Finite element modeling (FEM) has been undertaken to characterize the effect of copper (Cu) elasto-plastic behavior on the induction of stress in 3D crystalline silicon (Si) systems incorporating Cu through-silicon vias (TSVs). Using a linear isotropic hardening model, simulations of thermal annealing cycles in Cu TSVs indicate that, for sufficient anneal temperatures, plastic yield within the Cu leads to substantial residual stress in the neighboring Si following cool-down. Simulated Si stress profiles of annealed isolated TSVs agreed with experimental Raman microscopy measurements of post-anneal stress profiles in Si near isolated 5 × 25 μm cylindrical TSVs on a 300 mm Si wafer. Simulations were expanded to investigate the impact of Cu plasticity (yield stress and tangent modulus) on the residual stress profile in Si near isolated TSVs and linear TSV arrays. The results show that the magnitude and extent of the TSV-induced stress field in Si is a non-monotonic function of Cu yield stress. Moreover, the tensile or compressive nature of TSV-induced stress within and outside linear TSV arrays is also a strong function of the Cu yield stress. The simulated impact of Cu tangent modulus on TSV-induced stress in Si is less substantial. The implications of these results for TSV layout with respect to active device placement in a 3D system are discussed.

The thermal and spatial variation of Cu TSV-induced stress has been investigated for 1×4 arrays of 5 μm diameter × 50 μm TSVs using microRaman imaging. Following post-CMP annealing the measured Si Raman shift outside the TSV array is slightly modified. In strong contrast, the Si Raman shift midway between TSVs transitions from a tensile to compressive state as the annealing temperature increases. Topographic analysis implies this shift is associated with thermally-induced Cu extrusion.

The thermal and spatial variation of Cu through silicon via (TSV)-induced stress in 300mm Si wafers has been investigated for both isolated TSVs and TSV arrays using top-down and cross-sectional spectral microRaman imaging. The TSV-induced stress in Si results from plastic yield of the Cu, is compressive in the immediate vicinity of the TSV, and transitions to a tensile state at larger separations - in quantitative agreement with finite element modeling (FEM). TSV arrays (linear and square) lead to substantial tensile stress enhancement within the array. Moreover, thermal annealing showed that the intra-array Si stress field became more compressive with increased post-CMP thermal annealing while the Si stress-field external to the arrays exhibited little change. This may open potential avenues for reduction of TSV-induced Si stress in 3DICs.