A bump structure that may be used to interconnect one substrate to another substrate is provided. A recessed conductive pillar is formed on a first substrate such that the recessed conductive pillar has a recess formed therein. The recess may be filled with a solder material. A conductive pillar on a second substrate may be formed having a contact surface with a width less than or equal to a width of the recess. The first substrate may be attached to the second substrate such that the conductive pillar on the second substrate is positioned over or in the recess of the first substrate. The substrates may each be an integrated circuit die, an interposer, a printed circuit board, a high-density interconnect, or the like.