EEDF Determination by Numerical Processing of the Probe Data in Neon DC Discharge

Numerical processing of the data from single probe measurements allows determination of the electron energy distribution function (EEDF) from the second derivative of the probe current. The current‐voltage probe characteristics are measured by acquisition system for further smoothing and differentiation. The developed procedure is a combination of the Savitzky‐Golay (S‐G) smoothing filter and three‐point differentiator with varying step. The above methods are modified for irregularly sampled data which enables more accurate determination of EEDF. Advantages of this approach are data smoothing with minimum information loss and improved noise reduction at the differentiation procedure. The procedure is applied for EEDF calculation in low current low pressure neon discharge. The shape of EEDF shows deviation from both Maxwellian and Druyvesteyn distributions. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of nonlocal electron kinetics and transition from αto γ regime in an RF capacitive discharge in nitrogen

The electron kinetics and regime of operation of asymmetrically coupled RF (27-MHz) nitrogen discharges in two vessels with different interelectrode gaps over the range of 0.20-0.35 torr gas pressure are studied in terms of the electron energy distribution function (EEDF). The latter is measured by means of a computer-controlled data acquisition system, a Langmuir probe with cross-modulation second derivative technique applied. The experiments are performed with an axial resolution along the RF electric field and accompanied with a measurement of electrical discharge characteristics. The effects of local and nonlocal plasma response are considered. The transition between α and γ discharge regimes is registered by measuring the EEDF and its moments' changes with the increase of the RF discharge current density     

The reliability of measurements on electron energy distribution function in silane rf glow discharges

Electron energy distribution function (EEDF) is a key parameter of plasmas, which is directly proportional to the second derivative of the probe I-V characteristics. Because of an amplifying effect of unavoidable noises in the experimental probe I-V curves during the derivation process, the experimental I-V curves should be smoothed before performing the numerical derivation. This paper investigates the effect of adjustable factors used in the smoothing process on the deduced second derivative of the I-V curves, and an optimum group of the adjustable factors is selected to make the rms deviation of the smoothed I-V curves from the measured curves less than 1%. A simple differentiation circuit is designed and used to measure the EEDF parameter straightforwardly. It is the first time, so far as we know, to measure the EEDF parameters simultaneously by means of both numerical and circuit derivative methods under the same discharge conditions and on the same discharge equipment. The deviation between two groups of mean electron energy E and electron density n_e obtained by the above different methods is within about 7%. This apparently improves the reliability of the measurements of the EEDF parameters.     

射频低压等离子体电子能量分布函数的探针诊断

本文对于无内电极放电的射频低压等离子体,采用探针电流调制法,设计并建立了三探针诊断电子能量分布函数的测量系统,测量了压力在10^-3—10^-1Torr下氮气等离子体的电子能量分布函数。从理论和实验上研究了探针鞘层上射频干扰电压对测量电子能量分布函数的影响,给出了确定射频干扰值以及对射频干扰的影响进行修正的方法,并采用该方法对实验数据进行了修正,得到了正确的电子能量分布函数。根据所得到的电子能量分布函数计算的电子平均能量,与由探针伏安特性计算得到的电子平均能量相差不超过5％,该结果间接证明了本文实验测量系统的可靠性以及对射频干扰影响进行修正的正确性。     

Non-Maxwellian electron energy distribution function in He,He/Ar,He/Xe/H<Subscript>2</Subscript> and He/Xe/D<Subscript>2</Subscript> low temperature afterglow plasma

Experimental studies of the electron energy distribution function “EEDF” under well defined conditions in flowing afterglow plasma, using a Langmuir probe are reported. The EEDF is measured in He₂ ⁺ and Ar⁺ dominated plasmas and in XeH⁺ and XeD⁺ dominated recombining plasmas. He is used as a buffer gas at medium pressures in all experiments (1600 Pa, 250 K). The deviation of the measured EEDF from Maxwellian distribution is shown to depend on plasma composition and on the processes governing the plasma decay. The influence of energetic electrons produced during the plasma decay on the body and tail of the EEDF is observed. The mechanism of energy balance in afterglow plasma is discussed.     

Electron temperature in a decaying krypton plasma in the presence of a low electric field

The influence of low electric fields on the average electron energy in an afterglow krypton plasma is studied by means of probe diagnostics and theoretical analysis. It is shown that, when the average electron energy is lower than the energy corresponding to the minimum scattering transport cross section, the degree of plasma ionization substantially affects the shape of the electron energy distribution function (EEDF). The nonequlibrium character of the EEDF results in the density dependence of the coefficient of ambipolar diffusion, which leads to a change in the radial profile of the charged particle density, an increase in the drop in the ambipolar potential across the plasma, and an increase in the rate of diffusive plasma decay. These effects substantially enhance the diffusive cooling of electrons, which is probably a decisive factor influencing the electron energy balance in high-Z noble gases.     

Determination of mean electron energy in an elevated-pressure plasma by the probe method

The possibility of determining mean electron energy from the slope of the dependence of probe electron current on probe potential under conditions of a nonequilibrium electron energy distribution function (EEDF) and electron drain to the probe is demonstrated. To accomplish this one must use the portion of the current-voltage curve (CVC) in the region of the null of the third derivative of the probe current. Given a drain parameter < 1 for a wide class of EEDF and arbitrary value of . for a rapidly falling EEDF this permits determination of <> with an accuracy of 20%. For an EEDF close to equilibrium the maximum uncertainty of <> determination by this technique does not exceed 50%.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 44–49, May, 1988.     

Electron energy distribution function in a hollow-cathode glow discharge in mixtures of nitrogen with electronegative gases

The electron energy distribution function (EEDF) in a hollow-cathode glow discharge in mixtures of nitrogen with electronegative gases is investigated. It is shown that small admixtures of SF₆ or CCl₄ to nitrogen significantly increase the number of electrons in the energy range 2–6 eV, which corresponds to the inverse part of the EEDF. In nitrogen with small admixtures of F₂ or NF₃, the EEDF differ slightly from that calculated for pure nitrogen. The EEDF in these mixtures substantially depends on electron attachment to electronegative gas molecules.     

Electron Energy Distribution Function Extraction Using Integrated Step Function Response and Regularization Methods

Recently, electron energy distribution function (EEDF) extraction techniques have been evaluated using regularized solutions to the integral problem. These techniques do not assume any mathematical representation of the EEDF and solve the integral problem for any function that best represents the EEDF. Also, unlike the more widely used point-by-point extraction of the second-derivative relationship, the integrated relationship between electron current and the EEDF is used, instead of a relatively small fraction of the integrated data in the point-by-point method. In this paper, the electron current for an arbitrary distribution function is derived, assuming that the distribution is a sum of step functions representing such a function. This technique for EEDF extraction is validated by adding noise to numerically generated data and using a regularized least squares (RLS) method to calculate the original function by solving for the individual step function contribution to the total electron current. Comparisons are then made between the expected and the reconstructed solution to evaluate its accuracy with respect to EEDF reconstruction and integrated normalization of the electron density.      

射频感应耦合Ar-N2等离子体物理特性的Langmuir探针测量及理论研究

分别通过Langmuir探针测量和动力学模型模拟方法研究了射频感应耦合Ar-N₂等离子体中电子能量分布、电子温度、电子密度等物理量随N₂含量的变化规律.实验研究结果表明：电子能量分布呈现出非Maxwell型分布,并由双温分布向三温分布过渡;电子温度在不同的气压下随N₂含量的增加呈现出不同的变化规律.在放电气压小于1.3 Pa时,电子温度随N₂含量的增加而下降;当气压大于1.3 Pa时,电子温度随N₂关键词： 感应耦合等离子体 2混合气体放电')" href="#">Ar-N₂混合气体放电 电子能量分布 Langmuir探针     

Experimental investigation of nonlocality effects in the electron energy spectrum in an electronegative gas

The nonlocality of the electron energy distribution function (EEDF) in a dc discharge in oxygen is observed experimentally. A method is developed for measuring the isotropic part of the EEDF in a low-temperature plasma of electronegative gases. The radial dependence of the EEDF and the radial distributions of the electron density, the average electron energy, and the potential are determined. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 7, 511–516 (10 April 1996)     

Substantiation of the two-temperature kinetic model by comparing calculations within the kinetic and fluid models of the positive column plasma of a dc oxygen discharge

Results from kinetic and fluid simulations of the positive column plasma of a dc oxygen discharge are compared using commercial CFDRC software (), which enables one to perform numerical simulations in an arbitrary 3D geometry with the use of both the fluid equations for all the components (fluid model) and the kinetic equation for the electron energy distribution function (kinetic model). It is shown that, for both the local and nonlocal regimes of the formation of the electron energy distribution function (EEDF), the non-Maxwellian EEDF can satisfactorily be approximated by two groups of electrons. This allows one to take into account kinetic effects within the conventional fluid model in the simplest way by using the proposed two-temperature approximation of the nonequilibrium and nonlocal EEDF (2T fluid model).     

弱电离大气等离子体电子能量分布函数的理论研究

使用球谐展开的方法求解玻尔兹曼方程,得到了弱电离大气等离子体(79％氮气和21％的氧气)的电子能量分布函数(EEDF).发现当约化电场较小时(E/N＜100 Td),EEDF在2-3 eV急剧下降,在此情况下,高能尾部比麦氏分布要小;当约化电场增加,E/N＞ 400 Td,分布函数趋近于麦氏分布;当约化电场进一步增加,E/N＞ 2000 Td,EEDF的高能尾部(超过200 eV)相对于麦氏分布增加,在高频场作用下,EEDF更倾向于麦氏分布.当ω》vm时,有效电子温度只依赖于E/ω,而与碰撞频率无关;当ω《vm时,有效电子温度只依赖于E/N,与微波频率无关.与一些单原子分子等离子体中电子-电子碰撞在电离度大于10-6时就会影响EEDF不同,空气等离子体中,只有当电离度大于0.1％时,电子-电子碰撞才会对EEDF有明显影响.     

Detailed comparison between probe density measurements of glow discharge in argon and in helium

In this article we shall look a bit more closely at some of the fundamental plasma parameters obtained by a cylindrical Langmuir probe within low-pressure electrical gas discharge plasma. The presented measurements were made in argon and in helium glow discharge plasmas. We are mainly concerned with the densities of the charged particles (electrons and ions) within the plasma and the effect of the discharge conditions upon them. The electron density is calculated from the electron current at the space potential and from the integration over the EEDF. The ion density is calculated by using the OML collisionless theory. The parameterization of Laframboise's numerical results is also used for the ion density calculation. In the range of our experimental conditions the results of plasma density, for both gases, tend to show that the ion densities measured with the OML and Laframboise theories exceeds the measured electron densities. The results also show that the plasma electron and ion densities increased with both discharge power and gas pressure.     

Variations in the electron energy distribution function in discharge plasma of a unipolar gas breakdown

It is experimentally demonstrated that the electron energy distribution function (EEDF) and electron density in plasma of a little-studied pulse discharge of a unipolar gas breakdown (UGB) significantly vary in time. The revealed behavior of its plasma parameters is explained based on the proposed physical model of a UGB discharge.     

Tonks-Langmuir problem for a bi-Maxwellian plasma

An analytical solution of the Tonks-Langmuir (TL) problem with a bi-Maxwellian electron energy distribution function (EEDF) is obtained for a plasma slab. The solution shows that the ambipolar potential, the plasma density distribution, and the ion flux to the wall are mainly governed by the cold electrons, while the ionization rate and voltage drop across the wall sheath are governed by the hot electrons. The ionization rate by direct electron impact is found to be spatially rather uniform, contrary to the T-L solution where it is proportional to the plasma density distribution. The temperature of hot electrons defined by the ionization balance is found to be close to that of the T-L solution for a mono-Maxwellian EEDF, and is in reasonable agreement with experiments carried out in a low pressure capacitance RF discharge. The energy balance for cold electrons in this discharge shows that their heating by hot electrons via Coulomb interaction is equalized by the cold electrons' escape to the RF electrodes during collapse of the RF sheath     

Transformation of the Electron Energy Distribution Function near a Rectangular Hollow Cathode

Physics of Atomic Nuclei - Using the improved method of single Langmuir probes, the electron energy distribution functions (EEDF) are obtained in a short (10 mm) discharge gap between a rectangular...     

Floating double probe in non‐Maxwellian plasmas: Determination of the electron density and mean electron energy

A theoretical study of the floating double probe based on the Druyvesteyn theory is developed in the case of non‐Maxwellian electron energy distribution functions (EEDFs). It is used to calculate the EEDF in the electron energy range larger than –e(V_f ? V_p) from the I–V double probe characteristics. V_f and V_p are the floating and plasma potential, respectively. The analytical distribution function corresponding to the best fit of EEDF in the energy range larger than e(V_f ? V_p) allows the determination of the total electron density (n_e) and the mean electron energy (<?_e>). The method is detailed and tested in the case of a theoretical Maxwell–Boltzmann distribution function. It is applied for experiments that are performed in expanding microwave plasmas sustained in argon. Analytical EEDFs determined by this method are compared with those measured by means of single probes under the same experimental conditions. A good agreement is observed between single and double probe measurements. Results obtained under different experimental conditions are used to define the best conditions to obtain reliable results by means of the double probe technique.     

Pathways in the molecular fragmentation for the C2H5OH/He electrical discharge

ABSTRACT

This study focuses on the glow discharge generated with a gases mixture of Ethanol (C₂H₅OH) and Helium (He), at different concentrations maintained at a total pressure of 2.0 Torr. We used optical emission spectroscopy (OES) to analyze the discharge mixture at different concentrations of Helium. Single Langmuir probe data was used to determine the Electron Energy Distribution Function (EEDF). For the total C₂H₅OH/He mixture plasma concentrations, the EEDF has a Maxwellian distribution function. A decrease in He concentration results in significant changes in the EEDF, this behavior is related to the increase in the C₂H₅OH percentage must increase the energy loses of the electrons in the inelastic collision with C₂H₅OH producing a significant change in the EEDF, therefore, the EEDF pattern results in an increase of electron–molecule reaction rates. The rise in electron temperature for increasing Helium percentage is explained by the decreasing electron energy loss in the inelastic collisions with C₂H₅OH molecule. It observes a decrease of electron density ne as a function of the Helium percentage, which can be related to the ratio between ionization cross sections of Helium and C₂H₆O molecule. The active species are generated in the electron-molecule processes, which are associated with electron impact dissociation of C₂H₅OH and Helium electronic impact excitation in the gas phase. The emission optical spectra (OES) show changes in the intensity of the most important peaks of the plasma mixture, which indicates the dependence in the formation of the plasma as a function of the percentage of the gases. The changes in the intensities of the same observed species are due to different processes of excitation and ionization energies of the system, in addition to the increase of He metastable states He I. Hydrogen is the main product obtained from the decomposition of C₂H₅OH.