The effect of a thermal gradient on the electromigration-driven surface morphological stabilization of an epitaxial thin film on a compliant substrate

摘要

We report a theoretical analysis on the surface morphological stability of a coherently strained thin film that has been grown epitaxially on a deformable substrate and is simultaneously subjected to an external electric field and a temperature gradient. Using well justified approximations, we develop a three-dimensional model for the surface morphological evolution of the thin film and conduct a linear stability analysis of the heteroepitaxial film's planar surface state. The effect of the simultaneous action of multiple external fields on the surface diffusional anisotropy tensor is accounted for. Various substrate types are considered, but emphasis is placed on a compliant substrate that has the ability to accommodate elastically some of the misfit strain in the film due to its lattice mismatch with the substrate. We derive the condition for the synergy or competition of the two externally applied fields and determine the optimal alignment of the external fields that minimizes the critical electric field-strength requirement for the stabilization of the planar film surface. We also examine the role of the temperature dependence of the thermophysical properties and show that the criticality condition for planar surface stabilization does not change when the Arrhenius temperature dependence of the surface diffusivity is considered. Our analysis shows that surface electromigration and thermomigration due to the simultaneous action of properly applied and sufficiently strong electric fields and thermal gradients, respectively, can inhibit Stranski-Krastanow-type instabilities and control the onset of island formation on epitaxial film surfaces.