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 alpha (1/3 ML coverage) and beta (1 ML coverage) phases of Si(1 1 1) root3 x root3-Bi surface: The determined structures are found to be consistent with experimental results, i.e., the T-4 site is the most stable one for the alpha phase, and the milkstool structure is the most stable for the beta 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 studies. (C) 2004 Elsevier B.V. All rights reserved.