Scaling and universality in the kinetic smoothening of interfaces: Application to the analysis of the relaxation of rough vicinal steps of an oxide surface

TL;DR

This paper investigates the thermal relaxation of rough interfaces, revealing three distinct scaling regimes and a super-universal exponent, with applications to analyzing AFM images of sapphire surface step edges.

Contribution

It generalizes the Family-Vicsek scaling to the smoothening regime and identifies a super-universal exponent independent of specific models.

Findings

Identified three scaling regimes during interface relaxation.

Generalized Family-Vicsek scaling for smoothening.

Observed a super-universal exponent in transient smoothening.

Abstract

Relaxation of initially out-of-equilibrium rough interfaces in presence of thermal noise is investigated using Langevin formalism. During thermal equilibration towards the well-known roughening regime, three scaling regimes observed over three successive ranges of length-scales are evidenced: thermal roughening (late stage) at small scales, transient smoothening at intermediate scales and remnant of the initial conditions at large scales. A generalization of the Family-Vicsek scaling is found for the smoothening regime. A distinctive feature of the transient smoothening regime resides in the existence of a super-universal exponent, i.e. independent of the considered model. This approach allows interpreting a series of AFM images of sapphire surfaces showing the thermal evolution of initially rough step edges.