1 s2.0 S2452262717300892 main
FlatChem 4 (2017) 1–19
Contents lists available at ScienceDirect
FlatChem
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl a t c
Transition metal dichalcogenides: structural, optical and electronic
property tuning via thickness and stacking
Juan Xia, Jiaxu Yan ⇑, Ze Xiang Shen ⇑
Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
a r t i c l e
i n f o
Article history:
Received 2 June 2017
Revised 9 June 2017
Accepted 9 June 2017
Available online 19 June 2017
Keywords:
Transition metal dichalcogenides
Interlayer coupling
Raman spectroscopy
Photoluminescence
Spin-valley polarization
Second harmonic generation
Electronic performance
a b s t r a c t
Two-dimensional (2D) transition metal dichalcogenides (TMDs) have attracted intense interests owing to
their fascinating physical properties and potential applications. In addition, the properties of few-layer
TMD materials can be tuned by their thickness as well as the stacking sequence. For instance,
MoS2/WS2/MoSe2/WSe2 undergoes a transition from the indirect-band-gap to direct-band-gap semiconductors with their thickness reduced to monolayer; the weak van der Waals (vdWs) interaction between
the layers in TMDs endows various stacking sequences that can be facilely obtained by different methods.
Hence, thickness and stacking sequence can be used to modulate the electronic band structures, valley
polarization and nonlinear optical properties, providing additional useful and convenient ways to manipulate the materials and fabricate devices with novel functionalities. Here we review recent progress in
thickness and stacking engineering for TMD materials in structural, optical and electronic properties.
Last, we offer our perspectives and challenges in this research field.
Ó 2017 Published by Elsevier B.V.
Contents
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Growth and stacking characterization of layered TMDs . .
Thickness- and stacking-dependent interlayer coupling .
Spin-valley polarization in few-layer TMDs . . . . . . . . . . .
Second harmonic generation (SHG) in stacked-TMDs. . . .
Thickness and phase engineered TMD electronic devices
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Introduction
Layered transition metal dichalcogenides (TMDs) have attracted
intense attention among the two-dimensional (2D) materials,
which stem from their intriguing physical properties that have
great potential for many applications, such as optical, electronic
and optoelectronic devices [1–3]. Moreover, these physical properties of layered TMDs are strongly correlated to thickness [4], strain
[5], pressure [6], stacking sequence [7] and electromagnetic field
⇑ Corresponding authors.
E-mail address: [email protected] (Z.X. Shen).
http://dx.doi.org/10.1016/j.flatc.2017.06.007
2452-2627/Ó 2017 Published by Elsevier B.V.
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1
2
4
9
13
16
17
17
18
[8]. For instance, it is already known that MoS2/WS2/MoSe2/WSe2
undergoes a transition from the indirect-band-gap to directband-gap transition when the thickness is reduced to monolayer
[1,4]. This thickness-dependent bandgap in TMDs can be explored
to the next-generation electronic and optoelectronic devices.
Beyond this, the weak van der Waals (vdWs) force between the
layers allows TMD materials to be grown with different stacking
sequences that governs the crystal symmetry and in turn significantly influence the electronic band structures, magnetism, superconductivity, valley polarization, nonlinear optical effects, and
other physical properties [9–11]. Hence stacking provides another
convenient method to manipulate TMDs functionalities.
2
J. Xia et al. / FlatChem 4 (2017) 1–19
Our group has reported detailed experimental study and theoretical simulation of Raman vibrations and band structures for
AA/AB bilayer (2L) and AAB/ABB/ABA/AAA trilayer (3L) MoS2 samples by chemical vapor deposition (CVD) method, which exhibit
different coupling phenomena in both photoluminescence (PL)
and Raman spectra [12]. The ultra-low-frequency (ULF) Raman
vibrational bands are particularly sensitive to the interlayer interaction and hence the stacking sequence between layers. We
demonstrate that the evolution of interlayer interaction with
various stacking configurations correlates strongly with the
layer-breathing mode (BM) and interlayer shear mode (SM). Ab
initio calculations reveal that the thickness-dependent properties
arise from both the spin-orbit-coupling (SOC) and interlayer coupling in different structural symmetries [13]. A bond polarizability
model is used by Luo et al. [14] to show the Raman intensity of SM
is sensitive to the stacking configurations and these stackingdependent ULF Raman features in layered TMDs provide a practical
and efficient method to identify the stacking configurations.
Another intriguing character related to spin-valley polarization
in TMDs is also mediated by stacking configurations [15–17]. Specific to 1L MoS2 (WS2), the SOC splits the valence bands by 160 meV
(500 meV) with opposite spin signs near the K/K’ valley. Together
with the time-reversal symmetry, the spin and valley are inherently
coupled, leading to valley-contrasting optical dichroism. Consequently, one can selectively excite the carriers using circularly
polarized light, i.e. left (right) circularly polarized light for excitation of spin up (down) electrons at K (K’) valley, making monolayer
MoS2 the ideal material for valleytroincs [18]. Bilayer TMDs offers
another degree of freedom named as layer pseudospin [19–24],
which refers to the carriers’ location, either upper, middle or lower
layer and so on. The interplay among spin, valley pseudospins and
layer pseudospins opens an unprecedented platform for the control
of quantum states, where both spin and valley possess magnetic
moments and can be manipulated by magnetic and optical means
[25–28], while the layer pseudospin can be tuned by an electric
field [24]. Numerous have been published in the literature to
exploit these quantum controls in monolayer and bilayer TMDs.
In even-layer TMD samples, the presence of inversion symmetry
and time-reversal symmetry ensures that the electronic states are
doubly spin-degenerate. However, the inversion symmetry is broken in odd-layer TMDs, resulting in the splitting of valence bands
due to the presence of SOC. Along with the layer number, stacking
configuration also has a significant influence on the properties
[9,11,29]. For instance, 2H bilayer MoS2 is inversion symmetric
without SOC, and hence the valley-contrasting optical selection rule
becomes invalid [16]. Recently, pioneering experiments have
demonstrated that valley-dependent spin polarization can be realized in non-centrosymmetric phases including 3R phase, folded
bilayer [19,30], and bilayer systems under perpendicular electric
fields [20,21]. Such manipulation of intrinsic symmetry and spin
in even-layer or bulk TMDs has greatly enriched the scope of valley
physics and plays a crucial role towards spintronics and valleytronics [31,32].
Besides the structural, electronic, and linear optical properties
of TMDs, their nonlinear optical properties, especially second harmonic generations (SHG) have been studied, where the lack of
inversion symmetry in monolayer TMDs leads to a strong optical
SH response. Bulk 2H-MoS2 crystal belongs to space group D6h,
which possesses inversion symmetry different from monolayer.
Consequently, the second-order nonlinear response for 2H-MoS2
bulk should vanish [32]. It has been reported that the secondorder nonlinear susceptibility for MoS2 bulk is around 10 14 m/V,
much smaller than that of monolayer (10 7 m/V). This SHG effect
proves to be highly sensitive to the thickness, crystalline
orientation, as well as stacking configuration [33,34]. So far,
thickness-dependent optical SHG in odd-layer TMDs have been
found [35–38], attributed to the non-trivial second-order
nonlinearity due to the broken inversion symmetry. Hsu et al. have
studied the SHG of artificially stacked bilayer MoS2 with various
twist angles. The SHG signals can be described as the coherent
superposition of SH signal from individual layer involving a phase
difference relying on the twist angle. Therefore, the stackingdependent polarization of SHG intensity can be served as one accurate and powerful characterization tool to identify their atomic
stacking orders [39].
The nature of TMDs, such as appropriate bandgap, high carrier
mobility, high current on/off ratios, and thickness-dependent band
structure makes TMDs as promising materials for various devices
[40,41], such as field-effect transistors (FETs), photovoltaics, photodetectors, and nonvolatile memories [42–46]. From literature,
most electronic devices are constructed using the p-n junctions
through heavy doping, Schottky junctions between metal and
semiconductor, vdWs heterojunctions by mechanical transfer and
thickness-/strain-induced homojunctions. For example, the
diode-like rectification effect and remarkable drain-source current
have been demonstrated in TMDs-based materials, such as
thickness-dependent MoX2 homojunctions [47–49], phasemodified 1T’-2H MoX2 Schottky junctions [50], WS2-WSe2 [51],
WX2-MoX2 [52–56] heterojunctions. In ref [47], He et al. reported
that a series of thickness -dependent 3R-MoSe2 junctions exhibit
current rectification and photovoltaic behaviors, and yet without
heavily doping strategies in TMDs [50] or TMDs heterojunction
fabrication [17]. The first-principles calculations show that the
thickness -dependent band alignment determines the electronic
and optoelectronic behaviors in such junctions. Moreover, layerengineered homojunctions can be prepared through one-step
CVD growth approach that is much simpler than the preparation
processes for TMD heterojunctions. Such strategy provides guidance for designing and fabricating possible layer-engineered
devices. Similarly, the layer-engineered homojunctions with 2H
stacking and the stacking-dependent (e.g. 2H-3R bilayer) TMD
homojunctions are expected to exhibit novel electronic and optoelectronic properties.
Growth and stacking characterization of layered TMDs
In general, there are two mainstream strategies to fabricate
few-layer 2D TMDs: top-down and bottom-up. The top-down
strategy consists of mechanical exfoliation (ME) [57] and liquidphase exfoliation (LPE) [58]. Fig. 1 shows the typical ME process
to obtain few-layer MoS2 from pristine crystals, where the screw
dislocations observed in the optical micrographs (Fig. 1A) from
the 2H (left) and 3R (right) single crystals present their hexagonal
and trigonal structures respectively [16]. The detailed exfoliation
processes and optical/AFM morphology for obtaining few-layer
MoS2 samples are shown in Fig. 1B, C [30,57]. Due to the low productivity of few-layer TMD sheets in top-down approach, bottomup strategy becomes more and more popular, which can be extensively realized by CVD [59], physical vapor deposition (PVD) [12],
atomic layer deposition (ALD) [60], as well as epitaxy growth.
Compared with ME, the sample growth processes by these methods can be controlled more easily with much higher yield of fewlayer samples, where large amount of one to four layered TMD
flakes with various stacking configurations have been obtained,
while ME method yields predominately 2H stacking sequence only.
We used both CVD and PVD to grow MoS2 samples (Fig. 2). We
obtained a large amount of multilayer MoS2, especially 2L and 3L
MoS2 with various stacking configurations by PVD. The typical
growth process and morphologies of 1L-4L samples using the
PVD method are shown in Fig. 2A. We acquired mostly 1L MoS2
flakes with various shapes by the CVD method (Fig. 2B). Fig. 2C
compares the structural and electronic properties of graphene
J. Xia et al. / FlatChem 4 (2017) 1–19
3
Fig. 1. (A) Optical micrograph images of the surface morphologies for MoS2 single crystals with 2H (left) and 3R (right) stacking. Reproduced with permission from Ref. [11].
Copyright 2014, Nature Publishing Group. (B) Micromechanical exfoliation processes. Reproduced with permission from Ref. [55]. Copyright 2012, IOP Publishing Group. (C)
Optical morphology (a) and AFM image (b) of few-layer MoS2 by micromechanical exfoliation. Reproduced with permission from Ref. [30]. Copyright 2010, American
Chemical Society.
Fig. 2. Vapor deposition of few-layer MoS2 samples. The temperature ramping diagram of the growth process and morphologies of as grown MoS2 flakes by PVD (A) and CVD
(B) respectively. (C) Mobility comparison of graphene and MoS2 grown by various methods. The red curve shows the mobility of graphene on SiO2, and the blue curve is for
MoS2 on SiO2. The mechanically cleaved samples show the best structural and electronic quality for both graphene and MoS2. Reproduced with permission from Ref. [59].
Copyright 2014, Nature Publishing Group.
Fig. 3. Atomic structures of bilayer (2L) and trilayer (3L) MoS2 grown by CVD method. (A) All five classic atomic structures of bilayer MoS2. (B) Optical and Z-contrast STEM
images of the monolayer (left), AA- (middle) and AB- (right) stacking MoS2 bilayer (C) Top and side views of 3L MoS2 with four typical stackings, ABA, AAA, AAB(ABB). Insets
are the optical images and Raman mappings of these 3L MoS2 samples. Reproduced with permission from Ref. [12]. Copyright 2015, American Chemical Society.
and MoS2 prepared by different methods [61]. The red and blue
curves show the mobility of graphene and MoS2 samples on SiO2.
On one hand, both graphene and MoS2 samples from the mechanically cleaved method show the best structural and electronic quality, due to fewer defects. On the other hand, CVD/PVD grown
samples provide more stacking variations to investigate interlayer
coupling effect on optical, electronic, electrical and other intriguing
physical properties.
From the first-principles calculations, there are five highsymmetry stacking configurations for bilayer MoS2 as shown in
Fig. 3A, which can be classified into two groups depending on
whether the S (Mo) atoms in the top layer are directly situated
above the Mo (S) atoms of the bottom layer. The optical image
(Fig. 3A centre) shows that PVD grown bilayer MoS2 sheets exhibit
two typical configurations: two triangles in the same orientation
(marked as AA) and in reverse orientation (marked as AB). Our
previous results indicate that AA and AB stackings are the most
favorable among all configurations while other three are energetically unstable. The two natural polytypes of MoS2 are known as 2H
(space group: P63/mmc) and 3R (space group: R3m) respectively,
both of which have trigonal prismatic coordination of the Mo
atoms but with distinct stacking orders [11,12]. Fig. 3B shows the
optical and Z-contrast scanning transmission electron microscopy
(STEM) images of the 1L (left), AA- (middle) and AB- (right) stacked
2L MoS2. The STEM images clearly show the distinct arrangements
between AA and AB stacked bilayer samples. In STEM, the intensity
sensitively relies on the atomic weight and the number of layer,
where the high intensity sites correspond to the heavy atoms
(Mo) and thicker samples, leading a contrast difference. In the 3L
MoS2 samples, there are four typical stacking patterns: ABA, AAA,
4
J. Xia et al. / FlatChem 4 (2017) 1–19
AAB and ABB following the nomenclature of bilayer system, which
lead to three distinct stacking configurations as the ABB and AAB
configurations are completely equivalent. The top and side views
of atomic structures for ABA-, AAA- and AAB-stacked 3L MoS2 are
shown in Fig. 3C, where the layer number is determined by both
optical images and Raman intensity mapping [12,31].
Thickness- and stacking-dependent interlayer coupling
The electronic properties of 2D materials are affected by both
layer number and stacking configurations through interlayer coupling [62–64]. The different Raman behaviors for both highfrequency and low-frequency modes as a function of layer number
have been revealed and widely discussed in recently years. Raman
spectroscopy is a greatly potent and efficient approach to investigate the thickness variation and phase transition behaviors in 2D
materials, especially the ultra-low-frequency (ULF) Raman spectroscopy, which is highly sensitive to interlayer interactions and
can reflect even the minute changes and discrepancies of structure.
Affected by layer numbers and layer stacking, both shear modes
(SMs) and layer breathing modes (BMs) have been observed that
exhibit strikingly different features for different configurations,
which can be well modeled using linear chain simulations [12].
Thus, polarized ULF Raman technique can be used as a fast and
convenient nondestructive method to identify stacking sequence,
which is otherwise very difficult using other techniques.
The Raman frequency trends in MoS2 crystal from 1L to 12L are
studied both theoretically and experimentally in Fig. 4. The
Raman-active in-plane E12g mode stiffens whereas the out-of-plane
A1g mode softens with decreasing thickness. The black curves are
the experimental results and the density functional theory (DFT) calculations are plotted in blue bars, showing the consistent frequency
evolution trends (Fig. 4A). The red shift of the A1g mode with
decreasing layer number is attributed to the smaller restoring force,
while there are several explanations to the blue shift of E12g mode,
which has been ascribed to thickness-induced structure modification, long-range coulomb interactions, or enhanced surface force
constant of Mo-S intralayer interactions in few-layer MoS2 [65]. Similar thickness-dependent phonon evolutions can be also found in
low-frequency SMs and BMs, as shown in Fig. 4B and C, where two
optical configurations (z(xx)z (4B) and z(xy)z (4C)) are utilised.
Based on the Raman tensor, the interlayer SMs and E12g mode are
shown in both z(xx)z and z(xy)z configurations, whereas the interlayer BMs and A1g mode are observed only in the z(xx)z configuration. In Fig. 4B and C [66], from bulk to 2L, the S1 peak red shifts
from 32 cm 1 to 22 cm 1. In contrast, the other predominant
peak B1 blue shifts and crosses the S1 peak at 3L. As discussed
before, the frequency evolutions of E12g and A1g have been used to
determine the layer number of TMD samples [29]. However, these
two peaks are much less sensitive to the thickness than the interlayer SM and BM peaks. Two weak peaks, labelled S2 and B2, exhibit
the similar trends versus thickness with S1 and B1. Fig. 4D and E
show the phonon dispersions and density of states (DOS) for 1L
(4D) and bulk MoS2 (4E) with experimental data plotted in black
dots [67]. Different from monolayer MoS2, the bulk phonon dispersion has three acoustic modes, the in-plane longitudinal acoustic
(LA) mode, transverse acoustic (TA) mode and out-of-plane acoustic
(ZA) mode, whereas, the low-frequency optical modes are found at
35.2 and 57.7 cm 1, corresponding to the rigid-layer lateral and ver-
Fig. 4. Thickness-dependent Raman behaviors of MoS2. (A) Experimental and LDA-calculated high-frequency Raman for few-layer and bulk MoS2. Reproduced with
permission from Ref. [63]. Copyright 2013 American Physical Society. The E12g mode blue shifts and the A1g mode red shifts as the thickness of the MoS2 sample decreases. The
green and red dashed lines are the frequency evolution trends for the experimental and LDA results, respectively. (B, C) Ultra-low-frequency (ULF) Raman spectrum evolutions as
a function of layer number in 1L-12L MoS2 using z(xx)z (B) and (xy)z (C) polarization configuration. Reproduced with permission from Ref. [64]. Copyright 2013, American
Chemical Society. (D, E) Phonon dispersion curves and density of states for single-layer (D) and bulk (E) MoS2. Reproduced with permission from Ref. [65]. Copyright 2011
American Physical Society.
J. Xia et al. / FlatChem 4 (2017) 1–19
5
Fig. 5. Displacement representations for the Gama-point phonon vibrational modes in bulk MoS2 with vibrational frequencies shown below. R and I represent Raman active
and inactive vibrations respectively. Reproduced with permission from Ref. [63]. Copyright 2013 American Physical Society.
tical motion, respectively. Based on group theory [50], the phonon
modes at C-point for bulk MoS2 can be decomposed into the
irreducible representation: C = 2A2u + 2E1u + 2B2g + 2E2g + A1g +
E1g + B1u + E2u. These 12 irreducible representations in bulk MoS2
can be divided into six conjugate pairs (E11u and E22g, E1g and E2u,
E21u and E12g, A12u and B22g, A1g and B1u, A22u and B12g), as shown in
Fig. 5. In each conjugate pair, there is an inversion centre between
the two layers, and one phonon mode differs from the other by an
interlayer phase shift of 180°. Fig. 5 shows all the displacement representations for the C-point vibrational modes in bulk MoS2 with
frequencies shown below, where R and I represent Raman active
and inactive vibrations respectively. All these calculated phonon frequencies are consistent with previous experimental results [65].
It has been reported that MoS2/WS2/MoSe2/WSe2 undergoes a
transition from the indirect-band-gap to direct-band-gap semiconductor with their thickness reduced to monolayer. Correspondingly, the PL quantum yield (QY) shows an obvious enhancement
while the TMD crystal undergoing from the indirect-gap bulk to
the direct-gap monolayer [68]. Systematic studies of the evolution
of the optical properties and electronic structures in layered TMD
crystals as a function of layer number (N) have been reported. With
the reduction of thickness, the confinement-induced band gap varies from the bulk value of 1.29 eV to over 1.90 eV in monolayer.
Moreover, the change in the energy of indirect band gap at C point
is about 0.7 eV, much larger than that of the band gap at K point of
about 0.1 eV (Fig. 6A). The corresponding PL spectra obtained from
samples of different layer thickness are shown in Fig. 6B. The direct
bandgap of the 1L MoS2 produces the strongest PL intensity, while
its intensity decreases with increasing MoS2 thickness along with
the direct-to-indirect bandgap transition. Two prominent exciton
PL peaks at 1.83 eV and 1.98 eV are identified as the direct
transition at the K-point in the MoS2 Brillouin zone [30,69]. The
main PL peak (Peak A) of 1L MoS2 samples has a narrow width of
50 meV, with exciton energy at 1.90 eV, and few-layer samples
display multiple emission peaks (labelled A, B, and I). Peaks A
and B agree with the 1L emission that shift to the red and slightly
broadens with increasing N, where Peak B possesses the energy
150 meV larger than that of Peak A. Peak I systematically red
shifts and becomes less prominent with increasing N, approaching
the indirect-gap energy of 1.29 eV for bulk [17,70]. To explore the
origin of the observed PL properties, the comparison between PL
and absorption spectra has been done. The absorption spectra
for MoS2 crystals with different layer thickness are displayed in
Fig. 6C [68]. The two peaks in the absorption spectra at 1.88 eV
and 2.03 eV correspond to the A and B exciton transitions in the
PL spectra in Fig. 6A. The energy separation between the A and
B exciton peaks is 0.15 eV in the 1L MoS2 and gradually
increased with increasing MoS2 layer number, close to 0.19 eV
for the bulk MoS2. This valence band splitting arises from the
remarkable SOC effect and interlayer interactions in few-layer
MoS2 samples [1,9]. DFT calculations [22] have been employed
to explore the band structures for 4L, 3L, 2L, and 1L MoS2, as
shown in Fig. 6A. The indirect bandgap gradually increases monotonically with the decreasing of layer number while the direct
exciton transition energy at K point almost shows no changes.
The variation of the electronic structure using the first-principles
calculations in few-layer MoS2 is in accord with previous PL and
absorption data [30].
Stacking significantly influences the crystal symmetry and
hence can mediate the magnetism, superconductivity, electronic
Fig. 6. Layer-dependent electronic band structure without spin-orbit coupling (A), PL (B) and absorption (C) of MoS2 crystals. Reproduced with permission form Ref. [30].
Copyright 2010, American Chemical Society. In B, the band-gap energy of thin layers of MoS2, inferred from the energy of the PL feature I for N = 2–6 and from the energy of
the PL peak A for N = 1. The dashed line represents the (indirect) band-gap energy of bulk MoS2. Reproduced with permission form Ref. [68]. Copyright 2014, Royal Society of
Chemistry.
6
J. Xia et al. / FlatChem 4 (2017) 1–19
Fig. 7. Stacking-dependent Raman behaviors of bilayer MoS2. (A) Optical image of CVD grown 2L MoS2 with AA and AB stacking. (B, C) High-frequency (B) and ULF (C) Raman
spectra of AA- and AB-stacked 2L MoS2. (D) The linear chain models of bilayer MoS2 with AB and AA stacking. The labels on the atoms are used for constructing the notation of
force constants and the weak interlayer interaction is indicated by a spring. The arrows depict the vibrational diagrams of shear (S, left) and breathing (B, right) mode for 2L
MoS2. Reproduced with permission from Ref. [12]. Copyright 2015, American Chemical Society. (E, F) ULF Raman spectra for 2L WSe2 (E) and MoSe2 (F) with different
stackings. Reproduced with permission from Ref. [69]. Copyright 2016, Nature Publishing Group.
band structure and other physical properties [9,11,39]. Such
stacking-dependent effects are obviously projected onto MoS2
and have been widely investigated in recent years. For bilayer
TMDs system, there are two typical stacking polytypes (AA and
AB) as demonstrated before. An optical image containing both
AA- and AB-stacked bilayer MoS2 is shown in Fig. 7A. The Raman
spectra for AA- and AB-stacked 2L MoS2 in the high-frequency
range (350–440 cm 1) are shown in Fig. 7B, where the intensity
of both E12g and A1g peaks for AB stacking is larger than that of
AA stacking and no significant frequency change in the two highfrequency modes. Hence the Raman bands in the high-frequency
range is not sensitive to the vdWs interactions caused by stacking.
Distinct behaviors are found in ULF Raman modes (Fig. 7C), in
which the two peaks located at 22.6 (22.8) and 41.6 (38.7)
cm 1 for AB (AA) stacking 2L MoS2 belong to the in-plane SM
and out-of-plane BM respectively. We note that the SM almost
shows no stacking-dependent shift while the BM obviously red
shifts for AA stacking. As for the peak position shift, we analysed
the force constants in AB- and AA-stacked 2L MoS2 up to the
second-nearest neighbours [12]. As shown in Fig. 7D, the stacking
sequence not only changes the interactions between the two layers
(k34), but also involves the interactions up to the second-nearest
neighbours (k24). Firstly, the force constants for the SM are smaller
than those of the BM. Furthermore, the stacking affects both k24
and k34, leading to the different behaviors for BM and SM. For
instance, the BM force constant k34 increases slightly but k24
decreases significantly from AB to AA stackings, resulting in an
overall redshift of BM. However, the SM is not sensitive to stacking,
which can be attributed to the almost equal change in force constant of k34 (decreasing) and k24 (increasing) from AB to AA stacking. More importantly, the intensity ratio between the BM and SM
is very distinct: 1.2 for AB and 4.1 for AA stacking, calculated
using the integrated areas of the Stokes Raman peaks. Therefore,
the ratio of BM and SM can be used as a convenient method to
identify the stacking orders of 2L MoS2 and confirm the previous
STEM results: macroscopic AA and AB stacking patterns correspond to 3R and 2H atomic stacking orders, respectively.
Fig. 7E and F also compare the stacking-dependent ULF Raman
responses for WSe2 and MoSe2 [71]. Similarly, for the behaviors
of SM and BM in few layer WSe2, a clear decrease in intensity of
the SM from 2L-2H to 2L-3R stacking is observed, yet with a corresponding increase in the BM. The ULF Raman peaks shown here
agree well with different stacking configurations of 2L WSe2
reported previously [72]. In Fig. 7F, ULF Raman spectra for different
stackings of 2L MoSe2 are shown, corresponding to 2H (max at
18 cm 1), 3R (max at 18 cm 1, but significantly lower in relative
intensity), and 3R⁄ (max at 29 cm 1) as reported in ref [69]. The difference between 3R and 3R⁄ is attributed to one being 3R, and the
other being the vertically flipped 3R [73], which show different
phonon behaviors. The stacking-dependent electronic features for
2L MoS2 are also demonstrated in Fig. 8. The larger emission intensity of A exciton and the larger energy difference between A and B
excitons for AB-stacked 2L MoS2 compared with AA stacking can be
obviously found in Fig. 8A, which agree with previous reports [12].
Moreover, the calculated band structures for AA and AB 2L MoS2 in
Fig. 8B and C clearly depict the splitting of top valence bands in AB
stacking is larger than that of AA stacking, which in turn supports
the experimental discoveries in Fig. 8A.
Liu et al. [74] successfully grew more diverse 2L MoS2 samples
on fused silica with different twist angles, as shown in Fig. 9, by a
specialized CVD method. As the atomic twist bilayer structures are
directly correlated with the microscopic crystal orientation of the
two vertically stacked triangles, the evolution of high-frequency
phonon vibrations in twisted 2L MoS2 using Rama spectroscopy
J. Xia et al. / FlatChem 4 (2017) 1–19
7
Fig. 8. Stacking-dependent PL features (A) and electronic band structures for 2L MoS2 with AA (B) and AB (C) stackings.
Fig. 9. Stacking-dependent Raman and PL behaviors of CVD grown 2L MoS2 with stacking angles at 0°, 15°, 60°. (A–D) Optical images of 1L and 2L MoS2 with different
stacking angles. The insets are corresponding atomic models. (E) Raman spectra of a MoS2 monolayer and bilayers with different twist angles of 0°, 15°, 60°. (F) Raman peak
separation between the A1g and E12g in 2L MoS2 of different twist angles. (G) PL spectra of MoS2 monolayer and bilayers with different twist angles. (H) Dependence of PL peak
energies on the twist angle for a batch of 2 L MoS2. Reproduced with permission from Ref. [72]. Copyright 2014, Nature Publishing Group.
are investigated in Fig. 9E. As the two prominent peaks, the inplane E12g and out-of-plane A1g phonon modes are sensitive to the
layer number, in which the E12g mode softens and A1g mode stiffens
through an enhanced dielectric screening with increasing layer number [67,75], the separation between these two peaks can serve as an
indicator for the interlayer coupling strength, in which the larger
separation means the stronger coupling. Fig. 9F clearly shows that
AA or AB stacking has the strongest coupling and the others exhibit
weaker coupling strength.
The PL spectra (Fig. 9G) of twisted 2L MoS2 samples show three
prominent peaks at around 2.05 eV, 1.85 eV and 1.50 eV, corresponding to the two direct (A exciton-Peak I and B exciton) and
indirect exciton peak II that originates from the interlayer exciton
transition and depends sensitively on the interlayer electronic coupling strength: the smaller the indirect bandgap, the stronger the
coupling strength. Fig. 9H displays the energy difference between
peak I and II in twisted bilayer samples. Unlike Peak I that remains
almost unchanged, the energy for Peak II is the lowest for AA- and
AB-stacked 2L MoS2, and higher but nearly constant value for all
other twist angles. Such trend shows the similarity to that of the
interlayer coupling strength reflected in Raman vibrations (Fig. 9F),
indicating that the repulsive steric effects play a crucial role in the
evolution of interlayer coupling between the bilayers for various
stacking orders [74].
Beyond the stacking-dependent phonon and electronic properties in CVD grown 2L MoS2 samples, similar stacking effects also
exist in folded 2L MoS2 with random twist angles [9,76,77]. In
Fig. 10A, three MoS2 bilayer regions labelled as A, B and C are prepared by folding the ME monolayer samples, leading to the modulation of the interlayer coupling and the band structures [78,79].
Fig. 10B and C present the PL spectra of the natural 2H bilayer,
and folded bilayers A, B and C and the corresponding band structures with SOC effects. The A exciton peaks at 1.86 eV are almost
unchanged among various stacking configurations, while the
indirect-gap transitions at 1.6 eV vary significantly. The origin
of peaks at 1.86 eV (A exciton) is the direct-gap transition
between the strongly localized Mo-d orbitals and exhibit little
interlayer overlapping. Therefore, it almost shows no stackingdependent feature [30]. For peaks at 1.6 eV (indirect exciton),
the indirect-gap transition occurs between the band extrema arising from linear combinations of Mo-d and S-p orbitals with strong
interlayer overlapping and thus is sensitive to the layer stacking
[79]. Among various stacking configurations, the interlayer coupling strength relies on the interlayer spacing: the enlarged interlayer spacing means the reduced interlayer coupling and the
decreased band gap value. Based on above argument, the most reasonable structure of region A is 2H-like(Mo) bilayer and region B is
3R-like bilayer, while the region C is identified to align between the
8
J. Xia et al. / FlatChem 4 (2017) 1–19
Fig. 10. Stacking-dependent PL behaviors in folded 2L MoS2 with random stacking angles. (A) Optical images of 2L MoS2 folded with different stacking angles and folding
edges highlighted by dashed red, black and green lines. (B) PL spectra of the natural 2H bilayer (purple), bilayer A (red), bilayer B (black) and bilayer C (green) excited at
2.33 eV. (C) Electronic band structures of 2H, 2H-like (Mo, A) and 3R-like (B) bilayers by ab initio calculations with spin–orbit coupling (SOC). Reproduced with permission
from Ref. [9]. Copyright 2014, Nature Publishing Group.
Fig. 11. Stacking-dependent Raman behaviors of 3L MoS2. (A) Raman spectra of ABA-, ABB-, AAB-, AAA-stacked 3L MoS2. (B) ULF Raman of 3L MoS2 with different stackings,
collected under unpolarised (black)), (
z(xx)z (k) (blue) and (
z(xy)z (\) (red) configurations. (C) The intensity ratio of the (
z(xx)z (k) and (
z(xy)z (\) collection for 3L MoS2 in
(B) with error bars of experimental standard deviation for several samples. Reproduced with permission from Ref. [12]. Copyright 2015, American Chemical Society.
2H and 3R-like bilayers supported by its SHG signals discussed in
ref [9].
Trilayer TMD samples endows more stacking configurations
and hence generate more diverse stacking-induced coupling
effects. We obtained four typical stacking patterns: ABA, AAA,
AAB and ABB, where the ABB and AAB atomic configurations are
completely equivalent in symmetry based on our previous discussion [12]. As for the Raman vibration modes in the high frequency
region, distinct behaviors also exhibit for trilayer system as shown
in Fig. 11A. The E12g mode almost remains unchanged while the A1g
mode blue shifts with altering the 2H (ABA) stacking, leading to
the largest frequency difference in AAA stacking samples
(25.35 cm 1), followed by AAB (ABB) trilayer (24.25 cm 1), and
the smallest for ABA stacking (24.07 cm 1). For few-layer samples
with various stacking orders, each monolayer MoS2 is identical and
just assembled in various sequences, leading to different lateral registrations but almost identical interlayer distances. The stackingdependent Raman feature manifests the stacking-dependent interlayer coupling, similar with the trend on the layer number
[13,65,67,73]. Beyond the stacking-dependent features in high frequency, the ULF Raman spectra give additional information about
the interlayer coupling. In Fig. 11B, the SM and the BM in ULF range
are merged into one peak, where Ib/Is cannot be directly used to
identify the stacking configurations as in bilayer samples. Instead,
we use the polarization measurements to identify the different features between the SM and BM (Ik/I\). Here, Ik is the sum of the parallel components for both SM and BM bands, while I\ contains only
the perpendicular component of SM, as the BM is entirely sup-
pressed under perpendicular collection configuration. Thus, the
Ik/I\ ratio can be used to identify stacking configurations for trilayer
systems, while Ib/Is was used for bilayer systems. As shown in
Fig. 11B, the intensity ratio Ik/I\ for AAA stacking is the highest, followed by AAB (ABB) stacking, with ABA stacking having the lowest
ratio. We summarize the intensity ratio Ik/I\ of the interlayer BM
to SM for 3L MoS2 (3 for ABA stacking, 6 for AAB and ABB stacking, 8 for AAA stacking) in Fig. 11C. Beyond MoS2, stackingdependent Raman intensities for the SM and BM are also found in
other TMD materials, for instance, 3L MoSe2 as shown in Fig. 12.
The atomic structure (top) and displacements of the interlayer SMs
(down) in ABA- and AAA-stacked 3L MoSe2 are shown in Fig. 12A,
similar to our previous 3L MoS2 systems. Fig. 12B shows the Raman
spectra of ABA- and AAA-stacked 3L CVD grown MoSe2 samples. The
peak around 13.3 cm 1 was attributed to the lowest frequency SM
(S1) in AAA-stacked 3L MoSe2, while the peak at 23.1 cm 1 corresponds to the theoretically predicted value of 25.5 cm 1 for highest
frequency SM (sN-1) in ABA-stacked 3L MoSe2 [14]. The samples with
both S1 and sN-1 modes indicate the coexist AAA and ABA phases
with either a sharp boundary [80], or a few-hundred nanometer
wide transition area [81]. They also measure the sN-1 Raman peak
of exfoliated 3L MoSe2sample with ABA stacking and confirm that
the samples that show a peak around 23.1 cm 1 are ABA stacked.
Fig. 13A plots the PL spectra of a set of 3L MoS2 samples with
various stackings [12]. The gray dashed lines indicate the stacking
dependence of the PL peak separation between two prominent
peaks PA and PB, which attribute to the direct A and B exciton transitions. Interestingly, the splitting in AAA stacking samples is the
J. Xia et al. / FlatChem 4 (2017) 1–19
9
Fig. 12. (A) Atomic structure (top) and vibrational displacements of the interlayer shear modes (down) in ABA- and AAA- stacked 3L MoSe2. (B) Raman spectra of the 3L
MoSe2 with different stackings. Reproduced with permission from Ref. [14]. Copyright 2015, Nature Publishing Group.
Fig. 13. Stacking-dependent PL features of 3L MoS2. (A) PL spectra of ABA-, ABB-, AAB-, AAA-stacked 3L MoS2. (B) Calculated electronic band structures of ABA-(left), AAAstacked (right) 3L MoS2. The band curves in red and blue correspond to the spin-up and spin-down states. Reproduced with permission from Ref. [12]. Copyright 2015,
American Chemical Society.
smallest (48 nm), followed by those with ABB (AAB) stacking
(56 nm), while ABA stacking has the largest splitting (62 nm).
Similar trend is also found in our previous 2L systems with AA
and AB stacking. Such stacking-dependent splitting patterns in
few-layer samples arise from the SOC and the interlayer hopping
effects in TMDs. In even-layer samples with inversion symmetry,
both SOC and interlayer hopping effects contribute to the splitting
between A and B peaks at K points. The different behaviors in splitting patterns have been reported in optical reflection spectra and
transmission spectra for the 2H and 3R bulk phases of TMDs
[11,82]. By first-principle calculation, Fig. 13B shows the spinpolarized band structures of ABA- and AAA-stacking 3L MoS2 considering SOC effects. The band curves in red (blue) represent the
spin-up (spin-down) states. SOC effects dominate the energy splitting in the top valence bands for ABA-stacking, while both SOC and
interlayer hopping effects contribute to the splitting patterns for
AAA-stacking 3L MoS2, which corresponds to the observed
stacking-dependent PL peaks separation in Fig. 13A. Another interesting feature is the different spin-valley polarizations in different
stackings: the valence band edges at K point in ABA stacking are
dominantly from spin-up states with some mixing of spin-down
states, while in AAA stacking, the VBM bands are completely
spin-polarized. Our ab initio calculations indicate the enhanced
spin-valley polarization in the AAA stacking contrast to the ABA
stacking, which is similar to the observed spin-polarized states in
the 3R phase TMDs by circularly polarized photoluminescence
(CP-PL) measurements [11].
Spin-valley polarization in few-layer TMDs
Following the band structure discussions for virous stacking
configurations in few-layer TMDs, we then investigate how layer
and stacking affect the spin and valley features. As reported, one
of the most appealing applications of TMDs is the so called ‘valleytronics’. The concept of valleys originates from that of spin
and suggests the promising devices, analogous to spintronics, for
next-generation electronics and optoelectronics. The key step
towards valleytronics is to achieve the valley polarization through
creating non-equilibrium charge carrier imbalance between K and
K’ valleys [83–86]. The principal mechanism usually involved is
circularly polarized optical excitation [3,4], in which the two valleys absorb left- (r ) and right- (r+) hand photons respectively,
leading to a valley-selective circular dichroism (CD) within a honeycomb lattice due to the absence of inversion symmetry. There-
10
J. Xia et al. / FlatChem 4 (2017) 1–19
Fig. 14. Thickness-dependent circularly polarized PL (CP-PL) in few-layer MoS2. (A) Three-dimensional band structure of 1L MoS2 with top valence band and bottom
conduction band marked in blue and pink. The centre hexagon is the Brillouin zone coloured by the degree of circular polarization, q. Reproduced with permission from Ref.
[85]. Copyright 2012, Nature Publishing Group. (B) Schematic of valley-dependent selection rules at K and -K points in crystal momentum space: left (right)-handed circularly
polarized light in blue (red) only couples to the band-edge transition at K (-K) points (C) CP-PL spectra at 4K for 1L, 2L, 3L and 4L 2H- (left) and 3R- (right) MoS2, excited by a
left circularly polarized (r ) 633 nm laser. (D, E) Spin-resolved energy distribution curves (EDCs) for spin along the z axis, collected at the inequivalent valleys of the K and -K
points for 2H (D) and 3R (E) MoS2. (F, G) Calculated spin polarizations Pz/P of the valence bands along (0, ky, 0) for 2H-(F)/3R-(G) MoS2. Reproduced with permission from Ref.
[11]. Copyright 2014, Nature Publishing Group.
fore, in 1L TMDs without crystal inversion symmetry, the valley
pseudospins can be distinguished by opposite signs at the corners
(K and K’) in the hexagonal Brillouin zone. The giant SOC separates
the valence bands at each valley into the spin-up and spin-down
states. Such inherent spin-valley coupling can significantly protect
the valley polarization as the intervalley scattering requires a
simultaneous spin flip. Only carriers with selective spin can be
emitted under the valley optical selection rule, which have been
widely demonstrated in the literature [18,84]. The colored band
structure of 1L MoS2 with top valence band and bottom conduction
band marked in blue and pink is shown in Fig. 14A. Fig. 14B depicts
the schematic of valley-dependent selection rules for monolayer
TMDs at K and K0 points in crystal momentum space: r- (r+) circularly polarized light in blue (red) only couples to the band-edge
transition at K (K0 ) points. Therefore, the direct-bandgap transition
at the two degenerate valleys, together with this valley-contrasting
selection rule, suggest that one can optically generate and detect
valley polarizations in a TMDs monolayer [16].
Beyond monolayer, few-layer TMDs introduce another intrinsic
degree of freedom named as layer pseudospin. The interlayer hopping of electrons/holes further affects the spin–valley coupling in
TMDs [21–23]. The layer pseudospin refers to the carriers’ location,
either upper or lower layer in bilayer TMDs for instance. The natural AB-stacked bilayer TMDs, in which the lower layer is rotated
by 180° with respect to the upper layer, possess the crystal inversion symmetry. Consequently, the layer rotation switches two valleys but leave the spin unchanged, which results in a sign change
for the spin-valley coupling from layer to layer. In theory, the
valley-dependent effect should vanish in the presence of inversion
symmetry [84–86]. Fig. 14C presents CP-PL spectra of thicknessdependent 3R- and 2H-MoS2 collected at 4 K with r excitation
of 633 nm (1.96 eV), where r+ and r denote right and left circu-
larly polarized light, respectively. All the spectra are composed of
sharp Raman and broad PL peaks, with the latter showing a peculiar thickness-dependent circular polarization. For 2H stacking, the
intensity difference between the r+ and r PL peak becomes smaller with increasing layer number, whereas that for 3R stacking
does not show a clear layer number dependence. Therefore, the
degree of circular dichroic polarization q, defined as
½Iðr Þ Iðrþ Þ=½Iðr Þ þ Iðrþ Þ under r excitation, shows obviously different evolution trends versus layer number for 2H and
3R stacking TMD crystals. In summary, the valley polarization q
in 3R MoS2 is almost independent on thickness, suggesting the
strongly preserved excitons at the K (K0 ) point, while q decreases
significantly in 2H MoS2.
In theory, inversion-symmetric even-layer 2H-MoS2 should
possess negligibly small q and yet the thickness-dependent q in
the 2H stacking is rather unexpected. In fact, such a noticeable q
in inversion-symmetric 2L TMDs has been widely reported in previous literature [15,25]. One plausible reason is the carrier localized effects, where the electrons/holes are localized in each layer
rather than interlayer hopping [26]. In detail, the generated carriers under the circularly polarized laser (r or r+) in the K (K0 ) valley tend to localize within the upper (lower) layer, and the value of
q decreases due to the intralayer-intervalley hopping and
interlayer-intravalley
hopping.
However,
the
interlayerintervalley hopping should be improbable owing to the giant
momentum change and layer crossing barrier. As for 3R MoS2, both
interlayer and intralayer hopping are negligible and carriers are
locked in each layer, leading to a larger q compared to that of 2H
stacking. These results are also confirmed by spin- and angleresolved photoemission spectroscopy (SARPES) in Fig. 14D and E.
The valence bands near the Fermi level at the K point for 2HMoS2 and 2H-WSe2 are almost unpolarized. For 3R stacking cases,
J. Xia et al. / FlatChem 4 (2017) 1–19
the SARPES (sz) spectra at the K and K0 points in Brillouin zone
(Fig. 14E) show the inversion of spin polarization. Therefore, this
technique offers direct and powerful evidence of the valley/spin
coupled state realized in bulk 3R-MoS2. Fig. 14F and G show the
calculated spin polarizations Pz/P of the valence bands along
(0, ky, 0) for 2H-(Fig. 14F)/3R-(Fig. 14G) MoS2, respectively. The
white bands in Fig. 14F are the summation of spin-up and spindown states for 2H-stacked MoS2, while the red and blue bands
stand for the individual spin polarization contributions by SOC
and interlayer hopping effect (Fig. 14G). Therefore, both SARPES
and calculated results provide a firm and clear image of the different spin-valley polarization behaviors for 2H and 3R stacking TMDs
versus layer number [11].
In addition to valley and layer pseudospins demonstrated
above, we proposed a new degree of freedom in our previous work
- stacking pseudospin in 2L and 3L TMD systems, where diverse
stacking configurations can be facilely grown by CVD method.
Based on previous discussions, certain stacking orders can break
the inversion symmetry and reduce the interlayer coupling, which
are prerequisites for valley- and/or spin-selective circular dichroism. Among all stacking configurations, intralayer-intervalley hopping between the K and K0 valley is the most dominant valley
relaxation path, followed by the interlayer-intravalley hopping.
The latter path can preserve the momentum of the excitons and
is dominated by interlayer coupling, whic
Contents lists available at ScienceDirect
FlatChem
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl a t c
Transition metal dichalcogenides: structural, optical and electronic
property tuning via thickness and stacking
Juan Xia, Jiaxu Yan ⇑, Ze Xiang Shen ⇑
Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
a r t i c l e
i n f o
Article history:
Received 2 June 2017
Revised 9 June 2017
Accepted 9 June 2017
Available online 19 June 2017
Keywords:
Transition metal dichalcogenides
Interlayer coupling
Raman spectroscopy
Photoluminescence
Spin-valley polarization
Second harmonic generation
Electronic performance
a b s t r a c t
Two-dimensional (2D) transition metal dichalcogenides (TMDs) have attracted intense interests owing to
their fascinating physical properties and potential applications. In addition, the properties of few-layer
TMD materials can be tuned by their thickness as well as the stacking sequence. For instance,
MoS2/WS2/MoSe2/WSe2 undergoes a transition from the indirect-band-gap to direct-band-gap semiconductors with their thickness reduced to monolayer; the weak van der Waals (vdWs) interaction between
the layers in TMDs endows various stacking sequences that can be facilely obtained by different methods.
Hence, thickness and stacking sequence can be used to modulate the electronic band structures, valley
polarization and nonlinear optical properties, providing additional useful and convenient ways to manipulate the materials and fabricate devices with novel functionalities. Here we review recent progress in
thickness and stacking engineering for TMD materials in structural, optical and electronic properties.
Last, we offer our perspectives and challenges in this research field.
Ó 2017 Published by Elsevier B.V.
Contents
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Growth and stacking characterization of layered TMDs . .
Thickness- and stacking-dependent interlayer coupling .
Spin-valley polarization in few-layer TMDs . . . . . . . . . . .
Second harmonic generation (SHG) in stacked-TMDs. . . .
Thickness and phase engineered TMD electronic devices
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Introduction
Layered transition metal dichalcogenides (TMDs) have attracted
intense attention among the two-dimensional (2D) materials,
which stem from their intriguing physical properties that have
great potential for many applications, such as optical, electronic
and optoelectronic devices [1–3]. Moreover, these physical properties of layered TMDs are strongly correlated to thickness [4], strain
[5], pressure [6], stacking sequence [7] and electromagnetic field
⇑ Corresponding authors.
E-mail address: [email protected] (Z.X. Shen).
http://dx.doi.org/10.1016/j.flatc.2017.06.007
2452-2627/Ó 2017 Published by Elsevier B.V.
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1
2
4
9
13
16
17
17
18
[8]. For instance, it is already known that MoS2/WS2/MoSe2/WSe2
undergoes a transition from the indirect-band-gap to directband-gap transition when the thickness is reduced to monolayer
[1,4]. This thickness-dependent bandgap in TMDs can be explored
to the next-generation electronic and optoelectronic devices.
Beyond this, the weak van der Waals (vdWs) force between the
layers allows TMD materials to be grown with different stacking
sequences that governs the crystal symmetry and in turn significantly influence the electronic band structures, magnetism, superconductivity, valley polarization, nonlinear optical effects, and
other physical properties [9–11]. Hence stacking provides another
convenient method to manipulate TMDs functionalities.
2
J. Xia et al. / FlatChem 4 (2017) 1–19
Our group has reported detailed experimental study and theoretical simulation of Raman vibrations and band structures for
AA/AB bilayer (2L) and AAB/ABB/ABA/AAA trilayer (3L) MoS2 samples by chemical vapor deposition (CVD) method, which exhibit
different coupling phenomena in both photoluminescence (PL)
and Raman spectra [12]. The ultra-low-frequency (ULF) Raman
vibrational bands are particularly sensitive to the interlayer interaction and hence the stacking sequence between layers. We
demonstrate that the evolution of interlayer interaction with
various stacking configurations correlates strongly with the
layer-breathing mode (BM) and interlayer shear mode (SM). Ab
initio calculations reveal that the thickness-dependent properties
arise from both the spin-orbit-coupling (SOC) and interlayer coupling in different structural symmetries [13]. A bond polarizability
model is used by Luo et al. [14] to show the Raman intensity of SM
is sensitive to the stacking configurations and these stackingdependent ULF Raman features in layered TMDs provide a practical
and efficient method to identify the stacking configurations.
Another intriguing character related to spin-valley polarization
in TMDs is also mediated by stacking configurations [15–17]. Specific to 1L MoS2 (WS2), the SOC splits the valence bands by 160 meV
(500 meV) with opposite spin signs near the K/K’ valley. Together
with the time-reversal symmetry, the spin and valley are inherently
coupled, leading to valley-contrasting optical dichroism. Consequently, one can selectively excite the carriers using circularly
polarized light, i.e. left (right) circularly polarized light for excitation of spin up (down) electrons at K (K’) valley, making monolayer
MoS2 the ideal material for valleytroincs [18]. Bilayer TMDs offers
another degree of freedom named as layer pseudospin [19–24],
which refers to the carriers’ location, either upper, middle or lower
layer and so on. The interplay among spin, valley pseudospins and
layer pseudospins opens an unprecedented platform for the control
of quantum states, where both spin and valley possess magnetic
moments and can be manipulated by magnetic and optical means
[25–28], while the layer pseudospin can be tuned by an electric
field [24]. Numerous have been published in the literature to
exploit these quantum controls in monolayer and bilayer TMDs.
In even-layer TMD samples, the presence of inversion symmetry
and time-reversal symmetry ensures that the electronic states are
doubly spin-degenerate. However, the inversion symmetry is broken in odd-layer TMDs, resulting in the splitting of valence bands
due to the presence of SOC. Along with the layer number, stacking
configuration also has a significant influence on the properties
[9,11,29]. For instance, 2H bilayer MoS2 is inversion symmetric
without SOC, and hence the valley-contrasting optical selection rule
becomes invalid [16]. Recently, pioneering experiments have
demonstrated that valley-dependent spin polarization can be realized in non-centrosymmetric phases including 3R phase, folded
bilayer [19,30], and bilayer systems under perpendicular electric
fields [20,21]. Such manipulation of intrinsic symmetry and spin
in even-layer or bulk TMDs has greatly enriched the scope of valley
physics and plays a crucial role towards spintronics and valleytronics [31,32].
Besides the structural, electronic, and linear optical properties
of TMDs, their nonlinear optical properties, especially second harmonic generations (SHG) have been studied, where the lack of
inversion symmetry in monolayer TMDs leads to a strong optical
SH response. Bulk 2H-MoS2 crystal belongs to space group D6h,
which possesses inversion symmetry different from monolayer.
Consequently, the second-order nonlinear response for 2H-MoS2
bulk should vanish [32]. It has been reported that the secondorder nonlinear susceptibility for MoS2 bulk is around 10 14 m/V,
much smaller than that of monolayer (10 7 m/V). This SHG effect
proves to be highly sensitive to the thickness, crystalline
orientation, as well as stacking configuration [33,34]. So far,
thickness-dependent optical SHG in odd-layer TMDs have been
found [35–38], attributed to the non-trivial second-order
nonlinearity due to the broken inversion symmetry. Hsu et al. have
studied the SHG of artificially stacked bilayer MoS2 with various
twist angles. The SHG signals can be described as the coherent
superposition of SH signal from individual layer involving a phase
difference relying on the twist angle. Therefore, the stackingdependent polarization of SHG intensity can be served as one accurate and powerful characterization tool to identify their atomic
stacking orders [39].
The nature of TMDs, such as appropriate bandgap, high carrier
mobility, high current on/off ratios, and thickness-dependent band
structure makes TMDs as promising materials for various devices
[40,41], such as field-effect transistors (FETs), photovoltaics, photodetectors, and nonvolatile memories [42–46]. From literature,
most electronic devices are constructed using the p-n junctions
through heavy doping, Schottky junctions between metal and
semiconductor, vdWs heterojunctions by mechanical transfer and
thickness-/strain-induced homojunctions. For example, the
diode-like rectification effect and remarkable drain-source current
have been demonstrated in TMDs-based materials, such as
thickness-dependent MoX2 homojunctions [47–49], phasemodified 1T’-2H MoX2 Schottky junctions [50], WS2-WSe2 [51],
WX2-MoX2 [52–56] heterojunctions. In ref [47], He et al. reported
that a series of thickness -dependent 3R-MoSe2 junctions exhibit
current rectification and photovoltaic behaviors, and yet without
heavily doping strategies in TMDs [50] or TMDs heterojunction
fabrication [17]. The first-principles calculations show that the
thickness -dependent band alignment determines the electronic
and optoelectronic behaviors in such junctions. Moreover, layerengineered homojunctions can be prepared through one-step
CVD growth approach that is much simpler than the preparation
processes for TMD heterojunctions. Such strategy provides guidance for designing and fabricating possible layer-engineered
devices. Similarly, the layer-engineered homojunctions with 2H
stacking and the stacking-dependent (e.g. 2H-3R bilayer) TMD
homojunctions are expected to exhibit novel electronic and optoelectronic properties.
Growth and stacking characterization of layered TMDs
In general, there are two mainstream strategies to fabricate
few-layer 2D TMDs: top-down and bottom-up. The top-down
strategy consists of mechanical exfoliation (ME) [57] and liquidphase exfoliation (LPE) [58]. Fig. 1 shows the typical ME process
to obtain few-layer MoS2 from pristine crystals, where the screw
dislocations observed in the optical micrographs (Fig. 1A) from
the 2H (left) and 3R (right) single crystals present their hexagonal
and trigonal structures respectively [16]. The detailed exfoliation
processes and optical/AFM morphology for obtaining few-layer
MoS2 samples are shown in Fig. 1B, C [30,57]. Due to the low productivity of few-layer TMD sheets in top-down approach, bottomup strategy becomes more and more popular, which can be extensively realized by CVD [59], physical vapor deposition (PVD) [12],
atomic layer deposition (ALD) [60], as well as epitaxy growth.
Compared with ME, the sample growth processes by these methods can be controlled more easily with much higher yield of fewlayer samples, where large amount of one to four layered TMD
flakes with various stacking configurations have been obtained,
while ME method yields predominately 2H stacking sequence only.
We used both CVD and PVD to grow MoS2 samples (Fig. 2). We
obtained a large amount of multilayer MoS2, especially 2L and 3L
MoS2 with various stacking configurations by PVD. The typical
growth process and morphologies of 1L-4L samples using the
PVD method are shown in Fig. 2A. We acquired mostly 1L MoS2
flakes with various shapes by the CVD method (Fig. 2B). Fig. 2C
compares the structural and electronic properties of graphene
J. Xia et al. / FlatChem 4 (2017) 1–19
3
Fig. 1. (A) Optical micrograph images of the surface morphologies for MoS2 single crystals with 2H (left) and 3R (right) stacking. Reproduced with permission from Ref. [11].
Copyright 2014, Nature Publishing Group. (B) Micromechanical exfoliation processes. Reproduced with permission from Ref. [55]. Copyright 2012, IOP Publishing Group. (C)
Optical morphology (a) and AFM image (b) of few-layer MoS2 by micromechanical exfoliation. Reproduced with permission from Ref. [30]. Copyright 2010, American
Chemical Society.
Fig. 2. Vapor deposition of few-layer MoS2 samples. The temperature ramping diagram of the growth process and morphologies of as grown MoS2 flakes by PVD (A) and CVD
(B) respectively. (C) Mobility comparison of graphene and MoS2 grown by various methods. The red curve shows the mobility of graphene on SiO2, and the blue curve is for
MoS2 on SiO2. The mechanically cleaved samples show the best structural and electronic quality for both graphene and MoS2. Reproduced with permission from Ref. [59].
Copyright 2014, Nature Publishing Group.
Fig. 3. Atomic structures of bilayer (2L) and trilayer (3L) MoS2 grown by CVD method. (A) All five classic atomic structures of bilayer MoS2. (B) Optical and Z-contrast STEM
images of the monolayer (left), AA- (middle) and AB- (right) stacking MoS2 bilayer (C) Top and side views of 3L MoS2 with four typical stackings, ABA, AAA, AAB(ABB). Insets
are the optical images and Raman mappings of these 3L MoS2 samples. Reproduced with permission from Ref. [12]. Copyright 2015, American Chemical Society.
and MoS2 prepared by different methods [61]. The red and blue
curves show the mobility of graphene and MoS2 samples on SiO2.
On one hand, both graphene and MoS2 samples from the mechanically cleaved method show the best structural and electronic quality, due to fewer defects. On the other hand, CVD/PVD grown
samples provide more stacking variations to investigate interlayer
coupling effect on optical, electronic, electrical and other intriguing
physical properties.
From the first-principles calculations, there are five highsymmetry stacking configurations for bilayer MoS2 as shown in
Fig. 3A, which can be classified into two groups depending on
whether the S (Mo) atoms in the top layer are directly situated
above the Mo (S) atoms of the bottom layer. The optical image
(Fig. 3A centre) shows that PVD grown bilayer MoS2 sheets exhibit
two typical configurations: two triangles in the same orientation
(marked as AA) and in reverse orientation (marked as AB). Our
previous results indicate that AA and AB stackings are the most
favorable among all configurations while other three are energetically unstable. The two natural polytypes of MoS2 are known as 2H
(space group: P63/mmc) and 3R (space group: R3m) respectively,
both of which have trigonal prismatic coordination of the Mo
atoms but with distinct stacking orders [11,12]. Fig. 3B shows the
optical and Z-contrast scanning transmission electron microscopy
(STEM) images of the 1L (left), AA- (middle) and AB- (right) stacked
2L MoS2. The STEM images clearly show the distinct arrangements
between AA and AB stacked bilayer samples. In STEM, the intensity
sensitively relies on the atomic weight and the number of layer,
where the high intensity sites correspond to the heavy atoms
(Mo) and thicker samples, leading a contrast difference. In the 3L
MoS2 samples, there are four typical stacking patterns: ABA, AAA,
4
J. Xia et al. / FlatChem 4 (2017) 1–19
AAB and ABB following the nomenclature of bilayer system, which
lead to three distinct stacking configurations as the ABB and AAB
configurations are completely equivalent. The top and side views
of atomic structures for ABA-, AAA- and AAB-stacked 3L MoS2 are
shown in Fig. 3C, where the layer number is determined by both
optical images and Raman intensity mapping [12,31].
Thickness- and stacking-dependent interlayer coupling
The electronic properties of 2D materials are affected by both
layer number and stacking configurations through interlayer coupling [62–64]. The different Raman behaviors for both highfrequency and low-frequency modes as a function of layer number
have been revealed and widely discussed in recently years. Raman
spectroscopy is a greatly potent and efficient approach to investigate the thickness variation and phase transition behaviors in 2D
materials, especially the ultra-low-frequency (ULF) Raman spectroscopy, which is highly sensitive to interlayer interactions and
can reflect even the minute changes and discrepancies of structure.
Affected by layer numbers and layer stacking, both shear modes
(SMs) and layer breathing modes (BMs) have been observed that
exhibit strikingly different features for different configurations,
which can be well modeled using linear chain simulations [12].
Thus, polarized ULF Raman technique can be used as a fast and
convenient nondestructive method to identify stacking sequence,
which is otherwise very difficult using other techniques.
The Raman frequency trends in MoS2 crystal from 1L to 12L are
studied both theoretically and experimentally in Fig. 4. The
Raman-active in-plane E12g mode stiffens whereas the out-of-plane
A1g mode softens with decreasing thickness. The black curves are
the experimental results and the density functional theory (DFT) calculations are plotted in blue bars, showing the consistent frequency
evolution trends (Fig. 4A). The red shift of the A1g mode with
decreasing layer number is attributed to the smaller restoring force,
while there are several explanations to the blue shift of E12g mode,
which has been ascribed to thickness-induced structure modification, long-range coulomb interactions, or enhanced surface force
constant of Mo-S intralayer interactions in few-layer MoS2 [65]. Similar thickness-dependent phonon evolutions can be also found in
low-frequency SMs and BMs, as shown in Fig. 4B and C, where two
optical configurations (z(xx)z (4B) and z(xy)z (4C)) are utilised.
Based on the Raman tensor, the interlayer SMs and E12g mode are
shown in both z(xx)z and z(xy)z configurations, whereas the interlayer BMs and A1g mode are observed only in the z(xx)z configuration. In Fig. 4B and C [66], from bulk to 2L, the S1 peak red shifts
from 32 cm 1 to 22 cm 1. In contrast, the other predominant
peak B1 blue shifts and crosses the S1 peak at 3L. As discussed
before, the frequency evolutions of E12g and A1g have been used to
determine the layer number of TMD samples [29]. However, these
two peaks are much less sensitive to the thickness than the interlayer SM and BM peaks. Two weak peaks, labelled S2 and B2, exhibit
the similar trends versus thickness with S1 and B1. Fig. 4D and E
show the phonon dispersions and density of states (DOS) for 1L
(4D) and bulk MoS2 (4E) with experimental data plotted in black
dots [67]. Different from monolayer MoS2, the bulk phonon dispersion has three acoustic modes, the in-plane longitudinal acoustic
(LA) mode, transverse acoustic (TA) mode and out-of-plane acoustic
(ZA) mode, whereas, the low-frequency optical modes are found at
35.2 and 57.7 cm 1, corresponding to the rigid-layer lateral and ver-
Fig. 4. Thickness-dependent Raman behaviors of MoS2. (A) Experimental and LDA-calculated high-frequency Raman for few-layer and bulk MoS2. Reproduced with
permission from Ref. [63]. Copyright 2013 American Physical Society. The E12g mode blue shifts and the A1g mode red shifts as the thickness of the MoS2 sample decreases. The
green and red dashed lines are the frequency evolution trends for the experimental and LDA results, respectively. (B, C) Ultra-low-frequency (ULF) Raman spectrum evolutions as
a function of layer number in 1L-12L MoS2 using z(xx)z (B) and (xy)z (C) polarization configuration. Reproduced with permission from Ref. [64]. Copyright 2013, American
Chemical Society. (D, E) Phonon dispersion curves and density of states for single-layer (D) and bulk (E) MoS2. Reproduced with permission from Ref. [65]. Copyright 2011
American Physical Society.
J. Xia et al. / FlatChem 4 (2017) 1–19
5
Fig. 5. Displacement representations for the Gama-point phonon vibrational modes in bulk MoS2 with vibrational frequencies shown below. R and I represent Raman active
and inactive vibrations respectively. Reproduced with permission from Ref. [63]. Copyright 2013 American Physical Society.
tical motion, respectively. Based on group theory [50], the phonon
modes at C-point for bulk MoS2 can be decomposed into the
irreducible representation: C = 2A2u + 2E1u + 2B2g + 2E2g + A1g +
E1g + B1u + E2u. These 12 irreducible representations in bulk MoS2
can be divided into six conjugate pairs (E11u and E22g, E1g and E2u,
E21u and E12g, A12u and B22g, A1g and B1u, A22u and B12g), as shown in
Fig. 5. In each conjugate pair, there is an inversion centre between
the two layers, and one phonon mode differs from the other by an
interlayer phase shift of 180°. Fig. 5 shows all the displacement representations for the C-point vibrational modes in bulk MoS2 with
frequencies shown below, where R and I represent Raman active
and inactive vibrations respectively. All these calculated phonon frequencies are consistent with previous experimental results [65].
It has been reported that MoS2/WS2/MoSe2/WSe2 undergoes a
transition from the indirect-band-gap to direct-band-gap semiconductor with their thickness reduced to monolayer. Correspondingly, the PL quantum yield (QY) shows an obvious enhancement
while the TMD crystal undergoing from the indirect-gap bulk to
the direct-gap monolayer [68]. Systematic studies of the evolution
of the optical properties and electronic structures in layered TMD
crystals as a function of layer number (N) have been reported. With
the reduction of thickness, the confinement-induced band gap varies from the bulk value of 1.29 eV to over 1.90 eV in monolayer.
Moreover, the change in the energy of indirect band gap at C point
is about 0.7 eV, much larger than that of the band gap at K point of
about 0.1 eV (Fig. 6A). The corresponding PL spectra obtained from
samples of different layer thickness are shown in Fig. 6B. The direct
bandgap of the 1L MoS2 produces the strongest PL intensity, while
its intensity decreases with increasing MoS2 thickness along with
the direct-to-indirect bandgap transition. Two prominent exciton
PL peaks at 1.83 eV and 1.98 eV are identified as the direct
transition at the K-point in the MoS2 Brillouin zone [30,69]. The
main PL peak (Peak A) of 1L MoS2 samples has a narrow width of
50 meV, with exciton energy at 1.90 eV, and few-layer samples
display multiple emission peaks (labelled A, B, and I). Peaks A
and B agree with the 1L emission that shift to the red and slightly
broadens with increasing N, where Peak B possesses the energy
150 meV larger than that of Peak A. Peak I systematically red
shifts and becomes less prominent with increasing N, approaching
the indirect-gap energy of 1.29 eV for bulk [17,70]. To explore the
origin of the observed PL properties, the comparison between PL
and absorption spectra has been done. The absorption spectra
for MoS2 crystals with different layer thickness are displayed in
Fig. 6C [68]. The two peaks in the absorption spectra at 1.88 eV
and 2.03 eV correspond to the A and B exciton transitions in the
PL spectra in Fig. 6A. The energy separation between the A and
B exciton peaks is 0.15 eV in the 1L MoS2 and gradually
increased with increasing MoS2 layer number, close to 0.19 eV
for the bulk MoS2. This valence band splitting arises from the
remarkable SOC effect and interlayer interactions in few-layer
MoS2 samples [1,9]. DFT calculations [22] have been employed
to explore the band structures for 4L, 3L, 2L, and 1L MoS2, as
shown in Fig. 6A. The indirect bandgap gradually increases monotonically with the decreasing of layer number while the direct
exciton transition energy at K point almost shows no changes.
The variation of the electronic structure using the first-principles
calculations in few-layer MoS2 is in accord with previous PL and
absorption data [30].
Stacking significantly influences the crystal symmetry and
hence can mediate the magnetism, superconductivity, electronic
Fig. 6. Layer-dependent electronic band structure without spin-orbit coupling (A), PL (B) and absorption (C) of MoS2 crystals. Reproduced with permission form Ref. [30].
Copyright 2010, American Chemical Society. In B, the band-gap energy of thin layers of MoS2, inferred from the energy of the PL feature I for N = 2–6 and from the energy of
the PL peak A for N = 1. The dashed line represents the (indirect) band-gap energy of bulk MoS2. Reproduced with permission form Ref. [68]. Copyright 2014, Royal Society of
Chemistry.
6
J. Xia et al. / FlatChem 4 (2017) 1–19
Fig. 7. Stacking-dependent Raman behaviors of bilayer MoS2. (A) Optical image of CVD grown 2L MoS2 with AA and AB stacking. (B, C) High-frequency (B) and ULF (C) Raman
spectra of AA- and AB-stacked 2L MoS2. (D) The linear chain models of bilayer MoS2 with AB and AA stacking. The labels on the atoms are used for constructing the notation of
force constants and the weak interlayer interaction is indicated by a spring. The arrows depict the vibrational diagrams of shear (S, left) and breathing (B, right) mode for 2L
MoS2. Reproduced with permission from Ref. [12]. Copyright 2015, American Chemical Society. (E, F) ULF Raman spectra for 2L WSe2 (E) and MoSe2 (F) with different
stackings. Reproduced with permission from Ref. [69]. Copyright 2016, Nature Publishing Group.
band structure and other physical properties [9,11,39]. Such
stacking-dependent effects are obviously projected onto MoS2
and have been widely investigated in recent years. For bilayer
TMDs system, there are two typical stacking polytypes (AA and
AB) as demonstrated before. An optical image containing both
AA- and AB-stacked bilayer MoS2 is shown in Fig. 7A. The Raman
spectra for AA- and AB-stacked 2L MoS2 in the high-frequency
range (350–440 cm 1) are shown in Fig. 7B, where the intensity
of both E12g and A1g peaks for AB stacking is larger than that of
AA stacking and no significant frequency change in the two highfrequency modes. Hence the Raman bands in the high-frequency
range is not sensitive to the vdWs interactions caused by stacking.
Distinct behaviors are found in ULF Raman modes (Fig. 7C), in
which the two peaks located at 22.6 (22.8) and 41.6 (38.7)
cm 1 for AB (AA) stacking 2L MoS2 belong to the in-plane SM
and out-of-plane BM respectively. We note that the SM almost
shows no stacking-dependent shift while the BM obviously red
shifts for AA stacking. As for the peak position shift, we analysed
the force constants in AB- and AA-stacked 2L MoS2 up to the
second-nearest neighbours [12]. As shown in Fig. 7D, the stacking
sequence not only changes the interactions between the two layers
(k34), but also involves the interactions up to the second-nearest
neighbours (k24). Firstly, the force constants for the SM are smaller
than those of the BM. Furthermore, the stacking affects both k24
and k34, leading to the different behaviors for BM and SM. For
instance, the BM force constant k34 increases slightly but k24
decreases significantly from AB to AA stackings, resulting in an
overall redshift of BM. However, the SM is not sensitive to stacking,
which can be attributed to the almost equal change in force constant of k34 (decreasing) and k24 (increasing) from AB to AA stacking. More importantly, the intensity ratio between the BM and SM
is very distinct: 1.2 for AB and 4.1 for AA stacking, calculated
using the integrated areas of the Stokes Raman peaks. Therefore,
the ratio of BM and SM can be used as a convenient method to
identify the stacking orders of 2L MoS2 and confirm the previous
STEM results: macroscopic AA and AB stacking patterns correspond to 3R and 2H atomic stacking orders, respectively.
Fig. 7E and F also compare the stacking-dependent ULF Raman
responses for WSe2 and MoSe2 [71]. Similarly, for the behaviors
of SM and BM in few layer WSe2, a clear decrease in intensity of
the SM from 2L-2H to 2L-3R stacking is observed, yet with a corresponding increase in the BM. The ULF Raman peaks shown here
agree well with different stacking configurations of 2L WSe2
reported previously [72]. In Fig. 7F, ULF Raman spectra for different
stackings of 2L MoSe2 are shown, corresponding to 2H (max at
18 cm 1), 3R (max at 18 cm 1, but significantly lower in relative
intensity), and 3R⁄ (max at 29 cm 1) as reported in ref [69]. The difference between 3R and 3R⁄ is attributed to one being 3R, and the
other being the vertically flipped 3R [73], which show different
phonon behaviors. The stacking-dependent electronic features for
2L MoS2 are also demonstrated in Fig. 8. The larger emission intensity of A exciton and the larger energy difference between A and B
excitons for AB-stacked 2L MoS2 compared with AA stacking can be
obviously found in Fig. 8A, which agree with previous reports [12].
Moreover, the calculated band structures for AA and AB 2L MoS2 in
Fig. 8B and C clearly depict the splitting of top valence bands in AB
stacking is larger than that of AA stacking, which in turn supports
the experimental discoveries in Fig. 8A.
Liu et al. [74] successfully grew more diverse 2L MoS2 samples
on fused silica with different twist angles, as shown in Fig. 9, by a
specialized CVD method. As the atomic twist bilayer structures are
directly correlated with the microscopic crystal orientation of the
two vertically stacked triangles, the evolution of high-frequency
phonon vibrations in twisted 2L MoS2 using Rama spectroscopy
J. Xia et al. / FlatChem 4 (2017) 1–19
7
Fig. 8. Stacking-dependent PL features (A) and electronic band structures for 2L MoS2 with AA (B) and AB (C) stackings.
Fig. 9. Stacking-dependent Raman and PL behaviors of CVD grown 2L MoS2 with stacking angles at 0°, 15°, 60°. (A–D) Optical images of 1L and 2L MoS2 with different
stacking angles. The insets are corresponding atomic models. (E) Raman spectra of a MoS2 monolayer and bilayers with different twist angles of 0°, 15°, 60°. (F) Raman peak
separation between the A1g and E12g in 2L MoS2 of different twist angles. (G) PL spectra of MoS2 monolayer and bilayers with different twist angles. (H) Dependence of PL peak
energies on the twist angle for a batch of 2 L MoS2. Reproduced with permission from Ref. [72]. Copyright 2014, Nature Publishing Group.
are investigated in Fig. 9E. As the two prominent peaks, the inplane E12g and out-of-plane A1g phonon modes are sensitive to the
layer number, in which the E12g mode softens and A1g mode stiffens
through an enhanced dielectric screening with increasing layer number [67,75], the separation between these two peaks can serve as an
indicator for the interlayer coupling strength, in which the larger
separation means the stronger coupling. Fig. 9F clearly shows that
AA or AB stacking has the strongest coupling and the others exhibit
weaker coupling strength.
The PL spectra (Fig. 9G) of twisted 2L MoS2 samples show three
prominent peaks at around 2.05 eV, 1.85 eV and 1.50 eV, corresponding to the two direct (A exciton-Peak I and B exciton) and
indirect exciton peak II that originates from the interlayer exciton
transition and depends sensitively on the interlayer electronic coupling strength: the smaller the indirect bandgap, the stronger the
coupling strength. Fig. 9H displays the energy difference between
peak I and II in twisted bilayer samples. Unlike Peak I that remains
almost unchanged, the energy for Peak II is the lowest for AA- and
AB-stacked 2L MoS2, and higher but nearly constant value for all
other twist angles. Such trend shows the similarity to that of the
interlayer coupling strength reflected in Raman vibrations (Fig. 9F),
indicating that the repulsive steric effects play a crucial role in the
evolution of interlayer coupling between the bilayers for various
stacking orders [74].
Beyond the stacking-dependent phonon and electronic properties in CVD grown 2L MoS2 samples, similar stacking effects also
exist in folded 2L MoS2 with random twist angles [9,76,77]. In
Fig. 10A, three MoS2 bilayer regions labelled as A, B and C are prepared by folding the ME monolayer samples, leading to the modulation of the interlayer coupling and the band structures [78,79].
Fig. 10B and C present the PL spectra of the natural 2H bilayer,
and folded bilayers A, B and C and the corresponding band structures with SOC effects. The A exciton peaks at 1.86 eV are almost
unchanged among various stacking configurations, while the
indirect-gap transitions at 1.6 eV vary significantly. The origin
of peaks at 1.86 eV (A exciton) is the direct-gap transition
between the strongly localized Mo-d orbitals and exhibit little
interlayer overlapping. Therefore, it almost shows no stackingdependent feature [30]. For peaks at 1.6 eV (indirect exciton),
the indirect-gap transition occurs between the band extrema arising from linear combinations of Mo-d and S-p orbitals with strong
interlayer overlapping and thus is sensitive to the layer stacking
[79]. Among various stacking configurations, the interlayer coupling strength relies on the interlayer spacing: the enlarged interlayer spacing means the reduced interlayer coupling and the
decreased band gap value. Based on above argument, the most reasonable structure of region A is 2H-like(Mo) bilayer and region B is
3R-like bilayer, while the region C is identified to align between the
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J. Xia et al. / FlatChem 4 (2017) 1–19
Fig. 10. Stacking-dependent PL behaviors in folded 2L MoS2 with random stacking angles. (A) Optical images of 2L MoS2 folded with different stacking angles and folding
edges highlighted by dashed red, black and green lines. (B) PL spectra of the natural 2H bilayer (purple), bilayer A (red), bilayer B (black) and bilayer C (green) excited at
2.33 eV. (C) Electronic band structures of 2H, 2H-like (Mo, A) and 3R-like (B) bilayers by ab initio calculations with spin–orbit coupling (SOC). Reproduced with permission
from Ref. [9]. Copyright 2014, Nature Publishing Group.
Fig. 11. Stacking-dependent Raman behaviors of 3L MoS2. (A) Raman spectra of ABA-, ABB-, AAB-, AAA-stacked 3L MoS2. (B) ULF Raman of 3L MoS2 with different stackings,
collected under unpolarised (black)), (
z(xx)z (k) (blue) and (
z(xy)z (\) (red) configurations. (C) The intensity ratio of the (
z(xx)z (k) and (
z(xy)z (\) collection for 3L MoS2 in
(B) with error bars of experimental standard deviation for several samples. Reproduced with permission from Ref. [12]. Copyright 2015, American Chemical Society.
2H and 3R-like bilayers supported by its SHG signals discussed in
ref [9].
Trilayer TMD samples endows more stacking configurations
and hence generate more diverse stacking-induced coupling
effects. We obtained four typical stacking patterns: ABA, AAA,
AAB and ABB, where the ABB and AAB atomic configurations are
completely equivalent in symmetry based on our previous discussion [12]. As for the Raman vibration modes in the high frequency
region, distinct behaviors also exhibit for trilayer system as shown
in Fig. 11A. The E12g mode almost remains unchanged while the A1g
mode blue shifts with altering the 2H (ABA) stacking, leading to
the largest frequency difference in AAA stacking samples
(25.35 cm 1), followed by AAB (ABB) trilayer (24.25 cm 1), and
the smallest for ABA stacking (24.07 cm 1). For few-layer samples
with various stacking orders, each monolayer MoS2 is identical and
just assembled in various sequences, leading to different lateral registrations but almost identical interlayer distances. The stackingdependent Raman feature manifests the stacking-dependent interlayer coupling, similar with the trend on the layer number
[13,65,67,73]. Beyond the stacking-dependent features in high frequency, the ULF Raman spectra give additional information about
the interlayer coupling. In Fig. 11B, the SM and the BM in ULF range
are merged into one peak, where Ib/Is cannot be directly used to
identify the stacking configurations as in bilayer samples. Instead,
we use the polarization measurements to identify the different features between the SM and BM (Ik/I\). Here, Ik is the sum of the parallel components for both SM and BM bands, while I\ contains only
the perpendicular component of SM, as the BM is entirely sup-
pressed under perpendicular collection configuration. Thus, the
Ik/I\ ratio can be used to identify stacking configurations for trilayer
systems, while Ib/Is was used for bilayer systems. As shown in
Fig. 11B, the intensity ratio Ik/I\ for AAA stacking is the highest, followed by AAB (ABB) stacking, with ABA stacking having the lowest
ratio. We summarize the intensity ratio Ik/I\ of the interlayer BM
to SM for 3L MoS2 (3 for ABA stacking, 6 for AAB and ABB stacking, 8 for AAA stacking) in Fig. 11C. Beyond MoS2, stackingdependent Raman intensities for the SM and BM are also found in
other TMD materials, for instance, 3L MoSe2 as shown in Fig. 12.
The atomic structure (top) and displacements of the interlayer SMs
(down) in ABA- and AAA-stacked 3L MoSe2 are shown in Fig. 12A,
similar to our previous 3L MoS2 systems. Fig. 12B shows the Raman
spectra of ABA- and AAA-stacked 3L CVD grown MoSe2 samples. The
peak around 13.3 cm 1 was attributed to the lowest frequency SM
(S1) in AAA-stacked 3L MoSe2, while the peak at 23.1 cm 1 corresponds to the theoretically predicted value of 25.5 cm 1 for highest
frequency SM (sN-1) in ABA-stacked 3L MoSe2 [14]. The samples with
both S1 and sN-1 modes indicate the coexist AAA and ABA phases
with either a sharp boundary [80], or a few-hundred nanometer
wide transition area [81]. They also measure the sN-1 Raman peak
of exfoliated 3L MoSe2sample with ABA stacking and confirm that
the samples that show a peak around 23.1 cm 1 are ABA stacked.
Fig. 13A plots the PL spectra of a set of 3L MoS2 samples with
various stackings [12]. The gray dashed lines indicate the stacking
dependence of the PL peak separation between two prominent
peaks PA and PB, which attribute to the direct A and B exciton transitions. Interestingly, the splitting in AAA stacking samples is the
J. Xia et al. / FlatChem 4 (2017) 1–19
9
Fig. 12. (A) Atomic structure (top) and vibrational displacements of the interlayer shear modes (down) in ABA- and AAA- stacked 3L MoSe2. (B) Raman spectra of the 3L
MoSe2 with different stackings. Reproduced with permission from Ref. [14]. Copyright 2015, Nature Publishing Group.
Fig. 13. Stacking-dependent PL features of 3L MoS2. (A) PL spectra of ABA-, ABB-, AAB-, AAA-stacked 3L MoS2. (B) Calculated electronic band structures of ABA-(left), AAAstacked (right) 3L MoS2. The band curves in red and blue correspond to the spin-up and spin-down states. Reproduced with permission from Ref. [12]. Copyright 2015,
American Chemical Society.
smallest (48 nm), followed by those with ABB (AAB) stacking
(56 nm), while ABA stacking has the largest splitting (62 nm).
Similar trend is also found in our previous 2L systems with AA
and AB stacking. Such stacking-dependent splitting patterns in
few-layer samples arise from the SOC and the interlayer hopping
effects in TMDs. In even-layer samples with inversion symmetry,
both SOC and interlayer hopping effects contribute to the splitting
between A and B peaks at K points. The different behaviors in splitting patterns have been reported in optical reflection spectra and
transmission spectra for the 2H and 3R bulk phases of TMDs
[11,82]. By first-principle calculation, Fig. 13B shows the spinpolarized band structures of ABA- and AAA-stacking 3L MoS2 considering SOC effects. The band curves in red (blue) represent the
spin-up (spin-down) states. SOC effects dominate the energy splitting in the top valence bands for ABA-stacking, while both SOC and
interlayer hopping effects contribute to the splitting patterns for
AAA-stacking 3L MoS2, which corresponds to the observed
stacking-dependent PL peaks separation in Fig. 13A. Another interesting feature is the different spin-valley polarizations in different
stackings: the valence band edges at K point in ABA stacking are
dominantly from spin-up states with some mixing of spin-down
states, while in AAA stacking, the VBM bands are completely
spin-polarized. Our ab initio calculations indicate the enhanced
spin-valley polarization in the AAA stacking contrast to the ABA
stacking, which is similar to the observed spin-polarized states in
the 3R phase TMDs by circularly polarized photoluminescence
(CP-PL) measurements [11].
Spin-valley polarization in few-layer TMDs
Following the band structure discussions for virous stacking
configurations in few-layer TMDs, we then investigate how layer
and stacking affect the spin and valley features. As reported, one
of the most appealing applications of TMDs is the so called ‘valleytronics’. The concept of valleys originates from that of spin
and suggests the promising devices, analogous to spintronics, for
next-generation electronics and optoelectronics. The key step
towards valleytronics is to achieve the valley polarization through
creating non-equilibrium charge carrier imbalance between K and
K’ valleys [83–86]. The principal mechanism usually involved is
circularly polarized optical excitation [3,4], in which the two valleys absorb left- (r ) and right- (r+) hand photons respectively,
leading to a valley-selective circular dichroism (CD) within a honeycomb lattice due to the absence of inversion symmetry. There-
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J. Xia et al. / FlatChem 4 (2017) 1–19
Fig. 14. Thickness-dependent circularly polarized PL (CP-PL) in few-layer MoS2. (A) Three-dimensional band structure of 1L MoS2 with top valence band and bottom
conduction band marked in blue and pink. The centre hexagon is the Brillouin zone coloured by the degree of circular polarization, q. Reproduced with permission from Ref.
[85]. Copyright 2012, Nature Publishing Group. (B) Schematic of valley-dependent selection rules at K and -K points in crystal momentum space: left (right)-handed circularly
polarized light in blue (red) only couples to the band-edge transition at K (-K) points (C) CP-PL spectra at 4K for 1L, 2L, 3L and 4L 2H- (left) and 3R- (right) MoS2, excited by a
left circularly polarized (r ) 633 nm laser. (D, E) Spin-resolved energy distribution curves (EDCs) for spin along the z axis, collected at the inequivalent valleys of the K and -K
points for 2H (D) and 3R (E) MoS2. (F, G) Calculated spin polarizations Pz/P of the valence bands along (0, ky, 0) for 2H-(F)/3R-(G) MoS2. Reproduced with permission from Ref.
[11]. Copyright 2014, Nature Publishing Group.
fore, in 1L TMDs without crystal inversion symmetry, the valley
pseudospins can be distinguished by opposite signs at the corners
(K and K’) in the hexagonal Brillouin zone. The giant SOC separates
the valence bands at each valley into the spin-up and spin-down
states. Such inherent spin-valley coupling can significantly protect
the valley polarization as the intervalley scattering requires a
simultaneous spin flip. Only carriers with selective spin can be
emitted under the valley optical selection rule, which have been
widely demonstrated in the literature [18,84]. The colored band
structure of 1L MoS2 with top valence band and bottom conduction
band marked in blue and pink is shown in Fig. 14A. Fig. 14B depicts
the schematic of valley-dependent selection rules for monolayer
TMDs at K and K0 points in crystal momentum space: r- (r+) circularly polarized light in blue (red) only couples to the band-edge
transition at K (K0 ) points. Therefore, the direct-bandgap transition
at the two degenerate valleys, together with this valley-contrasting
selection rule, suggest that one can optically generate and detect
valley polarizations in a TMDs monolayer [16].
Beyond monolayer, few-layer TMDs introduce another intrinsic
degree of freedom named as layer pseudospin. The interlayer hopping of electrons/holes further affects the spin–valley coupling in
TMDs [21–23]. The layer pseudospin refers to the carriers’ location,
either upper or lower layer in bilayer TMDs for instance. The natural AB-stacked bilayer TMDs, in which the lower layer is rotated
by 180° with respect to the upper layer, possess the crystal inversion symmetry. Consequently, the layer rotation switches two valleys but leave the spin unchanged, which results in a sign change
for the spin-valley coupling from layer to layer. In theory, the
valley-dependent effect should vanish in the presence of inversion
symmetry [84–86]. Fig. 14C presents CP-PL spectra of thicknessdependent 3R- and 2H-MoS2 collected at 4 K with r excitation
of 633 nm (1.96 eV), where r+ and r denote right and left circu-
larly polarized light, respectively. All the spectra are composed of
sharp Raman and broad PL peaks, with the latter showing a peculiar thickness-dependent circular polarization. For 2H stacking, the
intensity difference between the r+ and r PL peak becomes smaller with increasing layer number, whereas that for 3R stacking
does not show a clear layer number dependence. Therefore, the
degree of circular dichroic polarization q, defined as
½Iðr Þ Iðrþ Þ=½Iðr Þ þ Iðrþ Þ under r excitation, shows obviously different evolution trends versus layer number for 2H and
3R stacking TMD crystals. In summary, the valley polarization q
in 3R MoS2 is almost independent on thickness, suggesting the
strongly preserved excitons at the K (K0 ) point, while q decreases
significantly in 2H MoS2.
In theory, inversion-symmetric even-layer 2H-MoS2 should
possess negligibly small q and yet the thickness-dependent q in
the 2H stacking is rather unexpected. In fact, such a noticeable q
in inversion-symmetric 2L TMDs has been widely reported in previous literature [15,25]. One plausible reason is the carrier localized effects, where the electrons/holes are localized in each layer
rather than interlayer hopping [26]. In detail, the generated carriers under the circularly polarized laser (r or r+) in the K (K0 ) valley tend to localize within the upper (lower) layer, and the value of
q decreases due to the intralayer-intervalley hopping and
interlayer-intravalley
hopping.
However,
the
interlayerintervalley hopping should be improbable owing to the giant
momentum change and layer crossing barrier. As for 3R MoS2, both
interlayer and intralayer hopping are negligible and carriers are
locked in each layer, leading to a larger q compared to that of 2H
stacking. These results are also confirmed by spin- and angleresolved photoemission spectroscopy (SARPES) in Fig. 14D and E.
The valence bands near the Fermi level at the K point for 2HMoS2 and 2H-WSe2 are almost unpolarized. For 3R stacking cases,
J. Xia et al. / FlatChem 4 (2017) 1–19
the SARPES (sz) spectra at the K and K0 points in Brillouin zone
(Fig. 14E) show the inversion of spin polarization. Therefore, this
technique offers direct and powerful evidence of the valley/spin
coupled state realized in bulk 3R-MoS2. Fig. 14F and G show the
calculated spin polarizations Pz/P of the valence bands along
(0, ky, 0) for 2H-(Fig. 14F)/3R-(Fig. 14G) MoS2, respectively. The
white bands in Fig. 14F are the summation of spin-up and spindown states for 2H-stacked MoS2, while the red and blue bands
stand for the individual spin polarization contributions by SOC
and interlayer hopping effect (Fig. 14G). Therefore, both SARPES
and calculated results provide a firm and clear image of the different spin-valley polarization behaviors for 2H and 3R stacking TMDs
versus layer number [11].
In addition to valley and layer pseudospins demonstrated
above, we proposed a new degree of freedom in our previous work
- stacking pseudospin in 2L and 3L TMD systems, where diverse
stacking configurations can be facilely grown by CVD method.
Based on previous discussions, certain stacking orders can break
the inversion symmetry and reduce the interlayer coupling, which
are prerequisites for valley- and/or spin-selective circular dichroism. Among all stacking configurations, intralayer-intervalley hopping between the K and K0 valley is the most dominant valley
relaxation path, followed by the interlayer-intravalley hopping.
The latter path can preserve the momentum of the excitons and
is dominated by interlayer coupling, whic