Effect of Thickness on the Surface and Electronic Properties of Bi Film

Bismuth and its alloys exhibit a number of peculiarities and mysterious features due to its three-dimensional (3D) hexagonal crystal, and have attracted the interest of many researchers for many years. Currently, the trivial-to-topological and semimetal-semiconductor transitions have been focused, as the result of its semi-metallic and large spin-orbit coupling. The binary compounds of Bi2M3 and binary alloys BixM1-x (M=Se, Sb and Te) are found to be 3D topological insulators, as the result of small band gap and large spin-orbit coupling in Bi crystals and Bi compounds, which make these crystals topologically important. In the case of Bi films, strong spin-orbit (SO) coupling interaction is also a fundamental mechanism to induce the Z(2) topology. Recently, ultrathin Bi films have also been theoretically predicted to be an elemental two-dimensional topological insulator. And, all the ultrathin Bi(111) films are characterized by a nontrivial Z(2) number independent of the film thickness. In the past few years, ultrathin films of Bi with a thickness down to several BLs (bilayers) on Si substrate have been prepared in experiments, finding that thicknesses have an effect on the properties of Bi films. However, the effect of thickness on films had not be studied for microscopic mechanism experimentally in detail. In this work, the effects of thickness on the surface and electronic properties of (00l) and (012) oriented films of Bi using the first-principles method were studied. With the increase of thickness, (00l) oriented Bi films became more stable, and the film of the even-numbered layers was more stable than that of the odd-numbered layer. However, the (012) oriented Bi films presented totally different behavior comparing with the (00l) oriented Bi film. The stabilities of (012) oriented film became less stable as the thickness increased, and possessed the approximated surface energy of even-numbered layers (00l) oriented Bi films when their layer numbers were closed to four. Further analysis of the cohesive energy, geometry structure and electronic band structures showed that, all the thin films presented the transition from semi-conductors to semi-metal or metal as the thickness increases.