Analytical description of the out-of-plane equivalent mechanical properties of through-silicon via interposers

In this paper an analytical description of the equivalent thermomechanical properties of through-silicon via interposers in the out-of-plane direction is given. The equivalent properties can be used to describe the global behavior of an interposer in the elastic regime, and thus has important implications to predictive modeling of stress analysis for 3D IC integration. The properties include Young´s modulus, the rigidity modulus, and the coefficient of thermal expansion. This work complements our previous publication for the equivalent in-plane thermomechanical properties. Limitations of the formulas for these equivalent mechanical properties are discussed.