(196g) Nanopattern Formation from Current-Driven Dynamics of Single-Layer Epitaxial Islands on Crystalline Conducting Substrates

The directed assembly of nanostructures under the action of externally applied fields is of special significance to nanoelectronic and nanofabrication technologies. The current-driven response of single-layer adatom clusters, i.e., single-layer islands, on crystalline conducting substrate surfaces is of particular importance among such directed assembly processes. Here, we report a systematic and comprehensive theoretical and simulation study of epitaxial single-layer island dynamics under electromigration conditions on face-centered cubic (fcc) crystalline substrates. Our analysis provides guidance for developing external-field-driven surface nanopatterning strategies based on the directed assembly of single-layer islands.

We develop and validate a fully nonlinear model, which accounts for edge diffusional anisotropy, for the islands' driven morphological evolution on elastic substrates of fcc crystals in the regime where diffusional mass transport is limited to the island edge. For homoepitaxial islands, the model predicts that above a critical island size, the electric field, in conjunction with edge diffusional anisotropy, triggers morphological instabilities, such as fingering and necking instabilities, on the edge of the migrating islands. These instabilities result in parent island breakup and formation of organized regular or complex patterns such as arrays of parallel nanowires, single-layer nanorings, and nanodisc distributions. Other complex dynamical responses include transitions in the asymptotic states reached by parent islands from steady to time-periodic through subcritical Hopf bifurcations. In all of these cases, we explain the onset of instability based on linear stability theory and characterize the dynamics and the resulting stable nanopatterns. For time-periodic asymptotic states, we further characterize the island morphology at these stable states, determine the range of stability of these oscillatory states terminated by island breakup, and explain the morphological features of the stable oscillating islands on the basis of linear stability theory.

We also analyze the dynamics of coherently strained heteroepitaxial single-layer islands accounting for the effects of strain due to lattice mismatch on the edge atomic diffusivity and the edge stiffness. We examine cases where the single-layer islands are under compression or under tension. Using silver islands on platinum substrates as a benchmark system, we show that the current-driven dynamics for epitaxial islands under compression is similar to that observed for homoepitaxial islands, with the following key differences: (1) the critical island sizes for the onset of morphological instabilities in the Ag/Pt system are larger than those in the Ag/Ag system, (2) the rates of stable current-driven island migration and other pattern forming kinetic rates are faster than those observed in the homoepitaxial case, and (3) Ag islands of a particular size on Pt substrates exhibit dynamical behavior that is similar to that of homoepitaxial islands of smaller size. The final stable patterns obtained in the case of Ag/Pt heteroepitaxial islands are compared with those of homoepitaxial Ag islands and their geometrical differences are discussed. For example, starting with a rounded island of a given size, Ag nanowires formed on Pt substrate surfaces are shorter and wider than those formed on Ag substrates of the same surface crystallographic orientation. We explain the differences observed in the dynamics and in the final stable patterns obtained based on the differences in the characteristic dynamic length scales and diffusional time scales in the two cases.

Our study leads to a fundamental understanding of the very rich current-driven single-layer epitaxial island dynamics over a multi-dimensional parameter space and makes a strong case for the use of electric fields, as precisely controlled macroscopic forces, toward surface patterning involving complex nanoscale features.