This study concerns chip warpage caused by thermal expansion mismatch between tapered copper (Cu) through-silicon vias (TSVs) and the surrounding silicon (Si) matrix. Systematic numerical finite element modeling is performed to simulate the periodic array of Cu TSVs. It is demonstrated that significant chip curvature can develop as a result of the tapered TSV geometry. The effects of taper angle, diameter, and density of TSVs, wafer thickness, and intermediate layers between Cu and Si are investigated.Index Terms-Through-silicon vias, thermal stress, chip warpage, modeling 1530-4388 (c)