Simulation of linear magnetron discharges in 2D and 3D

In spite of being an established thin film coating technology for more than two decades, magnetron sputtering is still a subject of many interesting research activities with respect to its process and plasma discharge dynamics. While the magnetically confined magnetron discharge apparently forms an almost homogeneous plasma torus at the sputter target, recent investigations of high density magnetron discharges by high speed photography reveal that it actually consists of one or multiple propagating plasma waves. With circulation frequencies of several 10 kHz, these features are usually not discerned in practical magnetron sputtering setups; however they should play a significant role in the electron and ion transport dynamics influencing both, the current–voltage characteristics and/or the resulting ion energy distribution function. In order to analyze this in more detail, a minimalist 2D magnetron discharge model with periodic boundary conditions is compared with its 3D equivalent via the Particle-in-Cell Monte-Carlo simulation method. Propagating plasma waves are obviously only possible in 3D models, while the 2D model represents the “ideal” homogenous plasma torus. Thus, by comparing both models with equivalent power density, the impact of the plasma waves on the electric transport properties of the plasma can be analyzed.