Sulfur isotope engineering of exciton and lattice dynamics in MoS2 monolayers

The optoelectronic properties of two-dimensional (2D) atomically thin transition metal dichalcogenides (TMDCs) are predominantly governed by excitons and their interaction with lattice and various physical fields. Therefore, it is essential to understand the role played by excitons in the light–matter interaction processes. We introduce sulfur isotope engineering for the first time in the TMDC family, which enables us to disentangle the crucial role played by phonons in the optoelectronic properties of TMDCs. With the gradual introduction of heavier isotopes in chemical vapor deposition growth MoS2 , we discovered a systematic variation of lattice phonon energy. Consequently, the transient and steady-state spontaneous photoluminescence spectra were dramatically altered. Accordingly, the isotopically pure monolayers (MLs) show more intrinsic properties with enhanced emission efficiencies than isotopically mixed MoS2 MLs. The variation of the free exciton energies with temperature for the isotopically modified MoS2 MLs can be well described by Varshini’s equation. Along with the enormous significance for practical applications, our study provides a unique platform to understand the fundamentals of optical processes in 2D systems, where the lattice-related quasi-particles play a dominant role.


Introduction
Thin transition metal dichalcogenides (TMDCs) are flagship 2D materials for fundamental research and practical applications beyond graphene [1,2]. In TMDCs, transition metals are covalently bonded with chalcogens in trigonal prismatic coordination geometry in a layered arrangement, which induces a robust 2D confinement of charge carriers that results in unique optoelectronic/valleytronic properties of these atomically thin materials [3,4]. However, due to their ultra-thin nature, the properties of TMDCs are highly sensitive to any intrinsic and extrinsic perturbation. This extreme responsivity to external stimuli provides an additional degree of freedom for tunability via controlled manipulation of the electron band structure, as well as phonon dispersion. This manipulation can be achieved by electrostatic or chemical doping, providing uniaxial/biaxial strain, introducing lattice defects, etc [5]. Beyond the pure monolayer (ML) limit, it is possible to design van der Waals (vdW) heterostructures by vertical stacking of different MLs. These artificial vdW crystals have been shown to achieve intriguing functionalities that have never existed before [6,7].
However, despite decade-long efforts, the tunability of the electronic band structure via chemical substitution has remained at an early stage. In addition, replacing the coveted element by another introduces additional uncertainty in understanding the role of phonons and lattice disorder in the optoelectronic processes because both the number of electrons and the number of nucleons changes.
Isotopes represent a smart 'chemical' tool that can be used to engineer the physical properties of materials while keeping their chemical entity intact [8][9][10][11][12]. For instance, isotope variation in graphene can be used to enhance thermal conductivity and mechanical properties, engineer the bandgap, and tune the optical phonon modes [13,14]. Isotopic substitution in hBN MLs offers the prospect of tuning anharmonic phonon decay processes and controlling the van der Waals bonding in layered heterostructures [11,12]. Recently, Wu et al have also shown that vibrational modes vary in WSe 2 for natural and isotopically purified bulk crystals [15]. However, studies that have been conducted to explore the systematic impact of other isotopes in the vast family of 2D TMDCs are limited.
MoS 2 is one of the most extensively studied materials among 2D TMDCs [16][17][18][19][20]. Although one study shows enhanced thermal conductivity in MoS 2 ML via Mo isotope engineering [21], the optoelectronic properties are yet to be addressed.
In the present work, we studied how the sulfur isotope effect influences both the steady-state and temporal dynamics of excitons in MoS 2 ML. We used the chemical vapor deposition (CVD) method as a onestep tool to grow high quality MLs with different sulfur isotopes.
Sulfur occurs in 23 different known isotopes with atomic masses ranging from 27 to 49 [22,23]. The most stable and most abundant isotopes are 32 S and 34 S. In our work, we focused on the MLs composed of natural sulfur, isotopically pure 32 S and 34 S, and a 1:1 ratio of 32 S and 34 S. We carried out an extensive investigation of the lattice dynamics, reformed due to the isotopic abundance. We have also performed a thorough investigation of exciton formation and dynamics using temperature and timedependent photoluminescence (PL) measurements in the isotope-modified MLs. We have demonstrated that phonon scattering, exciton formation, and their lifetimes can be efficiently tuned via sulfur isotope engineering.

Synthesis of MoS 2 MLs
MoO 2 (60 mg) was placed in a quartz crucible. Silicon wafer with 300 nm of thermal SiO 2 (Microchemicals) was cleaned via subsequent sonication in deionized water, acetone, and isopropanol (Sigma-Aldrich). The wafer was placed face down on the top of the crucible, which was then inserted in the middle of a 40 cm long quartz tube with 15 mm in diameter. In the beginning, 100 mg of natural sulfur was placed in the tube 20 cm apart from the crucible, and the tube was inserted in a bigger quartz tube of length 80 cm and diameter 25 mm. The tube was connected to an argon gas line on one end and to a bubbler filled with 100 mM aqueous solution of KOH. The tube was flushed with argon for 15 minutes, and afterward part of the tube containing the crucible was heated under a constant flow of argon (120 cm 3 min −1 ) in a cylindrical furnace at a rate of 40 • C min −1 . When the temperature reached 770 • C, the tube was shifted, so the sulfur was also introduced into the furnace. After reaching 820 • C, the temperature was kept constant for 10 minutes, after which the furnace was opened and the system was allowed to cool. The process was followed for two isotopes of sulfur ( 32 S and 34 S) and natural sulfur as a reference. One more sample was synthesized by placing a mixture of 100 mg of both sulfur isotopes in the 1:1 weight ratio.

Optical/PL images and AFM
Optical and PL images of MLs were captured by an Olympus microscope. The PL images were obtained by using a green-dichroic filter under white LED light illumination. AFM images and thickness profiles were obtained using Bruker's AFM Dimension ICON system in the PeakForce Quantitative Nanomechanical Mappig mode with a Bruker silicon tip. The AFM data were processed and analyzed by Gwyddion software.

Raman and PL spectro-microscopy
Ambient Raman and PL spectral maps were recorded using a WITec Alpha300R spectrometer equipped with a piezo stage and a RayShield Coupler with laser power of 100 µW (532 nm and 633 nm) for all of the samples. All of the maps (20 × 20 µm) were scanned with 0.5 µm/line resolution using a 100 × objective. In addition, single PL spectra were recorded with laser power varying from 0.01 to 100 µW to obtain illumination intensity dependence of the PL emission.
For the tip-enhanced Raman spectroscopy, the CVD grown MoS 2 (50S) MLs were transferred on Au-coated SiO 2 /Si substrate using mechanical exfoliation and dry transfer method. The deposition of Cr (5 nm for strong adhesion) followed by Au (45 nm) on the thoroughly cleaned substrate was carried out by DC magnetron sputtering using Quorum (Q300T D) high vacuum deposition system under base and deposition pressure of about 10 −5 mbar 10 −3 mbar, respectively. The MoS 2 (50S) MLs were mechanically peeled off from the as-grown MoS 2 MLs on SiO 2 /Si substrate using soft PDMS (polydimethylsiloxane) polymer. The MLs on the polymer were then transferred onto the Au-coated SiO 2 substrate using a micro-positioning transfer arm while the substrate was heated up to 70 • C. Note that in order to distinguish Raman signature under 633 nm, PL of MLs was quenched by promoting stronger interaction to Au through annealing the sample at 100 • C for few hours.
The TERS measurements were performed using the LabRAM HR Evolution spectrometer (1800 l mm −1 grating), coupled to the OmegaScope SPM (Horiba Scientific). Omni TERS-SNC-Ag-3 AFM tips (AppNano) were used in combination with the side illumination setup and a 633 nm laser with an average power of 330 µW and an acquisition time of 1 second. The spectra were collected with an M Plan Apo 100 × objective (0.7 NA, Mitutoyo Corporation). In each point, the far field spectrum was subtracted from the spectrum obtained during the TERS measurement. The obtained data was processed with an in-house made program written in Mathematica. The position of each peak was modeled with a Lorentz function.
The temperature-dependent PL data were obtained using a low-temperature confocal Raman microscope insert (attoRAMAN, attocube) that was placed in a Physical Property Measurement System (PPMS) from Quantum Design. The PL maps were recorded down to 4 K with wavelength 532 nm and laser power 100 µW.
The PL and Raman spectral maps were analyzed using ORIGIN and a homemade routine in Matlab [24]. The individual Raman and PL modes were fitted as a sum of pseudo-Voigt functions corresponding to the contributions of the individual phonon modes and excitons. The Lorentzian component describes the intrinsic profile, while the Gaussian component is used to account for the distribution of the peak(s) parameters within the inspected area of the sample. The resulting peak parameters were used in the correlation and statistical analysis.

Time-resolved PL
Time-resolved PL (TRPL) mapping were performed on an Olympus FluoView1000 confocal microscope integrated with a PMT detector (tau-SPAD, Picoquant) of sub-nanosecond TCSPC capability (HydraHarp 400, Picoquant) with 2.33 eV pulsed laser excitation at a laser power of 25 µW, frequency 1 MHz, and a pulse duration of 50 ps. The photon arrival times with respect to the previous laser pulse were stored for each photon event, using ultra-fast electronics in a time-tagged TR recording mode. For spatially resolved lifetime measurement, the fluorescence lifetime imaging microscopy (FLIM) images were acquired by a fast-FLIM approach, in which every given pixel resembles the average arrival time of the emitted photons. Finally, the TR emission spectra (TRES) and excited state carrier lifetime were obtained at the region of interest (on the MoS 2 flake) using an iterative reconvolution process with PicoQuant Fluofit software to a multiexponential function convoluted with the experimental instrument response function (IRF).

Transmission electron microscopy (TEM)
The CVD-grown MLs were exfoliated from SiO 2 /Si substrate using poly-dimethylsiloxane (PDMS) and then were transferred onto gold coated single hole grid by a semi-robotic transfer apparatus in the glove box. The TEM images were obtained using Ultra High Resolution Transmission Electron Microscope JEM-2100Plus operating between 100 and 200 kV.

Results and discussion
A series of samples with different sulfur isotopes, containing high quality MLs MoS 2 were grown by CVD. Depending on the isotope abundance, the samples were labeled as follows: natural sulfur [MoS 2 (NS)], pure 32 figure S1). The thickness of the MLs is found to be comparable and is estimated about 0.7 nm using AFM, as shown in figures 1(e) and (f) for the case of MoS 2 ( 34 S).
Further characterization of the MLs was carried out using the Raman spectroscopy, which is a wellestablished tool to investigate 2D materials, including the TMDCs [25]. Figure 2(a) shows the Raman spectra for all of the isotope-modified MLs with 532 nm laser. The most pronounced peaks in the Raman spectra that characterize the MoS 2 MLs with natural sulfur are located around 405 and 384 cm −1 . They are associated with the in-plane mode (E ′ ) that arises due to contrasting vibration of two S atoms with respect to Mo atom and the out-of-plane mode (A ′ 1 ) that is associated with the vibration of S atoms in opposite direction [17]. The corresponding histograms and values of the Raman shifts of the in-plane (E ′ ) and out-of-plane (A ′ 1 ) modes are given in figure  S2, which more clearly depicts the change occurring in the Raman shifts of MLs with different isotope content.
It is observed that the Raman spectrum of the pure MoS 2 ( 34 S) shows a significant redshift of the Raman modes with respect to MoS 2 ( 32 S), as expected due to the difference in the sulfur atoms' mass. Additionally, a gradual redshift is observed with the increasing amount of ( 34 S) isotope in pure MoS 2 ( 32 S). It should be noted that natural sulfur constitutes about 95% of 32 S, 4.25% of 34 S and 0.75% of 33 S. Therefore, MoS 2 (NS) ML shows similar Raman spectrum with less significant red shift of the principal Raman modes compared to MoS 2 ( 32 S). On the other hand, both the Raman modes E ′ and A ′ 1 for MoS 2 (50S) are significantly red shifted and lie around 381 cm −1 and 397 cm −1 , respectively, which reflects that the ML equally constitutes both 32 S and 34 S. This redshift becomes more prominent in pure MoS 2 ( 34 S) as the concentration of 34 S is increased, hence E ′ and A ′ 1 modes move towards lower frequencies at ∼377 cm −1 and ∼393 cm −1 , respectively. This shift of about 7 cm −1 for E ′ corresponds to ∼0.87 meV and 12 cm −1 for A ′ 1 to 1.48 meV. The Raman frequency depends inversely on the square root of effective mass. Therefore, as effective mass increases on introducing 34 S, both the Raman peaks shift towards lower frequencies comparing to the MoS 2 (NS). This is depicted clearly in figure 2(b), which shows the Raman shift as a function of square root effective mass, µ eff of Mo-32 S x 34 S y , where x and y are relative concentration of 32 S and 34 S, respectively. It can be noted that the redshift is more pronounced for the out-of-plane mode; i.e. A ′ 1 . This effect can be qualitatively understood when considering the contribution of the Mo and S atoms to the particular vibrational mode. The out-of-plane modes correspond to the displacement of the S atoms only, while the in-plane modes are a result of both the S and Mo motion [17]. Therefore, the Raman shift of the A ′ 1 mode has much stronger dependence on the sulfur isotope occurrence.
Separation of the Raman shifts, δk between the E ′ and A ′ 1 modes is typically used to estimate the number of layers and crystalline quality of the sample [26]. The measured value of δk for MoS 2 ( 32 S) and MoS 2 (NS) is about 21 cm −1 , which is in the range of the typically reported values for CVD-grown MLs with natural sulfur [26]. Meanwhile, the δk ∼16 cm −1 for MoS 2 ( 34 S) is close to the value reported for the exfoliated MoS 2 ML, which tentatively suggests a superior crystalline quality of MoS 2 ( 34 S) due to the negligible isotopic disorder compared to isotopicallymixed samples [26]. However, for MoS 2 (50S), the δk value corresponds to ∼16 cm −1 , which is somewhat outside the expected range. Therefore, the use of the δk values as a simple measure of the 'lattice order' is not so relevant in this case which is also implicated by the non-linear behavior of the Raman shift with isotope atomic concentration (table 1).
It is important to stress that the lattice disorder results from a complex interplay of preparation procedure, post-treatment, and sample aging, and various defects (sulfur or molybdenum vacancies, line defects, etc) occur [27]. Changing the isotope abundance homogeneously within the lattice does not inevitably create any extra disorder. Therefore, the dominant source of lattice disorder in the MoS 2 (50S) sample is most likely the isotope disorder, while the growth-related effects dominate in the other samples. To address this ambiguity, we have performed additional analysis of the Raman modes considering large number of the spectra collected over the flakes. Figure 3 shows a relative comparison in the Raman maps of all the samples depicting the spread of peak width; i.e. full width at half maximum (FWHM) for both E ′ and A ′ 1 . It has been shown that A ′ 1 is sensitive to the lattice disorder, which is reflected as the change in shape and FWHM of the peak [28,29]. We observed the FWHM of the A ′ 1 is uniform over the flakes with the value of 3.9 ± 0.3 cm −1 and 3.4 ± 0.5 cm −1 for MoS 2 ( 32 S) and MoS 2 ( 34 S), respectively. This result suggests that both MLs reveal a very similar morphology and disorder, despite carrying a different sulfur isotope. The appearance of the dark blue region in the case of MoS 2 ( 34 S) in A ′ 1 mode is due to the formation of bilayers, which can be indicated as tiny triangles in the center of the ML.
In the case of MoS 2 (NS), FWHM of A ′ 1 is increased to 4.8 ± 0.4 cm −1 , corresponding to a moderate enhancement of the isotope disorder, due to the ∼5% abundance of the 34 S giving rise to the isotope inhomogeneity in the natural sulfur. This scenario is further supported with increase of the A ′ 1 's FWHM to 7.3 ± 0.6 cm −1 in the MoS 2 (50S), which features a further increase of the lattice disorder. These results clearly point to the high sensitivity of the A ′ 1 mode's width (FWHM) to the lattice disorder, which is introduced via varying the isotope ratios. However, it is observed that the FWHM of the E ′ mode remains unchanged, reaching 4-5 cm −1 for all the samples. This observation is in line with expectations because the in-plane mode comprising the S and Mo atoms is much less sensitive to the sulfur atomic mass.
The phonon scattering processes in 2D materials can also be inferred by the phonon lifetime which can be estimated from the peak width, i.e. the FWHM of the respective Raman peak using the relation, τ ph = h/(2πΓ), where τ is the phonon lifetime, h is the Planck constant, and Γ is the FWHM. The phonon lifetimes of the E ′ and A ′ 1 phonons are summarized in the table 1. The phonon lifetimes are influenced by the crystalline quality of the material and the isotope purity (disorder). This is clearly reflected in the resulting lifetimes derived for the A ′ 1 mode, where isotopically pure MLs exhibit longer phonon lifetime as compared to MoS 2 (NS) and MoS 2 (50S).
In our study, the Raman shift in different samples with different proportion of sulfur isotope is predominantly attributed to the relative change in the phonon modes due to effective mass of Mo-S; however, it is well-known that strain also induces a moderate phonon-related frequency shift in 2D TMDCs [27,30,31]. To disentangle the effect of the strain, the Raman correlation analysis can be used to quantify the spread of the relative strain and doping levels within the flakes of the MoS 2 MLs [32]. A Raman correlation plot can be constructed from the Raman shifts of the A ′ 1 and E ′ modes, as shown in figure 4. The axes for the doping (n) and strain (ε) are defined following the approach developed by Michail et al [32]. Because the unstrained and undoped sample is an immaterial situation, the zero strain/doping frequencies cannot be known exactly. Therefore, the origin of nε axes (depicted as a grey cursor in the crossing of the iso-strain and iso-doping lines) is premeditated at the mean frequencies obtained for the exfoliated MoS 2 ML at A ′ 1 = 405.3 cm −1 and E ′ = 383.6 cm −1 ), respectively [32].
From the spread of the respective clouds in the correlation plot corresponding to the MoS 2 samples with different isotope abundance, one can estimate the variation in strain and doping levels within the corresponding flake. It can be seen that for MoS 2 ( 32 S), MoS 2 (NS) and MoS 2 ( 34 S), the strain and doping level varies by 0.2%-0.3% and 0.5 ×10 13 cm −2 , respectively, within the flakes. For MoS 2 (50S), the variation in strain is slightly below 0.2% while the doping level varies by almost 1.0×10 13 cm −2 within the flake.
The results of the correlation analysis can be understood as follows. The isotopically pure MLs have a low degree of lattice disorder, which results in the similar distribution of the doping and strain within the flake reflected by a very similar cloud shape. The clouds extend mostly along the iso-doping lines. If a linear approximation is considered for shift of the center of the distribution due to the isotope variation (yellow solid line), then the correlation cloud for MoS 2 (50S) appears to be shifted slightly to the higher doping levels but lower strain. Meanwhile, the cloud clearly extends along the strain line suggesting a prevailing contribution of the strain. This observation just corroborates the important effect of the isotope substitution on the lattice disorder in the MoS 2 (50S) sample revealed by the large FWHM of the A ′ 1 because the variation of the sulfur atomic mass brings inhomogeneity in the lattice dynamics.   In order to extract the details of structural and defect information in the mixed phase ML, i.e. MoS 2 (50S), the samples were also analyzed with the 633 nm laser, to obtain resonant Raman spectra, which are shown in figure 5(a). Six peaks were identified in the measured range, namely peak 'a' which is assigned to the second-order transverse acoustic mode at the K high symmetry point in the Brillouin zone (BZ), 2TA (K), E ′ , A ′ 1 , peak 'c' which is assigned to the combination of the longitudinal   [33][34][35]. Similarly, to the measurements with the 532 nm laser, the peaks downshift with an increase in the 34 S atomic concentration, with the largest shift observed for the A ′ 1 peak, (see table 2). The E' mode downshifts as well but becomes inseparable from the 'a' peak in the 34 S sample. The 'a' peak is the only peak that does not shift with the atomic concentration of 34 S.
To elucidate the distribution of different isotopes in the MoS 2 (50S) sample on the nanoscale, a TERS map was performed over a 300 × 300 nm 2 area with a 10 nm step size. Typical TERS spectra are presented in figure 5(b). The out-of-plane modes have higher intensity than the in-plane modes when compared with the far field spectra, due to the perpendicular polarization of the laser light with respect to the surface [36]. The A ′ 1 peak position histogram in figure 5(c) clearly shows that the variation of the peak is low, indicating a homogeneous distribution of the sulfur isotopes. The A ′ 1 peak position map in figure 5(d) confirms this, as there are no obvious areas with specific peak position. The MoS 2 (50S) sample is thus homogenous in isotope distribution down to 10 nm in lateral size. However, there is some variation in the position of the other peaks present in the spectra in figure 5(b). This can be ascribed to strain variation present in the sample. When MoS 2 interacts with gold, the strain increases due to the lattice mismatch between the two materials, which is reflected in the downshift of the E ′ mode [35,37].
In our case, the MoS 2 surface was not completely flat, but bubbles formed due to the transfer process, as it is seen on the topography image in figure S3(a). By comparing the topography image with the peak positions of the E ′ , 'c' peak, and 2LA(M) mode (figures S3b-S3d), a strong correlation is observed. All of the presented peaks upshift on the bubbles due to strain relaxation as the MoS 2 interacts weakly with gold [37,38]. The weak MoS 2 /Au interaction can be also seen in the 2LA(M) peak amplitude, as the amplitude is lower on the bubbles due to a weaker interaction between the TERS tip and Au substrate plasmons ( figure S3(e)). The maximum calculated strain difference, determined from the largest E ′ peak shift, is approximately 0.8% [37]. This translates to a peak shift of 1 cm −1 for the A ′ 1 mode, which is within the peak position variation ( figure 5(c)). Supplementary TEM images of MoS 2 ( 32 S) and MoS 2 (50S) MLs are also presented in supplementary information ( figure S4).
In the next step, we focused on the isotope effect in PL as the strong PL in the visible range is a characteristic feature of the TMDCs MLs due to the direct band gap transition. A schematic illustration of PL emission from isotope engineered MoS 2 MLs is shown in figure S5(a) at incident excitation of 532 nm and 20 µW intensity, while keeping all of the experimental parameters identical. The present PL spectra were measured within the region between center and edge of the triangular flake to avoid the edge effects and the effect of the impurities at the nucleation centre of the flake [27]. It can be seen that isotopically pure MoS 2 ( 32 S) and MoS 2 ( 34 S) along with MoS 2 (NS) emit very strongly when compared to the isotopically mixed MoS 2 (50S). The PL intensity of the MoS 2 (50S) is decreased almost by an order of magnitude compared to the other samples. This observation suggests unambiguously that isotopically pure 2D materials with suppressed lattice disorder reveal superior optical properties. This hypothesis is corroborated by the Raman spectra analysis, as discussed above.
Though MoS 2 (NS) is also an isotopically mixed sample, a threshold ratio may exist where the disorder becomes significant to suppress the PL emission. For that purpose, excitation power dependence was measured; the results are shown in figure S5(b). At a certain threshold power, the ML becomes trap-free and intensity starts increasing, which is clearly apparent in the semi-log scale. For MoS 2 ( 32 S), MoS 2 ( 34 S) and MoS 2 (NS), the threshold excitation power is about 0.2 µW while for the MoS 2 (50S), this value is about 5 µW. These experiments confirm that the isotopically mixed MoS 2 (50S) sample carries substantial amount of the deep traps due to the relatively high lattice disorder manifested by increased amount of defects.
Let us now discuss the excited quasi-particles behind the optical processes in more detail. The optical properties of TMDCs are governed by the formation of tightly bound exciton species of binding energy of several hundred meVs, which make them stable at room temperature [39,40]. A schematic view of the different neutral and charged exciton in MoS 2 MLs is presented in figure 6(a). When the ML is illuminated, free electrons and holes are generated in the valley of the direct bandgap, and subsequently settle down on to extreme edge of the conduction and valence band separately to form the exciton [16]. The typically observed exciton species in the MoS 2 MLs at room temperature are A exciton (X 0 ), B exciton (X B ), free trion (X − ), biexciton (XX), and so on [41]. The energy separation between the A and B excitons emerges due to the spin-orbit coupling activated split in the valence band at K-point in the Brillioun zone. The free trion is represented by two electrons in conduction band and one hole in the valence band. In a pristine MoS 2 ML, the typical energies of the X − , X 0 and X B are 1.82, 1.84 and 1.97 eV, respectively.
To get a deeper insight to the excitonic processes, the respective PL spectra of the different MoS 2 MLs at 100 µW were deconvoluted using Pseudo-Voigt (PsdVoigt) profile function to resolve the contribution from the different exciton species, as shown in figures 6(b)-(e) for the MoS 2 (NS), MoS 2 ( 32 S), MoS 2 ( 34 S) and MoS 2 (50S), respectively. Figure S6 shows maps of integrated PL intensity of the triangular ML crystals obtained at around the A exciton energy. It is clear that the spatial distribution of the PL intensity across the flake is mostly uniform, except at the edges and corners, which are more luminescent than the central region due to defect-induced PL emission [27].
It has been demonstrated previously that the X 0 /X − intensity ratio (α) can be tuned by chemical doping or via dielectric screening, which can tune the excitonic lifetime and also provide an approach to selectively generate exciton or trion for optoelectronic and valleytronic applications [42,43]. Multiple intrinsic and extrinsic perturbations (including defects, substrate doping, photoinduced charges, etc.) may contribute with extra electrons to the formation of trions [44,45].
In the present study, we also discovered the variability of α via isotope engineering. To suppress the photoexcitation effects on the trion formation, we have performed the experiment at very lower excitation power, as shown in figure S7.
For MoS 2 ( 32 S) the α is found to be ∼4.0 (estimated from figure 6, which suggests a very low contribution from the negative trions. In MoS 2 (NS), the α reaches ∼4.5 suggesting presence of crystalline impurities that assist formation of the negatively charged trions. This can be attributed to the fact that a small amount of the 34 S and 33 S may still induce lattice deformations that cause such perturbations and also the growth-induced lattice perturbations. However, the α value for the MoS 2 ( 34 S) is about ∼2.8. This significantly lower value can be explained by the reduction of phonon energy that indirectly contributes to the trion binding energy at around the room temperature. Also, the higher doping correlates with the higher amount of the negatively charged trions. Note that the strain and doping also play an important role in the trion formation. The isotopically-mixed MoS 2 (50S) shows α ∼2.0 which can be attributed to the combined effect of the induced crystalline strain, phonon energy and lattice defects. It should be also noted that the B exciton-related emission (X B1 and X B2 ) is found to be enhanced only in case of MoS 2 (50S), while for other samples it remains almost negligible. This observation is also in agreement with the expectation that the lattice disorder enhances the B exciton formation.
Moreover, the formation of the trions in the isotopically mixed samples can also be correlated to the shorter phonon scattering lifetime, as discussed above. Interestingly, we have also observed a signature of biexciton in MoS 2 ( 34 S) and MoS 2 (50S). Though the formation and identification of the biexcitons are not common [46], our study shows that the formation of biexcitons can be promoted by the 34 S.
To further investigate the role of phonon scattering and defects, temperature dependent PL measurements were performed on MoS 2 ( 32 S) and MoS 2 ( 34 S), as shown in figures 7(a) and (b), respectively. Two distinct PL peaks attributed to the free exciton H and the defect generated bound exciton D arise at low temperature towards low energies [47]. For both the samples, H is found to shift towards higher energies at lower temperatures, due to the bandgap renormalization. The peak width of H in MoS 2 ( 32 S) is found to slightly broaden on cooling, which can be related to the trion emission enhancement, due to strong suppression of the phonon population. However, this effect is not prominent in case of MoS 2 ( 34 S) because the significant trion-related emission was already present in the system at room temperature. Figures 7(c) and (d) show the quantification of spectral shift of free exciton peak H as a function of temperature for MoS 2 ( 32 S) and MoS 2 ( 34 S), respectively. The plot is fitted with Varshini equation [48]: which expresses the temperature dependence of the bandgap, E g for different semiconductors. The estimated parameters obtained for the MoS 2 ( 32 S) and MoS 2 ( 34 S) are E g (0) = 1.87 eV, α = 2.9×10 −4 eV K −1 , and β = 230 K and E g (0) = 1.89(2) eV, α = 9.3×10 −4 eV K −1 , and β = 1140 K, respectively. The values are consistent with the previously reported study [48].
The D exciton-related emission is strongly temperature and isotope dependent. At higher temperatures, the D fingerprint is absent in the PL spectra because the strong electron-phonon scattering induces a non-radiative decay channel for such emission. Interestingly, the onset of the radiative emission due to the D exciton appears at around 80 K for MoS 2 ( 32 S) and around 120 K for MoS 2 ( 34 S) due to the suppression of the phonon population. The different threshold temperature observed for the D-related emission in isotopically different samples can be understood as the isotope-induced phonon energy variation. As the phonon energy for MoS 2 ( 34 S) is lower, we observed a higher threshold temperature for the non-radiative-radiative crossover of the D emission.
Below 10 K, the D emission becomes more intense and surpasses the H in the MoS 2 ( 34 S) ML. However, D remains moderate compared to the free exciton in the case of MoS 2 ( 32 S), even at 4 K. This result also suggests relatively a lower presence of the structural defects in MoS 2 ( 32 S), which is in correspondence with the previous experiments.
Usually, the lower energy peak D emerges due to radiative recombination of the bound excitons (deep level defect states) restrained to the neutral excitons [48]. These low energy bound exciton, whose energy is lowered by the binding to the defects, which can arise due to impurities at the interface, sample surface, or sulfur vacancies. Therefore, the strong emergence of the D-related peak in the MoS 2 ( 34 S) at low temperature can be associated with the presence of more impurity levels in comparison to the MoS 2 ( 32 S). In both the samples, the width of this defect peak is observed to be quite large ∼0.1 eV, which indicates the availability of different defect levels for the recombination of the excitons.
Further, we also measured the temperature dependent PL of MoS 2 (50S) as shown in figure S8(a). It can be seen that D peak is slightly enhanced as compared to MoS 2 ( 32 S), but appears on the shoulder of H which shifts insignificantly with temperature due to presence of strong B excition. Figure S8(b) shows the temperature dependence of bandgap estimated from position of H peak and its fitting analysis with different models as Varshini model could not be fit In general, the temperature dependence of the bandgap is usually driven by the lattice dilatation and electron-phonon interaction, which are significantly altered in isotopically mixed MoS 2 (50S) ML due to contribution of two randomly distributed atomic species ( 32 S and 34 S). Thus, we extended the analysis of the experimental data by applying other models, which have already been employed for other 2D semiconductors [49]: Bose-Einstein, Double Bose-Einstein, and Manoogian-Leclerc (the corresponding formulas, results and plots of the fits (figure S8) are summarized in the supplementary information). It can be seen that neither Varshini nor Bose-Einstein model revealed a sufficient agreement with the experimental data. However, Double Bose-Einstein and Manoogian-Leclerc models describe the experimental data at the whole temperature scale.
Finally, we focused on the transient decay dynamics of the excited state carriers in the MLs, as shown in figure 8(a). The obtained TRPL spectra of both isotopically pure samples, MoS 2 ( 32 S) and MoS 2 ( 34 S) show a slower decay process than those of the MoS 2 (50S) and MoS 2 (NS). For a more detailed understanding, we deconvoluted the spectra with the instrument response function (IRF) and triexponential decay function.
The obtained lifetimes are summarized in table 3 and the lifetime distributions over the flake for all samples are shown in figures 8(b)-(e). Interestingly, we observed that both of the isotopically pure MLs exhibit a similar character of the TRPL. Both MLs revealed two faster decay channels, τ 1 , and τ 2 : ∼0.7 ns and ∼2.10 ns, respectively. However, the pure MoS 2 ( 34 S) ML maintains a much faster third decay channel (τ 3 ), which can be correlated to the combined effects of the defects in the lattice and strain induced by the heavier isotope [43,50,51]. Due to the higher dynamic lattice disorder in the isotopically mixed samples, the first two decay pathways become relatively slower compared to the isotopically pure samples (see table 3).
Because the MoS 2 (NS) contains ∼95% of ( 32 S), the slower decay channel closely resembles the decay channel of the pure MoS 2 ( 32 S). In contrast, the relatively faster τ 3 channel of the MoS 2 (50S) can be attributed to the enhanced phonon scattering due to the lattice strain, as observed in the correlation analysis of the Raman modes (figure 4) [52,53].

Conclusions
We have demonstrated that the controlled variation of the sulfur isotopes in MoS 2 MLs causes significant changes of the lattice dynamics and optoelectronic properties. The characteristic phonon frequencies observed by the Raman spectroscopy scale with the √ µ eff were as expected. The changes are more evident for the out-of-plane A ′ 1 phonon mode, which originates purely from the motion of the S atoms. TERS measurement reveal that both the isotopes are homogenously distributed in the mixed phase MoS 2 (50S). We observed that in the isotopically pure layers, nonradiative decay pathways are suppressed for the lighter isotopes, whereas the presence of the heavier isotopes induces lattice strain and electrostatic doping, supporting faster radiative decay pathways and trion emission. In the natural and (most importantly) in the isotopically mixed MoS 2 MLs, the larger lattice inhomogeneity due to the isotopic disorder dramatically influences the phonon dynamics and light-matter interaction processes. Our study thus proposes a novel direction towards the manipulation of optoelectronic properties in TMDCs, and related vdW and mixed dimensional heterostructures, while keeping the chemical properties of the TMDCs intact. Our findings point to the importance and experimental feasibility of studying the isotope effects in TMDCs and other 2D materials with respect to other emerging phenomena, such as superconductivity, exotic magnetism, thermoelectricity, and so on.

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.