RF powered electrode) by studying the horizontal interaction with another particle (equally in size) when the angle of the flat part of the potential well is varied with respect to the earth's horizontal plane. Measured particle charges are within the error bars of earlier measurements of the charge of the same particles and comparable plasma conditions during experiments under hyper-gravity conditions in a centrifuge. [Preview Abstract] |
Tuesday, October 23, 2012 8:45AM - 9:00AM |
CT1.00003: Fast, Kinetically self-consistent simulation of RF modulated plasma boundary sheaths Mohammed Shihab, Ralf Peter Brinkmann A mathematical model is presented which enables the efficent, kinetically self-consistent simulation of RF modulated plasma boundary sheaths in all technically relevant discharge regimes. The model consists of a set of kinetic equations for the ions, Boltzmann's relation for the electrons and Poisson's equation for the electrical field. Boundary conditions specify the ion flux at a point deep in the bulk and a periodically modulated sheath voltage or sheath charge. The equations are solved in a statistical sense. However, it is not the well-known particle-in-cell (PIC) scheme that is employed, but an alternative iterative algorithm termed ensemble-in-spacetime (EST). Three modules are called in a sequence: a Monte Carlo module, a harmonic analysis module, and a field module. The iteration is started with the potential values of a self-consistent fluid model and terminates when the updates become sufficiently small, i.e. when self-consistency is achieved. A drastic reduction of the computational effort compared with PIC calculations is achieved. As a first application of the new model, the influence of ion inertia on the dynamics of a collisionless sheath is studied and a comparison of the simulated ion energy distribution with published analytical solutions is performed. [Preview Abstract] |
Tuesday, October 23, 2012 9:00AM - 9:15AM |
CT1.00004: Investigation of Presheath and Sheath Using a Full-Vlasov Simulation Kentaro Hara, Iain Boyd, Vladimir Kolobov A direct simulation method is used to solve the Vlasov equation coupled with collision terms. In comparison to particle simulations, statistical noise is significantly reduced in a direct Vlasov simulation making it attractive for resolution of velocity distribution functions (VDFs) in low-temperature plasmas.\footnote{V. Kolobov, R. Arslanbekov, J. Comput. Phys., 231 (2012), 839} Here, a one-dimensional full-Vlasov simulation is used to investigate the interaction of plasma and a floating wall. Firstly, a collisionless case is considered that assumes a Maxwellian VDF shifted by the Bohm velocity for ions at the sheath edge. The Vlasov solution shows good agreement with the analytic solution. Secondly, by including collisions and applying a quasineutral boundary condition, a smooth transition from presheath to sheath is observed without imposing the Bohm criterion. For a xenon plasma of 5 eV and 10$^{15}$ m$^{-3}$, the sheath potential is 5.5 T$_{e}$/e when the sheath edge is defined as the point where the ion mean velocity equals the ion acoustic velocity. This result agrees with the classical theory that suggests the sheath potential is 5.27 T$_{e}$/e. It is also observed that momentum exchange collisions are needed for a converged solution of the presheath-sheath structure. [Preview Abstract] |
Tuesday, October 23, 2012 9:15AM - 9:30AM |
CT1.00005: A sheath model for arbitrary radiofrequency waveforms M.M. Turner, Pascal Chabert The sheath is often the most important region of a rf plasma, because discharge impedance, power absorption and ion acceleration are critically affected by the behaviour of the sheath. Consequently, models of the sheath are central to any understanding of the physics of rf plasmas. Lieberman has supplied an analytical model for a radio-frequency sheath driven by a single frequency, but in recent years interest has been increasing in radio-frequency discharges excited by increasingly complex wave forms. There has been limited success in generalizing the Lieberman model in this direction, because of mathematical complexities. So there is essentially no sheath model available to describe many modern experiments. In this paper we present a new analytical sheath model, based on a simpler mathematical framework than that of Lieberman. For the single frequency case, this model yields scaling laws that are identical in form to those of Lieberman, differing only by numerical coefficients close to one. However, the new model may be straightforwardly solved for arbitrary current waveforms, and may be used to derive scaling laws for such complex waveforms. In this paper, we will describe the model and present some illustrative examples. [Preview Abstract] |
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