Effects of microstructure on vacancy and stress distributions in micro joints under current stressing

The vacancy diffusion and stress evolution in SnPb and SnCu micro solder joints under current stressing are studied based on simulated microstructure from a phase field model. The vacancies are driven to the cathode by electric current and accumulated in the phase with lower vacancy formation energy. Stress concentration is predicted at the interfaces between phases, which is more severe when more vacancyplated atom pairs are generated or annihilated. Compared to the Sn15Cu joint, there are more vacancies accumulated and annihilated at the cathode of the Sn27Pb joint and thus resulting in a higher von Mises stress. The effects of phase morphology on electromigration are further investigated. It is found that the decrease of the amount of interface due to phase coarsening in the Sn37Pb micro joint can accelerate vacancy accumulation. As a result, during electromigration the stress can quickly increase in the joint aged for a longer time. In addition, the connectivity of the Pb-rich phase also affects the electromigration behavior. A well-interconnected network of Pb-rich phase can accelerate the vacancy accumulation and thus stress concentration. Due to the combined effect of the connectivity of Pb-rich phase and the amount of interface, the maximum stresses caused by electromigration in three joints of different compositions, i.e. Sn47Pb, Sn37Pb, and Sn27Pb, are in the order of Sn37Pb>Sn47Pb>Sn27Pb. Introduction The risk of electromigration-induced failure increases in three-dimensional integrated circuits, due to a high current density in company with the miniaturization of interconnects. In order to improve reliability, the mechanisms causing failure due to electromigration need to be understood. As a form of mass diffusion driven by electron flow, the process of electromigration interacts with the microstructures in interconnects in a complicated way. The rate of electromigration can be influenced by microstructural features such as crystal grains, grain boundaries, and different phases, where the atom diffusivities are different [1,2]. The atom fluxes driven by electric current can in turn affect microstructural evolution [3,4]. It is of significant importance to consider the effects of microstructures on an accurate prediction of the electromigration behavior in interconnects. Extensive simulation studies on electromigration have been carried out for Cu and Al interconnects [5]. However, electromigration simulations for micro solder joints, especially those based on microstructure, are relatively few. Compared to Cu and Al, most micro joints are composed of binary or ternary alloys and possess microstructures with a multicomponent and multi-phase nature. Interdiffusion occurs in micro joints, which can lead to many failure modes, e.g. the rapid dissolution of Cu under-bump metallization [6], and the formation of Kirkendall voids [7]. In addition, fast diffusion of atoms can occur along the interfaces between different phases as well as along the grain boundaries [8], which may accelerate the electromigration process. Therefore, the electromigration behavior of micro joints can be different from that in Cu and Al interconnects [9] and is worthy of detailed investigations. In this work, the microstructure-based simulations of electromigration in micro solder joints are carried out. The microstructures in SnPb and SnCu micro joints are firstly modeled and simulated by using a phase field model developed by Dreyer and Müller [10]. Based on the simulated microstructure, the electromigration model developed by Sukharev et al. [11] is then applied to study the pre-void distributions of vacancy and stress under current stressing. Firstly, the electromigration behaviors of two micro joints with compositions of Sn27Pb and Sn15Cu are compared. The differences between the Pb-rich phase and the Cu6Sn5 intermetallic compound (IMC) in determining the vacancy and stress distributions during electromigration are discussed. In addition, the dependence of stress concentration on vacancy generation and annihilation is also studied. Secondly, the effects of phase morphology on electromigration are further investigated by considering two cases of morphological changes respectively: (1) the phase coarsening process in a Sn37Pb micro joint; (2) the changes in phase morphology by varying the composition and therefore Sn47Pb, Sn37Pb, and Sn27Pb micro joints are studied. Modeling Methodology 1. Microstructural Modeling by a Phase Field Model The phase field model for binary alloys developed by Dreyer and Müller [10] is used in this work to model and simulate the microstructure in micro solder joints. The mass fraction of component A, denoted as CA, in an A-B alloy is the order parameter of the simulated microstructures. A A C C represents the phase, i.e. the A-rich phase, and A A C C represents the phase, i.e. the B-rich phase, where A C and A C are the mass fractions of component A at thermodynamic 978-1-4673-4944-4©IEEE 2012 equilibrium in the phase and the phase, respectively. The evolution of the microstructure is simulated by solving the following equation [10]: