Groove profiles are computed under isotropic conditions for the intersection of a periodic array of grain boundaries with an external surface, assuming that grain boundary flux I is directed to (I≳0) or away from (I<0) the surface. When I=0, the surface assumes an equilibrium (time-independent) profile. For I≠0, in a range bounded by upper and lower limits that depend on geometry and material parameters, a global steady-state develops in which the entire surface advances (I≳0) or recedes (I<0) from its original position at constant velocity. Beyond these limits, the surface near the groove roots becomes diffusively detached from the remaining surface. A rapidly growing ridge (I≳0) or slit (I<0) then develops along each grain boundary, whose tip ultimately translates at constant velocity in a local steady state, leaving the remaining surface behind. These velocity regimes govern the ultimate stability of polycrystalline materials subjected to large electric (electromigration) or stress (creep) fields, especially in thin films where grain size approximates film thickness.

Statistics of stress migration and electromigration failures of passivated interconnect lines AIP Conf. Proc. 305, 15 (1994); 10.1063/1.45706Characterization of stress migration in submicron metal interconnects AIP Conf.

The thermodynamic condition characteristic of grain boundary wetting (GBW) causes an imbalance between grain boundary (GB) and solid–liquid interphase surface tensions γGB and γSL. This creates in turn a force acting at the root of the GB groove, and pointing into the solid. The “indentation” action of this force is suggested to cause stress-driven self-diffusion into the GB. This process removes the solid atoms from the groove cavity and causes their deposition along the GB (“internal solution”). Assuming that the GB acts as a perfect sink, this “self-indentation-internal solution” mechanism can account for a number of GBW features: the non-Mullins grooving morphology and linear kinetics, the origin of the singular stress field at the wetting front, the expansion of the solid under GBW, the influence of external stress on GBW, the GBW transitions with temperature, and the fast atomic penetration of the liquid metal ahead of the groove root.

The evolution of microstructure in Al and Cu thin film lines during electromigration has been studied using a transmission electron microscopy. Grain boundary migration was found to be critically involved in the electromigration induced hillock formation that can be described as a three-dimensional growth of a single grain.

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