We have grown Ar+ ion beam sputtered Si epitaxially on Si(100) at substrate temperatures, T, between 390 and 480 K. At 480 K and 0.65 nm/s deposition rate, epitaxy is sustained at 1 μm of film thickness. At lower T, we observed an abrupt transition to amorphous growth at a critical thickness, he, which exhibited an Arrhenius dependence on T, as has previously been observed in molecular beam epitaxy (MBE) [D. J. Eaglesham, H. J. Gossmann, and M. Cerullo, Phys. Rev. Lett. 65, 1227 (1990)]. Our slope, d(ln he)/d(1/T), was 3 times steeper than in MBE, resulting in much thicker he at the higher T. The steep slope shows that the high kinetic energy of the sputtered Si is not enhancing surface diffusion enough to overcome thermal surface diffusion. We propose instead that the arriving kinetic energy is preventing void formation and thereby decreasing the rate at which statistical surface roughness, Δh, increases with film thickness. In both deposition processes, we propose that the collapse of epitaxy occurs when Δh exceeds the thermal surface diffusion length.