Bandgap engineering of rippled MoS2 monolayer under external electric field
Jingshan Qi,1,a) Xiao Li,2 Xiaofeng Qian,3 and Ji Feng2,a)
1School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China2International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China3Department of Nuclear Science and Engineering and Department of Materials Science and Engineering,Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
(Received 25 March 2013; accepted 19 April 2013; published online 1 May 2013)
In this letter we propose a universal strategy combining external electric field with the ripple of
membrane to tune the bandgap of semiconducting atomic monolayer. By first-principles calculations
we show that the bandgap of rippled MoS2 monolayer can be tuned in a large range by vertical
external electric field, which is expected to have little effect on MoS2 monolayer. This phenomenon
can be explained from charge redistribution under external electric field by a simple model. This may
open an avenue of optimizing monolayer MoS2 for electronic and optoelectronic applications by
surface patterning. VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4803803]
In recent years, motivated by the discovery of gra-
phene,1,2 two dimensional (2D) materials have attracted more
attention for their physics and potential application in next-
generation electronics and optoelectronics.1,3–9 Although gra-
phene is the most studied 2D crystal,10 its lack of bandgap
hampers its application in semiconducting and photonic devi-
ces. This fact has motivated the research in other 2D crystals
with a large intrinsic bandgap, such as atomically thin
MoS2.11–16
Recently, monolayer MoS2 transistors have shown large
in-plane mobility and high current on/off ratio17 making this
material of great interest for electronic devices and sen-
sors.13,17,18 Especially, monolayer MoS2 is a direct bandgap
semiconductor, being attractive for optoelectronic applica-
tion, although bulk MoS2 is an indirect bandgap semiconduc-
tor.19 Further, the ability to manipulate the bandgap could
lead to other functionalities in these materials. Several strat-
egies have been employed to engineer bandgaps. For exam-
ple, tensile strain can be applied to tune bandgap of
monolayer MoS2.20,21 But, a direct-to-indirect bandgap tran-
sition occurs at only strain of 1%.20 Applying external elec-
tric field is another strategy to tune electronic properties of
materials. It has been shown that an external electric field
normal to flat monolayer MoS2 sheet cannot change its
bandgap.22 Although theoretical studies show that the
bandgap of double-layer MoS2 sheets can be modulated by
applying vertical external electric field,22 double-layer MoS2
is itself an indirect gap semiconductor, and indirect-to-direct
transition cannot occur under external electric field. It would,
therefore, be highly desirable to have capabilities to continu-
ously control the bandgap of large monolayer MoS2 and at
the same time can preserve its direct-gap character for build-
ing future photonic and optoelectronic devices. In this letter,
we propose an approach to meet this requirement. We first
built a monolayer MoS2 with rippled geometric modulation,
to which a vertical external electric field is applied.
We found that a small vertical electric field can reduce
largely the bandgap, distinctly different from flat monolayer
and at the same time preserve the direct-gap character. This
may open an avenue of optimizing monolayer MoS2 for
optoelectronic applications and shed light on the effect of
FIG. 1. (a) Monolayer MoS2 ripple structure. Band structures of zigzag
(b) and armchair (c) monolayer MoS2 ripple structures along y direction
under different external electric field (0.0, 0.1, 0.2 V/A) from first-principles
DFT calculation.
a)Authors to whom correspondence should be addressed. Electronic
addresses: [email protected] and [email protected].
0003-6951/2013/102(17)/173112/4/$30.00 VC 2013 AIP Publishing LLC102, 173112-1
APPLIED PHYSICS LETTERS 102, 173112 (2013)
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surface roughness, as represented by the nanopattern, on
electronic properties of thin films via surface wrinkling.
First, we take monolayer MoS2 as an example to show
our strategy. Experimentally spontaneous ripples have been
observed for monolayer MoS2.23 Here, we built a monolayer
MoS2 periodic ripple structure, as shown in Fig. 1(a). Period
length (l) of ripple structure along x direction is about 9.5 nm
and ripple height (h) along z direction is about 2 nm. The
lattice constant (c) along y direction (zigzag direction in hex-
agonal lattice) is 3.16 A (experimental value of bulk MoS2).
MoS2 ripple structures along armchair direction in hexagonal
lattice is similar to zigzag ripple structure, and lattice con-
stant along y direction is 5.473 A. Experimentally, periodic
ripple structure can be fabricated and controlled by putting
MoS2 monolayer on a wavy substrate, similar to graphene
case.24 First-principles density-functional theory (DFT) cal-
culations were performed in a supercell configuration using
the Vienna ab initio simulation package (VASP).25 We
employed projector augmented-wave (PAW) method,26 the
general gradient approximation (GGA)27 of exchange-
correlation functionals, an energy cutoff of 400 eV for the
plane-wave basis, and 1� 21� 1 Monkhorst-Pack k-points.
Geometry optimizations were performed with a criterion of
the maximum residual force less than 0.02 eV/A without any
symmetry constraints. The supercell was adjusted to main-
tain a sufficiently large separation between adjacent layers
(>20 A from surface to surface). A supercell used in calcula-
tion is shown by dashed line in Fig. 1(a).
We apply an external electric field on monolayer MoS2
ripple structure. External electric field is along z direction. The
most important finding is that the bandgap of MoS2 ripple
structure reduces rapidly with increasing the strength of elec-
tric field, although bandgap of flat monolayer MoS2 cannot
be changed under vertical external electric field. In Figs. 1(b)
and 1(c) we show, respectively, band structures of zigzag and
armchair monolayer MoS2 ripple structures under different
strength of electric field. For example, a 0.2 V/A of electric
field strength can reduce the bandgap from 1.76 to 1.0 eV, and
at the same time the direct gap character is preserved.
Furthermore, we also found that the decrease of bandgap is lin-
ear with the strength of electric filed, shown in Fig. 2. These
results indicate that the combination of electric field and ripple
is an effective strategy to tune bandgap of monolayer MoS2.
In addition, we also should point out the effect of ripple on
electronic properties of monolayer MoS2. Ripple introduces
strain into structure, resulting in the change of bond angles,
bond lengths, and curvature of atomic plane. Change of bond
angles and bond lengths will influence the electronic properties
of materials. We built several zigzag ripple structures with dif-
ferent curvatures, as shown in Fig. 3, and calculate their band
structures. We found that the bandgap decreases gradually with
FIG. 2. Bandgap versus applied electric field for zigzag monolayer MoS2
ripple structures with 19.5 and 23.5 A of h and armchair monolayer MoS2
ripple structures with 18.8 A of h. The fitted line is also shown. Bandgap
decreases linearly with increasing the strength of electric field.
FIG. 3. The band structures of zigzag
monolayer MoS2 ripple structures with
different curvatures. The bandgap
decreases gradually with the increase of
curvature, and a direct-to-indirect gap
transition occurs when bandgap decreases
to a certain value (about 1.73 eV).
173112-2 Qi et al. Appl. Phys. Lett. 102, 173112 (2013)
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the increase of curvature, and a direct-to-indirect gap transition
occurs when bandgap decreases to a certain value (about
1.73 eV). Although the strain introduced by ripple is not homo-
geneous, its influence on electronic properties is similar to a
homogeneous strain. Previous studies show that a direct-to-
indirect bandgap transition occurs at only strain of 1%.20 This
also indicates that strain engineering is not an applicable
method to tune the bandgap for preserving direct-gap character.
For armchair ripple structure, we do not find the direct-indirect
gap transition at curvature range studied. This can be well
understood from Brillouin zone (BZ) folding.28 As shown in
Fig. 1(a), the supercell of rippled MoS2 monolayer has a large
non-redundant lattice parameter (about 2 nm) along x direction,
while the lattice parameter remains small (3.16 A for zigzag
ripple and 5.473 A for armchair ripple) along y direction.
Accordingly, the hexagonal BZ of perfect MoS2 monolayer is
folded into rectangle for the supercell of rippled MoS2 mono-
layer, where the width in x direction is very narrow due to the
corresponding large period length in the real space. The K and
C points in original BZ are still well separated along y direction
in the momentum space for the BZ of zigzag ripple, while these
two points are adjacent with the same y-coordinate and a small
shift in x direction for the BZ of armchair ripple. With strain,
there is a transition from direct bandgap (K!K point) to indi-
rect bandgap (C!K point) for perfect flat MoS2.20 The transi-
tion is also clearly seen for zigzag ripple with the increase of
curvature in Fig. 3, due to well-separation of K and C point in
the momentum space. However, there is not an apparent direct-
to-indirect bandgap transition due to small dispersion between
the adjacent K and C points for armchair ripple.
In the following, we will explain why the bandgap of
rippled monolayer MoS2 can be tuned by vertical external
electric field, which is invalid for flat monolayer MoS2. A
schematic diagram for the decrease of gap under external
electric field is shown in Fig. 4. Position of curvature maxi-
mum in monolayer MoS2 ripple structure is called peak or
valley (marked in Fig. 4). Under external electric field along
þz direction, the electrostatic energy felt by an electron at
peak region becomes higher and that at valley region
becomes lower. This makes the band energy of electrons in
peak region rise and lower in valley region. Moving of
energy bands in opposite direction results in the decrease of
bandgap. Therefore, the Highest Occupied Molecular Orbital
(HOMO) level of electrons in peak region and the Lowest
Unoccupied Molecular Orbital (LUMO) level of electrons in
valley region become HOMO and LUMO level of overall
superstructure, respectively. According to this model, under
electric field the HOMO and LUMO should locate at peak
and valley regions of ripple, respectively. This is confirmed
by charge density distribution of HOMO and LUMO from
first-principles calculation, shown in Fig. 4(b). We also can
see that LUMO is primarily of Mo dz2 character, and HOMO
is primarily of Mo dxy and dx2�y2 in character. As a compari-
son, we should also point out that charge density distribution
of HOMO and LUMO in the absence of external electric
field is overlapped. The spatial separation of charge carriers
in such field-induced semiconducting MoS2 ripple structure
should give rise to interesting effects in transport measure-
ments and hold the promise of a bright future for use in pho-
tovoltaics. Moreover, we anticipate similar effects in the
presence of chiral rippled monolayer (that is, the ripples
propagate along neither armchair nor zigzag direction),
owing to the similar field modulation by the heights of
sample in an external potential gradient. This is a universal
strategy combining external electric filed with ripple of
membrane to tune the bandgap in semiconducting atomic
membrane.
According to above model, the change of bandgap can
be expressed as DEg ¼ eSEf ðhziHOMO � hziLUMOÞ, where
hziHOMO and hziLUMO represent the distribution center of
HOMO and LUMO along the direction of the applied exter-
nal field (z direction in Fig. 1), Ef is the strength of applied
external electric field, e is the electron charge, and S is the
FIG. 4. (a) Shows the schematic diagram for the decrease of bandgap under
external electric field. Position of curvature maximum in monolayer MoS2
ripple structure is called peak or valley. Under vertical external electric field
(direction marked by green arrow), the electrostatic energy felt by an elec-
tron at peak (valley) region is higher (lower). This makes band energy of
electrons in peak (valley) region rise (lower). The dashed lines represent
energy levels in the absence of external electric filed, and solid lines repre-
sent energy levels in the existence of electric filed, indicating the opposite
moving direction of band energy of electrons in peak and valley regions
under the external electric field. Moving of energy levels in opposite direc-
tion results in the decrease of bandgap. D1 and D2 are the change of energy
level of electron, respectively, in peak and valley regions, and thus the
change of bandgap is DEg ¼ D1þ D2. (b) Charge density distribution of
LUMO and HOMO under 0.1 V/A of electric field strength from first-
principles calculation.
173112-3 Qi et al. Appl. Phys. Lett. 102, 173112 (2013)
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coefficient describing the response intensity of material to
the external electric field and thus should be characteristic of
the material. Due to the screening effect of the induced
polarization under electric field, S is not equal to 1. Since the
HOMO and LUMO localize, respectively, on peak and val-
ley region, hziHOMO � hziLUMO should be close to ripple
height h. We calculated hziHOMO � hziLUMO for several struc-
tures under different electric field strength and found that the
values of hziHOMO � hziLUMO quickly converge with the
strength of electric field, shown in Fig. 5. This indicates that
HOMO and LUMO rapidly localize at peak and valley
regions under external field. In addition, the converged
values of hziHOMO � hziLUMO are 17.9, 18.0, and 21.8 A,
indeed close to h, 18.8, 19.5, and 23.5 A, respectively, for
three ripple structures. Approximate equality between
hziHOMO � hziLUMO and h also indicates strong localization
of HOMO and LUMO in peak and valley regions. So the
reduction of bandgap DEg is only function of electric filed Ef
for specific structure and material. By linear fitting of data,
shown in Fig. 2, we get S for several structures and found
that S is approximately 0.23 for all MoS2 ripple structures
including zigzag and armchair ripple with different h, indi-
cating S is a characteristic quantity for specific material.
In conclusion, in this letter we propose a universal strat-
egy combining external electric field with ripple of mem-
brane to tune the bandgap of semiconducting atomic
membrane. Taking monolayer MoS2 as an example, we
show that the bandgaps of rippled monolayer MoS2 can be
tuned largely by vertical external electric field, although this
is invalid for flat monolayer MoS2. This phenomenon can be
explained from charge redistribution of HOMO and LUMO
under external electric field by a simple model. A character-
istic coefficient S is used to describe the response intensity of
material to the external electric field. We find this character-
istic quantity is 0.23 for MoS2. Our model should be general
for semiconducting atomic membrane. This may open an
avenue of optimizing monolayer MoS2 for electronic and
optoelectronic applications by surface patterning.
This work was supported by the National Natural
Science Foundation of China (Grant No. 11204110), the
Natural Science Foundation of the Jiangsu Higher Education
Institutions of China (Grant No. 12KJB140005), and the
Priority Academic Program Development of Jiangsu Higher
Education Institutions (PAPD).
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FIG. 5. hziHOMO � hziLUMO versus applied electric field for zigzag mono-
layer MoS2 ripple structures with 19.5 and 23.5 A of h and armchair mono-
layer MoS2 ripple structures with 18.8 A of h.
173112-4 Qi et al. Appl. Phys. Lett. 102, 173112 (2013)
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