(711b) Electromechanically Driven Nonlinear Dynamics of Voids in Metallic Thin Films Under Anisotropic Mechanical Stress

Void migration and morphological evolution, driven by the combined action of mechanical stresses and electric fields, are the leading mechanisms of failure in metallic thin films, which are used widely in microelectronics.  This electromechanically driven void dynamics is extremely rich and complex and it 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 nonlinear void dynamics of biaxial mechanical loading of the film, in the form of a general applied stress tensor.

We have studied the electromechanically driven surface morphological evolution of voids in single crystalline thin films of face-centered cubic metals for <100>-oriented film planes, characterized by four-fold symmetry of surface diffusional anisotropy.  The thin film is subjected to an electric field and a mechanical load expressed by a transversely isotropic biaxial stress tensor.  We have investigated all the possible loading modes, i.e., purely tensile loading, purely compressive loading,  as well as a more general loading where the applied stress components can be either tensile or compressive, resulting in a mixed (tensile + compressive) loading mode in addition to the loading anisotropy.  We have conducted self-consistent dynamical simulations of the driven void surface morphological response according to a well validated, two-dimensional, and fully nonlinear model.  The model describes driven mass transport on the void surface and accounts for curvature-driven and stress-driven surface diffusion, electromigration driven by the electric field, and surface diffusional anisotropy.  In the simulations, a Galerkin boundary-integral method for the solution of the electrostatic and elastostatic boundary-value problems is combined with a front tracking method for monitoring the shape evolution of the void surface.  

We have analyzed the effects of the various mechanical loading modes on the surface morphological evolution of the void for electric-field strengths that are above and below a critical level, which corresponds to a Hopf-bifurcation transition from steady states to time-periodic states in the unstressed film; these asymptotic states of voids are solitons that migrate along the electric-field direction at constant speed.  We have spanned the entire range of mechanical loading anisotropy, from uniaxial loading to isotropic biaxial loading.  We have mapped the void stability domain boundaries and found that under isotropic or transversely isotropic biaxial loading that is either purely tensile or purely compressive, both steady and time-periodic states can be stabilized in the driven void morphological response; transitions between these states occur at supercritical Hopf bifurcation points.  Upon increasing the stress level beyond a certain limit, the void tip extends across the film width causing film failure.  Under the same loading anisotropy and stress level, purely compressive and purely tensile stresses result in very similar void morphological responses in terms of oscillation amplitude at the time-periodic states, ranges of stress that result in stable steady and time-periodic states, and level of stress that the film can sustain prior to failure.  However, under mixed tensile and compressive biaxial loading, we found that the stable steady states in the void morphological response become completely suppressed and only time-periodic states can be stabilized for stress levels below the critical stress for film failure.  Moreover, under such mixed loading, the levels of stress that the film can sustain prior to its failure are much lower than those it can sustain under purely tensile or purely compressive loading.  We conclude that such mixed mechanical loading modes make metallic films with voids more vulnerable to electromechanical failure.