Modeling of surface morphological response to the simultaneous action of multiple external fields

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 and numerical simulations have demonstrated that the competition between elastic strain energy and surface energy can cause the growth of perturbations from a planar surface morphology evolving into deep crack-like grooves by surface diffusion. These theoretical predictions are consistent with experimental findings over a broad class of materials. However, the effects of the simultaneous action of another external field on the surface morphological response of a stressed solid have not been explored systematically. The findings of this thesis contribute to our fundamental understanding of the morphological response of crystalline solid conductors to the simultaneous action of mechanical stresses and electric fields. A significant part of this thesis is focused on the surface morphological stability analysis of stressed conducting crystalline materials under the simultaneous action of an electric field. Combining the results of linear stability analysis with self-consistent dynamical simulations based on a fully non-linear model of driven surface morphological evolution, it is demonstrated that a sufficiently strong and properly applied electric field can inhibit the stress-induced surface instability and stabilize surfaces of crystalline solids that are otherwise vulnerable to surface cracking. Furthermore, the effects of surface crystallographic orientation and strength of surface diffusional anisotropy on the morphological stability of planar surfaces of stressed elastic solids under surface electromigration conditions are investigated systematically. The numerical simulations also have revealed a new long-wavelength surface instability that leads to the formation of patterns of ripples on the conducting solid surfaces; the rippled surface morphologies have been characterized in detail. Additionally, the thesis investigates complex oscillatory asymptotic states reached in the electromigration-driven morphological evolution of void surfaces in thin films of face-centered cubic metals under the simultaneous action of mechanical stress. Based on self-consistent dynamical simulations according to a realistic, well-validated, fully nonlinear model, the intriguing dynamics of electromechanically driven void surfaces has been analyzed. The corresponding complex asymptotic states range from time-periodic to fully chaotic. Specifically, in such thin films with \u3c110\u3e-oriented film planes, it is demonstrated that a sequence of period-doubling bifurcations sets the doubly driven nonlinear system on a route to chaos. Such a chaotic void morphological response is not observed in \u3c100\u3e-oriented thin films