Influence of Rhenium Concentration on Charge Doping and Defect Formation in MoS2

Substitutionally doped transition metal dichalcogenides (TMDs) are the next step towards realizing TMD-based field effect transistors, sensors, and quantum photonic devices. Here, we report on the influence of Re concentration on charge doping and defect formation in MoS2 monolayers grown by metal-organic chemical vapor deposition. Re-MoS2 films can exhibit reduced sulfur-site defects; however, as the Re concentration approaches 2 atom%, there is significant clustering of Re in the MoS2. Ab Initio calculations indicate that the transition from isolated Re atoms to Re clusters increases the ionization energy of Re dopants, thereby reducing Re-doping efficacy. Using photoluminescence spectroscopy, we show that Re dopant clustering creates defect states that trap photogenerated excitons within the MoS2 lattice. These results provide insight into how the local concentration of metal dopants affect carrier density, defect formation, and exciton recombination in TMDs, which can aid the development of future TMD-based devices with improved electronic and photonic properties.


Introduction
Monolayer transition metal dichalcogenide (TMD) semiconductors such as MoS2 are appealing candidates for next-generation optoelectronic devices due to their direct bandgap, 1 large surface area to volume ratio, 2 stable excitons at room temperature, 3 and high carrier mobilities. 4,5  future use of TMDs in transistor, light emitting diode, and quantum photonic applications requires the ability to tune the electronic and photonic properties of TMDs using controlled doping methods. 6Efforts to understand and control doping in TMDs focus on the influence of substrates, 7- 9 interactions with adsorbed molecular species, [10][11][12][13] and the substitutional doping of foreign atoms at TMD metal or chalcogen sites. 14,15 f these approaches, substitutional metal doping offers the most viable means of incorporating stable dopants into the TMD lattice. 16][21][22] However, TMDs synthesized using these methods often exhibit nonuniform dopant concentrations and poor spatial uniformity. 22,23 dditionally, the ionization energy of dopants in two-dimensional (2D) materials is higher than their bulk analogs due to quantum confinement effects and reduced dielectric screening at the monolayer level. 18,24 ][27] Dopant clustering and dopant-dopant interactions are expected to be prevalent when the concentration of metal dopants reaches the levels identified to enable carrier doping of TMDs. 17,28,29 I1][32] However, the impact of local dopant concentration on the structural and optoelectronic properties of substitutionally doped TMD monolayers remains an open area of research.
Uniform, electronic-grade TMDs with controlled dopant densities were recently synthesized from gas phase precursors using metal-organic chemical vapor deposition (MOCVD). 33,34 n particular, MOCVD grown single-layer MoS2 films doped with 0.05 to 1.0 atom% Re atoms 35 were shown to reduce the density of sulfur vacancy defects due to favorable dopant-defect interactions at the growth front of MoS2 grains during growth. 35Additionally, ReMo in the negative, neutral, and positive charge state could be stabilized due to the closely-space donor state manifold. 36The reduction of sulfur vacancy density and increased electron density following Re doping helped to improve electron transport in back gated field-effect transistors and reduce emission from defect states within Re-MoS2. 35 this work, we demonstrate that local concentration variations of Re dopants can have a pronounced effect on charge doping and defect formation in MoS2.Verified by X-ray photoelectron spectroscopy (XPS) and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS), we demonstrate that MOCVD enables controllable introduction of low (⪅ 1 atom%) to high (⪆ 1 atom%) Re concentrations in MoS2 monolayers.Z-contrast scanning transmission electron microscopy (Z-STEM) measurements reveal that Re doping reduces the density of sulfur-site defects in MoS2 over a range of dopant concentrations up to 6 atom%.However, valance band maximum (VBM), Raman, and photoluminescence (PL) measurements demonstrate that Re-MoS2 films doped with high concentrations of Re atoms exhibit reduced ntype doping, increased strain, and broad sub-bandgap emission from Re-based defect states.Using a combination of scanning tunneling microscopy (STM) and ab initio calculations, we show that Re clustering at high dopant concentrations is responsible for the observed behavior.

Results and Discussion
4][35] This process utilizes separate nucleation, ripening, and lateral growth stages to produce coalesced, monolayer MoS2 films (Figure S1). 35,37 e dopants are incorporated into the MoS2 lattice by flowing Re2(CO)10 during the growth process via a mass flow controller.
The relationship between Re concentration and Re2(CO)10 flow rate is highlighted in Figure S2.
The Re concentration (Figure S2) is obtained by XPS measurements of Re 4f7/2 and Re 4f5/2 peaks and LA-ICPMS (Figure S2).These results demonstrate that the MOCVD process can systematically tune the average Re concentration in MoS2 from low to high doping percentages, where we define the boundary of low-to-high concentration as 1 atom%.
Rhenium doping impacts the structural properties of MoS2.This is evident when comparing Z-STEM images (Figure 1a-c and Figure S3) of undoped, 1.4, and 6 atom% Re-MoS2 films.
Analysis of the Z-STEM images reveals reduced sulfur vacancies (yellow circles) and double sulfur vacancies (red circles) in Re-MoS2 films (Figures 1a-c).We acknowledge that the sulfur vacancies observed in our Z-STEM images may be filled with oxygen or carbohydrate species, 35,[38][39][40][41] therefore, we refer to these vacancies generally as sulfur-site defects.Sulfur-site defect reduction has been reported previously in MoS2 films doped with dilute amounts of Re (≤ 1 atom%).This defect reduction is attributed to Re atoms increasing the formation energy of sulfur vacancies at the growth front of MoS2 grains. 35The Z-STEM images shown in Figure 1 highlight that these favorable dopant-defect interactions persist at higher doping concentrations up to 6 atom%.However, while the 1.4 atom% film exhibits isolated Re dopants, the 6 atom% Re-MoS2 film exhibits non-uniform Re dopant clustering.The circled regions in the STEM image (Figure 1c) highlight this clustering.More examples of regular clustering patterns are discussed later in STM measurements.Furthermore, at 10 atom% doping levels, we observe Re dopant aggregation into ~3 nm phase-segregated domains whose crystal structure closely resembles that of ReS2 (Figure S4). 42e Re dopant concentration modifies charge carrier doping within Re-MoS2 monolayers.
Analysis of the electron binding energy at the XPS measured valance band maximum (VBM) provides direct evidence of n-type doping due to Re incorporation. 21The VBM edges of undoped, < 1 atom%, and 6 atom% Re-MoS2 films are shown in Figure 1d.Evaluation of the VBM positions shows that only Re-MoS2 films doped with low concentrations of Re atoms (<1 atom%) exhibit a VBM shift consistent with n-type doping. 21,35 onversely, samples doped with 6 atom% Re do not exhibit a shift in VBM position relative to undoped MoS2, indicating a lack of n-type doping from Re atoms in highly doped films.Raman measurements correlate well with reduced n-type doping and increased strain in highly doped Re-MoS2 films.The Raman spectra of undoped, 0.1, 1.4, and 6 atom% Re-MoS2 films collected following 532 nm excitation are shown in Figure 1e.
The spectra exhibit characteristic in-plane ( ` ~ 385 cm -1 ) and out-of-plane ( 1 ` ~ 405 cm -1 ) vibrational modes for monolayer MoS2. 7,43 he vibrational feature at ~417 cm -1 is due to the underlying sapphire substrate.][46][47] For MoS2, the relationship between biaxial strain (ε), charge doping, and  `and  1 ` peak positions is given by, 7 ∆  = −2γ   0  ε +     (Eqn. 1) where  0  and  0  are the frequencies of the MoS2  ` and  1 ` modes in the absence of strain and doping, γ  and γ  are Grüneisen parameters equal to 0.86 and 0.15 for the  `and  1 ` modes, 45  is electron concentration in units of 10 13 cm -2 , and    and    describe how charge doping shifts the  ` and  1 ` modes according to, 7    = −0.33The local concentration of Re atoms influences their charge state in Re-MoS2.On QFEG, STM measurements (Figure 2) reveal ReMo substitutional dopants in the neutral and positive charge state, as identified previously. 36We find that Re dopants in samples with an average doping level of 8 atom% tend to segregate into domains of high (~10 atom%) and low (~3 atom%) concentrations with abrupt transition regions as shown in Figure 2c,d.We suspect that the growth kinetics governs the formation of these domains, where the slower growth front accumulates more Re dopants (see model in Figure 2b).Additionally, Re dopant distributions may be affected by the edge terminations of Re-MoS2 domains during the growth process. 48Analyzing the charge state distribution, we find twice as many ionized dopants in low-density areas (Figure 2e Density functional theory (DFT) modeling reveals an increased Re dopant ionization energy at small Re-Re separations (Figure 3).Dopants in conventional semiconductors, such as phosphorus donors in silicon, are slightly repulsive, as reflected in a +0.05 eV pairing energy 50 (unless exposed near the surface in a nanowire environment). 51However, for the case of Re in monolayer MoS2, we estimate a Re-Re pairing energy of at least -0.44 eV, i.e., strongly attractive.
The strong stabilization of a Re-Re dopant pair is related to strong local distortions.When separated, each Re dopant contributes to a spin-polarized dopant level near the conduction band edge.Following the effective mass approximation, each occupied dopant state can be described by a 2D hydrogenic wavefunction envelope centered on a Re atom consisting of   2 orbitals inherited from the MoS2 conduction band edge at the K point.When two Re dopants are one lattice constant apart, and each held at a high-symmetry C3v configuration before relaxation,   2 orbital contributions persist.Since Re dopant ionization energies are on the order of 0.05-0.1 eV 52 for bulk MoS2 and 0.2 eV for monolayers, 53 we expect the stabilization energy of the Re-Re pair without relaxation to be much smaller.Indeed, DFT calculations yield a Re-Re pairing energy of only 0.03 eV for this configuration.However, relaxing the Re pair (Figure 3c) results in a pseudo Jahn-Teller distortion similar to a previous report on isolated Re (Figures 3d   and S7), where a significant   2 − 2 and dxy mix into the occupied dopant level.The mixing results in the relaxed (distorted) Re pair becoming a deep-level defect, and the effective mass approximation is no longer applicable.The strong Re pair attraction suggests Re-doping MoS2 may be unique from n-doping of conventional semiconductors, with donor deactivation caused by Re cluster formation manifesting at < 1% dopant concentrations.
A finite binding energy alone does not guarantee dimer formation since dimerization disfavors configurational entropy.That is, Re-Re dimer formation is only thermodynamically favored when Re-Re attraction (0.44 eV) is stronger than the defect formation energy of an isolated Re atom in the MoS2 lattice. 54Although evaluating Re dopant formation energies from firstprinciples requires a Re chemical potential, which is in general unknown, we can estimate the Re dopant formation energy (E f ) from the experimentally observed Re concentration c = 10% using  =  −  / .Assuming a growth temperature of T = 1200 K, we estimate a E f of 0.25 eV, weaker than Re-Re attraction.Thus, we conclude that Re dimer formation is moderately favored in the MoS2 lattice at the growth temperature.We next evaluate whether forming larger Re clusters is  55 Therefore, the reduced intensity of the 0.1 atom% film's emission spectrum compared to undoped MoS2 is due to enhanced trion formation in the former.We fit the spectra with two pseudo-Voigt curves centered at ~1.86 and 1.90 eV to determine the contribution of trions (red dashed line) and neutral Aexcitons (blue dashed line) to the overall emission. 11,35 rom the intensity ratio of the trion and Aexciton peaks, the electron densities of undoped and 0.1 atom% Re-MoS2 films were found to be ~5.0•10 12 and 1.2•10 13 e -/cm -2 , respectively, using a mass action model (See Supporting Information). 35The ~7.0•10 12 e -/cm -2 increase in electron density obtained from PL measurements following dilute, 0.1 atom% Re doping is consistent with our Raman and VBM measurements (Figure 1 For simplicity, the states that give rise to the ~1.75 eV emission band will be referred to as a Re-based defect.The reduced intensity of the 3.6 atom% film's emission spectra compared to undoped MoS2 suggests that the clustering of Re atoms creates defect states that quench emission in highly doped Re-MoS2 films.We note that the overlap between Re-based defect, trion, and A-exciton emission peaks in the PL spectrum of the 3.6 atom% film prevents us from accurately determining carrier densities from the PL spectrum as was done for the undoped and 0.1 atom% Re-MoS2 films.However, the sharpening of the 3.6 atom% sample's emission peak around 1.9 eV compared to the 0.1 atom% film suggests reduced trion formation in the former, in agreement with our VBM and Raman measurements.However, unlike the 0.1 atom% sample, the PL decay trace of the 3.6 atom% Re-MoS2 film exhibits a long-lived emission tail at time delays > 500 ps.We conclude that this emission tail does not originate from sulfur-site defects as in the undoped analog because of the marked reduction of sulfur-site defects in the highly doped sample (Figures 1c & S3).Instead, long-lived emission in the 3.6 atom% film is due to exciton trapping at Re-based defects.Spectrally resolved PL measurements of the 3.6 atom% Re sample support this conclusion (Figure 5b).Namely, the data show that excitons trapped in Re-based defect states (1.7-1.75 eV) have extended lifetimes compared to free excitons probed at 1.9 eV.Thus, the spectral overlap of Re-based defects and free exciton emission gives rise to the long-lived emission tail observed in the decay trace of the 3.6 atom% film collected at 1.85-1.9eV (Figures 5a and S9).The above results further support the conclusion that when Re atoms cluster, there is an increase in the ionization energy of the individual Re atoms, thereby leading to defect states that trap photogenerated excitons within the material.

Conclusion
We have demonstrated that the local concentration of Re dopants has pronounced effects on lattice strain, charge doping, and exciton trapping in Re-MoS2 monolayers.We show that Re doping reduces sulfur-site defects at doping concentrations from 0.1 to 6 atom%, as observed in Z-STEM.Valance band maximum (VBM) from XPS, Raman, and PL measurements confirm that isolated Re atoms act as n-type dopants in films doped with low concentrations of Re atoms.
However, at high dopant concentrations (⪆ 1 atom%), STEM and STM measurements reveal significant Re clustering and stripe-formation throughout the Re-MoS2 lattice.STM measurements and ab initio calculations show that the transition from isolated Re atoms to Re clusters at high doping concentrations increase the ionization energy and hence reduce doping from clustered Re atoms.Photoluminescence measurements demonstrate that Re clustering also creates new defect states that trap photogenerated excitons, resulting in broad sub-gap emission.However, while these states may be detrimental to charge doping, impurity-bound excitons from clustered dopants may benefit quantum photonic applications in which such states could act as single photon emitters. 58- 60 he results presented here emphasize the need to carefully understand the interplay between local dopant concentrations, carrier doping, and exciton recombination in TMDs when engineering novel devices based on doping 2D semiconductors.

Experimental
MOCVD Growth: MoS2 films were grown using a home built MOCVD reactor.The growth process for uniform monolayer MoS2 films is detailed in our earlier publication. 35The concentration of Rhenium dopants in the films was varied by adjusting the flow of H2 carrier gas through a stainless-steel bubbler containing rhenium decacarbonyl [Re2(CO)10] powders (99.99% purity, Sigma-Aldrich).The resultant concentration curve, as depicted in Figure S2, exhibits a linear relationship between the Re content and the Re2(CO)10 flow rate across a wide compositional range (from < 0.1 at.% to > 7 at.%).

STEM:
Scanning transmission electron microscopy (STEM) images were collected by using a dual spherical aberration-corrected FEI Titan G2 60-300 S/TEM with a high angle annular dark field (HAADF) detector.The parameters for the image collection were a collection angle of 42-244 mrad, camera length of 115 mm, beam current of 40 pA, and beam convergence of 30 mrad.

X-ray Photoelectron Spectroscopy:
XPS spectra were collected using a Physical Electronics Versa Probe II tool and a monochromatic Al Kα X-ray source (hν = 1486.7 eV).Samples were measured at high vacuum (<10 -6 Torr) using a pass energy of 29.35 eV and 0.125 eV energy step.An ion gun and floating electron neutralizer were used to obtain charge neutrality.XPS spectra were charge corrected to C1s spectrum at 284.8 eV.
STM: Re-doped (8 atom%) MoS2 samples were grown on QFEG on SiC.Subsequently, the samples were transported through air and annealed at 250-300°C in ultra-high vacuum (~2⋅10 −10 mbar).The STM measurements were performed with a commercial low-temperature STM from CreaTec Fischer & Co. GmbH operated at 5 K. STM topographic measurements were taken in constant current mode with the bias voltage applied to the sample.The tungsten tip was prepared on a clean Au(111) surface and confirmed to be metallic.

Computational Methods
First-principles density functional theory (DFT) calculations were performed using the generalized gradient approximation with the Perdew-Burke-Ernzerhof (GGA-PBE) 61 exchange-correlation functional using projector augmented wave pseudopotential, 62,63 as implemented in the Vienna Ab initio simulation package (VASP). 64,65A 5×10 MoS2 supercell with two Re impurities was used in our binding energy calculations.Binding energies obtained from these calculations are lowerbound estimates (i.e. could bind stronger), since they are obtained from a series of total energy calculations with two Re atoms separated by 1-5 lattice constants, where the furthest Re-Re separation structure serves as the reference.We used a Γ-point k-point sampling, a plane-wave expansion energy cutoff of 400 eV, and a force convergence cutoff of 0.01 eV/Å.Band-unfolding method 66 was performed to obtain band structures of the primitive unit cell.

PL and TRPL characterization
Steady-state photoluminescence was measured by first focusing the output of a continuous-wave laser onto the sample (Oxxius, LBX-445, 445 nm) using a 40 x 0.75 NA objective.
Photoluminescence from the sample was collected with the same objective before being coupled into an optical fiber.A 550 nm dichroic mirror and 600 nm long-pass filter placed before the optical fiber separated the photoluminescence from stray laser light.The fibers output was focused onto the slits of a spectrograph (Princeton Instruments, HRS-300SS, grating 300 grooves/mm) and detected using a back-illuminated CCD camera (Princeton Instruments, PIXIS 400 BR).

Section I: Characterization of Re-MoS2 Monolayers
AFM topography is collected using a Bruker Dimension Icon instrument equipped with a ScanAsyst-Air (k = 0.4 N/m) tip in tapping mode.The topographical image (Figure S1a) demonstrates that the MOCVD process produces coalesced, uniform monolayer films on csapphire. 1,2The underlying morphology observed in the AFM image arises from the sapphire substrate's step edges. 3We evaluated the layer uniformity of a MoS2 film grown on c-sapphire over a larger area (2500 µm 2 ) using Raman spectroscopy (Figure S1b).From the Raman maps, we obtain an average  `- 1 ` peak distance (Δω) of ~19.5 ± 0.2 cm −1 , which closely matches reported Δω values for monolayer MoS2 in the literature. 4Additionally, the spectra exhibit no lowfrequency modes associated with multilayer MoS2.

Section II: Raman characterization of charge doping and strain in Re-MoS2 Monolayers
Eqns. 1-2 in the main text can be expressed in matrix form by, Using Eqn.S1, the effects of Re concentration on strain and charge doping density can be determined by constructing a (-) map that describes the relationship between these parameters and Raman peak positions (Figure S5).

Section VI: Mass action model to determine electron density from PL spectra
The electron density within MoS2 films can be estimated from the film's photoluminescence spectra using a mass action model that describes the relationship between neutral excitons, trions, and excess electrons according to where A is the PL collection efficiency, G is the optical generation rate for excitons,   and   are the radiative decay rate constants for excitons and trions,   is the total decay rate constant for trions (  = 0.02  −1 ), 7 and   is the trion formation rate constant (  = 0.5  −1 ). 7ing Eqn.S5-6, the electron density of MoS2 films can be estimated from the spectral weight of trion PL according to where (τ1) and (τ2) are short and long lifetime components of the PL decay, and (a) determines the contribution each makes to the overall decay trace.Table S2 shows the short and long lifetimes, amplitudes, and weighted average lifetimes for the decay traces in Figure 4 of the main text.Figure S9 displays spectrally resolved PL spectra of a 3.6 atom% Re-MoS2 film collected at several time delays following photoexcitation at 445 nm.The comparison demonstrates that the spectral overlap between Re-defect and free exciton emission gives rise to the long-lived emission tail observed in the decay trace of the 3.6 atom% film collected at 1.9 eV (Figures 4a, main text).
Table S2.Biexponential fit parameters for the PL decay traces presented in Figure 4a of the main text.

Figure 1 .
Figure 1.Influence of Re concentration on structural disorder and n-type doping in Re-MoS2: Atomic resolution STEM images of (a) undoped, (b) 1.4, and (c) 6 atom% Re-MoS2 films highlighting sulfur-site defects (yellow circles) and double sulfur-site defects (red circles).The scale bar is 1 nm.The images show reduced sulfur-site defects in Re-MoS2 films.Re clustering is observed in 6 atom% films.(d) VBM edges of undoped, 0.1, and 6 atom% Re-MoS2 films measured by XPS.(e) Raman spectra of undoped, 0.1, 1.4, and 6 atom % Re-MoS2 films.The film's A 1 ` and E ` modes are fit with pseudo-Voight functions to characterize their line widths and positions.The vibrational mode at ~417 cm -1 is due to the sapphire substrate.(f) Raman-derived changes in strain (Δε) and charge doping (Δn) as a function of Re concentration.The error bars indicate the standard deviation of ten Raman measurements collected across the samples.

10 13 / 22 𝑐𝑚 − 1 10 13 /𝑐𝑚 2 .From Eqns. 1 - 2 ,
2 and    = −2.theeffect of Re concentration on strain and charge doping can be estimated by comparing the Raman peak positions of Re-MoS2 films to undoped MoS2 (see Supporting Information).Changes in lattice strain and charge doping as a function of Re atom% obtained from analysis of the Raman spectra (Figure 1e) are displayed in Figure 1f.The data show that strain (Δε) within the MoS2 lattice increases by ~ 0.3 % as the concentration of Re dopants increases from 0 (undoped) to 6 atom%.Additionally, the charge doping data (Δn) in Figure 1f shows that the electron density within Re-MoS2 films initially increases by ~ 7.4•10 12 e -/cm -2 at low dopant concentrations before decreasing as the concentration of Re atoms exceeds ~ 0.5 atom%.This result is consistent with our VBM measurements (Figure 1e) and indicates a lack of n-type doping and increased strain in highly doped films.

Figure 2 .
Figure 2. Rhenium clustering and stripe formation in 8% Re-doped MoS2 on QFEG: Constant current STM overview image of multilayer Re-doped MoS2 islands.Red and orange dotted lines indicate island edge and segregation boundaries, respectively.(b) Structural model of the MoS2 island with fast (dilute Re concentration) and slow (dense Re concentration) growth facets indicated.(c,d) Constant current STM topography in different areas of the island's monolayer shown in the insets in (a).The segregation boundary is identified from the abrupt change in Re concentration and distribution.e) STM topography of neutral (ReMo 0 ) and positively charged (ReMo + ) Re atoms in monolayer Re-MoS2.(f) STM topography highlighting the distribution of neutral (blue circles) and positively charged (magenta circles) Re atoms as well as sulfur-site defects (orange circles) within a monolayer Re-MoS2 film.
,f).In high-density regions, more Re atoms tend to be charge neutral if nearby Re atoms are already ionized, indicating an increase in their ionization energy.Interestingly, Re impurities exhibit a preference for aligning in stripes along the (100) direction, particularly on island edges, as observed in the STM topography shown in Figure2c.This stripe-like phase resembles previous reports on WxMo1-xS2 alloying.49In this phase, Re atoms often arrange along stripes in the fifthnearest neighbor configuration (two Mo rows skipped).This is verified by CO-tip nc-AFM imaging in FigureS6which reveals the lattice registry of Re atoms in such stripes, highlighted by dashed circles.A corresponding STM image is shown in FigureS6, suggesting that the Re stripes may emerge from a pseudo Jahn-Teller distortion of the single ReMo 0 that distorts the local crystal lattice and propagates along the stripe direction.36

Figure 3 .
Figure 3. Impact of clustering on electronic structure of Re in MoS2: (a) Re dopant pairing is strongly attractive in monolayer MoS2, at 0.44 eV per Re pair.(b) Ionization energy increases for shorter Re-Re separation.Wavefunction near a Re pair (c) before and (d) after allowing the dopant pair to relax into a locally distorted structure.(e) Unfolded band structures of a pair of Re dopant in monolayer MoS2 at separations of 1,2,3, and 5 lattice constants.Trends in Re dopant ionization energies are estimated by monitoring the separation between the donor level and the conduction band edge.The ionization energy (energy difference between defect state in red and CBM) is largest for a nearest neighbor Re-Re pair, at 0.51 eV.
).The PL spectrum of a highly doped (3.6 atom%) Re-MoS2 film collected under identical conditions is shown in Figure 4c.Unlike the PL spectra of undoped and 0.1 atom% Re-MoS2, the PL spectrum of the 3.6 atom% film exhibits a broad emission peak ~0.2 eV below the neutral A-exciton energy (grey dashed line, Figure 4c).The energy separation between this peak and the neutral A-exciton emission is notably more than the separation between trion and neutral A-exciton emission features (~30-40 meV).However, the position of this emission in Figure 4c closely matches the calculated energy of Re-related defect states in MoS2 (~1.7 eV) and the indirect bandgap of ReS2.

Figure 4 .
Figure 4. Emission properties of Re-MoS2 films: Photoluminescence (PL) spectra of (a) undoped and (b) 0.1 atom%, Re-MoS2 films.The spectra are fit with two pseudo-Voigt curves centered at 1.86 and 1.9 eV to determine the contribution of trions (red dashed line) and A-excitons (blue dashed line) to the PL spectra.(c) PL spectrum of a 3.6 atom% Re-MoS2 film.The spectrum exhibits a broad Re-defect emission band centered at ~1.75 eV (grey dashed line).

Figure 5 .
Figure 5. Influence of Re doping on exciton recombination in MoS2: (a) Exciton recombination kinetics of undoped, 0.1, and 3.6 atom% Re-MoS2 films measured between 1.85-1.9eV following optical excitation at 445 nm.(b) Spectrally resolved recombination kinetics of a 3.6 atom% Re-MoS2 film obtained by integrating the film's PL between 1.7-1.75eV and 1.85-1.9eV.Inset: Photoluminescence spectra of a 3.6 atom% Re-MoS2 film.The comparison demonstrates that excitons in the 3.6 atom% film relax into Re-defect states that extend exciton lifetimes.
Time-resolved photoluminescence (TRPL) was collected by first exciting the sample with 445 nm pulses produced by an optical parametric amplifier (Orpheus-F, Light Conversion) pumped by a 1 MHz Yb:KGW laser (Carbide, Light Conversion Ltd, Vilnius, Lithuania).The same 40 x 0.75 NA objective focused the laser onto the sample and collected the sample's photoluminescence after excitation.An optical fiber focused the photoluminescence onto the slits of a spectrograph before it was detected using a Hamamatsu streak camera (Hamamatsu, C14831-130).

Figure S3 .
Figure S3.Defect density analysis of Z-STEM images for (a-c) undoped and (d-f) 6 atom% Re-MoS2 films collected over a 100 nm 2 area.Weak Z-contrast intensity at sulfur sites corresponding to sulfur site-defects (vacancies or light substitutes) and double sulfur-site defects are marked in yellow and orange, respectively.The scale bars are 1 nm.

Figure S4 .
Figure S4.(a) Atomic resolution STEM image of a 10 atom% Re-MoS2 film on c-sapphire.(b) STEM image of the same Re-MoS2 film highlighting the presence of Re aggregation.The Re sublattice shown in maroon highlights the crystal structure of ReS2 domains.(c) Line profile depicting the relative Z-intensity of Re, Mo, 2S, and S (sulfur-site defect).Sulfur-site defects are present at the grain boundary between larger Re domains and the MoS2 lattice.This result suggests that the favorable dopant-defect interactions which suppress sulfur-site defects in Re-MoS2 films are reduced at 10 atom% doping concentrations.We speculate that this reduction may arise from increased strain due to phase segregated ReS2 domains.

Section III:
Figure S6.(a) STM topography and (b) corresponding nc-AFM image of a four-membered Re strip.The dashed rings indicate the Re position as a guide.

Figure S5 .
Figure S5.Raman-derived strain-charge doping (ε-n) map constructed from the linear relationship between strain, charge doping, and MoS2 Raman peak positions.The error bars indicate the standard deviation of ten Raman measurements collected across the samples.

Figure S7 .
Figure S7.Re pair wavefunctions before and after structural relaxation.The structure of the MoS2 lattice around two Re dopants (black circles) is highlighted (black lines).When separated, each occupied dopant state is described by a 2D hydrogenic wavefunction envelope consisting of   2 orbitals (see main text).After relaxation, the Re pair configuration distorts (right) and  ( 2 − 2 ) and dxy orbitals mix into the occupied dopant level.

Figure S9 .
Figure S9.Time-resolved PL of a 3.6 atom% Re-MoS2 film obtained by averaging several spectra from early (0−250 ps) to late (150−2500 ps) time delays following 445 nm excitation.The comparison demonstrates that emission from Re-defect states dominates at late time delays and overlaps significantly with emission from free excitons/trions.
Table S1 lists the Raman peak positions of undoped and Re-MoS2 films.We note that the  ` and  1 ` frequencies at zero strain and doping are challenging to obtain experimentally.Therefore, we instead compared the strain and carrier concentrations examined in this work to the Raman peak positions of an undoped film.As a result,  0  and  0

Table S1 .
Raman peak positions for Re-MoS2 films collected in ten spots across each sample.