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System Identification and Model Predictive Control of Microstructure during Thin-Film Growth

Amit Varshney, Pennsylvania State University, 23 Fenske Laboratory, Pennsylvania State University, University Park, PA 16802 and Antonios Armaou, The Pennsylvania State University, University Park, PA 16802.

The current trend of increasing device performance specifications and decreasing feature dimensions have necessitated the use of accurate process models for design, optimization and control of processes in the microelectronic industry. In this work, we address the problem of feedback control of thin film microstructure during deposition. The issue of the unavailability of closed-form dynamic models to accurately describe the evolution of product microstructure is addressed by deriving a low-order state-space model that approximates the underlying master equation (solved numerically through Monte Carlo sampling). 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 [1]. 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 then 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. The proposed controller design scheme is successfully applied to a representative deposition process; 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.

[1]. A. Varshney and A. Armaou. Identification of macroscopic variables for low-order modeling of thin-film growth. Ind. Eng. Chem. Res., in press, 2006.