Regulation of film thickness, surface roughness and porosity in thin film growth using deposition rate

This work focuses on distributed control of film thickness, surface roughness and porosity in a porous thin film deposition process using the deposition rate as the manipulated input. The deposition process includes adsorption and migration processes and it is modeled via kinetic Monte Carlo simulation on a triangular lattice with vacancies and overhangs allowed to develop inside the film. A distributed parameter (partial differential equation) dynamic model is derived to describe the evolution of the surface height profile of the thin film accounting for the effect of deposition rate. 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. Simulation results demonstrate the applicability and effectiveness of the proposed modeling and control approach in the context of the deposition process under consideration.