Predicted Thermal Stresses in a TSV Design

Physically meaningful and easy-to-use analytical predictive stress models are developed for a through-silicon-via (TSV) design using theory-of-elasticity based approach. Two extreme cases of the TSV height-to-diameter ratios are considered: disc-like vias, with the aspect ratios below 0.25 (plane stress approximation can be employed in this case), and rod-like-vias, with aspect ratios, above 2.5 (plane strain approximation is applicable in this case). The objectives of the analysis are 1) to evaluate the effect of the size of the opening in the silicon (Si) material on the pressure at its boundary with the disc/rod, when the TSV structure is heated up, and the Si material is in tension because of the elevated circumferential stresses, and 2) to assess the incentive for using a compliant surrogate layer to relieve the shearing stresses at the Cu-Si interface. While the pressure at the Si opening is important from the standpoint of the strength of the Si material, the level of the interfacial stress is critical from the standpoint of the adhesive and cohesive strength of the TSV structure