pubs.acs.org/NanoLett Letter Engineering Heat Transport Across Epitaxial Lattice-Mismatched van der Waals Heterointerfaces Emigdio Chavez-Angel, Polychronis Tsipas, Peng Xiao, Mohammad Taghi Ahmadi, Abdalghani H. S. Daaoub, Hatef Sadeghi, Clivia M. Sotomayor Torres, Athanasios Dimoulas, and Alexandros El Sachat* Cite This: Nano Lett. 2023, 23, 6883−6891 Read Online ACCESS Metrics & More Article Recommendations * sı Supporting Information ABSTRACT: Artificially engineered 2D materials offer unique physical properties for thermal management, surpassing naturally occurring materials. Here, using van der Waals epitaxy, we demonstrate the ability to engineer extremely insulating thermal metamaterials based on atomically thin lattice-mismatched Bi2Se3/ MoSe2 superlattices and graphene/PdSe2 heterostructures with exceptional thermal resistances (70−202 m2 K/GW) and ultralow cross-plane thermal conductivities (0.012−0.07 W/mK) at room temperature, comparable to those of amorphous materials. Experimental data obtained using frequency-domain thermore- flectance and low-frequency Raman spectroscopy, supported by tight-binding phonon calculations, reveal the impact of lattice mismatch, phonon-interface scattering, size effects, temperature, and interface thermal resistance on cross-plane heat dissipation, uncovering different thermal transport regimes and the dominant role of long-wavelength phonons. Our findings provide essential insights into emerging synthesis and thermal characterization methods and valuable guidance for the development of large-area heteroepitaxial van der Waals films of dissimilar materials with tailored thermal transport characteristics. KEYWORDS: phonon transport, thermal conductivity, frequency-domain thermoreflectance Bi2Se3/MoSe2, graphene/PdSe2 T he emergence of van der Waals (vdW) heterostructures and superlattices (SLs) has introduced new possibilities in nanoelectronics, optics, and heat transport engineering. the films. Nevertheless, recent works have demonstrated high thermal isolation across a few micrometer size exfoliated graphene/MoSe2/MoS2/WSe2 heterostructures,13 graphene/ These structures offer ultrahigh mobility, topological proper- MoS2 SLs,8 and polycrystalline WS2 films.10 In contrast, ties, high absorption, sensitivity, low scattering rates, and bottom-up epitaxial techniques, such as molecular beam highly anisotropic properties.1−4 Recently, researchers have epitaxy (MBE), enable wafer-scale growth of high-order vdW proposed thermodynamically stable misfit layer compounds, SLs with atomically smooth and abrupt periodic interfa- vdW heterostructures, and SLs with tailored thermal transport ces.1,14−16 The ability to control atomic layer thickness and and thermoelectric conversion properties for thermal manage- chemical composition also allows for the precise design of the ment applications.4−8 The periodic nature of SLs leads to the transport properties of the SLs. Moreover, vdW epitaxy offers formation of new phonon modes and bandgaps due to the great flexibility in integrating atomic layers of different folding effect, which significantly modifies the phonon group materials such as metals, semiconductors, superconductors, velocity and thermal conductivity based on the period or insulators, without considering lattice-matching require- thickness.9 Moreover, vdW SLs and thin films assembled ments.1,17 from layers with structural lattice mismatch and weak vdW Here, using wafer-scale heteroepitaxial growth, we demon- interactions or random interlayer rotations, could suppress strate superior cross-plane thermal insulation based on phonon transport along the c-axis while preserving their in- plane crystallinity.10 Despite significant efforts toward this direction, many Received: April 5, 2023 experimental studies have reported vdW stacks using top- Revised: June 27, 2023 down fabrication methods, such as exfoliation, which can only Published: July 19, 2023 prepare small flakes on a micrometer scale.8,11−13 Additionally, such flakes are most likely to have defects or contamination, which further create additional phonon scattering centers in © 2023 The Authors. Published by American Chemical Society https://doi.org/10.1021/acs.nanolett.3c01280 6883 Nano Lett. 2023, 23, 6883−6891 Nano Letters pubs.acs.org/NanoLett Letter Figure 1. Structural and chemical characterization of epitaxial vdW films. Top and side views of (a) Bi2Se3, and (b) MoSe2 and (c) PdSe2 crystal structures. The purple, blue, and orange spheres represent Bi, Mo, and Pd atoms, respectively, while Se atoms are shown with gray spheres. One QL Bi2Se3 consists of five atoms per unit cell, such as Se−Bi−Se−Bi−Se, while each monolayer MoSe2 consists of three atomic sublayers, in which Mo atoms are sandwiched between Se atoms. In PdSe2, each Pd atom is connected with four Se atoms, and each Se atom is bonded with two Pd atoms and another Se atom. (d) Cross-sectional STEM images of the as-synthesized vdW Bi2Se3/MoSe2 SLs with periods of n = 3 and n = 1 (inset) on STO substrates. After the growth, a 4 nm thick Se capping layer was deposited in situ to protect the SL from oxidation. RHEED patterns of 1 QL Bi2Se3 and Bi2Se3/MoSe2 SL with period n = 1 along the (e, g) [11−20] and (f, h) [11−10] azimuths. (i) STM image of the as grown monolayer PdSe2 on graphene and (j) the corresponding fast Fourier transform (FFT) image of the whole region. (k−n) XPS data of Bi2Se3/MoSe2 SL grown on the STO substrates. atomically thin crystalline vdW films assembled from highly Bi2Se3, MoSe2, and PdSe2 films have been investigated;18−22 dissimilar Debye temperature materials. Specifically, we while such high cross-plane thermal insulation has been directly grow high-quality lattice-matched Bi2Se3/MoSe2 SLs achieved only in polycrystalline films or exfoliated flakes. and graphene/PdSe2 heterostructures of varying thicknesses on We grew the epitaxial Bi2Se3 films, Bi2Se3/MoSe2 SLs, and different substrates, which exhibit tailored thermal transport graphene/PdSe2 heterostructures on various single-crystal properties at the atomic-scale. Combining contactless charac- substrates such as strontium titanate (STO), sapphire, and terization techniques, e.g., frequency-domain thermoreflec- silicon carbide (SiC) by MBE, yielding 2D thin films with tance (FDTR) and low-frequency Raman spectroscopy, we minimal disorder. A schematic representation of each material study the acoustic and thermal properties of these epitaxial is shown in Figures 1a−c. The structural and chemical films. We focus on unraveling the impact of vibrational characterization of the samples were studied by X-ray mismatch, phonon-interface scattering, temperature and film Photoelectron Spectroscopy (XPS), low-frequency Raman thickness on cross-plane thermal transport and we estimate the spectroscopy, scanning tunnelling microscopy (STM), and effective cross-plane thermal conductivity and total thermal high resolution scanning transmission electron microscopy resistance of the films taking into account all the interfacial (HR-STEM) measurements. HR-STEM images in Figure 1d contributions in our multilayer structures. Tight-binding confirmed the expected layering structures of Bi2Se3/MoSe2 phonon calculations support our experimental data and further SLs, consisting of vertically stacked Bi2Se3 and MoSe2 reveal the impact of the thermal contact resistance on the sublayers with atomically sharp and contamination-free thermal conduction of layered materials and the presence of interfaces. Reflection high-energy electron diffraction different thermal transport regimes in such atomically thin 2D (RHEED) patterns show that MoSe2 and Bi2Se3 layers are films. To date, only the in-plane thermal transport properties of repeatedly grown highly oriented on top of each other despite 6884 https://doi.org/10.1021/acs.nanolett.3c01280 Nano Lett. 2023, 23, 6883−6891 Nano Letters pubs.acs.org/NanoLett Letter Figure 2. Low-frequency Raman spectroscopy in epitaxial vdW films. Raman scattering spectra in (a) Bi2Se3 films of different thickness and (b) Bi2Se3/MoSe2 SLs. (c) Ratios of the Raman intensities for the out-of-plane (IA11g/IA21g) and in-phase shear modes (IE1g/IE2g) versus film thickness for the case of Bi2Se3 films (black squares) and Bi2Se3/MoSe2 SLs (red circles). (d) Low-frequency Raman scattering spectra in graphene/PdSe2 heterostructures of different thicknesses. The red-shaded area shows the frequency region where the Raman-inactive modes are detected. (e) Atomic displacements (gray arrows) of all the Raman modes detected in Bi2Se3 films, Bi2Se3/MoSe2 SLs, and graphene/PdSe2 heterostructures. The purple, blue, and orange spheres represent Bi, Mo and Pd atoms, respectively, while Se atoms are shown with gray spheres. their large lattice mismatch (∼20%) (see Figure S1 in the are observed. Specifically, the E1g, E2g, A11g, and A21g modes are Supporting Information (SI)). The RHEED patterns of one detected at ∼37 cm−1, ∼32 cm−1, ∼71 cm−1, and ∼173 cm−1, quintuple layer (QL) Bi2Se3 and Bi2Se3/MoSe2 heterostruc- respectively, in agreement with previous studies.25,26 Both out- tures (Figure 1e−h) show the difference in the relative of-plane modes (A11g, A21g) show a pronounced red shift positions of the streaks, which reflects the large lattice (about 2.7 cm−1) as the thickness decreases; while the in-plane mismatch between Bi2Se3 and MoSe2 at room temperature. modes (E1g, E2g) are red-shifted with decreasing thickness of Figures 1k−n displays in situ XPS data for the Bi2Se3 thin about 1.7 and 3.5 cm−1, respectively (see also Figure S11a). films and Bi2Se3/MoSe2 heterostructures. The binding energies We note that the A11g is more sensitive with thickness because of the Bi 4f7/2 and Se 3d5/2 core levels for 1 QL Bi2Se3 grown it reflects the out-of-plane vibrations of the Se and Bi atoms.26 directly on STO were 158.00 and 53.71 eV, respectively, in We also observe a broadening of the E2g mode as the film agreement with previous reports.23 After 2 monolayers MoSe2 thickness decreases (Figure 2a), in agreement with previous growth, the Mo 3d5/2 and Se 3d5/2 peak positions at 228.54 reports,26 suggesting that the layer-to-layer stacking strongly and 54.25 eV, respectively, indicated Mo−Se bonds and agreed affects the interlayer bonding. In SLs (Figure 2b) except of the well with the MoSe2 formation.24 The Se 3d peak in Figure 1n Raman modes that correspond to Bi2Se3, we detect the A1g is deconvoluted into four peaks to consider two types of bonds, mode in the spectral range of 240.1−241.1 cm−1, which namely, Bi−Se and Mo−Se bonds, keeping the Se 3d5/2-3d3/2 confirms the existence of MoSe2 layers.27,28 In Figure 2c we spin−orbit splitting fixed at 0.86 eV. The two distinct Se plot the ratios of the Raman intensities for the out-of-plane environments suggest Bi2Se3 and MoSe2 formation rather than (IA11g/IA21g) and in-phase shear modes (IE1g/IE2g) of the the formation of a mixed Bi−Mo−Se compound. The latter is adjacent layers versus thickness for the case of Bi2Se3 films and reinforced by the fact that the Bi 4f7/2 peak position remains Bi2Se3/MoSe2 SLs for direct comparison. We find that in the same after MoSe2 film growth (Figure S2). The XPS Bi2Se3 films, both IA11g/IA21g and IE1g/IE2g ratios decrease spectra of pristine graphene and graphene/PdSe2 hetero- with decreasing thickness of less than 3 nm, in agreement with structures are shown in Figure S3. a previous study.26 In the SLs, the ratios IA11g/IA21g and IE1g/ Next, we systematically study the phonon properties of IE2g are similar to those calculated in Bi2Se3 films and remain Bi2Se3 films, Bi2Se3/MoSe2 SLs, and graphene/PdSe2 hetero- almost constant with decreasing period. structures, using low-frequency Raman spectroscopy. Figure 2a In graphene/PdSe2 heterostructures, we detected 6 main shows the Raman spectra of Bi2Se3 films of varying thickness, peaks in the high-frequency region (>130 cm−1) that belong to where all of the out- and in-plane Raman active optical modes A1g, B11g, A2g, B21g, A3g, and B31g phonon modes of PdSe2 (Figure 6885 https://doi.org/10.1021/acs.nanolett.3c01280 Nano Lett. 2023, 23, 6883−6891 Nano Letters pubs.acs.org/NanoLett Letter Figure 3. Thermal conductivity and interfacial heat transport measurements. (a) Schematic illustrations of the FDTR technique and the multilayer system of the SLs. (b) Typical FDTR data measured in bilayer MoSe2 (green circles) and Bi2Se3/MoSe2 SLs with periods n = 2, 2.5, and 3 and the corresponding best model fits in the entire frequency range (20 kHz to 45 MHz). (c) Cross-plane thermal conductivity versus film thickness measured in bilayer MoSe2 (green solid rhomb), Bi2Se3/MoSe2 SLs (black circles), graphene/PdSe2 heterostructures (red squares), and Bi2Se3 films on STO (purple circles) and sapphire (pink squares) substrates. The blue triangles show previously reported kz values measured in thicker Bi2Se3 films.20 By extrapolating the kz trends, we find the minimum film thickness from which phonon-interface scattering starts to have a strong impact on cross-plane heat dissipation, i.e., kz(SLs)< kz(Bi2Se3) < kz(MoSe2). (d) Total thermal resistance, Rtot = Rint + Rfilm, of the Bi2Se3/MoSe2 SLs (black solid circles) and graphene/PdSe2 heterostructures (red squares) versus film thickness. The uncertainty of the estimated Rtot was calculated on the basis of the error propagation for the input parameters. Total thermal resistance measurements in Au/graphene/SiO249 (purple open triangles) and Al/graphene-MoS2 (SLs)/SiO28 (green open rhombs) are included for comparison. The colored lines in parts c and d are guides for the eye. 2d). These modes can be attributed to the intralayer vibrations Thermal measurements were performed using a custom- of PdSe2. The Raman peak positions of all phonon modes built FDTR setup, which combines simultaneous measure- showed a red shift with increasing the number of layers, in ments of cross-plane thermal conductivity (kz) and interface agreement with previous CVD grown PdSe2 films.29,30 thermal conductance.34,35 For the case of SLs, our multilayer Interestingly, the intralayer vibration at 149.1 cm−1, originating structures consist of Au (transducer)/SLs/substrate stacks from the intralayer Se−Se bonds, exhibits sufficiently strong (Figure 3a). The effective kz and the interface thermal Raman intensity in 3, 5, and 7L PdSe2, indicating its strong resistances between Au/SLs (R1) and SLs/substrate (R2) coupling to the electronic states.29 Furthermore, we observe were obtained for each SL following a multilayer three- dimensional heat diffusion model.36 Material properties Raman-inactive modes in the frequency region between 50− required for the model were the thickness (t), the volumetric 130 cm−1, which are activated due to the breakdown of heat capacity (C), R1, R2, and kz. The kz and C of Au as well as translation symmetry in few layers, as has been recently the volumetric specific heat of Bi2Se3 and MoSe2 were taken shown.30,31 The phonon modes detected in the frequency from the literature.37,38 To estimate the unknown parameters region between 100 and 300 cm−1 are also consistent with the (kz, R1, and R2), first we quantified the sensitivity of the ones found in exfoliated graphene/PdSe2 heterostructures.32 recorded phase signal to different parameters (Figure S4) using Finally, the two Raman peaks, SiC1 and SiC2 at 196.6 and our previously reported methodology.34,35 204.3 cm−1, respectively, originated from the undoped SiC Examples of the recorded phase signal and the correspond- substrate.33 We note that the mode A2g is not very visible, ing best model fits are shown in Figure 3b. To extract the kz of because it partially overlaps with the SiC2 mode. each SL from a single measurement, we followed the same 6886 https://doi.org/10.1021/acs.nanolett.3c01280 Nano Lett. 2023, 23, 6883−6891 Nano Letters pubs.acs.org/NanoLett Letter approach that used in previous works,34−36,39 and supported by phonons are diffusely scattered at interfaces, thus losing their the sensitivity analysis. First, we extract kz by fitting the coherency.43 experimental data in a low frequency range (20 kHz to 1 To understand whether coherent or incoherent thermal MHz), where the sensitivity to R1, R2, and C is negligible. transport occurs, we quantify the impact of cross-plane ballistic Then, we fix kz and fit the high frequency range (1−45 MHz) phonon transport on the total thermal resistance in our to estimate R1 and R2. The same procedure was followed to epitaxial films. Specifically, we estimate the total thermal extract kz, R1, and R2 for all films. The sensitivity analysis and resistance per unit area, Rtot, which can be written as the sum FDTR data for the case of graphene/PdSe2 are shown in of the combined interface thermal resistance, Rint = R1 + R2, Figures S5 and S6, respectively. In Figure S9, we also show all and volumetric cross-plane thermal resistance, Rfilm = t/kz.34,44 the interface thermal resistance values, Rint = R1 + R2, where R1 From these calculations, we found that in the SLs Rtot is = 1/G12 and R2 = 1/G23 extracted by the FDTR experiments linearly proportional to the total thickness (or number of and compare them with previous reports. periods, n), such that Rtot, n=3 > Rtot, n=2,5 > Rtot, n=2 > Rtot, n=1,5> In SLs, we found that kz slightly increases with increasing Rtot, n=1 (Figure 3d). Furthermore, we observe that Rint thickness with values between 0.059−0.07 W/mK (Figure 3c). increases with increasing thickness (Figure S9), in agreement However, in graphene/PdSe2 heterostructures, we found a with previous thermal resistance measurements in short-period strong thickness-dependent kz. Specifically, the kz increased by SLs.8,40 We note that the large lattice-mismatch between Bi2Se3 a factor of 6 with increasing thickness of the PdSe2 from one to and MoSe2 (∼20%) most likely enhances the phonon-interface seven layers. To confirm the robustness of our approach to scattering and further contributes to the increased values of measuring the intrinsic kz of thin films, we performed FDTR Rtot. This is in agreement with previous studies that showed measurements in Bi2Se3 films of different thicknesses on both that lattice-mismatched interfaces exhibit reduced interface STO and sapphire substrates. We found that the kz increases thermal conductance and phonon transmission due to the by a factor of 5 with increasing thickness from 1 to 20 QL. The increased lattice disorder.45,46 excellent agreement in kz values is shown in Figure 3c. However, in graphene/PdSe2 heterostructures, Rtot remains The weak thickness dependence of kz in SLs can be constant with increasing the thickness of PdSe2 from 1 to 7 understood considering both interface-phonon scattering and layers. In fact, the different slopes in Figure 3d suggest different size effects. Considering diffusive thermal transport, it is likely thermal transport regimes. The similar values of Rtot in that short-wavelength thermal phonons are scattered by graphene/PdSe2 indicate strong ballistic thermal transport multiple Bi2Se3−MoSe2 interfaces with increasing film thick- taking into account the variations of both Rint (see Figure S9) ness, thus reducing their contribution to cross-plane thermal and Rfilm with thickness as we show later on. We note that transport. However, as the volume fraction of the SLs cross-plane ballistic transport in graphene/PdSe2 is favorable constituents increases, more long-wavelength phonons are since SiC/graphene interfaces exhibit excellent interfacial allowed to propagate and contribute to kz until they are coupling and superior cross-plane thermal conductance,47,48 scattered at the sample boundaries. These opposite effects which reduce interfacial phonon scattering. Similarly, cross- resulted in the suppressed thickness-dependent kz trend plane ballistic or quasi-ballistic thermal transport has been presented in Figure 3c. Therefore, despite the influence of phonon-interface scattering on kz, the increase of kz with found in graphene,49 MoS2,44 and PtSe234 thin films. However, increasing thickness in SLs indicates that in this thickness the increased values of Rtot with increasing thickness observed range, finite size effects are still dominant. This is in agreement in SLs indicate additional phonon scattering (diffusive regime). with previous studies that showed that the transmission of We attribute this result to the scattering of high-frequency phonons across short-period AlN/GaN40 and SiGe41,42 SLs phonons (>58 THz − Debye frequency of Bi2Se3) at multiple strongly depends on the phonon wavelength, suggesting that Bi2Se3/MoSe2 interfaces i.e., lattice mismatch destroys the long-wavelength phonons are the dominant carriers of heat. coherence of high-frequency phonons. Note that the relatively Molecular dynamics simulations have also shown that the kz of high Debye temperature ratio between Bi2Se3 and MoSe2 (see SLs with lattice-mismatched interfaces increases monotonically calculations in Figure S13a,b) further suggests the formation of with period length.43 high-interface thermal resistance heterointerfaces. However, the absence or limited mismatched interfaces in To further support the previous analysis and exclude the top pure Bi2Se3 and graphene/PdSe2 allow the majority of the and bottom interfacial contributions to Rtot, we plot the thermally excited phonons to contribute to cross-plane thermal variations of the volumetric thermal resistance component transport; i.e., kz is limited mainly by finite size effects. This is versus thickness (see Figure S12). In the SLs, we observe that reflected in the different rates of the kz increase observed in Rfilm is increasing by more than a factor of 2 as the thickness Figure 3c. In particular, for the same thickness range, in increases from 1.4 to 7.2 nm, which suggests phonon diffusive Bi2Se3/MoSe2 SLs we found only a 28% increase in kz with scattering at interfaces. Notably, in ultrathin graphene/PdSe2 increasing thickness, while in Bi2Se3 and graphene/PdSe2 films, stacks, we observe that Rfilm remains almost constant ∼54 m2 it was about 42% and 68%, respectively. We note that to study K/GW with thickness, i.e., ballistic phonon transport. The coherent and incoherent effects in SLs, the volume fraction of similar thermal resistance trends observed in Figure 3d and the constituents and total thickness of the films should remain Figure S12 confirmed the distinct nature of cross-plane heat constant while the thickness of each layer in a period must be transport between graphene/PdSe2 and Bi2Se3/MoSe2 SLs. adjusted to vary the interface density.16 Therefore, in our SLs, Similarly, Sood et al. using density functional theory (DFT) the apparent linear scale of kz versus period is not sufficient to calculations have estimated a ballistic resistance of 10 m2 K/ conclude if phonons propagate coherently across the film GW in MoS2 films in the limit of 2−3 monolayers.44 The thickness. For instance, previous calculations showed that significant contribution of the Rfilm component to the Rtot in all despite the linear kz increase with thickness, the lattice- the epitaxial films suggests that interfacial effects do not mismatch destroys the Bragg reflection conditions and entirely govern cross-plane thermal transport. 6887 https://doi.org/10.1021/acs.nanolett.3c01280 Nano Lett. 2023, 23, 6883−6891 Nano Letters pubs.acs.org/NanoLett Letter Figure 4. Tight-binding phonon calculations. (a) Schematic structure of a Bi2Se3/MoSe2 vdW heterostructure between electrodes. The calculated cross-plane thermal conductivity of (b) Bi2Se3, (c) bilayer MoSe2, and (d) Bi2Se3/MoSe2 heterostructures of different thicknesses as a function of temperature (0−400 K) considering weak and strong coupling of the vdW films with the electrodes. (e) The calculated room temperature cross- plane thermal conductivity as a function of thickness for MoSe2, Bi2Se3, and Bi2Se3/MoSe2 heterostructures with weak (solid star symbols) and strong (open star symbols) coupling with the electrodes. The experimental kz values for MoSe2, Bi2Se3, and Bi2Se3/MoSe2 are shown with green, purple, and black solid circles in (e) for direct comparison with the calculations. The difference in the calculated values indicated in blue and red shaded areas in (e) show the importance of quantifying interfacial thermal transport in vdW films bonded to a substrate. To gain further insight into the influence of phonon- to large or small interface resistance, respectively, they are interface scattering on cross-plane thermal conductance, we closely related. For example, when the coupling to the developed a tight-binding model50 and calculated the trans- electrode is weakened, the width of the phonon transport mission coefficients of phonons with different frequencies resonances decreases, leading to lower thermal conductance. traversing through MoSe2, Bi2Se3, and Bi2Se3/MoSe2 hetero- Figure 4b−d shows the calculated kz of different thickness structures from one metallic electrode to the other (Figure 4a). Bi2Se3, MoSe2, and Bi2Se3/MoSe2 heterostructures as a The DFT calculations indicate that the Debye frequencies of function of temperature. The kz increases with increasing MoSe2 and Bi2Se3 are 5.8 THz and 11.6 THz, respectively.51,52 temperature and starts to saturate at higher temperatures. We adjusted the parameters of our tight-binding model to Specifically, in films with strong coupling to electrodes, the obtain similar Debye frequencies for both materials and took width of the phonon transmission resonances increases, into account the lattice-mismatch between the heterostructure leading to faster increase in the thermal conductivity with layers by selecting different coupling strengths and config- temperature. Figure 4e shows the room temperature kz as a urations between MoSe2 and Bi2Se3 (see SI Section 4 and function of film thickness, which is in good qualitative Figure S13). agreement with the experimental data when we consider In these calculations, the Bi2Se3/MoSe2 heterostructures, which are considered new crystals, show modified phonon strong coupling between films and electrodes (blue-shaded dispersions and vibrational properties. The large mismatch and area). Specifically, the kz trends follow a similar order to that in weak phonon coupling between the Bi2Se3 and MoSe2 layers the experiment, and unlike Bi2Se3, the kz in the SLs varies lead to localized phonon modes and suppressed thermal slowly with thickness. When we consider a weak coupling to conductance. Classically this can be effectively regarded as the electrodes, the calculated absolute kz values are in much strong suppression of phonon transport at the interfaces, as we better quantitative agreement with the experiments (red- discussed above. To account for the effect of contact resistance shaded area). This suggests that Rint is increased when the films to electrodes on the overall thermal conductance, we are weakly coupled with the top and bottom electrodes, considered two scenarios with weak and strong couplings to confirming the relatively high Rint values obtained from FDTR electrodes. We note that although weak and strong coupling to experiments (Figure S9). These results highlight the role of electrodes in our nonequilibrium Green’s function (NEGF)- thermal contact resistance in cross-plane thermal conductivity based phonon transport calculations are not directly equivalent of ultrathin layered materials. 6888 https://doi.org/10.1021/acs.nanolett.3c01280 Nano Lett. 2023, 23, 6883−6891 Nano Letters pubs.acs.org/NanoLett Letter In summary, we have successfully developed highly Authors insulating thermal metamaterials based on ultrathin epitaxial Emigdio Chavez-Angel − Catalan Institute of Nanoscience vdW films comprising of dissimilar atomically thin layers of 2D and Nanotechnology (ICN2), Barcelona 08193, Spain; semiconductors (MoSe2 and PdSe2), the 3D topological orcid.org/0000-0002-9783-0806 insulator Bi2Se3 and monolayer graphene. The following Polychronis Tsipas − Institute of Nanoscience and phonon engineering approach was based on creating vertical Nanotechnology, National Center for Scientific Research vdW SLs consisting of atomic layers with large acoustic and “Demokritos”, Athens 15341, Greece; orcid.org/0000- structural lattice mismatch. In particular, short period Bi2Se3/ 0001-9064-9601 MoSe2 superlattices can be used to achieve a superior thermal Peng Xiao − Catalan Institute of Nanoscience and resistance up to 202 m2K/GW and ultralow cross-plane Nanotechnology (ICN2), Barcelona 08193, Spain; thermal conductivity down to 0.059 W/mK. We attribute this orcid.org/0000-0002-4711-2566 result to the large lattice mismatch between the constituent Mohammad Taghi Ahmadi − School of Engineering, layers of the superlattices that boosts phonon-interface University of Warwick, Coventry CV4 7AL, United Kingdom scattering and suppress cross-plane heat dissipation. Con- Abdalghani H. S. Daaoub − School of Engineering, University versely, graphene/PdSe2 heterostructures exhibit a strong of Warwick, Coventry CV4 7AL, United Kingdom thickness-dependent kz and a constant total thermal resistance Hatef Sadeghi − School of Engineering, University of Warwick, of 70 m2K/GW (ballistic transport), mainly due to the Coventry CV4 7AL, United Kingdom; orcid.org/0000- excellent interfacial thermal coupling between graphene-SiC 0001-5398-8620 interfaces. Given the sub-3 nm thickness of these hetero- Clivia M. Sotomayor Torres − Catalan Institute of structures, their kz at room temperature are estimated between Nanoscience and Nanotechnology (ICN2), Barcelona 08193, 0.012 and 0.06 W/mK. Our tight-binding calculations align Spain; ICREA, Barcelona 08010, Spain; orcid.org/0000- well with the experimental results and further uncover the 0001-9986-2716 impact of interfacial thermal resistances between ultrathin Athanasios Dimoulas − Institute of Nanoscience and heterointerfaces and top and bottom metallic contacts on Nanotechnology, National Center for Scientific Research cross-plane thermal transport. “Demokritos”, Athens 15341, Greece; orcid.org/0000- Importantly, this work has yielded significant advancements 0003-3199-1356 in the epitaxial growth of high-quality heterogeneous interfaces Complete contact information is available at: over large areas as well as in the quantitative understanding of https://pubs.acs.org/10.1021/acs.nanolett.3c01280 interfacial thermal transport across atomically thin vdW films on various substrates. The implications of these findings are Author Contributions extensive for the design of heat-sensitive electronic compo- A.E. conceived and supervised the research work. P.T. and nents and 2D electronic devices, such as 2D transistors and A.D. fabricated the MBE samples, performed the XPS microchips, that can operate without thermal limitations, e.g., measurements, and provided inputs in the structural analysis. overheating. The ability to obstruct heat dissipation in the A.E., E.C.-A., and P.X. performed the Raman and TEM vertical direction while maintaining in-plane crystallinity in measurements and analysis. A.E. and E.C.-A. built the FDTR wafer-scale engineered vdW stacks not only facilitates thermal setup and performed the thermal measurements and data management applications but also enhances their suitability as analysis. M.T.A., A.D., and H.S. performed the thermal active materials in thermoelectric devices. Combining with conductance calculations and provided support to the bandgap engineering strategies and careful selection of theoretical analysis. All authors reviewed and edited the materials with compatible thermal expansion coefficients to manuscript and have given approval to the final version of the avoid strain, the followed phonon engineering approach could manuscript. The manuscript was written by A.E. with inputs provide a promising route to realize a wide variety of functional from E.C.-A., P.T., H.S., and C.M.S.T. semiconductor heterojunctions and superlattices for nanoscale electronic and thermoelectric devices. Notes The authors declare no competing financial interest. ■ * ASSOCIATED CONTENT sı Supporting Information ■ ACKNOWLEDGMENTS A.E. acknowledges funding from the EU-H2020 research and The Supporting Information is available free of charge at innovation program under the Marie Sklodowska Curie https://pubs.acs.org/doi/10.1021/acs.nanolett.3c01280. Individual Fellowship THERMIC (Grant No. 101029727). RHEED patterns; XPS spectra; FDTR sensitivity H.S. acknowledges the UKRI for Future Leaders Fellowship analysis; FDTR experimental data; Raman experimental numbers MR/S015329/2 and MR/X015181/1. E.C.A. and data; tight-binding phonon calculations; experimental C.M.S.T. acknowledge support from the project LEIT funded and computational methods (PDF) by the European Research Council, H2020 Grant Agreement No. 885689. ICN2 is supported by the Severo Ochoa program ■ AUTHOR INFORMATION Corresponding Author from the Spanish Research Agency (AEI, grant no. SEV-2017- 0706) and by the CERCA Programme/Generalitat de Catalunya. The authors acknowledge Prof. Aaron Schmidt Alexandros El Sachat − Catalan Institute of Nanoscience and for sharing the numerical code for the FDTR analysis. 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