Effects of Anisotropic Mechanical Loading On the Current-Driven Dynamics of Voids In Metallic Thin Films

Electromechanically induced failure of metallic thin-film interconnects is one of the most challenging materials reliability problems in microelectronics. It has been established that void migration and morphological evolution, driven by the combined action of mechanical stresses and electric fields, are the leading mechanisms of failure in such metallic thin films. This void dynamics depends strongly on the void size, the strength of the applied electric field, mechanical loading conditions, as well as diffusional anisotropy parameters for diffusion on the void surface. In this presentation, we report results for the effects on the current-driven void dynamics of mechanical loading, in the form of a general applied stress tensor, as part of a comprehensive study of the rich electromechanically driven nonlinear dynamics of voids in metallic thin films.

We have conducted a systematic computational analysis of electromechanically driven void dynamics in thin films of face-centered cubic metals for <110>- and <100>-oriented film planes, characterized by two-fold and four-fold symmetry of surface diffusional anisotropy, respectively. The voids are located at one edge of the metallic film and the film is subjected simultaneously to an external electric field and a general 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 levels of isotropic or transversely isotropic biaxial tension, 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 <110>-oriented film planes under isotropic biaxial tension, 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, for <100>-oriented film planes under both isotropic and transversely isotropic biaxial tension, 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. In both cases, we have determined the stability domain boundaries of the various asymptotic states and their dependence on the anisotropy of the applied stress tensor. However, thermomechanical stresses that develop in modern microelectronic devices exhibit a rather complex nature that can be better represented by a generally anisotropic loading tensor that consists of tensile, compressive, and shear stresses over a broad range of loading anisotropy. To capture the effects of such loading complexity on the void dynamics, we have conducted a systematic study of electromechanically driven void dynamical response under generally anisotropic mechanical loading. We report the results of this study for mechanical loadings that include isotropic and transversely isotropic compression, as well as combinations of tensile and compressive stress components. Specifically, the analysis addresses the mobility of stable voids migrating along the interconnect line at constant speed, the existence of stable time-periodic and chaotic asymptotic states in the void dynamical response, and the limits of film failure in comparison to those under biaxial tension.