Study of the Influence of Elastic Anisotropy of Cu on Thermo-Mechanical Behavior and Cu Protrusion of Through Silicon Vias Using Combined Phase Field and Finite Element Methods

Abstract

Drastic reduction in the diameter of the Cu-filled through silicon via (TSV) leads to the TSV feature size becoming comparable with the grain size in the Cu filler, and accordingly Cu grain characteristics strongly influence thermo-mechanical behavior and Cu protrusion of the TSV due to the elastic anisotropy of Cu, which poses new emerging issues and challenges for reliability analysis of the TSV. In this paper, a 2-D phase field model is combined with a finite element model to study comprehensively and quantitatively the grain morphology characteristics, thermo-mechanical behavior and Cu protrusion in a typical Cu-filled TSV structure, while considering the mechanical property anisotropy of Cu. Results show that Cu grains with different orientations make distinct contributions to the deformation behavior of the Cu filler which undergoes three stages of deformation, that is, elastic, elasto-plastic, and plastic as temperature increases, consequently resulting in the anisotropic thermo-mechanical behavior of the Cu-filled TSV and the dependence of Cu protrusion on the average grain size of the Cu filler. Moreover, both the average von Mises stress and equivalent plastic strain of the Cu filler decrease with the increase in Cu grain size, and the average von Mises stress in fine grains is higher than that in coarse grains. Furthermore, Cu protrusion decreases with the increase of the average size of Cu grains. However, for limited grains in the Cu-filled TSV, the average von Mises stress, equivalent plastic strain, and Cu protrusion increase with an increase in the average size of Cu grains.