Crossover from BKT-Rough to KPZ-Rough Surfaces for Interface-Limited Crystal Growth/Recession

TL;DR

This study investigates the transition from BKT to KPZ rough surfaces in crystal growth using Monte Carlo simulations, revealing new insights into the influence of driving force and surface features on surface roughness classes.

Contribution

It introduces a non-equilibrium Monte Carlo model for interface-limited crystal growth, showing the crossover point differs from kinetic roughening and depends on growth parameters.

Findings

Crossover point from BKT to KPZ roughness differs from kinetic roughening point.

Driving force influences whether the surface exhibits BKT or KPZ behavior.

Surface features like islands and ad-atoms block fluctuations, affecting roughness class.

Abstract

The crossover from a Berezinskii--Kosterlitz--Thouless (BKT) rough surface to a Kardar--Parisi--Zhang (KPZ) rough surface on a vicinal surface is studied using the Monte Carlo method in the non-equilibrium steady state in order to address discrepancies between theoretical results and experiments. The model used is a restricted solid-on-solid (RSOS) model with a discrete Hamiltonian without surface or volume diffusion (interface limited growth/recession). The temperature, driving force for growth, system size, and surface slope dependences of the surface width are calculated for vicinal surfaces tilted between the (001) and (111) surfaces. The surface velocity, kinetic coefficient of the surface, and mean height of the locally merged steps are also calculated. In contrast to the accepted theory for (2+1) surfaces, we found that the crossover point from a BKT (logarithmic) rough surface to a KPZ (algebraic) rough surface is different from the kinetic roughening point for the (001) surface. The driving force for crystal growth was found to be a relevant parameter for determining whether the system is in the BKT class or the KPZ class. It was also determined that ad-atoms, ad-holes, islands, and negative-islands block surface fluctuations, which contributes to making a BKT-rough surface.