A thermally conductive structure for a semiconductor integrated circuit and a method for making the structure. The structure comprises one or more vertical and/or horizontal thermally conductive elements disposed proximate a device for improving thermal conductivity from the device to a substrate of the integrated circuit. In one embodiment a heat sink is affixed to the integrated circuit for heat flow from the integrated circuit. The method comprises forming openings in material layers overlying the semiconductor substrate, wherein the openings are disposed proximate the device and extend to the substrate. A thermally conductive material is formed in the openings to provide a thermal path from the device to the substrate.