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

Abstract

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 statespace 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.

Online system-identification using subspace algorithms for the control of microscopic processes

“…The linear controller that was designed based on the identified model, was used to control the lower order statistical moments of microscopic distributions. In a different approach [22] the problem of non availability of closed form models was addressed by deriving a low-order state space model through offline system identification, based on finite set of "coarse" observables. The identified state space model was used to design a receding horizon controller to regulate the roughness, during thin film growth, at a particular setpoint.…”

“…We build upon the approach of [1], [22] and develop a computationally tractable online process model identification and adaptive control methodology, which takes into account the change in the underlying process dynamics as the process traverses different regions in the variable state space. The computationally tractable online system-identification component of the approach is based on subspace-system identification (SSI).…”