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Localized state effect and exciton dynamics for monolayer WS2

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Abstract

The two-dimensional transition metal dichalcogenides (TMDCs) have been considered as promising candidates for developing a new generation of optoelectronic devices. Accordingly, investigations of exciton dynamics are of great importance for understanding the physics and the performance of devices based on TMDCs. Herein, after exposure to ambient environment for six months, monolayer tungsten disulfide (WS2) shows formation of localized states. Photoluminescence (PL) and time-resolved PL (TRPL) spectra demonstrate that these localized states have significant impacts on the exciton dynamics, including energy states filling, thermal activation and redistribution, and the decay behavior of excitons. These observations not only enrich the understanding for localized states and correlated exciton dynamics of aged monolayer WS2, but also reveal a possible approach to modulate the optical properties of TMDCs via the aging process.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

As a fascinating platform for basic research and atomically thin device applications, layered two-dimensional transition metal dichalcogenides (TMDCs) have been considerably investigated due to their unique electronic structure and featured optical properties [18]. Notably, monolayer TMDCs present many novel characteristics in comparison with their multilayer counterparts, such as high quantum yield, direct bandgap transition, valley polarization and coherence effects [912]. These unique properties make monolayer TMDCs building blocks for fabricating optoelectronic devices like efficient light emitting diodes [13,14], high-sensitive transistors [15,16], and valleytronics [17,18]. In monolayer TMDCs, defects caused by crystalline structure and imperfect interface such as vacancies, adatoms, grain boundaries, and substitutional impurities play an important role in determining the performance of TMDCs, because these defects can produce localized states to impact the excitonic properties [1922]. Therefore, exploration of the localized states and related exciton dynamics is indispensable for the development of TMDCs based devices.

Among monolayer TMDCs, the monolayer WS2 is attracting growing interest due to the large exciton binding energy and spin-orbit coupling. The energy difference between A exciton and B exciton is up to about 420 meV so that the monolayer WS2 is one ideal candidate to investigate exciton properties related to localized states in two-dimensional materials. [2325] Recently, Toshiaki et al. found the surface impurities on monolayer WS2 can generated highly localized states for excitons [26]. Tan et al. observed that the boundaries of WS2 became bound states to trap free excitons, which is believed to be a possible candidate for the single photon source [27]. In addition, WS2 materials are likely unstable after being exposed in ambient condition due to aging effect and the consequent generation of localized states. Although some reports have investigated the structure and chemistry evolution for TMDCs materials due to aging, the underlying mechanism and the influence on the optical response, especially the influence on exciton dynamics is still unclear for WS2. [2830]

In this research, after about six months being exposed to ambient air, monolayer WS2 clearly exhibit aging effect. There are sulfur atoms to be substituted by the oxygens and some organic pollutants are also absorbed on sample surface, which accelerate the formation of defects resulting in localized states. Photoluminescence (PL), excitation-dependent as well as temperature-dependent PL, and time-resolved PL (TRPL) have been meticulously measured to reveal the exciton dynamics, including energy states filling, thermal activation and redistribution, and decay behavior of localized state excitons in the aged monolayer WS2.

2. Experiments and methods

The monolayer WS2 samples were grown by the chemical vapor deposition (CVD) method [31]. A quartz boat loaded with pure WS2 powders was placed at the center of a heating zone and a piece of Si/SiO2 (300 nm) wafer (1 cm × 3 cm) as the substrate was loaded on the silica boat at the downstream. First, high purity argon (Ar) gas (60 SCCM) was introduced to clean the system for 20 minutes. Then the temperature of the center of the heating zone was set at 1050 °C and the substrate temperature was linearly increased from room temperature to 530°C in 35 minutes. After that, a gas flow of 60 SCCM from left to right was applied to carry the chemical vapor source to the substrate, enabling the growth of WS2 on the substrate. The growth time for WS2 on the substrate was controlled to be 5 minutes. Finally, the system was cooled down to room temperature and large area WS2 samples were obtained.

In this research, the as-grown monolayer WS2 sample and one aged monolayer WS2 sample (stored for about six months under ambient atmosphere in a container with no desiccant to fully age the monolayer WS2) are comparatively studied. At first, ultralow-frequency Raman technique was used to determine the layer number to be monolayer for both samples. Then Room temperature Raman measurements were performed in a backscattering geometry using a LabRam HR Evolution system with a 532 nm laser as the excitation source. In addition, the X-ray Photoelectron Spectroscopy (XPS) was measured by Thermo Scientific ESCALAB 250Xi equipped with a monochromatic Al Kα source gun. All the XPS results were fitted by Avantage software and 284.8 eV adventitious C 1s peak was used to calibrate other chemical state peaks in XPS spectra. For PL measurements, the WS2 samples were loaded into an ARS DE204 closed-cycle cryostat with temperature variable from 7 K to 300 K. The samples were excited by a continuous-wave 532 nm laser with the spot diameter measured to be about 5 µm through a 50× long working distance objective lens (NA = 0.42), then the PL signal was sent into the input slit of one Acton-2750 spectrometer and detected by a liquid-nitrogen-cooled charge-coupled detector (CCD) array. One optical microscope is integrated with the cryostat and the PL setup in order to in situ monitor the sample surface during luminescence measurements. In TRPL experiment, the samples were excited by a NKT EXW-12 Supercontinuum laser (output wavelength 532 nm, pulse width ∼ 13 ps, frequency 48 MHz), and the decayed signal was measured by a PicoHarp-300 time-correlated-single-photon-counting (TCSPC) system.

3. Results and discussion

The microscope images under bright-filed of the as-grown WS2 monolayer sample and the aged sample are shown in Figs. 1(a) and 1(b). Both samples exhibit triangular shape with continuous and uniform surface apart from some multilayer regions in the aged sample. In addition, some conspicuous small particles are attached on the surface of the aged sample while none on the as-grown sample. Probably when the WS2 sample is transferred and stored, organic pollutants can be absorbed on the aged sample surface to form charge traps [32].

 figure: Fig. 1.

Fig. 1. The microscope images for (a) the as-grown and (b) the aged monolayer WS2. (c) and (d) show Raman spectra measured at room temperature by using the 532 nm laser. (e) and (f) are XPS spectra (calibrated according to the adventitious carbon C 1s peak) of as-grown and aged monolayer WS2, with Gaussian fitting for each peak conducted by Avantage.

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In order to further investigate the variation of monolayer WS2 due to aging process, Raman spectroscopy is a powerful tool. Defect related modes can be observed in Raman spectrum from defective sample regions [3335]. Raman spectra measured at room temperature for the fresh and six-months aged WS2 monolayer samples from similar optical contrast areas have been presented in Figs. 1(c) and 1(d). We utilized multi-Lorentzian functions to fit different Raman modes. There is no prominent frequency difference or new Raman modes observed in overall spectra while multi-positions are measured for each sample. The two representative peaks located at about 354 cm−1 and 418 cm−1, are assigned to $\textrm{E}_{2\textrm{g}}^1(\Gamma)$ and ${\textrm{A}_{1\textrm{g}}}(\Gamma)$ vibration modes, respectively. The $\textrm{E}_{2\textrm{g}}^1(\Gamma)$ is related to in-plane vibration of tungsten and sulfur atoms while the ${\textrm{A}_{1\textrm{g}}}(\Gamma)$ is associated with out- of- plane sulfur atoms. The ∼64 cm−1 frequency difference between these two Raman peaks further illustrate that both WS2 samples are exactly monolayer. [36,37]

To compare the chemical states for monolayer WS2 sample before and after aging process, room temperature XPS has been introduced in Figs. 1(e) and 1(f). For the as-grown WS2 sample, the ratio between tungsten and sulfur atom (W:S) is ∼1:2. There is only one chemical state doublet in the W 4f core level spectra (corresponding to W 4f7/2 at ∼33.3 eV and W 4f5/2 at ∼35.5 eV), while the extra peak in higher binding energy is attributed to W 5p3/2. However, for the aged sample the W:S ratio decreases to ∼1:1.71 and another chemical state doublet arises in higher binding energy (∼3.4 eV above core level W 4f spectra), indicating the loss of sulfur atoms and the existence of higher oxidation state for tungsten atoms. By fitting the XPS spectra into several peaks, it is found that the three peaks with lower binding energy in red color yield to the W-S bond while the new peaks originate from W-O bond. Furthermore, the S 2p peaks were shown in XPS in the insets of Figs. 1(e) and 1(f), illustrating that no SOx chemical states were observed from the spectra for both samples. In consideration of the above observations, one possible hypothesis is proposed. Because monolayer WS2 is composed of three atomic layers with the tungsten atom layer sandwiched between two sulfur atom layers, monolayer WS2 is terminated with a layer of sulfur atoms on the top. The sulfur- tungsten bond could be partly broken due to water vapor etching, resulting the oxygen atoms to substitute the sulfur atoms. Similarly, some organic molecules can also be absorbed and condensed on the surface during the aging process. Defects and localized states are expected to be generated with sulfur- tungsten bond broken and the organic molecules absorption.

The formation of localized states makes the aged monolayer WS2 differentiate from ideal crystals, which can directly be reflected in the PL behaviors. Figures 2(a) and 2(b) present the room temperature PL spectra excited by the 532 nm laser under an excitation intensity of 2.3 W/cm2, with the PL peak energy and the linewidth (full width at half maximum, FWHM) listed in the plots. The two samples show very similar PL profile with a single peak located at 1.964 eV, which yields the A exciton resonance for monolayer WS2 and excitons transition at K point in the Brillouin zone without phonon involved [38]. In contrast, cryogenic PL spectra usually reveal the intrinsic features that cannot be exhibited at room temperature. We measured the PL spectra for both samples under the same excitation condition at 7 K. As shown in Fig. 2(c), the as-grown monolayer WS2 emits a single asymmetrical peak at 2.039 eV (marked as XF to represent the free excitons) due to the excitons transit at K point in the Brillouin zone. The PL also shows a clear low energy tail (marked as XL to represent excitons bound at the localized states). With the temperature decreasing to room temperature in the CVD growth, the strain results from different thermal expansion coefficient between the WS2 and substrate made the WS2 lattice disordered, which form a band tail in the density of states [39]. Photon-excited carriers can be trapped in these states at low temperature and thereafter generate emission to form the low energy tail in PL spectrum.

 figure: Fig. 2.

Fig. 2. PL spectra measured at room temperature (295K) and at cryogenic (7K). (a) and (b) are the room temperature PL spectra for the as-grown and the six-months aged monolayer WS2. (c) and (d) are PL spectra at 7 K for both samples with the peak marked as XL to represent excitons bound at the localized states while XF for the free excitons.

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Very different from the as-grown sample, in Fig. 2(d) two discrete peaks have been observed in PL spectrum for the aged monolayer WS2, marked as XL and XF respectively. The narrow, weak XF peak is still observed at high energy of 2.039 eV, but its intensity decreases to one-sixth of that in Fig. 2(c) for the as-grown sample. The broad, strong XL peak at low energy of 1.969 eV becomes dominant in the emission. The domination of XL peak in the cryogenic PL spectrum for the aged monolayer WS2 indicates that the aging process can aggravate the defect formation. Thus, more photon-generated excitons are trapped into the localized states. In addition, the PL spectra at both room temperature and low temperature indicate that the aged sample has its overall integrated PL intensity decrease from that of the as-grown sample. If we suppose that the laser photon absorption and the exciton generation coefficients are the same for two samples, the decrease of PL intensity hints that the aging process can also aggravate the generation of non-radiation trap centers due to defect formation.

Excitation intensity dependent PL have been investigated at 7 K for both samples. By carefully varying the laser intensity from 0.1 W/cm2 to 78 W/cm2, we were trying to avoid the influence from laser heating effect. The results are summarized in Fig. 3. For convenience, all the spectra are normalized and shifted up in Fig. 3(a) for the aged sample and in Fig. 3(b) for the as-grown sample. The integrated PL intensity of full spectrum is extracted and then plotted as a function of the excitation intensity in Fig. 3(c). It can be seen that the full spectrum integrated PL intensities increase nearly linearly for both samples as the excitation intensity increases from 0.1 W/cm2 to 78 W/cm2, following very well with the power law [40]:

$${\textrm{I}_{\textrm{PL}}} \propto {\textrm{P}^\mathrm{\alpha}}$$
where ${\textrm{I}_{\textrm{PL}}}$ represents the integrated PL intensity, P is the laser excitation intensity. The exponent, α, is related to different exciton recombination mechanisms. The fitting value of α is 1.02 for the as-grown sample, indicating the emission originates from the free exciton recombination, while it is 0.89 for the aged sample so that the aged sample may have localized states effect. We also observe that the as-grown monolayer WS2 sample shows no variation on the peak energy and linewidth with the laser intensity increasing from 0.1 W/cm2 to 78 W/cm2.

 figure: Fig. 3.

Fig. 3. (a) and (b) are the PL spectra measured at 7 K with the excitation intensity increasing from 0.1 W/cm2 to 78 W/cm2 for the aged sample and the as-grown sample, all the spectra are normalized based on the maximum peak intensity and shifted up. (c) is the integrated PL intensity of full spectrum as a function of laser excitation intensity for both samples. (d), (e) and (f) are the integrated PL intensity, the peak energy, FWHM of XF peak and XL peak as a function of laser excitation intensity, respectively.

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Additionally, in order to further study the two peak behavior for the aged sample, the integrated PL intensity, the peak energy, and linewidth are extracted for XF and XL and then plotted as a function of the excitation intensity in Figs. 3(d) – 3(f), respectively. The fitting value of α is 0.8 for XL and 1.04 for XF in Fig. 3(d), reiterating the localized exciton feature for XL with respect to the free exciton recombination for XF. As shown in Figs. 3(e) and 3(f), the XL peak experienced a ∼23 meV blueshift with the linewidth broadening from 63.2 meV to 71.3 meV. But the XF peak has almost no change for either the peak energy or FWHM. This behavior can be attributed to the localized states filling process. At low excitation intensity, photon-generated excitons bound by Coulomb force preferentially occupy the localized states with lower energy, and then fill those shallow energy states with higher local potential as further increasing the excitation intensity. Therefore, we observe the blue-shift of peak energy and linewidth broadening for XL with increasing the excitation intensity for nearly three orders of magnitude.

Figures 4(a) and 4(b) show the temperature-dependent PL from 7 K to 300 K for the aged and the as-grown WS2 sample, respectively. For both samples the XF peak exhibits competition with XL. The XF peak becomes relatively stronger than the XL peak with increasing the temperature. In particular for the aged WS2 sample, the XL emission initially dominates at the low temperature of 7 K and then thermally quenches to unnoticeable, while the XF peak grows to become dominant with increasing the temperature to above 100 K. This intensity transition is clearly shown by variation of the integrated PL intensity percentage in the full spectral emission for each peak in Fig. 4(c).

 figure: Fig. 4.

Fig. 4. (a) and (b) are the PL spectra measured from 7 K to 300 K with the laser excitation intensity at 7 W/cm2 for the aged monolayer WS2 and the as-grown monolayer WS2, respectively. (c) Percentage of integrated PL intensity of XL and XF in the whole spectrum as a function of temperature for the aged sample. (d) Peak energy of XL and XF as a function of temperature for the aged sample. (e) Peak energy of XF and the shift of XF peak in the inset as a function of temperature for both samples. (f) Peak position of XF as a function of temperature from 7 K to 300 K for the aged sample, the blue and purple lines are the fitting results by the Donnell and Manoogian-Wooley equation, respectively. The inset zoom the plot in the range from 7 K to 100 K.

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The peak energy of XL and XF are extracted in Fig. 4(d) for the aged WS2. Interestingly, XL exhibits a redshift of ∼5 meV when the temperature increases from 7 K to 25 K, and then monotonically blueshifts with further increasing the temperature. However, in the same temperature range the XF peak monotonically redshifts, exhibiting a special ‘S’ shape for the peak energy. Such abnormal behaviors are explained by thermally activation and redistribution of the excitons. Due to low phonon energy in the temperature range of 7 K ∼ 40 K and the large energy separation between XL and XF, thermally activation and redistribution happen only among the same kind of excitons, but there is no exciton exchange between XF and XL. So we observe that the PL intensities have almost no change for XL and XF in Fig. 4(c), but the XF peak energy has a slowly redshift and the XL peak energy even shows a ‘V” shape in Fig. 4(d) with increasing the temperature from 7 K to 40 K. In this temperature range the excitons bound at shallow localized states can escape and be captured again by the deeper ones as the temperature starts to increase from 7 K, resulting a loss of the high energy side of XL emission and a minor redshift of XL peak. However, as the temperature further increases from 40 K, excitons in localized states can jump out to become free excitons. In other words, thermally activation and redistribution happen between the two kinds of excitons, resulting XL and XF show variations on both intensity and peak energy.

The peak energy of XF is extracted in Fig. 4(e) as a function of temperature for both samples. It can be seen that the as-grown sample has the peak energy of XF smoothly redshifts with increasing the temperature from 7 K, but the aged sample has the XF peak exhibiting a special ‘S’ shape due to activation and redistribution of excitons. We select the aged sample to fit its experimental data of XF peak energy by Donnell equation [41,42]

$${\textrm{E}_\textrm{g}}\left( \textrm{T} \right) = {\textrm{E}_{\textrm{g}}}\left( 0 \right) - \textrm{S}< {\hbar }\mathrm{\omega}> \left[ {\textrm{coth}\frac{{< {\hbar }\mathrm{\omega}> }}{{2{\textrm{k}_\textrm{B}}\textrm{T}}} - 1} \right]$$
in which ${\textrm{E}_\textrm{g}}(0 )$ is the exciton energy at 0 K, $\textrm{S}$ is the exciton-phonon coupling constant, $<\mathrm{\hbar} \mathrm{\omega}>$ and ${\textrm{k}_\textrm{B}}$ are average phonon energy and Boltzmann constant. The fitted curve in 4(f) gives that the average photon energy equals to 12.87 ± 0.77 meV for the direct exciton transition, whereas $\textrm{S}$ is around 1.8. Because the lattice dilatation effect is not considered in the Donnell equation, a discrepancy exists between the fitting curve and the experimental results below 50 K. Then we used the Manoogian-Wooley equation to fit the experimental results again. The Manoogian-Wooley equation can be described as [43,44]
$${\textrm{E}_\textrm{g}}(\textrm{T} )= {\textrm{E}_{\textrm{g}}}(0 )+ \textrm{U}{\textrm{T}^\textrm{S}} + V\mathrm{\theta} \left[ {\textrm{coth}\left( {\frac{\mathrm{\theta} }{{2\textrm{T}}}} \right) - 1} \right]$$
where the first term represents the peak energy at 0 K, the second and third term are lattice dilatation and electron-phonon interaction. Moreover, $\theta $ is a coefficient related to the Debye temperature. According to the fitting results, ${\textrm{E}_{\textrm{g}}}(0 )$=2.04 eV, U=−2.37×10−5 eV/K, V= −2.1×10−4 eV/K, $\theta $=153 K and the average photon energy S is 1.42 that is consistent with previous reports. [27,39] By the purple line in Fig. 4(f) the Manoogian-Wooley equation fitting curve matches better with the actual experimental results in comparison to that fitted by Donnell equation, which indicates the lattice dilatation is an essential factor for the peak shifts observed in the temperature dependent PL measurements. However, there is still difference between the fitting curve and the experimental data points below 50 K. Therefore, the activation and redistribution of excitons are the main mechanisms for the abnormal XL and XF peak shifts in the low temperature range.

To further investigate the influence of localized states on the relaxation and recombination of photon-generated excitons, TRPL measurements have been conducted for XL peak from 1.937 eV to 2 eV with a step of ∼15 meV (5 nm). As shown in Fig. 5(a), the TRPL decay curves consist of two components, indicating that both neutral excitons and charged excitons (trions) likely exist in our experiment although the trion emission is not directly observed in the spectra. The initial fast decay component is driven by the recombination of neutral excitons whereas the slow decay component is ascribed to the trions emission, as the excess carriers within trions need to spend a longer time to find a unoccupied state after the radiative recombination of trions [3]. Similar nonlinear decays have also been recorded in other mechanically exfoliated and chemical vapor deposited TMDCs [39,45]. We use a bi-exponential decay function to fit the experimental results to obtain the lifetimes for neutral excitons and trions [46]

$$\textrm{I}(\textrm{t} )= {\textrm{A}_1}\textrm{exp} [{ - ({\textrm{t} - {t_0}} )} ]/{\mathrm{\tau}_1} + {\textrm{A}_2}\textrm{exp} [{ - ({\textrm{t} - {t_0}} )} ]/{\mathrm{\tau}_2}$$
where A1, A2 are the amplitude coefficients representing magnitudes of the two decay processes, t0 is the initial time, τ1 and τ2 are the time constants for the slow decay and fast decay, respectively. As shown in Fig. 5(b), the lifetime of neutral excitons decreases from 0.36 ns at 1.937 eV to 0.21 ns at 2 eV, while the lifetime of trions decreases from 1.7 ns at 1.937 eV to 0.7 ns at 2 eV. In addition, the lifetime of free excitons for XF is measured to be very short and we cannot deliver reliable results due to the equipment limitation.

These PL results confirm that the emission from excitons rely on not only the recombination but also the relaxation process in monolayer WS2. Lattice defects can produce localized states (the shallow ones and deep ones) with potential fluctuations. At low temperature, more photon-generated excitons can relax into and be trapped inside localized states to generate dominant emission signal due to localized exciton recombination. Such localized states result to long lifetime for localized excitons. Meanwhile, the relaxation time for excitons to the shallow localized states with higher potential is shorter than those to deep localized states with lower potential. Therefore, the lifetime for the localized excitons of XL monotonically decreases form low energy side to high energy side.

 figure: Fig. 5.

Fig. 5. TRPL measurements. (a) PL decay curves of XL at different emission energy from 1.937 eV to 2 eV with a step of ∼15 meV. (b) PL spectrum and the fitting lifetime of neutral and charged excitons at 7 K.

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4. Conclusions

We have carefully investigated the localized state effect and exciton dynamics via luminescence measurements for monolayer WS2 sample before and after six-months aging process. First, cryogenic PL spectra clearly display discrete double peaks for the aged monolayer WS2 sample, demonstrating that the aging process can aggravate the formation of localized states to trap more excitons to give dominant emission. Excitation intensity dependent PL reveal a different state filling behavior due to these localized states. In addition, the temperature dependent PL indicate that there are different mechanisms for thermal activation and redistribution of excitons in the aged sample. Furthermore, TRPL spectra shows much longer lifetime for localized excitons in comparison with free excitons. These observations confirm that the localized states resulting from the aging effect play a very important role for exciton dynamics, including states filling, thermal activation and redistribution, thermal quenching, and the decay behavior of excitons.

Funding

Advanced Talents Incubation Program of the Hebei University (8012605); Natural Science Foundation of Hunan Province (2018JJ1005); Natural Science Foundation of Hebei Province (A2020201028, F2019201446); National Natural Science Foundation of China (51525202, 61574054, 61635001, 61774053).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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Figures (5)

Fig. 1.
Fig. 1. The microscope images for (a) the as-grown and (b) the aged monolayer WS2. (c) and (d) show Raman spectra measured at room temperature by using the 532 nm laser. (e) and (f) are XPS spectra (calibrated according to the adventitious carbon C 1s peak) of as-grown and aged monolayer WS2, with Gaussian fitting for each peak conducted by Avantage.
Fig. 2.
Fig. 2. PL spectra measured at room temperature (295K) and at cryogenic (7K). (a) and (b) are the room temperature PL spectra for the as-grown and the six-months aged monolayer WS2. (c) and (d) are PL spectra at 7 K for both samples with the peak marked as XL to represent excitons bound at the localized states while XF for the free excitons.
Fig. 3.
Fig. 3. (a) and (b) are the PL spectra measured at 7 K with the excitation intensity increasing from 0.1 W/cm2 to 78 W/cm2 for the aged sample and the as-grown sample, all the spectra are normalized based on the maximum peak intensity and shifted up. (c) is the integrated PL intensity of full spectrum as a function of laser excitation intensity for both samples. (d), (e) and (f) are the integrated PL intensity, the peak energy, FWHM of XF peak and XL peak as a function of laser excitation intensity, respectively.
Fig. 4.
Fig. 4. (a) and (b) are the PL spectra measured from 7 K to 300 K with the laser excitation intensity at 7 W/cm2 for the aged monolayer WS2 and the as-grown monolayer WS2, respectively. (c) Percentage of integrated PL intensity of XL and XF in the whole spectrum as a function of temperature for the aged sample. (d) Peak energy of XL and XF as a function of temperature for the aged sample. (e) Peak energy of XF and the shift of XF peak in the inset as a function of temperature for both samples. (f) Peak position of XF as a function of temperature from 7 K to 300 K for the aged sample, the blue and purple lines are the fitting results by the Donnell and Manoogian-Wooley equation, respectively. The inset zoom the plot in the range from 7 K to 100 K.
Fig. 5.
Fig. 5. TRPL measurements. (a) PL decay curves of XL at different emission energy from 1.937 eV to 2 eV with a step of ∼15 meV. (b) PL spectrum and the fitting lifetime of neutral and charged excitons at 7 K.

Equations (4)

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I PL P α
E g ( T ) = E g ( 0 ) S < ω > [ coth < ω > 2 k B T 1 ]
E g ( T ) = E g ( 0 ) + U T S + V θ [ coth ( θ 2 T ) 1 ]
I ( t ) = A 1 exp [ ( t t 0 ) ] / τ 1 + A 2 exp [ ( t t 0 ) ] / τ 2
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