G. Gousset

ELECTRON AND HEAVY-PARTICLE KINETICS IN THE LOW PRESSURE OXYGEN POSITIVE COLUMN

A kinetic model for the low-pressure oxygen positive column is presented and discussed. The model is based on the electron Boltzmann equation and the rate balance equations for the dominant heavy-particle species, which are solved simultaneously in order to take into account the coupling between the electron and the heavy-particle kinetics. The effects of vibrationally excited molecules, dissociated atoms and metastable states on the electron kinetics are analysed in detail. The predicted populations of O2(X3 Sigma ), O2(a1 Delta ), O(3P), and O- are shown to agree satisfactorily with previously reported measurements. A combination of this kinetic model with the continuity and transport equations for the charged species e, O-, and O2+ is shown to provide characteristics for the maintenance field that agree reasonably well with experiment.

Quasi-neutral theory of positive columns in electronegative gases

A theory of the positive column in electronegative gases based on fluid-type momentum equations to describe charged particle motion is presented. It is assumed that quasi-neutrality conditions prevail and the ion inertial terms are neglected. The positive ions are assumed to be created by electron collisions with neutral molecules and the negative ions to be formed by dissociative electron attachment and destroyed by detachment in reactions with neutral species. The mathematical formulation consists of a two-point boundary value problem involving two independent parameters, functions of collisional and transport data, and two eigenvalues. One of these is the central ratio of the negative ion density to the electron density, while the other is related to the ionisation-loss balance and embodies a discharge characteristic for the maintenance field. These eigenvalues and the radial density distributions of the charged species were calculated for a wide range of variation of the independent parameters. An application of the theory to a positive column in oxygen is given as an illustrative example.

Systematic characterization of low-pressure capacitively coupled hydrogen discharges

This paper presents a systematic characterization of pure hydrogen capacitively coupled discharges, produced in a parallel plate cylindrical setup. A two-dimensional, time-dependent fluid model is used to describe the production, transport, and destruction of electrons and positive ions H+, H2+, and H3+, at different frequencies (13.56–60 MHz), pressures (0.2–8 Torr), rf applied voltages (50–450 V) and geometric dimensions (1.6–12.8 cm radii and 1.6–6.4 cm interelectrode distances). A good agreement is found between calculation results and experimental measurements for the coupled electrical power, the plasma potential, and the self-bias potential, at various frequencies and rf applied voltages. However, the model generally underestimates the electron density with respect to its measured values. The paper discusses different space-time events, such as the development of double-ionization structures or the occurrence of field inversion and field reversal phenomena. The dependencies on pressure and frequenc...

Two-dimensional fluid modelling of charged particle transport in radio-frequency capacitively coupled discharges

This paper reviews the formulation and updates some numerical procedures usually adopted in two-dimensional, time-dependent fluid models to study the transport of charged particles in radio-frequency capacitively coupled discharges. The description of charged particle transport is made by solving the continuity and momentum transfer equations for electrons and ions, coupled with Poissons equation and the electron mean energy transport equations. Inertia terms are considered in the ion momentum transfer equations, by generalizing the earlier definition of effective electric field. The electron mean energy equations are written using specific energy transport parameters, deduced from integration over the electron energy distribution function (EEDF). The model adopts the local mean energy approximation, i.e. it computes the electron transport parameters as a function of the electron mean energy, using either a homogeneous, two-term Boltzmann equation solver or a Maxwellian EEDF. More appropriate boundary conditions for the electron and ion fluxes are used successfully. The model is solved for a GEC Cell reactor type (with 6.4 cm radius and 3.2 cm interelectrode distance) operating at frequency 13.56 MHz, pressures between 10 mTorr and 10 Torr and applied voltages from 100 to 500 V, in electropositive (helium) and electronegative (silane–hydrogen) gases or gas mixtures. The ion kinetics in silane and hydrogen is updated with respect to previous works, by further considering SiH2+, H+ and H3+ ions. In general, simulation results for some typical electrical parameters are closer to experimental measurements available than calculations reported in previous works.

Two-dimensional modelling of - radio-frequency discharges for a-Si:H deposition

A two-dimensional numerical code, including three fluid modules to account for the description of electrical, thermal and chemical phenomena, has been developed for the modelling of hydrogenated amorphous silicon deposition from radio-frequency glow discharges in a cylindrical PECVD reactor. The results of the model are compared to experimental data, obtained by different diagnostic techniques. The calculated radical densities are compared to those measured by threshold ionization mass spectrometry, at the centre of the substrate; the calculated SiH density profile between the electrodes is compared to those measured by laser-induced fluorescence and the radial distribution of the deposition rate on the substrate is compared to profilometry measurements. Globally, the model correctly predicts the main discharge characteristics for experimental conditions normally used for amorphous silicon deposition in the dust-free regime. The moderate agreement between model and experiment occurring for the hydrogen-dominated condition can be attributed to the simplified surface kinetics adopted in the model.

A collisional-radiative model for microwave discharges in helium at low and intermediate pressures

A stationary collisional-radiative model for helium microwave discharges in cylindrical geometry is developed by coupling the rate balance equations for the n<or=6 excited states of helium to the continuity and transport equations for the electrons, He+ atomic ions and He2+ molecular ions, and to the homogeneous Boltzmann equation. The latter is solved using the DC effective field approximation but taking into account stepwise inelastic and superelastic processes from the 23S, 21S and 23P states, as well as electron-electron collisions. A coherent set of electron cross sections is deduced in order to solve the Boltzmann equation. Special attention is paid to the atomic collisions considered (by taking into account /-change reactions and associative ionization reactions), and to the effects of radiation imprisonment. This, together with the inclusion of the kinetics of the molecular ions, allows the range of validity of the model to extend up to atmospheric pressure. The theoretical populations for the excited states, characteristics for the steady-state reduced maintenance electric field and mean absorbed power per electron at unit gas density agree very well with experimental data from surface wave discharges.

Two-dimensional fluid approach to the dc magnetron discharge

A two-dimensional (r, z) time-dependent fluid model was developed and used to describe a dc planar magnetron discharge with cylindrical symmetry. The transport description of the charged species uses the corresponding first three moments of the Boltzmann equation: continuity, momentum transfer and mean energy transfer (the last one only for electrons), coupled with the Poisson equation. An original method is proposed to treat the transport equations. Electron and ion momentum transport equations are reduced to the classical drift?diffusion expression for the fluxes since the presence of the magnetic field is introduced as an additional part in the electron flux, while for ions an effective electric field was considered. Thus, both continuity and mean energy transfer equations are solved in a classical manner. Numerical simulations were performed considering argon as a buffer gas, with a neutral pressure varying between 5 and 30?mTorr, for different voltages applied on the cathode. Results obtained for densities of the charged particle, fluxes and plasma potential are in good agreement with those obtained in previous studies.

Modelling of low-pressure surface wave discharges in flowing oxygen: I. Electrical properties and species concentrations

This paper describes a self-consistent kinetic model of cylindrically symmetric surface wave discharges in flowing oxygen at low pressures consisting of: (i) the homogeneous electron Boltzmann equation; (ii) the radial continuity and transport equations for the electrons and the dominant ions, that is, and ; (iii) the axial equations of change of mass and momentum for the reacting gas mixture composed of the heavy species and . The model is solved using measured distributions of the electron density and gas temperature along the plasma column as inputs, and its predictions are compared to experiment. It is shown that the predicted discharge maintenance field, average absorbed power per electron-ion pair and populations of the main species along the column agree well with experimental data.

Kinetics of O(1S) and O(1D) metastable atoms in a DC oxygen glow discharge

The concentrations of O(1D) and O(1S) metastable atoms are measured in the positive column of a DC oxygen glow discharge by vacuum ultraviolet absorption spectroscopy at 115 and 122 nm respectively. In the investigated range of pressures p=0.2-2 torr and discharge currents Id=10-80 mA, the concentrations of O(1D) and O(1S) atoms range from 1011-1012 and from 1010-1011 cm-3 respectively. In these conditions the main creation and destruction processes are discussed: the O(1D) atoms are created by electron impact dissociation of O2(X3 Sigma ) and O2(a1 Delta ), and excitation of O(3P), and lost through quenching by oxygen molecules. It is shown that it is necessary to add to the electron impact excitation another creation term of O(1S) atoms to balance the destruction through quenching by O2(X3 Sigma ), O2(a1 Delta ) and O(3P).

Simulation of pulsed high-frequency breakdown in hydrogen

We present a simulation of the breakdown stage of high-power, short-pulse high-frequency discharges in hydrogen, produced when an electric field of the form E(t)=EmaxIW(1−e−t/τ)sin(ωt) is applied to a cylindrical resonant cavity. Typical discharge operating conditions considered are applied powers 1–15 kW, gas pressures 0.1–20 Torr, cavity diameter of 25.71 cm, tube radius of 0.8 cm, field frequency ω/2π=1.12 GHz, pulse width tP=10 μs, and rising times τ of a few microseconds. Under these conditions, discharge breakdown occurs before the electric field reaches its maximum amplitude EmaxIW, this situation corresponding to the so-called increasing wave (IW) regime. The simulation is based on a Monte Carlo model to calculate the breakdown times, tb, and fields, Eb, for different field rising slopes EmaxIW/τ≃10−1−103 V cm−1 ns−1. The results obtained show that a breakdown criterion based on the electron energy balance (egain=eloss, where egain and eloss are, respectively, the mean electron energy gain and los...