(433a) Electromechanically-Driven Complex Void Dynamics In Metallic Thin Films | AIChE

(433a) Electromechanically-Driven Complex Void Dynamics In Metallic Thin Films


Tomar, V. - Presenter, University of Massachusetts
Gungor, M. R. - Presenter, University of Massachusetts Amherst
Maroudas, D. - Presenter, University of Massachusetts

Electromigration-driven nonlinear void dynamics in metallic thin films has been studied widely in order to fundamentally understand metallic interconnect failure that is responsible for serious 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 results from the analysis of the nonlinear dynamics of void surface morphological response in metallic thin films under the combined action of electric fields and mechanical stresses. We place emphasis on the role of the symmetry of surface diffusional anisotropy in determining electromechanically driven complex void dynamics. Most importantly, we report complex shape evolution that sets the material system on a route to chaos characterized by a sequence of period-doubling bifurcations.

Our nonlinear analysis is based on self-consistent numerical simulations of current-induced and stress-induced migration and morphological evolution of void surfaces in metallic thin films. 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. A Galerkin boundary-integral method is used for the computation of the electrostatic potential and the elastic displacement field in conjunction with a front tracking method for monitoring the evolution of the void surface morphology.

In the absence of stress, the electromigration-induced void surface morphological response is studied for single-crystalline films with twofold and fourfold symmetry of surface diffusional anisotropy, characteristic of <110>- and <100>-oriented film planes in face-centered cubic (fcc) metals. Variation of the electric-field strength, the surface diffusional anisotropy strength, and the void size past critical values is found to cause transitions from stable steady to stable oscillatory morphological responses on voids migrating along the films at constant speed through Hopf bifurcations at the corresponding critical points. The nature of the Hopf bifurcation is determined by the symmetry of the surface diffusional anisotropy on the film plane: the bifurcation is supercritical for fourfold symmetry and subcritical for twofold symmetry. Our simulations reveal hysteresis phenomena and bistability for both twofold and fourfold symmetry. For twofold symmetry, the transitions are between a stable steady state and a stable time-periodic state. For fourfold symmetry, the transitions may also be between two stable steady states, one of which bifurcates to a time-periodic state at the corresponding Hopf point.

For twofold symmetry, under the simultaneous action of an electric field and mechanical (biaxial tensile) stress, our analysis predicts that increasing the applied stress level leads to morphological transition from a steady state to a time-periodic state through a subcritical Hopf bifurcation. Further increase of the applied stress level leads to a second critical point where a period-doubling bifurcation occurs, resulting in more complex surface wave propagation. The bifurcation sequence continues 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 complex time-periodic state, characterized by three periods. Further increase in stress pushes the system into another chaotic regime and leads to film failure beyond a certain stress level. The complex shape evolution is characterized in detail over the range of stress and electric field levels examined and the features of the resulting chaotic states (strange attractors) are reported. An analogous study for the effects on the nonlinear void dynamics of the simultaneous action of an electric field and mechanical stress also is presented for <100>-oriented thin films with fourfold symmetry of surface diffusional anisotropy.