Space- and Time-dependent electron velocity distribution in VHF-CCP in CF$_{4}$/Ar

ORAL

Abstract

The electron velocity distribution (EVD) is fundamentally important for all aspects in plasma electronics. EVD given as a solution of the Boltzmann equation provides the swarm parameter as functions of external E/N and B/N utilized for a plasma simulation. Two-term expansion was traditionally employed for solving the Boltzmann equation. This method, however, cannot give EVD in a large E/N appearing in the ion sheath region in front of a wall surface. Particle simulation (PIC/MC) was also used to estimate EVD, but heavy computational load prohibits the sample of a large number of particles in order to eliminate the statistical fluctuation. A solution of the Boltzmann equation in phase space (velocity, position-space, and time) intrinsically involves numerical diffusion resulting from the differenciation of the advection terms. In this study, we develop the numerical procedure for predicting space- and time-dependent EVD. That is, the Boltzmann equation is solved in velocity space by using our direct numerical procedure (DNP) under the presence of 2D-t electric field distribution in VHF-CCP, calculated by the RCT model. Nonlinear behavior of EVD in the bulk plasma during one cycle of VHF (100 MHz) is discussed depending on the collisional relaxation time for energy and momentum of electrons. Also, we will investigate the temporal change of EVD in the sheath region under a large E/N.

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Authors

  • Takashi Yagisawa

    Keio University

  • Tug Yasar

    Theoretical Electrical Engineering, Ruhr-Universit\"at Bochum, Tokyo Electron AT LTD, Ruhr University Bochum, Pusan National University, Department of Electronic Engineering, Tohoku University, GE Historian, TET, AEPT, Nagoya Institute of Technology, Korean Institute of Energy Research, Department of Materials Science and Engineering, Kunsan National University, University of California at Berkeley, Dept. of Chemistry, Ajou University, GE Global Reseach, Niskayuna, US, TRINITI, Troizck, Russia, Kintech Lab, Moscow, Russia, HanYang University, West Virginia University, Morgantown, WV 26506, Air Force Research Laboratory, Wright-Patterson AFB, OH 45433, Norwegian University of Science and Technology (NTNU), University of Wisconsin-Madison, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, Chubu University, NEC Corporation, Nagoya University, Universit\'e Paris-Sud, Dong-A University, Saga University, University of Ryukyus, Sasebo National College of Technology, Faculty of Stomatology, Belgrade, Serbia, Institute of Physics, Belgrade, Serbia, Seagate Technology, NIBEC, LPP, Ecole Polytechnique, France, State University, Saint-Petersburg, LPP, Ecole Polytechnique, Dept. of Physics, California State University, Fullerton, CA, Institute of High Performance Computing, Singapore, Dept. of Physics, UAE University, Abu Dhabi, United Arab Emirates, Dept. of Physics, Missouri University of Sci. \& Tech., Rolla, MO, Tsinghua University, Beijing, China, University of Adelaide, Australia, Missouri University of Science and Technology, M.M.H. College, Ghaziabad, The Open University, University of Kentucky, Department of Applied Physics, Hanyang University, Ansan, Kyunggi-Do 426-791, South Korea, Hiden Analytical Ltd, Warrington, UK, Queens University Belfast, UK, University of Nevada, Reno,USA, Stalder Technologies and Research, Redwood City, USA, Queen's University Belfast, Loras College, Auburn University, LBNL, University of Nebraska-Lincoln, University of Newcastle-Ourimbah, Pacific Union College, University of Manchester (UK), Los Alamos National Laboratory, IMEC, Leuven, Belgium, Nuclear Physics Institute, Moscow State University, Moscow, Russia, Kintech Lab Ltd, Tokyo Electron Ltd., Kyoto University, Zeon Corporation, CAMS, University of Adelaide, South Australia, University of North Texas, Denton, CAMS, Australian National University, Canberra, Drake University, University of Western Australia, Fraunhofer Institute IVV Freising, Ruhr-University Bochum, University of California, San Diego, CAMS, Flinders University, Adelaide, South Australia, Univ. Groningen, IBM T.J. Watson Research Center, Surfx Technologies, Cymer, Inc., Department of Physics, Florida A\&M University, Dept. of Physics, UAE University, Abu Dhabi, United Arab, Dept. of Physics, Missouri University of Science \& Technology, Rolla, Mo, Institute for Plasma and Atomic Physics, Ruhr-University Bochum, 44780 Bochum, Germany, Faculty of Physics, Sofia University, 5, J. Bourchier Blvd., BG-1164 Sofia, Bulgaria, Faculty of Science and Technology, Keio University, RRC Kurchatov Inst., Moscow, Russia, Keio University, Yokohama, Japan, Macquarie University, University of Windsor, Mattson Technology Inc, Plasma Dynamics, RF Plasma Consulting, James Cook University Townsville, Institute of Physics Belgrade, University of Alberta, Edmonton, Canada, Princeton Plasma Physics Laboratory, Princeton, NJ, USA, Department of Aeronautics and Astronautics, Kyoto University, GE Global Reseach, Niskayuna,US, IPFN - IST, Portugal, St. Kliment Ohridski University of Sofia, Texas A\&M Mechanical Engineering, B \& W Group Ltd, UK, Belgrade, Institute of Physics, NIBEC University of Ulster, Dep. Fis/UCO, Cordoba, Spain, IPFN/IST, Lisbon, Portugal, ICMSE/CSIC, Sevilla, Spain, St. Petersburg State University, Russia, LPGP/UPS, Orsay, France, Seoul National University, Daehak-dong, Kwanak-gu, Seoul, Korea, Hanyang University, Plasmetrex GmbH Berlin, LATMOS/UVSQ, Verrieres le Buisson, France, Hungarian Academy for Science, Plasma Physics Division, Naval Research Laboratory, Global Strategies Group (North America), Sandia National Laboratories, Lebedev Physics Institute, Moscow, Department of Physics, Kurdistan region, Duhok University, Iraq, SPbSU, AFRL, Instituto de Ciencias Fisicas, UNAM, UES Inc., 4401 Dayton-Xenia Rd., Beavercreek, OH 45322, USA, Seoul National University, Samsung Electronics Co., University of Illinois at Urbana Champaign, Queen`s University Belfast, GE Research Laboratory, US, TRINITI, Troitsk, Russia, Dept. of Math \& Physics, Troy University, CPP Queens University Belfast, Department of Electrical Engineering, Hanyang University, Nagoya University, JST-CREST, NIST, Katagiri Engineering Co., Ltd., NU System Co., Ltd., Meijo University, Wakayama University, NU EcoEngineering Co., Ltd., University of Kansas, Princeton University, The von Karman Institute for Fluid Dynamics, Varian Semiconductor Equipment Associates, Institute of Physics, Faculty of Transport and Traffic Engineering, VSEA, Center for Atomic and Molecular Technologies, Osaka University, Princeton Plasma Physics Laboratory, Tokyo Electron, US. 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