Complex Pattern Formation from Current-Driven Dynamics of Single-Layer Homoepitaxial Islands on Crystalline Conducting Substrates

Abstract

We report a systematic study of complex pattern formation resulting from the driven dynamics of single-layer homoepitaxial islands on surfaces of face-centered cubic (FCC) crystalline conducting substrates under the action of an externally applied electric field. The analysis is based on an experimentally validated nonlinear model of mass transport via island edge atomic diffusion, which also accounts for edge diffusional anisotropy. We analyze the morphological stability and simulate the field-driven evolution of rounded islands for an electric field oriented along the fast edge diffusion direction. For larger-than-critical island sizes on {110} and {100} FCC substrates, we show that multiple necking instabilities generate complex island patterns, including not-simply-connected void-containing islands, mediated by sequences of breakup and coalescence events and distributed symmetrically with respect to the electric field direction. We analyze the dependence of the formed patterns on the original island size and on the duration of application of the external field. Starting from a single large rounded island, we characterize the evolution of the number of daughter islands and their average size and uniformity. The evolution of the average island size follows a universal power-law scaling relation and the evolution of the total edge length of the islands in the complex pattern follows Kolmogorov-Johnson-Mehl-Avrami kinetics. Our study makes a strong case for the use of electric fields, as precisely controlled macroscopic forcing, toward surface patterning involving complex nano-scale features.

Temperature transitions and degeneracy in the control of small clusters with a macroscopic field

“…Since τ φ (s, s) = 0 on the target, the recursion equation (5) shows that the expected time to reach the target is equal to the residence time τ φ (s, s) = t φ (s). This quantity is also equal to the expected return time to the target τ r ∞ (s) from equation (11).…”

“…However, these forces also have the ability to alter the shape of the clusters. For example in the case of electromigration of large monolayer clusters, complex cluster shapes are known to emerge from instabilities [5,6] and from the coupling of the electric field direction to the cluster edge anisotropy [2,7,8]. Another example of non-trivial morphologies emerging in the presence of an external field is the shaping of small nano-particle clusters by light [9].…”

“…Another example of non-trivial morphologies emerging in the presence of an external field is the shaping of small nano-particle clusters by light [9]. In these systems, efforts have been devoted to the identification of the nontrivial set of morphologies that emerge from cluster dynamics under external fields [5][6][7][8][9]. Here, we wish to ask a different question: can we start by defining arbitrarily a target cluster shape that we want to reach, and then find a way to reach it in a given physical system?…”