Anisotropy and boundary scattering in the lattice thermal conductivity of silicon nanomembranes

We present a calculation of the full thermal conductivity tensor for (001), (111), and (011) surface orientations of the silicon-on-insulator (SOI) nanomembrane, based on solving the Boltzmann transport equation in the relaxation-time approximation with the full phonon dispersions, a momentum-dependent model for boundary scattering, as well as three-phonon and isotope scattering. The interplay between strong boundary scattering and the anisotropy of the phonon dispersions results in thermal conduction that strongly depends on the surface orientation and exhibits marked in-plane vs out-of-plane anisotropy, as well as slight in-plane anisotropy for the low-symmetry (011) SOI. In-plane thermal conductivity is highest along [100] on Si(011) and lowest in Si(001) due to the strong scattering of the highly anisotropic TA modes with (001) surfaces. The room-temperature in-plane conductivities in (011) and (001) nanomembranes with thicknesses around 10 nm differ by a factor of 2, and the ratio can be much higher at lower temperatures or in rougher samples. We discuss surface facet orientation as a means of tailoring thermal conduction in low-dimensional nanostructrures and address the role of out-of-plane thermal conductivities in predicting vertical phonon transport in superlattices.