Quasi-Ballistic Thermal Transport Across MoS ₂ Thin Films

Layered two-dimensional (2D) materials have highly anisotropic thermal properties between the in-plane and cross-plane directions. Conventionally, it is thought that cross-plane thermal conductivities (κ _z ) are low, and therefore c-axis phonon mean free paths (MFPs) are small. Here, we measure κ _z across MoS ₂ films of varying thickness (20-240 nm) and uncover evidence of very long c-axis phonon MFPs at room temperature in these layered semiconductors. Experimental data obtained using time-domain thermoreflectance (TDTR) are in good agreement with first-principles density functional theory (DFT). These calculations suggest that ∼50% of the heat is carried by phonons with MFP > 200 nm, exceeding kinetic theory estimates by nearly 2 orders of magnitude. Because of quasi-ballistic effects, the κ _z of nanometer-thin films of MoS ₂ scales with their thickness and the volumetric thermal resistance asymptotes to a nonzero value, ∼10 m ² K GW ^-1 . This contributes as much as 30% to the total thermal resistance of a 20 nm thick film, the rest being limited by thermal interface resistance with the SiO ₂ substrate and top-side aluminum transducer. These findings are essential for understanding heat flow across nanometer-thin films of MoS ₂ for optoelectronic and thermoelectric applications.