Improving the Lumped Element Model of a Radio Frequeny Magnetron Discharge

Magnetron sputtering is an established technology to deposit thin films with high quality. Employing RF power (instead of the conventional DC power) allows to deposit not only electrically conductive materials but also dielectrics like optical coatings or semiconductors. In this work two different approaches are used to study the discharge numerically which is otherwise investigated experimentally. An implicit energy-conserving 2d3v PIC/MCC code in rz-geometry simulates the plasma spatially and temporally resolved. Global parameters like the voltage drop in the bulk region and in the magnetized zone, currents to the surfaces, and the bias voltage are extracted from this simulation. These parameters are used to improve a lumped element model. This model is an extension of a previously published lumped circuit description of unmagnetized RF discharges¹. As its predecessor, the discharge is represented by separate bulk, and sheath zones and in addition a new magnetized zone which are linked via Kirchhoff relations. The model is efficient in terms of computation time, it only needs a fraction of the time compared to the PIC simulation. Nevertheless, it can be used to gain a fundamental understanding of the discharge. It was successfully used to identify the origin of the Magnetic Asymmetry Effect in a previous work². With help of the global parameters extracted from the PIC simulations the length of each zone can be determined. The current voltage behavior in the magnetized zone can be fitted, too, to have a suitable description. Due to the magnetic field structure there are sheath areas at the powered electrode where electrons reach the electrode. This information can be gained from the simulation as well and used for the lumped element model. The results of the improved lumped circuit model pertaining to the electron dynamics, plasma series resonance and power dissipation are verified against the results of the PIC simulations.