Characterization of in-plane stress in TSV array — A unit model approach

This paper presents an analytical model to describe the in-plane thermomechanical stresses of a unit TSV model. The goal is to use this model to evaluate the influence of key design parameters in TSV interposers prior to rigorous investigations. The key parameters considered herein are via pitch and array size. This analytical model is based on a circular unit TSV structure, the size of which (in terms of its radius R) determines both the via's volume fraction and the behavior of the stress. The value of R can be V(Aft), where A is the area of a unit polygonal pattern in a fabricated TSV array. With a superposition of many such unit TSV structures at a given pitch, we illustrate the stress-interplay issue that becomes apparent in densely populated TSVs. We also use this simple strategy to highlight the stress concentration at the Cu/Si interface, which is critical to thermomechanical reliability design of TSV interposers.