Step Bunching In Conserved Systems: Scaling And Universality

TL;DR

This paper investigates step bunching in one-dimensional models, deriving scaling laws and revealing different types of bunching behavior depending on drift magnitude, with implications for understanding surface evolution.

Contribution

It introduces a unified analysis of three step flow models, identifying scaling relations and universality classes in step bunching phenomena.

Findings

Identified two types of step bunching depending on drift magnitude.

Derived scaling relations for long-time step bunching behavior.

Showed universality in the scaling laws across different models.

Abstract

We study the step bunching process in three different 1D step flow models and obtain scaling relations for the step bunches formed in the long times limit. The first one was introduced by S.Stoyanov [Jap. J.Appl. Phys. 29, (1990) L659] as the simplest 'realistic' model of step bunching due to drift of the adatoms. Here we show that it could lead to (at least) two different types of step bunching, depending on the magnitude of the drift. The other two models are minimal models: the equations for step velocity are constructed ad hoc from two terms with opposite effects - destabilizing and, respectively, stabilizing the regular step train.