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Transient Absorption of Transition Metal Dichalcogenide Monolayers Studied by a Photodope-Pump-Probe Technique

We report three-pulse photodope-pump-probe measurements on photocarrier dynamics in semiconducting transition metal dichalcogenide monolayers of MoS2, WS2, MoSe2, and WSe2. The samples are fabricated by chemical vapor deposition and mechanical exfoliation techniques and characterized by photoluminescence spectroscopy. In the time-resolved measurement, the samples are first photodoped by a prepulse, which injects background photocarriers of various densities. A pump pulse then excites photocarriers, whose dynamics is monitored by measuring differential reflection of a time-delayed probe pulse. We found that the ultrafast decay component of the differential reflection signal, which has been widely reported before, shows minimal dependence on the background exciton density. This observation shows that a previously suggested carrier-trapping model cannot account for this component. The results thus further support an exciton-formation model that was previously proposed based on spectroscopic evidence.

In transient absorption measurements of 2D TMDs, one commonly observed feature is an ultrafast decay process that causes loss of about half of the signal in about 1 ps. This feature is remark- So far, three models have been proposed on the origin of this ultrafast decay process, based on exciton-exciton annihilation 11,29,53 , extrinsic effects of defect states 25,29,31,54,57 , and the intrinsic effect of exciton formation 58 . At first, it has been established that in 2D semiconductors, the exciton-exciton annihilation can be significantly more efficient than in 3D systems due to the enhanced exciton-exciton interaction [13][14][15][16][17][18] . Thus, at elevated densities, the exciton-exciton annihilation can cause rapid loss of the exciton population, resulting in the ultrafast decay of the transient absorption 11,29,53 . Second, lattice defects in the samples can cause loss of photocarriers by trapping or defect-assisted Auger-type recombination, which can dominate carrier dynamics at low densities and cause this ultrafast decay process 25,29,31,54,57 . Finally, the intrinsic effect of exciton formation from free electron-hole pairs have been proposed as a possible mechanism of the ultrafast decay process 58 .
Here we utilize a three-pulse photodope-pump-probe technique to study the origin of the ultrafast decay process in MoS 2 , WS 2 , MoSe 2 , and WSe 2 at low carrier density regimes by testing the hypothesis of the defect-trapping mechanism. We use a prepulse to optically dope the samples, followed by injection of photocarriers by a pump pulse and measurement of differential reflection of a probe pulse. If the trapping of carriers by defects is the main mechanism for this ultrafast decay process, the carriers injected by the prepulse are expected to fill these states and thus suppress or even eliminate this component. Our measurements over a large range the photodoping densities in all four materials show that the ultrafast decay process is not influenced by photodoping.
The results thus prove that the defect-related processes are not responsible for the ultrafast decay process observed in these samples, suggesting the importance of the contributions from exciton formation. The photodope-pump-probe measurements were performed in the reflection geometry with a home-made setup, as schematically shown in Figure 1. The laser system includes an 80-MHz Ti:sapphire oscillator, an optical parametric oscillator (OPO), a supercontinuum generator (SCG), and a second harmonic generation (SHG) unit. The Ti:sapphire oscillator produces 100-fs pulses in the range of 700 -900 nm. One part of this output is guided into the photonic-crystal fiber SCG, which generates a coherent and broadband irradiation. A bandpass filter (with a bandwidth of 10 nm) is used to select the desired wavelength component for the experiment. Another part of the Ti:sapphire output pumps the OPO, which produces near infrared pulses that are converted to visible light by SHG in a nonlinear crystal. The output of the Ti:sapphire oscillator can also produce its second harmonic directly by the SHG unit, or be directly used.

II. EXPERIMENTAL TECHNIQUE AND PROCEDURES
In a measurement, depending on the desired wavelength range, one of these outputs (blue beam in Figure 1) is split by a beamsplitter (BS) and is used as the prepulse and the pump pulse. The former is sent to a retroreflector and then combined with the latter by another BS. By moving the retroreflector on a linear stage, the path length (and therefore the time delay) of the prepulse with respect to the pump pulse can be adjusted. The combined prepulse/pump are reflected by a BS to a microscope objective lens, which focuses them to the sample. Typical spot sizes are in the range of 1 -2 µm. A mechanical chopper is used to modulate the pump intensity at about 3 kHz.
Another output of the laser system is used as the probe (red beam in Figure 1). It is sent to another retroreflector for time-delay adjustment, and is focused to the sample by the same objective lens. The reflected probe from the sample (purple beam in Figure 1) is collected by the objective lens and goes through the BS's. A camera monitors the focused spots and the sample surface during the alignment process. A filter is used to block the unwanted prepulse/pump reflection, allowing only the probe to reach the photodiode, which voltage output is measured by a lock-in amplifier that is referenced by the chopping frequency.
With this setup, we use the prepulse to photodope the sample prior to the arrival of the pump at the sample, and then measure the differential reflection of the probe induced by the pump, ∆R/R 0 = (R − R 0 )/R 0 . Here, R and R 0 are the reflectance of the sample with and without the presence of the pump beam, respectively; however, they are both with the presence of the prepulse. It is important to note that the carriers injected by the prepulse alter both R and R 0 by the same amount and therefore do not influence ∆R/R 0 : Since only the pump beam is modulated by the chopper and the lock-in amplifier measures the signal at that modulation frequency, only the differential reflection induced by the pump-injected carriers is detected. All the measurements were performed with the samples at room temperature and under ambient condition.

III. RESULTS AND DISCUSSION
The samples were first characterized by photoluminescence (PL) spectroscopy. Figure 2 shows the room temperature PL spectra of the four samples under the excitation of a continuous-wave laser with a photon energy of 3.06 eV. The PL intensities plotted are normalized against the integration time and the excitation power; hence, their comparison approximately reflects the relative PL yields of these samples. As shown in Figure 2, the normalized PL count varies from about 12 in MoS 2 to over 3500 in WS 2 . Furthermore, the observed PL yields, the peak positions, and 5 the peak widths are all consistent with previously reported results from the corresponding TMD monolayers 59 , confirming the monolayer thickness of the samples. Figure 3 schematically shows our approach to study photocarrier dynamics in the photodoped TMD monolayers. At first, a prepulse injects electron-hole pairs in a TMD monolayer at -4 ps (a). That is, the prepulse arrives at the sample 4-ps before the pump pulse. This time is long enough for the completion of the carrier thermalization, energy relaxation, and exciton formation processes, but is short enough so that the loss of photocarriers due to recombination is negligible. Since the probe is tuned to the exciton resonance of the sample [ Figure 3(d)], one might assume that it only senses excitons. However, this assumption is invalid. It has been well established through early studies on excitons in semiconductor quantum wells that free electron-hole pairs can also saturate the exciton oscillator strength. This is because the exciton wave function is composed of free-carrier states; hence, occupation of these states can alter the excitonic oscillator strength through the phase-space state filling effect 60 . In fact, when their thermal energy is much smaller than the exciton binding energy (a condition that is typically fulfilled in 2D semiconductors due to their large exciton binding energies), the free electron-hole pairs can alter the absorption at the excitonic resonance even more efficiently than an exciton population of the same density 60 .
We first perform standard pump-probe measurements with either the prepulse or the pump pulse exciting the sample along, to confirm their effectiveness of injecting carriers and their optimal alignment. The red circles in Figure 4 show the differential reflection signal measured from the WS 2 monolayer sample, as an example. In this measurement, the prepulse was blocked and the  These probe photon energies are then used for the rest of the study. The pump photon energy is 3.12 eV for all the samples except MoSe 2 , which is pumped by 1.97 eV due to the limitations of the laser configuration. However, in each sample, the pump photon energy is large enough to inject free electron-hole pairs 58 .
We first focus on the results from MoS 2 . The black squares in Figure 5 the electron-hole pairs or excitons is about 30 nm, much larger than the exciton Bohr radius of a few nm. We use such a low injection density for this study so that multi-exicton processes, such as exciton-exciton annihilation, can be ignored. As shown in Figure 5  We can exclude any direct nonlinear interactions between the pump and the probe pulses as the origin of the ultrafast decay component, such as sum frequency generation, SHG, or nondegenerate two-photon absorption. Such processes only occur when the two pulses overlap, while this component clearly persists far beyond the pulses. To illustrate this, the dashed gray curve is the calculated cross correlation of the pump and probe pulses, which is significantly narrower.
As we discussed above, one possible origin of the ultrafast decay process proposed was the loss of carriers due to defects in the sample. Hypothetically, if the main mechanism responsible for the loss of carriers is defect-assisted Auger-type carrier recombination, without carriers occupying these states, the entire carrier population should be drained by this process. The existence of the long-lived signal (of tens to hundreds of picoseconds) generally observed after the ultrafast decay process could rule out this mechanism. In other words, the observation that these defects can cause ultrafast decay of part of the carrier population, and then become inactive to the remaining carrier population shows that the only plausible mechanism is the trapping of carriers by these states.
That is, once these states are filled, they no longer cause decay of the carrier population. 9 To test this hypothesis, we use the prepulse to produce background excitons, so that these traps can be prefilled. The different symbols in Figure 5(a) shows the differential reflection signal measured when the prepulse injects various densities of background excitons, as indicated in the label.
When the background density produced by the prepulse is comparable to or higher than the maximal carrier density that these states can capture (which is about half of the pump injected density, or about 0.5 × 10 11 cm −2 , based on the trapping mechanism), the ultrafast decay component should be significantly quenched. However, as shown in Figure 5 In a previous study, we have shown spectroscopic evidence that such an ultrafast decay component is not associated with loss of carrier population and that it only exists under nonresonant excitation of free electron-hole pairs 58 . Based on these features, we proposed that this process is associated with formation of excitons from the free electron-hole pairs 58 . This explanation is also consistent with a well-established model on transient absorption of semiconductor quantum wells, which predicted that under the conditions relevant to 2D TMDs at room temperature, free electron-hole pairs induce transient absorption at the excitonic resonance that is twice of that induced by excitons of the same density 60 . By ruling out the trapping mechanism, the result of photodope-pump-probe experiment provides strong evidence supporting this model. We note that our experimental observations do not imply lack of effects of defects on the photocarrier dynamics and the optical response of TMD monolayers. To the contrary, defects are known to significantly reduce the photocarrier lifetime by providing nonradiative recombination channels 62 . Our study merely shows that their effects on ultrafast time scales are miner and they are not responsible for the generally observed ultrafast decay process.
We now discuss some detailed observations from the results shown in Figure 5 that are not strongly related to our conclusion. First, the peak signal decreases slightly at high background densities in each sample. To better illustrate that, the top panels of Figure 6 show the peak signal as a function of the background density for each sample. This feature could be attributed to the effect of absorption saturation. That is, the differential reflection is related to the exciton density by ∆R/R 0 = AN/(N + N s ), where N s is the saturation density 62 . Although the background excitons do not directly contribute to the signal detected, as their density is not modulated, they still contribute to this saturation effect. Second, we characterize the magnitude of this fast-decay component by taking the ratio between the signal at 3 ps to the peak signal. This ratio is plotted in the middle panels of Figure 6. As shown in Panels (a) and (b), this ratio is in the range of 0.4 -0.5 and is independent of the background density in MoS 2 and WS 2 monolayers. For the other two samples, however, the ratio slightly increases (MoSe 2 ) and decreases (WSe 2 ) with the background density.
Finally, the decay times deduced by exponential fits to this component (curves in Figure 5) are shown in the bottom panels of Figure 6. Small variations from material to material can be seen, while the background-density dependence is rather weak.
The time scale of exciton formation based on this model is consistent with previous studies with other techniques. If the ultrafast decay process is due to exciton formation, the decay times shown in the bottom panels of Figure 6 correspond to the exciton formation times in these materials, energy of WS 2 by photoexcitation based on the exciton-formation model 55 . We also note that once an exciton is formed, it can capture an additional charge carrier to form a trion 66 . A previous study has shown that in MoSe 2 this trion formation time is about 2 ps 67 . Hence, trion formation process, which happens after excitons are formed, is not expected to impact this ultrafast decay process.
Furthermore, the decay of the differential reflection signal reflects the loss of free electron-hole pair population, which could be due to the formation of both bright and dark excitons. Hence, the exciton formation times deduced here include both types of exciton formation process.

IV. CONCLUSION
We have performed three-pulse photodope-pump-probe experiments on monolayer semicon-