A novel approach for calculating the plasma resonance behavior excited by wall-integrated planar diagnostic probes with arbitrary geometry

ORAL

Abstract

Active Plasma Resonance Spectroscopy (APRS) is a diagnostic technology that makes use of the natural ability of plasmas to resonate on or near the plasma frequency. Different from the passive plasma resonance spectroscopy, which observes the excitation already existing in the plasma, APRS could obtain important plasma parameters such as electron density or temperature by establishing reliable mathematical relations to the recorded spectral response from the dynamic interaction between plasma and the radio frequent signal (usually in the GHz range) by the probe. Among all the types of probe designs, wall-integrated planar diagnostic probes provide the optimal condition for monitoring plasmas by introducing the minimum undesired disturbance. In this work, a novel approach is presented which allows to determine the dynamic interaction by separating the calculation of the dissipated energy inside the wall-integrated planar diagnostic probe with an arbitrary geometry from the rest part of the computation regions, where the cold plasma model is applied. The advantage of this approach is shown for different available designs and can be utilized by more sophisticated plasma models and even more complicated probe configurations.

–

Publication: [1] The multipole resonance probe: characterization of a prototype ,M. Lapke et al., Plasma
Sources Sci. Technol. 20, 042001 (2011).
[2] Plasma Resonance in a Radio-Frequency Probe,K. Takayama, H. Ikegami, und S. Miyazaki,
Phys. Rev. Let. 5, 238 (1960).
[3] High-Frequency Dielectric Resonance Probe for the Measurement of Plasma Densities,A. M.
Messiaen and P. E. Vandenplas, J. Appl. Phys. 37, 1718 (1966)
[4] RF Admittance Measurements of a Slotted-Sphere Antenna Immersed in a Plasma,J. A. Waletzko
and G. Bekefi, Radio Sci. 2, 489 (1967).
[5] The impedance of a dipole antenna in the ionosphere: 1. Experimental study,N. Vernet, R.
Manning, and J. L. Steinberg, Radio Sci. 10, 517 (1975).
[6] Measurement of absolute electron density with a plasma impedance probe ,D. D. Blackwell,
D. N. Walker, and W. E. Amatucci, Rev. Sci. Instrum 76, 023503 (2005).
[7] Plasma Absorption Probe for Measuring Electron Density in an Environment Soiled with
Processing Plasmas,H. Kokura, K. Nakamura, I.P. Ghanashev, and H. Sugai, Japan. J. Appl.
Phys 38, 5262 (1999).
[8] Practical implementation of a two-hemisphere plasma absorption probe ,C. Scharwitz, M.
Böke, J. Winter, M. Lapke, T. Mussenbrock, and R. P. Brinkmann, Appl. Phys. Lett. 94,
011502 (2009).
[9] The multipole resonance probe: A concept for simultaneous determination of plasma density,
electron temperature, and collision rate in low-pressure plasmas ,M. Lapke, T. Mussenbrock,
and R. P. Brinkmann, Appl. Phys. Lett. 93, 051502 (2008).
[10] Interaction of an antenna with a hot plasma and the theory of resonance probes ,J. A. Fejer,
Radio Sci. 68D, 1171 (1964)
[11] THE BEHAVIOR OF THE RESONANCE PROBE IN A PLASMA ,R. S. Harp, Appl. Phys.
Lett. 4, 186 (1964)
[12] Characteristics of the Plasma Resonance Probe ,R. S. Harp and F. W. Crawford, J. Appl.
Phys. 35, 3436 (1964)
[13] Characteristics of Resonance Probes ,T. Dote and T. Ichimiya, J. Appl. Phys. 36, 1866 (1965).
[14] An Investigation of Boundary Theories for the Resonance Probe ,R. J. Kostelnicek, Radio
Sci. 3, 319 (1968).
[15] Linear and Nonlinear Response of a Plasma Sheath to Radio Frequency Potentials ,A. J.
Cohen and G. Bekefi, Phys. Fluids 14, 1512 (1971).
[16] The impedance characteristic of a spherical probe in an isotropic plasma ,J. Tarstrup and W.
J. Heikkila, Radio Sci. 4, 493 (1972).
[17] Impedance of an ion-sheathed spherical probe in a warm, isotropic plasma ,T. Aso, Radio Sci.
8, 139 (1973).
[18] Radio-Frequency Probes in a Nonlinear Isotropic Plasma ,C. C. Bantin and K. G. Balmain,
Can. J. Phys. 52, 291 (1974).
[19] A novel technique for plasma density measurement using surface-wave transmission spectra
,S. Dine, J.P. Booth, G.A Curley, C.S. Corr, J. Jolly, and J. Guillon, Plasma Scources Sci.
Technol. 14, 777 (2005).
[20] On collisionless energy absorption in plasmas: Theory and experiment in spherical geometry
,D. N. Walker, R. F. Fernsler, D. D. Blackwell, W. E. Amatucci, and S. J. Messer, Phys.
Plasmas 13, 032108 (2006).
[21] Modeling and simulation of the plasma absorption probe ,M. Lapke, T. Mussenbrock, R. P.
Brinkmann, C. Scharwitz, M. Böke, and J. Winter, Appl. Phys. Lett. 90, 121502 (2007).
[22] Simulation of resistive microwave resonator probe for high-pressure plasma diagnostics ,J.
Xu, K. Nakamura, Q. Zhang, and H. Sugai, Plasma Sources Sci. Technol. 18 045009, (2009).
[23] Advanced high-pressure plasma diagnostics with hairpin resonator probe surrounded by film
and sheath ,J. Xu, J. Shi, J. Zhang, Q. Zhang, K. Nakamura, and H. Sugai, Chinese Phys. B
19 075206, (2010).
[24] Experimental and Simulational Studies on the Theoretical Model of the Plasma Absorption
Probe ,B. Li, H. Li, Z. Chen, J. Xie G. Feng, and W. Liu, Plasma Sci. Technol. 12, 513 (2010).
[25] Modeling Microwave Resonance of Curling Probe for Density Measurements in Reactive
Plasmas ,I. Linag, K. Nakamura, and H. Sugai, Appl. Phys. Express 4, 066101 (2011)
[26] Active plasma resonance spectroscopy: a functional analytic description ,M. Lapke, J. Ober-
15
rath, T. Mussenbrock und R. P. Brinkmann, Plasma Scources Sci. Technol. 22, 025005 (2013).
[27] Active plasma resonance spectroscopy: eigenfunction solutions in spherical geometry ,J. Oberrath and R. P. Brinkmann, Plasma Sources Sci. Technol. 23, 065025 (2014)
[28] The Multipole Resonance Probe: Progression and Evaluation of a Process Compatible Plasma
Sensor ,C. Schulz and I. Rolfes, IEEE Sensors Journal 14 Issue: 10,Sensors Applications
Symposium (SAS), IEEE (2014)
[29] M. Friedrichs and J. Oberrath,"The planar multipole resonance probe: a functional analytic
approach," EPJ Techn Instrum, vol. 5, Aug. 2018.
[30] M. Friedrichs, D. Pohle, I. Rolfes and J. Oberrath, "Planar Multipole Resonance Probe:
Comparison of Full-wave Electromagnetic Simulation and Electrostatic Approximation," 2019
Kleinheubach Conference, 2019, pp. 1-3.
[31] C.Wang, M. Friedrichs, J.Oberrath and R.P. Brinkmann 2021 Plasma Sources Sci. Technol.
30 105011
[32] The Planar Multipole Resonance Probe: Challenges and Prospects of a Planar Plasma Sensor,
C. Schulz, T. Styrnoll, P. Awakowicz and I. Rolfes, IEEE Transactions on Instrumentation
and Measurement 64, 14981187 (2015)
[33] Flat cutoff probe for real-time electron density measurement in industrial plasma processing,
H J Yeom et al 2020 Plasma Sources Sci. Technol. 29 035016

Presenters

  • Peng Liang

    South Westphalia University of Applied Science Soest

Authors

  • Michael Friedrichs

    South Westphalia University of Applied Science Soest

  • Peng Liang

    South Westphalia University of Applied Science Soest

  • Chun Jie Wang

    Ruhr-University of Bochum

  • Ralf Peter Brinkmann

    Ruhr-University of Bochum, Institute of Theoretical Electrical Engineering, Faculty of Electrical Engineering and Information Technology, Ruhr-University Bochum, Germany

  • Jens Oberrath

    South Westphalia University of Applied Science