Effect of niobium doping on excitonic dynamics in MoSe2

Transition metal dichalcogenides (TMDs) have emerged as attractive two-dimensional semiconductors for future electronic and optoelectronic applications. Their charge transport properties, such as conductivity and the type of charge carriers, can be effectively controlled by substitutional doping of the transition metal atoms. However, the effects of doping on the excitonic properties, particularly their dynamical properties, have been less studied. Using Nb-doped MoSe2 as a case study, we experimentally investigate the effect of doping on excitonic dynamics in TMDs. Transient absorption measurements are used to directly compare the dynamical properties of excitons in Nb-doped MoSe2 across monolayer, bilayer, and bulk flakes with their undoped counterparts. The exciton lifetimes in Nb-doped flakes are significantly shorter than those in their undoped counterparts. This effect is attributed to the trapping of excitons in defect states introduced by Nb impurities. These results reveal an important consequence of Nb doping on excitonic dynamics in TMDs.

Doping is a crucial technique for tailoring the electrical and optical properties of semiconductors.This process involves introducing carefully selected impurities into a semiconductor lattice in precisely controlled concentrations.Such manipulation enables the creation of n-type (electron-doped) and p-type (hole-doped) semiconductors, offering tunable conductivity.The doping of silicon crystals has been a pivotal factor in the development of the semiconductor industry.Similarly, doping TMDs is expected to be a key step in advancing the application of these materials.Recently, there has been significant progress in developing effective strategies for doping TMDs, as highlighted in several reviews [24][25][26][27][28][29][30].
Despite this progress, the effects of niobium doping on the excitonic properties of TMDs, particularly their dynamical properties, have been less explored.In optoelectronic and photonic applications that utilize 2D semiconductors, excitons play central roles.Substitutional Nb doping at the transition metal atom site introduces local states that could trap or scatter these excitons, thus affecting their behavior.Understanding these effects is crucial for optimizing doping parameters for various applications.In this study, we report on a transient absorption investigation of excitonic dynamics in Nb-doped MoSe 2 , compared to its undoped counterparts.Our findings show that the exciton lifetimes in Nb-doped monolayer, bilayer, and bulk samples are significantly shorter than those in their undoped counterparts.These results underscore an important impact of Nb doping on excitonic dynamics, a key factor in determining the performance of TMDs in optoelectronic devices.

Experimental methods
Sample fabrication.Undoped and Nb-doped MoSe 2 flakes were fabricated using the mechanical exfoliation technique.Initially, the flakes were exfoliated from their bulk crystals (with 2 H stacking order) by pressing and peeling with adhesive tape.The flakes that adhere to the tape were then transferred to polydimethylsiloxane (PDMS) substrates using the same procedure.Large and uniform flakes, particularly those with monolayer and bilayer thicknesses, as well as thicker ones (identified by their optical contrasts), were carefully selected.These selected flakes were subsequently transferred onto Si/SiO 2 substrates.
Transient absorption.The excitonic dynamics were investigated using a custom-built transient absorption setup, as depicted in figure 1.This setup includes a passive mode-locked Ti:sapphire laser, operating at an 80 MHz frequency.The laser has a tunable wavelength range from 770 to 830 nm and produces pulses with a duration of approximately 100 fs.The laser output is divided by a beamsplitter: one part serves as the probe beam for the measurement, while the other part is frequency-doubled by a beta barium borate (BBO) crystal, functioning as the pump beam.The polarization and power of both the pump and probe beams are precisely controlled using a halfwave plate and a polarizer.A color filter, positioned after the BBO crystal, blocks the fundamental beam, ensuring that only the pure pump pulse at the second harmonic frequency is used.These pulses are then focused onto the sample via a microscope objective.The reflected probe light is collected by the same objective.To prevent interference from the reflected pump beam, a color filter is placed before the silicon photodiode, which is responsible for converting the reflected probe power into a voltage signal.This signal, indicative of the differential reflectance ∆R/R 0 = (R − R 0 )/R 0 -where R and R 0 represent the probe reflectance with and without the pump respectivelyis measured by a lock-in amplifier.The amplifier is synchronized to a mechanical chopper that modulates the pump intensity at approximately 2 KHz.During the experiments, ∆R/R 0 is recorded as a function of the pump-probe time delay.This delay is systematically varied by adjusting the probe's path length using a motorized translation stage.

Results and discussions
Undoped and doped 2H MoSe 2 crystals used in this study were sourced from HQ Graphene.The nominally undoped crystal exhibits an n-type carrier density as low as 10 15 cm −3 .The doped crystal has a nominal Nb concentration of 0.7 atomic percent (At%) and a confirmed hole density of 10 19 cm −3 .
The left column of figure 2 illustrates the hexagonal lattice structure of undoped (top) and Nb-doped MoSe 2 (bottom).Each monolayer in this structure consists of two layers of Se sandwiching a layer of Mo, bonded covalently.These monolayers are combined to form a bulk crystal through weak van der Waals interactions.In the case of Nb-doped MoSe 2 , Nb atoms randomly substitute for 0.7% of the Mo atoms, yet this substitution does not distort the original hexagonal lattice structure.
The monolayer, bilayer, and bulk flakes of each crystal type were prepared using the mechanical exfoliation method, as described above.Figure 2 displays optical microscope images of the undoped (top) and Nb-doped (bottom) flakes.We determine the flake thickness based on their optical contrast, calculated  by dividing the difference in green channel counts between the flake and the substrate by the count of the substrate.Previous studies have established that for thin flakes, this contrast is proportional to thickness [68,69].We classify the undoped flake with a 19.2% contrast as a monolayer, a designation to be further substantiated by subsequent photoluminescence analysis.Notably, none of the exfoliated flakes exhibited a contrast below this threshold.The undoped flake with a 39.7% contrast is identified as a bilayer.The doped flakes in the bottom row demonstrate contrasts similar to their undoped counterparts, reinforcing our thickness determination.All bulk flakes exhibit a distinctive yellowish hue, indicating they are at least 10 layers thick.For our purposes, the exact thickness of these bulk flakes is less critical, as they are considered infinitely thick (within the bulk limit) concerning their electronic and optical properties.
The monolayer samples were characterized using photoluminescence (PL) spectroscopy at room temperature.In figure 3(a), the black curve represents the PL spectrum obtained from the undoped MoSe 2 monolayer, while the red curve corresponds to the PL spectrum from the Nb-doped MoSe 2 monolayer.Both samples were subjected to continuous-wave excitation at a wavelength of 532 nm with a power setting of 0.8 mW.The PL spectrum of the undoped monolayer exhibits a characteristic peak at 789 nm, which is attributed to the A-exciton recombination in MoSe 2 .This observation is in agreement with findings reported in previous studies [70,71].In the Nbdoped MoSe 2 monolayer, the A-exciton peak is significantly reduced, approximately by a factor of 4, and an additional peak emerges at 826 nm.
To the best of our knowledge, there has been no published direct PL comparison specifically for undoped and Nb-doped MoSe 2 monolayers.However, there are reports on the PL characteristics of other TMDs doped with Nb, which show some inconsistencies.For instance, one study of Nb-doped MoS 2 monolayers revealed a blue-shift and enhancement in the PL spectrum.This suggests that doping could lead to the suppression of the trion peak [49].Contrastingly, another study reported a red-shift and decrease in the PL peak for Nb-doped MoS 2 monolayers compared to undoped samples.This finding suggests that defect states, introduced by doping, contribute to the PL characteristics.Such discrepancies in results highlight the complex nature of doping effects on the optical properties of TMDs and underscore the need for further investigation [50].Similarly, several studies have reported that Nb doping leads to a redshift and a decrease in the PL peak for other TMDs, such as WS 2 [42][43][44][45]47] and WSe 2 [57,72].These findings further support the idea that Nb doping consistently influences the optical properties of various TMD materials, although the specific effects can vary depending on the material and conditions.In this study, we attribute the observed 826 nm peak in the Nb-doped MoSe 2 monolayer to excitons trapped at the defect states introduced by doping.The energy difference between this peak and the A-exciton peak is 68 meV.This difference aligns reasonably well with the energy level gap between niobium and the valence band of MoSe 2 , as obtained from DFT calculations and scanning tunneling spectroscopy measurements [55].This correlation suggests that the defect states caused by Nb doping significantly impact the electronic structure of the material, thereby influencing its optical properties.
Raman spectroscopy was performed to further characterize the samples.As shown in figure 3(b), the Raman spectra of the undoped and Nb-doped monolayer and bulk flakes all exhibit two peaks.The dominant peak at 241 cm −1 corresponds to the A 1g mode, which is indicative of out-of-plane lattice vibrations.The weaker peak at 286 cm −1 , identified as the E 1 2g mode, arises from in-plane vibrations.Due to the low Nb doping concentration, the Raman features in the Nb-doped samples are similar to those in the undoped ones.These measurements confirm the lattice integrity is not comprised by doping nor the exfoliation procedure.Notably, the transition from the 2 H to the 3 R lattice structure, which has been observed in heavily doped MoS 2 , is not presented here [59].
Transient absorption measurements were conducted to investigate the effect of Nb doping on the excitonic dynamics in MoSe 2 .We first present results from these measurements on the undoped monolayer sample.A 395 nm pump pulse excites free electron-hole pairs in the sample, whose dynamics are monitored by a 790 nm probe pulse.Figures 4(a) and (b) display the measured differential reflectance, ∆R/R 0 = (R − R 0 )/R 0 , in short and long time ranges, respectively, at various pump fluences.Using a previously reported absorbance of 0.10 for monolayer MoSe 2 at the pump wavelength [73], we estimate the carrier density injected by a 1 µJ cm −2 pump pulse to be approximately 7 × 10 10 cm −2 .As depicted in figure 4(c), the peak signal is proportional to the pump fluence.This linear relationship between the signal and the pump fluence (which is proportional to the injected carrier density) confirms that the signal's time evolution can effectively monitor the carrier dynamics.The decay of the signal under each fluence is well described by a bi-exponential function, ∆R/R 0 = A 1 exp(−t/τ 1 ) + A 2 exp(−t/τ 2 ) + B, as illustrated by the orange curves in figures 4(a) and (b).The two time constants, along with the weight of the fast (τ 1 ) process, are plotted as a function of pump fluence in figures 4(d) and (e).Furthermore, the peak signal exhibits a strong resonant feature around the A-exciton energy of MoSe 2 , as shown in figure 4(f).
To interpret the observed time-resolved differential reflectance, we refer to the scheme shown in the left part of figure 5 [74].Upon photoexcitation from the ground to the continuum states, free electron-hole pairs are injected.These hot carriers initially undergo an ultrafast thermalization and relaxation process, lasting only a fraction of 100 fs [10].Subsequently, the electron-hole pairs form excitons.The τ 1 time constant of about 0.4 ps is  consistent with previously reported exciton formation times in TMD 8,75].We observe that the formation of excitons from free carriers results in a decrease in differential reflectance.This is because, in 2D systems at room temperature, free carriers are more efficient at producing transient absorption at the exciton resonance than excitons of equal density [76].Once formed, the excitons recombine, primarily nonradiatively, returning the system to the ground state.The τ 2 time constant of 40 ps reflects the exciton lifetime, aligning with previously reported values [69].
Next, we repeated the differential reflectance measurements on the Nb-doped MoSe 2 monolayer sample to examine the effects of doping.The results, summarized in figure 6, show similarities to the undoped monolayer sample.In both cases, the differential reflectance signal is proportional to the pump fluence.Although the PL of Nb-doped monolayer flake exhibits a significant contribution from defect levels at 826 nm, the peak differential reflectance signal still occurs at 790 nm, confirming the dominance of the A-exciton resonance.Additionally, the signal decay in both samples follows a biexponential pattern.In the Nb-doped sample, the short time constant, accounting for about 90% of the signal, remains at 0.4 ps, similar to that in the undoped sample.This similarity suggests that Nb doping does not significantly affect the exciton formation process.However, a notable difference is observed in the long decay time constant: in the Nb-doped sample, it is approximately 15 ps, roughly one-third shorter than that in the undoped sample.This finding indicates that Nb doping effectively shortens the exciton lifetime in monolayer MoSe 2 .
The reduction in exciton lifetime due to doping is attributed to defect states introduced by the dopants, as depicted in the right part of figure 5. Generally, exciton lifetime is indicative of a material's crystalline quality, with lattice defects often introducing energy states within the forbidden band.These defects can trap carriers, particularly because they possess lower energy levels.Previous research has demonstrated that Nb atoms introduce energy levels above the valence band maximum [31][32][33][34][35]. Consequently, these dopant states can capture holes from the valence band, leading to the formation of bound excitons at dopant sites.These introduced states thus serve as efficient and additional pathways for recombination, thereby shortening the exciton lifetime.As we above, the red-shifted 826 nm PL peak observed the Nb-doped sample (figure 3(a)) is attributed to these bound excitons.
Excitonic dynamics in the undoped bilayer flake were studied using a similar procedure, as summarized in figure 7. Here, the initial sub-picosecond decay associated with exciton formation is not analyzed; however, the fit to the data after 2 ps yielded a short time constant, τ 1 , of a few ps, and a longer one, τ 2 , of about 60 ps.Since bilayer MoSe 2 is an indirect semiconductor, with its conduction band minimum and valence band maximum located at the T and Γ points in momentum space, respectively [77], the τ 1 process could be associated with the transfer of carriers from the K valley to these energy valleys.This transfer reduces the signal, as the probe is tuned to the K-valley exciton resonance.The 60 ps process can be safely attributed to the exciton lifetime, which is longer than that of the undoped monolayer flake.This is consistent with the direct-to-indirect bandgap transition from monolayer to bilayer MoSe 2 .
Figure 8 summarizes the differential reflectance measurements performed on the Nb-doped bilayer flake.One noticeable difference observed is that the signal peaks at about 808 nm, instead of 788 nm as in the undoped bilayer.According to the PL spectrum of the Nb-doped monolayer (figure 3), the dopants introduced defect transitions at 826 nm.Hence, the red shift of the peak in differential reflectance wavelength suggests contributions from the transient absorption at the defect levels.The long time constant, reflecting the exciton lifetime, is shortened to about 40 ps.This observation is consistent with that for the two monolayer flakes, confirming the effect of doping on exciton dynamics.
Finally, we compare the two bulk flakes.Figure 9 shows the differential reflectance results of the undoped bulk flake.The peak signal occurs at 790 nm, which is consistent with those observed in the undoped monolayer and bilayer flakes.The signal decay is biexponential, as confirmed by the fits.We deduce an exciton lifetime of about 300 ps.Bulk MoSe 2 is an indirect semiconductor, similar to its bilayer form.The longer exciton lifetime could be attributed to the reduced surface recombination contribution compared to that in the  bilayer.We note that although the probe is tuned to the direct K valley exciton resonance, it senses the entire carrier population.This is because transient absorption at the exciton resonance includes contributions from the entire carrier population, encompassing both excitons and electron-hole pairs [7,8,75].
We repeated the measurements on the Nb-doped bulk flake, as summarized in figure 10.While other features are similar to those observed in the undoped  sample, the long time constant is reduced to about 20 ps, illustrating the significant effect of doping on excitonic dynamics.Furthermore, the peak signal is red-shifted to about 820 nm, compared to the undoped bulk flake, mirroring the behavior observed in the bilayers.

Conclusion
In our study, using Nb-doped MoSe 2 as an example, we investigated the impact of doping on excitonic dynamics in TMDs.Transient absorption spectroscopy was employed to directly compare the exciton decay dynamics in Nb-doped MoSe 2 monolayer, bilayer, and bulk flakes with their undoped counterparts.Our findings reveal that the exciton lifetimes in Nb-doped monolayer, bilayer, and bulk MoSe 2 are substantially shorter than those in their undoped counterparts.Consequently, we deduce that Nb doping effectively shortens the exciton lifetime in MoSe 2 .This phenomenon is attributed to the trapping of carriers in defect energy levels introduced by Nb impurities.When excitons interact with these charge defect sites, they become localized in space and are prone to recombine.Notably, while the exciton lifetimes in undoped samples systematically increase from 30 ps in monolayers to 60 ps in bilayers and 300 ps in bulk, the lifetimes in Nb-doped samples remain within a narrower range of 15-40 ps.Overall, our study underscores the significant influence of Nb doping on excitonic dynamics, a factor that is critical in determining the performance of TMDs in optoelectronic devices.

Figure 1 .
Figure 1.The transient absorption setup to measure time-resolved differential reflectance.

Figure 2 .
Figure 2. Schematics of the crystalline structure and optical microscope images of monolayer, bilayer, and bulk flakes of undoped (top) and Nb-doped (bottom) MoSe2.

Figure 3 .
Figure 3. (a) Photoluminescence (PL) spectra of undoped and Nb-doped MoSe2 monolayers under continuous-wave excitation of 532 nm.(b) Raman spectra of undoped and Nb-doped MoSe2 monolayer (ML) and bulk flakes measured by using a 532 nm laser.

Figure 4 .
Figure 4. (a) and (b) Differential reflectance of the undoped monolayer MoSe2 flake measured with a 395 nm pump and a 790 nm probe under various pump fluences as labeled.The orange curves are bi-exponential fits.(c) Peak differential reflectance as a function of the pump fluence.The red line is a linear fit.(d) Decay time constants deduced from the biexponential fits to the data.(e) The weight of the fast-decay component (τ 1).(f) Peak differential reflectance as a function of the probe wavelength.

Figure 5 .
Figure 5. Schematics of the excitonic dynamics in the undoped (left) and doped (right) MoSe2 monolayer.

Figure 6 .
Figure 6.(a) and (b) Differential reflectance of the Nb-doped monolayer MoSe2 flake measured with a 395 nm pump and a 790 nm probe under various pump fluences as labeled.The orange curves are bi-exponential fits.(c) Peak differential reflectance as a function of the pump fluence.The red line is a linear fit.(d) Decay time constants deduced from the biexponential fits to the data.(e) The weight of the fast-decay component (τ 1).(f) Peak differential reflectance as a function of the wavelength.

Figure 7 .
Figure 7. (a) and (b) Differential reflectance of the undoped bilayer MoSe2 flake measured with a 394 nm pump and a 788 nm probe under various pump fluences as labeled.The orange curves are bi-exponential fits.(c) Peak differential reflectance as a function of the pump fluence.The red line is a linear fit.(d) Decay time constants deduced from the biexponential fits to the data.(e) The weight of the fast-decay component (τ 1).(f) Peak differential reflectance as a function of the probe wavelength.

Figure 8 .
Figure 8.(a) and (b) Differential reflectance of the Nb-doped bilayer MoSe2 flake measured with a 404 nm pump and a 808 nm probe under various pump fluences as labeled.The orange curves are bi-exponential fits.(c) Peak differential reflectance as a function of the pump fluence.The red line is a linear fit.(d) Decay time constants deduced from the biexponential fits to the data.(e) The weight of the fast-decay component (τ 1).(f) Peak differential reflectance as a function of the probe wavelength.

Figure 9 .
Figure 9. (a) and (b) Differential reflectance of the undoped bulk MoSe2 flake measured with a 395 nm pump and a 790 nm probe under various pump fluences as labeled.The orange curves are bi-exponential fits.(c) Peak differential reflectance as a function of the pump fluence.The red line is a linear fit.(d) Decay time constants deduced from the biexponential fits to the data.(e) The weight of the fast-decay component (τ 1).(f) Peak differential reflectance as a function of the probe wavelength.

Figure 10 .
Figure 10.(a) and (b) Differential reflectance of the undoped bulk MoSe2 flake measured with a 410 nm pump and a 820 nm probe under various pump fluences as labeled.The orange curves are bi-exponential fits.(c) Peak differential reflectance as a function of the pump fluence.The red line is a linear fit.(d) Decay time constants deduced from the biexponential fits to the data.(e) The weight of the fast-decay component (τ 1).(f) Peak differential reflectance as a function of the probe wavelength.