Random surface texturing of an optically thick film to increase the path length of scattered light rays, first proposed nearly thirty years ago, has thus far remained the most effective approach for photon absorption over the widest set of conditions. Here, using recent advances in computational electrodynamics, we describe a general strategy for the design of a silicon thin film applicable to photovoltaic cells based on a quasi-resonant approach to light trapping where two partially disordered photonic-crystal slabs, stacked vertically on top of each other, have large absorption that surpasses the Lambertian limit over a broad bandwidth and angular range. (C) 2014 AIP Publishing LLC.