(219c) Surface Morphological Stability of Crystalline Solids Under Simultaneous Electromigration, Thermomigration, and Stress-Driven Surface Diffusional Mass Fluxes

Surface morphological instability underlies various reliability problems of technologically important materials, which have a broad range of applications in microelectronics and nanotechnology. For example, the competition between elastic strain energy and surface energy is responsible for surface morphological instabilities in stressed elastic solids, such as the well-known Asaro-Tiller or Grinfeld (ATG) instability under conditions that promote surface diffusion; under such conditions, it has been demostrated that surface cracking can occur through the rapid evolution of a planar surface of a stressed elastic solid to a cusped surface, with smooth tops and deep crack-like grooves. 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 surface morphological stability of crystalline solids under the simultaneous action of applied mechanical stresses, electric fields, as well as imposed temperature gradients that are commonly present in materials processing and in service has not been examined systematically.

In this presentation, we report a detailed analysis of the morphological stability of planar surfaces of electrically and thermally conducting stressed elastic crystalline solids under the simultaneous action of an electric field and an imposed temperature gradient using linear stability theory and self-consistent dynamical numerical simulation. The applied electric field and temperature gradient are directed parallel to the crystalline solid surface so that they drive surface mass fluxes due to surface electromigration and surface thermomigration. The solid is under uniaxial tension, also directed parallel to the surface, which is responsible for stress-driven surface diffusion. Our analysis is based on a fully nonlinear surface transport model that accounts for curvature-driven surface diffusion, surface electromigration, surface thermomigration, and stress-driven surface diffusion along with surface diffusional anisotropy. Our self-consistent dynamical simulations combine Galerkin boundary-integral computations of elastic displacement fields, temperature fields, and electrostatic potentials with a front tracking method for monitoring surface morphological evolution.

We report results on the effects of material properties (surface diffusional anisotropy parameters) on the morphological stability of <111>-, <100>-, and <110>-oriented planar surfaces of face-centered cubic (fcc) metals under the simultaneous action of the multiple external fields. We determine the surface morphological stability domain boundaries and the critical values of the applied electric field strength and temperature gradient required to stabilize the planar surface morphology against surface cracking through an ATG instability. Special emphasis is placed on exploring the synergistic or competing effects on the surface morphological response of the simultaneously applied thermal and electric fields, aiming at the optimization of the electric-field strength and temperature gradient requirements for planar surface stabilization. The results of our analysis are used to derive systematic surface engineering rules, expressed by the dependence of the critical electric-field strength and simultaneously imposed temperature gradient for stabilization of the surface morphology of the stressed solid as a function of the surface diffusional anisotropy parameters.