The expanding use of low pressure (p⩽10 Torr), high frequency plasmas in various applications has stimulated research toward increased operating efficiency. In order to optimize a particular plasma process, the operator can vary several “external” (operator-set) parameters, among which the excitation frequency f has received relatively little attention in the literature over the years, probably due to the difficulties encountered in designing meaningful frequency-dependent experiments. These difficulties can be avoided by the use of surface-wave discharges (SWDs), which possess great flexibility: a very broad (continuous) range of excitation frequencies, and wide ranges of operating pressures and plasma densities, under noncritical, almost perfect impedance matching with the power source. In earlier work in these laboratories, we have examined the f dependence of plasma deposition and etching experiments; the present experiments have been designed to investigate the f dependence more “directly” by turning to the plasma through its optical emission. The vacuum ultraviolet to visible emission from SWD plasmas in pure hydrogen or 7%H2 in Ar mixture has been investigated over a broad range of excitation frequency (50⩽f⩽200 MHz) using a spectrophotometer with a known transfer function. The observed f dependence of emission intensity (atomic lines and molecular bands) as f is increased is interpreted in the case of the pure H2 discharge in terms of changes from a nonstationary to a stationary electron energy distribution function (EEDF) while, in the 7%H2/Ar mixture, it is related to changes in the form of the stationary EEDF.

Vacuum ultraviolet to visible emission from hydrogen plasma: Effect of excitation frequency

Using a new method for solving the time-dependent electron Boltzmann equation in higher order accuracy, studies of the temporal behaviour of electrons in weakly ionized, collision-dominated plasmas under the action of rf fields have been performed. The method is based upon a multi-term approximation of the Legendre polynomial expansion of electron velocity distribution function and is applied to investigate the established periodic behaviour of the electron velocity distribution in helium, argon and CO plasmas.



The results obtained in various approximation orders are discussed. The analysis has shown that the simplified treatment using only two terms of the velocity distribution expansion can fail in several conditions. In general, the four-term approximation gives already a good representation of the convergent solution of the electron Boltzmann equation at each instant of the rf period. The discrepancies between two-term and convergent results are found to depend sensitively on the specific atomic data, in particular on the magnitude of the various electron collision cross sections involved.



Furthermore, the results obtained in the multi-term approximation are compared with corresponding ones obtained by accurate Monte Carlo simulations. Very good agreement between convergent eight-term Boltzmann and Monte Carlo calculations is found.

Time ‐ Dependent Multi ‐ Term Treatment of Plasma Electrons Acted upon by RF Electric Fields

We present a two-dimensional (2D) plasma model for a coaxial microwave discharge. The microwave energy at driving frequency of 2.45 GHz is fed into a coaxial configuration in which the plasma acts as an outer conductor in such a way that a spatially extended surface wave is created. This geometry permits large surface treatment, especially if a set of such coaxial lines are used. The 2D model describes the plasma as a two-temperature non-chemical equilibrium fluid sustained by electromagnetic surface waves. We present results for argon as a working gas. The importance of wave–plasma power coupling and electron heat transport is discussed. The radial localization of electron density in the coaxial plasma waveguide is observed and compared with experimental results. Moreover, a parameter study allows one to investigate the dependence of radial contraction of the electron density as a function of pressure in the range 2–8 mbar, and also the dependence of electron density with power input in the range 120–1200 W. In order to verify the model, the modelling results are compared with experimental results for the electron density and temperature and good agreement is found.

https://iopscience.iop.org/article/10.1088/0022-3727/47/12/125204/pdf

A two-dimensional modelling study of a coaxial plasma waveguide

A two-fluid theory of a positive column in a cylindrical geometry having an internal coaxial wall is given. The space charge density throughout the whole plasma and inertia and diffusion controlled conditions are taken into account. An eigenvalue problem with a free boundary is solved. The radial distributions of the number densities and of the drift velocities of the ions and electrons and the profile of the electric potential are calculated. The boundary of the regions of particle collection for the inner and outer walls is exactly determined. The results show that the particle fluxes and the number densities of ions and electrons and, in particular, the floating potential at the inner wall are different from the values at the outer wall. The differences increase with an increasing ratio of the radii of the outer and inner walls. Under these conditions a so called impressed voltage or electromotive force occurs within the plasma which compensates the electric voltage between the inner and the outer wall since no radial electric current flows.

Sheaths, particle fluxes, floating potentials and electromotive force in a cylindrical discharge plasma containing an internal coaxial wall

The theory of positive column is generalized including additional non-emitting electrodes within the plasma and at the wall. Taking into consideration cylindrical and spherical geometries yields a theory of current carrying sheaths and presheaths and a theory of asymmetric double probes. Single probe operation in bounded plasmas can be approximated. A steady state compressible two-fluid model is used throughout the plasma. Various conditions for probe operations can be described as collision dominated and collisionless plasmas, the thick and the thin sheath regime and the transition regions. The radii of the regions of electron collection and of ion collection for the inner and outer walls are calculated. Detailed results are given for number densities, drift velocities, the electrical potential and the current-voltage characteristics. The floating potentials depend on the curvature of the electrode as shown analytically and numerically.

Modelling of sheaths, presheaths, current-voltage characteristics and double probes in low-pressure plasmas in coaxial and concentric geometries

The well known diffusion theory of the positive discharge column is extended considering a plasma which burns between two coaxial cylindrical walls. Recent experimental investigations carried out with the goal to enlarge the fluxes of ultraviolet radiation in fluorescent lamp tubes motivate such an extension. Indeed, an enhancement of the efficacy could be found installating a glass rod along the tube axis which acts as an additional recombination surface. In order to understand this effect also a description of the radial plasma behaviour, especially that of the electron density, and of the necessary charged particle production by ionization is of interest. The paper reports about such an extension, including a representation of a suitable numerical solution approach and a discussion of the results.

Extension of Schottky's Theory to a Cylindrical Discharge Plasma Containing a Coaxial Rod

In a preceding part of the paper, based on the Fourier expansion technique, a new method was developed to study the electron kinetics in weakly ionized, spatially uniform bulk plasmas of rf discharges in the established periodic state. Starting from the electron Boltzmann equation the Fourier expansion technique has been applied to the partial differential equation system for f and fA, the isotropic part and the first contribution to the anisotropy of the electron velocity distribution function, where both the distribution parts are the first two coefficients of the Legendre Polynomial expansion of the distribution function. In this part of the paper the new method will be applied to investigate the behaviour of the electron velocity distribution of the rf bulk plasma in molecular hydrogen and, in addition, of main macroscopic quantities.



The study of the latter quantities will be possible since these are determined by appropriate energy space averaging over f and ft, respectively. Thus, a comprehensive harmonics analysis of the electron component of the rf H2 bulk plasma could be made in a wide rf field frequency range. This includes the determination of the harmonics contributions to the isotropic and anisotropic distribution and to relevant macroscopic quantities as dependent on the field frequency for the mentioned wide rf field frequency range as well as of the phase angles between the different harmonics. It could be proved that the so-called 10-term approximation is sufficient for the description. Further on the periodic alteration of important macroscopic quantities, as mean electron energy, power input from the rf field and power loss in collision processes etc., and their period averages will be investigated in this truncation order. The results obtained are discussed and could be especially interpreted within a physical concept based on a comparison of the rf field frequency with the lumped collision frequency for energy dissipation and that for impulse dissipation.

Harmonics Analysis of the Electron Component of rf Bulk Plasmas II. Electron Distribution Function and Relevant Macroscopic Quantities in H2

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Extension of Schottky's Theory to a Cylindrical Discharge Plasma Containing a Coaxial Rod

Harmonics Analysis of the Electron Component of rf Bulk Plasmas II. Electron Distribution Function and Relevant Macroscopic Quantities in H2