Measurement Of Electron Energy Distribution Function Research Articles

Measurement of the electron energy distribution functions in low density RF plasmas through a tunable external RF filter

Abstract The electron energy distribution function (EEDF) measurement in radio frequency (RF) plasmas is of fundamental interests, especially in low-density RF capacitively coupled plasma. For this purpose, a new external filter with very high impedances is developed. The impedance of the filter at the fundamental and its harmonic frequencies (13.56, 27.12 and 40.68 MHz) through careful circuit design is maximized. Experimental verifications are performed by measuring the EEDFs in RF discharges. The result shows that the RF distortion in the EEDF measurement is significantly reduced by tuning the filter under various discharge conditions in an inductively coupled plasma. Accurate plasma densities can be obtained and the electron heating mode transition is observed through high-quality EEDF measurement in an capacitively coupled plasma, where RF plasma potential fluctuates severely.

Langmuir probe characterisation of an Ar–H2 non-thermal plasma loaded with carbon nanoparticles

In this contribution, we describe the development of a test-bed for the characterisation of non-thermal dusty plasmas via Langmuir probe. This technique, while allowing the precise determination of plasma parameters and electron energy distribution function (EEDF), is notoriously difficult to apply in dust-forming chemistries. We overcome this limitation by utilising a two-plasmas system in which the particle precursor, in this case acetylene, is fully consumed and converted into nanoparticles in a first plasma reactor, followed by the injection of the dust into a second plasma reactor where the Langmuir probe measurement is performed. This approach allows studying the influence of the variation of process parameters on the dusty plasma properties, all while leaving the nucleation and growth phase of the particles unaffected and fully decoupled from the discharge in which the measurement takes place. We have applied this approach to the case of graphitic carbon nanoparticles dispersed in an argon–hydrogen mixture. We have monitored the quality of the Langmuir probe measurement, and found that it is minimally affected by the presence of the graphitic particles even after several EEDF measurements. Our measurements confirm the unipolar charging of nanoparticles in non-thermal plasmas, consistent with previous observations and theoretical predictions. We also observe an unexpected trend with plasma input power: the charge carried by the particles does not monotonically increase with increased power, instead starts decreasing at sufficiently high input power levels.

Comparative analyses of plasma probe diagnostics techniques

The subject of this paper is a comparative analysis of the plasma parameters inferred from the classical Langmuir probe procedure, from different theories of the ion current to the probe, and from measured electron energy distribution function (EEDF) obtained by double differentiation of the probe characteristic. We concluded that the plasma parameters inferred from the classical Langmuir procedure can be subjected to significant inaccuracy due to the non-Maxwellian EEDF, uncertainty of locating the plasma potential, and the arbitrariness of the ion current approximation. The plasma densities derived from the ion part of the probe characteristics diverge by as much as an order of magnitude from the density calculated according to Langmuir procedure or calculated as corresponding integral of the measured EEDF. The electron temperature extracted from the ion part is always subjected to uncertainty. Such inaccuracy is attributed to modification of the EEDF for fast electrons due to inelastic electron collisions, and to deficiencies in the existing ion current theories; i.e., unrealistic assumptions about Maxwellian EEDFs, underestimation of the ion collisions and the ion ambipolar drift, and discounting deformation of the one-dimensional structure of the region perturbed by the probe. We concluded that EEDF measurement is the single reliable probe diagnostics for the basic research and industrial applications of highly non-equilibrium gas discharge plasmas. Examples of EEDF measurements point up importance of examining the probe current derivatives in real time and reiterate significance of the equipment technical characteristics, such as high energy resolution and wide dynamic range.

Effects of RF bias power on electron energy distribution function and plasma uniformity in inductively coupled argon plasma

Changes in the plasma non-uniformity and the electron energy distribution function (EEDF) by increasing RF bias power were observed in inductively coupled plasma using spatially resolved radial EEDF measurements. As the bias power was increased at a fixed ICP power at a low gas pressure, The EEDF was evolved from a bi-Maxwellian to a Maxwellian distribution. The plasma density was decreased in all radial positions and thus plasma non-uniformity was slightly changed. However, strongly improved plasma spatial non-uniformity was observed at a high gas pressure with a decrease in the center-plasma density and an increase in the radial edge-plasma density. This result could be understood by combined effects of the ion acceleration loss and the non-uniform power deposition due to the RF bias power.

Reduction of EEDF Measurement Distortion in Regularized Solutions of the Druyvesteyn Relation

Electron energy distribution function (EEDF) extraction from Langmuir probe data is an ill-posed problem due to the integral relationship between electron current and probe voltage. Both curve fitting of experimental data and reconstruction of the integral problem through methods, such as Tikhonov regularization, address this to some measure, with regularized solutions offering an advantage in overall EEDF accuracy over curve fitting. Although Tikhonov regularization provides a more accurate estimation of EEDF overall energy space, it typically also can distort the overall shape of the reconstructed distribution, particularly at high energies and energies below the distribution peak. This, combined with the relative ease of use that simple data smoothing algorithms provide, has limited the use of the more advanced reconstruction algorithms in EEDF analysis. In this paper, we will shed some light on these limitations and offer an alternative method to overcome these limitations.

Short DC Discharge with Wall Probe as a Gas Analytical Detector

AbstractA new approach leading to the development of gas analytical detectors is reported. The approach is based on measurements in the near‐cathode plasma of fine structures associated with atomic and molecular plasma processes of the high energy portion of the electron energy distribution function (EEDF). A short (without positive column) dc discharge with cold cathode and conducting walls was used. The EEDF measurements in a dc discharge are technically simpler and have dramatically better sensitivity than in the afterglow since temporal resolution is not required. Additional increased probe sensitivity is achieved by using a large‐area, larger‐radius‐of‐curvature conducting wall as the probe instead of the more common thin cylindrical Langmuir probe. The wall probe, being almost flat, also greatly reduces the ion current contribution to the measurements. The new approach allows for the development of micro‐analytical, dc plasma electron spectroscopy (PLES) gas detectors that are operational up to atmospheric pressure (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dynamic investigation of mode transition in inductively coupled plasma with a hybrid model

Industrial inductively coupled plasma (ICP) sources are always operated in low gas pressure 10–100 mTorr, therefore in order to accurately investigate the mode transition of ICP, we developed our pure fluid model (2009 J. Appl. Phys. 105 083306) into a hybrid fluid/Monte Carlo (MC) model, where the MC part is exploited to take in more dynamic characteristics of electrons and self-consistently calculate the rate coefficients and electron temperature used in the fluid module, and more crucially to study the electron energy distribution function (EEDF) evolution with mode transition. Due to the introduction of the nonlocal property of the electrons at relatively low pressures, the dependences of the plasma density on the coil current, including the mode transitions, are distinctly different at low and high pressures when simulated by this improved hybrid model (HM), while the trends for different pressures obtained from the original pure fluid model (PFM) are the same in all cases. Furthermore, the computed peaks of the electron density profile by the HM shift from the discharge centre in the E mode to the intense inductive field heating area (about half of the radius of the reaction chamber under the dielectric window) in H mode. In addition, the electron temperature profiles of two modes under different pressures simulated by HM are totally higher than the results of PFM. When the pressure is low, there is a minimum exhibited in the bulk plasma of the electron temperature profiles of the E mode, and along with the mode transition the distribution area of low temperature is substantially reduced. Moreover, this phenomenon disappears when the gas pressure is increased. Accompanied by this, the calculated EEDF of the E mode in the low pressure also demonstrates an absolutely dominant low energy electron fraction (about ⩽5 eV); while transforming to the H discharge most of the electrons carry an energy of 1–10 eV. The tendencies of the calculated EEDF evolution with mode transition under relatively high pressures agree well with the experimental measurements of EEDF of Lee et al (2009 Appl. Phys. Lett. 90 191502), but the determination mechanisms are still in dispute and require further examination.

Measurements of EEDF in recombination dominated afterglow plasma

Electron energy distribution functions (EEDF) have been measured in decaying plasma in Flowing Afterglow Langmuir Probe (FALP) experiment. The measurements have been carried out in diffusion and recombination governed plasmas used for studies of recombination of KrD+ and H3+ ions.

Operation of an Annular Helicon Plasma Source

The plasma parameters of a nominally 1.5 kW annular helicon plasma source are measured and its feasibility as an ionization stage of a two-stage Hall thruster is investigated. All experiments are performed in a 4 by 7 m stainless steel vacuum chamber at pressures below 3.1 x 10 ―5 torr for argon and 5.6 x 10 ―5 torr for xenon. Ion number density, electron temperature, and electron energy distribution function measurements are taken at several axial and radial locations inside the device at each operating condition with a ratio-frequency-compensated Langmuir probe. The annular helicon plasma source is characterized over a range of applied radio frequencies (2―14 MHz), magnetic field strengths (0―400 G), and radio frequency forward-power settings (100―1400 W) for both argon and xenon propellants. The peak ion number density measured in the annular helicon is 2.6 x 10 17 m ―3 for argon and 2.4 x 10 17 m ―3 for xenon at 1000 W of radio frequency power. The annular helicon electron energy distribution function peak and shape vary with the radio frequency, from a minimum of 3.7 eV at 13 MHz to a maximum of 15.0 eV at 11 MHz for argon propellant over the preceding operating conditions.

On the first derivative probe method for electron energy distribution function measurements in tokamak edge plasma

The applicability of the first derivative Langmuir probe method in strongly magnetized tokamak plasmas is discussed. The method is used for processing the electron part of the current-voltage (IV) probe characteristics measured in the CASTOR tokamak edge plasma (Institute of Plasma Physics, Association EURATOM-IPP, Prague, Czech Republic). The comparison of the results obtained with the results given by the Stangeby method yields a satisfactory agreement.

Hysteresis and mode transition in terms of electron energy distribution function for an inductively coupled argon discharge

The electron energy distribution function (EEDF) with respect to the hysteresis loop of an inductively coupled argon discharge has been studied experimentally. Contrary to H mode, knowledge of EEDF in E mode is still limited, and an elaborate EEDF measurement with regard to power and pressure for this mode is presented. The Langmuir probe measurements reveal two regions with distinct EEDFs in E mode, which might be a critical missing factor in explaining the unresolved hysteresis and mode transition phenomenon of inductive discharges. Furthermore, a Poynting vector representation has been used to explain the power coupling in an inductive discharge, where (azimuthal) eθ component is proposed to be dominant in the “hybrid mode” region.

EEDF measurements in plasma expansion region of a high-frequency driven hydrogen discharge

The production of negative hydrogen ions by volume processes depends on the electron energy in the expansion region of a plasma source. The study presents experimental results for the electron energy distribution function (EEDF) obtained by probe diagnostics in this region. Measurements are performed in axial and radial directions at low gas pressures. The results for the EEDF show that its shape changes along the chamber axis because the plasma density and the electron temperature decrease to a nearly constant value in the main part of the expansion chamber. The EEDF is Maxwellian-like with tail up to 40 eV close to the driver. The nonlocal formation of the EEDF is experimentally obtained in expanded plasma.

EEDF probe measurements: differentiation methods, noise, and error

An instrumentation approach to electron energy distribution function measurements using Langmuir probes is presented. The noise and error limitations of the most common differentiation techniques are analysed, it is shown how instrumental accuracy can be improved or how acquisition time can be drastically decreased, and a pertinent performance comparison of the harmonic vs. the numerical differentiation schemes is made. In addition, we stress the nasty effects of pink and of coherent noise, and we show how they can be minimised.

Measurement of EEDF and distribution of primary electrons in a bucket ion source

A tool for investigating the electron energy distribution function (EEDF) in plasmas was developed and used to study the primary electron behaviour in a bucket type ion source. The spatial variation of the EEDF in filter magnetic fields, which optimize the negative ion production, is extensively studied. It is verified that the high energy component of the EEDF damped over a shorter characteristic length than the low energy component. Similar behaviour is also observed and studied in the cusp regions of the plasma.

Electron Energy Distribution Function Measurements in an Inductively Driven Tandem Plasma Source

AbstractSummary: Electron energy distribution functions (EEDF) are obtained from probe measurement data along the axis of the metallic chamber of an inductively driven tandem plasma source. The numerical procedure for calculating the second derivative of the probe current combines Savitzky‐Golay smoothing filter and the three‐point differentiator with a varying step. The EEDF is obtained through the Druyvesteyn formula from the calculated second derivative. The shape of the EEDFs in argon gas at low pressures is investigated for the case of a tandem plasma source. Experimental EEDFs are compared with Maxwellian distributions, and deviations in the tail are observed at higher pressures, which are explained in terms of the ratio between the electron‐electron collision frequency and the excitation frequency. Axial variations of the slope and of the area below the EEDF curve result in electron temperature and concentration decrease along the axis.Electron energy distribution function (EEDF) measured for gas pressure of 26 mTorr, at an axial position of 12 cm.imageElectron energy distribution function (EEDF) measured for gas pressure of 26 mTorr, at an axial position of 12 cm.

Dependence of plasma characteristics on dc magnetron sputter parameters

Plasma discharge characteristics of a dc magnetron system were measured by a single Langmuir probe at the center axis of the dual-side process chamber. Plasma potential, floating potential, electron and ion densities, and electron temperature were extracted with varying dc power and gas pressure during sputter deposition of a metal target; strong correlations were shown between these plasma parameters and the sputter parameters. The electron density was controlled mostly by secondary electron generation in constant power mode, while plasma potential reflects the confinement space variation due to change of discharge voltage. When discharge pressure was varied, plasma density increases with the increased amount of free stock molecules, while electron temperature inversely decreased, due to energy-loss collision events. In low-pressure discharges, the electron energy distribution function measurements show more distinctive bi-Maxwellian distribution, with the fast electron temperature gradually decreases with increased gas pressure.

Measurements of electron energy distribution functions and electron transport in the downstream region of an unbalanced dc magnetron discharge

In this study, electron energy distribution functions (EEDFs) are measured using a Langmuir probe in conjunction with the ac superposition method in the downstream region of a planar and unbalanced magnetron argon discharge and the effects of an anode sheath boundary on the discharge characteristics are investigated. The potential of the anode sheath can be controlled by applying a dc voltage to the substrate, and the nonlinear behaviour of the plasma potential with respect to the dc substrate voltage causes the distinctive evolution of the potential of the anode sheath. It is found that when the potential of the anode sheath reaches a specific value, which is related to the threshold energies of argon for the inelastic collisions, an outstanding EEDF transition from a bi-Maxwellian distribution to a single Maxwellian distribution occurs. We introduce the concept of the total electron bounce frequency as an indicator of how the electron collisions such as the electron–electron collision and the inelastic collisions affect the EEDF features as the potential of the anode sheath changes. This result provides the decisive clue to explaining the appearance of the bi-Maxwellian distribution in magnetron discharges. The results of the spatially resolved measurements of EEDF and plasma characteristics are also presented. From these results, we will discuss the electron transport in the downstream region in detail.

Langmuir probe and mass spectrometric measurements in inductively coupled CF4 plasmas

Electron and ion energy distribution functions and other plasma parameters such as plasma potential (Vp), electron temperature (Te) andelectron and ion number densities (ne and ni) in low-pressure CF4 plasmas have been measured. The experiments were conducted in a GEC cell using an inductively coupled plasma device powered by a 13.56 MHz radiofrequency (rf) power source. The measurements were made at 300 W of input rf power at 10, 30 and 50 mTorr gas pressures. Langmuir probe measurements suggest that ne, ni and Vp remain constant over 60% of the central electrode area, beyond which they decrease. Within the limits of experimental error (±0.25 eV), Te remains nearly constant over the electrode areaand peaks towards the electrode edge before falling rapidly. Te and Vp increase with a decrease in pressure. ne and ni are not affected as significantly as Te or Vp by variation in the gas pressure. The electron energy distribution function measurements indicate a highly non-Maxwellian plasma. CF3+ is the most dominant ion product of the plasma, followed by CF2+ and CF+. Significant amounts of etch products, SiFx/COFx(x = 0-3), of the quartz window were also detected. The concentrations of CF2+ and CF+ are much larger than that is possible from direct electron impact ionization of the parent gas. The cross-section data suggest that the direct electron impact ionization of fragment neutrals and negative ion production by electron attachment may be responsible for increase of the minor ions.

Observation of a plasma-sheath resonance in a parallel-platelow-pressure rf discharge

An experimental method for the observation of a plasma-sheathresonance in a low-pressure rf capacitively coupled discharge was proposed.The method is based on secondary electron energy distribution functionmeasurements. It was shown that the plasma-sheath resonance potentialfluctuations could be observed as peaks at the secondary electron energyspectra. Depending on discharge conditions, the resonant oscillation was detected on the frequency in the range 21-30 harmonics of the driven frequency.The experimental determination of the plasma-sheath resonancefrequency provides the possibility for independent measurement of the plasmadensity. Thus, this method can be used as a plasma density diagnostic inlow-pressure capacitive discharges.

Temporally and spatially resolved plasma parameters and EEDF measurements in a low-frequency discharge

A time-resolved Langmuir probe technique is used to measure the dependence of the electron density, electron temperature, plasma potential and electron energy distribution function (EEDF) on the phase of the driving voltage in a RF driven parallel plate discharge. The measurements were made in a low-frequency (100-500 kHz), symmetrically driven, radio frequency discharge operating in H2, D2 and Ar at gas pressures of a few hundred millitorr. The EEDFs could not be represented by a single Maxwellian distribution and resembled the time averaged EEDFs reported in 13.56 MHz discharges. The measured parameters showed structure in their spatial and temporal dependence, generally consistent with a simple oscillating sheath model. Electron temperatures of less than 0.1 eV were measured during the phase of the RF cycle when both electrodes are negative with respect to the plasma.