Predominance of thermal contact resistance in a silicon nanowire on a planar substrate

At low temperatures, thermal transport in single crystalline nanowires with sub-10-nm diameters is defined in terms of the universal quantum of conductance. In the case of a nanowire connected to plane substrates, additional conductances appear due to the contacts. We calculate the contact conductances and prove that they are much smaller than the conductance of the nanowire. The reason is that the number of excited modes per unit volume in the substrates becomes smaller than the one in the wire at low temperatures. The substrate then generates the predominant thermal resistance because its specific heat becomes smaller than the one of the wire. From these considerations, the wire-membrane and membrane-plane substrate thermal conductances can also be predicted.