Observability analysis and substrate state estimation of nonlinear reactive sputter processes

The substrate state of reactive sputter processes is a quality indicator of the deposited film. However, this state variable is not easily measurable during deposition. This contribution proposes a new method to design a nonlinear reduced observer that determines the substrate state by means of the reactive gas partial pressure, the self-bias voltage and reactive gas inflow. An observability analysis of the Berg model, which is the standard model to describe such processes, is presented. The main result is the proof that the estimated substrate state converges asymptotically. Furthermore, it is proven that the order relation of the plant substrate state and the estimated substrate state is preserved over time.