Cross-plane thermal transport in ${\mathrm{MoS}}_2$

We study the cross-plane thermal transport in ${\text{MoS}}_2$ using density functional theory by adequately accounting for the effect of widespread van der Waals (vdW) forces. We show that past studies report a large variation in the reported values of cross-plane thermal conductivity due to no or limited benchmarking of vdW functionals in computations and variations in sample sizes in experiments. In particular, we show that the validation of the considered vdW functionals based on the correct reproduction of harmonic properties (structural parameters, heat capacity) only is insufficient for the correct description of the thermal transport physics. Further, after having validated the suitability of different functionals, we find that the phonons contributing to cross-plane conductivity have an order of magnitude larger mean free path than that for the basal-plane thermal transport in ${\text{MoS}}_2$ at room temperature. The cross-plane transport is quasiballistic with a more than 80% contribution coming from phonons having mean free paths larger than 500 nm. Furthermore, we demonstrate that four-phonon scattering lowers the cross-plane thermal conductivity by more than 35% at room temperature and is required for a correct description of cross-plane thermal transport physics in layered materials.

Figure 1

Phonon dispersion and density of states (in arbitrary units) as obtained from no-vdW, Grimme-D2, and vdW-DF2 functionals for (a) monolayer and (b) bulk ${\text{MoS}}_2$. Experimentally measured frequencies [50] are also included for bulk ${\text{MoS}}_2$ in (b) using open symbols.

Figure 2

(a) Temperature-dependent basal- and cross-plane thermal conductivities of bulk ${\text{MoS}}_2$ using the Grimme-D3 vdW functional, (b) Basal- and cross-plane thermal conductivity accumulation function with phonon mean free paths at 300 K. The thermal conductivities are obtained by considering phonon-boundary scattering corresponding to a characteristic length of $10\mu \mathrm{m}$.

Figure 3

The effect of four-phonon scattering on the basal- and cross-plane thermal transport properties of bulk ${\text{MoS}}_2$ at a temperature of 300 K. The results are obtained using the RTA solution of the BTE with a characteristic boundary scattering length of $10\mu \mathrm{m}$.