Recently, a systematic effort has been undertaken in developing efficient energy harvesting devices on thin Si films. Two main mechanisms have been identified for the efficient light harvesting. One is related to minimizing reflection losses, while the other is related to coupling to quasi-guided modes supported by the silicon film. However, the effects associated with the homogeneity and isotropy of the structures have not attracted much attention. Here, we employ hyperuniform disordered structures(HUDS) to achieve very efficient light harvesting in the wavelength range from 400 to 1000 nm. We show that the surface patterning has a dramatic impact on the number modes that are involved in the absorption process and that the structure needs to be optimized such that the scattering promotes minimization of the energy directed in radiative channels, i.e. inside the light cone of the surrounding air. To provide a through comparison, we also fully optimize a periodic structure taking into account the patterning of the AR layer refractive index. We then examine various HUDS architectures and demonstrate not only the importance of the scattering components, but also the dramatic impact of the structure homogeneity and isotropy on the devices performance. Using this design strategy, we report a broadband solar energy absorption of 84% in a one micron-thick Si membrane, which is, to the best of our knowledge, the best value achieved in such ultra-thin Si membranes.