Atomic self-organization at the nanometer scale is a complex interplay between kinetic and thermodynamic phenomena. This interplay is evident in Al(110) homoepitaxy. In experimental studies of Al(110) homoepitaxy, it is observed that over a certain temperature window (330-500K), three-dimensional nanohuts form and self-organize over the micron scale [1,2]. The factors leading to this self-organization are currently unclear.

Using ab initio calculations based on density-functional theory with VASP, we determined the pair and multi-body interactions between Al adatoms on this surface. Within the framework of the lattice-gas model, we find that multi-body interactions (four-body, five-body, and higher) are significant. However, lattice-gas models become complicated with such high-order multi-body interactions. We developed a simple and accurate model to estimate the energies of clusters of any size. Employing this model, we see a transition from linear chains to rectangular islands as we increase the cluster size.

We used the climbing-image nudged elastic band method [3] to calculate the energy barriers for surface diffusion on Al(110). Exchange diffusion is seen to be the favorable mechanism. In the presence of neighboring adatoms, the activation energy changes due modifications of the initial, transition, and final state energies. In previous work, simple models have been used to estimate the effect of neighboring adatoms from the activation energy for isolated adatoms and the energy of the initial state [4] or from both the initial- and final-state energies [5]. These simple models cannot accurately describe the effect of neighboring adatoms on exchange. We present a model that considers all possible paths for exchange and provides the energy barrier by taking into account the actual transition-state configurations. Results from kinetic Monte Carlo simulations show that our model predicts a higher island density than previous ones, in agreement with experiment. The insight gained in this study could be employed to accurately predict nano-scale self-assembly in different growth scenarios.

[1] F. Buatier de Mongeot, W. Zhu, A. Molle, R. Buzio, C. Boragno, U. Valbusa, E. Wang, and Z. Zhang, Phys. Rev. Lett. 91, 016102 (2003).

[2] K. Fichthorn and M. Scheffler, Nature 429, 617 (2004).

[3] G. Henkelman, B.P. Uberuaga, and H. Jonsson, J. Chem. Phys. 113, 9901 (2000).

[4] A. Videcoq, F. Hontinfinde, R. Ferrando, Surf. Sci. 515, 575-587 (2002).

[5] K. A. Fichthorn and M. Scheffler, Phys. Rev. Lett. 84, 5371 (2000).

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