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Abstract
The characteristics of a hot carrier distributed in the C excitonic state of the monolayer WS2 is investigated by exploiting the transient absorption (TA) spectroscopy. The hot carrier cooling lifetime gradually prolongs from 0.58 ps to 2.68 ps with the absorbed photon flux owing to the hot phonon bottleneck effect, as the excitation photon energy is 2.03 eV. Meanwhile, the normalized TA spectra shows that the spectral feature of hot carriers is different from that of normal carriers. Based on the modified Lennard-Jones model, the average distance among hot carriers can be estimated according to the peak shift of TA spectra and the diffusion velocity can also be calculated simultaneously. The hot carrier limits the diffusion of the photo-generated carrier at the initial several picoseconds. These results help people to elucidate the hot carrier dynamics in 2D TMDCs and give guidance on the designing and optimizing the TMDC-based electronic devices of high performance.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Two-dimensional transition metal dichalcogenides (2D TMDCs) involving MoS2, WS2, MoSe2 and MoTe2 [1] is a family of fascinating materials with superior physical characteristics [2], spatial structure [3] and valley band structure [4]. Nowadays, 2D TMDCs have been extensively applied in the field of photovoltage [5], microelectronics [6], lithium ion battery [7] etc. Their reduced dimensionality and weak dielectric screening can lead to the highly enhanced coulomb interactions in the atomically thin layers, which eventually affect the property of excited transient species involving exciton, trion, biexciton and free carriers [8] in 2D TMDCs. Besides the transient excited species as mentioned above, the hot carriers consist of electrons/holes in a Boltzmann distribution with initial kinetic energies more than kBT [9,10], can also be induced in the 2D TMDCs [11]. In addition, the hot carriers are able to improve the performance of optoelectronic devices such as photovoltage [12] devices and light emitting diode [13]. However, hot carriers own much complicated spectral features [14] in comparison with that of the normal photo-generated carriers. Thus, it is difficult to probe and investigate the physical mechanism of hot carriers, since its lifetime is super-short and less than picosecond (ps) [15].
Recently, femtosecond time-resolved spectroscopy, acting as an effective method, is extensively employed to probe the behavior of hot carriers (HC) in 2D TMDCs [16,17]. For example, Kumar et al. induced the hot carriers in bulk MoS2 and probe their diffusion and mobility characteristics with the transient absorption microscopy [16]. Wen et al. measured the hot carrier injection lifetime from plasmonic nanostructure to bilayers WSe2 by employing transient absorption spectroscopy [17]. Yuan et al. studied the hot carriers diffusion coefficient and the atomic layer interface thermal resistance in few layer MoS2 by employing energy transport state resolved Raman spectroscopy [18]. Sundaram et al. analyze the role of hot carriers in the electroluminescence of monolayer MoS2 based on field-effect transistors [13]. Actually, the core of hot carrier application mainly depends on its cooling lifetime and diffusion process, which can determine the extraction of hot carriers on the interface. However, the study of hot carrier characteristics in 2D TMDCs is at the beginning stage. The report on the cooling lifetime and the diffusion velocity of hot carriers in 2D TMDCs is much limited. This hinders people to analyze the physical properties of 2D TMDCs and restrict the applications of 2D TMDCs in the electronic fields.
Herein, femtosecond transient absorption (TA) spectroscopy is employed to investigate the property of hot carriers in the C excitonic state of the monolayer WS2 (M-WS2), involving its cooling lifetime, spectral feature and diffusion behavior. It is found that the hot phonon bottleneck is responsible for the delaying the cooling process of hot carriers at high absorbed photon flux. The spectral feature of hot carriers changes obviously in comparison with that of normal carriers. Based on the modified Lennard-Jones model, the average distance among hot carriers in C excitonic state of M-WS2 at the initial timescale is also estimated according to the shift of photo-induced absorption peak relative to C excitonic state. These results give a further understanding on the physical properties of 2D TMDCs and broaden the application of 2D TMDCs materials in the electronic fields.
2. Methods
2.1 Materials
The monolayer WS2 is grown on a sapphire substrate via a chemical vapor deposition (CVD) technique method by SixCarbon Technology company. The monolayer WS2 is continuously distributed on the substrate (1×1 cm2). Thus, it can make sure that all the laser can interact with the sample.
2.2 Basic characterization
The Raman spectrum is recorded via a Raman microscope (Renishaw) with a spectral resolution of 1 cm−1 with 532 nm laser excitation. The scanning electronic microscopy (SEM) imaging of WS2 uses a Magellan 400 (FEI). The steady-state absorption spectrum is collected by UV–vis absorption spectrometer (Purkinje, TU-1810PC). All the measurements are made at room temperature (298K).
2.3 Transient absorption spectroscopy
The femtosecond transient absorption spectroscopy under room temperature (298K) has been reported elsewhere [19]. The probe is generated by focusing the femtosecond laser onto a 3mm thick sapphire crystal, which spectral range is cover from 1.6 to 3.2 eV. The pump laser of 610 nm (2.03 eV) was generated via an optical parameter amplifier (Coherent, TOPAS). The pump laser is then sent to a delay line and modulated by a synchronized optical chopper (Terahertz Technologies Inc., C-995) with a frequency of 250 Hz. It means the time interval between the two pump pulses is 4 ms, which is much longer than the photo-excited species lifetime in M-WS2. The time-dependent transient absorption spectra are recorded with a highly sensitive spectrometer (Avantes AvaSpec-2048×16). The polarization direction of the pump and the probe pulse was horizontal. The pump spot is ∼0.3 mm in diameter, and the probe spot is ∼0.2 mm in diameter. The pump flux can be adjusted by variable neutral density filter. The probe intensity is much weaker than pump laser and ∼1×1011 photon cm−2.
3. Results and discussion
The steady-state absorption spectrum of M-WS2 [22] (as seen in Fig. 1(a)) shows the spectral feature of A, B and C excitonic state (named A-X, B-X and C-X) is located at 2.03, 2.43 and 2.91 eV [20]. The schematic diagram of energy structure as seen in Fig. 1(b) exhibits that A-X and B-X transition correspond to the transition at the K point in the Brillouin zone from the split valence bands (named VB1 and VB2) maximum to the bottom of conduction band at the LDA (local density approximation) level (named CB1) [20]. C-X transition corresponds to the transition at the K point in the Brillouin zone from the valence band (VB1) maximum to the bottom of conduction band at the GW (corresponding to the approximation based on the Green’s function (G) and the screened Coulomb interaction (W)) level [23] (named CB2). Meanwhile, the previous reports point out that C-X transition is also affected by the band nesting effect originated from inter-band transitions around Γ [20,24]. Apparently, the origin of C-exciton is much complicated. Considering M-WS2 is direct band-gap semiconductor [25], the schematic diagram of energy structure we exhibit only involve energy level, without an x-axis (wave-vector) in comparison with the theoretical calculation [20–22,25]. Moreover, the state density of CB1, CB2, VB1 and VB2 are broad and some of them are overlapped with each other as seen in Fig. 1(b).Therefore, the photo-generated carriers can simultaneously distribute on the A-X, B-X and C-X after photo-excitation [26]. Figure 1(c) shows that the Raman spectrum of the M-WS2 is composed of the E12G mode and the A1G mode, which are assigned to the in-plane and out-of-plane motion of W and S atom [27]. They are located at 355 and 418 cm−1 and their difference is 63 cm−1, which is consistent with the previous report [28], suggesting that the WS2 in our experiment is monolayer. The TA map of M-WS2 with excitation photon energy of 2.03 eV are exhibited in Supplement 1 Fig. S1, which owns rich spectral features. The TA spectrum of M-WS2 with the delay time of 0.96 ps is given in Fig. 1(d), showing three positive peaks corresponding to the photo-bleaching (PB) [29] of the A-X, B-X and C-X based on the steady-state absorption spectrum in Fig. 1(a), as well as two negative peaks related to the photo-induced absorption (PIA). Considering the spectral feature of TA spectra in Fig. 1(d) and the previous reports [20,26], we identify the origin of PIA signals in TA spectra owing to four reasons. Firstly, the A-X and B-X is originated from the splitting of valence band. Since they share the same conduction band (CB1), they own the same PIA signal. Secondly, the position of CB2 is higher than that of CB1. Thus, the PIA signal in the low energy region of TA spectra is attributed to the C-X and that in the high energy region is closed to the contribution of A/B-X. Thirdly, the two PIA signals are located at 2.42 and 1.84 eV based on the five Gaussian peaks. Their difference is ∼0.58 eV, which well matches the energy difference between CB1 and CB2 according to the theoretical calculation [20,21,25,30]. Fourthly, the previous report [31] points out that the contribution of bandgap renormalization can lead to the bandgap shrinkage phenomenon, which can modulate the shape and the position of the TA spectrum apparently. As seen in Fig. 3 and Supplement 1 Figs. S1 and S4, the peak positions of A-PB, B-PB and C-PB in our experiment almost don’t shift under the different absorbed photon flux. This indicates that the bandgap renormalization effect in the TA spectra is much limited in our experiment. Therefore, it is reasonable to consider that the PIA signals located at 2.42 and 1.84 eV are attributed to the transition of A/B-X and C-X, respectively. In addition, the excitation photon energy in the TA setup is 2.03 eV, which is mainly resonant with A-X, and the population of photo-generated carriers in CB2 (C-X) is lower in comparison with those in CB1 (A-X). Therefore, the contribution of band nesting should be so weak [32,33] that cannot affect the analysis of our experimental data. In a word, the complicated TA spectra of M-WS2 is originated from its rich energy state structure.
Fig. 1. Intrinsic physical characteristics of monolayer WS2. (a) Steady-state absorption spectrum, (b) Schematic diagram of energy structure, (c) Raman spectrum of M-WS2 and (d) the TA spectrum of M-WS2 with the excitation photon energy of 2.03 eV at the delay time of 0.96 ps, where the absorbed photon flux is fixed at 1.01×1013 photon cm−2. CB1: Conduction band at the LDA level at the K point in the Brillouin zone [20]; CB2: Conduction band at the GW level at the K point in the Brillouin zone [21]; VB: Valence band. The absorption peak of A/B-X are fitted with Gaussian shape and marked with red and orange color. The A-PB, B-PB and C-PB corresponds to the transition of A, B and C exciton.
Fig. 2. Dynamic Characteristics of Hot Carriers in C-X. Normalized absorbed photon flux-dependent (a) C-PIA curve and (b) A-PB curve of M-WS2 with the excitation photon energy of 2.03 eV. Inset: Absorbed photon flux-dependent τHC-C.
Fig. 3. Spectral Characteristics of Hot Carriers in C-X. Absorbed photon flux-dependent normalized TA spectra of M-WS2 with the excitation photon energy of 2.03 eV at the delay time when C-PIA amplitude rises to the maximum. Inset: Schematic diagram of the hot carrier mechanism in C-X of M-WS2. PE: phonon emission; CB: Conduction band; VB: Valence band.
3.1 Cooling characteristics of hot carriers in C-X
As mentioned above, the position of CB2 related to C-X in the energy band structure of M-WS2 is much higher in comparison with that of CB1 related to A/B-X. Therefore, the hot carrier of C-X in CB2 owns high activity and have much larger potential to drive chemical and physical processes in comparison with that of A/B-X in CB1. Therefore it should play a much important role in the fields of hot carrier-based devices [34]. In order to identify the hot carrier dynamics of C-X, the absorbed photon flux-dependent C-PIA curve located at 1.84 eV is given in Fig. 2(a). Actually, the PIA signal can be used to probe the carriers characteristics in polymer heterojunction [35] and Metal-Organic Framework [36] and scan the hot carriers in the system of black phosphorus quantum dots [37] and hybrid perovskites materials [38]. The excitation photon energy (2.03 eV) is resonant to the A-X and marked with brown arrow in Fig. 1(a). Herein, a rising component appears in the C-PIA curves at the initial timescale and slows down apparently with the absorbed photon flux. Since the initial energy state position of photo-generated carriers after photoexcitation is higher than the bottom of CB2 (as seen in the inset of Fig. 3), it is reasonable to consider that this rising behavior in C-PIA should be attributed to the hot carriers cooling process [37]. Note that the initial component of A-PB curves are almost invariable with absorbed photon flux (as seen in Fig. 2(b)). Moreover, the absorbed photon flux-dependent rapid decay component doesn’t appear in the A-PB curves (in Fig. 2(b)), B-PB and C-PB curves (in Supplement 1 Figs. S2 and S3). It suggests that the Auger recombination doesn’t happen and the Auger reheating effect can be excluded in the generation mechanism of hot carriers. In addition, the polaron-mediated hot carriers cooling happens in ionic crystal, like perovskite materials [39]. Since M-WS2 is not an ionic crystal, the polaron-mediated hot carriers cooling process can also be excluded in our experiment. According to the value of absorbed photon flux (from 1.51 to 6.04×1013 photon cm−2) and the experimental phenomenon as seen in Fig. 2(a), the prolonging behavior of hot carriers cooling in C excitonic state of M-WS2 can be assigned to the hot phonon bottleneck effect [40,41]. In the cooling process, the hot carriers in C-X can gradually relax to the bottom of CB2 and emit the excess energy to longitudinal-optical (LO) phonon through nonadiabatic coupling. The excess energy finally dissipate to the environment via coupling to substrate phonons [42] or anharmonic phonon-phonon scattering [43]. Since a large number of LO phonons are heated into a non-equilibrium state at high carrier density, the re-absorption of LO phonons happens and is able to slow down the hot carriers cooling process [40,41] as illustrated in the inset of Fig. 3. Based on the multi-exponential function fitting, the cooling lifetime of hot carriers (τHC-C) in C-X can be extracted from the TA curves and summarized in the inset of Fig. 2(a). It shows that the τHC-C approximately linearly increases with the absorbed photon flux, implying that the increasing of absorbed photon flux can effectively slow down the hot carriers cooling in our test region.
3.2 Spectral characteristics of hot carriers in C-X
The absorbed photon flux-dependent TA spectra when the C-PIA amplitude rise to the maximum is given in Supplement 1 Fig. S4 and the spectral shapes in TA spectra are much similar to each other. As the absorbed photon flux increases, their spectral features in TA spectra enhance with different enhancement rate. So as to distinguish them accurately, these TA spectra are normalized by the maximum A-PB signal (as seen in Fig. 3). Considering the percentage of hot carriers in the photo-generated carriers increase with absorbed photon flux, the difference of normalized TA should be attributed to the population increase of hot carriers. In other words, the absorption coefficient of hot carriers should be higher than that of normal photo-generated carriers. Such phenomenon has also been observed in many semiconductors [38,44].
3.3 Interaction and diffusion characteristics among hot carriers in C-X
As seen in Supplement 1 Fig. S1 and Fig. S5, the peak position of C-PIA exhibits a blue and then red shift behavior with time. Actually, in addition to electric field force, photo-generated hot carriers of high density tend to repel each other due to the Pauli exclusion of overlapping electron orbitals, which give rise to positive inter-carrier potential energy [45,46]. As the carriers diffuse with time, the proportion of van der Waals forces in the inter-carrier interaction increases gradually [47]. Meanwhile, the inter-carrier potential energy can cause the shrinkage of CB1 and CB2 [48], and then lead to corresponding spectral shift [49]. In order to analyze the physical mechanism related to the peak shift of C-PIA, the Gaussian shape is used to fit the C-PIA (as seen in Supplement 1 Fig. S5). The fitting result of C-PIA peak position under different absorbed photon flux as function of delay time is summarized in Supplement 1 Fig. S6. Inspired by the Lennard-Jones potential between atoms [47], a simple phenomenological model with two power laws is built, so as to quantify the carrier contribution to the energy shift (ΔE) in the entire density range [48,50]. Note Lennard-Jones model describes the interaction between electrically neutral atoms or molecules, here we add an electrostatic energy term (EES) to describe the additional interaction among carriers [51,52]
Thus, the diffusion characteristics among hot carriers is discussed based on a modified Lennard-Jones model:
Here rs is the radius of disk occupied by a carrier (nπrs2 = 1). Meanwhile, ɛ, r0, k, ɛ0, q1 and q2 are the fitting parameters, which can be interpreted in a similar way as the usual “12−6” power-law potential between atoms [53]. The first term describes the C-PIA blue shift caused by the short-range repulsion. Considering that the interaction among photo-generated carriers is non-bonded interaction, we use the rs−8 functional form for better fitting of the Pauli repulsion in this system instead of the usual rs−12 typically chosen in atomic system, which makes the calculation accurately [54]. The second term models the carrier redshift caused by the long-range van der Waals attraction [55]. In general, the functional form of this attraction potential is different from the usual London dispersion force rs−6, hence we parametrize it as rs−k [56,57]. By fitting the ΔE−rs data through the least-squares method with ɛ = 135 meV, r0 = 2 nm, and k = 1.4, our simple model matches the density dependence of energy shift (ΔE). The fitting details is given in Supplement 1 Note 4. Figure 4(a) exhibits the relationship between the rs and the ΔE according to the model we build.
Fig. 4. Diffusion among carriers in Monolayer WS2. (a) C-PIA energy shift (ΔE) as a function of average radius (rs) occupied by a carrier in the carrier gas with the modified Lennard-Jones model. (b) The peak position of C-PIA shift and (c) the corresponding inter-particle separation and (d) the corresponding differential coefficient among carrier at C excitonic state as function of delay time under different absorbed photon flux.
With the help of the modified Lennard-Jones model as mentioned above, the diffusion dynamics among photo-generated carrier can be deduced by substituting the peak energy shift (ΔE) to the model as seen in Fig. 4(a). Since the cooling lifetime of hot carriers is less than 5 ps, we focus on the peaks-shift process in the first 5 ps (as exhibited in Fig. 4(b)), which should be much sensitive to the diffusion characteristics among hot carriers. Figure 4(c) exhibits the time-dependent inter-particle separation of hot carriers under different absorbed photon flux, indicating that the average distance (rs) among hot carriers decreases with the increasement of absorbed photon flux under the same delay time. The diffusion velocity among hot carriers also decreases under high absorbed photon flux (as shown in Fig. 4(d)). This suggests that the high-density of hot carriers limits the diffusion of photo-generated carrier, even though the increasement of photo-generated carrier population can lead to strong repel potential energy. After analyzing the absorbed flux-dependent A/B-PIA curves (as seen Supplement 1 Fig. S9), it is found that hot carriers can also appear in A-X and gradually relax to the bottom of CB1. Note that only the peak shift of C-PIA is observed, the hot carriers originated in C-X may also impacted by the photo-generated carriers in A-X in M-WS2 through this interaction. Actually, the diffusion characteristics of carriers can be estimated by transient grating [58], transient absorption microscopy [38] and the Hall Effect [59], besides our method. However, the transient grating technique need the carriers follow the monomolecular recombination and is not suitable to estimate the diffusion of hot carriers at high carrier density [58], which accompanied with Auger recombination, bimolecular recombination and monomolecular recombination. The transient absorption imaging can effectively offer the diffusion velocity of hot carriers, but its system is much complex [38]. The Hall effect can offer the carrier mobility driven by electric field and can’t estimate the diffusion length of hot carriers driven by carrier concentration [59]. Therefore, our method based on modified Lennard-Jones model is much effective and easily to operate.
4. Conclusions
We successfully investigate the hot carrier characteristics of C-X in the monolayer WS2 by employing the transient absorption spectroscopy and discuss their cooling behavior, the transient spectral shift and the diffusion characteristics. Through changing the absorbed photon flux, the cooling lifetime and spectral features of hot carriers can be enhanced apparently. In addition, the diffusion process among hot carriers in C-X is estimated according to modified Lennard-Jones model and the corresponding diffusion velocity can be also given at the same time. These results can help explain the ultrafast carrier dynamics in the monolayer TMDCs for a broader range of fundamental research and practical applications.
Funding
China Scholarship Council (201906170158); National Natural Science Foundation of China (11574112, 11774122, 21573094, 61575079, 11904123).
Disclosures
The authors declare that they have no conflicts of interest.
Supplemental document
See Supplement 1 for supporting content.
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