Langmuir Probe Characterization of a RF Discharge Excited in Ar/C2F3Cl Mixtures during Plasma Deposition Processes

The apparatus for measurements of probe characteristic and its second derivative during plasma assisted thin film deposition is described. To avoid the probe surface contamination an impulse method combined with ion bombardment of the probe surface was used. Experimental evidence of the effectiveness of this method in the discharge fed with Ar/C₂F₃Cl mixtures is given. Measurements of the second derivative of the probe current have indicated an electron distribution different from the Maxwellian. Negative ions have been found in the discharge, the concentration of which has been estimated to be at most by one order of magnitude higher than the electron density.     

The Influence of the Fluctuation Amplitude on the Probe Characteristic

The time-averaged probe current is calculated by using a sampling method for sinusoidal and sawtooth-like oscillations of the space potential. The effect of oscillations on the measured plasma parameters obtained with the aid of the single probe method, double probe method and the method of the second derivative of the probe characteristic is discussed, with the electron saturation current being taken into account. In the ion current the values r_p/λ_D, λ/r_p and M_i characterizing the working regime are varied. The calculated results are checked by corresponding measurements in a beam generated plasma.     

A contribution to the assessment of the influence of collisions on the measurements with Langmuir probes in the thick sheath working regime

In the present work we investigate theoretically and experimentally the influence of elastic collisions in a probe sheath on a cylindrical Langmuir probe. The analysed probe working regime covers conditions under which the following probe characteristic parameters are comparable: the probe radius, the Debye length and both the ion and electron mean free paths.The preliminary investigations under almost collisionless conditions show good agreement between theoretical and experimental values of the ion saturation currents and of the floating potentials only when the ion currents for the studied working regime of the cylindrical Langmuir probe are calculated according to the theory of Chen (Plasma Phys.7 (1965)47). These collisionless currents form the basis for the calculation of the collision-corrected probe characteristics according to the presented procedure by Talbot and Chou (Rarefied Gas Dynamics, Academic Press, New York, 1966, p. 1723).The applied theoretical analysis covers the influence of the collisions on the electron and ion current of the single probe characteristic and on the estimation of the space potential. The results of the calculations are presented in graphical overviews for the series of cases of practical importance. The other working regimes can be covered using the calculating procedure presented.For comparison of the calculated collision-corrected characteristics with those from an experiment we used the positive column plasma of the He glow discharge where the electron density is known and the space potential can be experimentally estimated from the lowest excitation potential of He. The comparison was carried out for the ion and electron currents, the floating potential and the zero-cross of the probe characteristic second derivative.The estimation of the secondary electron current contribution to the total probe current shows that it limits the applicability of the collision-corrected probe characteristic to the plasma diagnostic in the transition to the collision-determined working regime.     

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.     

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)     

Measurement of the electron energy distribution function in flame plasma at atmospheric pressure

The measurement of the electron distribution function in the lighting gas flame plasma at atmospheric pressure is described. The influence of the collision in the probe sheet and the ion current component is investigated. The experimental results show that the second derivative method for measurement of the electron distribution function is valid for sufficiently negative biassed probe.     

Determination of the electron energy distribution in a plasma from the first and second derivatives of the probe current

An approach to the reconstruction of the electron energy distribution function (EEDF) as the sum of the second derivative of the electron current to the probe and some value proportional to its first derivative is proposed (hereafter we mean derivatives with respect to voltage). Solutions to model problems for typical electron distributions in a plasma show that this approach lowers the systematic error of EEDF reconstruction by several times in comparison with the conventional techniques using Langmuir and diffusion probes. The approach is applicable in a wide range of the ratio of the probe radius to the free path of electrons. It can be used for the determination of fast nonequilibrium electron distribution in neon discharge afterglow and also for the evaluation of the Maxwellian electron temperature in the low-energy range of nitrogen discharge afterglow.     

Langmuir Probe Diagnostics of a Low Temperature Non-Isothermal Plasma in a Weak Magnetic Field

This article presents measurements by a cylindrical Langmuir probe in the plasma of a DC cylindrical magnetron discharge át the pressure 1.5 Pa that aim at the experimental assessment of the influence of a weak magnetic field to the estimation of the electron density when using conventional methods of probe data interpretation. The probe data was obtained under the presence of a weak magnetic field in the range 1.10^?2?5.10^?2 T. The influence of the magnetic field on the electron probe current is experimentally assessed for two cylindrical probes with different radii, 50 μm and 21 μm. This assessment is based on comparison of the values of the electron density estimated from the electron current part with the values of the positive ion density estimated from the positive ion current part of the probe characteristic respectively by assuming that at the magnetic field strengths used in the present study the probe positive ion currents are possible to be assumed as uninfluenced by the magnetic field. For interpretation of the probe positive ion current two theories are used and compared to each other: the radial motion model by Allen, Boyd and Reynolds [10] and Chen [11] and the model that accounts for the collisions of positive ions with neutrals in the probe space charge sheath that we call Chen-Talbot model [8]. At lower magnetic field 3 · 10^?2 T the positive ion density values interpreted by using the Chen-Talbot model [8] are in better agreement with the values of electron density compared to those obtained by using the theory [10,11]; therefore the model [8] is used for calculation of the positive ion density from the probe data at higher magnetic fields. The comparison of the positive ion and electron density values calculated from the same probe data at higher magnetic fields shows that up to the magnetic field strength 4 . 10^?2 T with the probe 100 μm and up to 5 . 10^?2 T with the probe 42 μm in diameter respectively the decrease of the magnitude of the electron current at the space potential due to the magnetic field does not exceed the error limits that are usual for Langmuir probe measurements (absolute error ±20%).     

Investigation of a Drifting Plasma Containing Negative Ions by Cylindrical Langmuir Probe Ion Mass Spectrometer

The study of drifting plasma in the laboratory or the ionsphere is not a straightforward problem because of the many variables such plasma will encounter. The presence of negative ions will add to the complication due to the detachment mechanism and other physical processes. It is not easy to separate the negative ion current component from the electron current component. To study negative ion population and mass spectra in the lower ion-sphere the value of the mean free path ? and the Debye shielding radius ?o of the medium should be taken into consideration together with the collision frequency of the different charged particles. Cylindrical Langmuir probes have been used successfully as dianostic techniques for the drifting plasma. A cylindrical probe of suitable radius in relation to ? and ?o was chosen. The probe was swept by a composite wave-form which contained a sawtooth sweep and two audio -frequency signals. The experiment was flown on board a stabilised rocket "Centaure" at high latitudes at Norway. The outputs yielded information about : 1. The first derivative of the current i with respect to the applied probe voltage -V 2. Percent modulation from which d2 i/dv2 was obtained. The second derivative is a function of the energy distribution function of the charged particles. The negative ion Gaussian peaks of energy are easily detached on the energy distribution function graph from those of thermal electrons.     

Experimental Study of the Creation of a Fire‐rod I: Temporal Development of the Electron Energy Distribution Function

Positive voltage steps are applied to a planar electrode (collector) immersed in a magnetized discharge plasma column with its surface perpendicular to the magnetic field lines. If the voltage step and the neutral gas pressure are high enough additional ionization occurs in front of the collector and a fire‐rod is created. Time resolved measurements of the plasma response are performed by a one‐sided plane Langmuir probe using standard boxcar technique. The temporal development of the electron energy distribution function after the application of a positive voltage step to the collector is measured by a one‐sided plane Langmuir probe. In a magnetized plasma the electron energy distribution function is proportional to the first derivative of a plane Langmuir probe characteristics. It is found that immediately (∼1 μs) after the application of a positive voltage step to the collector a short lifetime electron population is created. This electron population disappears in approximately 2 μs. It is related to the anomalously large initial electron current collected by the collector “current overshoot”. When the initial current overshoot to the collector is terminated, a high potential (anode) plasma starts to form in front of the collector if the voltage step and the pressure are high enough. The formation of the anode plasma electron population is followed experimentally.     

Langmuir probe in magnetized plasma: Study of the diffusion parameter

In low-temperature magnetized plasma, Langmuir probe measurements must be corrected because of the electron diffusion through the sheath, which is formed around the probe collector. The correction factor, which is called the electron diffusion or electron sink parameter, depends on many other parameters such as the probe geometry, the electron diffusion coefficient, the sheath thickness, or the potential profile through the sheath. Based on a previous work, we determine the values of this parameter under different experimental conditions and we study the effect of the electron energy, of the probe-biased voltage, and of the magnetic field intensity on this parameter. The results are compared with theoretical models published in the literature. An empirical equation is determined to fit the diffusion parameter value versus magnetic field intensity.     

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     

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.     

Is the Collecting Surface of a Flat One-Sided Probe Constant when Measuring the Ion Distribution Function?

The correctness of the known plane single-ended probe method for measuring the anisotropic ion distribution functions in a gas-discharge plasma has been considered. Analysis has been performed for positive probe potentials relative to the plasma with magnitudes on the order of the mean ion energy, which as a rule is much lower than the mean electron energy. We have analyzed the dependence of the collection surface area of a plane probe on its potential in this range. The structure of the near-probe layer has been determined for an isotropic electron distribution function of the Maxwellian or Druvestein type and an anisotropic ion distribution function. These results are used to derive analytic relations for the correction to the second derivative of the probe current with respect to the plane probe potential. It has been shown that, when the ion distribution function is measured in a wide range of conditions in the gas-discharge plasma, when the approximation of a collisionless probe layer is applicable, and the probe does not perturb the plasma, the dependence of the collection surface area of the probe on the potential can be disregarded in this range.     

Langmuir单探针诊断射频辉光放电等离子体及其数据处理

Langmuir探针是诊断等离子体参数的重要手段.报道了在氩气射顿(13.56MHz)辉光放电等离子体中使用调谐单探针进行诊断,对探针I-V特性曲线的统计噪声进行了数字滤波的光滑化处理,而后求二次微商.在相同的放电条件下,使用自行设计的微分电路,对探针特性二次微商进行在线测量.这两种方法得到的二次微商结果能够较好地符合. 关键词： Langmuir探针 二次微商 数值滤波 微分电路     

Measurement of electron distribution function by means of direct differentiation of probe characteristic

Conclusion Using the above described method we measured the electron distribution function in homogeneous positive column of a low-pressure discharge for different repetition frequencies and different time intervals of recording the probe characteristic. An example of the second derivative of the probe charecteristic measured at a repetition frequency of 1 kHz is shown in Fig. 3. The probe characteristic was recorded in 10 us intervals, i.e. 0.01 period.The method can be easily applied for measurements in a steady state as well as in a periodically changing discharge. Substantial advantage of this method lies in the possibility to measure the electron distribution function and its changes during short time intervals (of the order of several us), which enables to apply the method for measurements in unstable and extinguishing plasmas.Works on improving this method even further are presently under way; they are focussed in the first place on using this method for the measurements of the electron distribution function in an extinguishing plasma, where the maximum of electron distribution function lies at energies of the order of 0.1 eV. The method of superimposing a small harmonic signal on the probe bias is virtually impracticable for such low energies, because this method gives accurate results only for the probe voltages that are much higher than the amplitude of superimposed signal.The procedure for testing the correct operation of the apparatus and its accuracy in determining the second derivative, as described above, is applicable also for other methods used in differentiating the probe characteristic, where only indirect methods were used so far.     

射频辉光放电等离子体的电探针诊断及数据处理

Langmuir探针是等离子体诊断的一个重要方法.对探针I-V曲线进行求解二次微商是获得等离子体中的电子能量分布函数的关键.由Fourier变换导出一个求解微商的数值解方法.克服了现有方法所存在的缺点.实现了对探针I-V曲线求解二次微商的精确、自动运算.测量了硅烷射频辉光放电等离子体的平均电子能量(温度)和浓度随放电功率的变化. 关键词：     

Comment on determination of electron temperature from Langmuir probe data in tokamak edge plasma

Langmuir probe measurements of electron temperature in a plasma in the limiter shadow of a tokamak are presented together with a method of probe data analysis which takes into account the influence of the ion current vs voltage dependence in the determination of electron temperature, The method is based on the transformation of a single into a double probe characteristic. Values of the electron temperature calculated using this method are compared with the values estimated from single probe characteristic data.     

Relation between the Grüneisen ratio and the pressure dependence of Poisson's ratio for metals

The Grüneisen ratio of crystalline solids is shown to be dependent on a parameter n whose values are characteristic of each solid, and can be determined by two independent ways: from experimental shock data and from the pressure derivative of Poisson's ratio. The determinations are made for several metals, using data on the pressure derivatives of polycrystalline elastic moduli or of the second order elastic constants measured on single crystals, and giving the pressure derivatives of Poisson's ratio by means of the Voigt-Reuss-Hill averaging procedure. The values of the parameter n deduced from shock data are found to be in good agreement with those deduced from the pressure derivatives of Poisson's ratio. Positive and negative values of parameter n correspond respectively to increasing and decreasing Poisson's ratio with increasing pressure. Discussion of the results is made using the linear and the quadratic relationships between shock velocity and particle velocity. It is shown that shock wave data cannot yield directly an accurate estimation of the derivative of the initial slope of the Hugoniot.