Abstract
The 1s exciton—the ground state of a bound electronhole pair—is central to understanding the photoresponse of monolayer transition metal dichalcogenides. Above the 1s exciton, recent visible and nearinfrared investigations have revealed that the excited excitons are much richer, exhibiting a series of Rydberglike states. A natural question is then how the internal excitonic transitions are interrelated on photoexcitation. Accessing these intraexcitonic transitions, however, demands a fundamentally different experimental tool capable of probing optical transitions from 1s ‘bright’ to np ‘dark’ states. Here we employ ultrafast midinfrared spectroscopy to explore the 1s intraexcitonic transitions in monolayer MoS_{2}. We observed twofold 1s→3p intraexcitonic transitions within the A and B excitons and 1s→2p transition between the A and B excitons. Our results revealed that it takes about 0.7 ps for the 1s A exciton to reach quasiequilibrium; a characteristic time that is associated with a rapid population transfer from the 1s B exciton, providing rich characteristics of manybody exciton dynamics in twodimensional materials.
Introduction
Photogenerated electronhole (e–h) pairs in solids create bound states, whose elementary quasiparticle state is called 1s exciton in a Wannier–Mott exciton model. Since the optoelectronic response is governed by the lightinduced dynamic behaviour of this elementary ground state, knowledge of the 1s exciton response to the optical stimuli has been a crucial issue in many optoelectronic applications, such as phototransistors^{1,2}, photovoltaics^{3}, lightemitting diodes^{4,5}, van der Waals heterostructurebased optoelectronics^{6,7,8} and valleytronic device applications^{5,9,10,11,12}. In transition metal dichalcogenides (TMDCs), this is particularly the case as the twodimensional (2D) materials approach a monolayer limit, where the reduced dielectric screening results in a strong Coulomb interaction^{13,14,15,16,17,18,19,20,21}, leading to an unusually large 1s exciton binding energy E_{bind}, typically a few hundreds of meV below the electronic bandgap of a few eV (refs 16, 22, 23, 24, 25, 26, 27).
Above the fundamental 1s exciton, theories predicted the presence of densely spaced exciton states in monolayer MoS_{2} with 1s exciton E_{bind} of 0.4–0.54 eV (refs 18, 19, 20, 21, 28, 29, 30, 31), whose (slike) bright and (plike) dark exciton characters were later confirmed by a series of seminal experiments via linear onephoton absorption^{21,22}, twophoton photoluminescence excitation (PLE)^{22,23,24,32} and nonlinear wavemixing spectroscopy^{25,32}, whereby E_{bind} was experimentally measured to be between 0.22 (ref. 26) and 0.44 eV (refs 23, 26); the reported E_{bind}, however, shows somewhat discrepancy depending on the measurement methods and is varied from samples to samples^{23,26,27}. These experimental techniques, although they are appropriate to clarify the optical state of the excitons, may address indirectly the dynamic transient information between the 1s ‘bright’ and the excited np ‘dark’ exciton (n is the principle quantum number); we denoted the exciton states in analogy to the hydrogen series^{21}. By contrast, if one measures the 1s→np transitions, then the data should describe the internal excitonic transients, directly providing the transient optical nature of the fundamental 1s exciton dynamics. This, so called intraexcitonic spectroscopy^{33}, fundamentally differs from bandtoband and other timeresolved spectroscopies^{8,34,35,36}, and the technique can not only explain the transient response of the 1s exciton, but more importantly, may provide experimental manoeuvre in exploiting the photoinduced excitonic responses to the TMDCbased optoelectronic devices. For example, knowledge of the 1s and np exciton energies and their associated dynamics afford the firstorder quantitative information on the exciton dissociation energy, where in an ideal case at least E_{bind}/e (e is the electron charge) of an external or internal potential is required to dissociate the bound e–h pairs. In addition, because intraexcitonic spectroscopy can access the plike dark excitons, one may design a scheme of coupling an infrared (IR) light to the 2D TMDC materials, via belowgap twophoton excitation, for the lightharnessing applications.
Here we explore the 1s intraexcitonic transient dynamics in monolayer MoS_{2} by using timeresolved midIR spectroscopy. Inspired by a theoretical GW–Bethe–Salpeter result^{19}, where the fundamental 1s→2p transitions are predicted to be 0.32 and 0.3 eV for the A and B exciton in isolated, suspended monolayer MoS_{2}, we employed an ultrafast midIR spectroscopy (0.23–0.37 eV probe) in conjunction with an ultrafast whitelight continuum spectroscopy (Fig. 1a). The midIR measurements show that there are two 1s→3p transitions for A and B exciton and 1s→2p between 1s A and 2p B exciton. The timedependent IR absorption rapidly subdues over broad probe–photon energies, representing the transient absorption from the 1s to the quasicontinuum states after pump excitation.
Results
Timeresolved intraexcitonic and bandtoband dynamics
The samples used in our experiment were monolayer MoS_{2}, grown by chemical vapour deposition method, and were transferred to a CaF_{2} substrate (see Supplementary Note 1 for the sample characterization). As schematically shown in Fig. 1a, the sample was nonresonantly excited by a 70 fs, 3.1 eV pump pulse, and the corresponding differentialtransmission changes ΔT/T_{0} were measured in a vacuum cryostat (Methods). The 3.1 eV pump excites carriers into the quasicontinuum of the A and B excitons^{37,38} or into the bandnesting Cband near the Γ point^{39,40}. The former generates the unbound e–h plasma above the A and B excitons and the latter case experiences a rapid intervalley scattering into K and K′ valley. Nevertheless, both cases generate carriers in much higher energy compared with the A or B exciton resonance. Figure 1b shows a direct comparison of two representative data measured by midIR probe (0.35 eV) and interband Aexciton probe (1.86 eV) with the same pump fluence F=24.4 μJ cm^{−2} (equivalent to e–h pair density of 7.4 × 10^{12} cm^{−2} given 15% absorption)^{8,41} measured at 77 K. The polarization of pump and probe beam are linear and orthogonal with respect to each other, such that we do not account for the recently discovered valleyexcitonlocked selection rule^{32}. The fact that two ΔT/T_{0} transients exhibit an opposite sign implies the kinetic origin of the photoresponses is indeed different. For the 1.86 eV dynamics, the increased probe transmission is typically attributed to the groundstate bleaching^{35,42,43}, where the increased occupation probability of electrons in conduction band and holes in the valance band leads to the reduced probe absorption, that is, increased ΔT/T_{0}>0. On the other hand, given that the 0.35 eV probe is far below the bandtoband Aexciton energy, one may attribute the decreased ΔT/T_{0}<0 (increased probe absorption) to the transition within the bands, that is, intraband freecarrier absorption. However, considering that the midIR peak signal is only 36.2% of the 1.86 eV one, we can exclude this possibility because the intraband oscillator strength is much smaller than the interband one, usually by an order of magnitude, as revealed by prior works on the quasi2D quantum wells^{44} or recent 2D MoS_{2} (ref. 45); as discussed later in Figs 2, 3, 4, we provide compelling experimental evidences to support our rationale (see also Supplementary Note 2 (refs 46, 47, 48)). The increased probe absorption of the midIR suggests that there exists an occupied state below the electronic gap.
We find that there exists a clear time departure between the two rising dynamics, where the onset of the 0.35 eV probe peak appears ∼0.2 ps later than the 1.86 eV probe (dashed line in Fig. 1b). Immediately after the pump, the 1.86 eV probe rapidly increases, while the 0.35 eV dynamics emerge rather slowly. We observed that this rapid upsurge of the 1.86 eV is not a local spectral behaviour, but being presented in a broad range of highenergy probes (Supplementary Notes 3 and 4), evidencing the quasiinstantaneous groundstate bleaching^{35}. Understanding this highenergy dynamics has been a subject to debate; different investigations have proposed different kinetic origins of the 1s exciton, such as exciton linewidth broadening^{35}, stimulated emission^{42}, dynamic bandgap renormalization^{49} and biexciton formation^{38}. As discussed, more details in Supplementary Note 4, both earlier^{50,51,52} and recent studies^{35,42,53}, have shown that the 3.1 eV photoexcitation into the quasicontinuum of unbound states generates a significant amount of freecarriers. Because the exciton formation occurs after exciton–free carrier scattering, the initial decaying kinetics of midIR is slightly delayed compared with the rising transient of the interband one, explaining the observed timedelay between the two transients of Fig. 1b. Since the midIR probe can resonantly measure the internal exciton dynamics, the measured intraexcitonic transients are expected to provide pure population dynamics of the ground 1s exciton^{33,54}.
Temperally and spectrally resolved intraexcitonic dynamics
Figure 2 is the temporally and spectrally resolved midIR dynamics. Here we probed not only the broad midIR transients (0.23–0.37 eV), but also measured the IR dynamics (0.47–0.67 eV). This scheme affords a simultaneous access to the dynamic transitions from the 1s ground exciton to the higher lying np excitons or quasicontinuum states. The measured −ΔT/T_{0} spectra show peculiar energydependent behaviours. At Δt≤0.4 ps, the −ΔT/T_{0} spectra are strongly reshaped, exhibiting a relatively small increase of differential absorption (not absolute absorption) near 0.27 eV compared with the increased absorption around 0.3–0.5 eV. The increased absorption is more prominent at Δt>0.4 ps, where one can see that −ΔT/T_{0} is gradually larger near 0.27 eV with increasing Δt, and the differential absorption at 0.3–0.5 eV is concurrently smaller with increasing Δt. Between 0.4<Δt≤0.9 ps, −ΔT/T_{0} above 0.3 eV is rapidly vanished, while the absorption resonance below 0.3 eV is accordingly increased. After Δt>0.9 ps, the absorption resonance below 0.3 eV keeps reserved and it slowly subdues with featureless IR spectra above 0.3 eV.
For a quantitative analysis of the observed transient spectra, we use the following model consisted of multioscillator components^{55}:
The term of summation represents the intraexcitonic absorption from 1s to either A or B excitonic np state and the second term Θ(E−E_{bind}) is a steplike transition^{21} from 1s to the continuum with E_{bind} of 0.44 eV. In the equation, ɛ (=4.2) (refs 14, 27) and ɛ_{0} are the dielectric constant of monolayer MoS_{2} and the vacuum dielectric constant, respectively. There, the absorption amplitude S_{1s→np}, or the spectral weight of the intraexcitonic 1s→np transition, is proportional to the product of the oscillator strength f_{1s→np} and the ground exciton density n_{1s} (refs 39, 40, 55, 56). Because the 3.1 eV pump excitation creates e–h plasma in the band nesting resonance, an accurate estimation of n_{1s} requires both theoretical study of intervalley scatterings and the corresponding ultrafast measurements, which is beyond the scope of our ultrafast midIR intraexcitonic spectroscopy. In fact, the spectral weight from 1s→np is not only proportional to the population, but also depends on the probability of finding an empty final np state. As discussed about the transient spectra dynamics above, the photoexcited unbound e–h pairs experience rapid relaxation and start to form a groundstate exciton within ∼0.4 ps. It is strictly true that the np exciton population is negligible only at Δt⩾0.4 ps. Similar studies on 1D and quasi2D quantumwell structures have shown that the contribution from np→continuum is negligible^{33,54,56,57,58}. We found that the spectral fit matches well the measured data when we used up to three midIR oscillators, with the following transition energy E_{n} of E_{1}=0.27 eV, E_{2}=0.31 eV, and E_{3}=0.36 eV. On the basis that the observed E_{n}s do not vary Δt, we fix E_{n} to fit the timeresolved midIR spectra, but vary S_{1s→np} and the phenomenological exciton broadening parameter Γ. For the IR transients, the spectra are featureless representing the stepfunctionlike 1s to the continuum transition^{21}; this featureless IR spectrum is deviated from the steplike absorption at Δt≤0.4 ps, which might be due to the timedependent thermalization process after the pump excitation.
Given that the magnitude of S_{1s→np} differs only by a factor of 2 for each E_{n}, these transitions cannot simply be assigned to the phenomena taking place within single exciton Rydberg series of the A (or B) exciton branch. This is because even when the nonhydrogenic excitonic nature of a monolayer TMDC is considered, where a strongly (weakly) screened Coulomb potential is dominant when n≤2 (n⩾3) (ref. 21), the spectral weight should be substantially decreased by nearly an order of magnitude with increasing n, which is too large to account for our measurement results. Of course, care should be taken to estimate the precise strength of intraexcitonic transition in a monolayer TMDC because the nonhydrogenic exciton is dominant when n≤2, thus the 1s→np transition can deviate from the hydrogenic excitonic nature for n⩾3. This is because any intraexcitonic 1s→np transition depends both on the wavefunction of the nth exciton as well as the 1s exciton state, and the latter certainly deviates from the 2Dhydrogen model. Recent PLE^{23} revealed that the energy levels of the exciton Rydberg series are 1.88 eV (1s), 2.05 eV (2s) and 2.15 eV (3s) for A exciton and 2.03 eV (1s), 2.24 eV (2s) and 2.34 eV (3s) for B exciton. By considering 0.15 eV energy splitting between A and B excitons and the difference of reduced exciton masses of 0.25m_{0} (A exciton) and 0.28m_{0} (B exciton)^{18}, we estimated the intraexcitonic transition energies of 0.27 eV for E_{1A→3A}, 0.31 eV for E_{1B→3B} and 0.36 eV for E_{1A→2B}, which are exactly matched our measured intraexcitonic transition energy E_{n}. Interestingly, these values are somewhat deviated from the GW–Bethe–Salpeter prediction^{19}, possibly due to the substrate dielectric screening effect. Nevertheless, our measurements agree well with the experimental PLE investigation due to similar dielectric constant of CaF_{2} and fused silica^{23} as a substrate. Although there is a small difference (∼20 meV) for the A exciton energy between PLE (1.88 eV) and our photocurrent spectra and ultrafast absorption measurement (1.86 eV, Supplementary Notes 1 and 3), the difference is very marginal^{19,28,30,31} and the intraexcitonic spectroscopy can measure the energy difference between 1s and np, regardless of the Aexciton resonance. In accordance with PLE and our midIR measurements, we expect the fundamental 1s→2p would be 0.17 eV for the A exciton and 0.21 eV for the B exciton, and this is beyond our capability of tuning the midIR spectrum. Therefore, as schematically shown in Fig. 3a, we understand our intraexcitonic transition energy of E_{1} as 1s_{,A}→3p_{,A} within A exciton, E_{2} as 1s_{,B}→3p_{,B} within B exciton and E_{3} as 1s_{,A}→2p_{,B} between A and B exciton. Indeed, our energy assignment wellcorroborates a recent manybody Bethe–Salpeter prediction on the nonhydrogenic characters of excited excitons^{19,20,28,30,31}, underscoring a distinct capability of our intraexcitonic spectroscopy in measuring the relative energy difference between 1s and np. For the exciton broadening parameter Γ, since the effective mass of A and B exciton is different, Γ (=28.2 meV) for 1s_{,A}→3p_{,A}, Γ (=37.4 meV) for 1s_{,B}→3p_{,B} and Γ (=30 meV) for 1s_{,A}→2p_{,B} are slightly different due to the different exciton dispersion.
Dynamics of 1s→np intraexcitonic spectral weights
For further analysis, we show the temporal dynamics of S_{1s,A→3p,A} (Fig. 3c, blue), S_{1s,B→3p,B} (Fig. 3d, orange) and S_{1s,A→3p,A} (Fig. 3e, green). We identify three different kinetic regimes: immediately after the pump, the rising transients of all three spectral weights show similar behaviours, representing the hotcarrier relaxation from the quasicontinuum to the A and B exciton branch. This kinetics clearly differs from the dynamics of 1.86 eV probe (Fig. 3b), where the latter arises from the quasiinstantaneous bleaching dynamics. At 0.4≤Δt≤0.7 ps, the dynamics of S_{1s,B→3p,B} rapidly decrease, while the peak S_{1s,A→3p,A}and S_{1s,A→3p,B} emerge ∼0.3 ps later. Because the 1s B exciton is 0.15 eV higher than that of A exciton (Fig. 3a), the 1s B exciton serves as a population supplier to the energetically lower 1s A exciton, thereby the two transients show a complementary dynamics. At longer Δt>0.7 ps, because the 1s A excitons are thermalized and reaches a quasiequilibrium condition, the dynamics of S_{1s,A→3p,A} nearly follows that of S_{1s,A→2p,B}. This highlights that although S_{1s,A→3p,A} and S_{1s,A→3p,B} are spectrally separated apart, that is 0.27 and 0.36 eV, respectively, both transients are closely interrelated because these absorptions originate from the same 1s_{,A} ground state exciton.
Discussion
At an elevated temperature, the freecarrier absorption from 1s, 2s, 2p, 3s, 3p… may contribute to the increased probe absorption with ΔT/T_{0}<0. This scenario typically shows a strong temperature dependence of the relaxation rate, in which the higher temperature the larger the electron–phonon scattering rate, resulting in the dynamics to be highly temperature dependent. Here given that the formation time scale of the 1s exciton is very fast within 0.4 ps (see Figs 2 and 3) and the Drude scattering rate cannot be extended to the midIR range (Supplementary Note 2), the contribution of np→continuum transition may be very insignificant to the temperaturedependent midIR intraexcitonic response. Figure 4a shows that our midIR transients, fitted by a biexponential function, exhibit nearly temperature independent of the relaxation components (Fig. 4b,c). This implies that the effect of freecarrier absorption is negligible. We additionally show in Fig. 4b that the recombination of excitons arises on subps and tens of ps time scale. At T=77 K, the midIR peak ΔT/T_{0} linearly increases with F up to 32.5 μJ cm^{−2} (equivalent to e–h pair density of 9.86 × 10^{12} cm^{−2}) (refs 8, 41). The linear Fdependence reflects that there exists no highorder nonlinear excitonic interaction, ensuring that our midIR transients represent the firstorder population dynamics. A recent belowgapprobe study^{45} reported very similar relaxation times to our results. These time components were explained using defectassisted exciton recombination. Given that we observed negligible Fdependent relaxation dynamics (Fig. 4e,f), we can infer that our midIR decay transients do not arise from the photoinduced absorption of filled e–h pair in the localized states, but arise from the exciton capture into the defects.
In summary, we report the experimental observation of the 1s intraexcitonic transition. Recently, Poellmann et al.^{47} investigated a similar investigation of intraexcitonic transition in monolayer WSe_{2}, reporting the presence of strong absorption in a 2D TMDC, whose fundamental optical absorption originates from the 1s ground exciton. Our ultrafast midIR measurements reveal twofold 1s→3p transition energies to be 0.27 eV and 0.31 eV for A and B exciton, respectively. We additionally uncover an intraexcitonic relaxation channel of 1s→2p to be 0.36 eV between 1s A and 2p B exciton. The large excitonbinding energy due to the nonlocal dielectric screening ensures not only 1s→2p transition^{47} to be observable, but also a higherorder transition of 1s→3p in a monolayer 2D TMDC at an elevated temperature, which cannot be accessible using conventional interband spectroscopy, or any in quasi2D quantumwell structures. In addition, looking to the future, the availability of electricgate tuning may enable to investigate the coherent manybody interexcitonic correlations among exciton, biexciton^{38,59} and trion^{12,13,18,48} in a timeresolved controlled manner, which is nontrivial to study in other lowdimensional inorganic semiconductor structures.
Methods
Ultrafast optical pump–probe spectroscopy
Using 250 kHz, 50 fs Ti/sapphire laser system (Coherent RegA 9050), optical parametric amplifier (Coherent OPA 9850) yields signal (0.77–1.12 eV) and idler (0.47 eV–0.67 eV) pulses that are used to generate midIR pulse (0.23–0.37 eV) via difference frequency generator (Coherent DFG). The idler and DFG output serve as the probe pulse in the IR and midIR range, respectively. The chirp of midIR pulse is discussed in Supplementary Note 5. Highenergy interband response was measured by using a whitelight continuum (1.76–2.03 eV) generated by focusing 1.55 eV pulses into a 1 mm sapphire disk. For the groupdelay dispersion (GDD) of the whitelight continuum pulse, we compensated using a pair of prism, and further checked the GDDinduced delay via crosscorrelation of the whitelight pulse and 1.55 eV pulse, whose details are explained in the Supplementary Note 3. The 3.1 eV pump pulse was created by second harmonic generation of 1.55 eV pulse in a 1mmthick beta barium borate (BBO) crystal. Due to the combination of OPA and DFG, where both signal and idler from OPA were used to generate the midIR DFG output, the only available seed pulse for 3.1 eV pump pulse was 1.55 eV in our system, so that the midIR measurement with resonant pump excitation at either A or B 1s exciton was not possible in our current system. For the each midIR or IR measurement, pump pulse and probe pulse are simultaneously focused on the sample in the cryostat equipped with two CaF_{2} windows, and pump–probe delay is controlled by a mechanical delay stage (Newport MIMS300LM). The spot size of our pump and probe beams were 100 μm, and 50 μm, respectively, which were simultaneously focused using f=50 mm lens before the temperaturecontrolled vacuum cryostat. In our optical geometry, the 3.1 eV pump passes through a mechanical delay stage, so called ‘pump delay’. Because the pump delay is recorded in a computer as an absolute length, we performed crosscorrelation measurement to estimate the probe delay using BBO (visible upconversion) and KTA (midIR upconversion) crystals. More detailed information for determining the pump–probe ‘timezero’ is explained in Supplementary Note 6. Differential transmission signal (ΔT/T_{0}) was recorded in a lockin amplifier (Stanford Research Systems SR850) with 10 kHz chopping frequency (Scitec 300CD). The schematics of midIR and IR setup are illustrated in the Supplementary Fig. 9.
Additional information
How to cite this article: Cha, S. et al. 1s intraexcitonic dynamics in monolayer MoS_{2} probed by ultrafast midinfrared spectroscopy. Nat. Commun. 7:10768 doi: 10.1038/ncomms10768 (2016).
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Acknowledgements
S. Cha, S. Sim, J. Park and H. Choi were supported by the National Research Foundation of Korea (NRF) through the government of Korea (MSIP) (Grants No. NRF20110013255, NRF20090083512, NRF2015R1A2A1A10052520), Global Frontier Program (2014M3A6B3063709), the Yonsei University YonseiSNU Collaborative Research Fund of 2014 and the Yonsei University Futureleading Research Initiative of 2014. J.H.S., H.H. and M.H.J. were supported by Institute for Basic Science (IBS), Korea under the contract number of IBSR014G12016a00.
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S.C. and H.C. conceived the idea and designed the experiments. H.H., J.H.S. and M.H.J. fabricated and characterized vapourphasegrown MoS_{2} monolayer crystals; and S.C., S.S. and J.P. conducted the ultrafast optical pump–probe spectroscopy. S.C., J.H.S. and S.S. analysed the results. All authors discussed the results and prepared the manuscript.
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Supplementary Figures 110, Supplementary Notes 18 and Supplementary References. (PDF 1004 kb)
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Cha, S., Sung, J., Sim, S. et al. 1sintraexcitonic dynamics in monolayer MoS_{2} probed by ultrafast midinfrared spectroscopy. Nat Commun 7, 10768 (2016). https://doi.org/10.1038/ncomms10768
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