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Electronic properties of the MoS2-WS2 heterojunction

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a r X i v : 1 2 1 2 . 0 1 1 1 v 3 [ c o n d - m a t . m e s - h a l l ] 2 8 F e b 2 0 1 3
Electronic properties of the MoS
2
−
WS
2
heterojunction
K. Ko´smider
1
, J. Fern´andez-Rossier
1
,
2
(1)
International Iberian Nanotechnology Laboratory (INL),Av. Mestre Jos´e Veiga, 4715-330 Braga, Portugal
(2)
Departamento de F´ısica Aplicada, Universidad de Alicante, 03690 San Vicente del Raspeig, Spain
(Dated: March 1, 2013)We study the electronic structure of a heterojunction made of two monolayers of MoS
2
andWS
2
. Our ﬁrst-principles density functional calculations show that, unlike in the homogeneousbilayers, the heterojunction has an optically active band-gap, smaller than the ones of MoS
2
and WS
2
single layers. We ﬁnd that that the optically active states of the maximum valence and minimumconduction bands are localized on opposite monolayers, and thus the lowest energy electron-holespairs are spatially separated. Our ﬁndings portrait the MoS
2
−
WS
2
bilayer as a prototypical examplefor band-gap engineering of atomically thin two-dimensional semiconducting heterostructures.
Engineering the electronic properties of semiconduc-tors by using heterojunctions has been the central con-cept in semiconductor science and technology for 5decades.
1,2
With the advent of quantum wells, band-gap engineering of quasi-two dimensional semiconductorsmade it possible to observe a wealth of new physical phe-nomena, including the integer and fractional quantumHall eﬀects in modulation doping GaAs/GaAlAs,
3,4
thecondensation of both excitons in double GaAs quantumwells of GaAs,
5
and exciton-polaritons in II-VI quantumwells
6,7
and, more recently, the Quantum Spin Hall phasein CdTe/HgTe quantum wells.
8
The isolation
9
of truly two dimensional crystals, suchas graphene and MoS
2
, and their use to fabricate ﬁeld ef-fect transistors,
10,11
has opened a wealth of new venues inphysics and material science in general, and more specif-ically in the design heterostructures.
12
Thus, graphenebilayers
13
and graphene on boron nitride
14
have diﬀerentelectronic properties than freestanding graphene.The properties of bulk MoS
2
and its nanostructures,such as nanotubes,
15,16
fullerenes,
17
and nanoislands,
18
have been studied for a long while, including even chem-ically exfoliated single planes.
19
More recently, the studyof electronic and optoelectronic devices based on a singleMoS
2
layer has taken impetus for several reasons. First,it was found that monolayers of MoS
2
feature a directband gap of 1.8 eV with strong photoluminescence,
20,21
as opposed to bulk MoS
2
which has indirect band gapof 1.29 eV. Second, the fabrication of a high mobilityﬁeld eﬀect transistor based on single MoS
2
layer hasbeen reported.
22
Third, the combination of hexagonalsymmetry, large spin-orbit coupling and lack of inversionsymmetry, give rise to gapped graphene like bands, withtwo valleys and strong spin-valley coupling.
23
Taking ad-vantage of these unique properties, optical spin pump-ing is turned into valley-polarized photo carriers,
24–28
which opens new possibilities in the emerging ﬁeld of valleytronics.
23
Importantly, other transition metal dichalcoghenides,such as WS
2
, as well as MoSe
2
and WSe
2
are expectedto have similar properties,
29–32
and the ﬁrst experimen-tal demonstrations of monolayer WS
2
have just beenreported.
33
All of the above naturally leads us to investi-
FIG. 1. (Color online) Schematic views of the MoS
2
−
WS
2
heterojunction of diﬀerent stacking (i.e. C7, C27, AA, T).Each stacking is obtained either by a monolayers translationT and /or a rotation R with respect to each other. Red, gray,and yellow spheres represent W, Mo, and S atoms respectively.
gate the electronic properties of transition metal dichal-chogenide (TMD) multilayers
34–36
. Here we report ourresults on the simplest case, a bilayer of MoS
2
and WS
2
,which both have the same crystal structure and very sim-ilar lattice constant. In particular we are interested inhow the stacking of diﬀerent TMD monolayers (see Fig.1) can result in heterostructures with electronic prop-erties diﬀerent from the homogeneous TMD monolayersand multilayers,Our calculations were performed with the Vienna
ab-initio
package (
VASP
),
37
based on the local density-functional approximation,
38
plane-wave basis (
E
cut
=400 eV) and non-collinear projector-augmented waves(PAW) method.
39,40
We treat the both the transitionmetal orbitals 4
p
, 5
s
, 4
d
together with the Sulphur orb-tials 3
s
and 3
p
as valence states, and the rest are con-sidered as core. We use the Perdew-Burke-Ernzerhof’s
41
version of generalized gradient approximation to describethe exchange correlation density functional. All calcu-lations are carried out using a 1
×
1 supercell with vac-uum thickness not smaller than 17 ˚A. The Γ-centeredMonkhorst-Pack’s
42
mesh (6
×
6
×
1) of the
k
-points was
2
-7-6-5-4-3
E - E
v a c
( e V )
MoS
2
WS
2
Γ
M K
Γ
K’
MoS
2
-WS
2
Γ
M K
Γ
K’
Γ
M K
Γ
K’-7-6-5-4-3
E - E
v a c
( e V )
1 M L 2 M L
a) b)c)d) e)f)
1
FIG. 2. (Color online) Band structures of: a) MoS
2
mono-layer, b) WS
2
monolayer, d) MoS
2
bilayer, e) WS
2
bilayer,f) MoS
2
−
WS
2
heterojunction. The stacking of bilayers is C7(see Fig. 1(b)). c) scheme of the BZ with the line along whichthe band structures are calculated. E
vac
stands for vacuumenergy. The Fermi energy lies at the intersection of white andyellow regions.
used to sample the BZ.For reference, we discuss ﬁrst the electronic propertiesof isolated MoS
2
and WS
2
monolayers (MLs).
29–32,43,44
The crystal structure of 2H-MoS
2
(2H-WS
2
) consists of two 2D parallel triangular lattices of S atoms separatedby the same lattice of Mo (W) atoms translated by 1
/
3of the unit-cell diagonal, with lattice constant
a
= 3
.
19 ˚A(
a
= 3
.
20˚A).
29
The corresponding Brillouin zone (BZ) isalso hexagonal, with two inequivalent
K
and
K
′
points(valleys). We show the corresponding energy bands inFigs. 2(a) and 2(b)), which are in agreement with pre-
vious work using the same methodology.
30,31
Both MLsare direct band semiconductors with a maximum valenceband (VB) and minimum conduction band (CB) locatedin the
K
and
K
′
valleys. The band-gap values equal1.58 and 1.50 eV for MoS
2
and WS
2
respectively. Ourcalculations also show that, when referred with respectto the vacuum energy, the band structures of both MLsare shifted (cf. Figs. 2(a) with 2(b)), on account of the
diﬀerent electronegativity of the Mo and W.Because of the lack of inversion symmetry and a strongspin-orbit coupling (SOC) the valence and conductionbands are spin-split at the
K
and
K
′
points. The signof the spin splitting changes from
K
to
K
′
resulting inthe so called strong spin-valley coupling.
23
The splittingis higher in WS
2
ML (435 and 27 meV for VB and CBrespectively) than MoS
2
ML (147 and 3 meV for VB andCB respectively) due to the higher atomic number of Wthan Mo.The band-dependence of the spin splittings is ac-counted for by the atomic orbital composition of thestates. Our population analysis reveals that, at the
K
point, the CB minimum is mostly made by Mo
d
z
2
(
l
= 2
,m
= 0) orbitals, whereas the VB maximumdominant contribution comes from the
d
xy
and
d
x
2
−
y
2
(
l
= 2
,m
=
±
2) orbitals. To leading order in theSOC, this should yield a non-zero valley dependent spin-splitting only in the VB, in agreement with the toy modelproposed by Xiao
et al.
23
However, both VB and CBstates at the
K,K
′
points have small contributions com-ing from the Sulphur
p
x
and
p
y
orbitals (
l
= 1
,m
=
±
1).These are probably behind the small but ﬁnite splittingin the CB.We now discuss the electronic properties of the bilayersthat can be formed stacking the WS
2
and MoS
2
mono-layers. We have veriﬁed that the main features of theelectronic structure are quite insensitive to the stacking(see Fig. 1 for the diﬀerent stackings), thereby we focuson the band structure of the C7 stacking (see Fig. 1(b))presented in Fig. 2(f). This is the stacking of bulk MoS
2
and WS
2
. Comparison of monolayer and bilayer bandsin Fig. 2 indicates that interlayer coupling is not strong.The electronic structure of Mo-Mo and W-W bilayers(Figs. 2(d), (e)) can be rationalized in terms of two con-cepts: interlayer coupling of degenerate monolayer states,which splits most of the monolayer states, and the exis-tence of a symmetry center in the C7 stacking, whichprevents spin splittings. The interlayer splitting is signif-icantly stronger for the valence band at the Γ point thanfor the VB and CB at K points. As a result, the highestVB state moves to the Γ point for the W-W and Mo-Mobilayers, which become indirect gap systems.In the case of the Mo-W heterojunction the inter-layer coupling competes with the energy diﬀerence of themonolayer states, shown in Fig. 2 (a),(b). As a result,the VB at the Γ point is almost degenerate (∆
E
VB
= 27meV) with the top of the VB at the K and K’ points.Consequently, a signiﬁcant population of photoexcitedholes will be available at the K and K’ points, and pho-toluminescence will be not quenched. In this sense, theMoS
2
−
WS
2
heterojunction – unlike the homogeneous bi-layers – will be optically active. In addition, the Mo-Wbilayer does not have inversion symmetry, so that spinsplittings at the K and K’ points occur like in the mono-layers.A summary of the electronic states in the neighbor-hood of the
K
point, relevant for the inter-band opticalexperiments, both for MoS
2
, WS
2
and the Mo-W bilayeris shown in Fig. 3. It is apparent that interlayer cou-pling at this point is negligible and the bilayer bands arenothing but a superposition of the monolayer states. Asa result, the top of the VB is in the W layer and thebottom of the CB name lies in the Mo layer, forminga type II structure.
2
In addition the Mo-W bilayer gapis 1.2eV, 0.3eV smaller than the gap of the monolayers.In contrast, the top of the VB at the Γ point is delo-calized in both planes. The resulting scheme of levels isshown in Fig. 3(d). We expect that intra-layer transi-tions have a stronger quantum yield, on account of theirlarger electron-hole overlap,
2
but relaxation to the lowerenergy spatially separated electron-hole pair is expected.
3
K
-6-5-4
E - E
v a c
( e V )
MoS
2
K
WS
2
K
MoS
2
-WS
2
WS
2
MoS
2
T
W - W
T
M o - M o
T
W - M o
T
W - M o
ΚΚ Γ Γ Κ
a) b) c) d)
FIG. 3. (Color online) Zoom of band structures at the
K
point for : a) MoS
2
monolayer, b) WS
2
monolayer, c) MoS
2
−
WS
2
bilayer, d) scheme of possible optical transitions in the MoS
2
−
WS
2
bilayer. Blue (red) lines describe the bands of the stateslocalized on the W (Mo) atoms. Bold (dashed) lines describe the states of spin up (down).
We ﬁnally comment on the limitations of our method-ology. First, PBE is known to underestimate the bandgap. The use of either non-local functionals
31
and/orGW approximation
30,43
yields a better agreement withthe experiments. Second, excitonic eﬀects, not includedin the band structure calculation, are known to produce alarge shift in the absorption threshold and photolumines-cence peaks.
31
In spite of this, we expect that the band-gap reduction and the segregation of electrons and holesin diﬀerent atomic planes will be conﬁrmed by experi-mental work and/or more sophisticated methodologies.In summary, we have studied the electronic proper-ties of the MoS
2
−
WS
2
system as an example of transi-tion metal dichalcogenide two-dimensional heterostruc-ture. We ﬁnd that, in contrast to the Mo-Mo and W-Wbilayers, the band-gap is direct. Additionally we ﬁndthat the lowest energy electron and highest energy holestates in the optically active
K
point are localized on dif-ferent monolayers. In this sense, the Mo-W bilayer formsa type II heterostructure. The combination of band gapengineering in heterojunctions found here, together withthe reported electrical control of electronic and opticalproperties in these systems
22,35,36,45
, hold the promiseof a bright future for optospintronics in two dimensionaltransition metal dichalcogenides.We acknowledge J. W. Gonz´alez and F. Delgado forfruitful discussions. This work has been ﬁnancially sup-ported by MEC-Spain (Grant Nos. FIS2010-21883-C02-01, FIS2009-08744, and CONSOLIDER CSD2007-0010)and Generalitat Valenciana, grant Prometeo 2012-11.
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