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

摘要

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