VOID INTERGRANUAL MOTION UNDER THE ACTION OF ELECTROMIGRATION FORCES IN THIN FILM INTERCONNECTS WITH BAMBOO STRUCTURE

Ersin Emre OREN and Tarik O. OGURTANI
Department of Metallurgical and Materials Engineering, Middle East Technical University, Ankara 06531, Turkey

In these studies the rigorous formulation of the internal entropy production, and the generalized forces and conjugate fluxes associated with the virtual displacement of a triple junction are developed. A well-posed moving boundary value problem describing the kinetics of interphasial layers and surfaces is obtained for the ordinary points as well as for the triple junction. Extensive computer simulations are performed on the void configurational evolution during the intergranual motion under the actions of capillary and electromigration forces in thin film metallic interconnects with bamboo structure. Very rich, and also unusual void grain-boundary interaction morphologies such as penetration and detrapping, fragmentation and daughter void formation are observed, at high-normalized electron wind intensities. Singular points associated with a triple junction is treated rather rigorously by using micro-discrete (straight) interfacial elements as convenient mathematical tools as proposed by Ogurtani. The generalized forces and conjugate fluxes associated with the triple junction are obtained in terms of the asymmetric dihedral angles and the specific Gibbs free energies releated to the void surface layer and the grain boundary interphase respectively. Displacement velocities of the triple junction, longitudinal and transverse are also deduced as a by-product of this treatment. Mathematical model of the void shape evolution dynamics in the presence of the void-grain boundary interaction is developed by utilizing the results of our theory on the ordinary points at the void surface layer.