Two-Dimensional Nucleation with Edge and Corner Diffusion

TL;DR

This paper investigates how edge and corner diffusion affect island shapes and densities during nucleation on surfaces, revealing shape transitions and specific scaling laws for island density.

Contribution

It provides a detailed analysis of the influence of edge and corner diffusion on island morphology and density, including new scaling relations and shape transition mechanisms.

Findings

Increased edge diffusion leads to cross-shaped islands.

Corner diffusion results in square islands with specific growth instabilities.

Island density scales with flux and diffusion constants in predictable ways.

Abstract

The effect of edge and corner diffusions on the morphology and on the density of islands nucleated irreversibly on a flat substrate surface is studied. Without edge and corner diffusion, islands are fractal. As an edge diffusion constant $D_e$ increases, islands tend to take a cross shape with four needles in the $< 10 >$ direction. Additional corner diffusion with a diffusion constant $D_c$ yields square islands. When $D_e$ is small relative to the surface diffusion constant $D_s$, the square corner shows the Berg instability to produce hopper growth in the $<11>$ direction. The corner diffusion influences the island number density $n$. At a deposition flux $F$ with a small $D_c$, mainly monomers are mobile and $n \propto (F/D_s)^{1/3}$. At large $D_c$, dimers and trimers are also mobile and $n \propto F^{3/7} D_s^{-5/21} D_c^{-4/21}$. The $F$ dependence is in good agreement to the rate equation analysis, but the dependence on $D_c$ cannot be explained by the theory.