1. Introduction

Atomically thin TMDCs have triggered a surge of research interest owing to their intriguing electronic and optical properties [1–6]. One remarkable application of TMDCs is the saturable absorber based on mode-locking or Q-switching, which acts as passive optical switches in laser cavity to enable short-pulse generation. Different from the conventional semiconductor saturable absorbers mirrors (SESAMs) and carbon nanotubes (CNTs), which only allow for narrowband operation, monolayer and few-layer TMDCs have showed broadband saturable absorption behaviors from visible [7,8] to infrared range [9–12]. Interestingly, few-layer TMDCs with excitonic energies greater than 1 eV are experimentally observed to exhibit saturable absorption even at the wavelength of 2μm (photon energy of 0.62 eV) [9, 11, 13]. In case of excitation photon energies greater than the excitonic energy, saturable absorption mechanism is explained by single-photon absorption and Pauli blocking [9]. Though commonly inferred as absorption of longer wavelength induced by defect states, the mechanism of this novel sub-bandgap saturable absorption behavior has yet to be well understood [9–12].

Furthermore, with photon energy below the excitonic energy, the trapped carriers can be absorbed and excited from shallow defect states to conduction or valence band states. There should be an adequate concentration of defects in the monolayer and few-layer TMDCs, given the fact that they can exhibit obvious saturable absorption even for the photons with energy below their bandgap energies. As a matter of fact, we found that few-layer WS₂ with less defect can also exhibit obvious saturable absorption, which is promising to generate mode-locked laser pulses at 2 μm in our previous work [12]. Thus, it is possible that other existing mechanisms are responsible for the novel broadband saturable absorption, in addition to the absorption induced by defects states.

The recent attempts to utilize the strong light-matter interaction inside 2D TMDCs for new generation broadband saturable absorbers, have attracted intense research efforts to explore the fundamental physical properties of these materials. A variety of novel approaches have been explored to alter the optical properties of such materials, including bandgap renormalization [14,15], ultrahigh-density responses [16] and ultrafast structural deformation [17]. In particular, the giant excitonic band renormalization phenomena caused by strong Coulomb interaction between interband carriers, may be employed in the broadband modulation of TMDCs. However, the relevant dynamics of the excitonic structure renormalization and its application in broadband absorbers have been little studied.

The necessity to clarify the fundamental mechanism has motivated extensive studies in aspect of ultrafast spectroscopies. In case of low-dimensional semiconductors, excitonic quasi-particles appear as pronounced resonances in optical responses due to extraordinarily weakened dielectric screening and strong Coulomb interactions [18]. Especially for monolayer TMDCs, two efficient excitonic transitions, namely A and B excitons, are derived from the conduction band (CB) and spin-orbit split valence band (VB) around the K (K’) point in the Brillouin zone [18]. To better unravel the excitonic band renormalization process, there is an urgent need for a clear understanding of the ultrafast exciton and charge dynamics in TMDCs.

In this work, we present an in-depth analysis of the evolution of A and B excitons after photoexcitation in the monolayer WS₂. Specifically, the broadband transient absorption spectroscopy is measured to characterize the mechanisms of giant excitonic band structure renormalization and related photo-induced ultrafast broadband nonlinear absorption. We comprehensively analyze the evolutions of A and B excitons, and their contributions to the excitonic band structure renormalization. A dramatic excitonic energy shrinking is also observed, which stems from the heavy overlap of A and B excitonic bands induced by the strong Coulomb interactions between photoexcited carriers. Our studies indicate that in the monolayer WS₂ the photoinduced excitonic band structure renormalization occurs within a few picoseconds, while the full recovery takes hundreds of picoseconds. Moreover, the interactions between photoexcited carriers and phonons, as well as the resulting transient increase of the lattice temperature, have been demonstrated to make a better illustration of the overall scenario of this physical process.

2. Samples characterization and experimental methods

The growth of WS₂ monolayers was performed on sapphire substrate via low-pressure chemical vapor deposition (LPCVD) [19]. From the scanning electron microscopy (SEM) image of Fig. 1(a), one can see that the monolayer WS₂ almost covers the whole sapphire substrate, which is suitable for transient absorption (TA) spectroscopy measurements. In addtion, the atomic force microscopy (AFM) result shown in Fig. 1(b) indicates that the thickness of WS₂ sample is $~$ 0.7 nm, which confirms the monolayer thickness of the sample. For completeness, the Raman and photoluminescence (PL) spectra measurements were also performed, with their results illustrated in Figs. 1(c) and 1(d), respectively. The difference between $E_{2g}^1$ (in-plane vibration) and $A_{1g}^{ }$ (out-of-plane vibration) Raman modes is 61.25 $c{m}^{-1}$, in agreement with previous observations of monolayer WS₂ [20]. The PL spectrum of WS₂ sample excited by a 405 nm laser peaks at ~2.02 eV, confirming the PL feature of monolayer WS₂ [21].

 

Fig. 1 (a) SEM image of WS₂ monolayer samples on sapphire substrate. (b) AFM image of monolayer WS₂. Inset: Height profile of the white line marked in (b). (c) Raman spectra of the WS₂ sample. (d) PL spectra of the smaple under 405 nm laser excitation.

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In order to investigate the ultrafast photoexcited carrier dynamics of monolayer WS₂, the femtosecond pump-probe technique [22–24] is performed. With a broadband white-light probe, the measurements can extend to the entire visible and near infrared spectrum, and thus cover the broadband saturable absorption range of monolayer WS₂. The research aim is to verfity that under large photo-injected condition the excitonic band structure renormalization within monolayer WS₂ is an alternative reason that contributes to the ultrafast broadband saturable absorption. Therefore, it is of great significance to investigate the different evolution processes of the excitonic band structure within WS₂ monolayer, considering both linear and saturable excitation condition. In this context, the pump fluence was set from 50 μJ/cm² up to 1200 μJ/cm², covering the linear to saturable absorption region of monolayer WS₂. According to the report of H. Zhao et al. [25], the range of excited carrier density is from $1.7\times {10}^{13}$ cm⁻² to $4.08\times {10}^{14}$ cm⁻², covering experiemntal conditions from normal photoexcitation to extremely large photoexcitation.

3. Results and discussion

3.1 TA spectra of WS₂ at linear and saturable absorption region

The dependence of TA results of monolayer WS₂ on the probe photon energy and time delay, is presented in Fig. 2(a). Here, a pump photo energy of 3.1 eV with fluence of 75 μJ/cm² is employed, at the temperature of T = 78 K. It can be easily derived that the spectra in Fig. 2(a) are characterized by two positive (red) and two negative (navy) features. The common factors that contribute to the above phenomena include photo-induced enhanced or reduced absorption, excitonic resonance, and the shift of the absorption peak [26]. Precisely, a positive feature may be attributed to photo-induced absorption (PA) [27, 28] and a negative feature may indicate a photo-induced bleach (PB) [13] of the pump-induced excited states.

 

Fig. 2 (a) Differential absorption (ΔA/A₀) map of monolayer WS₂ as the function of both delay time and probe photon energy with the pump photon energy of 3.1 eV at average pump fluence of 75 μJ/cm² and probe with the supercontinum white light at T = 78 K. (b) TA spectra of monolayer WS₂ at different time delays, absorption spectra adapted from Y. Li et al [28]. and PL spectra for the same monolayer WS₂. (c) ΔA/A₀ map of monolayer WS₂ at average pump fluence of 1200 μJ/cm² at T = 78 K. (d) TA spectra of monolayer WS₂ at different time delays with pump fluence of 1200 μJ/cm².

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Based on the previous discussion [18], the four features of excitonic nature at ~1.95 eV, 2.03 eV, 2.28 eV and 2.40 eV represent PA and PB of A and B exciton of WS₂ monolayer, respectively, as marked in Fig. 2(a). The PB features in TA spectra are usualy caused by the state filling effect [13]. After the photon absorption, hot electrons cool down and fully occupy the states near the photon energy, preventing further absorption. According to Pauli’s exclusion principle, it is impossible to have two identical electrons filling the same state, rendering the occurrence of the bleach of light absorption. This explains why the negative PB signal in TA spectra appears. Furthermore, the two bleaching signals in TA measurements of Fig. 2(a) are in good agreement with the absorption peaks of monolayer WS₂ observed in the steady line absorption spectra, which is illustrated in Fig. 2(b). Another significant finding is that due to the Stark effect [14, 29], the peak of absorption spectra will slightly shift, resulting in the positive PA signal near the PB signal. Last but not least, since no obvious defect absorption feature is observed in TA and PL spectra of WS₂, we can assume that the defect states play an insignificant role in optical absorption.

Additional insights into the contribution of nonlinear effects to the TA spectra are provided by the evolution of the saturable absorption response of monolayer WS₂, the corresponding contour map being presented in Fig. 2(c). We have investigated the monolayer WS₂ under a pump photo energy of 3.1 eV with fluence of 1200 μJ/cm², at the temperature of T = 78 K. Different from the case of linear excitation discussed above, four different processes can be identified in the TA spectra of Fig. 2(c), including rise, decay, recover and steady. Firstly, after excitation two PB and two PA features appear within the initial 1 ps. Then, three features disappear during 2~10 ps, where only the PB feature of A exciton is found. However, in the third stage (10~150 ps), the PB feature of B exciton gradually appears again. Finally, the TA spectra recover to the four features configuration, reaching a stready state. To conclude, the evolution of exciton features is a rise-decay-recover-steady process. To obtain an in-depth understanding of the above four processes, four typical TA spectra at the delay time of 0.2 ps, 2.1 ps, 72 ps and 320 ps, are shown in Fig. 2(d). One main conclusion is that under strong photoexcitation the light absorption is enhanced significantly within the whole spectra, when compared with the linear excitation case shown in Fig. 2(b). Importantly, the curves of Fig. 2(d) exhibit the photo-induced broadband absorption of the monolayer WS₂.

Since the broadband absorption mechnism is a crucial factor characterizing the WS₂-based devices, we proceeded to analyze in more in-depth the evolution processes of A and B excitons. The results of this study, determined for the rise-decay and recover processes, are presented in Fig. 3. Here, the delay time of 0.2 ps (i.e., the earliest time ΔA signal occurs) is selected as the reference. From Fig. 3, one can observe the relative absorption difference measured with different delay times, considering pump fluences of 400 μJ/cm², 800 μJ/cm² and 1200 μJ/cm².

 

Fig. 3 Absorption difference spectra at time delay range from (a) 0.3 ps to 1.5 ps and (b) 1.5 ps to 60 ps with the pump fluence of 400 μJ/cm². Difference spectra at time delay from (c) 0.3 ps to 1.5 ps and (d) 1.5 ps to 60 ps with the pump fluence of 800 μJ/cm². Difference spectra at time delay from (e) 0.3 ps to 1.5 ps and (f) 1.5 ps to 60 ps with the pump fluence of 1200 μJ/cm². (a), (c) and (e) are results during the rising process of TA spectra. (b), (d) and (f) are results during the recovering process of TA spectra.

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One remakable finding is that the resonances of A and B excitons gradually disappear with the increasing pump fluence during the rise-decay process, as shown in Figs. 3(a), 3(c) and 3(e). Moreover, these resonances reappear during the recovering process shown in Figs. 3(b), 3(d) and 3(f), indicating that the photo-induced broadband absorption process of WS₂ is reversible.

Importantly, for monolayer TMDCs, the high order Auger recombination process takes place within the first several ps after excitation. The hot carrier density rapidly deduces, resulting in weakening of the bleach effect, which can be contributed to the extra absorption. From Fig. 3(b), one can see the recovering process of TA spectra within the following 70 ps time scale, under the pump fluence of 400 μJ/cm². Interestingly, the absorption features at A exciton’s resonance increases with delay times, whereas at B exciton’s resonance the absorption feature almost remains unchanged. Additionally, the resonance peaks of A and B excitons turn farther apart, with the whole rising intensity curve exhibiting blueshift. Next, with the decrease of carrier density, the interexcitonic interaction becomes weaker and the exciton bandgap recovers. However, when considering the rising process under the pump fluence of 800 μJ/cm² shown in Fig. 3(c), only absorption peaks at A exciton resonance (~2.01 eV) occur, which may be caused by strong interexcitonic interaction and totally overlap between A and B excitons. On the other hand, the absorption peaks at resonances of A and B excitons gradually appear again within 70 ps, as shown in Fig. 3(d). A reasonable explanation for this phenomenon is the recovery process of renormalized excitonic band structure. When it comes to even stronger photoexcitation, as shown in Fig. 3(e), neither of the two resonance absorption peaks appears, inferring the dramatic change of band structure in monolayer WS₂. Due to the extremely large photoexcited carrier density, energy bands of A and B excitons may overlap with each other to a great extent, probably forming a new energy band with a uniform electron distribution. During the Auger recombination process (i.e., first 2 ps), the bleaching effect of the excited carriers fades, leading to an extra absorption in TA spectra. The recovering process of TA spectra shown in Fig. 3(f) reveals the recovery process of WS₂’s band structure, which takes about 50 ps.

3.2 excitonic band structure renormalization of WS₂ at saturable region

As discussed above, the rising process of TA spectra occurs within the first 1.5 ps after excitation. An important aspect pertaining to the mechanism of nonresonance broadband absorption is to study the TA spectra within this time period in details. To fulfill this goal, TA spectra at 0.8 ps under different pump fluence are investigated, as shown in Fig. 4(a). Variations of exctonic band structure can be extracted from the absorption features [30]. The photo-induced absorption feature around 1.85 eV corresponds to the change of A exciton band, whereas the PA feature at ~2.2 eV is relative to B exciton band. Redshift of PA features is due to the decrease of exciton energy, while blueshift of PA features is usually caused by the increase of exciton energy. One significant finding from Figs. 4(b) and 4(c) is that under higher pump fluence PA feature of A exciton shows redshift, while PA feature of B exciton exhibits a redshift first, followed by a blueshift. To demonstrate this, the excitonic band structure of monolayer WS₂ is presentedin Fig. 4(d). Notably, the valence band and conduction band are referred as VB and CB, respectively, with Δ denoting the binding energy of quasiparticals. The splitting of VB, resulting in v₁ and v₂, is attributed to the spin-orbit coupling effect [31]. After photoexcitation, A and B excitons are rapidly formed by electrons in the minimum of CB and holes in the maximum of split VB [18]. The energy of A and B excitons will slightly reduce because of the existance of excited carriers [2, 15]. Addtionally, the energy degradation with regard to A and B excitons turns stronger when more excited carriers are generated, along with overlap of these two excitons, as dipicted in Fig. 4(d). The maximum of the v₂ band submerges in the v₁ band, where only holes exist. Therefore, electrons in lower position of the v₂ band give rise to PA signal of B exciton, which contributes to the abnormal blueshift of PA feature at B exciton, as displayed in Fig. 4(c).

 

Fig. 4 (a) TA spectra of monolayer WS₂ under different pump fluence from 40 to 1080 μJ/cm² at time delay of 0.8 ps after excitation. Position for the PA feature of (b) A exciton and (c) B exciton as the function of pump irradiance. (d) Schematic illustration of WS₂ band structure at equilibrium and at small and high photoexcited carrier density.

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Key parameters on the dynamics of excitions are the time constant and reduction of exciton energies. Here, we have measured the PA and PB features of A and B excitons, which is shown in Fig. 5. One important conclusion is that the exciton energy of A exciton shows a fast decay, by ~230 meV, whereas B exciton exhibits more complex behaviours. According to the description of Fig. 4(d), the bands of A and B excitons largely overlap with each other, especially at high carrier density. During the recombination process of excited carriers, the PA features of B exciton will undergo a blueshift-redshift-recover process, which is in reverse to what is presented in Fig. 4(d). The shift of PB features at A and B excitons reveals the warming and cooling process of lattice. As shown in Fig. 5, when at highter temperature, PB features of both A and B excitons show redshift, followed by the cooling process that is responsible for the blueshift phenomenon. Equally important, when excited by different pump fluence, redshift behaviours are observed at PB features of A and B excitons within various time scales, namely 0.7 ps, 1 ps, and 7 ps. These characteristic times indicate the variation of lattice warming process at different excited carrier densities.

 

Fig. 5 The shift of the PA and PB features of A and B excitons as the function of time delay after excitation at T = 78 K with pump fluence of (a) 400 μJ/cm², (b) 800 μJ/cm² and (c) 1200 μJ/cm², respectively.

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3.3 The electron-phonon interaction process

The influence of pump fluence is studied for the relaxation process of A exciton, with TA kinetics shown in Fig. 6(a). In case of linear photoexcitation, the decay curves of A exciton show a monotonous decline. However, when pump fluence exceeds 800 μJ/cm², these decay curves exhibit a drop-upraise-decline process. Notably, the TA dynamics under linear photoexcitation condition are fitted by a third-order multi-exponential decay function and the singular value decomposition (SVD). Three time constants of 0.44 ps, 7.60 ps, and 126.8 ps can be extracted from Fig. 6(a), which are in good agreement with reported time constants [25, 27, 30, 32]. To be more specific, the fast component $t_1$ is typically assigned to the fast Auger scattering [27, 32]. The second time component $t_2$ of 7.60 ps may be contributed by electron-phonon interaction process [30] or slow Auger scattering [33], whereas the final component $t_3$ is related to radiative recombination, whose reported results range from hundreds of ps to nanoseconds [27, 32, 34, 35]. Moreover, the proportions of these three time components are about 80%, 10% and 10%, respectively. This suggests that the majority of photoexcited carriers are recombined in the fast Auger scattering process ($t_1$). Additionally, $t_3$ accounts for less than 10% of the signal intensity on average, which is consistent with the low-quantum yield of emission observed from monolayer TMDCs [20, 27].

 

Fig. 6 (a) Decay curves for the bleach of A exciton with pump fluence between 80 μJ/cm² and 1200 μJ/cm² at T = 78 K. (b) Decay curves for the bleach of A exciton of monolayer WS₂ with the pump fluence of 1200 μJ/cm² at T = 78 K, 200 K and 300 K. (c) Temperature dependence for TA spectra of WS₂ monolayer at 3 ps after excitaiton with the pump fluence of 50 μJ/cm². (d) Schematic illustration of the overall scenario after optical excitation of the WS₂ monolayer, consistent with the observed photo-induced changes in optical responses.

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An additional important factor in the electron-phonon interaction is temperature. To start with, the decay curves of PB features at A exciton under saturable excitation, measured at different temperatures, are presented in Fig. 6(b). Precisely, the density of excited A excitons accumulates within ~600 fs, followed by fast decay within ~2 ps. The fast Auger scattering effect is responsible for the strong interaction among a large number of hot carriers in this period. This results in the carrier temperature is much higher than the lattice temperature [36]. The following important process is the electron-phonon interaction, whose energy is transferred from hot carriers to lattice, resulting in the cooling of hot carriers and warming of lattice [37]. The lattice warming process may lead to the anomaly rise for the decay curve from 2 ps to 20 ps after excitation. For completeness, TA spectra measurements of monolayer WS₂ under the linear excitation condition (pump fluence of 50 μJ/cm²) are performed at different temperature, as shown in Fig. 6(c). Particularly, the processes of thermalization and relaxation inside WS₂ occur within several ps in this case. The thermalization and relaxation process generally occur within < 1 ps at small photoinjecting condition, therefore electrons share the same temperature with lattice at 3 ps, when at temperatures of 78 K, 200 K, and 300 K shown in Fig. 6(c). Moreover, the PB peak values of A exciton increases at lower lattice temperature. In other words, the lower temperature lattice remains, the larger value of the ΔA feature for A exciton’s PB peak might be. Therefore, the lattice warming phenomenon provides a reasonable explanation for the upraising process of the decay curves from 2 ps to 20 ps, as illustrated in Figs. 6(a) and 6(b). The lattice warming process may take longer time at lower experimental temperature for it will cost longer time to cool down, consistent with temperature dependent results for the rising process in Fig. 3(b), in which the corresponding time scales are 18.8 ps, 25.4 ps and 34 ps at 300 K, 200 K and 78 K, respectively.

The overall scenario of monolayer WS₂ under strong photoexcitation is presented in Fig. 6(d). Firstly, the pump-generated excitons would induce the bleaching effect at the exciton resonance, accompanied by the blueshift of energy for both A and B excitons. Then, a majority of excitons (~80%) would recombine in a fast time scale of ~2 ps, which is dominated by high order Auger-type recombination. Additionally, with the weakening of bleaching effect, an extra broadband absorption is found in the TA spectra. Next, at the time scale of ~7 ps, energy is transferred from carriers to the lattice via electron-phonon interaction, leading to an increase of local lattice temperature and the redshift of PB features for both A and B excitons. In the final stage, the lattice cooling process and rediative reconbination process would occur at ~200 ps. Importantly, the two processes play an opposite role on the amplitude of PB features in TA spectra. In particular, the competition between such two processes may lead to an abnormal rising behaviour of A exciton’s decay curve, within the time scale of ~20 ps.

4. Conclusion

In conclusion, we have presented a comprehensive analysis of atomically thin WS₂ by performing femtosecond white-light pump-probe measurements, with injected electron-hole pair density varying between $1.7\times {10}^{13}$ and $4.08\times {10}^{14}$ cm⁻². We have investigated not only the femtosecond time-resolved TA spectra, but also the dynamics of excited carriers. Under linear excitation, the monolayer WS₂ exhibits strong excitonic resonances, suggesting that the defects have little influence on optical absorption response. On the other hand, with strong photoexcitation, the WS₂ monolayer shows different optical responses, which are contributed by the broadband photo-induced absorption, giant optical bandgap renormalization of hundreds of meV, and ultralong lattice heating process. The experimental results reveal that the strong photo-induced change of optical responses in WS₂ monolayers has ps lifetime, and their full recovery undergoes hundreds of ps. Moreover, the heavy overlap of A and B excitonic bands is observed in monolayer WS₂. In addition, strong Coulomb interactions is assumed to play a crucial role on band structure renormalization and interactions between photoexcited carriers and phonons. This work provides deep insight into the ultrafast dynamics of excited carriers and excitonic band structure of WS₂ monolayers, which are prerequisites for applying TMDCs in ultrafast light-emitting and light-harvesting devices. Furthermore, the features of broadband absorption and saturable absorption render WS₂ excellent potential for broadband optical modulators and absorbers operating from visible to mid-infrared region.