(212c) Analysis of Current-Driven Morphological Evolution of Monolayer-Thick Coherently Strained Heteroepitaxial Islands On Substrates

Surface morphological evolution under the action of external fields has attracted considerable attention over the past two decades. In addition to the interest in a fundamental understanding of field-induced nonlinear response and stability of surface morphology, the problem has been technologically significant in various engineering applications such as microelectronics and nanofabrication. Of particular interest is the driven assembly of confined quantum structures, such as islands grown epitaxially on substrates of different chemical composition than that of the islands. The lattice mismatch between the island and substrate materials induces a misfit strain, which is the source of elastic deformation of the islands. The surface morphological dynamics induced by an externally applied field, such as an electric field, under the simultaneous action of the misfit strain can give rise to morphological patterns, the stability and control of which may have significant impact on fabrication technologies.

In this presentation, we report the results of a theoretical and computational analysis of the current-driven morphological response of coherently strained heteroepitaxial islands on elastic substrates. We have developed a fully nonlinear model for studying the current-driven morphological evolution of one-monolayer-thick coherently strained heteroepitaxial islands on elastically deformable substrates. The model follows a two-dimensional (2D) approximation of island evolution, according to which diffusional mass transport is limited to the island circumference.  Within this approximation (i.e., for 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 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.  We have also developed self-consistent dynamical simulators of the driven morphological evolution of such islands, combining front tracking methods with an analytical solution for the corresponding electric-field component tangential to the island’s circumference and a numerical computation of the corresponding elastic displacement field. Simulation results are reported together with systematic parametric studies to investigate thermal and size effects on the island’s migration and morphological evolution, as well as effects on the island driven dynamical response of elastic properties of the substrate and island materials (such as elastic moduli and misfit strain). We demonstrate a variety of stable asymptotic states in the driven dynamical response of such heteroepitaxial islands and characterize in detail the resulting morphological patterns.

The simulation results validate our theory for stable heteroepitaxial island driven migration. The results also generate experimentally testable hypotheses and motivate experimental measurements that can be compared directly with the theoretical predictions.  Finally, the present modeling study sets the stage for designing simulations of the current-driven evolution of populations of heteroepitaxial islands and examination of collective phenomena, such as island coalescence.