Multivariable predictive control of thin film deposition using a stochastic PDE model

Abstract

In this work, we construct a 2-dimensional (2D) stochastic partial differential equation (PDE) model for a thin film deposition process and design a multivariable predictive controller based on the constructed model to control thin film thickness and surface roughness. We focus on a thin film deposition process governed by three microscopic processes including molecule adsorption, migration and desorption. A 2D linear stochastic PDE model is initially constructed following the methodology proposed in our previous work [Ni, D. and Christofides, P. D., 2005]. Then, a stochastic PDE model-based multivariable controller is designed using the constructed stochastic PDE model. The control problem is formulated as a predictive control problem, in which the constructed stochastic PDE model is used to predict both the thin film thickness and the surface roughness. Moreover, the controller design is performed based on a finite stochastic ordinary differential equation (ODE) approximation of the stochastic PDE model to achieve high computational efficiency. The model-based predictive controller is applied to the kinetic Monte-Carlo (kMC) simulation of the deposition process to simultaneously control the thin film thickness and surface roughness. Closed-loop system simulation results demonstrate that the model is adequately accurate and that the controller is effective.