SCIENCE ADVANCES | RESEARCH ARTICLE
MATERIALS SCIENCE

Ultrahigh thermal isolation across heterogeneously
layered two-dimensional materials
Sam Vaziri1*, Eilam Yalon1*†, Miguel Muñoz Rojo1‡, Saurabh V. Suryavanshi1, Huairuo Zhang2,3,Connor J. McClellan1, Connor S. Bailey1, Kirby K. H. Smithe1, Alexander J. Gabourie1,
Victoria Chen1, Sanchit Deshmukh1, Leonid Bendersky3, Albert V. Davydov3, Eric Pop1,4,5§

INTRODUCTION

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 carriersfor 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 inheat management applications (4–6). This discrepancy is due to theshort 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 atnearly atomic-scale dimensions. The bosonic nature of phonons,
which cannot be voltage-gated like the charge carriers, also makes itchallenging to actively control heat transport in solids.
Previous efforts to manipulate thermal properties of solids reliedon nanolaminate films (9) and superlattices (10, 11) to reduce thermal
conductivity below that of the constituent materials. These wereachieved 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., 12C diamond (14) or graphene (15), andin the cubic boron arsenide compound through reduced phonon
scattering (16).
1

Department of Electrical Engineering, Stanford University, Stanford, CA 94305,
USA. 2Theiss Research Inc., La Jolla, CA 92037, USA. 3Materials Science and Engineering
Division, National Institute of Standards and Technology (NIST), Gaithersburg,
MA 20899, USA. 4Department of Materials Science and Engineering, Stanford
University, Stanford, CA 94305, USA. 5Precourt Institute for Energy, Stanford University,
Stanford, CA 94305, USA.
*These authors contributed equally to this work.
†Present address: Department of Electrical Engineering, Technion-Israel Instituteof Technology, Haifa 32000, Israel.
‡Present address: Department of Thermal and Fluid Engineering, University ofTwente, 7500 AE Enschede, Netherlands.
§Corresponding author. Email: epop@stanford.edu
Vaziri et al., Sci. Adv. 2019; 5 : eaax1325

16 August 2019

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 SiO2 across sub–2-nm-thin vdW heterostructures with clean, residue-free interfaces.
We also demonstrate the ability of tailoring thermal properties atatomic-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 newphononic 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.
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 MoSe2, MoS2,
and WSe2, all on a SiO2/Si substrate. The Raman laser illustrated
is used for simultaneously probing the individual layers in thestack, with single-layer accuracy. All 2D materials are monolayers,
separately grown by chemical vapor deposition (CVD) (20) andtransferred while avoiding polymer and other residues. (Details areprovided 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.
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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 ofheat 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, MoS2, and WSe2 with thermal resistance greater than 100 times
thicker SiO2 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.

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Figure 1B shows the Raman spectrum of such a Gr/MoSe2/
MoS2/WSe2 heterostructure on SiO2/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 uniquestrength 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 annulardark-field STEM (ADF-STEM) images of our Gr/MoSe2/MoS2/WSe2(Fig. 1C) and Gr/MoS2/WSe2 (Fig. 1, D to F) heterostructures with different lattice orientation alignments. Multiple STEM images reveal
atomically intimate vdW gaps without contaminants, allowing us toobserve the total thickness of these heterostructures, e.g., just below
2 nm for a three-layer stack (also see fig. S2). The interlayer coupling isfurther confirmed over larger areas by PL spectroscopy (Fig. 1G). The
PL signal of individual layers in the heterostructure is substantiallyquenched (over one order of magnitude) compared to isolated monolayers on the same substrate. This PL quenching is attributed to aninterlayer 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
Vaziri et al., Sci. Adv. 2019; 5 : eaax1325

16 August 2019devices (see Materials and Methods). The top graphene layer is contacted by Pd electrodes and used as a nearly transparent Joule heaterfor 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 characteristicsof three devices, one with only graphene and two with stacks of Gr/
WSe2 and Gr/MoSe2/WSe2. 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 inthe top graphene layer, its electrical conductivity being orders ofmagnitude higher than MoS2 and WSe2 (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 VDS, revealing smooth and linear
potential distributions. Figure 2E shows an SThM map of the electrically heated Gr/MoS2/WSe2 channel, displaying uniform surface
heating with high spatial resolution (see section S4).
Thermometry of the vdW heterostructures
While SThM confirms the surface temperature uniformity of ourdevices, we used Raman spectroscopy to quantify the temperatureof each individual layer. The spectral separation of key Raman
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Fig. 1. Optical and STEM characterization of vdW heterostructures. (A) Cross-section schematic of Gr/MoSe2/MoS2/WSe2 sandwich on SiO2/Si substrate, with theincident 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 inthe stack are obtained simultaneously. The graphene Raman spectrum is flattened to exclude the MoS2 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 SiO2. In (D), MoSe2 and WSe2 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 MoS2, monolayer WSe2, and a Gr/MoS2/WSe2 heterostructure after annealing. The PL
is strongly quenched in the heterostructure due to intimate interlayer coupling.

SCIENCE ADVANCES | RESEARCH ARTICLE
CA6VDS = 50 mV

B

ID (µA/µm)

5

Drain

5 µm

1

SourceKPM
VDS = 0

Pd

3

Pd

2

Pd

170
mV

Drain

Gr/MoS2/WSe2
SiO2
2 µm

2

4

6
x (µm)

810

50
VG (V)

10

15

E
Pd

Gr//MoS2/WSe2

0

ID
Pd

100 mV
80
60
40
20

0
0

–5

Pd

Source1Pd–15 –10

12

Pd
SThM at P = 2.61 ± 0.06 mW

0Fig. 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 SiO2. (C) Measured transfer characteristics of three test structure stacks, Gr/MoS2/WSe2, Gr/WSe2, 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/MoS2/WSe2 heterostructure device. The graph displays thesurface 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/MoS2/WSe2 heterostructure, here capped with 15-nm Al2O3, revealing homogeneous heating across thechannel. This confirms the uniformity of the thermal interlayer coupling in the stacks. The device dimensions are the same as in the (D) inset.

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 W to avoid
optical heating. (All devices have an area of ~40 m2, and the laser
spot size is ~0.5 m2.) Raman peak shifts during electrical heating
are converted to temperature rise using the calibration coefficient ofeach material in the heterostructure (see section S7).
Figure 3A shows the measured temperature rise (T) of eachlayer, including the Si substrate, as the graphene heater power (P) isramped up, in a Gr/MoS2/WSe2 heterostructure. The slopes ofthe linear fits for each material indicate the thermal resistanceRth = T/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
SiO2 thickness and the lateral thermal healing length, which is ~0.1 m(23). Rth,Si ≈ (WL)1/2/(2kSi) is the thermal spreading resistance into theSi substrate, yielding kSi ≈ 90 W m−1 K−1, which is the expected thermal
Vaziri et al., Sci. Adv. 2019; 5 : eaax1325

16 August 2019conductivity of the highly doped substrate (23). The difference between
Rth,WSe2 and Rth,Si is the sum of the well-known thermal resistance of
100 nm SiO2 (24) and the thermal boundary resistance (TBR) of theWSe2/SiO2 interface. [The TBR of the SiO2/Si interface is negligible
in comparison (25).] Then, Rth,MoS2 − Rth,WSe2 = TBRMoS2/WSe2 andRth,Gr − Rth,MoS2 = TBRGr/MoS2. Thus, from Fig. 3A, we can extract TBR
values for each of the WSe2/SiO2, MoS2/WSe2, and Gr/MoS2 interfaces.
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 SiO2 display an effective thermal resistance (normalized byarea) 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 SiO2. Given the sub–2-nm thickness of these heterostructures (Fig. 1, D to F), they have an effective thermal conductivityof 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.
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VDS (V)D 4

3
2

VoltageprobesChannel4

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Fig. 4. Summary of TBC trends. (A) Schematic of all TBCs measured (in MW m−2 K−1) across heterostructures consisting of, clockwise from top left, graphene (Gr), Gr/
MoS2, Gr/WSe2, and Gr/MoS2/WSe2, all on SiO2/Si substrates. (B) Measured TBC values of 2D/2D and 2D/3D (with SiO2) interfaces (red diamonds, left axis) and the calculated product of phonon density of states (PDOS), phonon transmission, and df/dT (blue circles, right axis). Calculated values are normalized to the minimum achieved for
Gr/WSe2 (see table S2). The dashed line between the simulation symbols is a guide to the eye. Lower TBC is noted at interfaces between 2D/2D materials and those between materials with larger mismatch in mass density. Three devices were measured for each structure, at two or more distinct positions of the Raman laser. No significant
TBC variation is seen between samples with different layer (mis)alignment, within the experimental uncertainty. All values are at room temperature.

Understanding the high thermal resistance
We return to the analysis of TBR between layers, ultimately responsible for the very large thermal resistance perpendicular to the heterostructures. Figure 4A summarizes the four measured structures andthe thermal boundary conductance (TBC = 1/TBR) of their interfaces. Three devices were measured at multiple positions for eachstructure, yielding consistent results. The individual 2D layers within the devices were not rotationally aligned, and no significant TBC
variation was seen between the different samples within the experimental uncertainty.
These are the first TBC measurements for atomically intimate
interfaces between individual monolayers (2D/2D) and the firstreport of TBC between monolayer WSe2 and SiO2. [Previous TBCs
between 2D materials had been reported for graphene and MoS2 on
thicker hexagonal boron nitride (h-BN) (26–28).] Recurring interfaces in different heterostructures (i.e., Gr/MoS2 and WSe2/SiO2)
exhibit similar TBC, confirming the quality of the interfaces and the
reproducibility of the measurements. The TBCs for Gr/SiO2 andMoS2/SiO2 interfaces are in agreement with previous studies (23, 24, 29).
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The TBC of the monolayer WSe2/SiO2 interface is lower than for
few-layer WSe2/SiO2 (30), which is not unexpected, because the monolayer has fewer flexural phonon modes available for transmission (31).
In general, we find that 2D/2D interface TBC is lower than 2Dinterface TBC with the three-dimensional (3D) SiO 2 substrate(Fig. 4B). In addition, the lowest TBC recorded belongs to Gr/WSe2,
the 2D/2D interface with the largest areal mass density mismatch.
We explain these trends using Landauer’s formalism (see section S9for details), wherein the TBC across the interface is proportional tothe product of the phonon density of states (PDOS) overlap, thetransmission coefficient, and df/dT, where f is Bose-Einstein distribution. Here, we consider the PDOS for flexural out-of-plane (ZA)
phonons, which have been shown to dominate cross-plane heat conduction in 2D materials (32). For the SiO2 substrate, we consider the
typical longitudinal acoustic (LA) and transverse acoustic (TA) phonon branches.
The phonon transmission at the interface is obtained from theacoustic mismatch model (AMM) as the ratio of mass density of the twomaterials (33). The AMM is a good approximation because the4 of 7

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Fig. 3. Thermal resistance of the heterostructures. (A) Measured temperature rise T versus electrical input power for each individual layer in a Gr/MoS2/WSe2 heterostructure, including the Si substrate, shown in the inset. Graphene (pink circles), MoS2 (blue diamonds), WSe2 (red triangles), and Si (black squares). All measurements arecarried out at VG < 0 (see section S6). The slopes of the linear fits (dashed lines) represent the thermal resistance Rth between each layer and the heat sink. (B) Comparisonof total thermal resistances (i.e., of the top graphene layer) measured by Raman thermometry and SThM for different vdW heterostructures. The Rth values obtained fromthese two techniques match within the uncertainty of the measurements. All devices have the same active area of ~40 m2.

SCIENCE ADVANCES | RESEARCH ARTICLE
vdW interfaces are nearly perfect, with any surface asperities (e.g.,
few dangling bonds) being much smaller than the phonon wavelengths. As shown in Fig. 4B, the TBC trends are captured by oursimple model of heat flow across the interfaces (additional details
are provided in the Supplementary Materials). These results also
support the dominant role of ZA phonons for cross-plane heattransport in 2D material vdW heterostructures. Thus, higher (or lower)interfacial heat transmission of 2D materials could be obtained by
maximizing (or minimizing) the PDOS overlap and reducing (orincreasing) the areal mass density mismatch.
CONCLUSIONS

MATERIALS AND METHODS

2D layer growth
Monolayer graphene was grown on Cu foil (99.8%, Alfa Aesar) using an Aixtron Black Magic Pro 4-inch CVD system. Before growth,
the Cu surface oxide was selectively etched in HCl–deionized water(DIW) (1:2) solution for 10 min. Then, the Cu foil was annealed at
1050°C in Ar/H2 flow for 30 min. The growth was done at 1050°C
under a flow rate of 10 standard cubic centimeters per minute (sccm)
CH4 and 30 sccm H2 for 15 min. Monolayer MoS2, MoSe2, and WSe2
were CVD-grown directly on SiO2/p+-Si (1 to 5 mΩ·cm) substrates
at 800° to 900°C using S or Se solid sources with solid MoO3 or WO3
in a 2-inch tube furnace (20) under a flow rate of 10 sccm Ar for
MoS2 and 25/5 sccm Ar/H2 for the selenides. To promote thegrowth, perylene-3,4,9,10-tetracarboxylic acid tetrapotassium salt
(PTAS) was used as a seed for the lateral epitaxial growth.
Fabrication
The multiple transfer process was done using a bilayer polymer
stack of poly(methyl methacrylate) (PMMA) (950,000, 2.5% massin chlorobenzene) and polystyrene (PS). PMMA was spin-coatedon graphene (on Cu substrate) at 3500 rpm for 1 min followed bybaking on a hot plate at 150°C for 45 s. Then, PS was spin-coated at
3000 rpm for 1 min followed by baking on a hot plate at 85°C for
5 min. The Cu substrate was etched in FeCl3, and then the polymer/
graphene stack was rinsed using diluted HCl and DIW. Subsequently,
the polymer/graphene stack was transferred, for instance, onto MoS2
on SiO2 substrate followed by baking at 60°, 90°, and 135°C for 30,
15, and 1 min, respectively. (We have found this gradual baking to
remove bubble formation.) The polymer-supporting layer was reVaziri et al., Sci. Adv. 2019; 5 : eaax1325

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TEM sample preparation
FEI Nova NanoLab 600 dual-beam scanning electron microscopy(SEM) and focused ion beam (FIB) system were used to preparecross-sectional TEM samples. A 1-m-thick carbon layer was initiallydeposited (by electron beam–induced deposition) on top of the device to protect the sample surface, followed by 2-m ion beam–
induced Pt deposition. To reduce Ga ions damage, in the final stepof FIB preparation, the TEM samples were thinned with 2-kV Ga
ions using a low beam current of 29 pA and a small incident angleof 3°. The surface damage of the samples was further reduced using
a precision ion polishing system (Gatan PIPS II) with 0.1-kV Ar ions.
STEM characterization
An FEI Titan 80-300 STEM/TEM equipped with a monochromatorand a probe spherical aberration corrector was used to acquire
atomic-resolution STEM images. Atomic-resolution ADF-STEM images were acquired with an operating voltage of 300 kV, a probe convergence angle of 24 mrad, and a collection angle of 34 to 195 mrad.
Scanning probe characterization
SThM and KPM were performed using an MFP-3D infinity atomic
force microscope (AFM) from Asylum Research with an added
thermal module from Anasys Instruments. The SThM used a thermo­
resistor probe from Anasys Instruments, which consists of a thin Pd
line on SiN. We used the probes in contact mode to sense the temperature at the surface of the heterostructures. The KPM was carriedout with a metal-coated tip from Asylum Research in noncontact
mode using amplitude modulation detection. In both SThM and KPM,
the graphene top layer was electrically contacted using the AFM probestation from Asylum Research and a Keithley 4200 instrument.
Raman and PL measurements
Raman and PL spectroscopy were carried out using a Horiba LabRAM
instrument with a 532-nm laser and 100× long working distanceobjective with a numerical aperture (NA) of 0.6. Step sizes in the
Raman maps varied between 0.4 and 0.6 m, and the acquisition
time of each device thermal map was ~20 to 30 min. The laser spot
radius was ~0.4 m, and the absorbed laser power was <5 W to
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The knowledge gained in this study will enable the realization of
atomically tailored thermal interfaces, in a manner similar to how
energy band (mis)alignments are tailored for modulation doping (1)and optoelectronic devices (2). We have demonstrated the ability toengineer extremely insulating thermal metamaterials, with properties
not otherwise available in nature, and to measure their temperature
with atomic layer precision. These heterostructures are an example
in the emerging field of phononics, manipulating the thermal properties of solids at length scales comparable to the phonon wavelengths.
Such layered 2D materials are promising as ultralight and compact
heat shields, e.g., directing heat away from hot spots in electronics.
They could also be used to improve the efficiency of thermoelectricenergy harvesters (5) or that of thermally activated devices like phase-­change memories (34), if the cross-plane electrical conductivity canbe simultaneously optimized.

moved in toluene before repeating the same procedure to transfer
the graphene/MoS2 stack onto the next substrate, etc. The transition
metal dichalcogenide (TMD) monolayers were delaminated fromthe SiO2 growth substrate in 1 M NaOH solution. After formationof the target vdW heterostructures, the samples were annealed at
275°C in vacuum to remove residual water between the layers andpromote interlayer coupling (22).
The heterostructure channels were defined using electron beamlithography and O2 plasma reactive ion etching. Subsequently, photolithography and liftoff were applied to make 50-nm Pd metal contacts
to the top graphene channel. Then, a similar process was repeatedto fabricate Ti/Au (5 nm/65 nm) electrical measurement pads. Last,
the devices were capped with 15-nm atomic layer deposition of Al2O3,
which induces n-type doping and protects the graphene channel fromthe ambient. All devices had a four-probe structure with identicaldimensions of the channel length, L = 8 m, and width, W = 5 m.
The four-probe structure was used to accurately identify the electricalinput power density. Before Raman thermometry, electrical measurements were carried out in air and at room temperature using a
Keithley 4200 instrument.

SCIENCE ADVANCES | RESEARCH ARTICLE

SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/
content/full/5/8/eaax1325/DC1
Section S1. Multiple transfer technique
Section S2. Atomic-resolution ADF-STEM
Section S3. PL quenching in 2D heterostructures
Section S4. SThM thermal maps
Section S5. SThM temperature calibration
Section S6. Raman temperature maps
Section S7. Temperature-dependent Raman coefficients
Section S8. Non–temperature-related Raman peak shifts
Section S9. Thermal transport modeling and analysis
Fig. S1. Transfer process and optical images.
Fig. S2. Atomic-resolution ADF-STEM images.
Fig. S3. PL quenching.
Fig. S4. Uniform heating maps.
Fig. S5. SThM calibration by metal line heaters.
Fig. S6. Raman maps.
Fig. S7. Temperature-dependent Raman coefficients.
Fig. S8. Raman shift dependence on doping and electrical gating.
Fig. S9. PDOS overlap.
Table S1. Material parameters.
Table S2. TBC comparison.
References (35–55)

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avoid laser heating in excess of the electrical heating and to maintainnegligible photocurrent. The Raman spectra of the four-layer heterostructure of Gr/MoSe2/MoS2/WSe2 (Fig. 1B) showed peaks at 241.5
and 404.6 cm−1 corresponding to out-of-plane A1′ modes for MoSe2
and MoS2, respectively. The in-plane E′ modes for MoSe2 and MoS2
were represented by the peaks at 286.5 and 383.1 cm−1, respectively.
Monolayer WSe2 showed the characteristic degenerate peak at
249.4 cm−1, which included both A1′ and E′, while the 2LA peak was
at 259.3 cm−1. Furthermore, the G and G′ (sometimes called 2D)
peaks of monolayer graphene were at 1585.3 and 2690.5 cm−1, respectively. We used the graphene G peak and the TMD out-of-planemodes for thermometry because they were less sensitive to strain.
For temperature-dependent Raman shift calibration, we used aLinkam THMS600 stage and carefully differentiated effects of strain(e.g., during the calibration on hot stage) and shifts due to electricalbias (gating effect from the substrate), following the calibration procedure outlined in section S7. The obtained Raman temperaturemaps were uniform (see section S6), similar to the SThM measurements shown in section S4. The uniform heating in the channel
indicated that there was no measurable nonuniform doping or pinchoff, which simplified the extraction of interlayer TBC. Changes in
the measured current along the graphene channel during mapping
were smaller than 5%. All thermometry measurements were performed in ambient and at room temperature.

SCIENCE ADVANCES | RESEARCH ARTICLE

Vaziri et al., Sci. Adv. 2019; 5 : eaax1325

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Acknowledgments: We thank Z.-Y. Ong for fruitful discussions regarding the modeling.
Funding: Device fabrication and measurements were performed in part at the Stanford
Nanofabrication Facility (SNF) and the Stanford Nano Shared Facilities (SNSF), which received
funding from the National Science Foundation (NSF) as part of National Nanotechnology
Coordinated Infrastructure Award ECCS-1542152. This work was supported in part by ASCENT,
one of six centers in JUMP, a Semiconductor Research Corporation (SRC) program sponsored by
DARPA, in part by Air Force Office of Scientific Research (AFOSR) grant FA9550-14-1-0251, NSF
EFRI 2-DARE grant 1542883, and the Stanford SystemX Alliance. The Knut and Alice Wallenberg
Foundation partially supported S.V. through a postdoctoral fellowship. A.J.G. acknowledged
support from the NDSEG Fellowship. K.K.H.S. acknowledged partial support from the Stanford
Graduate Fellowship (SGF) program and NSF Graduate Research Fellowship under grant no.
DGE-114747. H.Z. acknowledged support from the U.S. Department of Commerce, NIST underaward 70NANB17H249. C.S.B. acknowledged support from the NSF Graduate Research
Fellowship. Certain commercial equipment, instruments, or materials are identified in thispaper to specify the experimental procedure adequately. Such identification is not intended
to imply recommendation or endorsement by the National Institute of Standards andTechnology (NIST), nor is it intended to imply that the materials or equipment identified arenecessarily the best available for the purpose. Author contributions: S.V., E.Y., and E.P
conceived the experiments and wrote the manuscript with input from all authors. C.S.B.,
K.K.H.S., and S.V. grew the TMDs and graphene. S.V. developed the transfer process and madethe heterostructures. S.V., C.J.M., and V.C. fabricated the devices. S.V. performed electrical and
PL characterizations. E.Y. and S.V. conducted Raman characterization and thermometry. E.Y.
analyzed the Raman data. M.M.R. performed AFM, KPM, and SThM. M.M.R., E.Y., and S.V.
analyzed the SThM results. S.D. and S.V. fabricated the SThM calibration samples. S.D., M.M.R.,
and E.Y. performed calibration analysis to extract conversion factors. S.V.S., A.J.G., and S.V.
developed the TBC model and performed the simulations, with input from E.P. H.Z. conducted
TEM sample FIB preparation and performed atomic-resolution STEM imaging, STEM EDS, and
EELS spectrum-imaging measurements. H.Z., L.B., and A.V.D. conducted the STEM data
analysis. Competing interests: The authors declare that they have no competing interests.
Data and materials availability: All data needed to evaluate the conclusions in the paper arepresent in the paper and/or the Supplementary Materials. Additional data related to this paper
may be requested from the authors.
Submitted 25 February 2019
Accepted 10 July 2019
Published 16 August 201910.1126/sciadv.aax1325
Citation: S. Vaziri, E. Yalon, M. Muñoz Rojo, S. V. Suryavanshi, H. Zhang, C. J. McClellan, C. S. Bailey,
K. K. H. Smithe, A. J. Gabourie, V. Chen, S. Deshmukh, L. Bendersky, A. V. Davydov, E. Pop, Ultrahighthermal isolation across heterogeneously layered two-dimensional materials. Sci. Adv. 5, eaax1325(2019).

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Ultrahigh thermal isolation across heterogeneously layered two-dimensional materials
Sam Vaziri, Eilam Yalon, Miguel Muñoz Rojo, Saurabh V. Suryavanshi, Huairuo Zhang, Connor J. McClellan, Connor S. Bailey,
Kirby K. H. Smithe, Alexander J. Gabourie, Victoria Chen, Sanchit Deshmukh, Leonid Bendersky, Albert V. Davydov and EricPop

Sci Adv 5 (8), eaax1325.
DOI: 10.1126/sciadv.aax1325

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Supplementary Materials for
Ultrahigh thermal isolation across heterogeneously layered two-dimensional
materials
Sam Vaziri, Eilam Yalon, Miguel Muñoz Rojo, Saurabh V. Suryavanshi, Huairuo Zhang, Connor J. McClellan,
Connor S. Bailey, Kirby K. H. Smithe, Alexander J. Gabourie, Victoria Chen, Sanchit Deshmukh, Leonid Bendersky,
Albert V. Davydov, Eric Pop*
*Corresponding author. Email: epop@stanford.edu
Published 16 August 2019, Sci. Adv. 5, eaax1325 (2019)
DOI: 10.1126/sciadv.aax1325

This PDF file includes:
Section S1. Multiple transfer technique
Section S2. Atomic-resolution ADF-STEM
Section S3. PL quenching in 2D heterostructures
Section S4. SThM thermal maps
Section S5. SThM temperature calibration
Section S6. Raman temperature maps
Section S7. Temperature-dependent Raman coefficients
Section S8. Non–temperature-related Raman peak shifts
Section S9. Thermal transport modeling and analysis
Fig. S1. Transfer process and optical images.
Fig. S2. Atomic-resolution ADF-STEM images.
Fig. S3. PL quenching.
Fig. S4. Uniform heating maps.
Fig. S5. SThM calibration by metal line heaters.
Fig. S6. Raman maps.
Fig. S7. Temperature-dependent Raman coefficients.
Fig. S8. Raman shift dependence on doping and electrical gating.
Fig. S9. PDOS overlap.
Table S1. Material parameters.
Table S2. TBC comparison.
References (35–55)

Section S1. Multiple transfer techniqueFigure S1A shows the heterostructure fabrication process flow. The process starts withtransferring graphene, grown by chemical vapor deposition (CVD) on copper, onto the second
two-dimensional (2D) material which is, in this example, CVD-grown MoSe2 on SiO2 as shownin fig. S1A, I to III. This graphene sheet will be the topmost (first) layer of the final van der
Waals (vdW) heterostructure. The top graphene layer acts as an optically transparent electricalheater for Raman thermometry of the heterostructures. After removing the polymer followed byannealing, the sample is coated with another layer of transfer support polymer. Then, the stack ofpolymer/Gr/MoSe2 is delaminated from the SiO2/Si substrate using DI water or diluted NaOH
and transferred onto the third 2D material which is CVD-grown MoS2 in this example (fig. S1A,
IV and V). The same procedure can be repeated to form the target stack (fig. S1A, VI). In thismethod, the transfer-support polymer layer is only in contact with the top surface of the graphene
layer, leaving all the interfaces below polymer-free. Figures S1B,C,D show optical images of thefabricated heterostructures.
B

A
Graphene (Gr)

Gr/MoS2

IV) Polymer
spin-coating

Cu

SiO2

Gr/SiO2SiI) Polymer
spin-coating

50 µmV) Transferring on thethird 2D material

PolymerCCuII) Removing thesubstrate

Gr/MoS2

MoS2

Gr/MoS2/WSe2

SiO2
Gr/SiO2Si
Gr/WSe2VI) Transferring on the
fourth 2D material
III) Transferring on thesecond 2D-layer

Gr
MoSe2

D
Gr/MoS2

Gr/WSe2

MoS2
Gr/SiO2

WSe2

MoSe2
SiO2
Si

SiO2
Si

Gr/MoSe2

5 µm

Gr/MoSe2/MoS2/WSe2

Fig. S1. Transfer process and optical images. (A) Schematic of the multiple-transfer process
flow to fabricate a Gr/MoSe2/MoS2/WSe2 heterostructure on SiO2/Si substrate. Optical images of(B) Gr/MoS2, (C) Gr/MoS2/WSe2, and (D) Gr/MoSe2/MoS2/WSe2 on SiO2/Si substrates.

Section S2. Atomic-resolution ADF-STEM
The individual 2D monolayers have random lattice orientation and alignment with respect toeach other in the vdW heterostructures. This makes it challenging to simultaneously attainatomically sharp transmission electron microscopy (STEM) images of all layers in the stack.
A

Gr
MoS2
WSe2
1 nm

B

Gr
MoS2
WSe2
1 nm

C

Gr
MoS2
WSe2

1 nm

D
Gr
MoS2
WSe2
1 nm

E
Gr
MoSe2

MoS2
WSe2
1 nm

F
Gr
MoSe2

MoS2
WSe2

1 nm

Fig. S2. Atomic-resolution ADF-STEM images. (A-D) STEM images of Gr/MoS2/WSe2
heterostructures. (A) MoS2 and WSe2 are slightly misaligned with respect to each other along the1H [100] zone-axis. (B-D) MoS2 and WSe2 are misaligned ~21° with respect to each other alongthe 1H [100] zone-axis. In (B) imaging is with WSe2 in [100] zone-axis, in (C) imaging is with
MoS2 in [100] zone-axis, and in (D) imaging is with both layers far off [100] zone-axis. (E,F)
STEM images of Gr/MoSe2/MoS2/WSe2 heterostructures. In (E) MoSe2, MoS2 and WSe2 layers
are slightly misaligned with respect to each other along the 1H [100] zone-axis. In (F) all three
TMD layers are approximately aligned along 1H [100] zone-axis.

Figure S2 shows cross-sectional atomic-resolution annular dark field scanning transmission
electron microscopy (ADF-STEM) images of the three-layer (Gr/MoS2/WSe2) and four-layer(Gr/MoS2/WSe2) heterostructures in different samples. The monolayer graphene on top of eachheterostructure is hard to discern due to the much lower atomic number of carbon atoms. In thethree-layer heterostructure, atomic resolution images can be achieved for both layers when the
MoS2 and WSe2 layers are in relatively good lattice alignment (fig. S2A). Figures S2B,C show
similar, but misaligned, heterostructures when the bottom WSe2 layer or top MoS2 layers areimaged in [100] zone-axis, respectively. Figure S2D shows the three-layer heterostructure when
all the layers are off [100] zone-axis. Figures S2E,F show the four-layer heterostructures withrough alignment of MoSe2, MoS2 and WSe2 layers and approximately aligned all three TMD
layers, respectively. We note these are all STEMs in addition to the ones in Fig. 1 of the main
text, taken at different regions, highlighting the atomically clean and intimate nature of theinterfaces.

Section S3. PL quenching in 2D heterostructures
Light emission quenching of individual monolayers in 2D heterostructures is attributed tointerlayer charge transfer process due to strong interlayer coupling (35-37). In all ourheterostructures the PL is significantly quenched with respect to the isolated monolayers,
revealing intimate coupling between 2D monolayers over larger areas, and complementing the“zoomed in” view that is achievable by STEM (above). Figure S3 shows the photoluminescence(PL) spectra of isolated MoS2 and WSe2 monolayers, as well as Gr/MoS2 and Gr/WSe2
heterostructures before and after annealing. After annealing, the PL is further quenched, showing
enhanced coupling due to the removal of possible water residues between the layers (22). In
addition to PL quenching, interlayer breathing Raman modes and interlayer exciton emission canbe used to confirm layer coupling in vdW heterostructures with specific system of materials andmeasurement set up requirements (22,38).

Fig. S3. PL quenching. PL spectra of isolated monolayers of MoS2 and WSe2, andheterostructures of Gr/MoS2 and Gr/WSe2 as transferred and after annealing.

Section S4. SThM thermal maps
We used scanning thermal microscopy SThM (39) to map the surface temperature in the heatedchannels with high spatial resolution (~100 nm, determined by the thermal exchange radius)(40). Figures S4A to H show atomic force microscopy (AFM) topography and the corresponding
SThM thermal maps for graphene, Gr/MoS2, Gr/WSe2, and Gr/MoS2/WSe2 on SiO2/Si,
respectively. The SThM thermal maps reveal uniform temperature rise within the heated areas of
the heterostructures. The uniform power input and temperature rise allow us to use a simple
lumped thermal model to extract the thermal boundary conductance (TBC) of the interfaces of
the heterostructure. The SThM voltage signal was converted to temperature using a calibration
technique which is discussed in the next section.

C

Pd

E

G

60

Gr/MoS2

SiO2

Gr/MoS2/WSe 2

Gr/WSe 2
SiO2

SiO2

SiO2

10
0

Pd

Themal map

B

D

+V

30
20

2 µm

Pd

40

nm

50

Pd Graphene

F

H
100

I

I

I

I

80

60

mV

Topography

A

40

-V
P = 3.36 0.08 mW

P = 2.97

0.09 mWP = 2.78

0.05 mWP = 2.61

0.06 mW

20
0Fig. S4. Uniform heating maps. Topography and SThM thermal maps of (A,B) graphene,(C,D) Gr/MoS2, (E,F) Gr/WSe2 and (G,H) Gr/MoS2/WSe2 heterostructures, respectively. Thesesamples were capped with 15 nm of Al2O3 to electrically isolate the thermal probe from thesample when biasing the device. The topography images show smooth surfaces with some nonuniformities in the Gr/WSe2 and Gr/MoS2/WSe2 heterostructures. These non-uniformities are
localized in small areas and correspond to bilayer/multilayer triangular islands from the WSe2
CVD growth. The thermal maps reveal homogenous heating across the channel for the different
heterostructures studied with no visible hot spots associated to the multilayer islands.

Section S5. SThM temperature calibration
To calibrate the SThM mV signal to temperature we used metal line heaters with known
temperature. We fabricated 4-probe metal lines (30 nm Pd with 2 nm Ti adhesion layer) on SiO2
(90 nm) on Si substrates with length L = 30 µm and varying width W = 100 nm to 1 µm. The

metal heaters were capped by 15 nm Al2O3 to keep the same thermal contact as in the grapheneheater experiment. We first measured the temperature coefficient of resistance (TCR) of the Pdlines on a hot stage (fig S5A,B). With the measured TCR the temperature of the heater is givenby the change in its resistance: ΔT = ΔR/(R·TCR). Note that the voltage drops at contacts are
excluded in our 4-probe structure. We also measured the thermal resistance of the lines ΔT/ΔP.
Next, the SThM tip was scanned in passive mode over the metal lines, which acted as heaters
with a known temperature. Figure S5C,D shows the SThM voltage and topography of a heaterwith W = 1 µm. We repeated this procedure with varying input powers applied to the metal lines
and calibrated the readout SThM voltage signal (in mV) to the known (heater) temperature. It
should be noted that the calibration factor (K/mV) decreases for heater widths smaller than ~ 500
nm but since the graphene heaters in our experiment are wider (W = 5 µm) we used thecalibration factor 7 ± 1 K/mV which we obtained for heaters wider than 500 nm (41).

A 242

B

Tstage=24°C

250

R0 ()

R ()

240
238
236
234
0

C

2
3
P (mW)

245

TCR=0.00195 ±0.00005 K-1

240
235
230

R0
1

255

4

225
20

5

30

40 50
Tstage (C)

60

70

D
1 μm
Pd Line
SiO2

Fig. S5. SThM calibration by metal line heaters. (A) Representative measurement of electricalresistance vs. input power of a metal line (W = 1 µm) at 24°C showing the resistance at zero
power R0 extrapolated for P = 0. (B) Electrical resistance at zero power (R0) vs. stage
temperature, measured to obtain the temperature coefficient of resistance TCR = ΔR/(R·ΔT). The
extracted TCR near room temperature is shown in the inset. (C) SThM signal (in mV) for theelectrically heated metal line used for calibration. (D) AFM topography image of the metal line.

Section S6. Raman temperature maps
Uniform temperature maps were also obtained by Raman thermometry for each layer in theheterostructure. Figure S6A compares the conductance of a representative graphene FET and a
MoS2 FET on SiO2 substrates measured in vacuum. Even in the on-state of the MoS2 FET, thegraphene FET has over one order of magnitude larger conductance. During Raman thermometry
we applied VG = -20 V which turns off the MoS2 channel and all Joule heating dissipates in thegraphene heater. Figures S6B,C show the Raman temperature map for an electrically heated
Gr/MoS2 channel on SiO2/Si substrate. We follow procedures outlined in our previous work (23)with several modifications for the heterostructures used here (see for example sections S7 and S8
below). We note that the Raman signal is sensitive to the number of layers (42) and to defects(43), which becomes crucial when obtaining maps of the channel if the material is not entirely
uniform.

Conductance (mS/μm)

A

B
Graphene FET
FETGraphene

Graphene

Lch: 3 µm

3 :μm
10-2 L T=SiO2
100 nmtox = 100 nm

10-4

Gr
MoS2

MoS2 FETMoS
2 FET
L : 3 µm
L ch= 3 μm
TSiO2: 300 nm
tox = 300 nm

0
VG (V)

MoS2
SiO2
Si

10-6
-30

ΔT (K)

C

Si

30

Fig. S6. Raman maps. (A) Normalized conductance vs. gate voltage of a representativegraphene FET (on 100 nm-thick SiO2 substrate) and an MoS2 FET (as grown on 300 nm-SiO2
substrate). (B) Schematic of the Raman thermometry experiment with Graphene/MoS2/SiO2/Si
structure. (C) Map of temperature rise measured by Raman for representative device shown in B
with input power of P = 7 mW. The dimensions of the graphene channel are L = 8 µm and W = 5µm.

Section S7. Temperature-dependent Raman coefficients
For temperature-dependent Raman shift calibration, we used a Linkam THMS600 stage, andcarefully differentiated effects of strain (e.g. during the calibration on hot stage) and charge (e.g.
during electrical heating) (44), as explained in the next section.

1590
1588
0 20 40 60 80 100 120 140
T (C)

250.6

405
404.5
404
403.5
403

-1

251

-1

C
WSe2 peak (cm )1592

B 405.5'-1

G peak (cm )1594

MoS2 A1 peak (cm )

A

250.2
249.8
249.4

402.5
0 20 40 60 80 100120140
T (C)

249
0 20 40 60 80 100120140
T (C)Fig. S7. Temperature-dependent Raman coefficients. (A) Graphene G-peak position vs. stage
temperature for Gr on SiO2/Si (G in G, black), Gr on WSe2/SiO2/Si (G in GW, red) and Gr on
MoS2/SiO2/Si (G in GM, blue). All samples are capped by 15 nm Al2O3. (B) MoS2 A1’ peak vs.
stage temperature for MoS2 in Gr/MoS2 (M in GM, blue) and in Gr/MoS2/WSe2/SiO2/Si (M in
GMW, purple). (C) WSe2 peak position vs. stage temperature in Gr/WSe2/SiO2/Si (W in GW,red) and in Gr/MoS2/WSe2/SiO2/Si (W in GMW, purple).

Section S8. Non–temperature-related Raman peak shifts
8.1 Strain
The presence of strain can affect the peak position of the Raman signal which is used for thethermometry. To evaluate the effect of strain on the temperature measurements one should
consider only the difference between the calibration and the electrical heating experiment. The
effect of strain that may be present during the calibration procedure due to heating (of the entire
sample uniformly) above room temperature will also be present during electrical heating of thesame film, with one difference only due to the temperature gradient between that film and its
substrate. Hence, in the evaluation of the Raman peak shifts due to such a “parasitic” strain
effect, we should consider the difference in thermal expansion coefficient (TEC) between thematerials and the temperature difference between the layers. The TECs of the materials in our
samples and their Raman peak shifts due to strain of the 2D films are on the order of ~10-5 K-1(45) roughly an order of magnitude larger than the TEC of the substrate (46).

The Raman peak shift with strain was measured for the MoS2 A1’ mode as -0.4 cm-1 and E’mode as -2.4 cm-1 per 1% (47). For WSe2 the peak splitting with strain was discussed (48) andmeasured (49) but was not quantified. We also compare the Raman shifts of the MoS2 A1’ modewith the shifts in E’ mode, which is more sensitive to strain (47). The Raman peak position
during electrical heating (vs. input power) of the E’ and A1’ peaks are shown in fig. S8A,B, andthe temperature calibration of the E’ mode in a representative graphene-MoS2 sample is shown infig. S8C. The measured thermal resistance we extract using the out-of-plane A1’ mode is 3.7
K/mW and the one that would have been extracted using the in-plane E’ mode is 4.6 K/mW

(roughly ~25% larger). We assign the difference between these numbers to the effect of strain
that is more dominant in the E’ mode, but this result also confirms that our thermometry using
the A1’ mode is insensitive to strain within the reported uncertainty, as explained next. If, forexample, we assumed an extreme case for which the entire shift measured in the E’ peak (~0.8
cm-1) is due to strain, we would evaluate a maximum strain value < 0.4% (47). For the samestrain value, the A1’ peak would have shifted by ~0.16 cm-1 which corresponds to a temperatureof ~12 K, close to the uncertainty of our measurement. Given that the Raman peak shift is most
likely not only due to strain, we conclude that the effect of strain on the temperature
measurement using the A1’ peak in our experiment is negligible. We also note that this strainrelated A1’ peak shift is (at least partially) taken into account by the hot stage calibration.

For WSe2, no quantitative data for the peak shift with strain in monolayers are reported inliterature, however based on the above discussion, and the fact that we do not observe the peak
splitting in our experiment we can evaluate that the effect of strain (in electrical heatingcompared with stage heating) is negligible within the uncertainty of our measurement.
Finally, regarding the graphene temperature and its uncertainty, we refer to our SThM
measurements (Fig. 3B) which serve as a good indication that the obtained values are within thegiven uncertainty.
8.2 Doping
The electrical properties and the Raman signal of the top graphene layer could be sensitive toambient adsorbates and to the charge carrier concentration (doping). The G-peak position
becomes more sensitive to charge carriers when the quasi-Fermi level is near the Dirac point(50). We capped the devices with ~15 nm Al2O3 by atomic layer deposition (ALD), which
induces n-type doping and protects the graphene from the ambient. Figures S8F,G show theeffect of electrostatic gating and of capping on the graphene G peak.

To eliminate the effect of charge carriers we always used the same back-gate bias VG during
electrical heating (when current ID flows through the graphene channel) and during the reference
measurement (ID = 0, no heating). Furthermore, we carried out control measurements with largegate voltage (both positive and negative) compared with the drain voltage, so that the effectivegate-to-channel bias (which varies along the channel between VGS and VGD) remains relatively
uniform. Finally, we note that any change in carrier concentration due to temperature will bepresent not only during the electrical heating experiment but also during the calibration
procedure and is therefore considered in our measurement.

(a)
A

D

(b)
B

(c)

C
(c)

E

F

G

Fig. S8. Raman shift dependence on doping and electrical gating. (A) MoS2 A1’ Raman peak
position with input electrical power. (B) MoS2 E’ Raman peak position with input electrical
power. (C) Calibration of MoS2 E’ Raman peak position with stage temperature. (D) Graphene G
peak position vs. back-gate voltage before (blue) and after (red) capping with 15 nm Al2O3. (E)Intensity ratio of 2D (also known as G’) to G peaks vs. gate voltage before and after capping.
The capping layer induces a large (~10 cm-1) blue-shift of the G frequency and reduction in the
2D/G intensity ratio, indicative of electron doping (50). (F) Gate voltage dependence ofgraphene G peak before and (G) after capping with Al2O3, zoomed in to y-axis scale of 1 cm-1,
highlighting more sensitivity to VG in uncapped devices and less after capping. VG was kept
constant during the electrical heating and reference (no current) measurements to eliminate
Raman shifts due to electron (or hole) electro-static doping.

Section S9. Thermal transport modeling and analysis
For 2D materials, the thermal conductance across the interface is primarily dominated by the outof-plane or flexural phonon (ZA) modes (32). The dispersion for these flexural modes in 2D
materials is ω ≈ (σ/ρ)1/2k2 (σ is the flexural rigidity of the 2D material, ρ is the mass density, k is
the phonon wavevector) and the phonon density of states (PDOS) is given by DOSZA =1/[4π(σ/ρ)1/2]. The dispersion relationship for longitudinal and transverse (LA and TA) modes in
SiO2 is linear, ω = vgk, where vg is the group velocity of the LA or TA mode, and thecorresponding PDOS is DOSLA,TA = ω2/(2π2vLA,TA3). To calculate the PDOS overlap between thetwo materials, we also need the cut-off energies for the participating phonon branches. The
active modes are calculated by obtaining the area under the curve as shown in fig. S9Active modes ∝ PDOS overlap ×𝑑𝑓𝑑𝑇min(θ1,θ2)∝ ∫0min(DOS1 , DOS2 ) ×

𝑑𝑓(𝜃)
𝑑𝑇

𝑑𝜃

[S1]

Here, DOS1 and DOS2 are the PDOS for the two materials forming the interface withcorresponding cut-off energies of θ1 and θ2 respectively. df/dT is the derivative of the BoseEinstein distribution function with respect to temperature (T), near room temperature. The
material parameters considered for the calculations are shown in table S1.
A 2D/2DPDOS

B 2D/3D
PDOS

Active modes

DOSZA1DOSSiO2(θ)

DOSZA1DOSZA2

df / dT
df / dT
Active modes

θ1 θ2 Energy (eV)θ1Energy (eV)Fig. S9. PDOS overlap. Schematic representing calculation of PDOS overlap for (A) 2D/2D and(B) 2D/SiO2 interfaces. In this figure, DOSZA1 and DOSZA2 are the PDOS for ZA modes of two
distinct 2D materials with corresponding cut-off energies θ1 and θ2 respectively. For a 3D
substrate such as SiO2 we consider a PDOS from LA and TA phonon branches (DOSSiO2) asshown by the green dashed line in B. The derivative of the Bose-Einstein distribution is shownby black dashed line. The total active modes for the respective interfaces are given by the shaded
blue regions.
Table S1. Material parameters. List of material parameters used in modeling. References arelisted in parentheses with gray font, after each value where appropriate.

Gr
MoS2
WSe2
SiO2

Flexuralrigidity, σ (eV)
1.1 (51)
9.6 (53)
11.45 (54)-Mass density,ρ (g⋅cm-3)
2.27
5.06
9.32
2.2

Cut-off energy(meV)
60 (52)21 (21)15.5 (55)20Group velocity,vg (m/s)
5953 (LA)3743 (TA) (51)PDOS
(m-2s)
1.65 × 105
1.13 × 105
1.45 × 105
ω2/(2π2ν3)

2D material
thickness (Å)
3.35
6.15
6.5
-

We model the transmission at the interface using a simple acoustic mismatch model (AMM),
because the interfaces of these vdW structures are nearly perfect and any surface asperities (e.g.
dangling bonds) are much smaller than the phonon wavelengths. Transmission is, therefore,
given by the density mismatch between the two materials.

Trans. ~ min(ρ1/ρ2, ρ2/ρ1)[S2]

Finally, the interface TBC is proportional to the product of transmission, PDOS overlap, anddf/dT, as shown in the last column of table S2 below.

Table S2. TBC comparison. Comparison of transmission and PDOS overlap for various
interfaces.
Mass density mismatch
PDOS overlap
TBC ∝ Trans. × PDOS overlap ×
15(Transmission)(modes) × 10
df/dT (Normalized) [*]Graphene/WSe2
0.243
3.4
1
MoS2/WSe2
0.543
2.8
1.7
Graphene/MoS2
0.448
3.9
1.4
Graphene/SiO2
1.03
5.9
2.9
MoS2/SiO2
2.3
2.8
2.2
WSe2/SiO2
4.236
2.2
1.9
-3 -1
* This is equivalent to TBC/vg with units of Jm K , like the specific heat. We normalize our calculations
to the minimum of the Gr/WSe2 interface. The simple model accurately captures the TBC trends foundexperimentally in Fig. 4, with a constant offset included for the 2D/3D interfaces, which accounts for thedimensionality mismatch. This offset originates from the fact that the underlying heat transportmechanism (phonon modes) and dimensions are different at 2D/2D and 2D/3D interfaces. Green andpurple colors in the table denote 2D/2D and 2D/3D interfaces, respectively, like Fig. 4B in the main text.
Interfaces