Spectroscopic Study of the Excitonic Structure in Monolayer MoS2 under Multivariate Physical and Chemical Stimuli

Photoluminescence (PL) spectroscopy has proven to provide deep insights into the optoelectronic properties of monolayer MoS2$\left(\text{MoS}\right)_{2}$ . Herein, a corresponding study is conducted on the excitonic properties of mechanically exfoliated monolayer MoS2$\left(\text{MoS}\right)_{2}$ under multivariate physical and chemical stimuli. Specifically, midgap exciton states that originate from lattice defects are characterized and they are compared to existing models. Through statistical data analyses of substrate‐, temperature‐, and laser‐power‐dependent measurements, a PL enhancement is revealed through physisorption of water molecules of the controversially discussed excited‐state A biexciton ( AXX*$A^{\left(\text{XX}\right)^{\star}}$ ). In addition, analyses of monolayer MoS2$\left(\text{MoS}\right)_{2}$ on gold substrates show that surface roughness does not account for changes in doping level within the material. Also, a shift in the electron–phonon coupling properties that arises from thin films of water that are physisorbed on top of the samples is reported.


Introduction
Monolayer MoS 2 belongs to the family of transition-metal dichalcogenide (TMDC) 2D materials and has attracted great interest in recent years due to its remarkable potential for fundamental studies and applications.It exhibits strong spin-orbit coupling, [1][2][3][4][5][6] controllable spin-valley transport properties, [7][8][9] and a thickness-dependent bandgap. [10][13] These properties and their ample occurrence in bulk form in nature make TMDCs interesting and applicable to semiconductor sensors, [14][15][16][17] photodetectors, [18][19][20] field effect transistor [21][22][23] as well as for energy harvesting and solar cells. [24,25]ue to the lowered electron screening and localized electron wave functions through the dimensionality effect, monoand few-layer MoS 2 form excitons with high binding energies below the bandgap that are stable at room temperature.For the monolayer material, one finds a direct bandgap at the K and K' points resulting in strong optical absorption and a pronounced photoluminescence (PL) spectrum dominated by exciton transitions.Experimental and theoretical works have shown the occurrence of delocalized uncharged excitons such as the so-called A and B excitons [26][27][28][29] and their excited states, [30][31][32] as well as charged trions [30,[33][34][35] and biexcitons. [29,32,36,37]In particular, the excited-state A biexciton (A XX Ã ) represents a recently discovered transition that is crucial for the understanding of monolayer MoS 2 PL spectra. [29,38]n addition, material defects such as Stone-Wales defects, vacancies, adatoms, substitutional impurities, line defects, grain boundaries, and edges [39,40] result in changes of the carrier concentration, [41] the occurrence of additional excitonic transitions within the PL spectrum, [32] and a change of the band Photoluminescence (PL) spectroscopy has proven to provide deep insights into the optoelectronic properties of monolayer MoS 2 .Herein, a corresponding study is conducted on the excitonic properties of mechanically exfoliated monolayer MoS 2 under multivariate physical and chemical stimuli.Specifically, midgap exciton states that originate from lattice defects are characterized and they are compared to existing models.Through statistical data analyses of substrate-, temperature-, and laser-power-dependent measurements, a PL enhancement is revealed through physisorption of water molecules of the controversially discussed excited-state A biexciton (A XX Ã ).In addition, analyses of monolayer MoS 2 on gold substrates show that surface roughness does not account for changes in doping level within the material.Also, a shift in the electron-phonon coupling properties that arises from thin films of water that are physisorbed on top of the samples is reported.
[42] Such defects occur naturally during crystal growth.The intrinsic defect density of monolayers obtained by exfoliation from bulk crystals is commonly lower than for material directly grown by mono-and few-layer synthesis methods such as chemical vapor deposition. [43]For graphene, defecttype and defect-density characterizations can be performed via Raman spectroscopy, [44,45] but remain challenging for 2D TMDCs.Advances in this area thus represent an important contribution, for example, for improving carrier mobility in 2D MoS 2 for applications in optoelectronic devices. [11],47] For instance, vacancy defects give rise to highly localized excitonic states that are sensitive to temperature and to the physisorption and/or chemisorption of gas molecules. [42,46,48]Recently, localized defect states in 2D-TMDCs were shown to play an important role for the realization of single-photon emitters even in schemes that employ local straininduced bandgap renormalization. [49]xciton binding energies and resonance strengths strongly depend on the fabrication process, [43,50] the substrate, [35,51] the surrounding medium, [42] and the temperature. [41,52]In our work, we analyze monolayer MoS 2 under these multivariate physical and chemical stimuli.In particular, the effect of water condensation on the optical properties of TMDCs represents a little explored aspect in the field.However, it is an unavoidable phenomenon in a typical laboratory environment.We perform measurements on the laser-power and temperature dependence of the PL emission of monolayer MoS 2 , which demonstrate that water condensation in the vicinity of lattice defects enables the PL emission of the A XX Ã exciton and changes the mean phonon energy as well as the phonon coupling constant.Furthermore, we compare different models for defect excitons and perform substrate-dependent measurements to analyze doping effects on the PL spectra.We also show that the surface roughness of gold does not account for the substrate-induced changes of the PL as hypothesized in previous reports. [51]To obtain an accurate understanding of the spectral behavior, we review the status of PL spectroscopic findings related to monolayer MoS 2 and lay out a road map for detailed spectroscopic analyses of TMDCs.Furthermore, to analyze our experimental data, we build a comprehensive statistical analyses tool in Python which will be available as open source on the Python Package Index (PyPI) repository. [53]s a result, we organize the remainder of our manuscript as follows.In Section 3, we discuss the results and models for the PL measurements in detail, and in Section 4, we summarize our findings.Furthermore, we describe the main aspects of the experimental setup, the corresponding methods and samples in Section 5.The supplementary material provides more detailed information about the setup and additional analyses, which support and complement our findings.

Model for the Excitonic Spectra of MoS 2 -an Overview
To perform our analyses, we require a model for the resonance fluorescence of excitons.We describe the spectra by the intensity of the scattered light from a collection of two-level systems, one for each excitonic resonance.Starting from the optical Bloch equations in rotating wave and Markovian approximation, we find for each individual resonance a homogeneous line broadening given by a Lorentzian line shape, [54] which accounts for the corresponding intrinsic lifetime.To accurately describe the line shapes in our experiment, we need to consider the inhomogeneous broadenings of these resonances which originate from the thermal velocity distribution of the exciton ensemble.Consequently, for each resonance, the resulting distribution is a convolution of a Gaussian and a Lorentzian profile, which is generally known as the Voigt profile [55] VðE;σ,γÞ ¼ ðGÃLÞðE;σ,γÞ ¼ where w is the Faddeeva function, σ the Gaussian standard deviation, and 2γ the full width at half maximum of the Lorentzian distribution.
Our measured data suggest that the spectra are dominated by multiple overlapping resonances, making it difficult to discriminate them without further input.Earlier experimental and theoretical reports on the subject shed light on the excitonic composition of the material and give us a specific Ansatz for the expected number of resonances for our model.For monolayer MoS 2 within the relevant energy range, there exist two neutral delocalized excitons that relate to the transition from the spin-orbit split valence bands to the lowest conduction band at the K and K' points, named A and B exciton. [26,28,30]n addition, other resonances known to occur within the spectrum of monolayer TMDCs are associated with excited states of neutral A and B excitons.A description for these excited states was presented by Berkelbach et al., [30] using an excitonic Hamiltonian in effective mass approximation.For the neutral excitons, this reads as The effective in-plane 2D Coulomb interaction used in this approach is given by the nonlocally screened electron-hole interaction as derived by Keldysh [56] V eh ðrÞ ¼ À where H 0 and Y 0 , respectively, denote the Struve function and the Bessel function of the second kind, and r 0 ¼ 2πχ 2D [57] is the screening length with χ 2D as the 2D polarizability.In this context, the terminology from Rydberg states in the hydrogen series is adopted with annotations 1s, 2s, 3s, 2p, etc.Using this approach to compute binding energies of the excited states enabled the identification of excited states of excitons in monolayer WS 2 [31,31,32,58] MoS 2 as well as monolayer MoS 2 encapsulated by hexagonal boron nitride (hBN). [43,59]Regarding our spectral range and the results obtained from these works, the states that are relevant for our work are the A 1s , A 2s , and B 1s excitons.Based on the mentioned model in ref. [30] and the computations performed in ref. [59], Pandey et al. [32] found a binding energy of the A 2s state of E A 2s b ¼ E A 1s À E A 2s ¼ 0.17 eV at low temperatures.This result is confirmed by a recent theoretical work, where a tight-binding approach was used to predict the A 2s -binding energy of monolayer MoS 2 on SiO 2 (0.226 eV) and monolayer MoS 2 encapsulated by hBN (0.178 eV). [60]We note that the resonances associated with the A 2s and B 1s states overlap energetically, which makes an experimental identification within PL spectra challenging.
Monolayer MoS 2 , as a naturally n-doped material, contains an excess amount of electrons.Therefore, high populations of negatively charged trions A À (bound states of two electrons and one hole in the upper valence band at K and K' points) are found in the material.For the same reason, positively charged A þ trions are not observed within the PL spectrum.A recent theoretical analysis suggests that the A À resonance splits into two interband trions and one intraband trion A À ð1,2,3Þ [35] but it will be rather difficult to experimentally discern the associated splittings.
As shown by Lee et al., [29] discrepancies in earlier reports on resonance and binding energies of A À , A 1s , and B 1s excitons have led to the consensus that additional excitons contribute to the spectra.In this context, the existence of an additional multiexciton, the A biexciton (A XX ) and defect related excitons have been proposed.Computations of the binding energy of the A biexciton (0.02 eV) [36,61,62] have underestimated the observed value (0.07 eV) from an earlier observation. [37]It has been possible to resolve this issue by assigning the observed binding energy to an excited state of the positronium molecule using the stochastic variational method (SVM). [38,63]The associated state has an orbit momentum L ¼ 1 with positive parity and auto-dissociates into the 1s ground state and 2s excited state of the exciton.It is therefore written as A XX Ã .
In addition, computations suggest binding energies for B À=þ trions [30,35] that lie within the energy range relevant to our experiments.However, to the best of our knowledge, B À trions have not been observed in monolayer MoS 2 PL spectra so far, and B þ trions are mentioned in only one report, [64] where the material contained a high density of defects.
In summary, we expect a maximum of five resonances within our PL spectra and they originate from A 1s , A 2s , B 1s excitons, A À , and A XX Ã multiexcitons.In addition, we expect defect states at low energy values.Values for the resonance and separation energies depend, among others, on the specifics of the samples' fabrication process, [43,50] the temperature, [52] the substrate, [35,51] and the surrounding medium. [42]Corresponding values from earlier theoretical and experimental works are summarized in Section S1, Supporting Information, Supporting Information.In fact, we have computed mean values and standard deviations from results reported in those works by collecting data obtained in experiments below 100 K, at room temperature (300 K), and from computations.We display the obtained values in Table 1 which serves as a starting and reference point for the statistical analyses within our model.

Observations in the Proximity of Condensed Water
We have prepared a monolayer MoS 2 flake on a fused silica substrate (SiO 2 ) by mechanical exfoliation and studied its optical properties in a cryostat setup with a continuous wave laser at 561 nm.A detailed description of the sample and the cryostat setup can be found in Section 5 (see also Section S2-S5, Supporting Information).We have measured and analyzed the dependence of the PL spectra on laser power and on temperature in the proximity of water.More specifically, water has been introduced to the system in the form of condensation by lowering the cryostat sample-stage temperature, thus encouraging a layer of water to settle on the sample.We have observed the water condensation on the camera, and the images are shown in Section S3, Supporting Information.In addition, we have confirmed the water condensation effect by using nitrogen purging which resulted in complete disappearance of the bound excitonemission peaks (not shown here).

Laser Power Dependence of the PL Spectrum
We have measured and analyzed the dependence of the PL spectra on laser power at a temperature of 25 K in the proximity of water.
Table 1.Exciton resonance energies E and energy separations ΔE A1s with respect to the A 1s exciton for monolayer MoS 2 on a SiO 2 substrate from references for experiments below 100 K, at room temperature (300 K), and from theory.

14[27]
A 1s 1.91 [27] -A À -0.032 AE 0.003 [30,36,38,[61][62][63] A XX -0.0224 AE 0.0003 [36,38,[61][62][63] A XX Ã -0.0695 [38,63] In Figure 1, we display our measured data and the corresponding fitting results for three different values of the laser power.Note that to better bring out the underlying physical processes, we have normalized all measurements with the cryostat setup by the instrument detection efficiency of the setup (obtained in a separate experiment; for details, we refer to Section S5, Supporting Information).We have estimated the uncertainties of the counting measurements, with an underlying Poissonian distribution, and have obtained the goodness of fit from the corresponding χ 2 and p values, which are available in Section S6, Supporting Information.
Fitting Model of the Defect Spectrum: As pointed out in the previous section, we expect that the higher energy peak predominantly originates from the excitons listed in Table 1, sometimes also referred to as free, unbound, or band-edge excitons.Similarly, we expect that the low energy peak in the spectra originates from localized defect exciton states, also referred to as bound, trap, or mid-gap states.,52] As reviewed by Wu and Ni, [39] lattice defects may occur in 2D materials in various forms such as Stone-Wales defects, vacancies, adatoms, substitutional impurities, line defects, grain boundaries, and edges.We have obtained our sample through an exfoliation process which is known to create residual impurities [65,66] in the form of S or Mo vacancies.The condensed water molecules which we have observed are likely physisorbed by these vacancies and act as adatoms.Corresponding density functional theory (DFT) calculations predict a discrete number of additional bands that lie within the bandgap region [41,67] and, therefore, a discrete number of radiating localized defect states.Based on this, we have found that a minimum of three Voigt profiles has been required to obtain fit results with test statistics that indicate a reliable description of the data, and we display the results of our fits in Figure 1a.
Recent works [52] have suggested to represent the low energy peak by where ρ is the density of states for the localized defect states, and f FD represents Fermi-Dirac statistics.We have considered this model specifically in the context of the temperature dependence (see Section 3.1.2)and have fitted this model to our measured data.However, we have been unable to provide sufficient statistical evidence for the models' applicability (see Section S7, Supporting Information), and there appears little theoretical justification for both, the aforementioned form of the density of states and the application of the Fermi-Dirac statistics since excitons essentially are bosonic quasiparticles.
In the monolayer MoS 2 , we have observed PL emissions of defect-bound excitons only at low temperatures, as this reduces the probability of thermal delocalization of excitons from the defect sites.In addition, the presence of water also reduces the screening of excitons.In contrast, in a multilayer MoS 2 , it has been shown that large thermal energies are essential to change the electronic band structure and to enable the population inversion and subsequent radiative relaxations from the defect levels. [68]In agreement with ref. [68], we have also observed the suppression of PL emissions from defect-bound excitons in multilayer MoS 2 (see Section S11, Supporting Information).
Laser Power Scaling and Biexciton: We have observed increased defect and unbound exciton PL intensities with increasing laser power.This is not surprising since the laser optically dopes the material, and an increase in laser power consequently means an increase in the exciton generation rate.Regarding the relative peak heights with increasing laser power, it is apparent that the PL intensity of defect-bound excitons increases slower than that of unbound excitons.A theory to describe the laser-power dependence of near-band-edge PL of semiconductors was developed by Schmidt and Lischka, [69] which predicts the power scaling as where I is the PL intensity; P is the power of the exciting laser and 1 < α < 2 for exciton-like transitions; and α < 1 for free-tobound and donor-acceptor pair transitions.This relation has been applied to monolayer MoS 2 in an earlier work. [39]In fact, α < 1 for the bound exciton peak as well as 1 < α < 2 for the unbound excitons peak have been confirmed and this is in good agreement with our findings which we display in Figure 1b.
Based on the values compiled in Table 1, we assign a specific resonance to the excited A biexciton (A XX Ã ).Since we have access to the laser-power dependence of the PL intensities, we can do this biexciton assignment not only via its binding energy and peak position but also through the mass action law for biexcitons, [70] which predicts the relative population between biexcitons and ground-state A excitons (similar to Equation [14] ).In an ideal biexciton generation scenario, the biexciton PL intensity will depend quadratically on the ground-state A-exciton intensity: [29,71,72] .In Figure 1c, we provide a fit of the I A XX Ã À I A 1s relation from which we obtain a value of k ¼ 2.4.Furthermore, in Figure 1d, we display the laser-power dependence of the peak positions and observe a non-negligible shift of the biexciton peak position.This indicates that for an accurate description of the spectra, corrections to the model of the spectral shape for the trion PL, as proposed by Christopher et al., [73] are required.The expression they provide reads where E 0 tr is the zero-momentum trion energy and ε is the length of the low-energy tail of the trion PL.It is given by Here, m X ¼ m e þ m h is the exciton and m tr ¼ 2m e þ m h the trion mass, where m e and m h are the effective electron and hole masses.Furthermore, a is the effective trion size.
As a matter of fact, this corrected model accounts for the momentum and, therefore, temperature-dependent trion decay rate as well as for the fact that trions eject an electron when they decay, which changes the energy profile of emitted photons during recombination.Therefore, the spectral shape for trions has to be different from that of neutral excitons as described by Equation ( 1) and has a temperature-dependent asymmetric shape with a long tail toward low energies.Finally, this could also compensate for an overestimation of the biexciton intensities, as reflected by our previously discussed results for k.

Temperature Dependence of the PL Spectrum
Next, we study the influence of temperature on the PL spectra.In Figure 2a,b, we display the PL spectra for monolayer MoS 2 on SiO 2 for different temperatures and again focus on the biexciton.Specifically, we have recorded the spectrum at 3.6 K at a laser power of 145 μW, the spectrum at 25 K at 110 μW, and the remaining spectra in Figure 2b at 250 μW.The laser power does not affect the binding energy and energy separation but the exciton population.Therefore, we exclude the measurements in Figure 2a from our analyses of the temperature dependence of the bound exciton populations.
General Observations: Biexciton, Line Shift, and Line Narrowing: Similar to the power-dependent measurements, we again observe the occurrence of a peak that can be assigned to the excited A biexciton (A XX Ã ) (see Table 1).In an earlier work, [32] the relative spectral weight of A XX Ã has been seen to decrease with temperature which we, too, have found in our measurements (see Section S8, Supporting Information).The new model for the asymmetric PL shape of the trion A À by Christopher et al. [73] in Equation ( 6) provides an alternative description of the spectrum, but will not be able to resolve the discussion about the existence of an excited-state biexciton as proposed in ref. [29].This is due to the fact that the asymmetry below 70 K is minimal and difficult to extract with sufficiently high accuracy and also above 300 K the thermal broadening overshadows the tail. [73]n addition, we observe a blueshift and narrowing of all peaks for decreasing temperature.The observed temperature-dependent blueshift of the excitonic peaks can be understood in terms of an energy bandgap change.An expression for semiconductors has been derived by Varshni [74] in the late 60s, which reads where E g is the direct or indirect energy gap at temperature T, E 0 is its value at temperature T ¼ 0 K, and a and b are empirical constants.This expression has been widely used and has been successfully applied to monolayer MoS 2 in recent works. [34,75]nfortunately, the parameters a and b lack a proper physical interpretation, and, therefore, the theoretical basis for this model remains unclear.To account for electron-phonon coupling, [43,73,[76][77][78] O'Donnel and Chen [79] have derived a modification of Equation ( 8) which reads as For this model, E 0 X is the exciton peak energy at 0 K, S denotes the effective electron-phonon coupling constant, and ℏω h i represents the average energy of the phonon contributing to the In Figure 2c, we display the peak positions of the exciton contributions which we have obtained by applying the aforementioned expression to our data.Our test statistics confirm that the model describes the data accurately.This indicates that, indeed, the temperature-dependent bandgap change and the electron-phonon coupling are the cause the blueshift of the peaks.Upon comparing our fit results (see Table S2 in Section S10 of the Supporting Information) to earlier works, [43,73,76,78] we find increased values for S and ℏω h i.We attribute this to the water condensation on top of the monolayer MoS 2 sample, which changes the phonon properties and, hence, its coupling to the lattice.The widening of the resonances is a direct consequence of the thermal broadening which, in Equation ( 1), we describe via the Gaussian width σ.In Figure 2d, we depict the temperature-dependent binding energy of excitons in monolayer MoS 2 on SiO 2 .In general, the binding energy of excitons increases with the temperature which is especially pronounced for defect-bound excitons.
Intensities and Thermal Dissociation: In addition, as the temperature decreases, we observe an increase in the intensities for defect excitons (except for the D 2 ) and a decrease in the intensities for the unbound excitons.This observation is consistent with a thermal dissociation process where bound/localized defect excitons can be considered excitons in a quantum well that can thermally dissociate.For a system consisting of strained In x Ga 1Àx As=GaAs quantum wells, Bacher et al. [80] have solved the rate equations under the assumption that the exciton population is in a steady-state condition and have arrived at the expression where E A is the activation energy, τ denotes the excitonic lifetime, and τ 0 represents the effective scattering time.This equation has been used for bound-state PL intensities in monolayer WSe 2 [47,81]   and multilayer MoS 2 [76] and describes the observed temperature dependence well.We use this model to describe the temperature dependence of the bound exciton population and display our results in Figure 2e.We find that the total defect-bound exciton populations and individual defect-bound excitons D 1 and D 3 are well described with this model.However, D 2 is an exception which could indicate that the description of the defect-related PL emission via the model with three Voigt distributions requires further refinement.Specifically, different excitonic types that are trapped might have to be taken into account.This aspect will be of concern in future studies.In a simplified three-level model that distinguishes between general bound, unbound, and ground (exciton recombination) states, it is possible to describe the inner exciton dynamics that reflect the observations also with regard to unbound exciton intensities.Goodman et al. [52] have used this approach to set up and solve the corresponding rate equations.
From their considerations, it follows that for high temperatures, bound defect excitons are more likely to thermally dissociate and transient into an unbound state from which they then radiatively recombine.This recombination path is less likely for low temperatures, where unbound excitons are likely to get trapped by defects, that is, transient to a defect state and its recombination.
In turn, this reduces the intensity in observed unbound excitons' intensities.

Observations with Reduced Water Proximity
Next, we study whether water enables the A XX Ã -biexciton generation.To do so, we use the results from the previous two sections and design a setup that on one hand favors the generation of the biexciton and on the other hand reduces the proximity of water for the MoS 2 sample.From our observations in Figure 1 and 2a, we have learned that biexcitons can be generated at laser powers between 50 and 110 μW, and that the generation is enhanced for increasing laser powers.To avoid a biexciton generation that is solely driven by optical doping through the light source, [29] we make a trade-off in our decision.To favor the generation process, we choose a pulsed laser with a maximum peak power of 1.8 mW and an average power of 100 μW, a value that lies within the aforementioned interval.Further properties of the light source include a repetition rate of 80 MHz and pulse width of 70 ps.From our discussion about the temperature-dependent measurements, we have learned that the biexciton PL increases with temperature (see Figure S12 in Section S8, Supporting Information).Consequently, we place the sample into an open lab environment, thereby considerably reducing the water condensation film relative to our cryostat setup, and perform the measurement at 295 K with a commercial confocal fluorescence microscope (MicroTime 200 from Picoquant).
For the setup, we use a SiO 2 and a gold substrate.The effect of a gold substrate on the PL emission of a monolayer MoS 2 is a controversially discussed topic in the literature.It was shown that gold nanoparticles can induce an enhancement of the PL emission, [82] but also that charge transfer, induced by gold substrates, can lead to quenching. [83]][86] It has been shown that a gold substrate can also reduce the charge-carrier concentration in MoS 2 ; [51] and therefore, it should also enhance the excited-state biexciton PL emission by reducing the trion population and increasing the neutral exciton population.

SiO 2 Substrate Measurement and Biexciton
We display the spectrum of the SiO 2 substrate measurement in Figure 3c along with a fit of a model with four Voigt profiles.In fact, when employing models with fewer components, we obtain goodness-of-fit parameters that indicate a rejection of the hypotheses.When employing models with more components, we failed to obtain agreement with the values summarized in Table 1.For the details of the fitting process, we refer to Section S6, Supporting Information.
In apparent contrast to the previous measurements, we have not been able to provide statistical evidence that would substantiate the existence of the excited-state A biexciton.In earlier works, [29] it has been shown that the A XX Ã PL is enhanced through electrical doping, that is, by the application of an external voltage or through optical doping by exciting with higher laser powers and this is what we, too, have found in Section 3.1.1.Since the measurements in Figure 3 have been carried out with an average laser power of 100 μW, the biexciton occurrence in the 50 μW measurement at 25 K in Figure 1a and, hence, all measurements in Figure 1 and 2 neither be explained through the laser power nor the temperature.This leaves only the water film as the only remaining differing constituent between the measurements in Section 3.2.2 and the measurements on temperature and laser-power dependence.Specifically, water molecules are physisorbed by lattice defects and electrically dope the material.This is similar to the effects described by Tongay et al., [41] where it has been suggested that defect sites act for N 2 as electron-depletion channels, thereby lifting the screening on the excitons.This effect changes the relation between free electrons and excitons through thermodynamical equilibrium conditions, thus stabilizing neutral unbound and defect-bound excitons.For our setup, this effect becomes effective for the biexciton and reduces the concentration of negatively charged excitons such as the A À trion.This clearly suggests that the biexciton emission in the previous two sections is a direct consequence of the water condensation on top of the MoS 2 sample.

The Effect of a Gold Substrate on the PL Spectrum
We study the population density and composition of different excitons in monolayer MoS 2 on a single-crystalline gold flake (Au) at room temperature and compare it to that of a fused silica substrate (SiO 2 ).In Figure 3a, we depict the PL intensity map of the monolayer MoS 2 sample that we used for both substrates, and Figure 3b shows the PL spectra that we have recorded at the marked positions in Figure 3a.
In Table 2, we list the obtained values for exciton resonance energies E, energy separations ΔE A 1s , and integral values I, which are proportional to the intensities as defined in Equation ( 12), of the various components from the fitting.In agreement with the values obtained from the literature, we associate the peaks from our fitting with the A 1s , B 1s , A À , and  a defect exciton D. However, we could not provide statistical evidence about an excited-state biexciton A XX Ã .We make several observations concerning the substratedependent PL First of all, we observe a lower PL intensity for monolayer MoS 2 on SiO 2 in comparison to that on Au.Regarding the exciton components with respect to their peak height and total intensity as displayed in Figure 3c,d and Table 2, we observe that the trion contribution stays approximately constant, while contributions of the neutral excitons increase.The PL spectra can be affected through strain that is induced by nanobubbles [87] that form during fabrication.Atomic force microscope images of our sample (see Section S2, Supporting Information) reveal that they are also present in our case and are about 5 nm in height and 200 nm in width.This is small in comparison to the previous study.We have measured spectra at several different positions of the monolayer MoS 2 , but we could not observe any significant change in the spectra depending on the location on the monolayer MoS 2 on the same substrate.We attribute this to the fact that either the nanobubbles uniformly affect all measured spectra or have no effect at all due to the small size of the nanobubbles.
Interference and absorption within the substrate system affect the observed intensity of the PL spectra.Through the computation of reflection coefficients for the setups (using the formalism in refs.[88-90]), it is possible to compute the intensity enhancement or suppression I computed for a given frequency for free-standing monolayer MoS 2 and monolayer MoS 2 on either Au or SiO 2 .From these obtained intensities, one can compute an enhancement factor Γ À1 , which can be applied to the observed data via The corrected intensity, I corr , corresponds to the experimentally obtained free-standing monolayer MoS 2 and reflects the substrate-dependant intrinsic processes of the material.Buscema et al. [51] have conducted a thorough study on the effects of various substrates on monolayer MoS 2 using this recipe.Even after correcting the PL intensities, the spectra of monolayer MoS 2 on SiO 2 substrates are suppressed relative to gold substrates.In fact, this behavior can be traced back to the PL-emission reduction caused by SiO 2 through scattering with optical surface phonons. [51,91,92]However, we would like to note that also gold substrates are known to suppress PL emission by adding nonradiative paths for exciton recombination such as charge-transfer processes or dipole-dipole interaction. [51,93,94]onsequently, we should resort to relative intensities to further analyze the substrate effects on the excitonic structure of the monolayer MoS 2 .We follow the approach in ref. [51] and find for a two-level model, in which excitons radiatively recombine at decay rates γ, the intensity, up to a constant, can be written as where ρ is the exciton density.Then, the relative intensity solely depends on the ratio of decay rates and the ratio of exciton densities.The ratio of exciton densities ρ A 1s =ρ A À is described by the mass action law, which is based on the thermal equilibrium between free electrons, neutral excitons, and trions [95] and reads where η A 1s ¼ 8 and η A À ¼ 2 are the numbers of degenerate spin states [33,95] ε ¼ 18 AE 1.5 meV on binding energy, and μ represents the chemical potential.This expression ultimately depends on the free-electron density ρ e via the chemical potential, which is expressed as where m Ã is the effective mass. [33]The free-electron density results from intrinsic and optical doping.The Raman A 1g mode frequency ω A 1g is known to depend on the doping of the material, too.Using Equations ( 13)- (15) with [51,[96][97][98] ρ 0 % 5 À 7 ⋅ 10 12 cm À2 γ A 1s γ A À % 6.6 to substantiate a change in the doping level, that is, a drain of excess free electrons.This reveals that for monolayer MoS 2 on gold, the difference in the experimentally obtained relative intensity ratio in Equation ( 13) between the two substrates predominately stems from the substrate-induced change of the doping level. [51]It has been hypothesized that the reduced doping level originates from the MoS 2 being suspended due to the roughness of the gold substrate. [51]For this reason, we use gold with a very smooth surface (see Section S2, Supporting Information).Since our experiments display the same qualitative observations, we can state that surface roughness does not account for the change in doping level.
In addition, the substrate changes the screening and renormalizes both, exciton binding energies and the bandgap energy.In general, these two competing effects do not cancel each other, but rather lead to a redshift of the observed resonance energies. [35]For instance, we observe this effect for the A 1s exciton.In fact, changes in the binding energies are likely to go hand in hand with exciton decay rates changes, and thus the ratio γ A 1s γ A À in Equation ( 13) varies for different substrates.
We compare the relative PL intensities for the A trion and the ground-state A exciton at room temperature in the presence of water (see Figure 2b) to the relative intensities obtained for MoS 2 on gold.If water enhances the biexciton PL emission solely through electrical doping, it is surprising that we do not observe a biexciton peak for the measurement on gold.The relative intensities indicate a much more pronounced doping effect for the gold substrate than for the water layer.We attribute this to two possible explanations.Either water stabilizes the excitedstate biexciton emission, beyond merely doping MoS 2 , or the screening of gold suppresses the biexciton PL emission.

Conclusion
In this work, we have investigated monolayer MoS 2 under different physical and chemical stimuli via PL spectroscopy.Specifically, we have found clear evidence that water condensation enhances the excited-state biexciton A XX Ã PL emission.Similar enhancements have been observed earlier mainly through electrical doping via the application of an external voltage or through optical doping via excitation laser We conclude that water molecules are physisorbed by lattice defects and electrically dope the material, thereby enhancing the excited-state A-biexciton PL emission.In further conclusion to our substratedependent measurements, we find that gold enhances the PL of neutral excitons and suppresses the PL of the charged A À trion in comparison to a SiO 2 substrate through doping.We report the same but less pronounced effect for monolayer MoS 2 in the proximity of water.Since no biexciton emission is observed for the gold-related observations despite the more pronounced doping, we suspect that gold either suppresses the biexciton PL emission through, for example, screening or water stabilizes the biexciton emission beyond doping the material.Comparing our results with previous work, we report that the surface roughness of gold does not account for the change in the substrate-induced doping level.We have also shown that temperature-dependent PL spectroscopy can detect changes in the mean phonon energy and phonon coupling constant that is modified by molecularly thin water films.This provides opportunities for further investigations and potential sensing applications.
Furthermore, we have provided statistical evidence that the low-energy spectrum can be described by three discrete resonances, which we associate with defect-bound exciton states.We could not substantiate a description of the spectrum with a density of states in combination with Fermi-Dirac statistics.Our statistical tool was proven to be a reliable way to analyze PL spectra of TMDCs and to justify the existence of different excitons.We hope that our tool will become a valuable resource for future spectroscopic studies of excitonic states in TMDCs.For this purpose, we also publish our statistical tool open source in PyPI.

Experimental Section
Sample Preparation: Our sample consisted of a large mono-and few-to multilayer MoS 2 flake that covered a large area of a fused silica substrate and a single-crystalline triangular gold flake.The single-crystalline gold flake was chemically synthesized in-house and placed on the fused silica substrate by depositing ethanol liquid containing the gold flakes.The gold flake was intentionally placed before the MoS 2 transfer to study the effect of extra electrons from the gold flake on the PL emission of the monolayer MoS 2 .Figure S4a and S15a, Supporting Information, shows the white light optical microscope image and the phase-shift interferometry (PSI) image, respectively.In the PSI, the optical path length in the material was measured, and hence, it could be used to estimate the number of atomic layers of the material. [99,100]In Figure S15a, Supporting Information, the measured optical path length values are normalized by the value of the monolayer after confirming it with our theoretical estimation.Hence, the color scale in Figure S15a, Supporting Information, corresponds to the number of atomic layers.Note that these values were only valid for up to a few atomic layers.For many layers, the material could act like a Fabry-Perot resonator and give wrong results. [100]he 2H-phase MoS 2 (n-type) crystal was purchased from HQ Graphene.The conventional exfoliation method with adhesion tapes was used to fabricate the MoS 2 monolayer from its bulk crystal form.Here, consecutive transfer of MoS 2 bulk crystal between adhesive tapes helped to thin the bulk crystal down to a few atomic layers.The adhesive tape with a thin layer of MoS 2 was then applied onto a polydimethyloxane (PDMS) foil.By using small force, one could transfer the thin layer of MoS 2 on the adhesive tape onto the PDMS foil.When the thin layer of MoS 2 was confirmed to be a monolayer, the PDMS foil was then stamped onto the target substrate to fabricate the desired sample.A separate transfer setup (not presented here) was used to transfer the monolayer precisely on top of the gold flake and the fused silica substrate.
Experimental Cryostat Setup: Figure S6, Supporting Information, illustrates the experimental setup for measuring the PL emissions of a monolayer MoS 2 flake at low temperatures.The sample was placed onto a translation and cooling stage in the cryostat, where the thermal conductivity between them was ensured by applying a small amount of thermal paste.Once the sample was ready, the cryostat was vacuum pumped and cooled down to 4 K overnight.The cooling stage could also be cooled to different temperatures, and in case of a temperature change, we allowed a few hours of settling time to achieve a stable temperature on the sample.The high numerical-aperture imaging objective was also located in the cryostat; however, it was thermally isolated from the cooling stage and the sample.A continuous wave laser at 561 nm excited the monolayer MoS 2 flake.When required, the white light source illuminated the sample to observe and find the interest area on the sample.We place a dichroic mirror (HC-R561) in the PL detection beam path to separate the excitation laser light from the PL emission.We used a long pass filter (FELH600) before coupling the PL emission into a multimode fiber to suppress the excitation laser light further.The multimode fiber is connected to the Andor spectrometer for spectral measurement.

Figure 1 .
Figure 1.Photoluminescence (PL) spectra of monolayer MoS 2 on the fused silica substrate (SiO 2 ) for different laser excitation powers and at 25 K. a) Dotted lines show the measured spectra, while the solid red lines show the full fitted curves and filled colored lines the Voigt components.b) Power law as defined in Equation (5) of the excitonic components.c) Mass action law fit (black dashed lines) to observed data (black dots) for the biexciton A XX Ã .d) Peak positions of excitonic components.

Figure 2 .
Figure 2. PL spectra of monolayer MoS 2 on SiO 2 for different temperatures.a) Low temperature PL spectra that were excited with a laser power of 145 μW at 3.6 K and with a laser power of 110 μW at 25 K. b) Temperature dependence of the PL spectra for temperatures between 65 and 295 K with a constant laser power of 250 μW.As before, dotted lines show the measurement spectra, while the solid red lines show the full fitted curves and filled colored lines the Voigt components.c) Temperature dependence of the exciton resonance energies for various exciton components with fits (dashed black lines) according to Equation (9).d) Energy separations to the ground state A exciton, where dashed black lines serve as a guide to the eye.e) Intensities of the bound excitonic bodies and the total bound excitons for different temperatures, described by a thermal dissociation process with fits (black dashed lines) using Equation(10).

Figure 3 .
Figure 3. Room-temperature PL measurement.a) PL intensity map of monolayer MoS 2 on a gold flake (Au, the bright triangle) and SiO 2 obtained with Microtime 200 confocal fluorescence microscope.b) Comparison of the monolayer MoS 2 spectra on the Au (black line) and the SiO 2 (red line).c) Spectrum of the monolayer MoS 2 on the SiO 2 .d) Spectrum of the monolayer MoS 2 on the Au.The filled curves in red, green, orange, and blue in (c) and (d) are the fitted Voigt componnts of the B 1s , A 1s , A À , and the defect exciton D. In (b-d), the dotted lines are measured values, and the solid lines are the total fitted curves which are the sum of the four Voigt functions in each case.

Table 2 .
Exciton resonance energies E, energy separations ΔE A 1s , and integral values I of the various components from the PL fitting for monolayer MoS 2 on SiO 2 and Au substrates.