Profile scaling in decay of nanostructures

TL;DR

This paper investigates the decay of nanostructure profiles using a step flow model, revealing a specific scaling behavior and proposing a criterion for the unique solution of the profile evolution.

Contribution

It introduces a scaling scenario for the profile decay and proposes a selection criterion for the unique solution in nanostructure decay models.

Findings

Profile obeys dh/dr = F(r t^{-1/4})

Scaling function is flat for r<R(t) ~ t^{1/4}

Identifies a family of solutions and a selection criterion

Abstract

The flattening of a crystal cone below its roughening transition is studied by means of a step flow model. Numerical and analytical analyses show that the height profile, h(r,t), obeys the scaling scenario dh/dr = F(r t^{-1/4}). The scaling function is flat at radii r<R(t) \sim t^{1/4}. We find a one parameter family of solutions for the scaling function, and propose a selection criterion for the unique solution the system reaches.