A through-substrate vias structure includes a substrate having opposing first and second major surfaces. One or more conductive via structures are disposed extending from the first major surface to a first vertical distance within the substrate. A recessed region extends from the second major surface to a second vertical distance within the substrate and adjoining a lower surface of the conductive via. In one embodiment, the second vertical distance is greater than the first vertical distance. A conductive region is disposed within the recessed region and is configured to be in electrical and/or thermal communication with the conductive via.