A comparative analysis of the electron energy distribution function obtained by regularization methods and by a least-squares fitting

Gutiérrez-Tapia, C.; Llamas, Hector Flores

doi:10.1063/1.1802435

Cited by 6 publications

(1 citation statement)

References 19 publications

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“…where a n is a coefficient of V n p . We determine a n (n=0∼6) using the least-square method (LSM) [31] in V p V s because F is defined in V p V s and an approximation including all the values of V p throughout the whole range deteriorates the overall accuracy of calculated fitting curves. The functions f and g in figure 3 are given as…”

Section: Case Without Double-split-ring Resonatorsmentioning

confidence: 99%

Localized breaking of parameter uniformity by macroscopically-negative-permeability metamaterial in low-pressure microwave plasma

Iwai

Nakamura

Sakai

et al. 2020

Plasma Sources Sci. Technol.

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Measurements of plasma parameters and transmitted microwaves are performed in a composite of double-split-ring resonators (DSRRs) making magnetic permeability negative and plasmas excited by a 2.45 GHz microwave. We launch the microwave at 100-200 W, modulated by a pulse wave at a low frequency and a low duty ratio to detect time evolutions of plasma parameters. We perform the measurements at different positions with varying distance from the supporting plate of the DSRRs, and find enhanced wave transmission in the composite with nonuniform profiles of electron temperature. To reinforce the measurements of electron temperature, we evaluate the electron energy distribution function (EEDF) by deriving the second deviation of electron current, upon which data smoothing methods are applied, and the estimated EEDF becomes spatially non-uniform with a similar profile to electron temperature. In terms of the validity of results on the enhanced wave transmission, one-dimensional electromagnetic particle simulations reveal sneaking microwaves inside the composite. In comparison with cases of the negative-permeability and the passive (positive-permeability) DSRRs, we confirm that the nonuniformity is attributed to the magnetic resonance of the DSRRs, which is a microscopic effect of the DSRRs to plasma generation, whereas their macroscopic effect makes permeability negative and enhances wave energy transfer inside the composite.

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Section: Case Without Double-split-ring Resonatorsmentioning

confidence: 99%

Localized breaking of parameter uniformity by macroscopically-negative-permeability metamaterial in low-pressure microwave plasma

Iwai

Nakamura

Sakai

et al. 2020

Plasma Sources Sci. Technol.

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Measurements of the parallel ion velocity distribution at the plasma–sheath interface

Kočan

Gunn

Fuchs

et al. 2013

Journal of Nuclear Materials

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EEDF analysis of CCP plasmas using regularized reconstruction analysis of IV characteristics from an RF compensated Langmuir probe

ElSaghir

Kennedy

Shannon

et al. 2009

2009 IEEE International Conference on Plasma Science - Abstracts

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Electron energy distribution function (EEDF) extraction from Langmuir probe data is an ill-posed problem due to the integral relationship between electron current and EEDF with respect to probe voltage. Curve fitting solutions to extract this EEDF assume a specific type of distribution. Point by point extraction of the second derivative relationship uses a small fraction of the integrated data to extract the EEDF. Recently EEDF extraction techniques have been evaluated using regularized solutions to the integral problem for the collisionless, thin sheath condition. 1,2 These techniques do not assume any mathematical representation of the EEDF and solve the integral problem for any function that best represents the EEDF. Additionally, the regularized extraction of the EEDF from electron current data provides a mechanism for addressing the noise amplification effects of the reconstruction without smoothing or fitting of experimental data.In this study, this regularized extraction of the EEDF is used to study the evolution of the electron energy distribution in SF 6 and BCl 3 plasmas due to the addition of N 2 . Previous work in this regime has shown significant influence on ion density and electron energy distribution, as well as in the interaction of these discharges with GaAs in plasma etch applications. 3 This paper will present EEDF analysis of this process regime using a regularized reconstruction of Langmuir Probe VI characteristics, as well as a comparison of the regularized solution to current best known methods for both calculated electron currents and electron currents obtained from experiment.

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A comparative analysis of the electron energy distribution function obtained by regularization methods and by a least-squares fitting

Cited by 6 publications

References 19 publications

Localized breaking of parameter uniformity by macroscopically-negative-permeability metamaterial in low-pressure microwave plasma

Localized breaking of parameter uniformity by macroscopically-negative-permeability metamaterial in low-pressure microwave plasma

Measurements of the parallel ion velocity distribution at the plasma–sheath interface

EEDF analysis of CCP plasmas using regularized reconstruction analysis of IV characteristics from an RF compensated Langmuir probe

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