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Exciton and Trion Dynamics in Bilayer MoS 2
Jiajie Pei , Jiong Yang , Renjing Xu , Yong-Hui Zeng , Ye Win Myint , Shuang Zhang , Jin-Cheng Zheng , Qinghua Qin , Xibin Wang , Wugui Jiang , and Yuerui Lu *
PL spectra from bilayer MoS 2 could not be tuned by elec-
tric fi eld at room temperature owing to its indirect band gap
manner, [ 7 ] which makes the exciton and trion dynamics in
bilayer MoS 2 still underexplored.
In this paper, we demonstrate the valley control of
exciton and trion dynamics in bilayer MoS 2 , via the comodu-
lations by both temperature and electric fi eld. We found that
as temperature decreases from 300 to 100 K, the valley of
the conduction band at Λ point (named as Λ valley) moves
down relatively to the valley at K point (named as K valley)
in monolayer MoS 2 , while the Λ valley rises up relatively to
the K valley in bilayer MoS 2 ( Figure 1 ). This opposite tem-
perature dependence of the valley movements in mono- and
bilayer MoS 2 can signifi cantly change the photocarrier relaxa-
tion pathways in their PL processes, which leads to more than
twice faster increasing of the measured PL intensity from
bilayer MoS 2 than that from monolayer MoS 2 as temperature
decreases. More importantly, the rising up of the Λ valley in
bilayer MoS 2 at low temperature offers the electrical tun-
ability of the K–K direct PL transition, enabling the explora-
tion of the exciton and trion dynamics in bilayer MoS 2 . The
trion binding energy of bilayer MoS 2 was fi rstly measured to
be 27 meV at 83 K, which is smaller than the measured trion
binding energy of 39 meV in monolayer MoS 2 . Our fi ndings
provide insight into exciton and trion dynamics in bilayer
MoS 2 and enable new applications in photonics and opto-
electronics. [ 1,2,17 ] Moreover, the comodulation technique by
both temperature and electric fi eld provides a novel method
to explore the fundamental phenomena in few-layer 2D
semiconductors.
We calculated the band structures of mono- and bilayer
MoS 2 at various temperatures (Figure 1 ) within density
functional theory (DFT) molecular dynamics using Perdew–
Wang (PW) generalized gradient approximation (GGA)
based on a real-space numerical atomic orbital code. [ 18 ] From
the simulation results, as temperature decreases from 300 to
100 K, the Γ peak in the valence band (named as Γ peak)
of 2L MoS 2 signifi cantly moves down relative to the K peak,
which drives the indirect band structure of bilayer MoS 2 at
room temperature approaching direct band structure at the
temperature range of ≈50–250 K (Figure 1 and Figure S1,
Supporting Information). Meanwhile, Λ valley moves down
relatively to K valley in monolayer MoS 2 , while Λ valley
moves up relatively to K valley in bilayer MoS 2 (Figure 1 a,c),
which drives the direct band structure of monolayer MoS 2
at room temperature approaching indirect band structure at
the temperature range of ≈50–210 K (Figure 1 and Figures S1 DOI: 10.1002/smll.201501949
MoS 2
J. Pei, Prof. X. Wang School of Mechanical Engineering Beijing Institute of Technology Beijing 100081 , China
J. Pei, J. Yang, R. Xu, Y. W. Myint, S. Zhang, Prof. Q. Qin, Dr. Y. Lu Research School of Engineering College of Engineering and Computer Science the Australian National University Canberra , ACT 2601 , Australia E-mail: [email protected]
Y.-H. Zeng, Prof. W. Jiang School of Aeronautical Manufacturing Engineering Nanchang Hangkong University Nanchang 330063 , China
Prof. J.-C. Zheng Department of Physics and Institute of Theoretical Physics and Astrophysics Xiamen University Xiamen 361005 , China
2D transition metal dichacogenide (TMD) semiconduc-
tors, [ 1–10 ] such as molybdenum disulphide (MoS 2 ), have
attracted tremendous attentions owing to their unique
properties, such as strong interactions with light, [ 1–4 ] layer-
dependent energy gaps, [ 5,6 ] electrically tunable exciton
dynamics, [ 7,8 ] tightly bound trions, [ 9,10 ] and so on. The elec-
tronic band structure of MoS 2 strongly depends on the layer
number and layer-stacking sequences. [ 11–13 ] Especially, mono-
layer MoS 2 owns the most distinct properties comparing to
the few-layer counterparts, as there is no interlayer interac-
tion and reduced screening effect; [ 14 ] for few-layer TMDs,
interlayer interaction, screening effect, quantum confi nement,
and crystal symmetry jointly determine their electronic struc-
tures, [ 1,11–13 ] which gives rise to direct band gap emerging in
monolayer MoS 2 and indirect band gap in few-layer MoS 2 at
room temperature. [ 15 ] Most of previous studies and fi ndings
are limited to monolayers. [ 6,8,9 ] However, few-layer structures,
particularly bilayer structure, are extremely important, since
they offer us unique platforms to investigate the fundamental
phenomena arising from the interlayer van der Waals inter-
actions, which can enable many new optoelectronic devices
based on heterostuctures. [ 16 ] Owing to the direct band nature,
the photoluminescence (PL) intensity from monolayer MoS 2
can be electrically tuned by up to two orders of magnitude,
which enables the control of exciton and trion dynamics in
monolayer MoS 2 at room temperature; [ 8,9 ] in contrast, the
small 2015, DOI: 10.1002/smll.201501949
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and S2, Supporting Information). This opposite movement
of the valleys with temperature can also signifi cantly change
the photocarrier relaxation pathways in mono- and bilayer
MoS 2 , [ 17 ] since photoexcited electrons and holes will always
prefer the low energy states. Hence, the weight of the pho-
toelectrons relaxed into the K valley will decrease in mon-
olayer MoS 2 as temperature decreases (Figure 1 b), while
conversely in bilayer MoS 2 , more portion of photoelectrons
will relax into K valley at lower temperature (Figure 1 d).
Similarly, the holes in valence band follow the same rules as
shown in Figure 1 . In order to investigate this opposite tem-
perature dependence of the photocarrier pathways, we car-
ried out temperature dependent PL measurements on both
mono- and bilayer MoS 2 samples as a comparison.
Figure 2 shows the results of temperature dependent PL
measurements from mono- and bilayer MoS 2 samples. The
low temperature PL measurements were carried out with a
Horiba Yvon T64000 micro-Raman/PL system equipped with
a Linkam liquid nitrogen chamber, using a 532 nm green
laser for excitation. In the experiment, the low temperature
chamber was cooled down from room temperature (298 K)
to near liquid nitrogen temperature (83 K), with a step of
30 K. It is clear to see that the PL intensity increases with
the decrease of temperature for both mono- and bilayer sam-
ples, which are due to the suppressed nonradiative decays at
low temperature. [ 17 ] The PL peak location shows a blue shift
with the decrease of temperature, which can be explained by
the Varshni relation. [ 19 ] Yet the increasing PL intensity for
mono- and bilayer MoS 2 shows different trends. From 298 to
233 K, the PL intensity of monolayer MoS 2 is stronger than
that of the bilayer MoS 2 sample, owing to the direct band
gap in monolayer MoS 2 and the indirect band gap in bilayer
MoS 2 at this relatively high temperature range. However,
from 203 K, the PL intensity from bilayer MoS 2 surpasses
that from monolayer and reaches almost twice the intensity
from the monolayer MoS 2 sample at 83 K, as indicated in
Figure 2 c. A similar trend was also observed from another
batch of mono- and bilayer MoS 2 samples (Figure S3, Sup-
porting Information). At a low temperature of 83 K, the much
faster rising of the PL intensity from bilayer MoS 2 comparing
to monolayer can be explained with the tuning of band struc-
ture with decreasing temperature. More specifi cally, the K–K
carrier recombination pathway is suppressed with the moving
down of Λ valley in monolayer MoS 2 , while the K–K carrier
recombination pathway is strengthened with the rising up of
the Λ valley in bilayer MoS 2 .
In contrast to an exciton, a trion (charged exciton) has
an extra charge with nonzero spin, which can be used for
spin manipulation. [ 20,21 ] More importantly, the density of
trions can be electrically tuned by the gate voltage, offering
small 2015, DOI: 10.1002/smll.201501949
Figure 1. Calculated band structures of mono- and bilayer MoS 2 and the schematic of their photocarrier relaxation pathways at 100 and 300 K. a,c) Band structure of monolayer (labeled as “1L”) and bilayer (labeled as “2L”) MoS 2 .The solid black arrows indicate the moving directions of Λ valley and Γ peak as temperature decreases (K point is fi xed). b,d) Schematic of the photocarrier relaxation pathways in 1L (b) and 2L (d) MoS 2 . The orange and green lines indicate the VBM and CBM, respectively. The green circle “e” stands for electrons and orange circle “h” stands for holes. The dashed and solid lines present the situations at 100 and 300 K, respectively.
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remarkable optoelectronic applications. [ 22–26 ] Recently,
tightly bound trions have been observed in monolayer MoS 2
at room temperature, which is of considerable interest for the
fundamental studies of many-body interactions, such as car-
rier multiplication and Wigner crystallization. [ 27 ] However,
trions have not been observed in bilayer MoS 2 , since the PL
spectra in bilayer MoS 2 could not be tuned at room tem-
perature owing to its indirect band gap nature at room tem-
perature. Fortunately, we could use temperature to tune the
valley positions in bilayer MoS 2 and make its electronic band
structure approaching direct band gap manner, which offers
the electrical tunability of the exciton and trion dynamics in
bilayer MoS 2 at low temperature.
Using back-gated metal–oxide–semiconductor (MOS)
devices ( Figure 3 a,b), we demonstrate the tunability of
exciton and trion dynamics in bilayer MoS 2 at low tem-
perature, with the comodulations by both temperature and
electric fi eld. We used mechanical exfoliation to transfer [ 28 ]
a MoS 2 fl ake (with mono- and bilayer MoS 2 ) onto a SiO 2 /
Si substrate (275 nm thermal oxide on n + -doped silicon).
The MoS 2 fl ake was placed near a gold electrode that was
prepatterned on the substrate. Another thick graphite fl ake
was similarly transferred to electrically bridge the MoS 2 fl ake
and the gold electrode, forming a MOS device. This fabrica-
tion procedure kept the MoS 2 samples free from chemical
contaminations by minimizing the post-processes after the
MoS 2 fl ake was transferred. In the measurement, the gold
electrode is grounded, and the n + -doped Si substrate func-
tions as a back gate providing uniform electrostatic doping
in the MoS 2 (Figure 3 b). In the experiment, we tuned the
back gate voltage from 50 to −50 V. For the monolayer
MoS 2 , obvious gate-dependent PL spectra were observed
at both 298 and 83 K (Figure 3 c,d). In the PL spectra, the
higher-energy emission peak at ≈1.92 eV is attributed to
neutral exciton (A) emission, and the lower-energy emission
peak at ≈1.88 eV (Figure 3 c,d) is attributed to negative trion
(A − ) emission, which is consistent with previously report. [ 26 ]
MoS 2 sample is an n-type semiconductor owing to the initial
electron doping, [ 26 ] which makes the negative trion PL peak
dominant at zero back gate voltage (Figure 3 c,d). As the
back gate voltage V g was changed from −50 to 50 V, positive
charges were injected to monolayer MoS 2 layer sample and
makes the doping level close to neutral at −50 V. Therefore,
the exciton spectral weight was increasing with the injection
of positive charges by back gate voltages and negative trions
(A − ) will be converted to excitons (A). The conversion can
be represented as A − + h → A, where h represents a hole. In
monolayer MoS 2 , most photocarriers will recombine through
the K–K transitions at 298 K. When temperature is down
to 83 K, Λ valley slightly moves down relatively to K valley,
which reduces the weight of the photoelectrons relaxed into
K valley. However, as the photoelectrons still remain with a
moderate amount in K valley, the conversion from exciton
(A) to negative trion (A − ) will not be signifi cantly infl uenced,
so gate-dependent PL spectra could be observed from mon-
olayer MoS 2 at both 298 and 83 K as shown in Figure 3 c,d,
respectively.
On the other hand, we did not observe obvious
gate-dependent PL spectra from bilayer MoS 2 at 298 K
small 2015, DOI: 10.1002/smll.201501949
Figure 2. Temperature dependence of the photoluminescence (PL) from mono- and bilayer MoS 2 . a,b) The measured PL spectra from mono- and bilayer MoS 2 , respectively, at different temperatures ranging from 298 down to 83 K. c) PL intensity as a function of temperature for 1L and 2L MoS 2 samples, showing a more rapid increase of the PL intensity from 2L sample than that from1L MoS 2 as the temperature decreases.
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(Figure 3 e), which is consistent with previous observation. [ 7 ]
At 298 K, bilayer MoS 2 has an indirect band gap and the
quasi-Femi level locates within the lower-energy Λ valley,
but not the higher-energy K valley. The electric fi eld from the
back gate will only tune the photoelectron density within the
Λ valley, but not within the K valley. Since the main PL peak
in bilayer MoS 2 comes from the direct K–K transition, the
electric fi eld would not affect the main PL K–K emission at
298 K (Figure 3 e inset). This situation changes when the MOS
device was cooled down to 83 K, at which the clear gate-
dependent PL spectra emerged (Figure 3 f). Two clear emis-
sion peaks, located at ≈1.91 and ≈1.88 eV, respectively, could
be observed via back gate modulation. The higher-energy
peak at ≈1.91 eV is attributed to exciton (A) emission and
small 2015, DOI: 10.1002/smll.201501949
AuGraphite
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Photon energy (eV)
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Figure 3. Comodulations of the PL by both temperature and electric fi eld in mono- and bilayer MoS 2 samples. a) Schematic plot of a MoS 2 metal–oxide–semiconductor (MOS) device structure. b) Optical microscope image of the MOS device with mono- and bilayer MoS 2 (labeled as “1L” and “2L,” respectively). c–f) Measured PL spectra from 1L and 2L MoS 2 samples, under different back gate voltages (from −50 to 50 V) and at temperature of 298 and 83 K, respectively. Insets show the schematic plots of the corresponding band structures with indicated quasi-Fermi level tuned by back gate.
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the lower-energy peak at ≈1.88 eV is attributed to the nega-
tive trion (A − ) emission. [ 8 ] The trion binding energy [ 29 ] is the
energy difference of these two peaks A and A − . The emerging
gate-dependent PL spectra in bilayer MoS 2 at 83 K come
from the rising up of the Λ valley relatively to the K valley.
When the energy of Λ valley becomes comparable to that of
K valley, the weight of photoelectrons relaxed to K valley will
be highly enhanced (Figure 3 f inset), which leads to the elec-
trical tunability of the PL and the exciton and trion dynamics
in bilayer MoS 2 at 83 K.
In order to investigate the detailed exciton and trion
dynamics in mono- and bilayer MoS 2 , we measured their PL
spectra under various back gate voltages at different temper-
atures ranging from 298 down to 83 K. All the PL spectra are
fi tted using Lorentzian function to extract the exciton and
trion components (Figures S4 and S5, Supporting Informa-
tion). In monolayer MoS 2 , the intensity of excitons exhibits a
large gate dependence, while the intensity of trions approxi-
mately preserves when the back-gated voltage is changed
from −50 to 50 V at 83 K ( Figure 4 a), which is consistent with
previous report. [ 9 ] For bilayer MoS 2 , the back gate voltage
will have an obviously larger infl uence on the spectral weight
of trions than that of excitons at 83 K (Figure 4 b), which
could be related to the initial carrier density of K valley in
bilayer MoS 2 . [ 17 ] The trion binding energies of mono- and
bilayer MoS 2 are measured to be 39 and 27 meV at 83 K
(Figure 4 c,d), respectively. The lower trion binding energy
in bilayer MoS 2 could be due to the reduced quantum con-
fi nement. [ 9,30 ] For 2L MoS 2 at both 298 and 263 K, the PL
spectra can only be fi tted using one peak and this peak is
attributed to the emission of excitons, according to the tem-
perature evolution of exciton and trion peak energies for 2L
MoS 2 (Figure 4 d and Figure S5b, Supporting Information).
This is because most of the photoexcited electrons relax
to the Λ valley rapidly, making the neutral excitons domi-
nant in the K–K transition (Figure 3 e inset). We fi nd that
the peak positions of exciton and trion emissions in both
mono- and bilayer can be fi tted well (solid lines in Figure 4 d)
using a standard semiconductor band gap dependence [ 7,31 ]
of 0 coth2
1g gE T E SkT
� �ω ω( )( ) ( )= − −⎡⎣⎢
⎤⎦⎥, where 0gE ( ) is the
ground-state transition energy at 0 K, S is a dimension-
less coupling constant, and h ̄ ω is an average phonon
small 2015, DOI: 10.1002/smll.201501949
Figure 4. Exciton and trion dynamics in mono- and bilayer MoS 2 , at different back gate voltages and temperatures. a,b) PL intensity of emission peaks from excitons (“A”) and trions (“A − ”) as a function of gate voltages, from 1L (a) and 2L (b) MoS 2 at 83 K. c) PL peak energy of “A” and “A − ” emissions as a function of gate voltages for 1L and 2L MoS 2 at 83 K. d) PL peak energy as a function of temperature. For 2L, the “A” peak can only be fi t out below 233 K. All the peaks are fi t to Lorentzians by multipeak fi tting (see the Supporting Information). The solid lines are the fi tting curves using a standard semiconductor band gap dependence of E T E S
kT0 coth
21g g � �ω ω( ) ( )= − ⎛
⎝⎜⎞⎠⎟ −⎡
⎣⎢⎤⎦⎥, where E 0g ( ) is the ground-state transition energy at 0 K, S
is a dimensionless coupling constant, and �ω is an average phonon energy.
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energy. From the fi ts, we extract for excitons (trions) the
E g = 1.921 (1.883) eV, S = 1.668 (1.488), h ̄ ω = 26.92 (21.29)
meV in monolayer MoS 2 and E g = 1.909 (1.883) eV, S = 2.223
(1.887), h ̄ ω = 28.99 (23.81) meV in bilayer MoS 2 .
In conclusion, we successfully used comodulation tech-
nique by both temperature and electric fi eld to probe the
exciton and trion dynamics in bilayer MoS 2 . From numerical
calculations, we show that the band structure evolution of
bilayer MoS 2 is from indirect at room temperature toward
direct band structure as temperature decreases, while mon-
olayer MoS 2 shows an adverse trend. This opposite tem-
perature dependence of the band structure evolution in
mono- and bilayer MoS 2 can signifi cantly change the photo-
carrier relaxation pathways in their PL processes, which leads
to more than twice faster increasing of the measured PL
intensity from bilayer MoS 2 than that from monolayer MoS 2
as temperature decreases. More importantly, this indirect-
to-direct transition trend in bilayer MoS 2 at low tempera-
ture provides the electrical tunability of the K–K direct PL
transition, which enables the exploration of exciton and trion
dynamics in bilayer MoS 2 . The trion binding energy of bilayer
MoS 2 was then measured to be 27 meV at 83 K, which is
smaller than the measured trion binding energy of 39 meV in
monolayer MoS 2 . Our results pave a new way to enable new
excitonic devices using bilayer MoS 2 .
Experimental Section
Device Fabrication and Characterization : Mechanical exfolia-tion was used to transfer a MoS 2 fl ake onto a SiO 2 /Si substrate (275 nm thermal oxide on n + -doped silicon), near a prepatterned Au electrode. The Au electrodes were patterned by conventional photolithography, metal deposition, and lift-off processes. Another thick graphite fl ake was similarly transferred to electrically bridge the MoS 2 fl ake and the Au electrode, forming a MOS device. All PL measurements were conducted using a T64000 micro-Raman system equipped with a charge-coupled device (CCD) and InGaAs detectors, along with a 532 nm Nd:YAG laser as the excitation source. For low temperature measurements, the sample was placed into a microscope-compatible chamber with a low tempera-ture controller (liquid nitrogen as the coolant).The electrical bias was applied using a Keithley 4200 semiconductor analyser.
Trion Binding Energy Extraction : The binding energies of excions and trions are extracted from the measured PL spectra using multipeak Lorentz fi tting, which has been successfully used by Shan and co-workers [ 9 ] and Xu and co-workers. [ 29 ] Through Lor-entz fi tting, we can clearly see two peaks in each measured PL spectra. The higher-energy peak (A) is attributed to the neutral exciton emission, and the lower-energy peak (A − ) is due to the trion emission. [ 9,26 ] From the gate-dependence of these two peaks, we know the trion is negatively charged trion. The trion binding energy is the energy difference of these two peaks A and A − .
Band Structure Simulation : The band structures of 1–2 L MoS 2 were calculated at different temperatures within DFT molecular dynamics calculation using PW generalized gradient approxima-tion based on a real-space numerical atomic orbital code. [ 18 ] A double numerical polarized basis set was used with a k -point set of 25 × 25 × 1. All electrons are included in the calculation.
A vacuum space of at least 30 Å was kept to avoid mirror interac-tions. The temperature dependence of the electronic structure is based on modeling the effects of thermal lattice expansion and the electron–phonon interaction. Before performing the DFT molecular dynamics calculation, the total number of particles, the system’s volume, and the absolute temperature become constant and the system reaches an equilibrium state, after 10 ps relaxation (called the canonical NVT ensemble). At a certain temperature, molecular dynamics simulations at this temperature are conducted fi rst to determine the lattice parameters; and then band structure is cal-culated using ab initio method based on the lattice parameters.
Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.
Acknowledgements
J. Pei, J. Yang, and R. Xu contributed equally to this work. The authors would like to thank Prof. Chennupati Jagadish and Prof. Barry Luther-Davies and from The Australian National University, for their facility support. The authors acknowledge fi nancial support from ANU Ph.D. student scholarship, China Scholarship Council, National Natural Science Foundation of China (Grant No. 11162014), Aus-tralian Research Council and ANU Major Equipment Committee.
[1] L. Britnell , R. M. Ribeiro , A. Eckmann , R. Jalil , B. D. Belle , A. Mishchenko , Y.-J. Kim , R. V. Gorbachev , T. Georgiou , S. V. Morozov , A. N. Grigorenko , A. K. Geim , C. Casiraghi , A. H. C. Neto , K. S. Novoselov , Science 2013 , 340 , 1311 .
[2] G. Eda , S. A. Maier , ACS Nano 2013 , 7 , 5660 . [3] J. Yang , Z. Wang , F. Wang , R. Xu , J. Tao , S. Zhang , Q. Qin , B. Luther-
Davies , C. Jagadish , Z. Yu , Y. Lu , Light Sci. Appl. 2014 , 6200 , 1411 .
[4] M.-L. Tsai , S.-H. Su , J.-K. Chang , D.-S. Tsai , C.-H. Chen , C.-I. Wu , L.-J. Li , L.-J. Chen , J.-H. He , ACS Nano 2014 , 8 , 8317 .
[5] J. K. Ellis , M. J. Lucero , G. E. Scuseria , Appl. Phys. Lett. 2011 , 99 , 261908 .
[6] A. Splendiani , L. Sun , Y. Zhang , T. Li , J. Kim , C. Y. Chim , G. Galli , F. Wang , Nano Lett. 2010 , 10 , 1271 .
[7] A. K. M. Newaz , D. Prasai , J. I. Ziegler , D. Caudel , S. Robinson , R. F. Haglund Jr. , K. I. Bolotin , Solid State Commun. 2013 , 155 , 49 .
[8] J. S. Ross , P. Klement , A. M. Jones , N. J. Ghimire , J. Yan , D. G. Mandrus , T. Taniguchi , K. Watanabe , K. Kitamura , W. Yao , D. H. Cobden , X. Xu , Nat. Nanotechnol. 2014 , 9 , 268 .
[9] K. F. Mak , K. He , C. Lee , G. H. Lee , J. Hone , T. F. Heinz , J. Shan , Nat. Mater. 2013 , 12 , 207 .
[10] J. Yang , T. Lü , Y. W. Myint , J. Pei , D. Macdonald , J.-C. Zheng , Y. Lu , ACS Nano 2015 , 9 , 6603 .
[11] Q. H. Wang , K. Kalantar-Zadeh , A. Kis , J. N. Coleman , M. S. Strano , Nat. Nanotechnol. 2012 , 7 , 699 .
[12] X. Yin , Z. Ye , D. A. Chenet , Y. Ye , K. O’Brien , J. C. Hone , X. Zhang , Science 2014 , 344 , 488 .
[13] K. F. Mak , K. He , J. Shan , T. F. Heinz , Nat. Nanotechnol. 2012 , 7 , 494 .
www.MaterialsViews.com
7© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.small-journal.comsmall 2015, DOI: 10.1002/smll.201501949
[14] T. Cheiwchanchamnangij , W. R. L. Lambrecht , Phys. Rev. B 2012 , 85 , 205302 .
[15] A. Splendiani , L. Sun , Y. Zhang , T. Li , J. Kim , C.-Y. Chim , G. Galli , F. Wang , Nano Lett. 2010 , 10 , 1271 .
[16] A. K. Geim , I. V. Grigorieva , Nature 2013 , 499 , 419 . [17] D. Kozawa , R. Kumar , A. Carvalho , K. Kumar Amara , W. Zhao ,
S. Wang , M. Toh , R. M. Ribeiro , A. H. Castro Neto , K. Matsuda , G. Eda , Nat. Commun. 2014 , DOI: 10.1038/ncomms5543.
[18] B. Delley , J. Chem. Phys. 1990 , 92 , 508 . [19] Y. P. Varshni , Physica 1967 , 34 , 149 . [20] C. Galland , A. Imamo lu , Phys. Rev. Lett. 2008 , 101 , 157404 . [21] X. Xu , W. Yao , D. Xiao , T. F. Heinz , Nat. Phys. 2014 , 10 ,
343 . [22] V. I. Klimov , A. A. Mikhailovsky , S. Xu , A. Malko ,
J. A. Hollingsworth , C. A. Leatherdale , H.-J. Eisler , M. G. Bawendi , Science 2000 , 290 , 314 .
[23] S. G. Carter , V. Birkedal , C. S. Wang , L. A. Coldren , A. V. Maslov , D. S. Citrin , M. S. Sherwin , Science 2005 , 310 , 651 .
[24] G. D. Scholes , G. Rumbles , Nat. Mater. 2006 , 5 , 683 . [25] A. A. High , E. E. Novitskaya , L. V. Butov , M. Hanson , A. C. Gossard ,
Science 2008 , 321 , 229 . [26] K. Kheng , R. T. Cox , M. Y. d’ Aubigné , F. Bassani , K. Saminadayar ,
S. Tatarenko , Phys. Rev. Lett. 1993 , 71 , 1752 . [27] E. Wigner , Phys. Rev. 1934 , 46 , 1002 . [28] A. Castellanos-Gomez , M. Buscema , R. Molenaar , V. Singh ,
L. Janssen , H. S. J. v. d. Zant , G. A. Steele , 2D Mater. 2014 , 1 , 011002 .
[29] J. S. Ross , S. Wu , H. Yu , N. J. Ghimire , A. M. Jones , G. Aivazian , J. Yan , D. G. Mandrus , D. Xiao , W. Yao , X. Xu , Nat. Commun. 2013 , 4 , 1474 .
[30] A. Thilagam , Phys. Rev. B 1997 , 55 , 7804 . [31] K. P. O’Donnell , X. Chen , Appl. Phys. Lett. 1991 , 58 , 2924 .
Received: July 2, 2015 Revised: August 31, 2015 Published online:
Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2015.
Supporting Information
for Small., DOI: 10.1002/smll.201501949
Exciton and Trion Dynamics in Bilayer MoS2
Jiajie Pei, Jiong Yang, Renjing Xu, Yong-Hui Zeng, Ye WinMyint, Shuang Zhang, Jin-Cheng Zheng, Qinghua Qin, XibinWang, Wugui Jiang, and Yuerui Lu*
Supporting Information for
Exciton and trion dynamics in bilayer MoS2
Jiajie Pei,1,2† Jiong Yang,2† Renjing Xu,2† Yong-Hui Zeng,3 Ye Win Myint,2 Shuang Zhang,2
Jin-Cheng Zheng,4 Qinghua Qin,2 Xibin Wang,1 Wugui Jiang,3 and Yuerui Lu2*
1School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 100081, China
2Research School of Engineering, College of Engineering and Computer Science, the
Australian National University, Canberra, ACT, 2601, Australia
3School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University,
Nanchang 330063, China
4Department of Physics, and Institute of Theoretical Physics and Astrophysics, Xiamen
University, Xiamen, 361005, China
† These authors contributed equally to this work
* To whom correspondence should be addressed: Yuerui Lu ([email protected])
S1. Calculation of the band structures at different temperatures
We calculated the band structures of 1-2 L MoS2 under different temperatures within
density-functional theory (DFT) using Perdew-Wang (PW) generalized gradient
approximation (GGA) based on a real-space numerical atomic orbital code.[1] A double
numerical polarized basis set was used with a k-point set of 25×25×1. All electrons are
included in the calculation. A vacuum space of at least 30 Å was kept to avoid mirror
interactions. The temperature dependence of the electronic structure is based on modelling
the effects of thermal lattice expansion and the electron-phonon interaction. Before
performing the DFT molecular dynamics calculation, the total number of particles, the
system’s volume and the absolute temperature become constant and the system reaches an
equilibrium state, after 10 ps relaxation (called the canonical NVT ensemble). At a certain
temperature, molecular dynamics simulations at this temperature are conducted first to
determine the lattice parameters; and then band structure is calculated using ab initio method
based on the lattice parameters.
Figure S1 |Temperature induced evolution of the Λ valley and Γ peak. (a), calculated
energy difference between Λ valley (ECΛ) and K valley (ECK) in the conduction band (b) and
energy difference between Γ peak (EVΓ) and K peak (EVK) in the valence band of 1-2L MoS2,
as a function of temperature. The dashed lines are guides for the eye. Based on above
calculation results, 1L MoS2 owns a direct band gap at the temperature range of ~210-300 K
0 50 100 150 200 250 300
-0.04
0.00
0.04
0.08
En
erg
y d
iffe
ren
ce
(e
V)
Temperature (K)
1L ECΛ
- ECK
2L ECΛ
- ECK
0 50 100 150 200 250 300-0.4
-0.2
0.0
0.2
0.4
En
erg
y d
iffe
ren
ce
(e
V)
Temperature (K)
1L EVΓ
- EVK
2L EVΓ
- EVK
a b
or < 50 K and an indirect band at the temperature range of ~50-210 K; in contrast, 2L MoS2
shows a direct band at the temperature range of ~50-250 K.
Wang[2] et al has demonstrated that when thick MoS2 is thinned down to 1L, the Λ valley of
conduction band moves up and the Г hill of valence band moves down, because of the
reduction of interlayer coupling. Please note that above simplified simulation is based on the
DFT calculation of band structures at absolute zero temperature.
Figure S2 | Molecular structure of MoS2. "a" is the distance between S-S atoms; "b" is the
distance between S-Mo atoms, "c" is the distance between two layers.
In the real case, temperature can modulate the lattice parameters (Figure S2), a, b, c,
significantly. It should be noted that the in-plane thermal expansion (modulation of “a” and
“b”), also has distinct effects on the band structure, although the in-plane thermal expansion
is typically much smaller compared to “c” expansion.[3] For bilayer MoS2 in the real case, the
moving trends of Λ valley and Г hill are not only affected by the interlayer coupling (“c”), but
also the modulation of in-plane thermal expansion (“a” and “b”) as well as electron-phonon
interactions at elevated temperature. In addition, please note that the temperature-induced
modulation of band structure is also dependent on the material itself. For instance, compared
with 2L MoSe2, 2L MoS2 has totally opposite temperature dependence of photoluminescence
due to different band structure evolution as a function of temperature[4].
Typically, in order to simplify the simulation process, some DFT calculations only consider
c
a
Mo
S
interlayer coupling and ignore the influence of in-plane thermal expansion.[2, 4] Also, people
assume that thermal expansion causes the interlayer spacing to increase monotonously with
temperature, thus reducing the interaction between the layers. In the real case, for few-layer
MoS2, the temperature-induced modulation of the interlayer spacing is not monotonous.[5] It
is impossible to find the temperature modulation of such complex systems analytically;
therefore, we use MD simulation to circumvent this problem by using numerical methods.
From our MD simulation (Figure S1), the evolution of band structure as a function of
temperature is indeed not monotonous. In the temperature range of 300 - 100 K, our
simulation results can reasonably explain our experimental findings.
Figure S3 |Temperature dependence of PL intensity from another MoS2 sample with
mono-and bi-layers. (a), measured PL spectra of the 1L MoS2 under various temperatures.
(b), measured PL spectra of the 2L MoS2 in the same spectral range. (c), PL peak intensity of
the 1-2L samples as a function of temperature.
1.7 1.8 1.9 2.0 2.1-20
0
20
40
60
80
100
120
140
160
PL
in
ten
sity (
a.u
.)
Photon energy (eV)
83K
113K
143K
173K
203K
233K
263K
298K
1L
1.7 1.8 1.9 2.0 2.1
-20
0
20
40
60
80
100
120
140
160
180
200
2L
PL
in
ten
sity (
a.u
.)Photon energy (eV)
83K
113K
143K
173K
203K
233K
263K
298K
50 100 150 200 250 3000
20
40
60
80
100
120
140
160
180
200
1L
2L
PL
in
ten
sity (
a.u
.)
Temperature (K)
a b
c
Figure S4 |Exciton and trion dynamics as a function of back gate voltage in the mono-
and bi-layer MoS2 at 83 K. (a)-(b), measured PL spectra of 1L (a) and 2L (b) MoS2 samples
under different back gate voltages, with Lorentzian fittings (solid violet curves are the
measured raw data, solid red lines are the exciton (A) components, solid black lines are the
trion (A-) components, and solid green lines are the cumulative fitting results). The dashed
lines are added as guides to the eye for the peak energies of excitons (A, red line) and trions
(A-, black line).
1.80 1.84 1.88 1.92 1.96
0
35
70
0
35
70
0
35
70
0
35
70
0
35
70
0
35
70
PL
in
ten
sity (
a.u
.)
Photon energy (eV)
50V
30V
10V
A-
1L
-50V
-30V
-10V
A
1.80 1.84 1.88 1.92 1.96
0
90
180
0
90
180
0
90
180
0
90
180
0
90
180
0
90
180
PL
in
ten
sity (
a.u
.)
Photon energy (eV)
50V
30V
10V
A-
2L
-50V
-30V
-10V
A
a b
Figure S5 | Exciton and trion dynamics as a function of temperature, in mono- and
bi-layer MoS2. In order to clearly see the exciton (A) and trion (A-) peak, the PL spectra
under back gate voltages of 50 and -50V are plotted in the same panel. The dashed lines are
added as guides to the eye for the peak energies of excitons (A, red line) and trions (A-, black
line).
1.80 1.85 1.90 1.950
40
0
50
0
50
0
1000
1000
100
0
100
0
200
Photon energy (eV)
83K
113K
143K
173K
50V
-50V
PL
in
ten
sity (
a.u
.)203K
233K
263K
293K
2L
A-
A
1.80 1.85 1.90 1.95
0
50
0
50
0
50
0
70
0
70
0
70
0
70
0
70
Photon energy (eV)
PL in
tensity (
a.u
.)
83K
113K
143K
173K
203K
233K
263K
293K 50V
-50V
1LAA-
a b
References
1. B. Delley, J. Chem. Phys. 1990, 92, 508.
2. A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli, F. Wang, Nano Lett.
2010, 10, 1271.
3. W. Zhao, R. M. Ribeiro, M. Toh, A. Carvalho, C. Kloc, A. H. Castro Neto, G. Eda, Nano
Lett. 2013, 13, 5627.
4. S. Tongay, J. Zhou, C. Ataca, K. Lo, T. S. Matthews, J. Li, J. C. Grossman, J. Wu, Nano
Lett. 2012, 12, 5576.
5. R. Murray, B. Evans, J. Appl. Crystallogr. 1979, 12, 312.