464948 Current-Driven Dynamics of Single-Layer Epitaxial Islands on Crystalline Conducting Substrates
We develop and validate a fully nonlinear model for the islands’ driven morphological evolution on elastic substrates of face-centered cubic (fcc) crystals in the regime where diffusional mass transport is limited to the island edge and accounting for edge diffusional anisotropy. We establish a universal scaling theory to show that, if properly scaled, the stable island migration speed remains inversely proportional to the island size for all island sizes examined. For islands on <110>-, <100>-, and <111>-oriented substrate surfaces, we report a transition in the asymptotic states reached by such driven island dynamics from steady to oscillatory, mediated by Hopf bifurcation. We characterize the bifurcation and explore the dependence of the stable time-periodic state beyond the Hopf point on the misorientation angle between the applied electric field and fast edge diffusion directions, the strength of the edge diffusional anisotropy, and the island size. For islands larger than a critical size, depending on the orientation of the substrate surface, we observe fingering and necking instabilities in the island morphology. We carry out a comprehensive numerical simulation study and explore the complexity of the driven island dynamics with the variation of the problem parameters. A universal feature present in all the islands that exhibit stable oscillatory morphological response is that, for a given set of anisotropy parameters, the stable facet (i.e., straight island edge) orientations remain the same regardless of the island size. The stability of these facets is analyzed using linear stability theory.
In addition, we report the formation of complex nanopatterns emerging from individual larger-than-critical-size islands or from coalescence and break-up of pairs of islands. Following a sequence of breakup and coalescence events, the patterns formed upon turning off the electric field consist of distributions of islands that are symmetrically arranged with respect to the field direction, dispersed far from this symmetry axis and even containing symmetric distributions of stable voids (not simply connected domains). This rich variety of patterns and length scales can be exploited for a systematic physical, field-driven patterning of solid material surfaces. Our study advances our fundamental understanding of current-driven island dynamics on crystalline substrate surfaces as a means of directed assembly for physical nanopatterning.