Stochastic nonlinear model predictive control applied to a thin film deposition process under uncertainty

• A thin film deposition process is simulated using the multiscale approach.
• Models are developed to predict the statistical moments of thin film properties.
• An uncertainty analysis of the process is performed using PSEs.
• Sensitivities are obtained from data collected offline using the multiscale model.
• The model is applied as a basis of a stochastic NMPC framework.

This paper investigates the application of stochastic nonlinear model predictive control (NMPC) to a thin film deposition process in the presence of model-plant mismatch while ensuring constraints at a specific probability limit. To capture the multiscale nature of the process, the evolution of the thin film is modelled using nonlinear partial differential equations (PDEs) embedded with lattice-based kinetic Monte Carlo (KMC) simulations. To provide a computationally tractable closed-form expression for online predictive control applications, model identification is performed using data collected from the multiscale deposition model. The closed-form model predicts the expected value and the variance of the thin film properties based on the substrate temperature during the deposition process. The parameters of the closed-form model are determined offline employing power series expansion (PSE). The closed-form model allows the reformulation of probabilistic constraints into their corresponding deterministic expressions thus enabling the design of a computationally tractable stochastic NMPC. To show the effectiveness of the approach, a shrinking horizon stochastic NMPC framework is devised to minimize the final surface roughness while complying with actuator constraints and a probabilistic constraint on the final film thickness.