Tunable MoS2 bandgap in MoS2-graphene heterostructures
Abbas Ebnonnasir, Badri Narayanan, Suneel Kodambaka, and Cristian V. Ciobanu
Citation: Applied Physics Letters 105, 031603 (2014); doi: 10.1063/1.4891430
View online: http://dx.doi.org/10.1063/1.4891430
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APPLIED PHYSICS LETTERS 105, 031603 (2014)
Tunable MoS2 bandgap in MoS2-graphene heterostructures
Abbas Ebnonnasir,1,2 Badri Narayanan,1 Suneel Kodambaka,2,a) and Cristian V. Ciobanu1,a)
1
Department of Mechanical Engineering and Materials Science Program, Colorado School of Mines, Golden,
Colorado 80401, USA
2
Department of Materials Science and Engineering, University of California Los Angeles, Los Angeles,
California 90095, USA
(Received 10 April 2014; accepted 15 July 2014; published online 25 July 2014)
Using density functional theory calculations with van der Waals corrections, we investigated how
the interlayer orientation affects the structure and electronic properties of MoS2-graphene bilayer
heterostructures. Changing the orientation of graphene with respect to MoS2 strongly influences the
type and the value of the electronic bandgap in MoS2, while not significantly altering the binding
energy between the layers or the interlayer spacing. We show that the physical origin of this
tunable bandgap arises from variations in the S–S interplanar distance (MoS2 thickness) with the
interlayer orientation, variations which are caused by electron transfer away from the Mo–S bonds.
C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4891430]
V
Two-dimensional (2-D) materials can vary in terms of
their electronic properties (e.g., graphene is metallic,
hexagonal-BN (hBN) is insulating, and MoS2 is semiconducting) and, hence, are attractive, often in combinations, for
technological applications. Among this class of materials,
many studies have focused on molybdenum disulfide, which
exhibits a number of interesting properties such as bandgap
variation with the number of layers,1,2 high carrier
mobility,3,4 high Seebeck coefficient,5 photoconductivity,6,7
large excitonic effects,8 environmental sensitivity,9,10 and
high mechanical strength,11—properties which make this
material promising for next-generation optoelectronic and
nanoelectronic devices.12,13 Recent efforts have focused on
taking advantage of the individual properties of different 2-D
materials by fabricating heterostructures,14 which are vertical stacks of 2-D layers of dissimilar materials held together
by van der Waals (vdW) forces. Such heterostructures not
only can lead to opening of a bandgap in graphene (e.g., in
graphene-hBN bilayers)15 without impairing its electronic
mobility but can also develop direct bandgaps in multilayer
heterostructures16 or improve the on/off current ratios drastically (104 in graphene-MoS2).12,17,18
Motivation for the present study stems from the fact that
interlayer orientation can affect the electronic properties of
monolayers on their growth substrate,19,20 as well in multilayered structures of the same material.21 In this Letter, we
investigate the use of interlayer orientation between two different 2-D materials as a tuning parameter for the electronic
properties of the bilayer heterostructure. We present results
from vdW-corrected density functional theory (DFT) calculations on the effect of interlayer orientation on the electronic structure of the MoS2-graphene bilayers. We find that
the relative orientation of graphene with respect to the MoS2
layer strongly influences the value and type of the bandgap
in MoS2, while having little effect on both the interlayer
spacing and the binding energy. The physical origin of this
strong orientation dependence stems from particular atomic
a)
Authors to whom correspondence should be addressed. Electronic
addresses: cciobanu@mines.edu and kodambaka@ucla.edu
0003-6951/2014/105(3)/031603/5/$30.00
registries in which carbon atoms of graphene can effectively
weaken a significant number the MoS2 bonds, thus changing
both the thickness and the bandstructure of MoS2. Using a
tight-binding approach to rationalize the results of DFT calculations, we show that it is valence band edge at the C point
that is the most sensitive to the variations in MoS2 thickness,
sensitivity which gives rise to the computed changes in
MoS2 bandgap with graphene orientation. These results are
relevant for heterostructures as potential photovoltaic devices in which exciton pairs could be created in MoS2 and collected by graphene electrodes,22 and furthermore, provide
perspective on previous related works23–25 showing the tunability of the bandgap in single-layer MoS2 via tensile strain.
To study the effect that graphene has on the electronic
structure of the MoS2 monolayer, we constructed commensurate moire patterns of graphene on MoS2 for two interlayer
orientations with large spatial periodicities (refer to Fig. 1).
The DFT calculations were performed using the SIESTA
Package26 with Troullier-Martins pseudopotentials,27 vdW
exchange-correlation functional of Klimes et al. (optB88vdW version),28 and double-f basis set with polarization
functions. This basis set is sufficient, since the use of larger
sets did not lead to significant changes in the structural and
electronic properties.29 We have validated our computational
approach by reproducing the structural and electronic properties of MoS2 single-layers and bulk crystals; the validation
for graphene was performed in our earlier works20,21,30 on
epitaxial graphene. We have ensured commensurability of
the graphene and MoS2 layers by applying small biaxial
strains to graphene while keeping the lattice constant of
MoS2 at the relaxed equilibrium value of 3.204 Å. This value
for single-layer MoS2 is close to those reported from X-ray
diffraction experiments,31,32 and consistent with values from
other DFT approaches.33,34 Our use of the equilibrium value
for the lattice constant of MoS2 ensures that we do not introduce spurious strains that might obfuscate the effects of
interlayer orientation that we seek to reveal. For atomic
relaxations and bandstructure calculations, we used
Monkhorst-Pack C-centered 10 10 1 and 24 24 1
grids, respectively. The structural optimization was carried
105, 031603-1
C 2014 AIP Publishing LLC
V
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Ebnonnasir et al.
Appl. Phys. Lett. 105, 031603 (2014)
FIG. 1. Surface unit cells of the MoS2-graphene bilayer heterostructures
considered in this work: (a) 4:5z, denoting a 4 4 MoS2 cell and a 5 5 graphene cell, oriented so as the ½2
1
10 crystallographic directions of the two
layers in the heterostructure are parallel
pffiffiffi to one
pffiffiffianother, and (b) 4:3a, denoting a 4 4 MoS2 cell matched to a 3 3 3 3 graphene unit cell, in which
1
10 axis.
the armchair graphene direction is parallel to MoS2 ½2
out until the residual forces fell below 0.01 eV/Å. The electronic convergence tolerance was set to 106 eV. For all calculations, an energy cutoff of 250 Ry was chosen for the
integration mesh.
Our results on interlayer binding energies and structural
properties of the heterostructures35 shown in Fig. 1 are summarized in Table I. The strains in graphene are sufficiently
small that they do not unduly influence our conclusions
regarding the electronic properties of the MoS2 layer. The
binding energies and interlayer distance, measured between
graphene and the closest S atomic plane, do not change significantly with the graphene orientation. The atomic-scale
corrugations of MoS2 and graphene are practically inexistent. Large 2-D crystals undergo the formation of spontaneous long-range ripples, whose effect on the bandstructure is
presently not fully understood;36–40 by studying virtually flat
bilayers (i.e., without significant corrugation, Table I), we
ensure that the effects reported here are strictly due to interlayer orientation. The S–S interplanar spacing—i.e., the
thickness of the MoS2 layer—varies little with the orientation
(Table I); however, these small variations in thickness largely
control the electronic properties of the MoS2 layer.
As seen in the table, the binding energies are small,
since the two layers of the bilayer heterostructures are physically bonded. The binding energy is virtually the same for
the two structures (Table I), and, by itself, it does not affect
their electronic properties. The fact that there are no significant changes in the (weak) binding implies that many different graphene-MoS2 interlayer orientations would likely be
encountered in experiments, a situation which is typical for
weakly bonded 2-D systems;19,21,41 our models in Fig. 1 are
representative of two orientations. The properties of the heterostructure, as we shall see, are controlled by the interlayer
orientation. At a given interlayer orientation in a largeperiod moire pattern, the in-plane sliding of the layers does
not change their binding or the electronic properties.42
Figure 2 shows the bandstructures and orbital-decomposed
densities of states for the structures studied (Fig. 1). Graphene
retains its semi-metallic character, as there is no distinguishable
bandgap in the pz states. However, the bandgap in MoS2 varies:
1.674 eV for the 4:5z supercell, and 1.561 eV for 4:3a. As seen
in Fig. 2, the nature of the bandgap is different for the two
systems (Fig. 1): the gap is direct at the K point for the 4:5z
structure, and indirect (from K to C) for 4:3a. Although the
assignment of a bandgap type (direct versus indirect) when
using supercells that consist of multiple primitive cells is
affected by the well-known Brillouin zone folding effect,43 the
variations in badgap values and type are physically significant
for cells of the same size (4:5z and 4:3a) for which the folding
across the Brillouin zone is identical. Next, we will focus on
understanding why the orientation of graphene affects the
bandstructure of MoS2.
Figures 2(b) and 2(c) show that the MoS2 bandgap is
direct for the 4:5z configuration, but indirect for 4:3a. Since
both systems have the same 4 4 MoS2 cell, we focus on the
Table I information pertaining to MoS2 that can be influenced by the proximity of graphene. This key information is
the MoS2 thickness t, which changes from 3.227 Å to
3.174 Å. To understand how the thickness of MoS2 can affect
its bandstructure, we first study the bandgap as a function of
thickness using 1 1 unit cells—which ensures the removal
of zone folding artifacts. Our results for MoS2 1 1 are
shown in Figs. 3(a) and 3(b); in these calculations, the
atomic positions are kept fixed, and the bandgap is computed
for different values of t. At equilibrium (t ¼ 3.21 Å), the
bandgap is direct, while a slight decrease in the thickness
makes the bandgap indirect. As seen in Fig. 3(b), the
bandgap can be tuned over a span of 0.6 eV by varying the
MoS2 thickness over a span of only 0.2 Å—which is consistent with other reports.24,25 The reason for this high
TABLE I. Calculated properties of the MoS2-graphene systems: binding energy, corrugation of graphene, average spacing between graphene and MoS2, strain
imposed for commensurability, thickness, and corrugation of MoS2.
Strain %
System
4:5z
4:3a
Binding Energy
eV/Å2
Graphene Corrugation
Å
Interlayer Distance
Å
MoS2
Gr
MoS2 Thickness
Å
Corrugation
Å
0.051
0.051
0.086
0.014
3.110
3.131
0.0
0.0
þ3.0
0.7
3.227
3.174
0.001
0.002
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Ebnonnasir et al.
FIG. 2. Bandstructure and projected density of states for the bilayer heterostructures shown in Fig. 1. The pz, dxy =dx2 y2 , and dz2 characters of the bands
are indicated in black, green, and blue, respectively.
sensitivity of the bandgap is that the small variations in t
(e.g., 0.05 Å) amount to changing the length of the Mo–S
bonds by 1%: Since these bonds are strong and covalent, a
bondlength variation of 1% will significantly affect the
bandstructure.23,24
Fig. 3(a) shows that a small decrease in the thickness t
results in a large increase in energy of the valence band at C,
while the energy values of both the valence and conduction
edges at the K point remain largely unchanged. This disparity
in the thickness-dependence of the energies at the valence
band maxima at C and K causes the direct-indirect band gap
transition in the MoS2 layer [Fig. 3]. To understand the physical origin of such a disparity, we turn to a tight-binding (TB)
model that describes the band structure of MoS2 in terms of
electronic hopping processes associated with the 4d Mo and
3p S orbitals.44,45 In this description, the energy of the
valence edge Ej (j ¼ C, K) at C or K points is expressed as:45
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
j
s
2
2
j
h
þ
h
hj1 hj2
j
1
2
þ
E ¼
þ 2 hj3 ;
(1)
2
2
where hji are hopping terms related to different types of
atom-pairs. The terms hj1 and hj2 describe electronic Mo–Mo
FIG. 3. Bandgap variation for 1 1 MoS2 layer with respect to its thickness.
The direct bandgap is measured from the K point on valence band to the K
point on conduction band. The indirect bandgap is from the C point on the
valence band to the K point on conduction band.
Appl. Phys. Lett. 105, 031603 (2014)
hopping and S–S hopping, respectively, while hj3 is associated with Mo–S nearest-neighbor pairs.
In general, hopping terms hji (i ¼ 1, 2, 3; j ¼ C, K) in
Eq. (1) are influenced by the variation in the distances
between relevant atom pairs.44 However, in the range of
thickness values considered here (i.e., 3 Å–3.3 Å), the h1 and
h2 parameters should not be affected by t. This is because
they depend primarily only on the in-plane S–S and Mo–Mo
distances, which do not change. Therefore, the variations in
band edges at K and C (Eq. (1)) are mostly governed by
changes in hK3 and hC3 , respectively, which do vary significantly with t because the Mo–S bonds are directly affected
by thickness variations. Figures 4(a) and 4(b) show the
parameters and the correthickness-dependence of the hK;C
3
sponding valence band edges at K and C. The calculations
were performed35 using the parameters in Ref. 45. As seen in
Fig. 4, the variations of hC3 and EC are more pronounced than
their counterparts at the K point, which leads to significant
thickness-dependence of the valence band energy at C and to
the direct-to-indirect bandgap transition upon decreasing
layer thickness below its equilibrium value.
Last, we discuss the reason why the in-plane rotation of
graphene affects the MoS2 thickness, which, as we have
seen, leads to changes in the bandgap (Fig. 3). To this end,
we have determined the electronic transfer that occurs when
the two layers (graphene and MoS2) are brought together.
For the larger supercells, 4:5z and 4:3a, this electron transfer
is shown in Figs. 5(a) and 5(b). Focusing on Fig. 5(a), we
note that nine out of the 48 Mo–S bonds on the graphene
side (the three-lobed areas identified for clarity in Fig. 5(a)),
lose electronic density, meaning that they become weaker
and slightly longer (by 0.25%). In turn, the thickness t
increases beyond the equilibrium value of 3.22 Å and the
bandgap is direct according to Fig. 3. On the other hand, in
Fig. 5(b) where graphene is rotated by 30 , the three-lobed
clusters are not present because graphene has a different
registry with respect to the S atoms in MoS2. Consequently,
there is no electronic loss in the Mo–S bonds. Instead, we
find a weak and directional increase in the charge associated
with these bonds, which makes them slightly shorter; consequently, the S–S interlayer spacing t becomes smaller than
its equilibrium value, and the bandgap becomes smaller and
indirect.
FIG. 4. Effect of thickness on the MoS2 valence band, calculated via the
tight-binding model of Ref. 45. (a) Hopping terms hC3 and hK3 as functions of
thickness. (b) Energies of the valence band edges EC and EK at C and K
points, respectively, as functions of thickness. For clarity, we plot the variation of the quantities with respect to their corresponding equilibrium values
(e.g., DhC3 ¼ hC3 hC3;eq and DEC ¼ EC ECeq ). The inset shows a part of the
MoS2 structure (Mo: red, S: yellow) and defines the geometric parameters t,
rMoS ; rSS , and h.
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FIG. 5. Electronic charge transfer between the MoS2 and graphene layers
for two different relative orientations present in (a) the 4:5z and (b) the 4:3a
structures. The insets are side views for the normal cross-sections shown as
dashed lines in the main (top) views. The three-lobed contours in panel (a)
show the specific local registries that cause the weakening of Mo–S bonds.
In conclusion, we have shown that the orientation of
graphene in MoS2 heterostructures affects the bandgap of
MoS2, and have traced the physical origin of this result to
the highly sensitive dependence of the bandgap value on the
thickness of the MoS2 layer. Changes in registry between
graphene and MoS2 are accompanied by interfacial electronic transfer, which affects the Mo–S bondlengths and
hence the bandstructure. This suggests that graphene-MoS2
heterostructures are suitable for photovoltaic devices, in
which the exciton pair could be created in MoS2 and collected at graphene layers situated on either side of the MoS2
layer. Furthermore, our results provide another perspective
on previous works23,24 which showed tunability of the
bandgap via tensile strain in the MoS2 layer, and contributes
to an increasing body of work that exploits different stacking
registries for discovering useful electronic properties (e.g.,
Ref. 46).
The authors thank Dr. E. Cappelluti for discussions
regarding the tight-binding parametrization published in Ref.
45. The authors gratefully acknowledge funding from
National Science Foundation (A.E., B.N., and C.V.C.)
through Grant No. CMMI-0846858, and from the Office of
Naval Research (A.E. and S.K.), ONR Award No. N0001412-1-0518 (Dr. Chagaan Baatar). Supercomputer time for
this project was provided by the Golden Energy Computing
Organization at Colorado School of Mines.
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