Tunable Thermal Anisotropy Triggered by Quasi-Ballistic Heat Transport in WS ₂ Crystals

We investigate the influence of temperature and film thickness on the anisotropic thermal conductivity tensor of multilayer single-crystal WS₂ films of varying thickness (10 nm to 2.8 μm) across a wide temperature range (80-473 K). Experiments show that both in-plane (<i>k</i>_r) and out-of-plane (<i>k</i>_<i>z</i>) thermal conductivities increase with decreasing temperature, reaching, at 80 K in bulk WS₂, values up to <i>k</i>_r ∼ 1000 W m^-1 K^-1 and <i>k</i>_<i>z</i> ∼ 13 W m^-1 K^-1. The thermal anisotropy ratio η = <i>k</i>_r/<i>k</i>_<i>z</i> in bulk rises dramatically from 30 to 78 as the temperature decreases from 460 to 80 K, driven by the suppression of <i>k</i>_<i>z</i> due to phonon transport entering the quasi-ballistic regime. We further analyze the cumulative thermal conductivity as a function of phonon mean free path (MFP), showing that phonons with MFPs < 200 nm contribute to 70% of the total <i>k</i>_<i>z</i>. This work provides fundamental insight into the interplay between dimensionality, temperature, and anisotropic phonon transport in two-dimensional materials, where thermal anisotropy can be strategically leveraged for performance optimization.