Model predictive control of film porosity in thin film deposition

A model predictive controller is developed to regulate film porosity and minimize its fluctuation in thin film deposition. The deposition process is modeled via kinetic Monte Carlo (kMC) simulation on a triangular lattice. The microscopic events involve atom adsorption and migration and allow for vacancies and overhangs to develop. Appropriate definitions of film site occupancy ratio (SOR), i.e., fraction of film sites occupied by particles over total number of film sites, and its fluctuation are introduced to describe film porosity. Deterministic and stochastic ordinary differential equation (ODE) models are also constructed to describe the time evolution of film SOR and its fluctuation. The coefficients of the ODE models are estimated on the basis of data obtained from the kMC simulator of the deposition process using least-square methods. The developed ODE models are used as the basis for the design of model predictive control (MPC) algorithms that include penalty on the film SOR and its variance to regulate the expected value of film SOR at a desired level and reduce run-to-run fluctuations. Simulation results demonstrate the applicability and effectiveness of the proposed film porosity control method in the context of the deposition process under consideration.