It is shown that the formation of (2×1) reconstructed islands during the growth of Si on Si(0 0 1) and Ge(0 0 1) surfaces at moderate temperatures and the consequent anisotropic diffusion and sticking lead to roughening. As Si islands nucleate and expand, the dimer rows in neighboring rows need not, in general, align with each other. An anti-phase boundary (APB) will be found if two growing islands meet, but their internal dimer rows are not in the same registry. One type of APB runs perpendicular to the substrate rows, whereas the other runs along the substrate rows. As has been pointed out by Hamers et al. [J. Vac. Sci. Technol. A 8 (1990) 195] this first type of APB is a preferential center for nucleation of next layer islands and thus naturally leads to roughening. Here we show that the other type of APB leads, in combination with the anisotropy in sticking and diffusion of dimers, to the formation of long B-type double layer steps and narrow trenches. We argue that it is the kinetic suppression of filling of these trenches and not, as previously suggested the existence of step edge barrier for the double layer step edge that leads to roughening.