Thermal Conductivity Enhancement in ${\mathrm{MoS}}_2$ under Extreme Strain

Because of their weak interlayer bonding, van der Waals (vdW) solids are very sensitive to external stimuli such as strain. Experimental studies of strain tuning of thermal properties in vdW solids have not yet been reported. Under $\sim 9\%$ cross-plane compressive strain created by hydrostatic pressure in a diamond anvil cell, we observed an increase of cross-plane thermal conductivity in bulk ${\mathrm{MoS}}_2$ from 3.5 to about $25\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, measured with a picosecond transient thermoreflectance technique. First-principles calculations and coherent phonon spectroscopy experiments reveal that this drastic change arises from the strain-enhanced interlayer interaction, heavily modified phonon dispersions, and decrease in phonon lifetimes due to the unbundling effect along the cross-plane direction. The contribution from the change of electronic thermal conductivity is negligible. Our results suggest possible parallel tuning of structural, thermal, and electrical properties of vdW solids with strain in multiphysics devices.

Figure 1

Experimental setup, total, and electronic thermal conductivity under high pressure. (a) Schematic of thermal conductivity measurement with a diamond anvil cell integrated with a ps-TTR system. (b) Experimental data and fitting of ps-TTR measurements at two selected pressures, with $\pm 20\%$ confidence interval shown. (c) Extracted cross-plane thermal conductivity (both lattice and electronic) as a function of pressure. The red curve is included only as a guide to the eye. Semiconducting and intermediate regions are labeled based on Ref. [29]. (d) Electronic thermal conductivity of ${\mathrm{MoS}}_2$ against pressure, determined from measured electronic conductivity via the Wiedemann-Franz law [29]. Three regions of the semiconductor to metal transition are labeled.

Figure 2

Calculated lattice thermal conductivity, interatomic force constant and phonon dispersion curves. (a) Pressure-dependent in-plane and cross-plane lattice thermal conductivities obtained by first-principles calculations, with contributions to ${\kappa }_{\perp ,\text{lattice}}$ from acoustic, optical, longitudinal acoustic (LA) and two transverse acoustic (TA1, TA2) phonon branches. (b) Pressure-dependent interatomic force constants of the interlayer Mo-S bond, interlayer S-S (S1-S2) bond, and intralayer S-S bond from first-principles calculations. (c) First-principles calculations of the pressure induced change of phonon dispersion curves and phonon group velocities in multilayer ${\mathrm{MoS}}_2$ along both cross-plane ($\mathrm{\Gamma }\text{−}A$) and in-plane ($\mathrm{\Gamma }\text{−}M$) directions. Group velocities are shown using a color gradient, with warmer colors indicating higher group velocities.

Figure 3

CPS measurements and first-principles calculations of phonon frequency and lifetime. (a) Schematic of CPS measurements of coherent acoustic phonons in an uncoated ${\mathrm{MoS}}_2$ sample. (b) Pressure-dependent coherent oscillations of longitudinal acoustic phonons measured with CPS. (c) Pressure-dependent LAP frequencies extracted from CPS measurements (black circles) and LAP group velocities from first-principles calculations (red squares). (d) Pressure-dependent LAP lifetimes extracted from CPS measurements (black circles) and from first-principles calculations (red squares), as well as lifetimes of $A_{1g}$ optical phonons extracted from Raman measurements (green triangles).