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Dielectric nanoparticles placed on top of a thin-film solar cell strongly enhance light absorption in the cell over a broad spectral range due to the preferential forward scattering of light from leaky Mie resonances in the particle. In this study, we systematically study with numerical simulations the absorption of light into thin (1-100 μm) crystalline Si solar cells patterned with Si nanocylinder arrays on top of the cell. We then use an analytical model to calculate the solar cell efficiency, based on the simulated absorption spectra. Using realistic values for bulk and surface recombination rates, we find that a 20-μm-thick Si solar cell with 21.5% efficiency can be made by using the Si nanocylinder Mie coating.