(747c) Current-Driven Evolution of Single-Layer Epitaxial Islands and Island Pairs On Crystalline Solid Substrates

The driven assembly of confined quantum structures is of special importance to nanoelectronics and nanofabrication technologies.  In this context, a particularly interesting problem is the current-driven dynamical response of single-layer adatom and vacancy clusters, i.e., islands and voids of single-layer thickness/depth, on substrate surfaces.  In this presentation, we report theoretical and computational results on the current-driven morphological response of single-layer epitaxial islands and island pairs on crystalline elastic substrates based on a two-dimensional fully nonlinear continuum model, according to which mass transport due to curvature-driven diffusion, stress-driven diffusion, and electromigration is limited only to the island periphery (edge).  The model also accounts for diffusional anisotropy for such “edge diffusion”.  Within this edge-diffusion driven mass transport regime, we have carried out a theoretical analysis of the morphological stability of such isolated islands and of the current-driven migration dynamics of morphologically stable islands.  Employing well-tested front tracking methods, we have also developed direct dynamical simulators of the driven morphological evolution of such islands based on the model.  We have validated the model by comparing the simulation predictions for stable island morphology and island-size dependence of the stable island migration speed with recent experimental measurements of current-driven evolution of homoepitaxial islands on Ag(111) substrates based on in situ scanning tunneling microscopy.

We have explored systematically the migration dynamics of morphologically stable steady islands over a broad range of misfit strains and kinetic parameters and found that the islands’ driven translational speed v_m is inversely proportional to their size R_s up to a critical island size.  For larger-than-critical sizes, the v_m(1/R_s) relation becomes nonlinear and the island dynamics in the nonlinear regime is characterized by morphological transitions (such as faceting and fingering transitions), Hopf-bifurcation transitions to oscillatory asymptotic states, and morphological instabilities (such as necking instabilities).  We derive a universal linear relationship that can describe this complex nonlinear behavior through rescaling v_m with the proper island morphological metric.

We have also analyzed the current-driven dynamics of single-layer epitaxial island pairs, where the two islands of the pair are driven toward their contact, and explored the resulting coalescence and breakup phenomena and the complex patterns they facilitate on the surface.  Important geometric parameters in the analysis include the sizes of the two islands in the pair and the misalignment angle formed by the applied electric-field direction and the line connecting the centers of mass of the two islands in the initial configuration of the pair.  We have discovered dynamical responses that lead to steady states after the initial island coalescence event.  Depending on the initial island sizes, following coalescence, the resulting larger island may either form a single-island steady state or break up.  If a single steady island is formed, its size determines whether its migration speed is in the linear or in the nonlinear regime.  If island breakup happens following coalescence, the distribution of the resulting islands with respect to the applied electric-field direction is symmetric for aligned islands and asymmetric for misaligned islands.  The findings of this work set the stage for systematic computational and experimental studies of external-field-enabled surface nanopatterning.