A COMPUTER SIMULATION OF THE VOID DYNAMICS UNDER THE ACTION OF ELECTROMIGRATION AND CAPILLARY FORCES IN NARROW THIN INTERCONNECTS
Tarik O. OGURTANI and Ersin Emre OREN
Department of Metallurgical and Materials Engineering, Middle East Technical University, Ankara 06531,
In these studies a comprehensive picture of void dynamics in connection with the critical morphological evaluations has been thoroughly anticipated in order to understand main reasons as well as the conditions under which premature failure of metallic thin interconnects occurs. Our mathematical model on the diffusion and mass accumulation on void surfaces, under the action of applied electrostatic potential and capillary effects, follows a novel irreversible but discrete thermodynamic formalism of interphases and surfaces developed by the senior author in connection with thin interconnects.
Extensive computer simulation experiments have been performed on the configurational changes associated with voids during the intragranual motions in two-dimensional space, utilizing various initial void morphologies with and without growth processes. In the evaluation of the capillary effect as well as the void growth phenomenon, the irreversible thermodynamics theory of interphases strongly emphases the importance of the Gibbs specific free energies associated with surfaces as well as the interface controlled growth reactions rather than the Helmholtz free energies as suggested by Herring and others.
As a result, in addition to the wedge shape or slit formations (Figure 1 & Figure 2), very rich and also unusual void morphological variations such as fragmentations (Figure 3) or dendritic growth (Figure 4) have been obtained under the sever conditions (such as high normalized electron wind intensities) by the numerical solution of a nonlinear partial equation, which describes the void dynamics with respect to time and space. In these numerical experiments which shows excellent agreement with TEM studies reported in the literature, the Euler’s method of finite differences with an automatic time step self-adjustment has been utilized in combination with a rather powerful and fast boundary element method (BEM) for the solution of the Laplace equation. Whole system of mathematical connections are normalized and scaled with respect to time and space, which resulted great flexibility in computer simulations in terms of applied electric field, specific void surface Gibbs free energy, interconnect width and finally the initial void morphology.