Multivariable Predictive Control of Thin Film Deposition Using a Stochastic PDE Model

Abstract

In this work, we focus on a thin film deposition process which takes place on a two-dimensional (2D) lattice and is governed by three microscopic processes including molecule adsorption, surface migration, and desorption. A 2D linear stochastic partial differential equation (PDE) model is initially constructed which describes the spatio-temporal evolution of the film surface. Then, the control problem is formulated as the one of regulating the thin film thickness and surface roughness by manipulating the substrate temperature and adsorption rate. Subsequently, a computationally efficient multivariable predictive control algorithm is developed which uses a finite-dimensional approximation of the stochastic PDE model to regulate the thin film thickness and surface roughness at desired levels at the end of the deposition. The predictive controller is then applied to the kinetic Monte Carlo simulation of the deposition process. Closed-loop system simulation results demonstrate that the model is adequately accurate and that the controller is effective in enforcing the desired control objectives and reducing film variance.