Epitaxial growth of silicon on heavily boron-doped Si(111) surface was investigated. In our experiments, we found a new growth mode in the very initial stage for boron-coverage below 0.5 monolayer (ML) likely associated with defect-induced nucleation of Si islands. The initially stage of growth on boroncovered Si(111) could be interpreted by a quasi van der Waals like epitaxy, where Si adatoms catch sites on the surface with only slightly deeper depression in the flat surface potential without significant bonding to the neighboring atoms. Deposition of Si at temperature below 800 K results in a layer-by-layer growth via nucleation and coalescence of two-bilayer Si islands on top of the initially formed van der Waals like buffer Si buffer layer, before the transition in the normal double layer growth mode occurred. The grown Si layers were found in twin position with respect to the underlying Si(111) substrate, resulting in a stacking fault in the substrate/layer interface. Structures with twin boundaries arranged periodically along the [111]-direction and separated by only a few Si double layers were obtained by repetition of a multi-step procedure several times. In such a way we obtained structures with regions of a twin repeat sequence ranging from 12 Si bilayers, corresponding to a twinning-superlattice, down to 4 bilayers, what is equivalent to a hexagonal 8H-Si polytype.