(429d) Analysis of External-Field-Driven Surface Morphological Evolution: Stabilization and Nanopatterning

Directed assembly on material surfaces and surface morphological evolution are governed by strongly nonlinear dynamics and lead to intriguing pattern formation.  Externally applied fields, such as electric fields and temperature gradients, can be used to drive such surface morphological evolution and directed assembly in crystalline solids.  We have studied the use of external fields to prevent surface morphological instabilities in stressed solids and to drive the assembly of single-layer epitaxial islands.  Toward this end, in this presentation, we examine the surface morphological stability of electrically and thermally conducting crystalline elastic solids in uniaxial tension and of biaxially coherently strained epitaxial films on substrates under the combined action of an electric field and a temperature gradient.  We use linear stability theory and self-consistent dynamical simulations based on a surface mass transport model that accounts for surface electromigration and thermomigration induced by the applied electric field and thermal gradient, respectively, surface diffusional anisotropy, and the temperature dependence of surface diffusivity.  We find that properly directed external fields of magnitude higher than a critical value can stabilize the planar surface morphology and derive the conditions for synergistic action of the external fields, as well as the criticality conditions for surface stabilization.

We have also developed and validated a nonlinear model for the current-driven dynamics of single-layer epitaxial islands on crystalline substrates.  Simulations based on the model show that the dependence of the stable steady island migration speed on the inverse of the island size is not linear for larger-than-critical island sizes.  In this nonlinear regime, we report morphological transitions, Hopf bifurcations, and necking instabilities for various surface crystallographic orientations and island misfit strains.  Moreover, we have studied the evolution of pairs of different-size islands driven to coalescence and explored the effects of three key geometrical parameters: the sizes of the two islands of the pair and their center-to-center line misalignment with respect to the electric-field direction.  We discovered various patterns ranging from equal- and different-size stable steady island-pair configurations to many-island patterns that can be tailored by controlling the initial-pair geometrical parameters and the duration of application of the electric field.