(649b) Current-Driven Morphological Evolution of Monolayer-Thick Epitaxial Islands On Elastic Substrates

The driven assembly of confined quantum structures, such as monolayer-thick islands grown epitaxially on elastic substrates, of either the same or different material than that of the islands, is of particular importance to nanoelectronics and nanofabrication technologies.  A typical driving force for the morphological evolution of these islands is an externally applied electric field; this evolution gives rise to morphological patterns, the stability and control of which may have significant impact on nanofabrication approaches.  For coherently strained heteroepitaxial islands, it is particularly interesting to study their response to the action of the electric field simultaneously with the induced misfit strain.

In this presentation, we report theoretical and computational results on the current-driven morphological response of single-layer epitaxial islands on elastic substrates based on a two-dimensional fully nonlinear model, according to which mass transport due to curvature-driven diffusion, stress-driven diffusion, and electromigration is limited only to the island circumference.  The model also accounts for diffusional anisotropy for such “periphery diffusion” along the island’s edge.  Within this mass transport regime, we have carried out a theoretical analysis of the morphological stability of such isolated islands and of the current-driven migration dynamics of morphologically stable islands; the theory predicts the dependence of the stable island migration speed on the island size and on the heteroepitaxial system parameters, such as strain due to lattice mismatch.  We have also developed self-consistent dynamical simulators of the driven morphological evolution of such islands, combining front tracking methods with analytical expressions derived for the electric-field component tangential to the island’s circumference and the elastic strain energy density.

Prior to analyzing the current-driven motion of stable heteroepitaxial islands, we modeled systematically such motion for single-layer homoepitaxial islands in order to compare with published experimental results on Ag(111) surfaces and assess the predictive capabilities of the model.  The comparisons demonstrate an excellent quantitative agreement between our modeling predictions and the experimental findings for both the stable island morphology and the dependence of the current-driven island migration speed on island size.  This agreement provides strong validation for our model.

Results are reported of a detailed simulation study that determined the dependence of the island migration speed, v_m, on island size, R_s given by the square root of the island’s area, for stable steady states in the current-driven island motion on <110>-, <100>-, and <111>-oriented surfaces of single-crystalline face-centered cubic metals.  We found that as the island size increases, the stable island morphology changes from round to faceted; the faceted island morphology is determined by the surface orientation through its effect on the diffusional anisotropy.  In both homoepitaxial and heteroepitaxial islands, we found the island migration speed to be directly proportional to the inverse of the island size over much of the island size range examined starting from very small islands.  In all cases, we found that there exists a critical island size, which, if exceeded, causes the v_m(1/R_s) dependence to deviate from linearity: the dependence becomes nonlinear with a sublinear trend.  For <110>-oriented surfaces, further increase of the island size beyond a second, larger critical size leads to morphological instability.  For these {110} surfaces, the nonlinearity in the v_m(1/R_s) dependence at larger-than-critical island sizes is due to an island morphological transition, where one of the island’s facets that forms along a direction perpendicular to the electric field at smaller-than-critical island sizes splits into two such facets at steady state.  For {100} surfaces, the source of the nonlinearity in the v_m(1/R_s) dependence at larger-than-critical island sizes is a dynamical transition in the island’s motion: the island’s center-of-mass trajectory deviates from the direction of the applied electric field, a straight trajectory characteristic of all the stable islands at steady state for smaller-than-critical island sizes on {100} surfaces.

 Furthermore, we have conducted a systematic parametric study to investigate thermal and size effects on the island’s driven motion and morphological evolution, as well as effects on the island’s driven dynamical response of elastic properties of the substrate and island materials (such as elastic moduli and misfit strain).  We have predicted a variety of stable asymptotic states in the driven dynamical response of such single-layer islands and characterized in detail the resulting morphological patterns.  We have also developed a universal scaling theory for the dependence of the island’s migration speed on the island size that is validated by our simulation results for both homoepitaxial and heteroepitaxial islands over the entire parameter space explored.  Our work motivates experimental measurements that can be compared directly with our modeling predictions and sets the stage for examination of collective phenomena, such as island coalescence.