Analysis of current-driven surface morphological stabilization of a coherently strained epitaxial thin film on a finite-thickness deformable substrate

We report results for the surface morphological stability of a thin film that lies on a finite-thickness substrate and is subjected simultaneously to an external electric field. The film is grown epitaxially on the substrate and may undergo a Stranski–Krastanow instability due to its lattice mismatch with the substrate material. We develop a model for the surface morphological evolution of the thin film and conduct a linear stability analysis to examine the morphological stability of the epitaxial film’s planar surface state. Our analysis shows that surface electromigration due to a properly applied and sufficiently strong electric field can inhibit Stranski–Krastanow-type instabilities, which can be used to control the onset of island formation on the film surface. We find 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...