Dynamics and control of aggregate thin film surface morphology for improved light trapping: Implementation on a large-lattice kinetic Monte Carlo model

This work demonstrates the use of feedback control, coupled with a suitable actuator design, in manufacturing thin films whose surface morphology is characterized by a desired visible light reflectance/transmittance level. The problem is particularly important in the context of thin film manufacturing for thin film solar cells where it is desirable to produce thin films with precisely tailored light trapping characteristics. Initially, a thin film deposition process involving atom adsorption and surface migration is considered and is modeled using a large-lattice (lattice size=40,000) kinetic Monte Carlo simulation. Subsequently, thin film surface morphology characteristics like roughness and slope are computed with respect to different characteristic length scales ranging from atomic to the ones corresponding to visible light wavelength and it is found that a patterned actuator design is needed to induce thin film surface roughness and slope at visible light wavelength spatial scales, which lead to desired thin film reflectance and transmittance levels. Then, an Edwards–Wilkinson-type equation (a second-order stochastic partial differential equation) is used to model the surface evolution at the visible light wavelength spatial scale and form the basis for the design of a feedback controller whose objective is to manipulate the deposition rate across the spatial domain of the process. The model parameters of the Edwards–Wilkinson equation are estimated from kinetic Monte Carlo simulations and their dependence on the deposition rate is used in the formulation of the predictive controller to predict the influence of the control action on the surface roughness and slope throughout the thin film growth process. Analytical solutions of the expected surface roughness and surface slope at the visible light wavelength spatial scale are obtained by solving the Edwards–Wilkinson equation and are used in the control action calculation. The cost function of the controller involves penalties on both surface roughness and slope from set-point values as well as constraints on the magnitude and rate of change of the control action. The controller is applied to the large-lattice kinetic Monte Carlo simulation. Simulation results demonstrate that the proposed controller and patterned actuator design successfully regulate aggregate surface roughness and slope to set-point values at the end of the deposition that yield desired levels of thin film reflectance and transmittance.

► Elucidation of surface morphology evolution at visible light wavelength scale.
► Control relevant modeling, actuator design and predictive control.
► Implementation on a large-lattice kinetic Monte Carlo simulation.