Existing growth mechanisms of hydrogenated amorphous silicon (a-Si:H) and microcrystalline silicon (muc-Si) assume that the growth species SiH3 can diffuse over the hydrogen-saturated Si surface. However, recent calculations suggest that this could not happen. We have carried out local density formalism pseudopotential calculations of the binding of SiH3 to hydrogen-terminated (1 1 1)Si surfaces. The bound site is not the three-centre Si-H-Si bridging site previously assumed. It has a direct Si-Si bond between the SiH3 and the surface Si, and the surface hydrogen is displaced to a bond centre of a surface Si-Si bond. A bound site validates conventional models of growth of a-Si:M and muc-Si, in which a mobile growth species creates smooth surfaces.