By using first-principles calculations, we study the origin of the flat Bi film growth on the Si(1 1 1) surface. First, we confirm
the validity of the present first principles method by calculating the a (1/3 ML coverage) and b (1 ML coverage) phases of
Si(1 1 1)H3 H3-Bi surface: The determined structures are found to be consistent with experimental results, i.e., the T4 site is
the most stable one for the a phase, and the milkstool structure is the most stable for the b phase. Next, we study the energetics of
the Bi films grown on the wetting layer on the Si(1 1 1) surface.We find that even-number layer films are prominently stable and
thus conclude that the even numbers correspond to the magic thicknesses which induce experimentally observed flat film growth.
We conclude that appearance of the magic thicknesses is due to large atomic relaxation which paired each two neighboring
layers. Thus, the mechanism that induces the magic thicknesses is different from the quantum size effect argued in the past