Continuum description of profile scaling in nanostructure decay

TL;DR

This paper develops a continuum model to describe the decay of nanostructure profiles with facets, revealing universal shape equations and scaling laws that match kinetic simulations.

Contribution

It introduces a continuum framework incorporating step energies and interactions, deriving universal shape equations and scaling laws for facet decay.

Findings

Universal shape profile equation derived for facet decay

Layer thickness scales as (g_3/g_1)^{1/3}

Profile peak scales as (g_3/g_1)^{-1/6}

Abstract

The relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition is studied via a continuum approach that accounts for step energy g_1 and step-step interaction energy g_3>0. For diffusion-limited kinetics, free-boundary and boundary-layer theories are used for self-similar shapes close to the growing facet. For long times and g_3/g_1 < 1, (a) a universal equation is derived for the shape profile, (b) the layer thickness varies as (g_3/g_1)^{1/3}, (c) distinct solutions are found for different g_3/_1, and (d) for conical shapes, the profile peak scales as (g_3/g_1)^{-1/6}. These results compare favorably with kinetic simulations.