Collisionless electron heating in an inductively coupled discharge

Modeling of surface-wave discharges with cylindrical symmetry

This paper presents the modeling of microwave (2.45GHz) discharges with cylindrical symmetry, produced in the absence of an external magnetic field by TM00 surface waves (SW) within either cylindrical or coaxial structures. A stationary, one-dimensional (radial) moment model (including the continuity and the momentum-transfer equations for electrons and positive ions, and the electron mean energy transport equations) is solved self-consistently coupled to Poisson's equation for the space-charge electrostatic field and the appropriated Maxwell's equations for the SW electromagnetic field. The model is solved for argon discharges over a broad range of operating conditions: Average electron densities from 10;{11}to3x10;{12}cm;{-3} and gas pressures from 10;{-2}to5Torr . Results are compared to those of a simplified classical model that disregards charge separation near discharge boundaries, ignoring also the development of electron-plasma resonances caused by the severe electron density gradients within space-charge sheath regions. Simulations show that the presence of a sheath-resonance region has a strong influence on the values of the SW attenuation constant, particularly at low pressures and high electron densities, affecting also the local budget of the discharge power deposition (hence discharge maintenance).

Effective-viscosity approach for nonlocal electron kinetics in inductively coupled plasmas

In inductively coupled plasmas, nonlocal electron kinetics lead to the anomalous skin effect. We show that this can be approximately described through a fluid equation for electron momentum including a viscosity term with an effective-viscosity coefficient. The solution of this momentum equation coupled with the Maxwell equations is in good agreement with results from a particle-in-cell simulation over a wide range of conditions, reproducing the nonmonotonic structure of the anomalous skin with sometimes local negative power absorption.

Inductive heating and E to H transitions in capacitive discharges

Capacitive discharges have classically been modeled in the electrostatic approximation. However, electromagnetic effects become significant if the excitation wavelength lambda and the plasma skin depth delta are not infinite. An electromagnetic model valid in the entire range of lambda and delta of practical interest is solved. We find that the plasma may either be sustained by the usual capacitive (E) field or by an inductive (H) field, and that the discharge experiences E to H transitions as the voltage between the electrodes is raised.

Experimental measurement of the electron energy distribution function in the radio frequency electron cyclotron resonance inductive discharge

Recently, the existence of electron cyclotron resonance (ECR) in a weakly magnetized inductively coupled plasma (MICP) has been evidenced [ChinWook Chung et al., Phys. Rev. Lett. 80, 095002 (2002)]. The distinctive feature of the ECR effect in the MICP is efficacious heating of low-energy electrons. In the present paper, electron heating characteristics in the MICP have been investigated by observing electron energy distribution function dependencies on various external parameters such as gas pressure, driving frequency, and rf power (electron density). It is found that the ECR effect on electron heating becomes enhanced with decreasing pressure or increasing driving frequency. The ECR heating becomes weak at high rf power due to the electron-electron collisions.

Reduction of electron heating in the low-frequency anomalous-skin-effect regime

It is known that electron thermal motion in the anomalous-skin-effect regime of rf plasma discharges leads to enhancement of rf power absorption by plasma due to the resonant electron-wave interaction, which is a main mechanism of plasma heating in a typical inductively coupled plasma discharge. In this Letter we show, however, that the rf power absorption may be strongly reduced (compared to the Ohmic value) at low frequencies due to the electron thermal motion; an even further reduction occurs due to the nonlinear effects of the rf magnetic field. The absorption reduction occurs for omega<nu<v(th)/delta (omega is a driving frequency of rf wave, nu is the collision frequency, v(th) is the thermal velocity, and delta is characteristic skin depth of the wave) and may be observed in low pressure inductive plasmas driven at low frequency and in a dc plasma with strong field inhomogeneity.

Ion-acoustic waves in a complex plasma with negative ions

A self-consistent theory of linear waves in complex laboratory plasmas containing dust grains and negative ions is presented. A comprehensive model for such plasmas including source and sink effects associated with the presence of dust grains and negative ions is introduced. The stationary state of the plasma as well as the dispersion and damping characteristics of the waves are investigated. All relevant processes, such as ionization, diffusion, electron attachment, negative-positive ion recombination, dust charge relaxation, and dissipation due to electron and ion elastic collisions with neutrals and dust particles, as well as charging collisions with the dusts, are taken into consideration.

Electron energy distributions and anomalous skin depth effects in high-plasma-density inductively coupled discharges

Electron transport in low pressure (<10s mTorr), moderate frequency (<10s MHz) inductively coupled plasmas (ICPs) displays a variety of nonequilibrium characteristics due to their operation in a regime where the mean free paths of electrons are significant fractions of the cell dimensions and the skin depth is anomalous. Proper analysis of transport for these conditions requires a kinetic approach to resolve the dynamics of the electron energy distribution (EED) and its non-Maxwellian character. To facilitate such an investigation, a method was developed for modeling electron-electron collisions in a Monte Carlo simulation and the method was incorporated into a two-dimensional plasma equipment model. Electron temperatures, electron densities, and EEDs obtained using the model were compared with measurements for ICPs sustained in argon. It was found that EEDs were significantly depleted at low energies in regimes dominated by noncollisional heating, typically within the classical electromagnetic skin depth. Regions of positive and negative power deposition were observed for conditions where the absorption of the electric field was both monotonic and nonmonotonic.

Parameters and equilibrium profiles for large-area surface-wave sustained plasmas

The equilibrium profiles of the plasma parameters of large-area rf discharges in a finite-length metal-shielded dielectric cylinder are computed using a two-dimensional fluid code. The rf power is coupled to the plasma through edge-localized surface waves traveling in the azimuthal direction along the plasma edge. It is shown that self-consistent accounting for axial plasma diffusion and radial nonuniformity of the electron temperature can explain the frequently reported deviations of experimentally measured radial density profiles from that of the conventional linear diffusion models. The simulation results are in a good agreement with existing experimental data obtained from surface-wave sustained large-diameter plasmas.

Electron cyclotron resonance in a weakly magnetized radio-frequency inductive discharge

The evolution of the electron energy distribution function (EEDF) over a weak magnetic field range is investigated in magnetized radio-frequency (rf) inductive discharges under a collisionless regime where an anomalous skin effect and electron cyclotron resonance (ECR) can occur. A significant change in the low-energy range of the EEDF is found in the ECR condition during the evolution. The observed result reveals the low-energy electrons are efficiently heated by the rf ECR in the presence of the anomalous skin effect. The calculated result of the electron distribution based on kinetic theory is in good agreement with the experiment.

Lorentz force effects on the electron energy distribution in inductively coupled plasmas

Depletion of the electron energy distribution function by slow electrons in the skin layer has been observed in experiment in a cylindrical inductive discharge with a flat coil at low frequency and low gas pressure. The origin of the effect lies in the dependence of the ponderomotive force (caused by the rf magnetic field) on the electron thermal motion under conditions of the anomalous skin effect. Analysis of the electron energy distribution based on the existence of adiabatic invariants for collisionless electron motion at low frequencies reveals enhanced anisotropy and time dependence of the electron distribution function due to strong rf magnetic fields and a polarization electrostatic potential at twice the driving frequency. The electron energy distributions calculated in the skin layer using experimentally measured electromagnetic fields and rf and dc potential profiles are in reasonable agreement with the experimental electron distributions.

Nonlocal electron kinetics in a planar inductive helium discharge

A measurement of the electron energy distribution function (EEDF) using the ac superposition method is done over a helium pressure range of 10-100 mTorr in a planar inductive plasma, and the electron energy diffusion coefficient which describes the electron heating is calculated based on the same discharge conditions using a two-dimensional simulation. It is found that the measured EEDF shows a bi-Maxwellian distribution with a low-energy electron group at low pressures below 20 mTorr even in the inductive discharge using helium of the non-Ramsauer gas. The major factors which can affect the EEDF formation are investigated. In particular, the concept of the total electron bounce frequency, i.e., the electron residence time, is introduced as an indicator of how the electron-electron collision affects the EEDF shape. As a result, it is shown that the observed bi-Maxwellian distribution at low pressures is attributed to the combined effects of the formation of low-energy electrons through the cooling mechanism of energetic electrons enhanced by the capacitive field, the low heating rate of the low-energy electrons, the confinement of low-energy electrons by the ambipolar space potential, and the low electron-electron collision frequency which can be estimated from the total electron bounce frequency presented in this paper.

Discharge impedance of solenoidal inductively coupled plasma discharge

The discharge impedance is calculated for a solenoidal inductively coupled plasma (ICP) discharge, which is one of the important sources for plasma processing. To calculate this impedance, the electromagnetic field quantities are obtained by solving the two-dimensional Maxwell equations in a realistic geometry. Also considered in the calculation is the anomalous skin effect which is regarded as a collisionless heating mechanism of ICP discharge. The results show that the discharge impedance is a function of various discharge parameters, such as plasma density, electron temperature, antenna position, collision frequency, excitation frequency, and chamber geometry.