Ballistic phonon transport in ultra-thin silicon layers: Effects of confinement and orientation

We investigate the effect of confinement and orientation on the phonon transport properties of ultra-thin silicon layers of thicknesses between 1 nm and 16 nm. We employ the modified valence force field method to model the lattice dynamics and the ballistic Landauer transport formalism to calculate the thermal conductance. We consider the major thin layer surface orientations {100}, {110}, {111}, and {112}. For every surface orientation, we study thermal conductance as a function of the transport direction within the corresponding surface plane. We find that the ballistic thermal conductance in the thin layers is anisotropic, with the ${110}/⟨110⟩$ channels exhibiting the highest and the ${112}/⟨111⟩$ channels the lowest thermal conductance with a ratio of about two. We find that in the case of the {110} and {112} surfaces, different transport orientations can result in $∼50%$ anisotropy in thermal conductance. The thermal conductance of different transport orientations in the {100} and {111} layers, on the other hand, is mostly isotropic. These observations are invariant under different temperatures and layer thicknesses. We show that this behavior originates from the differences in the phonon group velocities, whereas the phonon density of states is very similar for all the thin layers examined. We finally show how the phonon velocities can be understood from the phonon spectrum of each channel. Our findings could be useful in the design of the thermal properties of ultra-thin Si layers for thermoelectric and thermal management applications.