Bayesian Reconstruction of Electron Energy Distributions from Emission Line Intensities

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

Publikation: Beitrag in Buch/Bericht/KonferenzbandSonstiger Beitrag in Buch/Bericht/KonferenzbandForschung

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.
Originalspracheenglisch
TitelMaximum Entropy and Bayesian Methods Garching, Germany 1998
Redakteure/-innenWolfgang von der Linden, Volker Dose, Rainer Fischer, Roland Preuss
Herausgeber (Verlag)Springer Netherlands
Seiten99-106
Seitenumfang8
ISBN (Print)978-94-010-5982-4 978-94-011-4710-1
PublikationsstatusVeröffentlicht - 1999

Publikationsreihe

NameFundamental Theories of Physics
Herausgeber (Verlag)Springer 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

Schlagwörter

    Dies zitieren

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

    Publikation: Beitrag in Buch/Bericht/KonferenzbandSonstiger Beitrag in Buch/Bericht/KonferenzbandForschung

    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 (Hrsg.), Maximum Entropy and Bayesian Methods Garching, Germany 1998. Fundamental Theories of Physics, Springer Netherlands, S. 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, Hrsg., Maximum Entropy and Bayesian Methods Garching, Germany 1998. Springer Netherlands. 1999. S. 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. Hrsg. / Wolfgang von der Linden ; Volker Dose ; Rainer Fischer ; Roland Preuss. Springer Netherlands, 1999. S. 99-106 (Fundamental Theories of Physics).
    @inbook{c40a8530847c44ef89be2960d2c53c8e,
    title = "Bayesian Reconstruction of Electron Energy Distributions from Emission Line Intensities",
    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.",
    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",
    author = "R. Fischer and W. Jacob and Linden, {W. Von Der} and V. Dose",
    note = "DOI: 10.1007/978-94-011-4710-110",
    year = "1999",
    language = "English",
    isbn = "978-94-010-5982-4 978-94-011-4710-1",
    series = "Fundamental Theories of Physics",
    publisher = "Springer Netherlands",
    pages = "99--106",
    editor = "Linden, {Wolfgang von der} and Volker Dose and Rainer Fischer and Roland Preuss",
    booktitle = "Maximum Entropy and Bayesian Methods Garching, Germany 1998",
    address = "Netherlands",

    }

    TY - CHAP

    T1 - Bayesian Reconstruction of Electron Energy Distributions from Emission Line Intensities

    AU - Fischer, R.

    AU - Jacob, W.

    AU - Linden, W. Von Der

    AU - Dose, V.

    N1 - DOI: 10.1007/978-94-011-4710-110

    PY - 1999

    Y1 - 1999

    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.

    AB - 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.

    KW - 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 St

    M3 - Other chapter contribution

    SN - 978-94-010-5982-4 978-94-011-4710-1

    T3 - Fundamental Theories of Physics

    SP - 99

    EP - 106

    BT - Maximum Entropy and Bayesian Methods Garching, Germany 1998

    A2 - Linden, Wolfgang von der

    A2 - Dose, Volker

    A2 - Fischer, Rainer

    A2 - Preuss, Roland

    PB - Springer Netherlands

    ER -