This work focuses on the development of a model predictive control algorithm to simultaneously regulate the aggregate surface slope and roughness of a thin film growth process to optimize thin film light reflectance and transmittance. Specifically, a two-stage thin film deposition process, which involves two microscopic processes: an adsorption process and a migration process, is modeled based on a one-dimensional solid-on-solid square lattice. The first stage of this process utilizes a uniform deposition rate profile to control the thickness of the thin film and the second stage of the process utilizes a spatially distributed deposition rate profile to control the surface morphology of the thin film. Kinetic Monte Carlo (kMC) methods are used to simulate this two-stage thin film deposition process. To characterize the surface morphology and to evaluate the light trapping efficiency of the thin film, aggregate surface roughness and slope corresponding to length scale of visible light are introduced as the root-mean squares of the aggregate surface height profile and aggregate surface slope profile. An Edwards-Wilkinson (EW)-type equation with appropriately computed parameters is used to describe the dynamics of the surface height profile and predict the evolution of the aggregate root-mean-square (RMS) roughness and aggregate RMS slope. A model predictive control algorithm is then developed on the basis of the EW equation model to regulate the aggregate RMS slope and the aggregate RMS roughness at desired levels. Closed-loop simulation results demonstrate the effectiveness of the proposed model predictive control algorithm in successfully regulating the aggregate RMS slope and the aggregate RMS roughness at desired levels that optimize thin film light reflectance and transmittance. © 2011 Elsevier Ltd.
Huang, J., Orkoulas, G., & Christofides, P. D. (2012). Simulation and control of aggregate surface morphology in a two-stage thin film deposition process for improved light trapping. Chemical Engineering Science, 71, 520–530. https://doi.org/10.1016/j.ces.2011.11.027