Modelling of the reactive sputtering process with non-uniform discharge current density and different temperature conditions

The majority of current models of the reactive magnetron sputtering assume a uniform shape of the discharge current density and the same temperature near the target and the substrate. However, in the real experimental set-up, the presence of the magnetic field causes high density plasma to form in front of the cathode in the shape of a toroid. Consequently, the discharge current density is laterally non-uniform. In addition to this, the heating of the background gas by sputtered particles, which is usually referred to as the gas rarefaction, plays an important role. This paper presents an extended model of the reactive magnetron sputtering that assumes the non-uniform discharge current density and which accommodates the gas rarefaction effect. It is devoted mainly to the study of the behaviour of the reactive sputtering rather that to the prediction of the coating properties. Outputs of this model are compared with those that assume uniform discharge current density and uniform temperature profile in the deposition chamber. Particular attention is paid to the modelling of the radial variation of the target composition near transitions from the metallic to the compound mode and vice versa. A study of the target utilization in the metallic and compound mode is performed for two different discharge current density profiles corresponding to typical two pole and multipole magnetics available on the market now. Different shapes of the discharge current density were tested. Finally, hysteresis curves are plotted for various temperature conditions in the reactor.