Scaling of the minimal step-step distance with the step-bunch size: Theoretical predictions and experimental findings (a mini-review)

TL;DR

This paper reviews theoretical and experimental studies on how the minimal step-step distance in step bunches scales with bunch size, focusing on electromigration effects on Si(111) surfaces and providing a general scaling relation.

Contribution

It synthesizes existing models and experimental data to present a comprehensive scaling relation for step bunching phenomena under electromigration.

Findings

Scaling exponent varies between models and experiments

Full scaling relation incorporates electromigration force and step interactions

Provides a unified framework for step bunching behavior

Abstract

We review the studies on the scaling of the minimal step-step distance lmin in the bunch with the bunch size N, l_min~N^(-{\gamma}). We build our retrospective around the different values of the exponent {\gamma} obtained from models and experiments. It was mainly studied in the context of the electromigration driven instability on Si(111) vicinal surfaces. In this context the full scaling relation is given in general form as l_min ~ (A/l_cFN^2)^[1/(n+1)], where A is the magnitude of the step-step repulsions with range n, F is the electromigration force acting on the charged surface atoms and l_c is a length-scale, characteristic for the regime of step bunching, diffusion-limited (DL) or attachment-detachment limited (KL).