Current-driven morphological evolution of single-layer epitaxial islands on crystalline substrates

We develop and validate a nonlinear model for the current-driven dynamics of single-layer epitaxial islands on crystalline substrates. Simulations based on the model show that the dependence of the stable steady island migration speed vm on the inverse of the island size is not linear for larger-than-critical island sizes. In this nonlinear regime, we report morphological transitions, Hopf bifurcations, and instabilities for various surface crystallographic orientations and island misfit strains. Proper rescaling of vm gives a universal linear relationship for its dependence on island size.