Photoluminescence Saturation and Exciton Decay Dynamics in Transition Metal Dichalcogenide Monolayers

Min Ju Shin, Dong Hak Kim and D. Lim*

Department of Applied Physics, College of Applied Science, Kyung Hee University, Yongin 449-701,

Republic of Korea

We report a photoluminescence (PL) and transient reflection spectroscopy study of

exciton dynamics in monolayer transition transition-metal dichalcogenides (TMDs). PL

saturation in monolayer MoSe2 occurs an excitation intensity more than two orders of

magnitude lower than in monolayer MoS2. Transient reflection shows that the nonlinear

exciton-exciton annihilation is the dominant exciton decay process in monolayer MoSe2 in

contrast to the previously reported linear exciton decay in monolayer MoS2. In addition, the

exciton lifetime in MoSe2, > 125 ps, is more than an order of magnitude longer than the

several-ps exciton lifetime in MoS2. We find that the dramatically different exciton decay

mechanism and PL saturation behavior of MoSe2 and MoS2 monolayers can be explained

by the difference in their exciton lifetime.

Corresponding author e-mail: [email protected] I. INTRODUCTION

The transition-metal dichalcogenide (TMD) MX2, such as MoS2, MoSe2, WS2 and WSe2, has a layered structure, where each layers are bonded by weak van der Waals interaction [1].

While the bulk MX2 is an indirect band gap semiconductor, they exhibit a crossover from indirect to direct bandgap in the monolayer limit [2-4]. Since the discovery of direct bandgap structure in monolayer MoS2, extensive research efforts have been made on few layer TMDs because of their excellent optical and electrical properties [2,5-7]. In addition, electrons in few-layer MX2 possess a valley degree of freedom as in graphene [8-10]. Graphene has been the material in the valleytronics research, but its drawbacks such as the inherent lack of inversion symmetry and bandgap limit their application [8,9]. In contrast, monolayer MX2 has a inherently broken inversion symmetry and direct bandgap structure at degenerate valleys, K and K’, located at the corners of the hexagonal Brillouin zone [10,11]. Near the conduction and valence band edges, the electronic states are of d-orbital character. Therefore, the strong spin-orbit interaction in the d-orbital together with the broken inversion symmetry spin-splits the valence band significantly and couples the spin and valley degree of freedoms in the monolayer MX2 [12].

The first optical generation of valley polarization was reported in 2012 for monolayer

MoS2 by using optical helicity[13,14]. Based on the circular polarization of photoluminescence (PL), they proposed a hole valley-spin lifetime > 1 ns. Afterwards, the valley polarization as well as the valley coherence have been reported for other monolayer and bilayer TMDs, such as WS2 and WSe2 [15,16]. The exciton and valley dynamics in monolayer MX2 has also been studied recently by using helicity-resolved transient absorption

[17,18], time-resolved photoluminescence [19], and Kerr rotation [20]. The obtained exciton lifetimes are typically several picoseconds [18,19] and the valley depolarization times range from sub-ps to several picoseconds [17,20], in stark contrast with > 1 ns valley lifetime estimated based on circular polarization of PL [14]. The short exciton lifetime of MoS2 cast some doubt on the validity of MX2 based valleytronics because a long exciton lifetime is a pre-requisite to valley based devices. Therefore, a better understanding of exciton dynamics in atomically thin TMDs is required for their future application.

In this paper, we report our work on the exciton decay dynamics in monolayer MoSe2 and MoS2 studied by excitation intensity/fluence dependent photoluminescence and transient reflection spectroscopy. We find a dramatically different PL saturation behavior and exciton decay mechanism between MoSe2 and MoSe2 monolayers. We find that the difference in the exciton lifetime can explain our explain results.

II. EXPERIMENTS

MoS2 and MoSe2 monolayer samples are obtained by mechanical exfoliation from bulk crystals on silicon substrates with 280 nm-thick thermal SiO2 or 70-nm thick pulsed-laser- deposited Al2O3 overlayer. The monolayer is first identified by optical microscope and then confirmed by raman and photoluminescence measurements.

A Ti:sapphire femtosecond oscillator with sub-100 fs pulse duration and 82 MHz repetition rate has been used to excite the monolayer MoSe2 samples, both in the photoluminescence and transient reflection spectroscopy measurements. 632-nm line from

He-Ne laser was used for MoS2 excitation. A long-working-distance 50X objective lens is used to focus the light onto the monolayers with a spot diameter of ~1.4 m. The PL measurement of MoSe2 is performed by using either 760-nm CW or mode-locked pulse laser beam. After passing through the objective lens, the pulse from Ti:sapphire oscillator is broadened to ~250 ps due to group velocity dispersion. Band pass filters are used to clean the laser beam before it is focused onto samples and edge pass filters are used to cut the laser line from PL emission. For transient reflection measurement, mode-locked 780-nm pulses from the oscillator are divided into pump and probe by a beam-splitter and the pump-excitation- induced reflection change of the probe is measured as a function of the pump-probe delay.

III. RESULTS and DISCUSSION

Fig. 1 shows the PL intensity as a function of excitation laser intensity for monolayer

MoSe2 and MoS2 samples. The PL responses are dramatically different for MoSe2 and MoS2 monolayers. The PLs from MoS2 monolayer on both SiO2 and Al2O3 overlayers are almost linear throughout the entire range of excitation intensity (MoS2 monolayer on SiO2 displays a slightly more nonlinear behavior, probably due to the low dielectric constant of SiO2). The PL from MoSe2, however, is completely different, showing a highly nonlinear behavior, even at very low excitation intensity. Since the PL intensity is proportional to the exciton density, the nonlinearity means that the steady-state exciton density in monolayer MoSe2 is not proportional to the excitation laser intensity (the nonlinearity is not from saturation of absorption as will be shown later) and that the exciton decay occurs via strong exciton- exciton interaction. The rate equation for exciton density N can be written by:

where is the exciton generation rate, is the linear exciton decay rate (exciton

lifetime), and is the nonlinear EEA coefficient. Since the steady-state exciton density N is constant for CW excitation, it can be expressed as a function of excitation intensity I,

Here, ( : excitation photon energy, a: absorbance

of the sample) is an excitation intensity where the dominant decay mechanism changes from linear exciton decay to nonlinear EEA. We fit the PL response from monolayer MoSe2 and plot the result in Fig. 2(a) as a red line. In the low excitation limit ( , nonlinear exciton- exciton interaction is insignificant and the PL intensity is proportional to the excitation intensity. If the excitation intensity is high ( , EEA dominates the decay process and the PL intensity becomes a nonlinear function of the excitation intensity. The contributions of linear and nonlinear decay terms to the total decay rate using the fitting results are calculated and plotted in the inset of Fig. 2(a). The decay rate due to EEA begins to exceed that of linear exciton decay at a very low excitation intensity, ~ 0.5 W/m2. In contrast, the PL from monolayer MoS2 doesn’t show much deviation from linear response even at more than two orders of magnitude higher excitation intensity, ~80 W/m2.

We also perform PL measurements using femtosecond pulse excitation and the resulting integrated PL from monolayer MoSe2 is plotted in Fig. 2(b) as a function of excitation pulse fluence. It can be seen clearly that the integrated PL saturates much faster than in CW excitation case at the same laser power. Since the exciton density is very high for pulse excitation case, especially just after excitation, the excitons will decay mostly through EEA.

In this regime, the integrated PL increases as ln(N0) as the injected exciton density N0 is increased. Assuming no appreciable saturation of absorption, the integrated PL then has a functional form of ln(F) for pulse fluence F. It can be seen that the PL saturation in the high fluence region can be fit well by using this functional form, supporting again strong EEA mechanism in monolayer MoSe2.

To understand the physics underlying the dramatically different PL saturation in monolayer TMDs, we perform degenerate transient reflection spectroscopy on monolayer

MoSe2 and study its exciton dynamics in the time-domain. Fig. 3 displays a typical differential reflection (DR) signal of monolayer MoSe2 measured by using degenerate pump- probe spectroscopy at wavelength 780 nm. During the overlap of the pump and probe pulses, a strong coherent artifact signal shows up, making it hard to observe the build-up process of excitons. Still, we can ignore the exciton decay during the pump-probe overlap because the exciton lifetime is much longer than the pulse duration. In the inset of Fig. 3, the maximum

DR signal is plotted as a function of pump fluence. The plotted maximum DR is not a linear function of pump fluence. It should be pointed out that although it may seem to indicate the saturation of absorption, it is not. The maximum DR signal of the probe is less than 1 %, so the change of absorption during the pump excitation should be less small too. Therefore, the nonlinear dependence of DR signal should be related to other causes, such as band gap renormalization and/or pump–heating induced A-exciton peak shift. Irrespective of its origin, we can exclude the saturation of absorption and safely assume that the injected exciton density is proportional to the pump fluence.

After pump excitation, the DR signal relaxes fast initially and then slows down as the probe delay is increased, as expected from density-dependent EEA rate. This is different from monolayer MoS2, where only an multi-exponential, linear exciton decay process has been reported. If EEA dominates over linear exciton decay, the linear exciton decay term in eq. (1) can be ignored and the exciton density then evolves with time as follows.

Eq. (2) indicates that if EEA dominates over linear exciton decay, the slope of the

graph should be proportional to the injected exciton density, thus to the pump

fluence. In the linear exciton decay process, however, the slope is given by the inverse of the

lifetime time, -1, which has no direct correlation with pump fluence. In Fig. 4(a), is

plotted as a function of probe delay for several pump fluencies. It can be clearly seen that the slope of the graphs increases as the pump fluence is increased, supporting a strong EEA in monolayer MoSe2. The slope, however, is not exactly proportional to the injected exciton density. This deviation may be explained by the residual linear decay term. Although the linear exciton decay term is ignored in Eq. (2), it always contributes to the total excition decay rate. This is increasingly so as the pump fluence is decreased. It adds an addition slope to Eq. (2) and makes the total slope deviate from the linear dependence, especially at low pump fluences.

When the exciton density is low, its linear decay can dominate over the nonlinear EEA.

This condition is met at ‘low pump fluence’ and ‘long delay time’. We can thus extract the exciton lifetime, or the lower limit of it because EEA always co-exists, by fitting the long delay part of the DR data pumped at a low fluence. Fig. 4(b) displays the DR signal measured at the lowest excitation fluence, ~5.3 J/cm2, together with a single-exponential fitting result as a red line (fitting region: delay > 50 ps). The exciton lifetime obtained is around ~125 ps.

This is more than an order of magnitude longer than the exciton lifetime of monolayer MoS2, which has been reported to be several picoseconds [18,19].

Our work shows that PL saturation behavior and exciton decay mechanism can change from one TMD to another. Here, we will discuss the physics underlying this dramatic change.

The relative magnitude of the nonlinear EEA to the linear exciton decay is . At a give exciton density, the longer the exciton lifetime or the larger the EEA coefficient, the more significant the EEA becomes. As can be seen in the transient reflection of monolayer MoSe2, exciton-exciton interaction is strong in 2-D TMDs. However, the EEA coefficients of MoS2 and MoSe2 monolayers should be of the same order, because the exciton binding energies and thus the exciton radii are similar. Therefore it does not explain the difference in the decay mechanism. On the other hand, the measured exciton lifetime of monolayer MoSe2 is more than an order of magnitude longer than that of monolayer MoS2. Therefore, the linear decay rate is much smaller in monolayer MoSe2 that in monolayer MoSe2, leaving EEA as the dominant decay mechanism.

The dramatically different PL saturation behavior can be explained also by the exciton lifetime. The saturation excitation intensity from EEA to linear exciton decay scales as

The absorbance a is reported to be around ~0.05 for both MoS2 and MoSe2

monolayers [21]. The difference is again the exciton lifetime . Since I0 is proportional to the

-2  , the longer exciton lifetime in monolayer MoSe2 makes the crossover from the linear to nonlinear exciton decay occur at more-than two orders of magnitude lower excitation intensity than in monolayer MoS2, as observed in our experiment.

IV. CONCLUSION

We study the exciton decay dynamics in monolayer TMDs. We observe a highly nonlinear PL response in monolayer MoSe2 in contrast to almost linear one in monolayer

MoS2. Transient differential reflection shows that the exciton decay in monolayer MoSe2 is dominated by exciton-exciton annihilation, in contrast to the linear exciton decay in monolayer MoS2. We find that the difference in the exciton decay mechanism and PL saturation behavior in monolayer TMDs can be explained by the different exciton lifetime.

AKNOWLEDGMENTS

This work was supported by grants from the Kyung Hee University Research Fund

(KHU- 20110464). List of Figures

Fig. 1. The PL intensity vs. excitation intensity graphs for monolayer MoS2 on 280-nm thick

SiO2/Si (red solid circle) and 70-nm thick Al2O3/Si (open black circle), and monolayer MoSe2 on 280-nm thick SiO2/Si (blue solid circle).

Fig. 2. (a) PL intensity vs. excitation intensity of monolayer MoSe2. The red line is a fitting result. (b) Integrated PL vs. excitation pulse fluence of monolayer MoSe2. The red line is a fitting result. The excitation is made using CW and mode-locked 760-nm beam from the

Ti:sapphire oscillator.

Fig. 3. Differential reflection of monolayer MoSe2. The center wavelength of the pump and probe is 780 nm and the pump fluence is 53 J/cm2. (Inset) The maximum DR as a function of excitation fluence.

Fig. 4. (a) Plot of vs. probe delay for pump fluencies 105, 53, 26 J/cm2 (from top

to bottom). The red lines are linear fits to the initial part (0 ~ 40 ps delay) of the graphs. (b)

Exponential fitting to the latter part (50 – 300 ps) of DR at a pump fluence of ~5.3 J/cm2.

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1.0

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