Low-order ODE approximations and receding horizon control of surface roughness during thin-film growth

The problem of feedback controller synthesis with objective to control the microstructure during thin-film growth is considered. The problem of the non-availability of closed form dynamic models for the evolution of the microstructure is circumvented by deriving low-order state-space models that approximate the underlying kinetic Monte Carlo simulations. Initially, a finite set of "coarse" observables is identified from spatial correlation functions to represent the coarse microscopic state and capture the dominant characteristics 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 receding horizon controllers that regulate the surface roughness of the thin-film at a specified set-point during the growth process by manipulating the substrate temperature. The above approach is applied to: (i) a deposition process modeled using solid-on-solid model on a one-dimensional lattice; and (ii) an anisotropic deposition process on a two-dimensional lattice. Closed-loop simulations at various growth rates and in the presence of disturbances are performed to demonstrate the effectiveness of the proposed controller design scheme.