(19d) Electromechanically-Driven Oscillatory and Chaotic Dynamics of Void Surfaces in Metallic Thin Films

Electromigration-driven void dynamics in metallic thin films is significant toward a fundamental understanding of interconnect failure that is responsible for 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 report a systematic comparison of the electromechanically driven void dynamics in thin films of face-centered cubic metals with two-fold and four-fold symmetry of surface diffusional anisotropy. We report oscillatory void dynamics in both cases and, most importantly, for two-fold symmetry, complex shape evolution that sets the material system on a route to chaos.

Our nonlinear analysis is based on self-consistent numerical simulations of driven migration and morphological evolution of void surfaces in metallic thin films according to a well-validated fully nonlinear model of surface mass transport in its two-dimensional implementation. The simulations account 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 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.

Under the simultaneous action of the electric field and mechanical stress, our analysis predicts the range of parameters over which a void present at the edge of a metallic thin film is morphologically stable and translates through the film with a steady shape and at a constant speed, i.e., the moving void corresponds to a soliton or a steady state in the frame of reference moving at the void velocity. A systematic exploration of parameter space has predicted that variations in the electric-field strength, or the mechanical stress level, or the void size, or the strength of surface diffusional anisotropy past certain critical values leads to morphological transition from the above steady state to time-periodic states through Hopf bifurcations; these time-periodic sates are characterized by wave propagation on the void surface with the void migrating along the film at a constant speed. For two-fold and four-fold symmetry of surface diffusional anisotropy, these Hopf bifurcations are sub-critical and super-critical, respectively. Focusing on the effects of mechanical stress on the driven void dynamics, we have found that, in the case of two-fold symmetry, increasing the applied stress level past the Hopf point results in increased complexity in the void dynamics through a sequence of sub-critical period doubling bifurcations. More importantly, we show that, for two-fold symmetry, this period-doubling bifurcation sequence sets the system on a route to chaos and, as the stress level keeps increasing, the void dynamics becomes chaotic. For four-fold symmetry, however, increasing the stress level past the original Hopf point leads eventually to a transition to steady state through a parameter range characterized by single-period time-periodic states. Finally, we present a systematic characterization of the void asymptotic states, including strange attractors, over the region of parameter space examined.