Predictive control of surface mean slope and roughness in a thin film deposition process

This work focuses on the development of a model predictive control algorithm to simultaneously regulate the surface slope and roughness of a thin film growth process to optimize thin film light reflectance and transmittance. Specifically, a thin film deposition process modeled on a one-dimensional triangular lattice that involves two microscopic processes: an adsorption process and a migration process, is considered. Kinetic Monte Carlo (kMC) methods are used to simulate the thin film deposition process. To characterize the surface morphology and to evaluate the light trapping efficiency of the thin film, surface roughness and surface slope are introduced as the root mean squares of the surface height profile and surface slope profile. An Edwards–Wilkinson (EW)-type equation is used to describe the dynamics of the surface height profile and predict the evolution of the root-mean-square (RMS) roughness and RMS slope. A model predictive control algorithm is then developed on the basis of the EW equation model to regulate the RMS slope and the RMS roughness at desired levels by optimizing the substrate temperature at each sampling time. The model parameters of the EW equation are estimated from simulation data through least-square methods. Closed-loop simulation results demonstrate the effectiveness of the proposed model predictive control algorithm in successfully regulating the RMS slope and the RMS roughness at desired levels that optimize thin film light reflectance and transmittance.