We evaluate the potential of three-dimensional (3D) thin-film silicon solar cells in the superstrate configuration deposited on hexagonally ordered arrays of ZnO nanocolumns (NCs). These nanostructures are prepared by hydrothermal growth, which is an effective and versatile method to obtain ZnO NCs of high optical and electrical quality at low temperature. For the periods P investigated, varied between 0.9 and 1.4m, 3D solar cells based on hydrogenated amorphous silicon (a-Si:H) exhibit a photocurrent (J(SC)) boost in the red wavelength range as compared to flat cells; this J(SC) gain (by more than 1.5mAcm(-2) for P=0.9m) is explained mostly by the increased effective optical thickness of the absorber layer grown on the vertical walls of the NCs. Combining this 3D concept with randomly textured interfaces, rigorous 3D optical simulations based on the finite element method predict that photocurrents significantly higher than those obtained with state-of-the-art substrates (up to 20mAcm(-2)) are within reach, if the experimental obstacles specific for 3D design are overcome.