Continuum description of profile scaling in nanostructure decay

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 g₁ and step-step interaction energy g₃>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 g₃/g₁<1, (a) a universal equation is derived for the shape profile, (b) the layer thickness varies as (g₃/g₁)1/3, (c) distinct solutions are found for different g₃/g₁, and (d) for conical shapes, the profile peak scales as (g₃/g₁)^-1/6. These results compare favorably with kinetic simulations.