Scaling properties of step bunches induced by sublimation and related mechanisms: A unified perspective

TL;DR

This paper develops a unified theoretical framework to understand the scaling laws and profiles of step bunches on crystal surfaces during sublimation, revealing universality classes and their limitations.

Contribution

It introduces a continuum model for step bunching during sublimation, deriving power law relations and identifying two types of stationary bunch profiles, extending universality concepts.

Findings

Power law relations between bunch width, height, and interstep distance.

Existence of two stationary bunch profile types with different scaling.

Results applicable to step bunching in growth and electromigration scenarios.

Abstract

This work provides a ground for a quantitative interpretation of experiments on step bunching during sublimation of crystals with a pronounced Ehrlich-Schwoebel (ES) barrier in the regime of weak desorption. A strong step bunching instability takes place when the kinetic length is larger than the average distance between the steps on the vicinal surface. In the opposite limit the instability is weak and step bunching can occur only when the magnitude of step-step repulsion is small. The central result are power law relations of the between the width, the height, and the minimum interstep distance of a bunch. These relations are obtained from a continuum evolution equation for the surface profile, which is derived from the discrete step dynamical equations for. The analysis of the continuum equation reveals the existence of two types of stationary bunch profiles with different scaling properties. Through a mathematical equivalence on the level of the discrete step equations as well as on the continuum level, our results carry over to the problems of step bunching induced by growth with a strong inverse ES effect, and by electromigration in the attachment/detachment limited regime. Thus our work provides support for the existence of universality classes of step bunching instabilities [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002)], but some aspects of the universality scenario need to be revised.