An acoustic and dimensional mismatch model for thermal boundary conductance between a vertical mesoscopic nanowire/nanotube and a bulk substrate

A theoretical model to calculate the thermal boundary conductance (Kapitza conductance) or, alternatively, thermal boundary resistance (Kapitza resistance) between a vertically grown mesoscopic nanowire/nanotube and a bulk substrate is presented. The thermal boundary resistance at the interface between the mesoscopic geometry and a three-dimensional substrate is primarily due to two reasons: (1) dimensional mismatch in the phonon density of states and (2) mismatch in the acoustic properties. Our model based on the solution of the elastic wave equation in the substrate and the mesoscopic geometry incorporates both these effects.