The molecular beam epitaxial growth of Si on SiC(0001), exhibiting a Stranski-Krastanov mode, was investigated by reflection high-energy electron diffraction. Several surface superstructures were observed in the initial stage of growth. After exceeding a critical coverage, Si island formation sets in. Under near-equilibrium conditions, the critical coverage was 1.4 monalayers and corresponds to the occurrence of a 3 x 3 superstructure remaining as a wetting layer after the island formation. island formation at high deposition rates (R) and low temperatures (T) is kinetically delayed, which can be described as function of R and the diffusivity D by a relationship t(c) proportional to rootR/D. Si islands, which were relatively uniform size of several nm with a density of 10(11) cm,were obtained under these conditions. At fewer R values the critical thickness is only a function of T, indicating that the incorporation time of adatoms is the relevant time scale for surface diffusion. Ordered arrays of small dots were also grown on vicinal surfaces at higher T and lower R values, which can be attributed to a lower diffusivity at step edges, acting as perfect sinks for the Si adatoms. Furthermore, two different kinds of islands were found with a (111)/(0001) and (110)/(0001) epitaxial relationship.