Robust multivariable estimation and control in an epitaxial thin film growth process under uncertainty

This study presents a multivariable robust estimator that predicts the controlled outputs in a thin film growth process for online applications. The evolution of the epitaxial growth process on a substrate is modeled based on a multiscale approach, coupling a continuum gas phase model and a kinetic Monte Carlo (KMC) model that describes the evolution of the thin film surface. In the estimator, the issue of computationally intensive KMC simulations is circumvented by developing reduced-order models that are identified offline based on data obtained from the multiscale model. This approach significantly reduces the simulation time over KMC and makes the online control and optimization feasible. The estimator evaluates the surface roughness and growth rate based on the substrate temperature and the bulk precursor mole fraction during the growth process. To provide robust estimations, the estimator is designed to evaluate the upper and lower bounds on the outputs under model parameter uncertainties. To assess the uncertainty propagation into the system's outputs, power series expansion (PSE) is employed in the presence of distributional parametric uncertainties. The sensitivities of the outputs with respect to the uncertain parameters are assessed offline at different substrate temperatures and bulk precursor mole fractions. Accordingly, upper and lower bounds on the outputs are determined at a specific confidence level and employed to identify a reduced-order model for online applications. To assess the efficiency of the estimator, proportional integral (PI) controllers are coupled with the estimator to control surface roughness and growth rate while manipulating the substrate temperature and the bulk precursor mole fraction, respectively. The robust control of the process under parameter uncertainties is investigated using the bounds estimated on the controlled outputs.