Mechanical models of polycrystalline 3D-IC interwafer vias

We discuss studies of stress induced grain boundary motion in polycrystalline Cu films, using 3D grain-continuum modeling; i.e., we represent a polycrystalline material as a system of distinct but interacting continua. Field variables are computed as functions of position in each grain; e.g., internal stresses and concentrations. To highlight the importance of anisotropy, we consider thermally induced stresses in an idealized thin Cu film, with hexagonal 3D grains, on a SiO2 film on a Si substrate. Stresses computed in a < 111 > textured film using the anisotropic elastic constants of single crystal Cu (rotated appropriately for each grain) are higher than the stresses computed using isotropic (bulk) properties. When one grain is < 100 > oriented in the midst of < 111 > oriented grains, strain energy gradients will lead to the growth of the < 100 > oriented grain. Grain boundary velocities and the time scales for significant evolution are calculated for strain energy induced grain boundary motion. The approach is then applied to a section of a polycrystalline Cu interconnect that is generated using a model in PLENTE, a 3D microstructure simulation software. Velocities are computed for strain energy-induced migration, and the grain structure is evolved using PLENTE.