Heterogeneous integration of nanomaterials has enabled advanced electronics and photonics applications. However, similar progress has been challenging for thermal applications, in part due to shorter wavelengths of heat carriers (phonons) compared to electrons and photons. Here, we demonstrate unusually high thermal isolation across ultrathin heterostructures, achieved by layering atomically thin two-dimensional (2D) materials. We realize artificial stacks of monolayer graphene, MoS 2 , and WSe 2 with thermal resistance greater than 100 times thicker SiO 2 and effective thermal conductivity lower than air at room temperature. Using Raman thermometry, we simultaneously identify the thermal resistance between any 2D monolayers in the stack. Ultrahigh thermal isolation is achieved through the mismatch in mass density and phonon density of states between the 2D layers. These thermal metamaterials are an example in the emerging field of phononics and could find applications where ultrathin thermal insulation is desired, in thermal energy harvesting, or for routing heat in ultracompact geometries.

A new frontier is enabled by two-dimensional (2D) materials, which are sub-nanometer thin in single monolayers and thus amenable to control device behavior at atomic length scales ( 17 ). For example, heterogeneous 2D assemblies have been used for novel tunneling field-effect transistors ( 18 ) and ultrathin photovoltaics with high efficiency ( 19 ). Here, we use van der Waals (vdW) assembly of atomically thin 2D layers to achieve unusually high thermal resistance across their heterostructures. Specifically, we show a thermal resistance equivalent to that of ~300-nm SiO 2 across sub–2-nm-thin vdW heterostructures with clean, residue-free interfaces. We also demonstrate the ability of tailoring thermal properties at atomic-scale dimensions, on the order of the phonon wavelength, by layering heterogeneous 2D monolayers with different atomic mass densities and vibrational modes. Such structures form new phononic metamaterials with unusual properties not commonly found in nature. These also represent a unique application of 2D materials and their weak vdW interactions, which can be assembled (here, to block or guide the flow of heat) without the requirement of epitaxially matched interfaces.

Previous efforts to manipulate thermal properties of solids relied on nanolaminate films ( 9 ) and superlattices ( 10 , 11 ) to reduce thermal conductivity below that of the constituent materials. These were achieved through structural disordering and high interface density, which introduce additional thermal resistance. Unusually low thermal conductivity was also found in silicon and germanium nanowires, from strong phonon-boundary scattering ( 12 , 13 ). On the other hand, large thermal conductivities have been achieved in isotopically pure materials, e.g., 12 C diamond ( 14 ) or graphene ( 15 ), and in the cubic boron arsenide compound through reduced phonon scattering ( 16 ).

Advanced electronic and photonic devices, like high-electron mobility transistors ( 1 ), quantum cascade lasers ( 2 ), and photonic bandgap crystals ( 3 ), take advantage of the fermionic nature of charge carriers for voltage gating or confinement, and of long photon wavelengths for interference. However, thermal nanoengineering and the emerging field of phononics offer fewer examples, despite high demand in heat management applications ( 4 – 6 ). This discrepancy is due to the short wavelengths of heat-carrying vibrations in solids, just a few nanometers for the dominant (median) phonon wavelength at room temperature ( 7 , 8 ), which poses difficulties in nanofabrication at nearly atomic-scale dimensions. The bosonic nature of phonons, which cannot be voltage-gated like the charge carriers, also makes it challenging to actively control heat transport in solids.

RESULTS

Microstructural and optical characteristics Figure 1A shows the schematic cross-section of a four-layer heterostructure with (from top to bottom) graphene (Gr) on MoSe 2 , MoS 2 , and WSe 2 , all on a SiO 2 /Si substrate. The Raman laser illustrated is used for simultaneously probing the individual layers in the stack, with single-layer accuracy. All 2D materials are monolayers, separately grown by chemical vapor deposition (CVD) (20) and transferred while avoiding polymer and other residues. (Details are provided in Materials and Methods and section S1.) To confirm microstructural, thermal, and electrical uniformity of the heterostructures, we use scanning transmission electron microscopy (STEM), photoluminescence (PL) spectroscopy, Kelvin probe microscopy (KPM), scanning thermal microscopy (SThM), as well as Raman spectroscopy and thermometry. Fig. 1 Optical and STEM characterization of vdW heterostructures. (A) Cross-section schematic of Gr/MoSe 2 /MoS 2 /WSe 2 sandwich on SiO 2 /Si substrate, with the incident Raman laser. (B) Raman spectrum of such a heterostructure at the spot indicated by the red dot in the inset optical image. Raman signatures of all materials in the stack are obtained simultaneously. The graphene Raman spectrum is flattened to exclude the MoS 2 photoluminescence (PL) effect. arb.u., arbitrary units. (C to F) STEM cross-sectional images of four-layer (C) and three-layer (D to F) heterostructures on SiO 2 . In (D), MoSe 2 and WSe 2 are approximately aligned along the 1H [100] zone axis, and in (E and F), the layers are misaligned by ~21° with respect to the 1H [100] zone axis. The monolayer graphene on top of each heterostructure is hard to discern due to the much lower atomic number of the carbon atoms. (G) PL spectra of monolayer MoS 2 , monolayer WSe 2 , and a Gr/MoS 2 /WSe 2 heterostructure after annealing. The PL is strongly quenched in the heterostructure due to intimate interlayer coupling. Figure 1B shows the Raman spectrum of such a Gr/MoSe 2 /MoS 2 /WSe 2 heterostructure on SiO 2 /Si at the location of the red dot in the inset. It reveals the signature of every 2D material monolayer in the stack, as well as that of the Si substrate. This is a unique strength of the Raman technique, allowing us to identify each material with nonoverlapping Raman modes and to measure its individual temperature. All characteristic Raman peaks of the constituent materials are observed (see Materials and Methods) (21), except for the D peak of graphene, indicating negligible disorder. Figure 1 (C to F) shows cross-sectional atomic-resolution annular dark-field STEM (ADF-STEM) images of our Gr/MoSe 2 /MoS 2 /WSe 2 (Fig. 1C) and Gr/MoS 2 /WSe 2 (Fig. 1, D to F) heterostructures with different lattice orientation alignments. Multiple STEM images reveal atomically intimate vdW gaps without contaminants, allowing us to observe the total thickness of these heterostructures, e.g., just below 2 nm for a three-layer stack (also see fig. S2). The interlayer coupling is further confirmed over larger areas by PL spectroscopy (Fig. 1G). The PL signal of individual layers in the heterostructure is substantially quenched (over one order of magnitude) compared to isolated monolayers on the same substrate. This PL quenching is attributed to an interlayer charge transfer process due to intimate interlayer coupling, which becomes even stronger after annealing (see section S3) (22).

Electrical characteristics and thermal uniformity To measure heat flow perpendicular to the atomic planes of the heterostructures, we pattern the stacks in the shape of four-probe electrical devices (see Materials and Methods). The top graphene layer is contacted by Pd electrodes and used as a nearly transparent Joule heater for the Raman thermometry measurements. This electrical heating method enables accurate quantification of the input power (23), whereas a purely optical heating method (24) would be more challenging without knowing the absorption coefficients of individual layers. Figure 2 (A and B) displays the schematic of the four-probe measurement and the top view of a test structure, respectively. Figure 2C shows the measured back-gated transfer characteristics of three devices, one with only graphene and two with stacks of Gr/WSe 2 and Gr/MoSe 2 /WSe 2 . These all show the well-known ambipolar behavior of graphene due to the absence of an energy bandgap. They also confirm that current conduction and heating occur in the top graphene layer, its electrical conductivity being orders of magnitude higher than MoS 2 and WSe 2 (see section S6). To demonstrate the uniformity of these devices, we also use KPM and SThM surface characterization. Figure 2D displays KPM measurements taken along the device at various V DS , revealing smooth and linear potential distributions. Figure 2E shows an SThM map of the electrically heated Gr/MoS 2 /WSe 2 channel, displaying uniform surface heating with high spatial resolution (see section S4). Fig. 2 Electrical and scanning probe characterization. (A) Cross-sectional schematic of the test structure showing the four-probe configuration. Electrical current flows in the graphene top layer, and heat dissipates across layers, into the substrate. (B) Optical image of a four-probe test structure. Devices are back-gated by the Si substrate through 100-nm SiO 2 . (C) Measured transfer characteristics of three test structure stacks, Gr/MoS 2 /WSe 2 , Gr/WSe 2 , and Gr-only control devices in vacuum (~10−5 torr). All measurements display the ambipolar property of the top graphene channel. (D) KPM of an uncapped Gr/MoS 2 /WSe 2 heterostructure device. The graph displays the surface potential along the channel (averaged across the channel width) at different bias conditions. The small potential jump near the Pd electrodes represents the relative work function difference (~120 mV). The KPM maps reveal no other heterogeneities in the surface potential, confirming the spatially uniform quality of these devices. The inset shows the zero-bias KPM map. (E) SThM thermal map of Gr/MoS 2 /WSe 2 heterostructure, here capped with 15-nm Al 2 O 3 , revealing homogeneous heating across the channel. This confirms the uniformity of the thermal interlayer coupling in the stacks. The device dimensions are the same as in the (D) inset.

Thermometry of the vdW heterostructures While SThM confirms the surface temperature uniformity of our devices, we used Raman spectroscopy to quantify the temperature of each individual layer. The spectral separation of key Raman features (Fig. 1B) enables sub-nanometer, effectively atomic-scale resolution of the temperature measurement across the 2D stack. We calibrate all temperature-dependent Raman peak shifts (see section S7 for details) and carefully differentiate or rule out nonthermal effects (see Materials and Methods and section S8). We measured three devices of each structure, varying the graphene heater power to 9 mW, while the absorbed laser power was below ~5 μW to avoid optical heating. (All devices have an area of ~40 μm2, and the laser spot size is ~0.5 μm2.) Raman peak shifts during electrical heating are converted to temperature rise using the calibration coefficient of each material in the heterostructure (see section S7). Figure 3A shows the measured temperature rise (ΔT) of each layer, including the Si substrate, as the graphene heater power (P) is ramped up, in a Gr/MoS 2 /WSe 2 heterostructure. The slopes of the linear fits for each material indicate the thermal resistance R th = ΔT/P between that layer and the backside heat sink. Because of uniform heating (Fig. 2E), these thermal resistances are easily analyzed, from bottom to top, normalizing by the channel area, WL. Here, L and W are the channel length and width, much larger than the SiO 2 thickness and the lateral thermal healing length, which is ~0.1 μm (23). R th,Si ≈ (WL)1/2/(2k Si ) is the thermal spreading resistance into the Si substrate, yielding k Si ≈ 90 W m−1 K−1, which is the expected thermal conductivity of the highly doped substrate (23). The difference between R th,WSe2 and R th,Si is the sum of the well-known thermal resistance of 100 nm SiO 2 (24) and the thermal boundary resistance (TBR) of the WSe 2 /SiO 2 interface. [The TBR of the SiO 2 /Si interface is negligible in comparison (25).] Then, R th,MoS2 − R th,WSe2 = TBR MoS2/WSe2 and R th,Gr − R th,MoS2 = TBR Gr/MoS2 . Thus, from Fig. 3A, we can extract TBR values for each of the WSe 2 /SiO 2 , MoS 2 /WSe 2 , and Gr/MoS 2 interfaces. Fig. 3 Thermal resistance of the heterostructures. (A) Measured temperature rise ΔT versus electrical input power for each individual layer in a Gr/MoS 2 /WSe 2 heterostructure, including the Si substrate, shown in the inset. Graphene (pink circles), MoS 2 (blue diamonds), WSe 2 (red triangles), and Si (black squares). All measurements are carried out at V G < 0 (see section S6). The slopes of the linear fits (dashed lines) represent the thermal resistance R th between each layer and the heat sink. (B) Comparison of total thermal resistances (i.e., of the top graphene layer) measured by Raman thermometry and SThM for different vdW heterostructures. The R th values obtained from these two techniques match within the uncertainty of the measurements. All devices have the same active area of ~40 μm2. We compare the total thermal resistances perpendicular to all heterostructures, measured by Raman and SThM in Fig. 3B. (Unlike Raman, SThM measures only the surface temperature, and its calibration is discussed in section S5.) Knowing the electrical input power, the total thermal resistance between the graphene top layer and the backside heat sink is obtained for all our heterostructures. The excellent agreement between the two thermometry techniques validates the obtained values. The bilayer and trilayer heterostructures on SiO 2 display an effective thermal resistance (normalized by area) in the range of 220 to 280 m2 K/GW at room temperature, which is equivalent to the thermal resistance (Kapitza length) of 290 to 360 nm of SiO 2 . Given the sub–2-nm thickness of these heterostructures (Fig. 1, D to F), they have an effective thermal conductivity of 0.007 to 0.009 W m−1 K−1 at room temperature, which is approximately a factor of 3 lower than that of ambient air.