Transient growth and evaporation kinetics at vicinal surfaces with non-local electromigration: step bunching instability

TL;DR

This paper develops a transient growth model for vicinal surfaces considering non-local electromigration, revealing conditions for step bunching instability influenced by adatom transparency and drift velocity.

Contribution

It introduces a novel transient growth model that accounts for non-local electromigration effects on step dynamics at vicinal surfaces.

Findings

Vicinal surface with transparent steps becomes unstable under certain drift conditions.

Most unstable mode's wavelength depends only on step transparency, not on surface orientation.

Instability occurs when adatom drift velocity exceeds a critical threshold.

Abstract

The steps at the crystal surfaces could be transparent for the migrating adatoms. In the case of significant transparency the velocity of a given step in a given moment is affected by detachment of atoms from rather distant steps in rather earlier moments. The reason is that the adatom needs time to cross many steps before attaching to a kink position. The theory of the crystallization should account for the time dependence of the adatom concentrations on the terraces. Such a transient growth model is developed here for the limit of slow kinetics at the steps and fast surface diffusion. The model accounts for the non-local electromigration of the adatoms. The central results of this study are: - The vicinal surface with transparent steps is unstable when the drift velocity of the adatoms multiplied with the relative deviation of the adatom concentration from equilibrium is larger than the critical velocity of the steps. - The most unstable mode has a wavelength (expressed as a number of terraces) which is independent of the surface orientation (the miscut angle of the vicinal) as well as on the magnitude of step repulsion and the electromigration force and depends only on the relative transparency of the steps.