(222b) Electromechanically-Driven Complex Morphological Evolution of Void Surfaces in Metallic Thin Films | AIChE

(222b) Electromechanically-Driven Complex Morphological Evolution of Void Surfaces in Metallic Thin Films


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

Electromigration-driven void evolution in metallic thin-film interconnects has been a problem of major interest both as an important concern for materials reliability in microelectronics and as an intriguing nonlinear dynamical phenomenon of driven mass transport and microstructural evolution in materials. 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 focus on the nonlinear dynamics of void surface morphological response induced by the action of mechanical stress simultaneously with the electric field. Most importantly, we report complex shape evolution that may set the driven material system on a route to chaos characterized by 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 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.

In the absence of stress, our analysis predicts the onset of stable time-periodic states (surface wave propagation) for the void surface morphological response as either the applied electric field strength, or the void size, or the strength of the diffusional anisotropy is increased over a critical value. Under the simultaneous application of mechanical (biaxial tensile) stress, for conditions beyond the onset of surface waves in the stress-free case, stable time-periodic states characterized by wave propagation on the moving void surface are observed for stress levels below a critical value. At this critical state, a period doubling bifurcation occurs leading to more complex surface wave propagation. Increasing the level of the applied stress further leads eventually to film failure through crack propagation from the void surface. For parameter values below the critical ones in the stress-free case, morphological evolution leads to stable steady states for the void surface morphology, i.e., the onset of surface waves corresponds to a Hopf bifurcation. All the stable asymptotic states computed correspond to morphologically stable voids that translate along the metallic film at constant speeds (i.e., solitons). When biaxial tensile stress is applied simultaneously with the electric field under electromigration conditions that lead to steady states in the absence of stress (i.e., for conditions before reaching the Hopf point in the stress-free case), a Hopf bifurcation occurs with increasing the applied stress level; this is followed by a period doubling bifurcation as the stress level increases further. This bifurcation sequence continues with increasing stress level, setting the system on a route to chaos. The complex shape evolution is characterized over the range of stress levels examined and the nature of the resulting chaotic state (strange attractor) is reported.