Photovoltaic cells (solar cells), especially, thin-film soar cells, are an important source of clean, sustainable energy. One of the main barriers that prevents the wide application of thin-film solar cells is the limited conversion efficiency of the solar power. To improve the efficiency of thin-film solar cells, optical and electrical modeling has been widely used to predict the optical and electrical behavior of thin-film solar cells [1, 2]. Specifically, the scattering properties of the thin film interfaces and their associated morphology are directly related to the light trapping process and play a decisive role in the efficiency of thin-film silicon solar cells [3, 4, 5]. Therefore, it is desired that the conversion efficiency of solar cells may be improved via the regulation of surface morphology of thin-film solar cells during the manufacturing process.
However, the characteristic variables of the thin film surface morphology, including surface roughness and surface mean slope that are defined as the root-mean-squares of the film surface height and slope profiles, respectively, are typically in the atomic length scale. Since the wavelength of visible light is of several orders of magnitude larger than the atomic length scale, surface roughness and mean slope may have different behaviors at different length scales and should be carefully defined and studied to be relevant to the light trapping efficiency of the surface/interface of thin films . Especially, the surface mean slope decrease quadratically as the length scale increases, which results in a smooth surface with very small surface slope at large length scales.
Motivated by these considerations, this work focuses on improving the light trapping efficiency of thin film solar cells by modeling and controlling the thin film surface roughness and mean slope at large length scales. Kinetic Monte Carlo (kMC) models are used to simulate a silicon thin film deposition process. Surface height profiles are obtained from the kMC simulations of the thin film growth process and are averaged within the aggregations of lattice sites with a related length scale, e.g., the wavelength of visible light. The average surface height profiles are then used to calculate surface roughness and mean slope that are relevant in this length scale. Spatially distributed control, i.e., the control actions are different at different spatial locations on thin film surface, is used to induce appropriate surface slope profiles at larger length scales; the adsorption rate is chosen as the manipulated variable. A distributed (partial differential equation) stochastic dynamic model is used to describe the evolution of the surface height profile and is used as the basis for the design of a model predictive control algorithm that includes penalty on the deviation of surface roughness and surface mean slope from their respective set-point values. Simulation results demonstrate the applicability and effectiveness of the proposed modeling and control approach in the context of the deposition process under consideration.
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