High-efficiency thin-film silicon triple-junction solar cells in p-i-n configuration have been fabricated using amorphous silicon top cell absorber layers, as well as microcrystalline silicon middle and bottom cell absorbers. The triple-junction cells were fabricated on boron doped zinc oxide (ZnO) films with different surface morphologies. To this end, the naturally grown rough ZnO surfaces were flattened using an Ar plasma for three different treatment times. For the shortest time, we achieved a summed current density over 30 mA/cm(2) and initial and stabilized conversion efficiencies of 13.5% and 12.5%, respectively. For the medium treatment time, we obtained the highest efficiencies (13.7% initial and 12.8% stable), whereas the longest treatment time led to the highest open-circuit voltage (V-OC) of 1.91 V but lower current densities, leading to efficiencies of 12.9% initial and 12.2% stable, respectively. These results were obtained by combining various recently developed features and approaches: first of all, we implemented high-quality mu c-Si: H cells with novel buffer layers, leading to very high efficiencies. Second, we applied randomly textured pyramids on the front glass to improve light in-coupling, and finally, we used very thin (similar to 140 nm) top cells that led to a low light-induced degradation (5%-7% relative loss in efficiency).