An analytical model of thermal mechanical stress induced by through silicon via**Project supported by the National Natural Science Foundation of China (Grant No. 61334003) and the Kunshan Innovation Institute of Xidian University.

Abstract

We present an accurate through silicon via (TSV) thermal mechanical stress analytical model which is verified by using finite element method (FEM). The results show only a very small error. By using the proposed analytical model, we also study the impacts of the TSV radius size, the thickness, the material of Cu diffusion barrier, and liner on the stress. It is found that the liner can absorb the stress effectively induced by coefficient of thermal expansion mismatch. The stress decreases with the increase of liner thickness. Benzocyclobutene (BCB) as a liner material is better than SiO2. However, the Cu diffusion barrier has little effect on the stress. The stress with a smaller TSV has a smaller value. Based on the analytical model, we explore and validate the linear superposition principle of stress tensors and demonstrate the accuracy of this method against detailed FEM simulations. The analytic solutions of stress of two TSVs and three TSVs have high precision against the finite element result.