Classification of step bunching phenomena

The classification of bunching of straight steps on vicinal crystal surfaces identifies two types according to the behavior of the minimal step-step distance in the bunch lmin with increasing the number of steps N in it. In the B1-type lmin remains constant while in the B2-type it decreases. Both types are illustrated by new results for well-known models. The precise numerical analysis is aimed at the intermediate asymptotic regime where self-similar spatiotemporal patterns develop. In the model of Tersoff et al. the regular step train is destabilized by step-step attraction of infinite range. It is shown that this model belongs to the B1-type and the same time-scaling exponent of 1/5 for N, terrace width and bunch width is obtained. An extended set of scaling exponents is obtained from the model of S.Stoyanov of diffusion-limited evaporation affected by electromigration of the adatoms. This model is of B2-type and shows a systematic shift of the exponents with respect to the predictions of the hypothesis for universality classes in bunching thus requiring further modification of it.

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