A semiconductor die stack includes a base die and core dies stacked over the base die. Each of the base die and the core dies include a semiconductor substrate, a front side passivation layer formed over a front side of the semiconductor substrate, a back side passivation layer over a back side of the semiconductor substrate, a through-via vertically penetrating the semiconductor substrate and the front side passivation layer, and a bump, a support pattern, and a bonding insulating layer formed over the front side passivation layer. Top surfaces of the bump, the support pattern, and the bonding insulating layer are co-planar. The bump is vertically aligned with the through-via. The support pattern is spaced apart from the through-via and the bump. The support pattern includes a plurality of first bars that extend in parallel with each other in a first direction and a plurality of second bars that extend in parallel with each other in a second direction.