The driven assembly of confined quantum structures is of special importance to nanoelectronics and nanofabrication technologies. In this context, a particularly interesting problem is the current-driven dynamical response of single-layer adatom and vacancy clusters, i.e., islands and voids of single-layer thickness/depth, on surfaces of crystalline conducting or semiconducting substrates. In this presentation, we report theoretical and computational results on the current-driven complex morphological response of single-layer epitaxial islands on crystalline elastic substrates with atomic diffusion along the island periphery or edge being the dominant mode of mass transport.
We develop and validate a fully nonlinear transport model for the current-driven dynamics of such single-layer epitaxial islands on crystalline substrates. Simulations based on the model show that the dependence of the stable steady island migration speed on the inverse of the island size is not linear for larger-than-critical island sizes. In this nonlinear regime, a systematic parametric study is conducted to understand the effect on the individual island dynamics of edge diffusional anisotropy parameters, including the misorientation angle formed between a fast edge diffusion direction and the direction of the externally applied electric field.
For islands on <110>-, <100>-, and <111>-oriented substrate surfaces, we find a transition in the asymptotic states reached by such driven island dynamics from steady to oscillatory, the onset of which is marked by a Hopf bifurcation. We characterize the bifurcation and explore the dependence of the stable time-periodic state beyond the Hopf point on the misorientation angle, the strength of the edge diffusional anisotropy, and the island size. For islands larger than a critical size, depending on the orientation of the substrate surface, we find that the island morphology may undergo fingering and necking instabilities. We have also carried out a linear morphological stability analysis of an isolated single-layer driven island by employing a small-amplitude asymptotic expansion of the island morphology perturbed from a rounded shape. The evolution of the lower modes in the expansion provides important insights into the complex current-driven dynamics of single-layer epitaxial islands.