(37e) Dynamics and Control of Aggregate Thin Film Surface Morphology for Improved Light Trapping: Implementation On a Large-Scale Kinetic Monte-Carlo Simulation

Zhang, X. - Presenter, University of California, Los Angeles

Photovoltaic (solar) cells are an important source of sustainable energy. Thin-film silicon solar cells are currently among the most important and widely used solar cells and their share of the overall solar cell market is steadily increasing (e.g.,[1]). Research on optical modeling of thin-film silicon solar cells indicates that the scattering properties of the thin film interfaces directly influence the light trapping process and the efficiencies of thin-film silicon solar cells (e.g., [2],[3] ). However, no efforts have been seen in improving the conversion efficiency of thin-film solar cells via the regulation of the thin film surface morphology during the manufacturing process by appropriately tailoring the surface slope and roughness to desired specifications. Thus, it is desirable to develop systematic approaches to manufacture thin film solar cells with optimal conversion efficiencies via computational modeling and real-time model-based control of the manufacturing process. Recently, we have initiated an effort towards modeling and control of thin film surface morphology to optimize the light reflectance and transmittance properties of thin films. In this direction, we have studied the dynamics and lattice size dependence of surface mean slope [4] and have developed predictive control algorithms to regulate both surface roughness and slope of KMC simulators with small domain size in one [5] and two [6] spatial dimensions. However, control of thin film surface morphology within a domain comparable to the visible light wavelength has remained unsolved.
This work focuses on the application of a model predictive controller to a large-scale kinetic Monte-Carlo model. The dynamics of the evolution of the thin film surface height profile are modeled by an Edwards-Wilkinson-type equation (a second-order stochastic partial differential equation) in one spatial dimension. The thin film surface morphology is characterized in terms of surface roughness and surface slope. Analytical solutions of the expected surface roughness and surface slope are obtained by solving the Edwards-Wilkinson equation and are used in the controller design. The model parameters of the Edwards-Wilkinson equation are estimated from large scale kinetic Monte-Carlo (KMC) simulations. This parameter 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 at the end of the growth process. The cost function of the controller involves penalties on both surface roughness and mean 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 a large-scale one-dimensional KMC model with a domain size comparable to the wavelength of visible light. Simulation results show that the proposed controller successfully regulates surface roughness and slope to set-point values at the end of the deposition that yield desired levels of thin film reflectance and transmittance.
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[6] X. Zhang, G. Hu, G. Orkoulas, and P. D. Christofides. Multivariable Model Predictive Control of Thin Film Surface Roughness and Slope for Light Trapping Optimization, Industrial & Engineering Chemistry Research, 49: 10510-10516, 2010.