Phonon thermal transport in transition-metal and rare-earth nitride semiconductors from first principles

The thermal properties of three transition metal and rare-earth nitride compounds, ScN, YN, and LuN, have been studied using a first principles approach, in which a $\mathrm{DFT}+U$ treatment is guided by accurate hybrid functional calculations of electronic structure. The phonon dispersions for the three compounds show large longitudinal optic--transverse optic (LO-TO) splitting and soft TO modes. The resulting strong anharmonic scattering between acoustic and TO phonons reduces the lattice thermal conductivities, ${\ensuremath{\kappa}}_{\mathrm{L}}$, of these compounds. The room temperature ${\ensuremath{\kappa}}_{\mathrm{L}}$ values of YN and LuN are more than an order of magnitude smaller than that found for the weakly polar III-V compound boron bismuth ($350\phantom{\rule{0.16em}{0ex}}\mathrm{W}{\mathrm{m}}^{\ensuremath{-}1}{\mathrm{K}}^{\ensuremath{-}1}$), in spite of the latter having much larger average atomic mass and smaller acoustic phonon velocities. This paper demonstrates the utility of first principles calculations in understanding the thermal properties of materials, and it highlights the importance of optic phonons in reducing ${\ensuremath{\kappa}}_{\mathrm{L}}$.