Green's Function Methods for Phonon Transport Through Nano-Contacts

Abstract

Formulations of the phonon transport problem depend on the length scale of interest. At the bottom end of the scale is the atomistic description. There are fundamental reasons for going to the atomic description level. One is that atomistic calculations can be used to extract parameters that are needed for coarser-grained descriptions. For example, descriptions like the equation of phonon radiative transfer [1,2], or at a coarser level, the heat diffusion equation, need to be provided with magnitudes such as interface thermal resistance and local thermal conductivity tensors. To obtain such local properties, atomistic approaches have been developed. Some examples are the Kubo formula for molecular dynamics, which yields the bulk thermal conductivity [3], the Allen–Feldman approach for the thermal conductivity of amorphous solids [4], and the method of lattice dynamics for interface thermal resistance [5–7].

In many cases, experimental validation of these local properties can only be carried out indirectly, by measurements on macroscopic samples. Nevertheless, experimental techniques have recently been developed that allow local thermal transportmeasurements on sampleswith characteristic dimensions in the sub-micrometer range [8–10]. Such ‘local probe’ experiments are generally based on measuring the heat flow across a nanoscale object linking two heat reservoirs which are kept at two different temperatures (see Fig. 3.1).