Nonlinear thermal stress analyses and design guidelines for through silicon vias (TSVs) in 3D IC integration

In this investigation, a set of empirical equations which predicts the maximum thermal stresses at the vicinity of a copper filled TSV for 3D IC integration has been proposed. The finite element model of a symmetrical single in-line TSV with redistribution layer has been created at first and the parametric study includes the TSV diameter, pitch, and thickness, and the thickness of SiO₂ passivation and Cu seed layer. The methodology of design of experiments (DOE) has been adopted to deliver a set of empirical equations which captures the most important mechanical parameters of TSVs to comprehend the corresponding thermal stress and strain responses. Through this set of empirical equations, the estimated maximum thermal stresses and strains for different TSV diameter (from 10μm to 50μm) can be explained and the significant geometrical parameters can be easily observed. In addition, based on the present parametric study and results, a set of design guidelines for optimizing the mechanical performance of copper filled TSV in 3D IC integration has been proposed. These results are helpful to engineers if thermal stress solutions for TSVs in 3D IC integration are required.