We investigate the growth process of twinned epitaxial Si layers on Si(111)root 3X root 3-B and their thermal stability. In the initial growth stages, twinned two-bilayer-high (2-BL-high) and untwinned BL-high islands are formed, and at higher surface B concentration, there are more twinned 2BL islands than untwinned BL islands. Domain boundaries of the root 3X root 3 reconstruction act as preferential island nucleation sites, especially for untwinned BL islands. Therefore, to grow epitaxial layers twinned with the already-grown twinned layers, post-growth anneal is essential to increase the surface B concentration and to reduce the domain boundary density. On the other hand, the temperature at which twinned layers are transformed into untwinned layers strongly depends on the thickness. We demonstrate the possibility of growing superlattices of layers that have twinned and untwinned orientations with the substrate (polytypes) by precisely controlling the growth and post-growth anneal parameters.