Glow discharge in low pressure plasma PVD: mathematical model and numerical simulations

TL;DR

This paper develops and analyzes mathematical models and numerical simulations of glow discharge in low pressure plasma PVD chambers, considering different geometries and operating conditions, to better understand plasma behavior in industrial settings.

Contribution

It introduces detailed mathematical models and numerical simulations for glow discharge in various chamber geometries, extending previous simplified models to more realistic industrial configurations.

Findings

Models reproduce key plasma features like dark spaces and glow regions.

Simulations show similarities with previous 1D and 2D models.

Results align with preliminary 3D case findings.

Abstract

In this paper we analyze the problem of glow discharge in low pressure plasma in industrial plant, for chambers of different shapes and various working parameters, like pressure and electric potential. The model described is based upon a static approximation of the AC configuration with two electrodes and a drift diffusion approximation for the current density of positive ions and electrons. A detailed discussion of the boundary conditions imposed is given, as well as the full description of the mathematical model. Numerical simulations were performed for a simple 1D model and two different 2D models, corresponding to two different settings of the industrial plant. The simpler case consists of a radially symmetric chamber, with one central electrode (cathode), based upon a DC generator. In this case, the steel chamber acts as the anode. The second model concerns a two dimensional horizontal cut of the most common plant configuration, with two electrodes connected to an AC generator. The case is treated in a "quasi-static" approximation. The three models show some common behaviours, particularly including the main expected features, such as dark spaces, glow regions and a wide "plasma region". Furthermore, the three shown models show some similarities with previously published results concerning 1D and simplified 2D models, as well as with some preliminary results of the full 3D case.