Low-pressure RF Discharge Research Articles

Calculation of discharge parameters in low-pressure diode-type radio frequency noble gas plasmas

A self-consistent model of capacitively coupled low-pressure rf discharge is formulated. The non-local mechanism of electron heating is considered under simple assumption about the plasma density profile. The transition of electron heating from the plasma body to electrode sheaths is observed. The criterion of a heating mode transition is formulated and expressed in terms of external discharge parameters. The asymptotic solutions for low- and high-current regimes are obtained. The comparison of calculation results with experimental data demonstrates the validity of the proposed model for a wide range of discharge conditions.

Rf breakdown of low-pressure gas and a novel method for determination of electron-drift velocities in gases

This paper reports the results of the detailed and comprehensive experimental and theoretical treatment of the rf gas breakdown. We give the measured breakdown curves of the low-pressure rf discharge in argon, hydrogen and air in a broad range of gas pressures and interelectrode distances. The different processes of generation and loss of charged particles participating in the rf gas breakdown are discussed. We suggest to distinguish the following sections on the rf discharge breakdown curves: multi-pactor, Paschen, diffusion-drift and emission-free ones. The analytic gas breakdown criterion of the combined (rf plus weak dc electric field) discharge taking into account the anisotropy of electron diffusion in the electric field is obtained. A novel method for determining the electron-drift velocity from the measured rf breakdown curves is suggested. The electron-drift velocity data in argon, hydrogen and air obtained with this technique in the range -2000 V are given and compared with those got by conventional means.

Analytical model for the behavior of electric fields in a collisional low-pressure RF discharge

A simple analytical model is presented making it possible to determine the amplitudes and phases of the rf field in the electrode sheaths and quasineutral plasma of an rf discharge in the presence of electronneural collisions. The collisional case ω≪ν is considered in detail. Measurements are also made of the electron temperature, plasma density, thickness of the electrode sheaths, and rf field amplitude in the quasineutral plasma of an rf discharge in argon. The rf field amplitudes predicted by this model are in satisfactory agreement with both our experimental data and the results of theoretical calculations of other authors.

Features of the α-γ transition in a low-pressure rf argon discharge

It is found that the region for the stable existence of the a regime of a radio-frequency ~rf! discharge is bounded not only on the moderate-pressure side, but also on the low-pressure side. One feature of the a ‐g transition in a low-pressure rf discharge is that the criterion for breakdown of the electrode sheath is not satisfied. It is shown that at low pressures the a ‐g transition of an rf argon discharge takes place abruptly and exhibits hysteresis. At intermediate pressures the a ‐g transition is continuous and lacks jumps; negative differential conductivity appears, double layers form, and nonmonotonic behavior of the plasma density is observed at the center of the discharge. The role of stochastic ~collisionless! electron heating in sustaining an rf discharge at intermediate gas pressures is discussed. © 1998 American Institute of Physics.@S1063-7842~98!01005-8#

Low-pressure inductive rf discharge in a rare gas-halogen mixture for economical mercury-free luminescence light sources

It is demonstrated that an inductive rf discharge in an Xe+Cl2 mixture may be used as the active medium of an efficient, mercury-free luminescence light source.

Kinetics of low pressure rf discharges with dust particles

The kinetics of dusty plasma in low pressure rf discharges is studied by solving self-consistently the time dependent electron Boltzmann and dust charging equations. The electron temperature, the excitation and ionization rate coefficients, and the dust particle charge are shown to be modulated in the periodic state. It is demonstrated that the presence of dust particles enhances the modulated amplitude, reduces the high energy content of the electron energy distribution, the corresponding effective electron temperature, and the electron excitation and ionization rate coefficients.

Dust charge in the sheath of collisional low-pressure capacitive RF discharges

Dust particles acquire electric charges by collecting electron and ion currents in plasma. These charged particles will be trapped in the sheath under some conditions. We consider the dust charge in the situation of a crystal, in which the dust particles are suspended in the collisional capacitive RF sheath at an equilibrium position. We use a cutoff like the two-temperature Maxwellian distribution to model the non-Maxwellian electron energy distribution function (EEDF) in capacitive RF discharges, and a /spl delta/ function to describe the density of dust particles; the equilibrium parameters are obtained analytically for a collisional sheath. It is found that the dust charge is very sensitive to the particle's radius, electron temperature, and ion initial velocity. The relationship between dust charge and electron temperature and the particle's radius in the sheath region is opposite to that in the plasma region.

On the role of strong turbulence in low-pressure rf discharges in a magnetic field

The results of an experimental and theoretical investigation of strong turbulence produced by an external rf field in the plasma of a beam-plasma discharge are presented. The modulation instability of a rf electric field, perpendicular to a constant magnetic field, in the frequency range between the lower-hybrid and ionic Langmuir frequencies, has been investigated. It is shown that the low-frequency fields can be used to control beam relaxation.

A fluid model of the bulk plasma in a cylindrical magnetized low-pressure RF discharge and comparison with PIC - MC simulation results

The modelling of a cylindrical low-pressure RF discharge in a strong axial magnetic field is analysed by a comparison of previously obtained kinetic particle-in-cell - Monte Carlo (PIC - MC) simulation results to a newly developed hydrodynamic model. We show that such a model is possible in the bulk of the discharge, where the electron distribution function is Maxwellian to good accuracy. The small electron diffusion coefficient perpendicular to the magnetic field is essential for the validity of the hydrodynamic analysis. As a result, we obtain good agreement between the hydrodynamic model and our kinetic simulation data. We furthermore exemplify the usefulness of the hydrodynamic approach by discussing the properties of the discharge bulk in terms of macroscopic quantities; we thus can show that the contribution of thermal diffusion to the electron current is of the same importance as that of ordinary diffusion, an issue usually overlooked in the analysis of magnetized discharges.

The influence of electron reflection at the electrode and secondary electron emission on a strongly magnetized low-pressure RF discharge

With the help of a particle-in-cell/Monte Carlo simulation, we study a strongly asymmetric cylindrical low-pressure RF discharge in an axial magnetic field. In particular, the effects of electron reflection from the electrodes and of ion-induced secondary electron emission are studied. The process alone does not change the plasma characteristics; this fact can be traced back to the gyro-motion of electrons in the electrode sheath, which brings non-colliding electrons back to the electrode. If electron reflection is allowed for, the overall plasma density is substantially increased. This effect is found qualitatively in experiments. We furthermore demonstrate the existence of high-energy electrons throughout the bulk plasma; this fact is reminiscent of the well-known -regime of unmagnetized RF discharges.

Dusty plasma formation: Physics and critical phenomena. Theoretical approach

Kinetics of the many-stage process of particle nucleation and growth in low-pressure rf discharge in silane SiH4–Ar is considered. The particle growth is considered in an analytical model as a chain of negative-ion molecular reactions, stimulated by vibrational excitation. In the framework of this model, a limitation of first generation particle size is explained as well as the strong temperature effect on cluster growth. A theory of critical phenomena of cluster trapping in discharge area has been elaborated to describe the neutral particle selection by size, and the particle concentration increases during a period exceeding the residence time in plasma. Finally, an analytical model of critical phenomena of particle coagulation and its influence on plasma parameters is developed to explain the latest experimental results on supersmall 2–10 nm cluster kinetics. All theoretical results are presented in comparison with corresponding new experimental data and with results of an especially made computer simulation.

A biased optical probe method for measurements of electron energy distribution in a plasma

A biased optical probe (BOP) method, i.e. novel technique for measurements of the electron energy distribution function (EEDF) in a range of such high energies as 10-50 eV has been developed. This method is based on the optical emission induced by electrons passing through a negatively biased mesh in a plasma. The BOP method was used to measure the EEDF in a DC glow discharge in He/Xe mixture while the low-energy part (<10 eV) of the EEDF was measured using the conventional Druyvesteyn method. The measured distribution function considerably deviates from an ideal Maxwellian distribution, because of abundant high-energy electrons generated in a cathode fall. On the contrary, the EEDF measured in a low-pressure inductive RF discharge was found to follow a single Maxwellian distribution over a wide energy range.

Self-consistent modelling of low-pressure RF discharges in oxygen plasma

A self-consistent numerical model has been developed for an RF plasma discharge in oxygen. The model contains about 100 ion-molecular reactions with 13 neutral and charged species of the RF plasma. The energy distributions of both charged and neutral plasma components with respect to the electrodes have been calculated using a Monte Carlo method. The angular distributions of fast neutral species have also been calculated.

Characterization of plasma-surface contacts in low-pressure rf discharges using ion energy analysis and langmuir probes'

The plasma-sruface contact in low-pressure of discharges in noble and reactive gases was studied by a combination of probe measurements and ion energy analysis at the surface. By comparing different methods, as the roost reliable density determination the integral of the second derivative of the probe curve was found. This method turned out to he not very sensitive to incomplete of filtering or compensation and even to coating of the probe. However, it depends strongly on the correct choice of the plasma potential. By comparing space potentials obtained from probes and from ion energy distributions, a most probable value can he attained that is situated between the negative minimum and the closest maximum of the1 ″(U) curve. The ion energy distributions are compared to an analytical sheath model. giving very good agreement in anab initio comparison. In plasmas depositing carbonized polymer filers, reproducible structares due to the influence of the coating air the probe characteristics can he analyzed, yielding nonlinearI (U) characteristics of the film. Using these characteristics, the film growth can be followed.

Experimental investigation and fast two-dimensional self-consistent kinetic modeling of a low-pressure inductively coupled rf discharge.

We present a fast self-consistent kinetic model for an inductively coupled low-pressure rf discharge. The electron kinetics in it is described in terms of a nonlocal electron distribution function, which depends only on the total electron energy (kinetic plus potential one in the stationary electric field). In this case, the Boltzmann equation reduces to a one-dimensional ordinary differential equation in total energy. The complete model also includes the equations for ion motion, for the rf oscillatory induction field, for the external circuit, and the quasineutrality condition. It allows us to express all the plasma characteristics---the electron distribution function, the plasma density profile, the profiles of the stationary and of the oscillatory electric fields, the profiles of the excitation and ionization rates, etc.---in terms of the external characteristics---the chamber geometry, gas pressure, frequency, and the current in the primary coil. The theoretical predictions are compared to experimental results. An experimental investigation has been performed on an inductively coupled low-pressure rf discharge in Ar at 13.56 MHz over a wide range of input powers at gas pressures from 1 to 12 Pa. A satisfactory agreement with the experiment and qualitative interpretation of the observed phenomena is achieved.

Influence of plasma extraction on a cylindrical low-pressure RF discharge: a PIC-MC study

A model is presented for plasma extraction from a cylindrical RF discharge. Even though the extraction geometry is two-dimensional, the model proposed here allows to discuss extraction in a one-dimensional geometry. Specific results are obtained for a low-pressure RF discharge between cylindrical electrodes with a high asymmetry. These are calculated with the help of a PIC-MC computer simulation. The influence of extraction on the plasma characteristics, the ionization efficiency, and the influence of an axial magnetic field are calculated and discussed. >

Nonlocal electron kinetics in collisional gas discharge plasmas

Nonlocal phenomena in electron kinetics of collisional gas discharge plasmas, their kinetic treatment by a nonlocal approach, and relevant experimental results are reviewed in this paper. Using the traditional two-term approximation for the electron distribution function, a general method to analyze electron kinetics in nonuniform plasmas in DC and RF fields for atomic gases is presented for the nonlocal case, when the electron energy relaxation length exceeds the characteristic spatial scale of bounded plasmas. The nonlocal method, which is based on the great difference between the electron mean free path for the momentum transfer and the electron energy relaxation length, considerably simplifies the solution of the kinetic equation and, in a number of cases, allows one to obtain analytical and semi-analytical solutions. The main simplification is achieved for trapped electrons by averaging the Boltzmann equation over space and fast electron motion. Numerous examples of spatial nonlocality are considered in the positive column and near the electrodes of DC glow discharges, in spatial relaxation of the electron distribution and in striations, and in capacitively and inductively coupled low-pressure RF discharges. The modeling of fast beam-like electrons is based on a continuous-energy-loss approximation with the assumption of forward scattering. Simple analytic expressions for the fast electron spectrum are obtained in cathode regions of DC discharges with planar and hollow cathodes. >

PIC/MC simulation of a strongly asymmetric low-pressure RF discharge

A PIC/MC simulation is performed on a cylindrical low-pressure gas discharge between two coaxial electrodes in an axial magnetic field. This case study employs an asymmetry of 1:7 between inner and outer electrodes. It is based on natural mass argon gas with experimentally given cross sections for elastic, excitation and ionization electron collisions, as well as elastic and charge exchange ion collisions. The simulation shows that ionization occurs mostly at the inner sheath edge. Negative space charge regions build up in front of the momentary anode sheath. These lower the plasma potential with respect to the electrode and induce electron leakage currents to the anode. The ionization degree is 3*10-4, and 10% of the dissipated power goes into ionization in this particular case. The improvement of these features for the design of an ion source is discussed.

Plasma particle interactions

We present some results from numerical, fluid and particle models of non-thermal low pressure RF discharges contaminated by dust particles. These models have been used (1) to show the effect of the presence of dust particles on the electrical characteristics of an RF discharge, (2) to study the charge and floating potential of dust particles in a low pressure plasma from situations where the particles can be considered isolated to situations where they interact electrostatically and (3) to study the effect of the electrode geometry on the spatial distribution of dust particles in an RF discharge. The results confirm the existence of electrostatic traps close to the plasma-sheath boundary whose shape is very sensitive to the electrode configuration.

On the influence of secondary electrons in RF discharges in helium

The transition from the alpha to the gamma mode in a low-pressure helium RF discharge between parallel plates is investigated by spatio-temporally resolved plasma induced emission spectroscopy. The time development of several levels of atomic helium and of the n=4 level of ionic helium is presented over a wide range of discharge pressure (40-300 Pa) and power input (75-300 W). Single photon counting is applied to resolve the time dependence. The transition to the gamma or secondary electron dominated state is observed directly in space and time dependent excitation of the helium ion level. The effect of the extreme lowering of the electron temperature resulting from the non-local sustaining mechanism is observed in the light of atomic helium lines, which show substantial differences between the singlet and the triplet systems due to spin changing collisions (singlet to triplet) coupling the metastable levels. The cross section of these collisions increases with a decrease of electron temperature below the threshold value of 0.79 eV. In addition, probe measurements in a similar, but symmetrically driven parallel plate discharge optimized for use with Langmuir probes are presented to give independent evidence to the rapid decrease of electron temperature when the transition occurs.