A simulation of electromigration-induced transgranular slits

Abstract

Articles you may be interested inTheoretical analysis of electromigration-induced failure of metallic thin films due to transgranular void propagation J. Appl. Phys. 85, 2233 (1999); 10.1063/1.369532Electromigration-induced failure of metallic thin films due to transgranular void propagation An on-chip aluminum interconnect carries an intense electric current at an elevated temperature, motivating atoms to diffuse in the solid state, and inducing voids that may cause an open failure. Recent observations have shown that a void sometimes collapses to a slit running nearly perpendicular to the electric current direction. Such a slit often lies inside a grain rather than along a grain boundary. An earlier calculation showed that diffusion on the void surface, driven by the electric current, can cause a circular void to translate in an infinite, isotropic interconnect. It was suggested recently that this solution may be unstable, and that two forces compete in determining the void stability: surface tension favors a rounded void, and the electric current favors a slit. A linear perturbation analysis, surprisingly, revealed that the translating circular void is stable against infinitesimal shape perturbation. Consequently, the slit instability must have resulted from finite imperfections. This article reviews the experimental and theoretical findings, and describes a numerical simulation of finite void shape change. We determine the electric field by a conformal mapping of complex variables, and update the void shape for a time step by a variational method. The simulation shows that a finite void shape imperfection or surface tension anisotropy can cause a void to collapse to a slit.

Real-Time TEM Imaging of the Formation of Crystalline Nanoscale Gaps

“…Investigating this phenomena is complicated by the exceedingly rapid evolution and thermal runaway that occur when the neck is narrower than about 20 nm [28][29][30][31][32][33][34][35][36][37], and by the variation in grain structure for different wires [38]. The current density at failure J F has been reported to both increase [39] and decrease [37] as the wire widths decrease.…”

Complex Shape Evolution of Electromigration-Driven Single-Layer Islands

“…A circular island moving at constant velocity is stable for (dimensionless) radii R < R c ≈ 3.26 [21]. Beyond the instability a bifurcation to two branches of non-circular stationary solutions occurs [20].…”

“…The isotropic version of (1), withγ, σ = const., has been studied previously by Suo and collaborators [19,20,21]. A circular island moving at constant velocity is stable for (dimensionless) radii R < R c ≈ 3.26 [21].…”

Nonlinear Dynamics of Surface Steps

“…As a consequence, the current distribution, and hence the distribution of electromigration forces, is strongly dependent on the void shape itself, and the shape evolution becomes a non-local moving boundary value problem for the electric potential [18]. It is possible to interpolate between the two cases depicted in Fig.1.10 by considering a conducting void and varying the conductivity ratio between the interior and the exterior regions [14].…”