S. B. Vrhovac

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.

Energy distributions of electrons in a low-current self-sustained nitrogen discharge

Electron energy distribution functions (EEDF) in N2 Townsend discharges for E/N between 1 and 30 kTd (1 Td=10−21 V m2) were measured using a multigridded energy analyzer behind a small (0.1 mm) aperture in the graphite anode. Experimental results are further analyzed by applying Monte Carlo simulations in order to describe nonequilibrium transport in steady state Townsend discharges and to determine the origin of the observed EEDF features. Boundary effects at electrodes are described by allowing exact representation of absorption, reflection, and secondary electron production at the anode. It was found that it is necessary to include electron reflection and secondary electron production in order to model the low energy part of the observed EEDF.

Semianalytical models of volt-ampere characteristics of diffuse low-current low-pressure discharges

We perform calculations of volt-ampere (V-A) characteristics of low-current low-pressure diffuse (Townsend) discharges in hydrogen and compare them to the experiment. The basis for the calculation is the numerical procedure for electric field calculation by solving integral equations for the surface charges. We have used analytic solutions for the homogeneous field as the initial approximation and made a cycle of calculations until the charge profile and the field were self-consistent. This procedure allows us to remove the field expansion from the physical perturbation theory of such discharges and to study the causes for negative differential resistances, oscillations, and nonlinear effects. Furthermore, we have developed a nonlinear version of the physical model of Phelps and coworkers which helps us identify the features of the ionization coefficient and secondary electron yield that give rise to nonlinear development of the V-A characteristics of Townsend regime discharges.

Third-order transport coefficients for charged particle swarms

Momentum-transfer theory has been used to obtain a relationship between the nth order tensorial transport coefficients in a swarm experiment, the (n−1)th derivative of the mobility, and the nth derivative of the reaction rate coefficient. Elastic, inelastic, and reactive collisions for gas mixtures have been taken into consideration. Numerical comparisons show that the results obtained from this relationship are in good agreement with those obtained by solution of the Boltzmann equation. Finally, we have analyzed the structure of the third-order tensorial transport coefficient by applying momentum-transfer theory and group theory; both approaches show that in general there are three independent components of this rank-three tensor.

Electron energy distribution functions in weakly ionized argon

The authors present measurements of the electron energy distribution functions (EEDF) for electrons in argon discharges at moderate and high E/N values (E being the electric field and N the gas density), for homogeneous electric fields and a low-current diffuse glow regime. Results were obtained for electric field to gas density ratios (E/N) from 500 Td to 50 kTd (1 Td=10-21 V m2). A multigrid energy analyser with a retarding grid potential was used to measure distribution functions of electrons sampled through an aperture in the anode. Experimental data are used to make a comparison with the two-term Boltzmann calculations for E/N<1 kTd, and the single-beam model predictions, normally used to model electron kinetics at high values of E/N.

Negative Differential Resistance, Oscillations and Constrictions of Low Pressure, Low Current Discharges

A brief review is given of the recent experimental and theoretical studies of low current diffuse discharges. Two models are developed, one that is based on phenomenological description by effective discharge circuit parameters and the other which is based on the calculation of the field profile from the ion distribution for uniform field. In the first case the physical process responsible for the development of the negative differential resistance is the dependence of the secondary electron yield on current through modification of the field close to the cathode. Experimental systems were developed to provide observables that include: breakdown voltage, voltampere characteristics (which in the low current limit is represented very well by a negative differential resistance), limits and the profile of the low current oscillations, frequency and damping of the induced oscillations, current growth coefficient and the onsets for constrictions. All of the observables are very well predicted by the theory based on the data taken from independent sources, once the steady state secondary electron yield has been fitted to predict the breakdown voltage.

Boltzmann equation theory of charged particle transport in neutral gases: perturbation treatment

This paper examines the formal structure of the Boltzmann equation (BE) theory of charged particle transport in neutral gases. The initial value problem of the BE is studied by using perturbation theory generalised to non-Hermitian operators. The method developed by Resibois was generalised in order to be applied for the derivation of the transport coecients of swarms of charged particles in gases. We reveal which intrinsic properties of the operators occurring in the kinetic equation are sucient for the generalised diffusion equation (GDE) and the density gradient expansion to be valid. Explicit expressions for transport coecients from the (asymmetric) eigenvalue problem are also deduced. We demonstrate the equivalence between these microscopic expressions and the hierarchy of kinetic equations. The establishment of the hydrodynamic regime is further analysed by using the time-dependent perturbation theory. We prove that for times t ? t0 (t0 is the relaxation time), the one-particle distribution function of swarm particles can be transformed into hydrodynamic form. Introducing time-dependent transport coecients ? *(p) (?q,t), which can be related to various Fourier components of the initial distribution function, we also show that for the long-time limit all ? *(p) (?q,t) become time and ?q independent in the same characteristic time and achieve their hydrodynamic values.

Jamming and percolation in random sequential adsorption of extended objects on a triangular lattice with quenched impurities

Random sequential adsorption (RSA) on a triangular lattice with defects is studied by Monte Carlo simulations. The lattice is initially randomly covered by point-like impurities at a certain concentration p. The deposited objects are formed by self-avoiding random walks on the lattice. Jamming coverage and percolation threshold are determined for a wide range of impurity concentrations p for various object shapes. Rapidity of the approach to the jamming state is found to be independent on the impurity concentration. The jamming coverage decreases with the impurity concentration p and this decrease is more prominent for objects of larger size. For a certain defect concentration, decrease of the jamming coverage with the length of the walk making the object is found to obey an exponential law, . The results for RSA of polydisperse mixtures of objects of various sizes suggest that, in the presence of impurities, partial jamming coverage of small objects can have even larger values than in the case of an ideal lattice. Percolation in the presence of impurities is also studied and it is found that the percolation threshold is practically insensitive to the concentration of point defects p. Percolation can be reached at highest impurity concentrations with angled objects, and the critical defect concentration p c is lowest for the most compact objects.