Bayesian Reconstruction of Electron Energy Distributions from Emission Line Intensities

R. Fischer, W. Jacob, W. Von Der Linden, V. Dose

Research output: Chapter in Book/Report/Conference proceedingOther chapter contributionResearch

Abstract

Low-pressure plasmas are nowadays widely used for technical applications of plasma-surface interactions, such as plasma etching, material deposition, sputtering, etc. For a thorough understanding of individual processes in plasma processing the electron energy distribution (EED) function in the bulk plasma is of great importance. The EED determines the rates of all electron induced reactions as ionization, excitation or dissociation of molecules. The ubiquitous assumption of a Maxwellian EED becomes progressively worse for hot and low-density plasmas. Measurements of the EED with probes penetrating the plasma result in deteriorating effects on the plasma and the probe, thus measurements without plasma contact are of great interest. A non-destructive measurement is the detection of radiation emitted by the plasma. The form-free reconstruction of the EED from a small number of measured emission intensities results in an ill-posed inversion problem. In order to avoid spurious features due to overfitting of the data (ringing) we apply Bayesian probability theory along with the adaptive-kernel method. The Bayesian approach will be applied to emission lines of helium, since in this case the relevant atomic input quantities are best known.
Original languageEnglish
Title of host publicationMaximum Entropy and Bayesian Methods Garching, Germany 1998
EditorsWolfgang von der Linden, Volker Dose, Rainer Fischer, Roland Preuss
PublisherSpringer Netherlands
Pages99-106
Number of pages8
ISBN (Print)978-94-010-5982-4 978-94-011-4710-1
Publication statusPublished - 1999

Publication series

NameFundamental Theories of Physics
PublisherSpringer Netherlands

Fingerprint

energy distribution
electron energy
plasma probes
probes
plasma etching
surface reactions
plasma density
low pressure
sputtering
distribution functions
helium
dissociation
inversions
ionization
radiation
excitation
molecules
electrons

Keywords

  • Adaptive Kernels, Artificial Intelligence (incl. Robotics), Coding and Information Theory, Discrete Mathematics in Computer Science, Electron Energy Distribution, Inverse Problem, Low-Pressure Plasma, Occam’s Razor, Over-Fitting, Probability Theory and Stochastic Processes, Statistics, general

Cite this

Fischer, R., Jacob, W., Linden, W. V. D., & Dose, V. (1999). Bayesian Reconstruction of Electron Energy Distributions from Emission Line Intensities. In W. V. D. Linden, V. Dose, R. Fischer, & R. Preuss (Eds.), Maximum Entropy and Bayesian Methods Garching, Germany 1998 (pp. 99-106). (Fundamental Theories of Physics). Springer Netherlands.

Bayesian Reconstruction of Electron Energy Distributions from Emission Line Intensities. / Fischer, R.; Jacob, W.; Linden, W. Von Der; Dose, V.

Maximum Entropy and Bayesian Methods Garching, Germany 1998. ed. / Wolfgang von der Linden; Volker Dose; Rainer Fischer; Roland Preuss. Springer Netherlands, 1999. p. 99-106 (Fundamental Theories of Physics).

Research output: Chapter in Book/Report/Conference proceedingOther chapter contributionResearch

Fischer, R, Jacob, W, Linden, WVD & Dose, V 1999, Bayesian Reconstruction of Electron Energy Distributions from Emission Line Intensities. in WVD Linden, V Dose, R Fischer & R Preuss (eds), Maximum Entropy and Bayesian Methods Garching, Germany 1998. Fundamental Theories of Physics, Springer Netherlands, pp. 99-106.
Fischer R, Jacob W, Linden WVD, Dose V. Bayesian Reconstruction of Electron Energy Distributions from Emission Line Intensities. In Linden WVD, Dose V, Fischer R, Preuss R, editors, Maximum Entropy and Bayesian Methods Garching, Germany 1998. Springer Netherlands. 1999. p. 99-106. (Fundamental Theories of Physics).
Fischer, R. ; Jacob, W. ; Linden, W. Von Der ; Dose, V. / Bayesian Reconstruction of Electron Energy Distributions from Emission Line Intensities. Maximum Entropy and Bayesian Methods Garching, Germany 1998. editor / Wolfgang von der Linden ; Volker Dose ; Rainer Fischer ; Roland Preuss. Springer Netherlands, 1999. pp. 99-106 (Fundamental Theories of Physics).
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N2 - Low-pressure plasmas are nowadays widely used for technical applications of plasma-surface interactions, such as plasma etching, material deposition, sputtering, etc. For a thorough understanding of individual processes in plasma processing the electron energy distribution (EED) function in the bulk plasma is of great importance. The EED determines the rates of all electron induced reactions as ionization, excitation or dissociation of molecules. The ubiquitous assumption of a Maxwellian EED becomes progressively worse for hot and low-density plasmas. Measurements of the EED with probes penetrating the plasma result in deteriorating effects on the plasma and the probe, thus measurements without plasma contact are of great interest. A non-destructive measurement is the detection of radiation emitted by the plasma. The form-free reconstruction of the EED from a small number of measured emission intensities results in an ill-posed inversion problem. In order to avoid spurious features due to overfitting of the data (ringing) we apply Bayesian probability theory along with the adaptive-kernel method. The Bayesian approach will be applied to emission lines of helium, since in this case the relevant atomic input quantities are best known.

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