Mathematical modeling of a direct current glow discharge in argon.

摘要

A glow discharge is obtained by inserting two electrodes (cathode and anode) in a low pressure gas environment {dollar}(sim{dollar}100 Pa) and applying a high voltage between the electrodes {dollar}(sim{dollar}1 kV). It is a complex kind of plasma, consisting of different plasma species (different kinds of atoms, ions, excited atoms, electrons, ...) that can all collide with each other. Glow discharges are used for etching, deposition and modification of layers, e.g. in the microelectronics industry, as metal vapor lasers, and also as spectroscopic sources in analytical chemistry. In the latter case, the cathode is constructed out of the material to be analyzed. Due to the sputter-bombardment by gas species onto the cathode, cathode-atoms are released and enter the plasma, where they are subject to a range of collisions (especially ionizaton and excitation). Therefore, the plasma is filled with atoms, ions and photons, representative for the material to be analyzed, which makes it useful as source for a variety of spectrometric techniques.; In order to improve the results in these application fields, a good insight in the fundamental processes of the glow discharge plasma is desirable. In this work, we try to achieve this by mathematical modeling, i.e., calculation of the behavior of the different plasma species. A set of three-dimensional models (Monte Carlo and fluid models) has been developed for a direct current glow discharge in argon, used in analytical chemistry. The species described in the models, include the argon gas atoms, argon ions, fast argon atoms, metastable argon atoms, electrons, and sputtered atoms and corresponding ions. The models are coupled to each other by the interaction processes between the plasma species. The combined models are solved iteratively until final convergence is reached, in order to obtain an overall picture of the glow discharge.; Typical results of the models include the densities, fluxes and energy distributions of the different plasma species, the electric field and potential distribution throughout the discharge, information about collision processes of the species, and the crater profiles and etching rates as a result of sputtering at the cathode. The results are presented in the three-dimensional geometry of a typical glow discharge cell and at typical discharge conditions for the VG9000 glow discharge mass spectrometer. The influence of pressure and voltage on the results is investigated. Moreover, to test the validity of the models, the results are compared with available literature data and experimental observations (e.g. Langmuir probe measurements, laser induced fluorescence spectrometry, measurements of energy distributions of ions bombarding the cathode, etc.). In general, the good agreement between theoretical and experimental results illustrates that the models present a realistic picture of the glow discharge.; Furthermore, the three-dimensional modeling results are compared with results of one-dimensional models. It was found that the latter yield already a satisfactory description of the glow discharge, but the three-dimensional models can give additional information and are therefore a progress when a more complete description of the discharge is intended.; Finally, as a spin-off, the models are used to explain differences in relative sensitivity factors in glow discharge mass spectrometry.