Nonlinear electron resonance heating in dual frequency capacitive discharges

ORAL

Abstract

Capacitively coupled plasmas (CCP's) play a major role in material processing. The drawback of conventional single frequency CCP's is that the ion bombardment energy and the ion flux to the substrate itself cannot be controlled independently. The problem can be remedied by the use of dual frequency CCP's. In such sources, the ratio of the applied frequencies is obviously an important control parameter. Rauf$^1$ found that at large ratios (e.g., $100\,\rm kHz$/$13.56\,\rm MHz$) the spectrum of the discharge current was just the superposition of two single-frequency spectra. For more comparable frequencies (e.g.,$6.78\,\rm MHz$/$13.56\,\rm MHz$), however, quite surprising nonlinear effects were observed. It is exactly this nonlinear behavior and its influence on the total energy budget that is discussed in this contribution - we present and analyze a nonlinear global model for a dual frequency CCP. Based on an exact analytical solution of the underlying equations we discuss the behavior of the model for various voltage ratios, frequency ratios, and gas pressures. We investigate in particular the heating at the plasma series resonance, either by direct excitation or via the nonlinear electron resonance heating mechanism$^2$.\par\noindent$^1$ S. Rauf and M.J. Kushner, IEEE Trans Plasma Sci. {\bf 27}, 1329 (1999)\\ $^2$ T. Mussenbrock and R.P. Brinkmann, Appl. Phys. Lett. {\bf 88}, 151503 (2006)

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Authors

  • Paule Maguire

    Department of Chemistry and Physics, Lamar University, Applied Materials, Sandia National Laboratories, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, D-44780 Bochum, Germany, Ecole Polytechnique, France, Assistant Research Professor, University of Saskatchewan, PPPL, University of Saskatchewan, Saskatoon, Canada, Plasma Physics Laboratory, Princeton University, Technische Universiteit Eindhoven, Institut fur Niedertemperatur Plasmaphysik, Old Dominion University, Norfolk, VA 23529, Korea Advanced Institute of Science and Technology \& New York University, Korea Advanced Institute of Science and Technology, St.Petersburg State Politechnical University, St.Petersburg, Russia, Hanyang University, University of Nantes, Eindhoven University of Technology, Universidad Nacional Autonoma de Mexico, Air Force Research Laboratory, Innovative Scientific Solutions, Inc, University of Cambridge, UK, University of Bristol, UK, University Kiel, Germany, INP Greifswald, Germany, KRISS, INP, Greifswald, Germany, Australian National University, Drake University, University of Central Florida, University of Missouri-Rolla, John Carroll University, Indiana University-Purdue University Fort Wayne, University of Southampton, UK and Hong Kong Polytechnic University, University of Nottingham, UK, University of Pittsburgh, Department of Physics, Pittsburgh, PA 15260, Department of Computer Science, Lamar University, Institute of Nuclear Physics, Moscow State University, Russia, Univ. of Houston, Dublin City University, Ireland, West Virginia University, Nagoya Institute of Technology, National University of Ireland, Maynooth, 3M Company, Samsung Electronics, Kyoto University, EM2C, Ecole Centrale, CNRS, Chatenay, France, University of Duisburg-Essen, Ruhr Uni Bochum, LSP, UJF, CNRS, Grenoble, France, Lawrence Berkeley National Laboratory, Tech-X Corporation, Dublin City University, Princeton Plasma Physics Laboratory, Plasma Physics Division, Naval Research Laboratory, The Open University, United Kingdom, Eindhoven University of Technology, The Netherlands, University of Minnesota, Universit\'e Joseph Fourier de Grenoble, France, Nagoya University, Japan, West Virginia University, Physics Department, Morgantown, WV 26506-6315, Dept. of Physics and Astronomy, The Open University, Milton Keynes, UK, Institute for Plasma and Atomic Physics, CPST, Ruhr-University Bochum, Germany, CAMS, Australian National University, Schuster Laboratory, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK, Centre for Antimatter-Matter Studies, Griffith University, ISAS/JAXA, University of Tokyo, Department of Aeronautics and Astronautics, Kyoto University, Kyoto, Japan, University of Texas at Austin, LTM, Grenoble, LSP, Grenoble, CPAT,Toulouse, LPGP, Orsay, France, NRL-NRC Postdoctoral Associate, SFA, Crofton, MD, Center for Plasma Science and Technology CPST, Ruhr University Bochum, D-44780 Bochum, Germany, Department of Physics, University Duisburg-Essen, D-45141 Essen, Germany, LACE, UCBL, CNRS, Lyon, France, LPTP, Ecole Polytechnique, CNRS, Palaiseau, France, Air Force Research Laboratory, Wright-Patterson AFB, OH, UES, INC., Dayton, OH, St. Petersburg State University, St. Petersburg, Russia, Suzuka National College of Technology, Japan, Plasma Research Laboratory, NCPST, Dublin City University, Dublin 9, Ireland, University Greifswald, Germany, Facultad de Ciencias, Universidad Autonoma del Estado de Morelos, Nagoya University, University of Liverpool, United Kingdom, LPTP, Ecole Polytechnique, Palaiseau, France, Laboratory for Optical Physics and Engineering, Dept. of Elec. and Computer Engr., University of Illinois, Laboratory for Optical Physics and Engineering, Dept. of Elect. and Computer Engr., University of Illinois, The Ohio State University (OH), Department of Physics, University of Rajshahi, Rajshahi, Bangladesh, CAMS, Murdoch University, Australia, Drake University, USA, Gothenburg University, University of Wisconsin- Madison, University of Wisconsin-Madison, Physics Dept., Sophia University, Chiyoda-ku, Tokyo 102-855, Japan, ARC Centre for Antimatter-Matter Studies, SoCPES, Flinders University, GPO Box 2100, Adelaide, 5001 Australia, Korea Advanced Institute of Science and Technology / New York University, National Fusion Research Center / Korea Advanced Institute of Science and Technology, Korea Advanced Institute of Science and Technology and Courant Institute-NYU, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, Korea Advanced Institute of Science and Technology / NewYork University, Sandia National Labs, Plasma, Pulsed-Power, and Microwave Lab, Nuclear Engineering and Radiological Sciences Dept., University of Michigan, Varian Semiconductor Equipment Associates, Gloucester, MA, Dominion University, Norfolk, VA, Sheffield Hallam University, GE Global Research, Kintech, University of Nebraska, University of Fribourg, Switzerland, CAMS, Flinders University, Australia, University of Nantes, France, CFD Research Corporation, Huntsville, AL, USA, Research Professor

  • T. Mussenbrock

  • Paule Maguire

    Department of Chemistry and Physics, Lamar University, Applied Materials, Sandia National Laboratories, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, D-44780 Bochum, Germany, Ecole Polytechnique, France, Assistant Research Professor, University of Saskatchewan, PPPL, University of Saskatchewan, Saskatoon, Canada, Plasma Physics Laboratory, Princeton University, Technische Universiteit Eindhoven, Institut fur Niedertemperatur Plasmaphysik, Old Dominion University, Norfolk, VA 23529, Korea Advanced Institute of Science and Technology \& New York University, Korea Advanced Institute of Science and Technology, St.Petersburg State Politechnical University, St.Petersburg, Russia, Hanyang University, University of Nantes, Eindhoven University of Technology, Universidad Nacional Autonoma de Mexico, Air Force Research Laboratory, Innovative Scientific Solutions, Inc, University of Cambridge, UK, University of Bristol, UK, University Kiel, Germany, INP Greifswald, Germany, KRISS, INP, Greifswald, Germany, Australian National University, Drake University, University of Central Florida, University of Missouri-Rolla, John Carroll University, Indiana University-Purdue University Fort Wayne, University of Southampton, UK and Hong Kong Polytechnic University, University of Nottingham, UK, University of Pittsburgh, Department of Physics, Pittsburgh, PA 15260, Department of Computer Science, Lamar University, Institute of Nuclear Physics, Moscow State University, Russia, Univ. of Houston, Dublin City University, Ireland, West Virginia University, Nagoya Institute of Technology, National University of Ireland, Maynooth, 3M Company, Samsung Electronics, Kyoto University, EM2C, Ecole Centrale, CNRS, Chatenay, France, University of Duisburg-Essen, Ruhr Uni Bochum, LSP, UJF, CNRS, Grenoble, France, Lawrence Berkeley National Laboratory, Tech-X Corporation, Dublin City University, Princeton Plasma Physics Laboratory, Plasma Physics Division, Naval Research Laboratory, The Open University, United Kingdom, Eindhoven University of Technology, The Netherlands, University of Minnesota, Universit\'e Joseph Fourier de Grenoble, France, Nagoya University, Japan, West Virginia University, Physics Department, Morgantown, WV 26506-6315, Dept. of Physics and Astronomy, The Open University, Milton Keynes, UK, Institute for Plasma and Atomic Physics, CPST, Ruhr-University Bochum, Germany, CAMS, Australian National University, Schuster Laboratory, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK, Centre for Antimatter-Matter Studies, Griffith University, ISAS/JAXA, University of Tokyo, Department of Aeronautics and Astronautics, Kyoto University, Kyoto, Japan, University of Texas at Austin, LTM, Grenoble, LSP, Grenoble, CPAT,Toulouse, LPGP, Orsay, France, NRL-NRC Postdoctoral Associate, SFA, Crofton, MD, Center for Plasma Science and Technology CPST, Ruhr University Bochum, D-44780 Bochum, Germany, Department of Physics, University Duisburg-Essen, D-45141 Essen, Germany, LACE, UCBL, CNRS, Lyon, France, LPTP, Ecole Polytechnique, CNRS, Palaiseau, France, Air Force Research Laboratory, Wright-Patterson AFB, OH, UES, INC., Dayton, OH, St. Petersburg State University, St. Petersburg, Russia, Suzuka National College of Technology, Japan, Plasma Research Laboratory, NCPST, Dublin City University, Dublin 9, Ireland, University Greifswald, Germany, Facultad de Ciencias, Universidad Autonoma del Estado de Morelos, Nagoya University, University of Liverpool, United Kingdom, LPTP, Ecole Polytechnique, Palaiseau, France, Laboratory for Optical Physics and Engineering, Dept. of Elec. and Computer Engr., University of Illinois, Laboratory for Optical Physics and Engineering, Dept. of Elect. and Computer Engr., University of Illinois, The Ohio State University (OH), Department of Physics, University of Rajshahi, Rajshahi, Bangladesh, CAMS, Murdoch University, Australia, Drake University, USA, Gothenburg University, University of Wisconsin- Madison, University of Wisconsin-Madison, Physics Dept., Sophia University, Chiyoda-ku, Tokyo 102-855, Japan, ARC Centre for Antimatter-Matter Studies, SoCPES, Flinders University, GPO Box 2100, Adelaide, 5001 Australia, Korea Advanced Institute of Science and Technology / New York University, National Fusion Research Center / Korea Advanced Institute of Science and Technology, Korea Advanced Institute of Science and Technology and Courant Institute-NYU, Institute for Theoretical Electrical Engineering, Ruhr University Bochum, Korea Advanced Institute of Science and Technology / NewYork University, Sandia National Labs, Plasma, Pulsed-Power, and Microwave Lab, Nuclear Engineering and Radiological Sciences Dept., University of Michigan, Varian Semiconductor Equipment Associates, Gloucester, MA, Dominion University, Norfolk, VA, Sheffield Hallam University, GE Global Research, Kintech, University of Nebraska, University of Fribourg, Switzerland, CAMS, Flinders University, Australia, University of Nantes, France, CFD Research Corporation, Huntsville, AL, USA, Research Professor