1. Introduction

Since 2010, transient metal dichalcogenides (TMDs), such as MoS₂ and WS₂ have attracted significant interests as their layered crystal structure allows fabrication of monolayers through simple but effective approaches such as mechanical exfoliation [1]. Although the bandgaps of these bulk TMDs are indirect and are in the near infrared range, their monolayers have direct bandgaps with lowest excitonic states in the visible range [2, 3]. Furthermore, these monolayers have shown other exotic properties, such as valley-selective optical coupling [4–6 ], large binding energies of excitons, trions, and biexcitons [7–10 ], and strong nonlinear optical responses [11–14 ]. In addition, these two-dimensional materials can be used to fabricate new van der Waals heterostructures [15–17 ].

So far, the most extensively studied TMD members are MoS₂, WS₂, MoSe₂, and WSe₂. They have qualitatively similar but quantitatively different electronic structures [1]. Hence, one natural way to expand the horizon of these materials is to fabricate their alloys. In 2013, monolayers of MoS_2(1−x)Se_2x were first produced by mechanical exfoliation [18]. Tuning of the bandgap by varying the composition was demonstrated by photoluminescence spectroscopy [18]. Chemical vapor deposition (CVD) of monolayer MoS_2(1−x)Se_2x was soon reported by several groups [19–27 ]. Similarly, CVD of monolayer WS_2(1−x)Se_2x with tunable bandgaps was achieved, too [28]. Alloying the transition metal atoms offers another approach to tune the electronic properties. Indeed, monolayers of Mo_1−xW_xS₂ have been produced by mechanical exfoliation [29], CVD [23, 30, 31], and sulfurization of oxide films [32, 33]. Monolayers of Mo_1−xW_xSe₂ have also been produced by CVD [34].

The fast progress in developing and optimizing fabrication techniques allows further studies on the properties of TMD alloys. For example, lattice structure and distribution of Mo and W atoms in Mo_1−xW_xS₂ monolayers were investigated by scanning transmission electron microscopy [35]. Effects of alloy engineering on controlling the detects were studied in Mo_1−xW_xSe₂ [34]. The electronic structure of monolayer Mo_1−xW_xS₂ was revealed by scanning tunneling microscopy and spectroscopy [36]. In contrast, optical studies of TMD alloys are rare and are limited to steady state measurements, such as photoluminescence [37], Raman spectroscopy [37], and photocurrent generation [27].

Here we report the first time-resolved study of carrier dynamics in TMD alloys by using femtosecond transient absorption technique. As an example, we investigated Mo_1−xW_xS₂ bulk crystals with x = 0.5. We deduced the lifetime of photocarriers and energy relaxation time of hot carriers. The photocarrier dynamics in Mo_1−xW_xS₂ is also compared with MoS₂ and WS₂. These measurements provide important parameters to understand performance of these TMD alloys in various applications in optoelectronic devices.

2. Experimental section

2.1. Sample preparation

We studied bulk alloy of Mo_0.5W_0.5S₂ provided by 2D Semiconductors. To ensure that the measurements were performed on a single-crystal domain, a mechanical exfoliation procedure was used to obtain films of Mo_0.5W_0.5S₂, which were transferred to a silicon substrate with an oxide layer. The films studied have thicknesses on the order of 100 nm, and can be treated as bulk materials. All the measurements were performed with the sample at room temperature.

2.2. Transient absorption

The dynamics of the photocarriers in Mo_0.5W_0.5S₂ was studied by transient absorption in the reflection geometry. As shown schemitically in Fig. 1, the setup is based on an 80 MHz Ti:sapphire laser that generates 100 fs pulses with a central wavelength of 800 nm. A portion of this beam is focused to a beta barium borate (BBO) crystal to generate its second harmonic at 400 nm. This beam is focused to the sample by a microscope objective lens. This pump pulse injects photocarriers to the sample by interband absorption. The other portion of the 800 nm beam is coupled to a highly chirped photonic crystal fiber (PCF) to generate a supercontinuum radiation in the visible and near infrared range. A dielectric bandpass filter with a central passing wavelength of 660 nm and a bandwidth of 10 nm is used to select that wavelength component from the supercontinuum. This probe beam is combined with the pump beam and focused to the sample through the same objective lens. The focused spot size is about 2.4 μm for both pump and probe beams, which is determined by an imaging system with a precision of about 0.2 μm. The reflected probe is sent to a silicon photodiode, which output is measured by a lock-in amplifier. A long-pass filter prevents the reflected pump beam from reaching the photodiode. A mechanical chopper modulates the pump intensity at about 2 KHz, in order to improve the signal-to-noise ratio. The pump and the probe pulses are orthogonally linearly polarized.

 

Fig. 1 Transient absorption setup.

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With this configuration, we measure the differential reflection of the probe, ΔR/R ₀ = (R − R ₀)/R ₀, where R and R ₀ are the reflection of the probe with and without the presence of the pump beam, respectively. The differential reflection is measured as a function of the probe delay, which is defined as the arrival time of the probe pulse at the sample with respect to the pump pulse. This quantity is controlled by a using a linear stage, which moves a reflector along a line, in the pump arm to vary the pump beam path length.

3. Results and discussion

The electronic bandstructure of Mo_1−xW_xS₂ alloys has not been precisely determined yet. However, since the bandgaps of MoS₂ and WS₂ bulk crystals are 1.2 and 1.4 eV, respectively [38], the bandgap of Mo_0.5W_0.5S₂ is expected to be in the range of 1.2 – 1.4 eV, and be close to 1.3 eV. In our experiment, the 400-nm pump pulse with a photon energy of 3.1 eV injects photo-carriers with an excess energy of about 1.8 eV, which is distributed between the electrons and the holes. These hot carriers injected are expected to relax their energy rapidly to the lattice, moving to the low-energy states in the conduction and valance bands. This energy relaxation process will be followed by a slower recombination process of the photocarriers, determined by their lifetime.

The dynamics of these injected photocarriers are monitored by the 660-nm probe pulse with a photon energy of about 1.9 eV. Hence, it directly probes states in the conduction and valance bands that are about 0.3 eV above the band edges. The observed differential reflection signal is shown in Fig. 2 for short (left) and long (right) time ranges. Different symbols represent measurements with different values of pump fluence, as labeled in the figure. So far, the absorption coefficient of TMD alloys has not been precisely measured, preventing us from accurately determining the injected photocarrier density from the pump fluence. If we assume that the absorption coefficient of Mo_0.5W_0.5S₂ at 400 nm is close to WS₂, which is about 7 × 10⁷ m⁻¹ [39], we can roughly estimate that a pump fluence of 1 μJ cm⁻² corresponds to a photocarrier density of 1.5 × 10¹⁸ cm⁻³ at the sample surface.

 

Fig. 2 Differential reflection signal over short (left panel) and long (right panel) time scales, with different values of the pump fluence as labeled. The solid red lines are fits to the data.

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As shown in the left panel of Fig. 2, the differential reflection signal reaches to a peak rapidly in a few picoseconds. This process can be attributed to the relaxation of photocarriers from the initially injected high energy states to the states probed. We model the rising part of the signal as N ₀(1 − e ^−t/τ_X), where N ₀ is the peak signal and τ_X describes the associated energy relaxation time [40]. By fitting the signals with probe delays from 0 to 2 ps, we find this simple model is consistent with the data, as indicated by the solid red curves. From these fits, we obtained the relaxation times and the peak values, as summarized in Figs. 3(a) and 3(b). No dependence of the relaxation time on the pump fluence is observed. This is expected, since the energy relaxation of carriers is achieved by phonon emission, which does not strongly depend on the injected carrier density. We obtain an average values of τ_X = 0.68 ± 0.10 ps. We also find that the peak signal increases with the pump fluence linearly when the fluence is low, and saturates at higher fluences, as shown in Fig. 3(b). This dependence can be satisfactorily described by the saturation model [41], ΔR/R ₀ ∝ F/(F + F_s), where F is the pump fluence and F_s the saturation fluence. From a fit, indicated as the red line, we obtain F_s = 32 ± 3 μJ cm⁻², which corresponds to a saturation density of about 5 × 10¹⁹ cm⁻³. This quantity describes the effectiveness of photocarriers in saturating the absorption coefficient, and is important for applications as saturable absorbers. Similar saturation effects have been observed in TMDs, too [42, 43].

 

Fig. 3 (a) The rising times of the differential reflection signal deduced from fits shown in Fig. 2 (left panel). The red line indicates an average value of 0.68 ps. (b) The peak value of differential reflection. The red line shows a fit to the data, corresponding to a saturation fluence of 32 μJ cm⁻². (c) Decay times of the differential reflection signal. (d) The values of the residual differential reflection signal at long probe delays.

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The right panel of Fig. 2 shows the differential reflection signal on a long time scale. The decay of the signal is caused by loss of photocarrier population due to their recombination. Since the exciton binding energies in TMD bulk crystals are much higher than the room temperature thermal energy [44], the photocarriers are expected to be mostly excitons during this process. We fit the data with a single exponential function, N ₀ e ^−t/τ_R + N_R, as shown as the solid red curves. Clearly, the decay can be satisfactorily described by the single exponential function. The deduced photocarrier lifetime, τ_R, is plotted as a function of the pump fluence in Fig. 3(c). We found that the lifetime decreases with the fluence: it changes from about 100 ps at relatively low fluence to about 50 ps at the highest fluence used in this study. Such an enhanced recombination at high injected carrier densities can be attributed to multi-carrier processes, such as exciton-exciton annihilation, that have been observed in transient metal dichalcogenides [45, 46].

As shown in the right panel of Fig. 2, there is a significant residual of the signal after this single exponential decay process. The magnitude of this residual is proportional to the pump fluence, as shown in Fig. 3(d). This indicates that there is a slower process induced by the pump pulse. Since no signal is observed at negative probe delays, this residual decays on a time scale shorter than 13 ns, which is the separation of two sequential pump pulses in the measurement. It is unlikely that this residual is caused by trapped carriers at defect sites, since it shows no saturation at rather high carrier densities. We attribute this residual to thermal effect left by the carriers, which causes the excited region of the sample to reach a higher lattice temperature.

Finally, we compare the photocarrier dynamics in Mo_0.5W_0.5S₂ with those in MoS₂ and WS₂ bulk crystals. Samples of MoS₂ and WS₂ films were prepared from bulk crystals with a similar procedure as Mo_0.5W_0.5S₂. For each sample, we injected photocarriers with a pump pulse of 400 nm wavelength and 4-μJ cm⁻² fluence, and used the same 660-nm pulse as the probe. The results are shown in Fig. 4 for short (left) and long (right) time scales. Under the same conditions, the signals from WS₂ and Mo_0.5W_0.5S₂ have similar magnitudes, while MoS₂ produced a signal of a few times larger. Both MoS₂ and WS₂ have a small peak right after zero delay, which is absent in Mo_0.5W_0.5S₂.

 

Fig. 4 Differential reflection signal over short (left panel) and long (right panel) time scales measured from MoS₂ (black squares), WS₂ (blue circles), and Mo_0.5W_0.5S₂ (purple triangles). The red lines are single exponential fits.

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We are mostly interested in comparing the recombination of photocarriers in the three materials. As shown in the right panel of Fig. 4, the decay of the signal in MoS₂ and WS₂ is noticeably slower than Mo_0.5W_0.5S₂. By fitting all the three curves with single exponential functions (red curves), we obtained photocarrier lifetimes of 360 ± 10 and 240 ± 20 ps in MoS₂ and WS₂, respectively, both are much longer than the 100 ps obtained in Mo_0.5W_0.5S₂ alloy. The shorter lifetime in Mo_0.5W_0.5S₂ can be attributed to its alloy nature, which results in lower crystalline quality of the lattice. This result also suggests that the recombination lifetime of photocarriers in all these materials are dominated by nonradiative recombination, and reflects the quality of the samples. The radiative recombination time of these indirect semiconductors are expected to be much longer.

4. Conclusion

In summary, we have time resolved photocarrier dynamics in TMD alloys. Differential reflection signals were observed in a Mo_0.5W_0.5S₂ bulk crystal, following interband absorption of an ultrafast pump pulse. An energy relaxation process shorter than 1 ps was observed. The photocarrier lifetime was found to be in the range of 50 – 100 ps, depending on the injected photocarrier density. This is a few times shorter than MoS₂ and WS₂, reflecting the relatively lower crystalline quality in the alloy. Saturable absorption of TMD alloys was also observed, with a saturation fluence of 32 μJ cm⁻². This effect can be utilized in nonlinear photonic and optoelectronic devices. These results provide important parameters on photocarrier properties in TMD alloys.