Extremely anisotropic van der Waals thermal conductors

Abstract

The densification of integrated circuits requires thermal management strategies and high thermal conductivity materials^1-3. Recent innovations include the development of materials with thermal conduction anisotropy, which can remove hotspots along the fast-axis direction and provide thermal insulation along the slow axis^4,5. However, most artificially engineered thermal conductors have anisotropy ratios much smaller than those seen in naturally anisotropic materials. Here we report extremely anisotropic thermal conductors based on large-area van der Waals thin films with random interlayer rotations, which produce a room-temperature thermal anisotropy ratio close to 900 in MoS₂, one of the highest ever reported. This is enabled by the interlayer rotations that impede the through-plane thermal transport, while the long-range intralayer crystallinity maintains high in-plane thermal conductivity. We measure ultralow thermal conductivities in the through-plane direction for MoS₂ (57 ± 3 mW m^-1 K^-1) and WS₂ (41 ± 3 mW m^-1 K^-1) films, and we quantitatively explain these values using molecular dynamics simulations that reveal one-dimensional glass-like thermal transport. Conversely, the in-plane thermal conductivity in these MoS₂ films is close to the single-crystal value. Covering nanofabricated gold electrodes with our anisotropic films prevents overheating of the electrodes and blocks heat from reaching the device surface. Our work establishes interlayer rotation in crystalline layered materials as a new degree of freedom for engineering-directed heat transport in solid-state systems.

Fig. 1. Structure of r-TMD films.

a, Conceptual strategy for engineering thermal anisotropy in a single material system, using random interlayer rotation in polycrystalline vdW layered materials. b, Schematic of an r-MoS₂ film with random crystalline orientation. c, Greyscale-inverted TEM electron diffraction patterns probed from a 500 nm × 500 nm area of a monolayer and an N = 10 r-MoS₂ film. Inset: darkfield TEM image of a monolayer; the scale bar denotes 400 nm and the colours denote different domain orientations from different crystal domains. d, HAADF-STEM image of a cross-section of an N = 10 r-MoS₂ film on AlO_x coated with Al, with an interlayer spacing of 6.4 Å. e, Large-area MoS₂ films transferred onto 1-inch diameter fused silica substrates.

Fig. 2. Through-plane thermal properties of r-MoS₂.

a, TDTR heat dissipation curves of N-layer r-MoS₂ films. Inset: TDTR sample geometry. b, Measured thermal resistances across r-TMD films, where the error bars are the TDTR measurement uncertainties. The thermal conductivities for r-MoS₂ and r-WS₂ are calculated from the slope using the formula R_TDTR = R₀ + Nd/κ_⊥, whereby R₀ is the total interfacial thermal resistance. c, Experiment and MD simulation results of κ(T) of MoS₂ and r-MoS₂ films. The error bars to the MD simulations originate from the simulation uncertainties. The dotted lines connecting the individual data points are guides to the eye. d, LA (top) and TA (bottom) phonon dispersion curves of r-MoS₂ along the Γ–A direction. The dotted lines denote the acoustic curves corresponding to bulk MoS₂. e, Lifetime of LA and TA phonons parallel to the Γ–A direction in bulk and r-MoS₂. The dashed line is the LA mode vibration period derived from the dispersion curve in d. Source data.

Fig. 3. In-plane thermal properties and thermal anisotropy of r-MoS₂ films.

a, 45° SEM micrograph of an N = 4 r-MoS₂ film suspended on a TEM grid for Raman thermometry. b, Raman spectra of an N = 2 r-MoS₂ film with different absorbed laser powers. Inset: Raman thermometry sample geometry. c, A_1g Raman peak shifts versus power absorbed by r-MoS₂ films of various N. Inset: layer-dependent thermal conductance values (absorbed power divided by temperature increase) in domain size D = 1 μm and D = 400 nm r-MoS₂ films. The error bars are the propagated uncertainties from the calculation of the conductance value for each N. d, Comparison of ρ (y axis), κ_s (x axis), and κ_f (diagonal dashed lines) measured for different anisotropic thermal conductors. r-MoS₂ has an ultrahigh ρ close to 900, which is larger than bulk MoS₂, PG, and disordered layered WSe₂. The error bar for ρ of r-MoS₂ comes from the propagated uncertainties of the calculated κ_⊥ and κ_|| values. Source data.

Fig. 4. Temperature profiles and heat spreader efficiencies of r-MoS₂ films on Au electrodes.

a, Schematic of the sample configuration of r-MoS₂ draped across a current-carrying Au electrode that is 100 nm wide, 15 nm thick and 10 μm long. b, Thermal finite element modelling results of Au electrodes (bare, covered with 10-nm-thick r-MoS₂) at constant heating power of 8 mW supplied through Joule heating. c, Lateral profiles of temperature increases across the Au/SiO₂ surface (solid dots) and on the r-MoS₂ top surface (open circles). Insets: cross-sectional temperature distribution of Au electrodes with and without r-MoS₂, using the same colour scale as in b. d, I–V curve of an Au electrode, with and without N = 16 r-MoS₂. Inset: optical micrograph of six fabricated Au electrodes. e, Histogram of I_c of Au electrodes with and without an N = 16 r-MoS₂ heat spreader and their median values. Source data.

Extended Data Fig. 1. Cross-sectional TEM images of N = 20 and 10 r-MoS₂ on AlO_x.

Each set of N images are taken from the same sample at different locations. The N = 10 films are coated with Al that was electron beam evaporated onto the surface.

Extended Data Fig. 2. GIWAXS data of N = 10 r-MoS₂.

The peak position corresponds to a 2θ value of 14˚, which translates to an interlayer spacing of 6.4 Å (scattering direction).

Extended Data Fig. 3. Additional TDTR measurements and details.

a, Microscope image of an N = 10 r-MoS₂ film coated with a square grid of Al pads. b, 4 × 4 TDTR map of R_TDTR of an N = 10 r-MoS₂ film. c, Histogram of R_TDTR array measurements. d, TDTR measurements of N ≤ 10 r-TMD films coated with Au or Al. The error bars denote s.d.; number of TDTR measurements per film sample, n = 3 for Au samples; n = 3–5 for the Al samples. e, Picosecond acoustics of a MoS₂ monolayer on thick sapphire substrate, coated with an Al transducer layer. The y axis V_in is the in-phase signal of the lock-in amplifier. The red arrows indicate the acoustic waves reflected at the Al/MoS₂ interface.

Extended Data Fig. 4. Low-frequency Raman modes of r-MoS₂.

a, Raman spectra reflecting the breathing modes (BM) of r-MoS₂ (blue) and the shear mode (SM) for MoS₂. b, The low-frequency Raman peak positions of r-MoS₂ and exfoliated MoS₂. The filled squares indicate the BM peak positions of r-MoS₂. The open squares indicate the BM peak positions of exfoliated MoS₂, and the open circles indicate the SM peak positions of exfoliated MoS₂.

Extended Data Fig. 5. Raman thermometry on r-MoS₂ films.

a, Δω–P_abs curves of representative N = 2 r-MoS₂ films at different pressures. The P_abs values along the x axis are normalized to account for the slight differences in beam spot sizes (Δr = 20%). The results at 15 torr and 4 mtorr signify no effect of reducing the pressure to below 15 torr. Δω was approximately five-fold smaller at atmospheric pressure due to the extra heat loss channel by air. b, Δω–P_abs curves of r-MoS₂ films made up of D = 400 nm (grain size) monolayers. c, Optical absorption of suspended r-MoS₂ films, which follows the trend $A=1-{\left(1-A_0\right)}^N$, where A₀ is the monolayer absorptance. From the fit, A₀ = 0.08 ± 0.003. d, ω–T calibration measurements of suspended r-MoS₂ films (D = 1 μm), with the N = 2 and N = 4 data as the representative curves. e, ω–T slopes versus layer number for all films, with D = 400 nm or 1 μm.

Extended Data Fig. 6. κ(T) and ρ of r-MoS₂.

a, κ(T) of r-MoS₂, with κ_|| measured using Raman thermometry of N = 4 r-MoS₂, and κ_⊥ measured via TDTR as reported in Fig. 2c. The error bars are the propagated uncertainties from the calculation of the conductance value for each N. The error bars denote the propagated uncertainty of the calculations from the input parameters. We observed that κ_|| decreased with T, alluding to phonon-mediated heat transport and attesting to the long-range crystallinity of the r-MoS₂ films in-plane. This was in contrast with the κ_⊥(T) behaviour (Fig. 2c), which showed a slightly increasing trend. b, Catalogue of experimentally measured anisotropy ratios at room temperature versus slow-axis thermal conductivity (κ_s) of thermally anisotropic materials from literature, by category.

Extended Data Fig. 7. r-MoS₂ efficacy as a heat spreader.

a, Finite element simulations of the linear temperature profiles of Au electrodes covered with MoS₂ and r-MoS₂. b, SiN_x as heat spreaders for Au electrodes. Electrical properties of 10-nm-thick, 100-nm-wide and 10-μm-long Au electrodes before and after 16 nm SiN_x film deposition onto the electrodes using plasma-enhanced chemical vapour deposition. In contrast to r-MoS₂, the direct deposition of an ultrathin inorganic film such as SiN_x with a comparable κ to κ_|| of r-MoS₂ negatively affects the performance of the Au electrodes.

Extended Data Fig. 8. Optimization of the MD simulations for κ calculations.

a, Optimization of the driving force of the system, where the grey zone denotes the error. b, Effect of thermal expansion on κ.