Abstract:
In a remarkable recent paper [PRL 88, 206103 (2002)], Pimpinelli and coworkers proposed a classification of step bunching instabilities in terms of scaling exponents characterizing the shape of the bunches and the time evolution of their size. In the talk I will scrutinize the relation between the continuum equations on which this analysis is based, and the underlying microscopic step dynamics. I will focus on a specific class of microscopic dynamics for which the destabilizing terms are linear in the terrace sizes, and which includes models of sublimation, growth, and surface electromigration. For this class of models the continuum equation can be derived rigorously, and the local scaling properties of the bunch can be accurately predicted. However, the description of the global bunch properties seems to require a treatment beyond the continuum equation.
This talk is based on joint work with V. Tonchev, S. Stoyanov and A. Pimpinelli.