Modeling current-voltage characteristics of DC reactive magnetron discharges and its application to superconducting NbTiN film deposition

A numerical model for simulating current-voltage characteristics (IVCs) of reactive magnetron discharges is developed. The model is built on the basis of equilibrium equations describing the steady state of reactive magnetron sputtering processes. This modeling technique allows an analytical expression of IVCs with a pair of parametric equations, which are computationally convenient. This approach is self-contained because some critical parameters that are not available from direct measurement can be determined by model fitting of measured IVCs. By using this IVC model, the dependence of various physical quantities on the discharge current and voltage can be systematically investigated. In addition, the conditions leading to hysteresis in IVCs are analyzed and clarified with this model. This modeling method is applied to a realistic case of superconducting NbTiN film deposition, and the simulation results suggest helpful guidance to the optimization of the plasma process for desired film quality and provide insight into the experimental phenomena.