Unstable vicinal crystal growth from cellular automata

TL;DR

This paper introduces cellular automata models to study unstable vicinal crystal growth, analyzing how biased diffusion and Ehrlich-Schwoebel barriers influence step bunching and surface pattern formation.

Contribution

It presents a novel cellular automata approach to simulate unstable vicinal crystal growth, highlighting the effects of specific instabilities on surface morphology.

Findings

Step bunching occurs with finite width in the presence of instabilities.

Scaling laws describe the transition from diffusion-limited to kinetics-limited regimes.

Different growth instabilities exhibit distinct time-scaling exponents for bunch size.

Abstract

In order to study the unstable step motion on vicinal crystal surfaces we devise vicinal Cellular Automata. Each cell from the colony has value equal to its height in the vicinal, initially the steps are regularly distributed. Another array keeps the adatoms, initially distributed randomly over the surface. The growth rule defines that each adatom at right nearest neighbor position to a (multi-) step attaches to it. The update of whole colony is performed at once and then time increases. This execution of the growth rule is followed by compensation of the consumed particles and by diffusional update(s) of the adatom population. Two principal sources of instability are employed: biased diffusion and infinite inverse Ehrlich-Schwoebel barrier (iiSE). Since these factors are not opposed by step-step repulsion the formation of multi-steps is observed but in general the step bunches preserve a finite width. We monitor the developing surface patterns and quantify the observations by scaling laws with focus on the eventual transition from diffusion-limited to kinetics-limited phenomenon. The time-scaling exponent of the bunch size N is 1/2 for the case of biased diffusion and 1/3 for the case of iiSE. Additional distinction is possible based on the time-scaling exponents of the sizes of multi-steps, these are 0.36-0.4 (for biased diffusion) and 1/4 (iiSE).