(302b) Morphological Stabilization of Solid Surfaces Induced By the Combined Action of Electric Fields and Thermal Gradients

Surface morphological instability of stressed solids underlies various reliability problems in technologically important materials, which have a broad range of applications in microelectronics and nanotechnology.  In stressed elastic solids, the competition between elastic strain energy and surface energy can destabilize the surface through the Asaro-Tiller or Grinfeld (ATG) instability.  In this presentation, we analyze the surface morphological stability of electrically and thermally conducting crystalline elastic solids in uniaxial tension under the simultaneous action of an electric field and a temperature gradient.  We use linear stability analysis of a surface mass transport model that accounts for surface electromigration and thermomigration induced by the applied fields and for surface diffusional anisotropy.  We find that a properly oriented applied thermal gradient can reduce the critical electric-field strength requirement for stabilization of the planar surface morphology.  We validate the conclusions of the linear stability theory based on self-consistent dynamical simulations of surface morphological evolution according to the fully nonlinear model, coupled with numerical solutions of the elastostatic, electrostatic, and thermal boundary-value problems (BVPs) using a Galerkin boundary-integral method.  

We also study the surface morphological stability of a coherently strained thin film grown epitaxially on a substrate and subjected to an external electric field and temperature gradient.  Due to its lattice mismatch with the substrate, the film may undergo a Stranski-Krastanow (SK) instability, resulting in formation of islands on its surface.  We consider various types of substrates placing emphasis on compliant substrates that partly accommodate elastically the lattice-mismatch strain in the epitaxial film.  To examine the morphological stability of the film’s planar surface state, we conduct a linear stability analysis based on a three-dimensional model of driven film surface morphological evolution.  We derive an evolution equation for the film’s height and solve analytically the elastostatic, electrostatic, and thermal BVPs that are coupled with it.  We find that the action of properly applied and sufficiently strong external fields is necessary to stabilize the planar film surface morphology; in such cases, surface electromigration and thermomigration can inhibit SK-type instabilities and control the onset of island formation on the film surface.  We derive the conditions for synergy and competition of the two external fields for surface stabilization and demonstrate the beneficial effects of the thermal field on reducing the critical electric-field strength required to stabilize the planar film surface morphology.

In both cases, we examine the effects on the surface morphological stability of the temperature dependence of the surface diffusivity and the thermal conductivity of the film and the bulk solid, as well as effects of Joule heating of the electrically conducting materials.  Our analysis generates experimentally testable hypotheses and motivates experimental measurements that can be compared directly with the theoretical predictions.