Electromigration-driven nonlinear dynamics of voids in metallic thin films underlies major materials reliability problems in integrated circuits. Recent theoretical work in this area has demonstrated extremely rich nonlinear dynamics for the electromigration-induced morphological evolution of void surfaces due to surface diffusional anisotropy and pronounced current crowding effects. In this presentation, we emphasize on the void surface morphological response under the combined action of the electric field and mechanical stress. Most importantly, we report that, under such conditions, the driven material system may be set on a route to chaos characterized by complex surface shape evolution.

Our nonlinear analysis is based on self-consistent numerical simulations of current-induced and stress-induced migration and morphological evolution of void surfaces in encapsulated (i.e., mechanically confined) metallic thin films. Our surface evolution model accounts rigorously for current crowding and stress concentration effects that become particularly important in narrow metallic films, as well as surface curvature effects that are particularly strong due to the strong anisotropy of adatom diffusion on void surfaces. The mass transport problem on the void surface is solved coupled self-consistently with the electrostatic and mechanical deformation problems in the conducting film that contains the morphologically evolving void, assuming that the metallic material responds to stress elastically. A two-dimensional (2D) implementation is followed in the xy-plane of a metallic film of finite width that extends infinitely in the x-direction; this 2D representation is based on the assumption that the void extends throughout the film thickness (in z), which is consistent with experimental observations. A Galerkin boundary-integral method is employed for the calculation of the electrostatic potential and the elastic strain field together with an interface tracking method for monitoring the void surface propagation.

Our analysis predicts that, in the absence of stress, increasing the electric field strength, or the void size, or the strength of the diffusional anisotropy past certain critical values leads to transitions from steady states to time-periodic states; the latter states are characterized by wave propagation on the surface of the void, which migrates along the film at a constant speed. The transition onset corresponds to a Hopf bifurcation that may be either supercritical or subcritical, depending on the symmetry of the surface diffusional anisotropy that is determined by the crystallographic orientation of the film plane. We focus on low-symmetry anisotropy and examine the void surface morphological response under the simultaneous application of tensile biaxial stress starting from conditions close to the Hopf point in the stress-free case. Propagation of stable surface waves on the void is observed again as the applied stress level increases beyond a critical value. Further increase of the applied stress level leads to a period-doubling bifurcation associated with more complex surface wave propagation. Such period-doubling bifurcations continue with increasing stress level, setting the system on a route to chaos. With further increase in the stress level, the system exits from the chaotic regime to a periodic window characterized by a complex time-periodic state with three periods. Further increase in stress drives the system to another chaotic regime, through a period-doubling bifurcation sequence, and ultimately to film failure beyond a certain maximum stress level. Detailed characterization of the complex shape evolution is performed over the range of stress levels examined and the nature of the resulting chaotic state (strange attractor) is reported. The corresponding bifurcation diagrams with the applied stress level as the bifurcation parameter are constructed for different values of the applied electric field.