Evaluation of Advanced Algorithms to improve EEDF extraction from Langmuir Probe data Using Tikhonov Regularization Methods

ORAL

Abstract

EEDF extraction from Langmuir probe data is ill-posed due to the integral relationship between the EEDF and probe current. Curve fitting of data and reconstruction of the integral problem using regularization address this to some extent, with regularized solutions offering an advantage in EEDF accuracy over curve fitting. However, both methodologies have limitations in their ability to extract accurate EEDF's over a wide energy range for moderate signal noise. The limitations confronting regularization can be summarized in over and under regularization. Over regularization captures the high energy portion of the distribution at the expense of the low energy; and vice versa with under regularization. Advanced reconstruction algorithms using weighting and iteration are studied in order to overcome such limitations. Weighting factors scale the regularized conditioning with respect to energy to decouple the regions of interest. Iterative techniques modify the regularizer and conditioning matrix to converge on an optimal solution. To illustrate this point, the reconstruction of EEDF's from probe data taken in an electronegative RF discharge is studied. The non-Maxwellian EEDF generated by this system shows many of the challenges in EEDF reconstruction for low temperature plasmas.

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Authors

  • A. El Saghir

    NCSU

  • C. Kennedy

    NCSU

  • Steven Shannon

    NCSU, North Carolina State 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. Holdings

  • 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. Holdings

  • 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. Holdings