Feedback control of surface roughness during thin-film growth using approximate low-order ODE model

The problem of feedback control of microstructure during thin film growth is addressed. The issue of the non-availability of closed form dynamic models for the evolution of microstructure is addressed by deriving a low-order state-space model that approximates the underlying kinetic Monte Carlo model. Initially a finite set of "coarse" observables is identified from spatial correlation functions to represent the coarse microscopic state that captures the dominant traits of the microstructure during the deposition process. Subsequently, a state-space model is identified, employing proper orthogonal decomposition and Carleman linearization, that describes the evolution of the coarse observables. The state space model is subsequently employed to design a receding horizon controller that regulates the surface roughness of the thin-film at a specified set point during the growth process by manipulating the substrate temperature. Closed-loop simulations at two distinct growth rates and in the presence of a step disturbance are performed to demonstrate the effectiveness of the controller