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

Abstract

We analyze the surface morphological stability of a coherently strained thin film that has been grown epitaxially on a compliant substrate of finite thickness and is subjected simultaneously to an external electric field, which drives surface electromigration. The compliant substrate has the ability to accommodate elastically some of the misfit strain that is developed in the epitaxial film due to the lattice mismatch between the film and substrate materials. We develop a three-dimensional model for the surface morphological evolution of the thin film and conduct a linear stability analysis for the morphological stability of the heteroepitaxial film’s planar state; of particular importance for the analysis is the elastostatic boundary-value problem for the heteroepitaxial film/substrate system. The analysis shows that surface electromigration due to a properly applied and sufficiently strong electric field can inhibit Stranski-Krastanow-type instabilities. Furthermore, we determine the critical electric-field strength as a function of material properties and heteroepitaxial system parameters, as well as the optimal direction of the electric field for the most efficient stabilization of the surface morphology. We find that using a compliant substrate reduces the critical strength of the externally applied electric field required for planar film surface stabilization by approximately two orders of magnitude compared to that needed to stabilize the planar surface of the same thin film when grown epitaxially on a practically infinite substrate. This critical electric-field strength also is found to be substantially lower than that required for planar film surface stabilization for the same film grown on an elastic substrate that is clamped to a holder and has thickness equal to the compliant substrate thickness. This critical strength requirement can be reduced further by decreasing the ratio of the film’s shear modulus with that of the substrate, and it can be minimized for an optimal value of the compliant substrate thickness. We conclude that surface electromigration can be used to control the onset of island formation on epitaxial film surfaces and that the required electric-field strength for such control can be optimized by efficient use of substrate engineering techniques.