Heat sink structures employing multi-layers of carbon nanotube or nanowire arrays to reduce the thermal interface resistance between an integrated circuit chip and the heat sink are disclosed. In one embodiment, the nanotubes are cut to essentially the same length over the surface of the structure. Carbon nanotube arrays are combined with a thermally conductive metal filler disposed between the nanotubes. This structure produces a thermal interface with high axial and lateral thermal conductivities.