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: qijingshan@jsnu.edu.cn and jfeng11@pku.edu.cn.

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.

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