(383e) Effects of the Combined Action of Electric Fields and Mechanical Stresses on the Morphological Stability of Solid Surfaces

Surface engineering of technologically important solid materials, such as metals and semiconductors, plays a crucial role in determining the function and reliability of components manufactured from such materials. Depending on the application, various defects ranging from dislocations to cracks can be introduced into the solid material during manufacturing and usage; these defects may have catastrophic effects on component/device functionality and performance. The action of external macroscopic forces is a key ingredient in the surface engineering of solid materials. Specifically, understanding the effects of the combined action of external fields, such as electric fields and applied mechanical stresses, on the morphological evolution of a solid surface is significant toward function and reliability predictions.

It is well known that applied mechanical stresses can induce morphological instabilities on solid surfaces with catastrophic effects. It has been demonstrated, for example [W. H. Yang and D. J. Srolovitz, Phys. Rev. Lett. 71, 1593 (1993)], that the surface of an elastically stressed solid can evolve rapidly into a cusped morphology with smooth tops and crack-like grooves due to surface mass transport (Grinfeld instability). These theoretical predictions are consistent with experimental findings over a broad class of materials. However, the effect of the simultaneous action of an electric field on the morphological response of a conducting stressed solid surface has not been explored systematically.

In this presentation, we report results of linear stability analysis in the form of a dispersion relation that describes the morphological response of an initially planar stressed surface to the simultaneous action of an applied electric field. The dispersion relation is derived based on a surface transport model that accounts for curvature-driven surface diffusion, surface electromigration, and stress-driven surface diffusion along with diffusional anisotropy. We find that the application of an electric field can have an important stabilizing effect on the dynamical response of a planar stressed solid surface that is otherwise unstable with respect to long-wavelength perturbations, i.e., application of an electric field may protect an electrically conducting solid material that would be otherwise vulnerable to surface cracking under certain thermomechanical conditions. In addition, we report results for the morphological evolution of a solid surface perturbed from an initially planar morphology under the simultaneous action of an electric field and mechanical stress, which confirms our linear stability analysis. The predictions for the morphological evolution are based on self-consistent dynamical numerical simulations according to the surface mass transport model that was employed in the stability analysis; in the simulations, the fully nonlinear model is solved self-consistently with the electric field and stress field distributions on the solid surface computed through a boundary integral method. The above findings can contribute to the development of surface engineering strategies for improved materials reliability over a broad range of electromechanical conditions.