(370f) Electromigration-Driven Surface Morphological Stabilization of a Coherently Strained Heteroepitaxial Thin Film

The competition between elastic strain energy and surface energy is responsible for surface morphological instabilities in stressed elastic solids; these include the well-known Asaro-Tiller or Grinfeld (ATG) instability under conditions that promote surface diffusion and the Stanski-Krastanow (SK) morphological instability in the heteroepitaxial growth of thin films on solid substrates. In heteroepitaxial systems, the lattice mismatch between the thin film and the substrate materials induces a misfit strain, which is the source of elastic deformation. In recent studies, we have shown that applying on a stressed elastic conductor an external electric field of sufficient strength and proper direction can inhibit the ATG instability. Nevertheless, the role of surface electromigration in stabilizing the surface morphology of coherently strained epitaxial films remains unexplored. In this presentation, we report the results of a linear stability analysis for the driven morphological response of an epitaxial film surface. The analysis is based on a three-dimensional model for the current-driven surface morphological evolution of a coherently strained epitaxial thin film on an elastic substrate. In particular, we consider an electrically conducting, coherently strained thin elastic film that has been grown epitaxially on an elastic substrate under the simultaneous action of an external electric field that is directed parallel to the film plane; the substrate can be either infinitely thick or a deformable one of finite thickness. Both the film and substrate materials are perfectly crystalline, they respond to stress according to isotropic linear elasticity in the small-displacement kinematic limit, and they have, in general, different elastic properties. The film/substrate interface is planar and fully coherent, i.e., there are no misfit dislocations at the interface. For this heteroepitaxial system, the analysis addresses the morphological stability of the planar state of the epitaxial film surface. We have determined the critical electric-field strength for the stabilization of the surface morphology, as well as the optimal direction of the electric field that maximizes its stabilizing effect. Furthermore, we have examined the role of the substrate thickness in the film surface morphological response. The analysis also emphasizes the important kinetic effects of surface diffusional anisotropies on such morphological instabilities. We demonstrate the possibility to control the motion, the complexity, and the onset of formation of surface features in heteroepitaxial films through the action of an external electric field; of particular interest is the onset of island formation through a SK instability. Our results generate experimentally testable hypotheses and motivate experimental measurements that can be compared directly with the theoretical predictions.