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

The thermal properties of four transition metal and rare earth nitride compounds: ScN, YN, LaN and LuN, have been studied using a first principles approach. The phonon dispersions for the four compounds show large LO-TO splittings and soft TO modes, which results in strong anharmonic scattering between acoustic and optic phonons that reduces the lattice thermal conductivities, $k_{L} $, of these compounds. The particularly soft TO mode at $\Gamma $ in LaN gives it a much lower $k_{L} $ than the other compounds. The room temperature $k_{L} $ value for LaN of only 6 Wm$^{\mathrm{-1}}$K$^{\mathrm{-1}}$ is four times smaller than that of LuN in spite of the latter having larger average atomic mass, similar acoustic phonon velocities, and similar mode averaged Gr\"{u}neisen parameters. Electronic structure calculations using the HSE06 hybrid functional including spin-orbit coupling show that LaN has highly anisotropic conduction and valence bands in the vicinity of the band extrema. These features combined with its small $k_{L} $ make LaN a potentially viable thermoelectric material.