Carbon nanotube-based structures and methods for removing heat from solid-state devices

One aspect of the invention includes a copper substrate; a catalyst on top of the copper substrate surface; and a thermal interface material that comprises a layer containing carbon nanotubes that contacts the catalyst. The carbon nanotubes are oriented substantially perpendicular to the surface of the copper substrate. A Raman spectrum of the layer containing carbon nanotubes has a D peak at ˜1350 cm−1 with an intensity ID, a G peak at ˜1585 cm−1 with an intensity IG, and an intensity ratio ID/IG of less than 0.7 at a laser excitation wavelength of 514 nm. The thermal interface material has: a bulk thermal resistance, a contact resistance at an interface between the thermal interface material and the copper substrate, and a contact resistance at an interface between the thermal interface material and a solid-state device. A summation of these resistances has a value of 0.06 cm2K/W or less.