(573d) Simultaneous Regulation of Film Thickness, Surface Roughness and Porosity in a Thin Film Growth
Modeling and control of thin film microstructure in thin film deposition processes has attracted significant research attention in recent years. Specifically, kinetic Monte Carlo (kMC) models were initially employed to describe the evolution of film microstructure and design feedback control laws for thin film surface roughness. Stochastic differential equations (SDEs) arise naturally in the modeling of surface morphology of ultra thin films in a variety of thin film preparation processes. Advanced control methods based on SDEs have been developed to address the need of model-based feedback control of thin film microstructure.
In the context of modeling of thin film porosity, kMC models have been widely used to model the evolution of porous thin films in many deposition processes. Deterministic and stochastic ordinary differential equation (ODE) models of film porosity were recently developed to model the evolution of film porosity and its fluctuation and design model predictive control (MPC) algorithms to control film porosity to a desired level and reduce run-to-run porosity variability. However, simultaneous control of film thickness, surface roughness and porosity within a unified control framework has not been addressed.
Motivated by these considerations, this work focuses on distributed control of film thickness, surface roughness and porosity in a porous thin film deposition process modeled via kinetic Monte Carlo simulation on a triangular lattice. The microscopic model of the deposition process includes adsorption and migration processes with vacancies and overhangs allowed inside the film. A distributed (partial differential equation) dynamic model is derived to describe the evolution of the surface height profile of the thin film. The dynamics of film porosity, evaluated as film site occupancy ratio, are described by an ordinary differential equation. The developed dynamic models are then used as the basis for the design of a model predictive control algorithm that includes penalty on the deviation of film thickness, surface roughness and film porosity from their respective set-point values with adsorption rate chosen as the manipulated variable. Simulation results demonstrate the applicability and effectiveness of the proposed modeling and control approach in the context of the deposition process under consideration.