Self-organized one-atom thick fractal nanoclusters via field-induced atomic transport

Abstract

We report on the growth of a monolayer thick fractal nanostructures of Ag on flat-top Ag islands, grown on Si(111). Upon application of a voltage pulse at an edge of the flat-top Ag island from a scanning tunneling microscope tip, Ag atoms climb from the edge onto the top of the island. These atoms aggregate to form precisely one-atom thick nanostructures of fractal nature. The fractal (Hausdorff) dimension, DH = 1.75 ± 0.05, of this nanostructure has been determined by analyzing the morphology of the growing nanocluster, imaged by scanning tunneling microscopy, following the application of the voltage pulse. This value of the fractal dimension is consistent with the diffusion limited aggregation (DLA) model. We also determined two other fractal dimensions based on perimeter-radius-of-gyration (DP) and perimeter-area (D′P) relationship. Simulations of the DLA process, with varying sticking probability, lead to different cluster morphologies [P. Meakin, Phys. Rev. A 27, 1495 (1983)]; however, the value of DH is insensitive to this difference in morphology. We suggest that the morphology can be characterized by additional fractal dimension(s) DP and/or D′P, besides DH. We also show that within the DLA process DP = DH [C. Amitrano et al., Phys. Rev. A 40, 1713 (1989)] is only a special case; in general, DP and DH can be unequal. Characterization of fractal morphology is important for fractals in nanoelectronics, as fractal morphology would determine the electron transport behavior.