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A comprehensive picture of void dynamics in connection with the critical morphological evolution has been developed in order to understand the conditions under which premature failure of metallic thin interconnects occurs. Our mathematical model on the mass flow and accumulation on void surfaces, under the action of applied electrostatic and elastostatic force fields, and capillary effects, follows an irreversible but discrete thermodynamic formulation of interphases and surfaces. This formalism also takes into account in a natural way the mass transfer process (the void growth), between bulk phase and the void region in multi-component systems, in terms of the normalized local values of Gibbs free energy of transformation with respect to the specific surface Gibbs free energy, in addition to the contribution due to local curvature of the advancing reaction front, rather rigorously.

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A theory of irreversible thermodynamics of curved surfaces and interfaces with triple junction singularities is elaborated to give a full consideration of the effects of the specific surface Gibbs free energy anisotropy in addition to the diffusional anisotropy, on the morphological evolution of surfaces and interfaces in crystalline solids. To entangle this intricate problem, the internal entropy production associated with arbitrary virtual displacements of triple junction and ordinary points on the interfacial layers, embedded in a multicomponent, multiphase, anisotropic composite continuum system, is formulated by adapting a mesoscopic description of the orientation dependence of the chemical potentials in terms of the rotational degree of freedom of individual microelements. The rate of local internal entropy production resulted generalized forces and conjugated fluxes not only for the grain boundary triple junction transversal and longitudinal movements, but also for the ordinary points. The natural combination of the mesoscopic approach coupled with the rigorous theory of irreversible thermodynamics developed previously by the global entropy production hypothesis yields a well-posed, nonlinear, moving free-boundary value problem in two-dimensional (2D) space, as a unified theory. The results obtained for 2D space are generalized into the three-dimensional continuum by utilizing the invariant properties of the vector operators in connection with the descriptions of curved surfaces in differential geometry. This mathematical model after normalization and scaling procedures may be easily adapted for computer simulation studies without introducing any additional phenomenological system parameters (the generalized mobilities), other than the enlarged concept of the surface stiffness.

The process of grain boundary ͑GB͒ grooving and cathode voiding in sandwich type thin film bamboo lines are simulated by introducing a mathematical model, which flows from the fundamental postulates of irreversible thermodynamics. In the absence of the electric field, the computer studies on the triple junction kinetics show that it obeys the first order reaction kinetics at early transient stage, which is followed by the familiar time law as t 1/4 , at the steady state regime. The applied electric field ͑EF͒ in constant current experiments modifies this time law drastically above the well-defined electron wind intensity ͑EWI͒ threshold, and puts an upper limit for the groove depth, which decreases monotonically with EWI. Below the threshold level, the capillary regime predominates, and EF has little effect on the general kinetics of GB grooving, other than the linear increase in total elapsed time with EWI. An analytical formula for the cathode failure time in constant voltage test is obtained in terms of the system parameters, which are closely associated with the cathode voiding or grain thinning by surface drift diffusion.