Phonon focusing and features of phonon transport in silicon nanofilms and nanowires at low temperatures

The influence of the elastic anisotropy on the thermal conductivity in silicon nanofilms and nanowires for the diffuse scattering of phonons at boundaries at low temperatures has been investigated. It is shown that for the correct description of the phonon transport in silicon nanofilms, in contrast to isotropic medium, it is necessary to introduce two orientation parameters, which take into account the dependencies of the kinetic characteristics of phonon system on the direction of heat flow and the orientation of the film plane with respect to the crystal axes. The optimum orientations of the silicon film plane and directions of heat flow, which provide maximum or minimum heat transfer from elements of the silicon microcircuits have been determined. It is shown that for the nanowires with a square cross-section the values of thermal conductivity depend mainly on the direction of heat flow. However, in rather wide silicon nanofilms they are mainly determined by the orientation of the film plane with respect to the crystal axes. The dependencies of the thermal conductivity and the mean free paths of the phonons in the boundary scattering regime on the geometric parameters of nanostructures have been analyzed.