Islands in the Stream: Electromigration-Driven Shape Evolution with Crystal Anisotropy

TL;DR

This paper investigates how electromigration and crystal anisotropy influence the shape evolution of two-dimensional islands on surfaces, revealing conditions for stationary shapes, instabilities, and oscillations through analytical and numerical methods.

Contribution

It provides analytical solutions for stationary island shapes without line tension and explores the full problem with line tension via numerical simulations, highlighting new shape behaviors.

Findings

Stationary shapes depend on electric field orientation and crystal symmetry.

No stationary shapes exist with an odd number of symmetry axes.

Shape oscillations and breakup occur under certain conditions.

Abstract

We consider the shape evolution of two-dimensional islands on a crystal surface in the regime where mass transport is exclusively along the island edge. A directed mass current due to surface electromigration causes the island to migrate in the direction of the force. Stationary shapes in the presence of an anisotropic edge mobility can be computed analytically when the capillary effects of the line tension of the island edge are neglected, and conditions for the existence of non-singular stationary shapes can be formulated. In particular, we analyse the dependence of the direction of island migration on the relative orientation of the electric field to the crystal anisotropy, and we show that no stationary shapes exist when the number of symmetry axes is odd. The full problem including line tension is solved by time-dependent numerical integration of the sharp-interface model. In addition to stationary shapes and shape instability leading to island breakup, we also find a regime where the shape displays periodic oscillations.