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.