Single (strained and relaxed) and polycrystalline Si_1-xGe_x samples have been bombarded using low-energy oxygen ions to study the impact of strain and relaxation-induced dislocations on their surface morphologies and subsequent formation of ripples. The as-grown relaxed sample surface exhibits cross-hatch patterns due to relaxation along its surface. Compared to Si, all the surfaces of these materials exhibit ripple formation at lower fluences. Moreover, the nature of the induced surface topography depends largely on the original surface morphology. Single crystalline layers show clear ripple formation whereas the polycrystalline surface leads to more isolated features. On a relaxed surface that exhibits the cross-hatch patterns due to relaxation along its surface, very long ripples tend to form along the dislocation ridges which eventually become shorter (and finally break up) with increasing distance from a particular ridge. A detailed temporal study has been done to understand the nature of ripple formation on the relaxed sample. A theoretical estimation of the crossover time indicates that the morphology of the relaxed sample is primarily governed by the nonlinear regime of ripple formation. It is found that the surface follows the scaling laws as dictated by the isotropic Kardar–Parisi–Zhang equation. The growth exponent (n) is found to be ~0.23, which is in agreement with the theoretical value. Ripple coarsening is observed which fits well with the recently predicted model indicating the contribution of nonlinear effects arising out of redeposition of the sputtered atoms and presence of mobile surface adatoms. The subsequent saturation of wavelength takes place as a result of geometrical shadowing.