PHYSICAL SCIENCE
2017 © The Authors,
some rights reserved;
exclusive licensee
American Association
for the Advancement
of Science. Distributed
under a Creative
Commons Attribution
NonCommercial
License 4.0 (CC BY-NC).
Interlayer couplings, Moiré patterns, and 2D electronic
superlattices in MoS
2
/WSe
2
hetero-bilayers
Chendong Zhang,
1
Chih-Piao Chuu,
2
Xibiao Ren,
3
Ming-Yang Li,
4,5
Lain-Jong Li,
4,5
Chuanhong Jin,
3
Mei-Yin Chou,
2,6,7
Chih-Kang Shih
1
*
By using direct growth, we create a rotationally aligned MoS
2
/WSe
2
hetero-bil ayer as a designer van der Waals hetero-
structure. W ith rotational alignment, the lattice mismatch leads to a periodic variation of atomic registry between
individual van der Waals layers, exhibiting a Moiré pattern with a well-defined periodicity. By combining scanning
tunneling microscopy/spectroscopy, transmission electron microscopy, and first-principles calculations, we investigate
interlayer coupling as a function of atomic registry. We quantitatively determine the influence of interlayer coupling on
the electronic structure of the hetero-bilayer at different critical points. We show that the direct gap semiconductor
concept is retained in the bilayer although the valence and conduction band edges are located at different layers. We
further show that the local bandgap is periodically modulated in the X-Y direction with an amplitude of ~0.15 eV,
leading to the formation of a two-dimensional electronic superlattice.
INTRODUCTION
Stacking two-dimensional (2D) atomic crystals with different bandgaps
into van der Waals (vdW) heterostructures has emerged as a very pow-
erful method to create designer heterostructures (1). In designing these
vdW heterostructures, the effect of interlayer coupling will play a critical
role. As shown in graphene–hexagonal boron nitride (hBN) hetero-
structures, interlayer coupling can be tuned through spatial alignments
between vdW layers, providing a designing parameter (without a coun-
terpart in conventi onal heterostructures) to tailor the electronic
structures of vdW heterostructures (2–8). The emergence of transition
metal dichalcogenide (TMD)–based heterostructures brought again the
role of interlayer coupling into the spotlight (9–12).Theissueofinter-
layer coupling in TMD heterostructures is inherently complex. It is al-
ready known that for bilayer TMDs (referred to as homo-bilayers),
interlayer coupling splits the degeneracy at the G point and transforms
the direct gap in the monolayer (ML) into an indirect gap semi-
conductor (13, 14). This splitting is shown to be quite large (~0.7 eV)
(14–16). It has also been seen that the rotational alignment can influence
the interlayer coupling in these homo-bilayers although all exhibit an
indirect bandgap (17–20). For heterostructures composed of two differ-
ent ML-TMD materials (referred to as hetero-bilayers), the role of in-
terlayer coupling remains an open issue (9–12, 21–25). Two questions
stand out prominently: (i) Does interlayer coupling lead to an indirect
gap in the hetero-bilayer, or is the direct gap retained? (ii) Can interlayer
coupling be used as a design parameter for vdW TMD heterostructures?
Here, we examine these critical issues by using a rotationally aligned,
lattice-mismatched MoS
2
/WSe
2
heterostructure. Even with rotational
alignment, the lattice mismatch between the two atomic layers produces
a periodic variation in the lateral atomic registry, facilitating a natural
platform for the investigation of how lateral registry affects interlayer
coupling. The structural information is directly probed using scanning
tunneling microscopy (STM) and transmission electron microscopy
(TEM). Direct correlation of the lateral registry between the two atomic
layers and the local electronic structures is revealed using comprehen-
sive scanning tunneling spectroscopy (STS). Experimental observations
are corroborated with first-principles calculations. We quantitatively
show how interlayer coupling affects the electronic structure at different
criticalpoints.Wefindthatthedirectgapisretainedwiththevalence
and conduction band edges located at the same K point but in different
layers. The local bandgap is modulated periodically in the X-Y direction
with an amplitude of ~0.15 eV, creating an electronic superlattice.
RESULTS AND DISCUSSION
Chemical vapor deposition (CVD) is used to achieve direct growth of
vertically stacked ML-MoS
2
on ML-WSe
2
on graphite substrates (de-
scribed in Materials and Methods) (26). Figure 1A is an STM image
of this hetero-bilayer on a graphite substrate. The Moiré pattern with
a lattice constant of 8.7 ± 0.2 nm can be clearly observed on the top
MoS
2
layer (zoom-in view shown in Fig. 1B). This superlattice periodic-
ity should appear in a rotationall y aligned MoS
2
/WSe
2
bilayer; namely,
the rotational angle between two atomic lattices is either 0° (R) or 180°
(H) (27, 28). A simulated Moiré supercell for 0° rotational angle is
displayed in Fig. 1C, resembling the STM observation well. However,
theSTMisunabletoresolvetheRorHstackingbecausethechalcogen
sublattice on the surface will look identical. We then use annular dark-
field scanning transmission electron microscopy (ADF-STEM) to un-
ravel the atomic structure that is consistent with an R stacking.
STEM samples are prepared by exfoliating the on-top TMD layers
together with a very thin graphite layer. The ADF image intensity in-
creases with the ato mic number and the number o f atomic layers. This
makes the signal from ultrathin graphite much weaker than the signals
from bilayer TMDs, which could be simply treated a s background
signals. The ADF-STEM image of the heterostructure stack is shown
in Fig. 1D. Although MoS
2
and WSe
2
are rotationally aligned, their
difference in lattice constants leads to locally different lateral registries,
resulting in a periodic variation of these local alignments (that is, the
Moirépattern).InFig.1E,weshowthe ADF-STEM images at different
local alignments [designated as AA, AB
Se
,Bridge(Br),andAB
W
]along
with the simulated ADF-STEM images, which fit well with the experi-
mental ones, and the corresponding models on the left. The symbol of
1
Department of Physics, University of Texas at Austin, Austin, TX 78712, USA.
2
Institute
of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei 10617, Taiwan.
3
State Key Laboratory of Silicon Materials and School of Materials Science and Engineer-
ing, Zhejiang University, Hangzhou, Zhejiang 310027, People’s Republic of China.
4
Physical Science and Engineering Division, King Abdullah University of Sci ence
and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia.
5
Research Center
for Appli ed Sciences, Academia Sinica, Taipei 10617, Taiwan.
6
School of Physics, Geor-
gia Institute of Technology, Atlanta, GA 30332, USA.
7
Department of Physics, National
Taiwan University, Taipei 10617, Taiwan.
*Corresponding author. Email: shih@physics.utexas.edu
SCIENCE ADVANCES
|
RESEARCH ARTICLE
Zhang et al. Sci. Adv. 2017; 3:e1601459 6 January 2017 1of7
on January 7, 2017http://advances.sciencemag.org/Downloaded from
Fig. 1. Atomic structure of as-grown MoS
2
/WSe
2
vdW heterostructures revealed by STM and STEM. (A) STM image for a MoS
2
/WSe
2
vdW heterostructure on the highly
oriented pyrolytic-graphite (HOPG) substrate. (B) Close-up STM image showing the hexagonal Moiré pattern with a periodici ty of 8.7 nm. (C) Schematic model of the Moiré pattern
on an R-stacked MoS
2
/WSe
2
hetero-bilayer. By using the lattice constants of 3.16 Å for MoS
2
and 3.28 Å for WSe
2,
the simulated supercell marked by bla ck solid lines shows a
periodicity of 8.64 nm. (D) Atomically resolved STEM image. Typical regions in an R-stacked heterostructure—AA, AB
Se
,Br,andAB
W
—are labeled in both (C) and (D). The close-up
STEM images for each region are shown in the right column of (E). The simulated images (based on an R-type stacking) and their correspond ing atomic models are displayed in the
middle and left columns of (E), respectively. (A and B) −3.0V,10pA.Exp.,experimental.
Fig. 2. First-principles calculations for the interlayer separations and electronic structures of representative sites in an R-stacked MoS
2
/WSe
2
heterostructure.
(A) Side views of the atomic models for AA, AB
Se
, Br, and AB
W
regions with an average lattice constant (Supplementary Materials). The calculated interlayer separations
for four atomic alignments are labeled in (A). (B) A perspective view of an STM image zoomed in on a unit cell of the Moiré pattern. A height profile along the diagonal
line from AA to AA [gray dashed line in (B)] is shown in (C). Energy band structure of the AA registry is displayed in (D), whereas its corresponding density of states
(DOS) diagrams are shown in (E). The size of the green (red) circles represents the projected weight on the d orbitals of Mo (W), and the states are labeled in the
subscript based on this project. The corrections for the strain resulting from the average lattice constant used in the calculation are labeled for the typical critical points
in the DOS diagram. Results for other sites can be found in the Supplementary Materials. (B) −3.0 V, 10 pA.
SCIENCE ADVANCES
|
RESEARCH ARTICLE
Zhang et al. Sci. Adv. 2017; 3:e1601459 6 January 2017 2of7
on January 7, 2017http://advances.sciencemag.org/Downloaded from
AB
Se
(AB
W
) means that the hexagonal la ttices of the metal atoms in the
two MLs are stacked in an AB manner (analogous to bilayer graphene),
with the Se(W) atoms in the bottom ML not covered by any atoms in the
upper ML. A more detailed ADF-STEM analysis, including intensity
line profile analysis in different regions, can be found in figs . S1 and S2.
The rotationally aligned MoS
2
/WSe
2
stack has a lattice constant of
8.7 nm, and a unit cell contains about 4000 atoms. Theoretically, it is
very challenging to use a very large unit cell for electronic structure
calculations with density functional theory (DFT). To circumvent this
difficulty, we first examinethe effect of different local interlayer atomic
registries on the electronic structure using the average lattice constant
for bothMoS
2
and WSe
2
(seethe Supplementary Materialsfordetails).
It is expected that the results reflect the corresponding changes caused
by the local registry in the large unit cell. The calculated band diagram
for the AA site is shown in Fig. 2D (other sites are shown in fig. S3).
The interlayer separations at different sites (labeled in Fig. 2A), which
show an order of AA > Br > AB
W
>AB
Se
, are also calculated. These
differences in height can be used to distinguish the high-symmetry
sites in STM observations (detailed discussion in the Supplementary
Materials). As shown in Fig. 2 (B and C), AA, AB
Se
,Br,andAB
W
are
labeled along the diagonal line of one supercell, following the same
sequence predicted by calculations despite a smaller amplitude in their
differences.
The second step of the theoretical calculation entails a posterior
strain correction to gain a more accurate description for the electronic
structure of individual “unstrained” MLs. This is justifiable because little
mixing exists between electronic states coming from different layers in
the bilayer system. These strain corrections lead to systematic shifts in
critical point energy l ocations, as labeled by the arrows shown in Fig. 2E.
It is found that significant differences exist in electronic structures be-
tween AA and AB
Se
sites, especially for electronic states at the G point
in the valence band. This is due to the fact that the interlayer coupling
at the G point is mediated through the chalcogen p
z
orbitals. The
difference in the local atomic registry (for example, AA versus AB
Se
)
is primarily in the lateral alignment of the chalcogen atoms, that is, Se in
the top WSe
2
layer and S in the bottom MoS
2
layer,asshowninFig.2A.
Consequently, interlayer coupling would be significantly influenced.
Theoretical calculations for energy locations (after strain correction)
of key critical points for these four different local atomic registrie s are
shown in Fig. 3D. Not all of them are resolved experimentally. Up arrow
Fig. 3. Scanning tunneling spectra of AA, AB
Se
, Br, and AB
W
regions. (A) dI/dV spectra. (B and C)(∂Z/∂V)
I
and decay constant k spectra of valence bands, respec-
tively. (D) Calculated energy values at key critical points for AA, AB
Se
, Br, and AB
W
sites, respectively. The energies are with respect to the vacuum level. The shaded
regions in (B) and (D) represent the valence band edges and show consistent movements of the energy locations of G
W
(black) and K
W
(cyan). In a deeper lying energy
range, the spectral features marked by red and green arrows in (A) to (C) correspond to the energy window where the Q
W↑,↓
, K
Mo↑,↓
, and G
Mo
states and a lower G
W
(labeled as G
W2
) state are located. The complicated movements in their relative energy locations result in a complex behavior in k spectra [red arrows in (C)], making the
direct identification of individual states nontrivial.
SCIENCE ADVANCES
|
RESEARCH ARTICLE
Zhang et al. Sci. Adv. 2017; 3:e1601459 6 January 2017 3of7
on January 7, 2017http://advances.sciencemag.org/Downloaded from
and down arrow subscripts are used to represent the higher and lower
energy levels in spin-orbit split K (Q) states, respectively.
STM and STS reveal detailed information on how interlayer atomic
registry affects the local electronic structures of the MoS
2
/WSe
2
hetero-
bilayer. In Fig. 3, three d ifferent STS modes are displayed: the
conventional dI/dV acquired at constant Z (Fig.3A),the∂Z/∂V at con-
stant current (Fig. 3B), and the tunneling decay constant defined as k =
−1/2 (dlnI/dZ ) (Fig. 3C). As discussed recently, the (∂Z/∂V)
I
spectrum
provides the signature for the onset of different thresholds in the
tunneling process, whereas the k spectrum helps us to identify the origin
of these thresholds in the Brillouin zones (29).
In the conventional dI/dV spectrum (displayed in the logarithmic
scale), several spectral features are identified (labeled with arrows in
different colors). The states marked by the black arrows are the G
W
states that reside primarily in the WSe
2
layer (Fig. 2D). This assign-
ment is corroborated by both the (∂Z/∂V)
I
and the k measurements
showninFig.3(BandC).Ataconstant current, when the sample
bias (V
S
) is scanned from below to above G
W
,thelossofG
W
states
forces the tip to move inward to compensate for this loss, resulting in
a dip in the (∂Z/∂V)
I
(that is, a sudden drop in Z). This allows us to
probe a critical point in the band structure. Moreover, because the
parallel momentum k
||
=0attheG point, one anticipates to observe
a sharp minimum in k,ask ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2mf
o
ℏ
2
þ k
2
∥
q
, where f
o
is the barrier
height. This is observed in Fig. 3C (marked by black arrows).
In the dI/dV spectra acquired with Z stabilized at V
S
= −2.6 V, the Z
value is not small enough to detect the states above G
W
(particularly
states near K
W↑
) because of their high decay constant. In the constant
current spectrum, this sensitivity issue is removed. The threshold at
K
W↑
appears as another dip in (∂Z/∂V)
I
. This occurs when the sample
bias is moved above the energy location of K
W
, and the tip needs to
move closer to the sample to achieve tunneling to the underlying graphite
states. The large decay constant k measured near K
W↑
also reflects the
high k
||
value. It should be noted that because of the mixing o f underlying
graphite states in tunneling, simulation becomes necessary for an accurate
determination of K
W
, which suggests that the location of K
W
is slightly
above the dip location of (∂Z/∂V)
I
by about 0.05 eV (29).
The behavior of the electronic states near the valence band maxi-
mum (VBM) corroborated very well with the theoretical calculations
shown in Fig. 3D, particularly for statesneartheVBM(shadedregion
in Fig. 3, B and D). These states (G
W
and K
W
) have spectral weights
located at the WSe
2
layer. The theoretical results are in excellent agree-
ment with the experimental result in energy locations of the G
W
(showing an order of AA < Br < AB
Se
<AB
W
) and the energy separa-
tions between G
W
and K
W↑
(labeled as D
K−G
and shown in Fig. 4A). The
K
W↑
state is located above G
W
, and its signature can be identified much
more clearly because it occurs in the bias range where G
W
no longer
contributes to the tunneling current. On the other hand, the state
K
W↓
is located below G
W
, making its signature difficult to be detected
because the tunneling current would be dominated by the states that
originated near G
W
. In a deeper lying energy range (marked by the
red and green arrows in Fig. 3A), theory shows that these states corre-
spond to the energy window where the Q
W
, K
Mo
,andG
Mo
states and a
lower G
W
(labeled as G
W2
in Fig. 3D) state are intertwined. The com-
plicated movements in their relative energy locations make the direct
identification of individual states nontrivial. Nevertheless, on the basis
of the comparison with theoretical calculations(Fig.3D),thefeatures
marked by the green arrows in Fig. 3A can be tentatively attributed
to be K
Mo↑
states.
In the conduction band, near the band edge, two clear thresholds
(labeled with blue and purple arrows in Fig. 3A) are observed at the
AB
Se
, Br, and AB
W
sites, similar to those observed in isolated ML-
MoS
2
(29, 30). These two thresholds have been previously identified
as thresholds at two different critical points, Q and K, with the conduc-
tion band minimum (CBM) located at the K point. At the AA site, the
lower threshold is not present becaus e o f a large tip-to-sample distance
attheAAsiteforthestabilizationvoltage(−2.6 V) used in constant Z
spectroscopy. The energy separation between these two thresholds re-
mains relatively unchanged (~0.20 eV), but their absolute energy loca-
tions are site-dependent. The positions of the conduction band Q point
follow the order of AA ~ AB
Se
>Br>AB
W
. The total change for the Q
point position from AB
Se
to AB
W
is ~0.1 eV (similarly for the K point).
Theoretical calculations show a similar order in the energy location (Fig.
3D), although the variation is smaller (only ~0.03 eV).
A very important consequence of interlayer coupling is that the lo-
cal bandgap E
g
is site-dependent. For example, at the AB
Se
site, E
g
=
1.30 eV with the VBM located at −0.98 eV and the CBM located at
+0.32 eV. On the other hand, at the AB
W
site, E
g
=1.14eVwiththe
VBM located at −0.93 eV and the CBM located at +0.21 eV. Experi-
mental results for E
g
at four different sites are shown in Fig. 4B, with
the calculated E
g
shown as brown circles. It is understood that DFT
calculations significantly underestimate the bandgap values (31, 32),
Fig. 4. Summary of the site-dependentelectronic structures in MoS
2
/WSe
2
hetero-
bilayers. (A) Energy differences between K
W
and G
W
(D
K−G
) for the four different local
lateral alignments. The experimental values are labeled as blue triangles, whereas the
calculated DFT results are presented as brown circles. (B)LocalbandgapE
g
formed be-
tween the CBM of MoS
2
and the VBM of WSe
2.
Experimental and calculated DFT results
are displayed in purple and brown, respectively.
SCIENCE ADVANCES
|
RESEARCH ARTICLE
Zhang et al. Sci. Adv. 2017; 3:e1601459 6 January 2017 4of7
on January 7, 2017http://advances.sciencemag.org/Downloaded from
but the current results excellently replicate the overall trend in band-
gap variations observed experimentally.
The periodic variation of local electronic structures as a conse-
quence of the variation of the interlayer coupling due to the difference
in local interlayer atomic registry of the MoS
2
/WSe
2
hetero-bilayer al-
so indicates the formation of an electronic superlattice. This is similar
to the case of the graphene-hBN hetero-bilayer, except that the ampli-
tude of bandgap variations is much larger in the current case. The
formation of this electron superlat tice is also visualized in the sequence
of bias-dependent images shown in Fig. 5.
At a high negative bias, that is, from −3.0 to −2.4 V, a similar STM
contrast is observed (Fig. 5, A and B). However, at −2.3 V, where the
spectral feature of the AA site at −2.4V(markedbytheredarrowin
Fig. 3A) is out of the tunneling range, a lowering of the topographic
height at the AA site occurs. Accompanying this lowering is the ap-
pearance of three new features surrounding AA. These new features
correspond to the locations of other bridge sites (labeled as Br
2
and
discussed in more detail in the Supplementary Materials). Theory in-
dicates that the electronic struc tures o f Br
2
and Br are nearly the same.
Indeed, at above −2.1 V, Br
2
andBrfeaturesmerge,formingacircular
ring feature. At −1.6 V, G
W
states at all four sites are still in the
tunneling window, and the AA site remains to have the highest topo-
graphic height. The most marked change is the turning of the bright
feature at the AA site into a deep hole at −1.4 V. This is due to the fact
that the G
W
state at the AA site moves out of the tunneling window,
whereas that of the other sites continues to contribute. The evolution
continues as states at different sites move out of the tunneling window
at a slightly different bias (discussed further in the Supplementary
Materials). In the positive bias range, when the bias is above 0.85 V,
all images have a “normal” contrast. At 0.5 V, the Q
Mo
states at AA
and AB
Se
start to move out of the tunneling window, and the topo-
graphic height drops (note that the AB
Se
site is the lowest in the
first place and the drop does not lead to a contrast change as marked
as that at the AA site). Because the AB
W
site has the lowest CBM
location (see Fig. 3A marked by the purple arrow), the AB
W
site be-
comes the highest topographic feature as the bias continues to de-
crease to 0.2 V.
These rich features in the evolution of the bias-dependent STM
images are just another manifestation of the lateral modulation of
the electronic structures due to the local variation of interlayer atomic
registry in the hetero-bilayer. The states that are affected the most are
the valence states at the G point. However, the VBM of the overall
double-layer stack remains at the K position, whose spectral weight
is completely at the WSe
2
laye r, whereas the CBM is also at the
K position, but the spectral weight is completely at the MoS
2
layer.
Thus, the notion of an interfacial exciton is unperturbed despite the
fact that there is a strong enough interlayer coupling that changes
other parts of the electronic structur e significantly, but most im-
portantly, the local bandgap of the double-layer stacks is modulated
periodically with an amplitude of ~0.15 eV, forming a 2D elec-
tronic superlattice define d by the Moi ré pattern. This would also
mean that the interfacial exciton will experience a periodic potential
modulation as large as 0.15 eV.
CONCLUSION
Our study clearly shows that the atomic registry between vdW layers
dictates the behavior of interlayer electronic coupling, which can be
used as a designing parameter for novel 2D electronic systems based
on vdW heterostructures. The same principle should be commonly ap-
plicable to twisted vdW hetero-bilayers as well. The large amplitude of
bandgap modulation raises the prospects for device applications at
room temperature for these 2D electronic superlattices. Our findings
will stimulate research interests in similar superstructures extensively
formed in the flourishing family of 2D materials (33–37).
MATERIALS AND METHODS
Growth of MoS
2
/WSe
2
vdW heterostructure samples
The WSe
2
/MoS
2
vdW heterostructures were grown using the devel-
oped two-step CVD method (26, 38). First, an ML WSe
2
single crystal
was grown on the HOPG substrate. The WO
3
powder (0.6 g) was
placed in a quartz boat located in the heating zone center, and the
HOPG substrat e was put at the downstream side. The Se powder
was placed in a separate quartz boat at the upper stream side of the
quartz tube. The Se powder was heated to 260°C and brought to the
downstream side by an Ar/H
2
flow [Ar = 90 standard cubic centi-
meters per minute(sccm)andH
2
= 6 sccm],and the chamberpressure
was controlled at 20 torr. The WO
3
powder was heated to 935°C for
growth. After reaching the desired growth temperature, it was kept for
15 min, and the furnace was then naturally cooled down to room tem-
perature. The as-grown WSe
2
sample was then put into a separate
furnaceforthesecondstepofMoS
2
growth. The setup for MoS
2
syn-
thesis is similar to that for WSe
2
, and the reactants were changed to
MoO
3
(0.6 g) and S. The Ar gas flow was set at 70 sccm, and the pressure
was controlled at 40 torr.The MoO
3
and S sources were heated to 755°
and 190°C, held for 15 min for synthesis, and then naturally cooled
down to room temperature.
Fig. 5. Bias-dependent STM images of the Moiré pattern. The corresponding
sample bias voltage is labeled for each image as shown. A dashed red rhombus in
(E)and(F) represents a unit cell of the superlattice. A color bar is shown at the
bottom to represent the relative height differences (that is, low and high) in (A)to
(L). Scale bars, 5 nm in all images.
SCIENCE ADVANCES
|
RESEARCH ARTICLE
Zhang et al. Sci. Adv. 2017; 3:e1601459 6 January 2017 5of7
on January 7, 2017http://advances.sciencemag.org/Downloaded from