(172e) Current-Driven Surface Morphological Stabilization of Coherently Strained Heteroepitaxial Thin Films

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 largely unexplored.

In this presentation, we report the results of a morphological stability analysis for the driven morphological response of an epitaxial film surface. We have analyzed the surface morphological stability of a coherently strained thin film grown epitaxially on an elastic substrate and subjected simultaneously to an external electric field; both thick and thin (finite-thickness) elastic substrates have been examined. Due to its lattice mismatch with the substrate material, the film may undergo a SK instability, resulting in formation of islands on the film surface. We have developed a three-dimensional (3D) model for the surface morphological evolution of the thin film and conducted a linear stability analysis to examine the morphological stability of the epitaxial film’s planar surface state. The analysis has shown that surface electromigration due to a properly applied and sufficiently strong electric field can inhibit SK-type instabilities, which can be used to control the onset of island formation on the film surface. We have also found that using a finite-thickness substrate can have the beneficial effect of reducing the critical strength of the electric field required to stabilize the planar surface morphology of the epitaxial film with respect to the field strength required in the case of an infinitely thick substrate.

We have determined the critical electric-field strength as a function of material properties and heteroepitaxial system parameters, as well as the electric field’s optimal direction for the most efficient stabilization of the surface morphology.  Furthermore, we have obtained detailed results for the effects of the finite-thickness substrate on the stabilization of the film’s surface over a range of mechanical properties of the heteroepitaxial system’s constituents.  Perhaps more importantly, we have analyzed the surface morphological stabilization of heteroepitaxial films on substrates by combining the use of externally applied electric fields with well-known strain engineering techniques, such as the use of thin compliant substrates; such substrates provide some elastic accommodation of the lattice-mismatch strain in the epitaxial film due to the substrate’s ability to relax parallel to its interface with the epitaxial film.  It should be mentioned that employing substrate engineering techniques alone is not sufficient for stabilizing the planar morphology of the epitaxial films; for such stabilization, the simultaneous action of the externally applied electric field is required. Our analysis has demonstrated the benefits of the substrate compliance, as measured by the reduction in the critical electric-field strength required for stabilizing the epitaxial film surface; we have found this reduction in the critical field strength to be as high as two orders of magnitude with respect to that required for epitaxial films grown on conventional thick substrates. Our results generate experimentally testable hypotheses and motivate experimental measurements that can be compared directly with the theoretical predictions.