Height transitions, shape evolution and coarsening of equilibrating quantum nanoislands

Abstract

Morphology evolution and coarsening of metal nanoislands is computed within the framework of a surface diffusion-type model that includes the effects of the electron energy confinement within the film, the charge spillage at the film/substrate interface, the energy anisotropy of the film surface and the surface stress. The conditions that result in large islands with flat tops, steep edges, and strongly preferred heights are determined. A strong influence of the film height on the coarsening dynamics and final morphologies is found; the conditions leading to interrupted coarsening are highlighted. The dependence of the geometric parameters of the equilibrium island on the film height and on the island initial volume is computed.

Morphologies, metastability, and coarsening of quantum nanoislands on the surfaces of the annealed Ag(110) and Pb(111) thin films

“…Thus α = 1.95 × 10 −8 cm/8.9 × 10 −7 cm= 0.022 1 and, as in Refs. [23,24,38,41,42], we expand the adimensionalized form of Eq. (1) in α and then retain the dominant contributions.…”

“…Recent modeling [54] of the morphological evolution of surfaces of stressed solids suggests that, at least in the framework of 2D model, the anisotropy of the diffusivity does not significantly affect the dynamic morphologies (unless surface electromigration is present). Also, computations using simpler version of our model [23] show that the surface energy anisotropy is not making a large impact on the 2D (metal) islands morphologies (for growth and coarsening of 3D metal islands the insignificance of the surface energy anisotropy was noted, see Ref. [55].…”

“…In Refs. [23,24] a basic surface diffusion equation-based continuum model was developed for studies of the evolving quantum island morphologies during annealing. The model was applied to a generic film/substrate system featuring the ad hoc simply-periodic surface energy oscillation (that is, without a beating pattern).…”

“…Other examples of the continuum models that enable the computation of the dynamic morphologies of an ultrathin films can be found in Ref. [23]. Recently, several sophisticated 2D and 3D continuum models of thicker film epitaxial growth and morphological evolution have been published [31][32][33][34][35][36][37].…”