2.1 Characterization of mechanically exfoliated WSe2 monolayer
In this study, WSe2 monolayers were mechanically exfoliated from layered bulk crystals by polydimethylsiloxane (PDMS) and then transferred to silicon wafers. All our measurements in this part were performed at room temperature. The WSe2 monolayers were confirmed by microscopy and PL spectroscopy. Figure 1a illustrates a typical optical microscope image of WSe2 monolayer, and the linear dimensions of areas with uniform monolayer flake are in the range from ∼20 μm to well above 50 μm. Combining confocal optical microscopy with spectrograph, excitation laser (continuous wave, 2.33 eV) was scanned over the sample and the PL emission spectra at different sites were recorded. Figure 1b shows the spatial distribution of total PL intensity, where the quantum efficiency of PL is homogeneous over the exfoliated WSe2 monolayer. The PL spectra along the white dotted line in Fig. 1b were depicted in Fig. 1c. There is no appreciable shift for exciton peak. Moreover, the average PL spectrum of WSe2 monolayer (gray line) was superimposed on Fig. 1c. The near symmetric spectral shape was well fitted by Lorentzian profile (red line) with the peak of 1.66 eV and linewidth of 39.4 meV, which can be attributed to A exciton. It is different from chemical vapor deposition-grown TMDC monolayers, where exciton emission is often accompanied by comparable trion emission due to electrons doping from defects and grain boundaries. Therefore, defects and grain boundaries have minimal effect on our experiments.
Besides, micro-Raman spectroscopy also can serve as an effective technique to delineate the spatial distributions of defects, strain, electron-doped concentration etc. As shown in Fig. 1e, the intensities of Raman signals for exfoliated WSe2 monolayer are homogeneous, coinciding with the PL mapping in Fig. 1b. Similarly, Raman spectra along the white dotted line in Fig. 1d were depicted in Fig. 1e, superimposing with the average spectrum. The WSe2 monolayer has a typical Raman spectrum with two dominant peaks at 248.8 cm−1 and 259.8 cm−1, corresponding to atomic displacements of the in-plane \(E_{2g}^{1}\) and out-of-plane \(A_{1g}^{{}}\) modes, respectively. The shift magnitudes of in-plane mode in different regions are often utilized to determine defects and strain distributions [40, 41]. The \(E_{2g}^{1}\) peak frequencies of Fig. 1d were extracted and depicted in Figs. 1f, where there is no discernible shift for \(E_{2g}^{1}\) mode, corroborating the uniformity of WSe2 monolayer. These findings suggest that mechanically exfoliated WSe2 monolayers can provide an ideal platform to explore the diffusion dynamics of 2D exciton.
2.2 Exciton diffusion dynamics modulated by phonon scattering and disorder potentials
The direct PL imaging technique was adopted to explore exciton diffusion dynamics modulated by phonon scattering and disorder potentials in the exfoliated WSe2 monolayer. Therefore, only the diffusion of bright exciton within the radiative cone can be recorded and discussed in this study, though the population of dark excitons plays an important role in the physical properties at low temperatures [42,43,44]. In our experiments, the flake was excited by the focused femtosecond laser with the photon energy of 2.06 eV and energy density of 2 μJ/cm2. The focused femtosecond laser spot was normalized and depicted in Fig. 2a. The pumped excitons undergo ultrafast Auger recombination and then diffuse and recombine with bright radiation around the uniformly high-quality flake [45,46,47], which were recorded simultaneously by an electron-multiplying charge-coupled device (EMCCD) camera. In Fig. 2a, the recorded PL images at different temperatures were normalized and depicted in both ordinary and semi-logarithmic coordinate systems, respectively (see Additional file 1: S1 for more temperatures). It can be observed that excitons spread much further than laser spot due to diffusion.
The theoretical exciton emission profiles (Additional file 1: Fig. S2a) for different effective diffusion coefficients Deff can be obtained based on the continuity equation of exciton diffusion dynamics. It is noted that the excitation location was fixed in the middle of the WSe2 sample to avoid scattering and other effects induced by boundary region. To extract exciton diffusion coefficient sensitively, the co-axial ring of PL images (inset of Fig. 2b) was adopted, by imitating the commonly used eclipsing Z-scan method in nonlinear optics [48, 49]. After determining the co-axial ring, the Deff can be obtained from Fig. 2a by comparing the theoretical and experimental results (see Additional file 1: S2 for more details), as shown in Fig. 2b with the red dashed arrowed line as a guide to the eye. As increasing temperature from 80 to 400 K, the effective diffusion coefficient of excitons was enhanced by > 200% at the vicinity of 280 K and then decrease rapidly. Additionally, the total PL intensities exhibit similar temperature dependence, as illustrated in Fig. 2c. It can be deduced that the temperature-dependent emission and diffusion of exciton originate from the same mechanism. Figure 2c seems in contradiction to the seminal work of Zhang et al. [50], where a clear and monotonous increase in PL intensity has been observed at enhanced temperatures due to the presence of energetically lowest dark excitons. In our work, the monotonous results were repeated for temperature lower than 280 K. However, the PL decrease was observed for temperatures higher than 280 K due to the bright exciton quenched by multi-phonons processes. Noted that the main purpose of Zhang et al. was to present experimental evidence for the existence of dark exciton, thus the multi-phonons quenching processes were ignored at higher temperature, though the decrease of the populations of bright state was observed for temperatures higher than 280 K. It proves that the non-monotonous behavior of PL intensity is reliable. Besides, it should be noted that in our experiment, the energy density is in the range of halo effects, as shown in Ref. [26], but the steady state exciton distribution is recorded by EMCCD, which is the integral of time-resolved the exciton distribution. Therefore, the instantaneous halo effects weren't observed.
Taking into account the population of bright state, exciton quenching induced by multi-phonons scattering and exciton localization in disorder potentials, the non-monotonous behavior of PL intensity can be quantitatively explained. Firstly, the conduction band splitting Δc results in an energy separation between bright state (AB) and dark state (AD) for A exciton and the lowest energy exciton is a dark state for WX2 (X = S, Se, Te). The populations of AB and AD obey Boltzmann distribution as given by \({{N_{{A_{B} }} } \mathord{\left/ {\vphantom {{N_{{A_{B} }} } {N_{{A_{D} }} }}} \right. \kern-\nulldelimiterspace} {N_{{A_{D} }} }} = \exp ({{ - \Delta_{c} } \mathord{\left/ {\vphantom {{ - \Delta_{c} } {k_{B} T}}} \right. \kern-\nulldelimiterspace} {k_{B} T}})\). Secondly, the average population of phonon gas in WSe2 monolayer is determined by temperature and can be written as \(\overline{n} = {1 \mathord{\left/ {\vphantom {1 {\left[ {\exp ({{\hbar \omega_{q} } \mathord{\left/ {\vphantom {{\hbar \omega_{q} } {k_{B} T}}} \right. \kern-\nulldelimiterspace} {k_{B} T}}) - 1} \right]}}} \right. \kern-\nulldelimiterspace} {\left[ {\exp ({{\hbar \omega_{q} } \mathord{\left/ {\vphantom {{\hbar \omega_{q} } {k_{B} T}}} \right. \kern-\nulldelimiterspace} {k_{B} T}}) - 1} \right]}}\). Finally, the process of excitons escaped from disorder potentials is similar to electrons emission from potential wells and the probability \(\eta_{e}\) is proportional to \(\left( {k_{B} T} \right)^{1/2} \exp \left( {{{ - \chi } \mathord{\left/ {\vphantom {{ - \chi } {k_{B} T}}} \right. \kern-\nulldelimiterspace} {k_{B} T}}} \right)\), where \(\chi\) is the average depth of disorder potentials. Therefore, the temperature-dependent PL intensity can be written as following (see Additional file 1: S3 for more details)
$$I_{PL} (T) = \frac{{\eta_{q} \eta_{e} N_{0} }}{{\exp ({{\Delta_{c} } \mathord{\left/ {\vphantom {{\Delta_{c} } {k_{B} T}}} \right. \kern-\nulldelimiterspace} {k_{B} T}}) + 1}}\exp ( - \eta_{p} \overline{n}^{x} \tau )$$
(1)
where \(\eta_{q}\) is the quantum efficiency from excitons to photons, N0 is the excitons population excited by photons, \(\eta_{p}\) is the probability of multi-phonons collided with exciton which is proportional to \(T^{x/2}\) (here x = 4 were adopted) and \(\tau\) is exciton lifetime. As depicted by the blue dotted line in Fig. 2c, the temperature-dependent PL intensities were well fitted by Eq. (1).
Similarly, the non-monotonous temperature-dependent behavior of the exciton diffusion coefficient can be also well explained by the competition of multi-phonons scattering and exciton localization in disorder potentials. According to reference [51], taking into account the interaction of exciton with longitudinal phonon mode, the quantum correction of exciton diffusion coefficient is negative and demonstrates sizeable variation with the temperature, that is, the exciton diffusion coefficient decreases with elevated temperature for the multi-phonons scattering dominated exciton diffusion. The temperature dependence of exciton diffusion coefficients prominently changes if the process that the excitons interacting with potential disorder is considered, and the diffusion coefficients increase with elevated temperature. Therefore, the exciton diffusion coefficients can be presented by a non-monotonic function of temperature due to the competition between multi-phonons scattering and exciton localization in disorder potentials, and the optimized temperature relates to the modulation depth of disordered potentials on the exciton energy landscape.
Note that both the measurements and calculations yield exciton diffusion coefficient in the range of 1~5 cm2/s at room temperature under the excitation of continuous laser due to the exciton-phonon scattering in TMDC monolayers [44, 51, 52]. As demonstrated in previous studies, a significantly higher value of diffusion coefficients D on the scale of 10 cm2/s can be achieved in the nonlinear regime of the exciton system, which are attributed to several possible effects including Auger-recombination, phonon drag, thermal drift (Seebeck) effects, etc. [26, 43, 53]. Specifically, the main origin of the nonlinear exciton diffusion at elevated densities, Auger recombination in the center of laser spot, leads to a flatten and additional broaden exciton distribution and thus to a giant enhancement of the extracted effective diffusion coefficient.
2.3 Temperature-dependent photoluminescence spectra
PL spectra can provide the frequency domain information of exciton evolution with temperature, which is instructive to verify the physical mechanism underlying exciton diffusion. Figure 3a displays the PL spectra of different temperatures. The PL intensities were acquired by integrating spectra, as depicted in Fig. 3b. The blue dotted line is the fitted curve according to Eq. (1), which agrees well with Fig. 2c. For clarity, all the PL spectra were normalized by each maximum, as illustrated in Fig. 3c. It can be clearly observed the exciton peak broadening and red shift with rising temperature. The amplitude of exciton peak broadening and shift were extracted and plotted as the red and blue balls in Fig. 3d, respectively.
In 2D TMDCs, the variation of exciton peak can be attributed to temperature-dependent lattice dilatation and exciton-phonon interaction. As shown by the blue dotted line in Fig. 3d, the exciton peak shift was well fitted by the well-known Varshni equation,\(E_{g} (T) = E_{g} (0) - {{\alpha T^{2} } \mathord{\left/ {\vphantom {{\alpha T^{2} } {(T + \beta )}}} \right. \kern-\nulldelimiterspace} {(T + \beta )}}\), which describes the temperature dependence of the energy gap for various semiconductors including 2D TMDCs. [54,55,56,57,58]. Here, α is the scaling factor of the mean occupancy of an average phonon, Eg(0) is the exciton bandgap energy at 0 K, and β is the average phonon temperature. The global optimal parameters of fitting curves are Eg(0) = 1.724 ± 0.001 eV, α = (4.73 ± 0.27) × 10–4 eV/K and β = 296 ± 40 K. The broadening excitons line-width results from the interaction of excitons with the longitudinal-acoustical (LA) and longitudinal-optical (LO) phonon modes of lattice for semiconductor without considerable impurity doping and defects. Accordingly, the temperature-dependent line-width of excitons can be written as Γ(T) = Γ0 + γLA T + γLO NLO(T) [59, 60], where the second term describes the contribution of the interaction between excitons and LA phonons, the third term describes the interaction between excitons and LO phonons, NLO(T) represents the LO phonons occupation with Bose–Einstein distribution, and the constant term arises from the scattering due to intrinsic imperfections. As depicted by the red dotted line in Fig. 3d, temperature-dependent line-width can be strictly described by Γ(T), where Γ0 = 24.52 ± 0.76 meV, γLA = 30 ± 4.7 μeV/K, and γLO = 2.72 ± 0.92 eV. It can be concluded that the linear broaden line-width mainly stems from LA phonons, while the superlinear broaden line-width is attributed to LO phonons, and the temperature-independent offset Γ0 can be ascribed to unavoidable fluctuations of samples.
In addition, the measured PL spectra gradually turn to asymmetric line shape with a sharp high-energy cutoff and an exponential low-energy tail when the temperature drops from 400 to 80 K, as shown in Fig. 3e. To quantify the asymmetric line shape, we define degrees of asymmetry (DOA) as |IL-IH|/|IL + IH|, where IL and IH are the integrated intensity for the photon energy lower and higher than exciton peak. As illustrated in Fig. 3f, DOA increases rapidly from near 0% at 400 K to 25% at 80 K with an exponential trend (blue dotted line). As is well known, exciton localization and phonon sidebands are the main origins for the asymmetric line shape of PL spectra [39, 55, 61]. The temperature-dependent asymmetric line shape can help us to determine the actual origin of asymmetric line shape. For the asymmetric line shape induced by phonon sidebands, the higher the temperature, the larger is the phonon population, the more pronounced are the sidebands. Meanwhile, the asymmetric line shape presents as an exponential high-energy tail and a sharp low energy cutoff [55, 61]. The phenomena mentioned above are remarkably reversed with our experimental results. Therefore, phonon sidebands can be reasonably excluded. Additionally, the excitation intensity dependence of the PL integrated intensity of the free exciton band and the low-energy band at 80 K were discussed. The contribution of the free exciton band increases gradually with the increase of excitation intensity, and the contribution of the low-energy band is contrary (see Additional file 1: S5 for more details). It can be further demonstrated that the asymmetric spectral shape mainly originates from exciton localization. Focusing on exciton localization, the exponential low-energy tail indicates the emergence of new excitonic states below existing exciton energy. The exponential low-energy tail reflects the density of new excitonic states, whereas a sharp high energy cutoff corresponds to mobility edge. Owing to the low electron-doped concentration, new excitonic states mainly stem from excitons localized by disorder potentials arising from unavoidable fluctuations of samples. It is consistent with decreased effective diffusion coefficients at cryogenic temperature. Moreover, Fig. 3e shows a PL emission with photon energy lower than that of the free exciton emission band at cryogenic temperature, which is the convolution of the intrinsic distribution of exciton energy and response function (RF, including the physical spectral broadening and instruments response) [62,63,64]. In order to extract the intrinsic exciton energy spectrum, deconvolution with RF (equivalent to the free exciton band) is essential, as shown in Fig. 3f. The phenomena depicted in Fig. 3 can be repeated for the excitation photon energy of 3.04 eV (see Additional file 1: S4 for more details).
2.4 Physical scenario of temperature-dependent exciton diffusion dynamics
As aforementioned, the decreased diffusion coefficients and asymmetric PL spectra of excitons at cryogenic temperature were attributed to the localized excitons in disorder potentials induced by surface fluctuations. The Raman spectra of excitons have been demonstrated as an effective technique to map the subtle fluctuations of samples. The mini-strain arising from surface fluctuations has minimal effect on Raman spectra at room temperature (Fig. 1d, e). However, owing to reduced thermal fluctuations, the intensity and peak of Raman spectra at cryogenic temperature can be significantly modulated by the mini-strain distribution on the sample, as shown in Fig. 4a and b. It has been proved that the in-plane mode is more sensitive to strain than the out-plane mode [18, 65, 66]. Therefore, the red-shift magnitudes of in-plane mode in different positions (Fig. 4b) enable us to estimate the mini-strain distribution of WSe2 monolayer. The formula ɛ = Δω/χ was generally adopted to calculate the strain strength corresponding to Raman shifts Δω, where χ is the shift rates of Raman vibrational modes [66]. The peak positions of in-plane mode induced by surface fluctuations were obtained as 249.89 ± 0.19 cm−1 through Lorentz fitting and statistical analysis (Additional file 1: Fig. S6a), where 249.89 cm−1 and 0.19 cm−1 are mean and standard deviation, respectively. Note that the Raman spectra at room temperature and 120 K were performed with the same instrument and setup. For the Raman mapping at room temperature, the Raman peak frequencies of the in-plane mode are almost entirely located at 249.02 cm−1 (Fig. 1f) for different positions of monolayer WSe2. It indicates that the standard deviation of 0.19 cm−1 (Fig. 4b) is derived from disorder potentials rather than measurement error. The shift rates of in-plane mode under strain were calculated as 1.12 cm−1 per % strain according to previous reports (Additional file 1: Fig. S6b) [66, 67]. Therefore, the applied strain from surface fluctuations is about 0.17%. Here the mini-strain is measured only at 120 K. The peak shift of Raman spectra induced by mini-strain at 120 K is only 0.19 cm−1. In addition, the mini-strain arising from surface fluctuations has little effect on Raman spectra at room temperature. Therefore, it is challenging to map the temperature dependence of mini-strain. Considering the mini-strain is determined by the relative changes in spatial position, it can be speculated that the uniform temperature distribution has a much smaller influence on strain than the defects and impurities [68]. Consequently, we temporarily ignore the influence of temperature on mini-strain.
To assess the modulation of strain on exciton energy, strain engineered band structures of WSe2 monolayer were investigated by first-principle calculations. Band gaps with the highest valence bands (VB) and lowest conduction bands (CB) and the trends of K-K band gap of WSe2 monolayer under various biaxial strains, both compressive and tensile, are shown in Fig. 4c and d, respectively. The strong spin–orbit coupling (SOC) introduces spin splitting of hundreds meV in the VB and of a few to tens of meV in the CB at the K valley. The spin splitting results in an energy separation between bright excitons and dark excitons, and the dark excitons in WSe2 materials are predicted to be at lower energies than the bright ones. The biaxial strains have a much greater impact on the lowest CBs than the highest VBs. The direct band gap without strain is about 1.37 eV, which is generally underestimated for first-principle calculation. Under compression, the direct band gap of K-K increases by about 100 meV at − 1% strain, while the indirect band gap of K-Q decreases. This results in a transition from direct to indirect band gap semiconductor. In contrast, under tensile the band gap decreases. The extracted K-K bandgaps in Fig. 4d show that the band gap of WSe2 monolayer decreases/increases linearly with the slope of − 105.2 ± 0.7 meV/% when tensile/compression is applied. In consequence, the modulation depth of disorder potentials arising from surface fluctuations is about 17.8 meV.
Considering phonon scattering and disorder potentials, the physical scenario of exciton nonequilibrium dynamics was established to explain the temperature-dependent exciton diffusion and PL spectra. As depicted in Fig. 4e, for the temperature higher than 280 K, the scale of thermal fluctuation can be evaluated as kBT > 26 meV, which is much larger than disorder potentials on the scale of 10 meV. Thus the phonon energy and density of states are large enough to facilitate excitons escape from disorder potentials. It means that phonons scattering dominates exciton diffusion rather than disorder potentials. Meanwhile, the phonons of high energy and density colliding with excitons can lead to exciton quenching effect and thus decreased PL efficiency. As the temperature is lowered, phonon energy and density of states decrease so that phonons effects are reduced. The disorder potentials dominate exciton dynamics and result in exciton localization, as shown in Fig. 4f. The localized exciton energy is determined by the modulation depth of disorder potential, thus the distribution of exciton energy has a bandwidth of 17 meV, which is proved by the exponential low-energy tail with a bandwidth of 14.8 meV after deconvolution with RF (Fig. 3f).
It can be concluded that the competition between disorder-induced localization and phonons scattering creates a dilemma for extending exciton diffusion length. The optimized strategy is refrigerating the semiconductor to mitigate exciton-phonon scattering and suppressing the disorder to avoid exciton localization. The successful encapsulation with hBN can effectively suppress the disorder including local fluctuations of inherent material properties (such as chemical and structural composition, doping or strain) and external dielectric environment. Therefore, exciton diffusion experiments on hBN encapsulated 2D semiconductor were performed [44, 52, 69, 70], and the crucial role of disorder in exciton diffusion was verified. Naturally, we can expect a greater optimal diffusion coefficient in the hBN encapsulated 2D semiconductor at lower temperatures that exciton-phonon scattering is mitigated simultaneously.
2.5 Exciton ultrafast dynamics dominated by phonon quenching and exciton localization
The femtosecond pump–probe technique is a powerful tool to clarify the modulation of phonon quenching and exciton localization on the occupancy of exciton states within a femtosecond-picosecond timescale. In our ultrafast measurements, photon energy and energy density of pump pulse are 3.04 eV and 10.0 μJ/cm2, respectively. Considering the blue shift of exciton peak with decreasing temperature (Fig. 3c and d), photon energy and energy density of probe pulse were chosen as 1.65 eV and 1.0 μJ/cm2 for 220 K–310 K, while chosen as 1.74 eV and 0.2 μJ/cm2 for 80 K–160 K, respectively.
Figure 5a depicts the differential reflection signals ΔR/R0 for different temperatures, which were normalized by globe maximum. The signals of 80 K–160 K were multiplied by 2 for clarity. Note that signals of 220 K–310 K reach their maximum at 260 K, when the absorption peak approaches to probe photon energy of 1.74 eV. When temperature drops to the range of 80 K–160 K, the ΔR/R0 signals are much smaller than 220 K–310 K arising from two reasons: the relatively lower energy density of probe pulses for 80 K–160 K and the lowest dark state that can’t couple with photons efficiently.
Focusing on the relaxation time of exciton, the ultrafast signals in Fig. 5a were normalized by the maximum of each temperature and presented in Fig. 5b. To quantitatively study exciton ultrafast dynamics modulated by phonon quenching and exciton localization, six representative ultrafast signals were extracted and sketched in Fig. 5c and d. In Fig. 5c, the ultrafast signals of 280 K, 295 K and 310 K rapidly decay to ~20%, which is consistent with previous measurements at room temperature [23]. However, the ultrafast signals of 260 K in Fig. 5d just drop down to ~50% in the first 2 ps, which means there is a relaxation channel weaken or even disappear, considering the strength of ΔR/R0 is proportional to the pumped exciton density [71]. Moreover, the ultrafast signal of 240 K continues to decline to ~10% after the first 8 ps, as shown in the middle of Fig. 5d. It implies that a new exciton relaxation channel appears at 8 ps. When temperature drops to 100 K, ultrafast signal (bottom of Fig. 5d) rapidly decays to ~20% again, similar to Fig. 5c.
Consistent with diffusion dynamics and PL spectra, phonon quenching and exciton localization can provide a reasonable interpretation for temperature-dependent relaxation dynamics of excitons. Generally, the high density excitons pumped by femtosecond pulses (the rising edge of ΔR/R0) undergo two decay processes before 10 ps: biexciton-biexciton annihilation (~ N4), exciton-exciton annihilation (~ N2) [72]. Integrating phonon quenching and exciton localization into the common rate equation, the modified rate equation that describes the ultrafast interaction dynamics among excitons, phonons and localized excitons can be written as following:
$$\frac{\partial N}{{\partial t}} = - \alpha N^{4} - \beta N^{2} - \sigma_{p} (T)N - \sigma_{d} (T,t > t_{s} )N$$
(2)
where N is exciton density, α and β are biexciton–biexciton annihilation rate and exciton-exciton annihilation rate, σp(T) is exciton decay rate of multi-phonons quenching, and σd(T, t > ts) is transition rate from free exciton to localized exciton owing to disorder potentials, which is related to temperature and delay time, and ts refers to the starting time of exciton localization. It should be noted that diffusion and radiative recombination of exciton can be safely disregarded on this time scale [21, 23, 26, 73]. Seemingly, the third and fourth terms describing the multi-phonons quenching and exciton localization cannot be distinguished. However, the time dominating exciton decay for phonon quenching and exciton localization is temperature dependent, so they were separated into temperature dependent two terms in Eq. (2). The differential Eq. (2) was numerically solved using the Runge–Kutta method, and the ultrafast signals at different temperatures were faithfully reproduced by the modified rate equation, as depicted by green dotted curves in Fig. 5c and d. The fitted parameters were summarized in Additional file 1: Table S1.
The physical scenario of temperature-dependent exciton relaxation dynamics was schematically summarized in Fig. 5e. For the temperatures of 280 K, 295 K and 310 K, the exciton relaxation is dominated by biexciton–biexciton annihilation, exciton-exciton annihilation and phonon quenching. The phonon quenching substantially weakens at 260 K, while exciton localization appears prominently at 8 ps for 240 K, which is about 16 ps for 260 K. Therefore, it can be expected that the onset of exciton localization brings forward as decreasing temperature until keeping up with the multi-excitons annihilation and eventually results in the rapid decay of ultrafast signal during 0–4 ps at 100 K.
