Effects of Loading Tensor Anisotropy On the Complex Electromechanically Driven Dynamics of Voids in Metallic Thin Films

Wednesday, November 10, 2010: 2:10 PM
Grand Ballroom E (Salt Palace Convention Center)
Georgios I. Sfyris, Rauf M. Gungor and Dimitrios Maroudas, Chemical Engineering, University of Massachusetts, Amherst, MA

Electromigration-induced failure mediated by the driven dynamics of voids in metallic thin-film interconnects is one of the most challenging materials reliability problems in microelectronics. It has been shown that electromigration-induced morphological evolution of void surfaces depends on the void size, the strength of the applied electric field, mechanical loading conditions, as well as the strength of the diffusional anisotropy for diffusion on the void surface. Toward a systematic study of the rich electromechanically driven nonlinear dynamics of voids in metallic thin films, in this presentation, we report results for the effects of the loading tensor anisotropy on the void dynamics. We have conducted a systematic computational analysis of the complex electromechanically driven void dynamics in thin films of face-centered cubic metals for film planes characterized by two-fold and four-fold symmetry of surface diffusional anisotropy. The voids are located at one edge of the metallic film and the film is subjected simultaneously to an external electric field and an anisotropic mechanical loading tensor. Our analysis is based on self-consistent dynamical simulations of driven void surface morphological response according to a well validated, two-dimensional, and fully nonlinear model. In the simulations, we combine a Galerkin boundary-integral method for the solution of the electrostatic and elastostatic boundary-value problems with a front tracking method for monitoring the surface shape evolution. Our analysis shows that, under certain conditions, the void is morphologically stable and translates through the film with a steady shape and at constant speed; at this state, the void corresponds to a soliton, or a steady state in the frame of reference that moves with the constant void migration velocity. By varying the governing parameters, we have found stable time-periodic states, which are characterized by wave propagation on the void surface, while the void migrates along the film at a constant speed. In the case of two-fold symmetry of surface diffusional anisotropy, we have found that increasing the mechanical stress level sets the system on a period-doubling-bifurcation route to chaos and we have characterized the corresponding stable asymptotic states. However, in the case of four-fold symmetry of surface diffusional anisotropy, the only possible stable asymptotic states in the void dynamical response are either time-periodic states characterized by a single period or steady states without any change in the void shape. For both symmetry cases, we have determined the stability domain boundaries of the various asymptotic states and their dependence on the anisotropy of the applied stress tensor.

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