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.

中文翻译：

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直流反应磁控管放电的电流-电压特性建模及其在超导 NbTiN 薄膜沉积中的应用

开发了一种用于模拟反应磁控管放电电流-电压特性 (IVC) 的数值模型。该模型建立在描述反应磁控溅射过程稳态的平衡方程的基础上。这种建模技术允许使用一对参数方程对 IVC 进行分析表达，这在计算上很方便。这种方法是独立的，因为直接测量无法获得的一些关键参数可以通过测量的 IVC 的模型拟合来确定。通过使用该 IVC 模型，可以系统地研究各种物理量对放电电流和电压的依赖性。此外，该模型还分析和阐明了导致 IVC 滞后的条件。