Table Of ContentMaterials properties of out-of-plane heterostructures of MoS -WSe and WS -MoSe
2 2 2 2
Bin Amin
Department of Physics, Hazara University, Mansehra, Karakoram Hwy, Dhodial 21120, Pakistan
Thaneshwor P. Kaloni, Georg Schreckenbach, and Michael S. Freund
Department of Chemistry, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
Abstract
6 Based on first-principles calculations, the materials properties (structural, electronic, vibrational, and optical properties) of
1 out-of-planeheterostructures formed from thetransition metal dichalcogenides, specifically MoS2-WSe2 andWS2-MoSe2 were
0 investigated. TheheterostructuresofMoS2-WSe2andWS2-MoSe2arefoundtobedirectandindirectbandgapsemiconductors,
2 respectively. However, a direct band gap in the WS2-MoSe2 heterostructure can be achieved by applying compressive strain.
n Furthermore, the excitonic peaks in both monolayer and bilayer heterostructures are calculated to understand the optical
a behavior of these systems. The suppression of the optical spectrum with respect to the corresponding monolayers is due to
J interlayercharge transfer. Thestability of thesystemsunderstudyis confirmed byperforming phonon spectrum calculations.
9
2
Transition metal dichalcogenides (TMDCs) are teractions enhance the coupling between the two mono-
] promising materials for various applications [1–5], for layers. An atomically thin p-n junction diode has been
i
c example field-effect transistors. Quantum confinement synthesized from a stacked MoS2-WSe2 heterojunction.
s in these semiconductors going from bulk to monolayer It shows an excellent current rectification and rapid
-
l results in the transition from indirect to direct band photo-response with a high quantum efficiency.[24] Lee
r gap semiconductor, which makes them superior in et al. [25] also fabricated atomically thin p-n hetero-
t
m nano-electronics applications as compared to the well junctions from MoS2 and WSe2 monolayers and demon-
. studied material graphene that has no band gap.[6–14] strated that the tunneling-assisted coupling between
t
a In addition, due to their distinct electronic properties, MoS2 andWSe2 layersisresponsibleforthetunabilityof
m TMDC monolayers have been utilized in logic circuits the electronic andoptoelectronicresponses. The van der
- [15] as well as in memory devices.[16] Waals heterostructures of MoS2-WSe2 and MoS2-MoSe2
d have been demonstrated using ultra-low frequency Ra-
Stacking of TMDCs monolayers in order to form het-
n
man spectroscopy.[26] It has been shown that a special
o erostructureswithvanderWaalsinteractionsenablesthe
Raman feature arises from the layer-breathing mode vi-
c creationofatomicallysharpinterfaces[17],andalsopro-
[ vides a route to a wide variety of semiconductor hetero- bration between two incommensurate monolayers. Due
junctions with interesting properties.[18] Type-II band to the charge transfer across the interface of the MoS2
1
v alignment in these heterostructures has been demon- and WSe2 heterostructures, a photovoltaic effect has
been observed.[27] Furthermore,a high gate coupling ef-
8 strated, which reduces the overlap between the electron
ficiency of about 80% has been demonstrated for tuning
2 and hole wave functions by slowing down the charge
0 recombination, which in fact is expected to be an effi- the band offsets at the MoS2-WSe2 vertical interface in
0 dual-gate device.[28]
cient way for light detection and harvesting.[17, 19] Re-
0
cently, the long-lived interlayer excitons have been in- However, the structural and electronic properties of
.
2 vestigatedintheMoSe2-WSe2 heterostructure,whichin- such heterostructures are not well understood. There-
0
deedopensthelargeavenueforlight-emittingdiodesand fore, in the present work, comprehensive insight is
6
1 pholvoltaic devices.[20]. The structural, electronic, pho- gained into the physical properties of the MoS2-WSe2
: tocatalytic,andopticalpropertiesofout-of-planeandin- and WS2-MoSe2 heterostructures that are investigated
v planeheterostructuresofTMDCshavebeeninvestigated with/without biaxial compressive strain using den-
i
X byemployingfirst-principlescalculations.[21]Ithasbeen sity functional theory calculations (see supplementary
demonstrated that all the out-of-plane heterostructures material).[29]Thereductionoftheopticalspectrumwith
r
a show an indirect band gap with type-II band alignment. respect to the corresponding monolayers is analyzed.
However, a direct band gap can be obtained by the ap- Furthermore, the stability of the systems under consid-
plication of tensile strain in specific cases, such as the eration is confirmed by means of the phonon spectrum.
heterostructures of MoSe2-WSe2 and MoTe2-WTe2. It The out-of-plane heterostructures were created by us-
has also been predicted by theoretical calculations that
ingtheaverageoftheexperimentallatticeconstantofthe
the direct band gaped bilayer can be generated by al-
constituentmonolayersandbykeepingonelayerontopof
teration of the individual monolayers of TMDCs in the
theothersuchthattheS/Seatomsofonelayersitontop
heterostructures.[22]
of the W/Mo of the other layer [22], see Fig. 1. We have
AverticalheterostructureofMoS2-WSe2hasbeenfab- also cross-checkedthe heterostructures by using the lat-
ricated by stacking of MoS2 and WSe2 monolayers.[23] tice parameters of the constituent monolayers individu-
Based on the shifts observed in the Raman and photo- ally. Aftertherelaxationofboththelatticeconstantand
luminescence spectra,it has been found that thermalin- positions,thelattice parameteroptimizedtothe average
1
MoS-WSe WS-MoSe
MoS2-WSe2 WS2-MoSe2 MoS2-WSe2 WS2-MoSe2 2 2 2 2 2
PBE HSE06
1
a (˚A) 3.25 3.25 3.22 3.22 V)
e
dspacing 3.37 3.36 3.33 3.34 E (F 0
X–S (˚A) 2.43 2.43 2.40 2.40 E- -1
X–Se(˚A) 2.53 2.52 2.50 2.50 -2
E (eV) -0.20 -0.21 -0.24 -0.25 2
b
Eg (eV) 0.33 0.87 0.94 1.58 V) 1
e
∆VB (eV) 0.46 0.19 0.44 0.18 E (F 0
∆CB (eV) 0.003 0.019 0.026 0.035 E- -1
TABLE I: Lattice constant, interlayer spacing, bond lengths -2Γ Κ Μ ΓΓ Κ Μ Γ
(X=Mo, W), binding energy, band gap, and band splitting
(valence and conduction bands) for the out-of-plane het- FIG. 2: Band structures of the out-of-plane heterostructures
erostructures. obtainedusingPBE(toprow)andHSE06(bottomrow)func-
tionals, where red bandsare obtained understrain.
(a) (b)
S Mo
The bandstructures presented in Fig.2 show that the
heterostructure MoS2-WSe2 is a direct band gap semi-
conductor, while WS2-MoSe2 is found to be an indirect
Se band gap semiconductor.[22] Normally, the PBE func-
W
tionalunderestimatesthebandgap,therefore,theHSE06
functionalisusedsinceithasalreadybeendemonstrated
that the HSE06 functional provides correct value of the
band gap in terms of experimental observation.[30] The
FIG. 1: Charge density difference isosurfaces for (a) MoS2- band structures shown in Fig. 2 indicate the direct and
WSe2 and (b) WS2-MoSe2 heterostructures with an isovalue indirectbandgapnatureoftheheterostructuresofMoS2-
of 0.001 eV/˚A, where red and blue color represent positive WSe2 and WS2-MoSe2, respectively. The indirect band
and negative charges, respectively. gap nature of the WS2-MoSe2 heterostructure is due to
the fact that the valence band maximum (VBM) is con-
tributed by the Mo atom, for which the spin-orbit split-
value of the corresponding monolayers, as summarized ting is smaller because of lower atomic number as com-
in Table I. In principle, the PBE calculations overesti- paredtotheWatom. Thus,theVBMliesattheΓ-point
mate, while HSE06 calculation give the correct value to of the Brillouin zone.
the average of the experimental lattice constant of indi- To understandthe contributionsfromdifferent atomic
vidualmonolayersincorrespondingheterostructures.[30] sites, we have investigated the weighted band structure
Hence,afterrelaxationthe MoSe2 andWSe2 monolayers of both the heterostructures of MoS2-WSe2 and WS2-
suffered from 1.8% compressive strain, while the MoS2 MoSe2. It is clear from Fig. 3 that the conduction
and WS2 monolayers suffered from the same amount band minimum (CBM) at the K-point is due to the Mo
of tensile strain in agreement with Ref. [23]. The ob- d3z2−r2 orbital and the VBM at the K-point is due to
tained value of the interlayer spacing agrees well with theWdx2−y2 andWdxy orbitalsoftheMoS2-WSe2 het-
experimentallyandtheoreticallyobtainedvaluesforhet- erostructure. This localization of the VBM and CBM
erostructuresmade of MoS2 and WS2 and graphene and in different monolayers physically separates the electron
WS2 or WSe2.[31, 32] The calculated bond lengths pre- hole pairs. The strong coupling between the S/Se p or-
sented in Table I for both MoS2-WS2 and WS2-MoSe2 bitals and Mo/W dxz and dyz orbitals leads to a large
agree well with those of the corresponding monolayers splitting between their bonding and anti-bonding states,
(Ref. [33]) inferring weak van der Waals interactions be- hencetheseorbitalsdonotcontributetothebandedges.
tween monolayers in the heterostructures. These results show that the VBM and CBM are con-
The binding energies were obtained as E = tributedfromdifferentmonolayers. Thistypeofarrange-
EMoX2-WX2 −EMoX2 −EWX2, where EMoX2-WX2 (X=S, mentwherethe holesandelectronsareattributedto dif-
Se)isthetotalenergyoftheheterostructure,andEMoX2 ferentlayersisknownastype-IIbandalignment.[17]The
and EWX2 are the total energies of the corresponding homogeneous bilayersof TMDCs do not possess this net
monolayers. The calculated binding energies presented charge separation,so that an external electric field is re-
in Table I show that the out-of-plane heterostructures quiredtoachieveatype-IIbandalignment[35]. However,
havenegativebindingenergies,whichconfirmsthatthese there is no electric field in our calculations for the het-
systems are energetically favorable. erostructures that nevertheless show type-II band align-
2
(a) (b) (c) 30
2 MoS2
V) 1 15
E (eF 0 30
E- --221 ε (ω)215 MoS2-WSe2
E (eV)F 01 3105 WSe2
E- -1
-2Γ Κ Μ Γ Γ Κ Μ Γ Γ Κ Μ Γ 0
30
WS
FIG.3: Weightedbandsof theMoS2-WSe2 out-of-planehet- 15 2
erostructure; Mo (first row), W (second row) for (a) d3z2−r2, 30
(b) dx2−y2, and (c) dxy orbitals. ε (ω)215 WS2-MoSe2
30
(a) (b) (c) MoSe
2 15 2
V) 1
E-E (eF-01 00 1Energy (eV)2 3
-2
2 FIG. 5: Imaginary part of the dielectric function of the het-
E (eV)F 01 efuronscttriuonctuofrepshiontocnomenpearrgisyo.n with the parent monolayers as a
E- -1
-2Γ Κ Μ Γ Γ Κ Μ Γ Γ Κ Μ Γ
FIG. 4: Weighted bands of WS2-MoSe2 out-of-plane het- WSe2 was found to be larger than that of pristine MoS2
(ebro)sdtrxu2−ctyu2r,ea;nMdo(c()firdsxtyroowrb)i,taWls.(second row) for (a) d3z2−r2, manodnoslmayaellresr(t∆haPsonBEth=at0.o1f5theVe parnisdti∆neHsoWSES=e20.2m0oenVol)ay[3e3rs]
(∆PBE=0.47 eV and ∆HSE=0.63 eV) [33]. The same
so so
behaviorisfound forthe heterostructureofWS2-MoSe2.
ment,whichmaybeduetotheintrinsicelectricfieldthat The splitting ofthe valenceband (holes)andconduction
arises due to the buckled structures.[36–38] band (electrons) indicates that the formation of the het-
In contrast to the MoS2-WSe2 heterostructure, the erostructure is a promising route to engineer the band
CBMattheK-pointoftheWS2-MoSe2heterostructureis gapandsplitting. Thesesystemsmaythereforebe inter-
due to the W d3z2−r2 orbital. Without applying strain, esting for optoelectronic and spintronic devices.[41]
the VBM is at the Γ-point, and it is also due to the Further, the imaginary parts of the dielectric function
W d3z2−r2 orbital with a major contribution from the ǫ2(ω) of the monolayers and the heterostructures were
Mo d3z2−r2 orbital. Hence, the heterostructure of WS2- calculated by solving the Bethe-Salpeter equation. The
MoSe2 possesses a type-I band alignment, in agreement results presented in Fig. 5 show that the optical transi-
withthepredictionmadebyRef. [39]. Strainengineering tions are dominated by excitons. For monolayer MoS2,
is a widely used strategy to achieve tunable band gaps excitonic peaks are observed at 1.77 eV and 1.92 eV,
for two-dimensional materials. [40] Therefore, with the while for monolayer WSe2 they appear at 1.50 eV and
application of 0.5% compressive strain, the VB at the 1.96 eV. Similarly, these peaks appear at 1.77 eV and
K-point shifts to higher energy, which is due to the Mo 2.24eVforWS2,while at1.48eVand1.72eVformono-
dx2−y2 andModxy orbitals. Whereas,theVBMattheΓ- layer MoSe2. The position of the first excitonic peaks
pointshifts tolowerenergies. Hence,boththe VBMand are in good agreement with the experimental values of
CBM separate the electron hole pairs to different layers MoS2 (1.85eV), WSe2 (1.59eV),WS2,andMoSe2 (1.56
and change the material to the type-II band alignment, eV).[20, 26, 42] Fig. 5 shows a systematic red shift of
see Fig. 4. Due to their type-II band alignment, these theexcitonicpeaksasthechalcogenatombecomesheav-
heterostructures can be used as active materials for fab- ier. In general, for the red shift the band gap decreases,
rication of heterojunction photovoltaic devices; type-II while for the blue shift the band gap increases [43]. We
band alignment is usually required for charge separation obtain exciton binding energies of 1.05 eV for MoS2,
or formation of p−n junctions.[25] 0.95 eV for WSe2, 1.04 eV for WS2, and 0.95 eV for
The strong spin-orbit coupling results in a significant MoSe2 monolayers. Strong modifications of the excitons
valence band splitting (∆VB) with a minute conduction inthe heterostructureswith respectto the parentmono-
band splitting (∆CB), see Table 1. The fact is that W layers were found, see Fig. 5. The excitonic peaks are
contributes much more to VB than Mo, and hence the shifted to 1.6 eV and 1.8 eV in the case of the MoS2-
VB is split. The situation is reversedfor the CB, result- WSe2 heterostructure, in agreement with photolumines-
ing in a split that is very small only, see Fig. 3. The cence spectroscopy.[26, 27] The remarkable decrease in
valence band splitting in the heterostructure of MoS2- the photoluminescence intensity of the heterostructures
3
500 ergies as for the corresponding monolayers of WSe2 and
400
MoS2. This indicates once more thatthere are onlyvery
-1m)300 smallvander Waals interactionsbetween the two layers.
ω (c200 ThephononspectraforpristinemonolayersofbothMoS2
100
andWSe2werealsocalculatedforcomparison. Thechar-
5000 acteristicbands observedat 410cm−1 and 380cm−1 are
400 in a good agreement indeed with the experimental val-
-1m)300 ues of 403 cm−1 and 385 cm−1 [23], which are due to
ω (c200 the A1 mode (out-of-plane vibrations)andE1 mode (in-
100 planevibrations),respectively,oftheMoS2 monolayerin
5000 the heterostructure. The bands at about 250 cm−1 to
400 260 cm−1 are due to the E1 and A1 modes of the mono-
-1m)300 layer of WSe2. These bands are also in good agreement
ω (c200 with the experimental values of E1 (248 cm−1) and A1
100 (260 cm−1).[23] The positions of these bands are also in
0Γ Κ Μ Γ Κ Μ Γ agreement with those of the corresponding monolayers
withasmallredshift(shifttolowerenergy)withrespect
FIG. 6: Phonon spectrum for MoS2 (top-left), WS2 (top- to isolated MoS2 and blue shift (shift to higher energy)
right),MoS2-WSe2 (middle-left),WS2-MoSe2 (middle-right), withrespecttoisolatedWSe2.[23]Bothoftheseblueand
WSe2 (bottom-left), and MoSe2(bottom-right). red shifts with respect to the corresponding monolayers
aredue to the factthat tensile strainis induced inMoS2
and compressive strain is induced in WSe2 while con-
with respect to the parent monolayer has also been re-
structing the heterostructures. The characteristic peaks
portedpreviously[25,26]andisduetotheefficientinter-
arewellreproducedwithrespecttothe experiments. Al-
layerchargetransfer. Notethat,intherealexperimental
though these peaks are not exactly the same as those
situation in the presence of dielectric medium, the posi-
obtained in experiment, the simulation results provide a
tion of an excitonic peak might change slightly.[44]
good approximation. The positions of the bands in the
The charge transfer rate is close to the rate of ex-
heterostructureofMoS2-WSe2 withrespecttothe corre-
citon generation. Due to the type-II band alignment,
sponding monolayersshow that the layers are decoupled
in case of the MoS2-WSe2 heterostructure the photoex- having a very small van der Waals interaction.
cited electrons in the WSe2 layer tend to flow to the
MoS2 layer,andthe holes inthe MoS2 layertendto flow In summary, we have investigated the structural and
to the WSe2 layer. The spatial separation of the elec- electronic properties and the vibrational and optical
trons and holes therefore suppresses the intralayer op- spectra of the van der Waals heterostructures of MoS2-
tical recombination processes and thus the optical spec- WSe2 andWS2-MoSe2. ItwasfoundthatMoS2-WSe2 is
trum. Toinvestigatethechargetransferbetweenthecon- adirectbandgapsemiconductorwithtype-IIbandalign-
stituents monolayers of the heterostructures, the charge ment. IncontrasttotheMoS2-WSe2heterostructure,the
density difference was addressed (see Fig. 1); calculated WS2-MoSe2heterostructureisanindirectbandgapsemi-
as ∆ρ=ρMoX2WY2−ρMoX2−ρWY2, where ρMoX2−WY2 conductor with type-I band alignment. A compressive
is the charge density of the heterostructure, ρMoX2 is strainisanefficientwaytochangetheheterostructureof
the charge density of the isolated MoX2 monolayer and WS2-MoSe2 fromindirecttodirectbandgapnaturewith
ρWY2 is the charge density of the isolated WY2 mono- type-IIbandalignment. Thesplittingofthevalenceband
layer. FromtheBaderpopulationanalysiswehavefiound (holes) and conduction band (electrons) indicates that
that the S atom gains 0.008 e, while the Se atom loses theformationofthe heterostructureisapromisingroute
0.012 e in the MoS2-WSe2 heterostructure. Similarly in to engineer the band gap and band splitting, such that
case ofWS2-MoSe2 Se atoms lose 0.009e, while S atoms thesesystemswouldbeinterestingforoptoelectronicand
gain 0.016 e, where for unstrained system this amount spintronicdevices. Thereductionoftheopticalspectrum
is 0.009 e for Se and 0.005 e for S. These results are in withrespecttothecorrespondingmonolayersisanalyzed
goodagreementwiththeavailablevaluesreportedinRef. and the stability of the systems under consideration is
[45], and show that the interlayer bonding of MoS2 and confirmed with the help of the phonon spectrum.
WSe2 should be rather weak and due to long-range van
der Waals forces. GS acknowledges funding from the Natural Sciences
In Fig. 6, the calculated phonon spectra for the het- and Engineering Council of Canada (NSERC, Discov-
erostructuresofMoS2-WSe2 andWS2-MoSe2 showgood ery Grant). MSF acknowledges support by NSERC, the
agreement with the experimental data presented in Ref. CanadaResearchChairprogram,CanadaFoundationfor
[23] In the case of the MoS2-WSe2 heterostructure the Innovation(CFI),theManitobaResearchandInnovation
acousticandopticalvibrationmodes areatthe same en- Fund, and the University o f Manitoba.
4
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5
Materials properties of out-of-plane heterostructures of MoS -WSe and WS -MoSe
2 2 2 2
Bin Amin
Department of Physics, Hazara University, Mansehra, Karakoram Hwy, Dhodial 21120, Pakistan
Thaneshwor P. Kaloni, Georg Schreckenbach, and Michael S. Freund
Department of Chemistry, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
6
1 I. COMPUTATIONAL DETAIL optimizations. It was further refined to a 12×12× 1
0 mesh for the subsequent calculation of the electronic
2 Density functional theory with the Perdew-Burke- and vibrational properties. Relativistic effects includ-
n Ernzerhof (PBE) [1] and Heyd-Scuseria-Ernzerhof ing spin-orbit coupling are significant for the heavy ele-
a (HSE06) functionals [2] implemented in the VASP pack- ments (Mo andW) andhence,spin-orbitandrelativistic
J age were used.[3]. The Van der Waals interactions pseudopotentials have been using in the calculations. In
9 (Grimme’s approach) were taken into account to op- order to study the optical spectrum, the quasi-particle
2 timize the geometries as well as to perform further self-energy corrections (GW0) approach has been used
calculations.[4] A vacuum layer of 18 ˚A is used to pre- to solve the Bethe-Salpeter equation (Tamm-Dancoff
]
i vent artifacts due to the periodic boundary conditions. approximation).[5] The 10 highest valence and 10 lowest
c
s The structures were optimized until the forces and en- conduction bands were taken into account in calculating
- ergy reached to 0.0001 eV/˚A with a high plane wave the excitonic eigenstates.
l
r cutoff of 700 eV. A 6×6×1 k-mesh was used for the
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m
.
t
a
m
[1] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. [4] S. Grimme, J. Comput. Chem. 27, 1787 (2006).
d- Lett. 77, 3865 (1996). [5] A.Chantzis,A.D.Laurent,C.Adamo,andD.Jacquemin,
n [2] J.Heyd,G.E.Scuseria,andM.Ernzerhof,J.Chem.Phys. J .Chem.Theory Comput. 9, 4517 (2013).
o 124, 219906 (2006).
c [3] G. Kresse and J. Hafner, Phys.Rev.B 47, 558 (1993).
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