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

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).