(375d) Complex Pattern Formation from Current-Driven Dynamics of Single-Layer Epitaxial Islands on Crystalline Conducting Substrates

The ability to assemble nanostructures using externally applied macroscopic forcing is an emerging paradigm in the field of nanofabrication. Macroscopic forcing provided in the form of an applied electric field can be used to drive atomic transport in a cluster of atoms through edge electromigration. A very interesting problem in this regard is of the current-driven dynamical response of single-layer adatom and vacancy clusters, i.e., islands and voids of single-layer thickness/depth, on conducting substrate surfaces.

In this presentation, we discuss the development and validation of a fully nonlinear model for the current-driven morphological evolution of single-layer epitaxial islands on elastic substrates of face-centered cubic (FCC) crystals in the regime where diffusional atomic transport is limited to the island edge. The model also accounts for edge diffusional anisotropy. We focus on the driven dynamics of large isolated rounded islands on crystalline substrates under the action of an electric field oriented along the fast edge diffusion direction. First, we analyze the edge morphological stability of these islands using linear stability theory. The theory predicts that, under the action of an external field, the edge of islands larger than a critical size becomes unstable. Direct dynamical simulations based on the model of the evolution of islands with larger-than-critical sizes shows that edge morphological instabilities lead to necking and breakup of the parent islands into a population of daughter islands, which evolves to form complex island patterns. For large islands on {110} and {100} FCC substrates, we show that multiple necking instabilities generate island patterns that may include not-simply-connected void-containing islands. This pattern formation is mediated by sequences of island breakup and coalescence events with the islands of the pattern distributed symmetrically with respect to the electric field direction; the corresponding equilibrium nanopatterns, obtained by switching the electric field off, are intriguing and may include single-layer nanorings with very appealing properties for technological applications. We analyze the dependence of the formed patterns on the original island size and the duration of application of the external field and characterize the evolution of the generated number of daughter islands as well as their average size and uniformity. We show that the evolution of the average island size follows a universal scaling relation and that the evolution of the total edge length of the formed island pattern follows Kolmogorov-Johnson-Mehl-Avrami kinetics. Our study makes a strong case for the use of electric fields, as precisely controlled macroscopic forces, toward surface patterning involving complex nano-scale features.