Thin-film silicon solar cells are often deposited on textured ZnO substrates. The solar-cell performance is strongly correlated to the substrate morphology, as this morphology determines light scattering, defective-region formation, and crystalline growth of hydrogenated nanocrystalline silicon (nc-Si:H). Our objective is to gain deeper insight in these correlations using the slope distribution, rms roughness (σ(rms)) and correlation length (lc) of textured substrates. A wide range of surface morphologies was obtained by Ar plasma treatment and wet etching of textured and flat-as-deposited ZnO substrates. The σ(rms), lc and slope distribution were deduced from AFM scans. Especially, the slope distribution of substrates was represented in an efficient way that light scattering and film growth direction can be more directly estimated at the same time. We observed that besides a high σ(rms), a high slope angle is beneficial to obtain high haze and scattering of light at larger angles, resulting in higher short-circuit current density of nc-Si:H solar cells. However, a high slope angle can also promote the creation of defective regions in nc-Si:H films grown on the substrate. It is also found that the crystalline fraction of nc-Si:H solar cells has a stronger correlation with the slope distributions than with σ(rms) of substrates. In this study, we successfully correlate all these observations with the solar-cell performance by using the slope distribution of substrates.