Stacking Order, Thickness and Strain Dependent Thermal Conductivity of ReS₂

Since the discovery of single atomic layer graphene, 2D thin films have been realized in hundreds of different materials. Fascinating physical phenomena have been observed and new applications have been demonstrated. The single atomic layers of these materials are bonded together via weak van der Waals (vdW) force, hence are also called vdW solids. Thermal properties of vdW solids are essential in determining the performance, stability, and durability of electronic devices. Thermal conductivities of vdW solids have been simulated and measured in a wide range of materials, such as graphene (including ribbons, thins films, etc.), Boron Nitride, transition metal dichalcogenides (e.g., MoS₂, ReS₂, WSe₂, and black phosphorus etc.). Majority of these studies focus on the high-value in-plane thermal conductivity (k_//). Only a few studies reported the thermal transport along the cross-plane direction (k_⊥).Based on the kinetic theory, where phonon mean free path (Λ) could be estimated through the measured k_⊥ via: k_⊥ ~ (1/3)Cν_g,⊥Λ_⊥ , where C is the heat capacity, ν_g is the phonon group velocity. For MoS₂, the phonon mean free path is estimated to be 1.5~4 nm, equivalent to 2~6 layers. Kinetic theory suggests that the thermal conductivity of these materials should not show any thickness dependence trend beyond 10 layers. However, among the few studies about k_⊥, both experimental and theoretical studies have shown clear thickness dependence in graphene and MoS₂, up to several hundred nanometers. The discrepancy between the kinetic theory with the experimental/simulation results suggests that the cross-plane phonon mean free path in vdW solids could be much longer than previously thought, our paradigm about the heat transport across vdW layers may be inaccurate, and the nature of the phonon scattering and thermal transport in this regime is not well understood.
We utilized the high pressure diamond anvil cell (DAC) to tune the interlayer vdW force in ReS₂ across a wide range and measured the evolution of thermal conductivity with picosecond transient thermo-reflectance technique. ReS₂ is chosen mainly due to two reasons: (i) It has the weakest interlayer vdW force among TMDs, hence can show the thermal transport change across a wide range of vdW force strength. (ii) It possesses a pure stacking order up to several microns, hence eliminates any complexity from effects of mixed stacking orders. ReS₂ possesses a distorted 1T triclinic crystal structure where the additional d valence electrons of Re atoms form zigzag Re chains parallel to the b axis, drastically reducing its symmetry. Recently, two distinct stacking orders of ReS₂ (AA and AB stacking) have been identified with the Raman spectroscopy. For AA stacking, the adjacent layers have no relative shift; while for AB stacking, there is a one-unit cell shift between adjacent layers along a axis.
Firstly, we measured the thickness dependent thermal conductivity in both AA & AB stacking samples, and found that (a) both stackings show long range phonon mean path, up to about 1µm; and (b) AA stacking has higher thermal conductivity than AB stacking over the whole thickness range. Secondly, we applied the compressive strain on both AA and AB stacking samples in DAC and observed that: (a) thermal conductivity of AA stacking sample oscillates between 2 W/mK to 18 W/mK with pressure; and (b) AB stacking sample oscillates between 1.5 W/mK to 5 W/mK. Together with Raman spectroscopy that monitors the structural change, we hypothesize the observed thermal conductivity patterns to layer sliding and lattice distortion under compressive strain.