Crossover from BKT-rough to KPZ-rough surfaces for interface-limited crystal growth/recession

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 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.

Faceted-rough surface with disassembling of macrosteps in nucleation-limited crystal growth

“…It should be noted that A and B for k B T/ǫ = 0.2 , 0.4, and 1.7 at equilibrium are the same within errors, as stated in Ref. 65 .…”

“…At non-equilibrium in the faceted-rough region, if we regard the amplitude w 0 = (W/L α p ) as a local degree of roughness, we can explain the anisotropy of the local roughness of the faceted-rough surface. In the facetedrough region, w 0 is 0.01-0.03, as seen from Table 2, whereas w 0 for a non-faceted vicinal surface is 0.08 65,69 . This anisotropy in w 0 is consistent with the anisotropies which were phenomenologically assumed [47][48][49] .…”

“…In our previous work on the original RSOS model 65 , where ǫ int = 0 , the vicinal surface for �µ/ǫ > 1.8 is shown to be KPZ-rough. Around �µ/ǫ ∼ 1 , a broad peak is observed corresponding to the kinetic roughening kr /ǫ for the (001) surface.…”

“…In our previous study on the surface width for the original RSOS model 65 , we found that the kinetic roughening point of the (001) surface �µ (001) kr is different from the crossover point between the BKT-rough surface and the KPZ-rough surface �µ B−K co (Table 1) with respect to the driving force for crystal growth �µ . For high �µ , the vicinal surface of the RSOS model near the (111) surface is KPZ-rough; whereas the vicinal surface of the RSOS model near the (001) surface is BKT-rough.…”

Slope–temperature faceting diagram for macrosteps at equilibrium

“…In the TSK model, excited structures contributing to the surface roughness, i.e., ad-atoms, ad-holes, islands, and negative islands (assembly of ad-holes), on the terrace surface are assumed to be irrelevant. However, recently, such excited structures were found to be relevant for fluctuating growing surfaces 35 . The appearance of the step droplet zone is one such surface-roughness relevant phenomenon.…”