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 The 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. 6 Efforts 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 Of these approaches, substitutional metal doping offers the most viable means of incorporating stable dopants into the TMD lattice. 16 However, the impact of substitutional doping on carrier density and photonic properties in TMDs has been mixed and may be complicated by non-uniform dopant densities and the high ionization energies of some metal dopants. [16][17][18] Substitutional doping is commonly achieved in techniques such as solid-source chemical vapor deposition by vaporizing powders or liquid precursors containing p-or n-type metal dopants during TMD growth. 16,[19][20][21][22] However, TMDs synthesized using these methods often exhibit nonuniform dopant concentrations and poor spatial uniformity. 22,23 Additionally, 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 As a result, carrier doping from metal dopant atoms is inefficient, prompting the use of > 1% dopant concentrations to tune the electronic properties of TMDs. 17,[25][26][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 In classical semiconductors, increased interactions between dopant atoms at dopant concentrations > 0.01% can create electronically inactive dopant centers or impurity-related bands within the material's bandgap. [30][31][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 In 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. 35 Additionally, ReMo in the negative, neutral, and positive charge state could be stabilized due to the closely-space donor state manifold. 36 The 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 In 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.
Re-MoS2 films (Figure S1) are synthesized onto c-plane sapphire and quasi-free standing epitaxial graphene (QFEG) substrates at 1000 o C using a multi-step MOCVD growth process previously described. [33][34][35] This process utilizes separate nucleation, ripening, and lateral growth stages to produce coalesced, monolayer MoS2 films (Figure S1). 35,37 Re 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. 35 The 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). 42 The 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. 21 The 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 Conversely, 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 (𝐸 ` ~ 385 cm -1 ) and out-of-plane (𝐴 1 ` ~ 405 cm -1 ) vibrational modes for monolayer MoS2. 7,43 The vibrational feature at ~417 cm -1 is due to the underlying sapphire substrate. The effect of strain and charge doping on the Raman modes of MoS2 is well established in the literature. 7,[44][45][46][47] For MoS2, the relationship between biaxial strain (ε), charge doping, and 𝐸 `and 𝐴 1 ` peak positions is given by, 7 ∆𝜔 𝐸 = -2γ 𝐸 𝜔 0 𝐸 ε + 𝑘 𝑛 𝐸 𝑛 (Eqn. 1)
where 𝜔 0 𝐸 and 𝜔 0 𝐴 are the frequencies of the MoS2 𝐸 ` and 𝐴 1 ` modes in the absence of strain and doping, γ 𝐸 and γ 𝐴 are Grüneisen parameters equal to 0.86 and 0.15 for the 𝐸 `and 𝐴 1 ` modes, 45 𝑛 is electron concentration in units of 10 13 cm -2 , and 𝑘 𝑛 𝐸 and 𝑘 𝑛 𝐴 describe how charge doping shifts the 𝐸 ` and 𝐴 1 ` modes according to, 7 𝑘 𝑛 𝐸 = -0.33 The 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. 36 We 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. 48 Analyzing the charge state distribution, we find twice as many ionized dopants in low-density areas (Figure 2e,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 Figure 2c. This stripe-like phase resembles previous reports on WxMo1-xS2 alloying. 49 In 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 Figure S6 which reveals the lattice registry of Re atoms in such stripes, highlighted by dashed circles. A corresponding STM image is shown in Figure S6, 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 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). 51 However, 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 𝑑 𝑧 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, 𝑑 𝑧 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 𝑑 𝑥 2 -𝑦 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. 54 Although 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 𝑐 = 𝑒 -𝐸 𝑓 /𝑘𝑇 . 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 thermodynamically favorable. From Emix = E(RexMo1-xS2) -x E(ReS2) -(1-x) E(MoS2)], where we have chosen x=1/9 as a close approximation to the experimentally observed doping level of 10%, we obtain a mixing energy per metal atom of 0.11 eV. This moderate energetic preference towards Re clustering (instead of being uniformly distributed) is compensated entropically by -TSmix = 2kBT [ x ln x + (1-x) ln (1-x) ] = -0.06 eV, again using a growth temperature of 1200 K. Thus, a moderate preference of 0.05 eV per metal atom towards Re clustering remains. This result is consistent with the analysis above for Re dimers. However, since this preference is on the same order of thermal energies (~0.10 eV) at 1200 K, we acknowledge that forming large Re clusters versus uniformly distributed dopants also likely depends on local fluctuations of the Re chemical potential. The calculated ionization energies of Re dopants as a function of Re-Re distance are shown in Figure 3b. These ionization energies are estimated by taking the difference (red shaded region in Figure 3e) between the pristine band gap and the VBM-defect energy interval, all taken at the DFT level; since we are using only Kohn-Sham levels, we focus on monitoring their trend as the Re pair forms. Donor levels in the unfolded band structures in Figure 3e can be identified by the projection onto Re orbitals shown as red dots. The estimated ionization energies increase from 0.06 eV when Re dopants are isolated to 0.37 eV when dopants are two lattice constants apart and then abruptly to 0.51 eV when dopants are one lattice constant apart. Therefore, Re atoms are less likely to ionize when closely neighboring other Re due to the increased ionization energies of clustered dopants. This result supports the lack of n-type doping observed in Re-MoS2 films that exhibit Re clustering at high dopant atom%. Rhenium incorporation, and its impact on defect formation in MoS2, heavily influences photoluminescence (PL) of MoS2. The PL spectra of undoped and 0.1 atom% Re-MoS2 films collected at room temperature following optical excitation at 445 nm are displayed in Figures 4ab. The film's absorption spectra are shown in Figure S8. Non-radiative recombination pathways associated with trion formation quench emission in monolayer MoS2. 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 From 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). 35 The ~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. Rhenium-based defects trap photogenerated excitons and extend photoluminescence lifetimes in MoS2. PL decay traces of undoped, 0.1, and 3.6 atom% Re-MoS2 films collected near the neutral Aexciton resonance between 1.85-1.9 eV following optical exciton (445 nm, 5 pJ/pulse) are shown in Figure 5a. The decay traces presented in Figure 5a exhibit an initial, fast component (< 500 ps) and a slow component (> 500 ps) previously assigned to the decay of free excitons and defect-related states 9, 35 We fit the decay traces with bi-exponential functions (see Table S2 for best-fit parameters) to obtained average exciton recombination lifetimes of 300, 126, and 220 ps for undoped, 0.1, and 3.6 atom% Re-MoS2 films, respectively. Several reports suggest that sulfur-site defects extend PL lifetimes in MoS2. 9,35,56,57 Therefore, we speculate that the extended PL lifetime observed in the undoped MoS2 film arises from sulfur-site defects within the MoS2 lattice. The faster recombination lifetimes of Re-doped samples likely originate from a reduction in these sulfur-site defects (Figure 1) and, for the 0.1 atom% Re film, enhanced non-radiative recombination due to increased trion formation. 9
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 1.85-1.9 eV (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.
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 The 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.
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. 35 The 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.%).
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.
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.
Raman Spectroscopy: Raman spectra were collected using a Horiba Jobin-Yvon LabRam Evolution Raman microscope (Horiba, Edison, NJ). Samples were measured using a 532 nm excitation wavelength.
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.
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 simulation package (VASP). 64,65 A 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.
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).
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. 1,2 The underlying morphology observed in the AFM image arises from the sapphire substrate's step edges. 3 We 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 𝐸 `-𝐴 1 ` peak distance (Δω) of ~19.5 ± 0.2 cm -1 , which closely matches reported Δω values for monolayer MoS2 in the literature. 4 Additionally, the spectra exhibit no lowfrequency modes associated with multilayer MoS2.
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 (𝜀-𝑛) map that describes the relationship between these parameters and Raman peak positions (Figure S5). Table S1 lists the Raman peak positions of undoped and Re-MoS2 films. We note that the 𝐸 ` and 𝐴 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, 𝜔 0 𝐸 and 𝜔 0 𝐴 equal the peak positions of the 𝐸 ` and 𝐴 1 ` modes for undoped MoS2 (𝜔 0 𝐸 = 𝐸 𝑝𝑟𝑖𝑠𝑡𝑖𝑛𝑒 `= 385.6 𝑐𝑚 -1 and 𝜔 0 𝐴 = 𝐴 𝑝𝑟𝑖𝑠𝑡𝑖𝑛𝑒 `= 405.5 𝑐𝑚 -1 ).
Table S1. Raman peak positions for Re-MoS2 films collected in ten spots across each sample. Sample Mode 𝒗 ̃ (cm -1 ) Mode 𝒗 ̃ (cm -1 ) Undoped 𝐴 1 ` 405.5 ± .1 𝐸 ` 385.6 ± .1 0.05 atom% Re 𝐴 1 ` 403.8 ± .1 𝐸 ` 385.1 ± .1 0.1 atom% Re 𝐴 1 ` 404.1 ± .1 𝐸 ` 385.1 ± .1 0.5 atom% Re 𝐴 1 ` 404.7 ± .13 𝐸 ` 384.7 ± .07 1.4 atom% Re 𝐴 1 ` 404.62 ± .16 𝐸 ` 384.8 ± .13 6 atom% Re 𝐴 1 ` 405.2 ± .15 𝐸 ` 383.8 ± .15 10 atom% Re 𝐴 1 ` 405.0 ± .15 𝐸 ` 383.1 ± .25 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 𝑁 𝑒𝑥 𝑛 𝑒𝑙 𝑁 𝑡𝑟 = 4𝑚 𝑒𝑥 𝑚 𝑒𝑙 𝜋ℏ 2 𝑚 𝑡𝑟 𝑘 𝑏 𝑇 • exp (-𝐸 𝑏 𝑘 𝑏 𝑇 ) (Eqn. S4) where 𝑁 𝑒𝑥 is the neutral exciton population, 𝑁 𝑡𝑟 is the trion population, nel is the doped electron density, T is temperature, 𝑘 𝑏 is the Boltzmann constant, 𝐸 𝑏 is the trion binding energy (~40 meV), and 𝑚 𝑒𝑥 , 𝑚 𝑡𝑟 , and 𝑚 𝑒𝑙 are the effective masses of excitons (0.8 m0), trions (1.15 m0), and electrons (0.35 m0), respectively. 7,8 The PL intensity of excitons (𝐼 𝑒𝑥 ) and trions (𝐼 𝑡𝑟 ) is given by 𝐼 𝑒𝑥 ≈ 𝐴𝐺𝛾 𝑒𝑥 𝑘 𝑡𝑟 (Eqn. S5) 𝐼 𝑡𝑟 ≈ 𝐴𝐺𝛾 𝑡𝑟 𝛤 𝑡𝑟 (Eqn. S6)
where A is the PL collection efficiency, G is the optical generation rate for excitons, 𝛾 𝑒𝑥 and 𝛾 𝑡𝑟 are the radiative decay rate constants for excitons and trions, 𝛤 𝑡𝑟 is the total decay rate constant for trions (𝛤 𝑡𝑟 = 0.02 𝑝𝑠 -1 ), 7 and 𝑘 𝑡𝑟 is the trion formation rate constant (𝑘 𝑡𝑟 = 0.5 𝑝𝑠 -1 ). 7 Using Eqn. S5-6, the electron density of MoS2 films can be estimated from the spectral weight of trion PL according to
𝐼 𝑡𝑟 𝐼 𝑡𝑜𝑡𝑎𝑙 = 𝛾 𝑡𝑟 𝛾 𝑒𝑥 𝑁 𝑡𝑟 𝑁 𝑒𝑥 1+ 𝛾 𝑡𝑟 𝛾 𝑒𝑥 𝑁 𝑡𝑟 𝑁 𝑒𝑥 ≈ 4.4•10 -14 𝑛 𝑒𝑙 1+4.4•10 -14 𝑛 𝑒𝑙 (Eqn. S7)
where 𝐼 𝑋 -/𝐼 𝑡𝑜𝑡𝑎𝑙 is the trion PL spectral weight. We determined 𝛾 𝑡𝑟 /𝛾 𝑒𝑥 to be ~0.1 from the intensity ratio of the trion and A-exciton PL curves.
We estimated the PL lifetimes of pristine, 0.1, and 3.6 atom% Re-MoS2 films by fitting normalized PL decay traces with a biexponential function given by 𝐷(𝜏) = 𝑎 * 𝑒𝑥𝑝 (-𝑡/𝜏1) + (1 -𝑎) * 𝑒𝑥𝑝 (-𝑡/ 𝜏2) (Eqn. S8)