Explicit model of thermal stress induced by annular through-silicon-via (TSV)

In this letter, an explicit analytical model for the stress induced by annular through-silicon-via (TSV) is developed according to the classical Lame theory. And then, the analytical model is verified by finite element method (FEM) using ANSYS software. It is shown that, 1) the error between the analytical and FEM results is less than 5.6%, which proves the accuracy of the analytical model; 2) annular TSV induces a tensile radial stress and a compressive circumferential stress in the surrounding silicon. Finally, the guidelines are given for transistor placement to prevent the performance degradation.