Morphological evolution of voids by surface drift diffusion driven by capillary, electromigration, and thermal-stress gradients induced by steady-state heat flow in passivated metallic thin films and flip chip solder joints. I. Theory

Abstract

The morphological evolution of intragranular voids induced by surface drift diffusion under the actions of capillary and electromigration (EM) forces and thermal-stress gradients (TSGs) associated with steady-state heat flow is investigated in passivated metallic thin films and flip chip solder joints via computer simulation using the front-tracking method. In the mesoscopic nonequilibrium thermodynamic formulation of the generalized driving forces for the thermal-stress-induced surface drift diffusion, not only the usual elastic strain energy density contribution but also the elastic dipole tensor interaction (EDTI) between the thermal-stress field and the mobile atomic species (monovacancies) are considered using the concept of elastic interaction energy promoted in unified linear instability analysis (ULISA) [T. O. Ogurtani, Phys. Rev. B 74, 155422 (2006)]. According to extensive computer experiments performed on voids, which are initially cylindrical in shape, two completely different and topographically distinct behaviors are observed during the development of quasistationary state void surface morphologies, even in the presence of strong EM forces. These behaviors strictly depend on whether or not heat flux crowding occurs in the regions between the void surface layer and the sidewalls of the interconnect lines due to proximity effects of the insulating boundaries. In both morphological cases, however, one also observes two well-defined regimes, namely, the EM and TSG dominated regimes in EM versus EDTI parametric space. In the case of the TSG dominated regime, the void center of gravity (centroid) exhibits uniform displacement (drift) velocity proportional and opposite to the induced TSG exactly as predicted by ULISA theory. These domains are bounded by a threshold level curve for the EDTI parameter, above which an extremely sharp crack tip nucleation and propagation occurs in the highly localized minima in the triaxial stress regions (i.e., hot spots) surrounding the void surface layer and extending along the longitudinal and off-diagonal directions (flux crowding). The most critical configuration for interconnect failure occurs even when thermal stresses are low if the normalized ratio of interconnect width to void radius is less than 4 (which indicates the onset of heat flux crowding). In the absence of EM this regime manifests itself by the formation of two symmetrically disposed finger-shaped extrusions (pitchfork shaped slits) on the upper and lower shoulders of the void surface on the windward side. In later stages these slits extend with an almost 54° inclination toward the sidewalls, and eventually cause a fatal catastrophic interconnect breakdown due to growth by condensation of supersaturated vacancies in the bulk matrix. At high thermal-stress levels this morphology is replaced by the fracture mode of diffusive-crack formation and propagation. Outside of the heat flux crowding regime and below the TSG threshold levels, the void takes an egg shape pointed toward the high temperature region of the interconnect and steadily drifts against the heat flow (upstream direction) without causing any transgranular damage. Above the TSG threshold levels, however, these modes are replaced by a sharp crack formation regime with an accelerated propagation that may eventually cause open-circuit interconnect failure.