Temperature-dependent thermal stress determination for through-silicon-vias (TSVs) by combining bending beam technique with finite element analysis

In this paper, temperature-dependent thermal stresses in Cu TSVs are measured by combining the bending beam experiment with a finite element analysis (FEA). The bending beam technique measures the averaged bending curvature induced by the thermal expansion of a periodic annular Cu TSV array. The structural complexity of the blind annular TSV necessitated the use of FEA to derive the TSV-induced thermal stresses which accounts for the beam bending during thermal cycles. The FEA simulations established linear relationships between bending curvature and stress components in TSVs. Such linear relationships were used to extract independent stress components from the bending beam measurements. The results provided an understanding to the temperature-dependent stress characteristics in TSVs.