Phonon focusing and temperature dependences of thermal conductivity of silicon nanofilms

The effect of phonon focusing on the anisotropy and temperature dependences of the thermal conductivities of silicon nanofilms is analyzed using the three-mode Callaway model. The orientations of the film planes and the directions of the heat flux for maximal or minimal heat removal from silicon chip elements at low temperatures, as well as at room temperature, are determined. It is shown that in the case of diffuse reflection of phonons from the boundaries, the plane with the {100} orientation exhibits the lowest scattering ability (and the highest thermal conductivity), while the plane with the {111} orientation is characterized by the highest scattering ability (and the lowest thermal conductivity). The thermal conductivity of wide films is determined to a considerable extent by the orientation of the film plane, while for nanowires with a square cross section, the thermal conductivity is mainly determined by the direction of the heat flux. The effect of elastic energy anisotropy on the dependences of the thermal conductivity on the geometrical parameters of films is analyzed. The temperatures of transition from boundary scattering to bulk relaxation mechanisms are determined.