Periodic surface topography is observed in Si films deposited on fused quartz when the films are crystallized by a scanning laser or electron beam. The formation and character of this topography depends upon the structure of the Si film. With amorphous Si, periodic features can be formed at the leading edge of the beam. We thick these are produced by self sustained crystallization as has been previously studied in Ge and other materials. Liberation of latent heat in the film enables the crystallization front to propagate a short distance ahead of the beam. In the moving temperature gradient this motion is periodic and therefore leaves a periodic crystal grain pattern. With polycrystalline silicon films, recrystallization requires the beam to melt the film. Periodic structures form at the trailing edge of the molten pool. Similar ripples have been studied in other materials. The temperature distribution in the melt can cause a surface tension gradient that pulls material to the edges. When this material solidifies, expansion of the silicon may enhance the ripple amplitude.