Epitaxial growth of 6H-SiC on 6H-SiC(0001) via two-dimensional nucleation was realized at 930 degrees C by solid-source molecular beam epitaxy using the alternate supply of Si and C. The deposition was controlled to an atomic level by surface superstructures. The growth was started on the (root 3X root 3)R30 degrees surface which turns into the (1X1) phase upon deposition of about 1 monolayer silicon and recurs after subsequent deposition of about 1 monolayer carbon. Deviations from the monolayer deposition and, moreover, growth around substrate related defects result in the deposition of 3C-SiC. (C) 1996 American Institute of Physics.