Electromechanically driven chaotic dynamics of voids in metallic thin films

Abstract

We report a systematic investigation of complex asymptotic states reached in the electromigration-driven morphological evolution of void surfaces in thin films of face-centered cubic metals with ͗110͘-and ͗100͘-oriented film planes under the simultaneous action of biaxial tension. The analysis is based on selfconsistent dynamical simulations according to a realistic, well-validated, and fully nonlinear model. For ͗110͘-oriented film planes, we show that upon increasing the applied mechanical stress level, morphologically stable steady states transition to time-periodic states through a subcritical Hopf bifurcation. Further increase in the stress level triggers a sequence of period-doubling bifurcations that sets the driven nonlinear system on a route to chaos. For ͗100͘-oriented film planes, a transition from steady to time-periodic states also is found to occur at a critical stress level; in this case, the corresponding Hopf bifurcation is supercritical and the nonlinear system is not set on a route to chaos.

Analysis of current-driven motion of morphologically stable voids in metallic thin films: Steady and time-periodic states

“…7 Moreover, we have shown that stable surface waves can propagate on void surfaces in stress-free films with high and low symmetry of surface diffusional anisotropy on the film plane driven by a strongerthan-critical electric field 26,27 or for larger-than-critical void sizes and anisotropy strengths; 27,28 we have also shown that such stable current-driven void surface states also exist in metallic thin films under biaxial stress on the film plane. 29 In all of these cases, the stable oscillatory void morphologies translate in the films along the electric-field direction at constant speeds. [26][27][28][29] The purpose of this article is to investigate the relationship between the void migration speed and the void size for current-driven stable void morphologies that reach steady or time-periodic asymptotic states under electromigration conditions.…”

“…29 In all of these cases, the stable oscillatory void morphologies translate in the films along the electric-field direction at constant speeds. [26][27][28][29] The purpose of this article is to investigate the relationship between the void migration speed and the void size for current-driven stable void morphologies that reach steady or time-periodic asymptotic states under electromigration conditions. 27,28 This is done through a systematic theoretical analysis based on self-consistent dynamical simulation of current-driven void surface morphological response over a broad region of parameter space that includes operating conditions and surface diffusional anisotropy.…”

Electromigration-driven complex dynamics of void surfaces in stressed metallic thin films under a general biaxial mechanical loading

“…Toward this end, we have shown that for thin films of face-centered cubic (fcc) metals with h110i-oriented film planes, upon increasing the level of an applied isotropic biaxial tensile stress, morphologically stable steady states transition to time-periodic states through a subcritical Hopf bifurcation, and upon further increase of the stress level, the driven nonlinear system is set on a route to chaos through a sequence of period-doubling bifurcations. 33 For h100ioriented film planes, a transition from steady to timeperiodic states also has been found to occur at a critical stress level; in this case, the corresponding Hopf bifurcation is supercritical and the nonlinear system is not set on a route to chaos. 33 For such h100i-oriented film planes, we have also examined the effects on the void morphological response of anisotropic biaxial tensile loading.…”

“…33 For h100ioriented film planes, a transition from steady to timeperiodic states also has been found to occur at a critical stress level; in this case, the corresponding Hopf bifurcation is supercritical and the nonlinear system is not set on a route to chaos. 33 For such h100i-oriented film planes, we have also examined the effects on the void morphological response of anisotropic biaxial tensile loading. 34 Over the range of electromechanical conditions examined, we have found that the only possible stable asymptotic states in the driven void dynamical response are either time-periodic states characterized by a single period of oscillation or steady states with no change in the void shape; in both cases, the void migrates along the film in the direction of the applied electric field at constant speed.…”

“…Among various problems of driven surface dynamics, these studies have addressed the formation and evolution of various surface wave patterns; these include solitary waves and nonlinear wave trains on surfaces of bulk metals, 14,19 soliton-like features that travel on large-size void surfaces preceding the failure of metallic thin films, 9,27 stable wave propagation on smaller-size void surfaces in films driven by a stronger-than-critical electric field, 16,17,28 current-driven homoepitaxial islands on electrically conducting substrates, 22 and current-induced step meandering on vicinal surfaces. 26 It has been established that mechanical stress plays a crucial role in determining the current-driven dynamics of conducting surfaces, including surfaces of voids in metallic thin films; 11,12,18,21,33 the resulting electromechanically induced void evolution depends on parameters that include the void size, the strength of the externally applied electric field, the mechanical loading mode and applied stress level, the crystallographic orientation of the film plane, as well as the strength of the diffusional anisotropy for diffusion on the void surface, 18,28,33 which depends strongly on temperature. 18 This high dimensionality of parameter space makes the void dynamical response extremely rich and complex and, consequently, worth investigating rigorously and systematically.…”