(19c) Current-Driven Surface Morphological Evolution and Pattern Formation in Stressed Elastic Solid Conductors

Surface morphological instability underlies various reliability problems of technologically important materials, which have a broad range of applications from aerospace engineering to microelectronics and nanotechnology. Applied mechanical stress has been known to induce surface morphological instabilities in crystalline solid materials. Specifically, linear stability analyses have demonstrated that the competition between elastic strain energy and surface energy can cause the growth of perturbations from a planar surface morphology and specified the conditions for the onset of the so-called Asaro-Tiller or Grinfeld (ATG) instability. In addition, numerical simulations accounting for all the important nonlinearities have addressed the surface dynamics beyond the instability onset and revealed instability mechanisms. In particular, it has been demonstrated that a planar surface of a stressed elastic solid can evolve rapidly into a cusped surface, with smooth tops and deep crack-like grooves by surface diffusion, in agreement with experimental observations. These theoretical predictions are consistent with experimental findings over a broad class of materials. However, the effects of the simultaneous action of an electric field on the surface morphological response of a conducting stressed solid have not been explored systematically. To address this need, this study focuses on the current-driven morphological evolution and pattern formation in stressed elastic solid conductors.

In this presentation, we report a detailed analysis of morphological stability of planar surfaces of electrically conducting, stressed elastic crystalline solids under the simultaneous action of an electric field using linear stability theory (LST) and numerical simulation. Our analysis is based on a fully nonlinear surface transport model that accounts for curvature-driven surface diffusion, surface electromigration, and stress-driven surface diffusion along with surface diffusional anisotropy. Our self-consistent dynamical simulations combine Galerkin boundary-integral computations of elastic displacement fields and electrostatic potentials with a front tracking method for monitoring surface morphological evolution. We present a detailed analysis of the effects of material properties (surface diffusional anisotropy parameters) on the morphological stability of planar surfaces of face-centered cubic (fcc) metals under the simultaneous action of mechanical stress and an electric field. We demonstrate that (a) there exists a preferred direction for the applied electric field that optimizes the surface morphological response; (b) under given electromechanical conditions, the surface morphological response of <111>-oriented surfaces of fcc metals is superior to that of <100>- and <110>- oriented surfaces; and (c) increasing the strength of the surface diffusional anisotropy, by lowering the temperature, has beneficial effects on the surface morphological stability of the stressed conducting solid under the simultaneous action of an electric field. These results have been used to derive systematic surface engineering rules, expressed by the dependence of the critical electric-field strength for stabilization of the surface morphology of the stressed solid as a function of the surface diffusional anisotropy parameters.

Based on self-consistent dynamical simulations according to the fully nonlinear model of driven surface morphological evolution, we have discovered complex aspects of surface morphological response and pattern formation that are not accounted for by LST. Specifically, we have found that, in addition to the ATG instability, a very-long-wavelength tip-splitting instability may be triggered forming a pattern of secondary ripples on the surface; such rippling occurs in the absence of electric field application, as well as for weaker-than-critical applied electric fields. Such shorter-wavelength ripples on an initially long-wavelength perturbation of a planar solid surface can accelerate surface cracking acting cooperatively with an ATG instability or they may induce surface cracking under conditions that do not trigger ATG instabilities according to LST. The critical wavelength for the onset of this secondary rippling is not predicted by LST, but it has been computed numerically. Most importantly, a stronger-than-critical electric field inhibits both the ATG and the rippling instability. Furthermore, we have characterized the morphology of the surfaces that undergo rippling instability. We have found that the number of ripples formed increases linearly with the wavelength of the initial perturbation scaled with the maximally unstable wavelength. Our analysis adds this new rippling instability to the mechanisms of stress relaxation through surface pattern formation that may lead to surface cracking.