Determination of electron energy probability function in low-temperature plasmas from current – Voltage characteristics of two Langmuir probes filtered by Savitzky–Golay and Blackman window methods

Roh, Hyun-Joon; Kim, Nam Kyun; Ryu, Sangwon; Park, Seolhye; Lee, Seok-Hwan; Huh, Sung-Ryul; Kim, Gon−Ho

doi:10.1016/j.cap.2015.07.003

Cited by 12 publications

(6 citation statements)

References 14 publications

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“…Dependent on the applied SG filter parameters the dynamic range of the DC EEPF is typically about 1 − 2 orders of magnitude higher than accessible with the current AC system. As shown by Roh et al 8 , a better smoothing in the high electron energy tail via numerical differentiation could be obtained with the use of a Blackman filter. However, at the same time this filter can lead to a more severe distortion in the low energy range than the SG filter.…”

Section: Proof Of Conceptmentioning

confidence: 98%

“…Dependent on the noise level, chosen filtering technique (e. g. Savitzky-Golay, Gaussian or Blackman filter) and the applied filter parameters, this can lead to a severe distortion of the maximum of the second derivative and a widening of the interval between the maximum and zero of several volts 6,8,9 . Furthermore, the voltage drop across various resistances in the probe circuit can affect the I-V characteristic particularly near the plasma potential where the probe current is high and the probe-sheath resistance is low.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the voltage drop across various resistances in the probe circuit can affect the I-V characteristic particularly near the plasma potential where the probe current is high and the probe-sheath resistance is low. Without consideration of these stray voltages, which are often hardly quantifiable, the applied voltage to the probe can be overestimated and double differentiation of an even slightly distorted I-V characteristic can lead again to a flattening effect near the plasma potential 5,8 . In radio frequency (RF) discharges interfering RF voltages in the probe sheath may lead to additional distortions caused by the measurement of time-averaged probe currents 1 .…”

Section: Introductionmentioning

confidence: 99%

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Application of a Langmuir probe AC technique for reliable access to the low energy range of electron energy distribution functions in low pressure plasmas

Heiler

Friedl

Fantz

2020

Journal of Applied Physics

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The electron energy distribution function (EEDF) in low pressure plasmas is typically evaluated by using the second derivative d 2 I/dV 2 of a Langmuir probe I-V characteristic (Druyvesteyn formula). Since measured probe characteristics are inherently noisy, two-time numerical differentiation requires data smoothing techniques. This leads to a dependence on the employed filtering technique and information particularly in the region near the plasma potential can easily get lost. As an alternative to numerical differentiation of noisy probe data, a well-known AC probe technique is adopted to measure d 2 I/dV 2 directly. This is done by superimposing a sinusoidal AC voltage of 13 kHz on the probe DC bias and performing a Fourier analysis of the current response. Parameters like the modulation amplitude (up to 1.5 V) and number of applied sine oscillations per voltage step of the DC ramp are carefully chosen by systematic parameter variations. The AC system is successfully benchmarked in argon and applied to hydrogen plasmas at a laboratory ICP experiment (4 − 10 Pa gas pressure, 300 − 1000 W RF power). It is shown that the EEDF is reliably accessible with high accuracy and stability in the low energy range. Hence, a trustworthy determination of basic plasma parameters by integration of the EEDF can be provided.

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Section: Proof Of Conceptmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of a Langmuir probe AC technique for reliable access to the low energy range of electron energy distribution functions in low pressure plasmas

Heiler

Friedl

Fantz

2020

Journal of Applied Physics

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“…In each of these possibilities, some parameters are needed and may not be obvious the optimal election of them. In this work in particular, we only use the Savitzky-Golay [51,52] filter (SG), and its parameters are: (M) the degree of the polynomial and (n) the number of points (frame length).…”

Section: Using Numerical Differentiation: Savitzky-golay Filtermentioning

confidence: 99%

New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma

Gonzalez

González

Soler

et al. 2022

Plasma Res. Express

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We describe a procedure to obtain the plasma parameters from the {\bf I-V} Langmuir curve by using the Druyvesteyn equation. We propose to include two new parameters, $q$ and $r$, to the usual plasma parameters: plasma potential ($V_p$), floating potential ($V_f$), electron density ($n$), and electron temperature ($T$). These new parameters can be particularly useful to represent non-Maxwellian distributions. The procedure is based on the fit of the {\bf I-V} Langmuir curve with the $q$-Weibull distribution function, and is motivated by recent works which use the $q$-exponential distribution function derived from Tsallis statistics. We obtain the usual plasma parameters employing three techniques: the numerical differentiation using Savitzky Golay (SG) filters, the $q$-exponential distribution function, and the $q$-Weibull distribution function. We explain the limitations of the $q$-exponential function, where the experimental data $V>V_p$ needs to be trimmed beforehand, and this results in a lower accuracy compared to the numerical differentiation with SG. To overcome this difficulty, the $q$-Weibull function is introduced as a natural generalization to the $q$-exponential distribution, and it has greater flexibility in order to represent the concavity change around $V_p$. We apply this procedure to analyze the measurements corresponding to a nitrogen $N_2$ cold plasma obtained by using a single Langmuir probe located at different heights from the cathode. We show that the $q$ parameter has a very stable numerical value with the height. This work may contribute to clarify some advantages and limitations of the use of non-extensive statistics in plasma diagnostics, but the physical interpretation of the non-extensive parameters in plasma physics remains not fully clarified, and requires further research.

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“…The Blackman window w is a standard moving average window, having zero value outside a chosen interval. It has been previously used to filter I-V characteristics in EEPF applications by Magnus and Gudmundsson 27 and Roh et al 47 . The Blackman window is defined by only one filtering parameter, i.e.…”

Section: Blackman Window Filtermentioning

confidence: 99%

Data Processing Techniques for Ion and Electron Energy Distribution Functions

Caldarelli¹,

Filleul²,

Boswell³

et al. 2022

Preprint

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Retarding field energy analyzers and Langmuir probes are routinely used to obtain ion and electron energy distribution functions (IEDF, EEDF). These typically require knowledge of the first and second derivatives of the I-V characteristics, both of which can be obtained in various ways. This poses challenges inherent to differentiating noisy signals, a frequent problem with electric-probe plasma diagnostics. A brief review of commonly used analog and numerical filtering and differentiation techniques is presented, together with their application on experimental data collected in a radio-frequency plasma. The application of each method is detailed with regards to the obtained IEDF and EEDF, the deduced plasma parameters, dynamic range, energy resolution and signal distortion.

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Determination of electron energy probability function in low-temperature plasmas from current – Voltage characteristics of two Langmuir probes filtered by Savitzky–Golay and Blackman window methods

Cited by 12 publications

References 14 publications

Application of a Langmuir probe AC technique for reliable access to the low energy range of electron energy distribution functions in low pressure plasmas

Application of a Langmuir probe AC technique for reliable access to the low energy range of electron energy distribution functions in low pressure plasmas

New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma

Data Processing Techniques for Ion and Electron Energy Distribution Functions

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