Ab initio calculations of energies and self-diffusion on flat and stepped surfaces of Al and their implications on crystal growth.

Abstract

Using density-functional theory we investigate properties of Al(111), Al(100), Al(110), and stepped Al(111) surfaces, including formation energies of surfaces, steps, adatoms, and vacancies. For adsorption and diffusion of Al on flat regions of Al(111) surfaces the hcp site is energetically slightly preferred over the fcc site. The energy barrier for self-diffusion on Al(111) is very low (0.04 eV). Close to either of the two sorts of close packed, monoatomic steps on Al(111), Al adatoms experience an indirect attraction of \ensuremath{\lesssim} 0.1 eV with the edge of the step, which has a range of several atomic spacings and is of electronic origin. At the lower step edge, an adatom attaches with no barrier at a low-energy fivefold coordinated site. Coming from the upper terrace, it incorporates into the step by an atomic exchange process, which has a barrier below 0.1 eV for both sorts of close-packed steps. The barrier for diffusion along the lower edge is 0.32 eV at the {100}-faceted step and 0.39 eV at the {111}-faceted step. Unexpectedly, the latter diffusion process proceeds by an exchange mechanism. Diffusion by an exchange mechanism is also found for the ``easy'' direction on the Al(110) surface, i.e., along the channels.We show that Al(110) is a model system for diffusion at the {111}-faceted step on Al(111) because of its similar local geometry. We estimate temperature ranges for different modes of homoepitaxial growth on Al(111). Of particular importance are the rather low barriers for diffusion across the descending steps and the rather high barriers for diffusion along the steps. We discuss island shapes on Al(111) during growth and in thermodynamic equilibrium. Depending on the temperature the growth shapes can be fractal, triangular, or hexagonal and mainly determined by kinetics; in equilibrium the island shape is hexagonal and determined by the different step formation energies. Many of these phenomena have been seen experimentally for other metals. \textcopyright{} 1996 The American Physical Society.