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, ${\kappa }_{\mathrm{L}}$, of these compounds. The room temperature ${\kappa }_{\mathrm{L}}$ 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 ($350\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$), 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 ${\kappa }_{\mathrm{L}}$.

Figure 1

Electronic structure along high symmetry directions for (a) ScN, (b) YN, and (c) LuN, calculated using the HSE06 hybrid functional. Note that all three compounds have indirect energy gaps with valence band maxima at Γ and conduction band minima at $\mathrm{X}$.

Figure 2

Phonon dispersions for (a) ScN, (b) YN, and (c) LuN for different values of the Hubbard $U$ parameters: Black dotted curves are $U=0$; red curves are Case 1, thin blue dashed curves are Case 2, as described in the text. Calculations for ScN and YN used $\mathrm{LDA}+U$, while those for LuN used $\mathrm{GGA}+U$.

Figure 3

Lattice thermal conductivity $k_{\mathrm{L}}$ as a function of temperature for ScN, YN, and LuN. The solid lines give $k_{\mathrm{L}}$ for the $U$ value that matches the measured lattice constant. Dashed curves give $k_{\mathrm{L}}$ for the $U$ value that matches the energy gap obtained from HSE06 hybrid functional calculations.

Figure 4

Contributions to three-phonon scattering rates of ScN, YN, LuN, and Si in the lowest TA phonon branch from processes involving (a) three acoustic phonons (aaa), (b) two acoustic and one optic phonon (aao), and (c) one acoustic and two optic phonons (aoo), scaled by the maximum acoustic phonon frequency.

Figure 5

The change in energy per atom upon Sc and N sublattice displacements. The displacements are along the [100] direction with magnitudes prescribed by the corresponding phonon eigenvectors for the TO modes at Γ.

Figure 6

Lattice thermal conductivity of BBi as a function of temperature. B has a mix of isotopes: $19.9{\%}^{10}\mathrm{B}$ and $80.1{\%}^{11}\mathrm{B}$. The blue curve is calculated for this isotope mix including phonon-isotope scattering, while the red curve assumes an isotopically purified case with $100{\%}^{11}\mathrm{B}$.