www.MaterialsViews.com

1© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.small-journal.com

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: yuerui.lu@anu.edu.au

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

communicationswww.MaterialsViews.com

2 www.small-journal.com © 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

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.

www.MaterialsViews.com

3© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.small-journal.com

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.

communicationswww.MaterialsViews.com

4 www.small-journal.com © 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

(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

MoS2

SiO2

n+ Si Vg

Au

Graphite

MoS2

1L

2L

20 m

1.8 1.9 2.00

20

40

60

80

100

1L 298K

).u.a(ytisnetni

LP

Photon energy (eV)

-50V -30V -10V 10V 30V 50V

1.8 1.9 2.00

40

80

120

160

1L 83K

PL

inte

nsity

(a.u

.)

Photon energy (eV)

A

A-

1.8 1.9 2.00

5

10

15

20

25

2L 298K

).u.a(ytisnetni

LP

Photon energy (eV)1.8 1.9 2.0

0

50

100

150

200

2L 83K

PL

inte

nsity

(a.u

.)

Photon energy (eV)

A

A-

a b

c d

e f

K

e-

h+

EF

e-

K

e-

h+

EF

e-

K

h+

EF 3

e-

K

e-

h+

EF

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.

www.MaterialsViews.com

5© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.small-journal.com

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.

communicationswww.MaterialsViews.com

6 www.small-journal.com © 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim small 2015, DOI: 10.1002/smll.201501949

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 (yuerui.lu@anu.edu.au)

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.