Heuristic model of the plasma impedance in magnetron sputtering

Due to the increasing demand on precision, homogeneity, process control and throughput of the reactive magnetron sputtering deposition in large in-line coaters, there have been considerable efforts in theoretical modeling of this process in the past. In the literature promising approaches for (i) the kinetics between sputtered material and reactive gas, (ii) the distribution of sputtered neutral particles as well as (iii) flow kinetics of diluted gas within complex recipient geometries can be found. However, these approaches do not comprise the current-voltage characteristics at the sputter target. This behaviour is shown to strongly depend on secondary electron emission characteristics of the target material as well as on the magnetic field and configuration of anodes. Especially for long targets, the ratio between total discharge current and ring current along sputter erosion tracks has crucial impact on the homogeneity of the sputter process along target direction. In this paper we present a heuristic model which couples external electric parameters of a target operating in DC mode with international quantities such as (i) ion current, (ii) secondary electron emission, (iii) coupling due to ring current and (iv) subsidiary effects such as the anode configuration. With the aid of this model, the current voltage characteristics of reactive sputtering process using materials such as silicon and titanium, which strongly differ in secondary electron emission, are modeled. We present implications of the simultation model on the process behavior, e.g. target homogeneity, deposition rate and film stoichiometry in comparision with experimental findings.