Analytic formulations for one-dimensional decay of rectangular homoepitaxial islands during coarsening on anisotropic fcc (110) surfaces

Abstract

Submonolayer homoepitaxial fcc (110) systems display behavior reflecting strong anisotropy at lower temperatures, including one-dimensional decay during Ostwald ripening of rectangular islands maintaining constant width in the $\ensuremath{\langle}001\ensuremath{\rangle}$ direction. To appropriately describe this behavior, we first develop a refined continuum Burton-Cabrera-Frank formalism, which accounts for a lack of equilibration of island shape and importantly also for inhibited incorporation of adatoms at almost-faceted $\ensuremath{\langle}\overline{1}10\ensuremath{\rangle}$ island edges through effective kinetic coefficients. This formalism is shown to describe accurately the adatom diffusion fluxes between islands and thus island evolution for a complex experimental island configuration, as confirmed by matching results from realistic atomistic simulations for this configuration. This approach also elucidates basic dependencies of flux on island geometry and temperature. Second, a further refinement is presented incorporating separate terrace and edge adatom density fields either in a continuum setting or alternatively in a spatially discrete diffusion equation setting. The second approach allows more flexibility and accuracy in accounting for edge-diffusion kinetics including corner rounding, a lack of equilibration of the edge adatom density at $\ensuremath{\langle}\overline{1}10\ensuremath{\rangle}$ island edges, and the effect of rare kinks on $\ensuremath{\langle}\overline{1}10\ensuremath{\rangle}$ island edges. Significantly, it suggests facile two-way corner rounding at the island periphery during island decay, contrasting the previous picture.