The ratio of electron and phonon thermal conductivity in nanoscale conductors

Background. Nanoscale conductors based on graphene nanoribbons and carbon nanotubes appear to be promising elements of nanoelectronics devices. Of practical interest are not only their high electrical conductivity, but also high thermal conductivity. Moreover, unlike electrical conductivity, the thermal conductivity of these nanoconductors is due not only to electronic, but also to phonon transport. Of particular interest is the study of the electron and phonon thermal conductivity of these nanoconductors in the mode of ballistic transport of heat carriers, when there is no electron scattering on phonons. The length of the ballistic path of electrons and phonons in graphene is about 1 micron. Therefore, this mode is attractive for practical use, since there are no losses on the release of Joule heat. The corresponding transverse dimensions of nanowires do not exceed 100 nm, therefore, quantum-dimensional effects must be taken into account when calculating electrical and heat transfer in them. In this regard, the study of the ratio of electron and phonon ballistic thermal conductivity and the number of corresponding quantum channels of electron and phonon transport in nanoconductors is an urgent task. The purpose of this work is to solve it. Materials and methods. Graphene nanoribbons with “zigzag” type edges and carbon nanotubes of “armchair” type are considered in this paper. The length of these nanoconductors is considered to be less than their ballistic length, and the transverse dimensions do not exceed 100 nm. The research is based on well-known methods of quantum physics, solid state physics and quantum theory of electrical conductivity and thermal conductivity of two-dimensional crystalline media. Results. By applying the principles of dimensional quantization to the theory of thermal conductivity of electron and phonon gases in graphene nanoribbons and carbon nanotubes, expressions are obtained for the quanta of electron and phonon thermal conductivity in these materials, as well as the number of channels of electron and phonon transport. Corresponding numerical estimates are made. Conclusions. The results obtained can be used to calculate heat transfer in nanoconductors based on graphene nanoribbons and carbon nanotubes.