Svetlan Bzenić

Benchmark calculations for Monte Carlo simulations of electron transport

Benchmark calculations have been performed for electron transport coefficients with an aim to produce a body of data required to verify the codes used in plasma modeling. The present code for the time resolved Monte Carlo simulation (MCS) was shown to represent properly DC transport coefficients in a purely electric field, in crossed electric and magnetic fields, and in the presence of nonconservative collisions, ionization, and attachment. In addition, we have suggested tests of the time dependent solutions. Relaxation of the initial transport coefficient may serve as an accurate test of the code as well as the input data for some fluid codes. In this paper, we show only one example, but several different sets of conditions and cross sections should be used as well. Finally, we propose application of the quasi-steady state results in RF fields. As an example we suggest calculation of the components of diffusion tensor showing anomalous longitudinal diffusion and calculations made with nonconservative collisions (ionization in this case). We also check the application of approximate formulas to determine drift velocity on the basis of total collision frequency and to determine a diffusion coefficient by using the Einstein relation. Other tests required to verify the transport data calculations are discussed as well.

On spatial distribution of optical emission in radio frequency discharges

In this paper we present calculations of the spatial distributions of emission in model argon discharges which correspond to the conditions of argon discharges in the GEC rf reference cell but are relevant for other similar rf discharges. The calculations on the basis of the particle in cell (PIC) code show that transitions with high threshold energy are predominantly excited by secondary electrons originating from the instantaneous cathode while the transitions with lower threshold energy are excited predominantly by electrons accelerated by sheath motion. In addition it is shown that the spatial distribution of 811 nm radiation of argon corresponds best to excitation by very low-energy electrons from the metastable state. The different kinetics of excitation of the three groups of transitions mentioned above, in conjunction with different energy dependences of the cross sections and special conditions when there is a significant if not dominant contribution of the gamma process in sustaining the discharge, give rise to the different spatial distributions of emission which are opposed to the intuitively expected distributions and raise questions about the applications of spatial distributions of emission in determining the sheath width and in diagnostic techniques such as actinometry.

Relaxation of electron swarm energy distribution functions in time-varying fields

Monte Carlo simulation code for RF fields was used to study the transition from the initial conditions to the quasi-steady state energy distribution functions. Signatures of the initial conditions were found to be recreated even when the distribution function appeared to have reached the relaxed shape. The inclusion of magnetic field changes the transition to the relaxed distribution as well as the final mean energy and other data.

Drift Velocities of Electrons in Time Varying Electric Fields

Monte Carlo simulations of electron transport have been performed in methane for time resolved rf fields under conditions where negative differential conductivity (NDC) occurs. It was found that the effect of NDC occurs for low frequencies as expected from the quasi stationary (temporally local) model. At higher frequencies the NDC disappears gradually but the NDC behavior is significantly different when field increases and when field decreases. In the latter case the NDC disappears while in the former it blends into one maximum occurring at the point of the maximum of the electric field with an intermediate frequency region with asymmetric time dependence.

The influence of excited states on the kinetics of excitation and dissociation in gas mixtures containing methane

Abstract In this paper, we extend the calculations for rare gas discharges, which aim to establish the influence of excited states on the kinetics of electron-induced excitation, to rare gas-methane mixtures and pure methane which are often used in diamond-like film deposition. In particular, we address the effect of non-thermal vibrational populations on the rate coefficients in methane-containing gas discharges using the procedure applied previously for pure silane. Furthermore, we investigate the kinetics of electronically excited levels of rare gases and methane in the presence of a significant population of excited states. These states may contribute to the overall ionization, excitation and dissociation rates through stepwise processes, superelastic collisions and energy transfer processes. The influence of superelastic processes on the development of the negative differential conductivity (NDC) is discussed on the basis of the momentum transfer theory, and it is shown that the NDC is reduced when significant populations of excited states are present. This is of importance for calculations of the transport coefficients for a.c. electric fields where NDC leads to a complex temporal dependence of the drift velocity and thus directly affects the power deposition in the discharge. Finally, we present the rate and transport coefficients calculated for methane in r.f. fields based on the Monte Carlo simulation for time-dependent fields. A good agreement with the effective field approximation and earlier Boltzmann calculations is found.

Dissociative excitation of hydrogen in rf and dc glow discharges through H2

Abstract The spectral and spatial profile of H β from the low pressure rf and dc glow discharges in hydrogen is studied in order to reveal the excitation mechanism of the fast excited H fragments. Measurements were performed both for the normal and abnormal dc glow discharges. Spatial distributions of the Balmer β radiation reflect the local plasma conditions in the discharge, especially the excitation efficiency which is used to determine the excitation kinetics in hydrogen discharges. Spectral H β profiles were measured and used to determine the kinetic energy of excited H atoms and to check which of the mechanisms describes best the results observed in our experiment. We have also calculated the number densities of vibrationally excited levels by solving a set of vibrational master equations for the conditions similar to those of our experiments, as excitation from the vibrationally excited ground-state hydrogen molecules may be used to explain the changes in the intermediate wing component of the line profile with the changing current.

Influence of excited molecules on electron swarm transport coefficients and gas discharge kinetics

In this paper we study different effects of excited molecules on swarm parameters, electron energy distribution functions and gas discharge modeling. First we discuss a possible experiment in parahydrogen to resolve the discrepancy in hydrogen vibrational excitation cross section data. Negative differential conductivity (NDC) is a kinetic phenomenon which manifests itself in a particular dependence of the drift velocity on E/N and it is affected by superelastic collisions with excited states. A complete kinetic scheme for argon required to model excited state densities in gas discharges is also described. These results are used to explain experiments in capacitively and inductively coupled RF plasmas used for processing. The paper illustrates the application of atomic and molecular collision data, swarm data and the theoretical techniques in modeling of gas discharges with large abundances of excited molecules. It is pointed out that swarm experiments with excited molecules are lacking and that there is a shortage of reliable data, while the numerical procedures are sufficiently developed to include all the important effects.

The influence of frequency on the efficiency of dissociation of freons by microwave discharges

We have performed calculations of the efficiency of dissociation by the microwave induced discharges at low pressures. Monte Carlo simulation of electron transport under the influence of high frequency electric field and collisions with gas molecules was used to determine the dissociation efficiency in microwave discharges in freons which have been proposed as a technique for reducing the depletion of the ozone layer by freons initiated chemical reactions with ozone in the upper atmosphere. It was found that the modulation of the mean energy and the electron energy distribution function becomes smaller at very high frequencies (1 GHz) leading to significant reduction of the dissociation rate. Above 3 GHz electrons cannot follow the field changes and gain energy efficiently. Thus operation at higher electric field values or E/N is required to achieve significant dissociation in the GHz frequency range.