Sustained Robust Exciton Emission in Suspended Monolayer WSe_2 within the Low Carrier Density Regime for Quantum Emitter Applications

The development of semiconductor optoelectronic devices is moving toward low power consumption and miniaturization, especially for high-efficiency quantum emitters. However, most of these quantum sources work at low carrier density region, where the Shockley-Read-Hall recombination may dominant and seriously reduce the emission efficiency. In order to diminish the affection of carrier trapping and sustain a strong photoluminescence emission under low power pumping condition, we investigated on the influence of Suspending to monolayered tungsten diselenide, novel two-dimensional quantum material. Not only the PL intensity, but also the fundamental photoluminescence quantum yield has exhibited a huge, order-scale enhancement through suspending, even surprisingly, we found the PLQY improvement revealed far significantly under small pumping power and came out an exponential increase tendency toward even lower carrier density region. With its strong excitonic effect, suspended WSe_2 offers a solution to reduce carrier trapping and participate in non-radiative processes. Moreover, in the low-power range where SRH recombination dominates, suspended WSe_2 exhibited remarkably higher percentage of excitonic radiation compared to contacted WSe_2. Herein, we quantitatively demonstrate the significance of suspended WSe_2 monolayer at low carrier density region, highlighting its potential for developing compact, low-power quantum emitters in the future.


INTRODUCTION
[22][23][24][25][26][27][28][29][30][31] Nowadays, developments for quantum and optical communication devices are undoubtedly the most critical issues among opto-electrical applications.3][34][35] However, these single photon sources usually work at low-pumping power region, where the non-radiative Shockley-Read-Hall (SRH) recombination most seriously.And the growth of large-area monolayer TMDC materials through chemical vapor deposition (CVD) unavoidably leads to a high density of defects (e.g., S-vacancy). 36,37[40] In addition, the interface effects of monolayer TMDCs are highly sensitive.When a monolayer TMDC semiconductor material is placed on a substrate, the interface effects may give rise to issues such as the induction of defect-mediated localized states or doping effects.These phenomena could potentially result in low efficiency of monolayer TMDCs light-emitting devices in the low-pumping power regime.5][46] While previous studies have reported the improvement in photoluminescence (PL) intensity of suspended TMDCs, the investigation of their individual influence on the SRH or Auger recombination rate remains unexplored.Particularly, in semiconductor light-emitting devices operating in the low-pumping power regime, the SRH recombination mechanism dominates.
In this study, we have compared the fundamental material characteristics differences of suspended and contacted monolayer tungsten diselenide (WSe2).Through suspending the material, monolayer WSe2 exhibited a dramatical photoluminescence quantum yield (PLQY) improvement, and showed an enhancement enlarge tendency toward smaller power pumping.Additionally, the values of SRH, radiative, and Auger recombination coefficients, revealing intrinsic changes in the carrier recombination pathways of suspended and contacted monolayer WSe2 material have quantitatively been determined through time-resolved photoluminescence (TRPL) measurement.
The SRH recombination rate in suspended WSe2 is found to be significantly slower than that in the contacted sample, particularly under low-power pumping.The visualized evidence of the intrinsic recombination tendency change through suspending is demonstrated by low-temperature PL measurements, showing dramatically difference at low carrier density region and manifesting the potential of suspended monolayer WSe2 for the future quantum optoelectronic devices.

RESULTS
To go under some deep investigations into material characteristics of suspended monolayer TMDCs, we first designed and etched down an μm-size square hole on the SiNx substrate, then the as-grown CVD-synthesized WSe2 monolayer was transferred and covered on top of the square hole [Fig.1(a)], forming suspended monolayer WSe2.For all the measurements in this paper based on suspended and contacted WSe2, the signal was collected at the red and blue mark site in Fig. 1(a), respectively.Two marks are separated more than 7 μm (the diameter of laser spot is around 1 μm) to avoid the interference from each site's photon emission or carrier diffusion.
To confirm the existence of monolayer WSe2, the Raman spectrum shows apparent  2 1 ,  1 peak at 251 cm -1 , 263 cm -1 , respectively, and with absence of interlayer  2 1 signal at near 310 cm -1 [Fig.8][49] Furthermore, based on the Raman spectrum analysis, we observe no significant peak shift between the suspended and contacted samples, indicating that there is no noticeable strain effect on our suspended WSe2 devices. 50,51 addition, it can be observed that the Raman peak intensities of the two structures are nearly comparable.In our measurement system, the input/output coupling efficiency of 2D materials on SiNx/Si structures and suspended structures results in only about a 5% optical enhancement.PL spectrum of contacted and suspended monolayer WSe2 were presented in Fig. 1(b), which are obtained by pumping with 450-nm continuous-wave (CW) laser in room temperature.Under same pumping condition (pumping power: 2 μW), the suspended WSe2 presented an order higher of PL intensity compared to the contacted one at near 745 nm, which comes from the excitonic emission of WSe2.This phenomenon is due to the "strong exciton effect" on the suspended TMDC [Fig.

1(c)]
. Although CVD-grown TMDC has its advantages to approach larger scale for practical devices, it still suffered from some defects' affection in the crystal lattice, e.g., S-vacancy.And these dense defect sites on the material surface often cause seriously trappings of carriers to localized state, going under defect-mediated localized state recombination, or so-called Shockley-Read-Hall (SRH) recombination.However, by suspending monolayer TMDC, the strengthened exciton effect can efficiently help carriers diminish trappings from localized states to go through the non-excitonic radiative SRH recombination.Therefore, the suspended WSe2 will further demonstrate stronger excitonic radiation than the contacted one.Furthermore, as we looked into the full width at half maximum (FWHM) of normalized PL spectrum [Fig.S2], the suspended WSe2's spectrum has obvious smaller FWHM (55 meV) than the contacted one (65 meV).Also, the contacted WSe2's spectrum shows more intensity distribution at lower-energy part (1.5 ~ 1.65 eV), which stands for the emission from multiple-carrier (e.g., trion, biexciton) or defect-mediated recombination, which then becomes another evidence to the stronger exciton effect exhibited in suspended than in contacted WSe2.It is worth to note that strongly PL enhancement from the suspended WSe2 had excluded out the factor of the optical interference in the vertical air suspended structure.However, the 200 nm shallow air regime would be enough to modify the carrier behaviors of the ultrathin TMDC atomic layer.dependent PL spectrum have good positive correlation between its pumping power and intensity, however, the absolute intensity is much higher and FWHM is obviously narrower in the suspended WSe2, which is coincided with the theory mentioned above.To quantify the difference of optical property and efficiency between contacted and suspended WSe2, we integrated the PL intensity from full-wavelength range, and the total photon numbers can further be obtained after some calibration.Fig. 2(c) shows the total photon number collected from contacted and suspended WSe2's radiation per second under different pumping power.Being similar to the tendency of PL intensity, there is over an order more of photons generated from suspended WSe2's radiation per second (Φ photon ) than the contacted WSe2's radiation under all different pumping power from 200 nW to 100 μW.To have an investigation into the WSe2's intrinsic change on quantum efficiency after suspending, the photoluminescence quantum yield (PLQY) has been calculated, which can be written as where Φ photon is the photon generated rate, G. R. pump (s −1 ) represent the pumping generation rate whose value is related to the pumping source and measurement system (please see suppl.
information S7).Fig. 2(d) shows the PLQY for contacted and suspended WSe2 under different but a wide range of pumping generation rate per area G. R. pump ( cm −2 s −1 ).3][54] With suspending the material, the PLQY can have over an-order of improvement, especially at low G. R. pump region.By calculating the ratio between PLQY of contacted and suspended WSe2, we surprisingly found the PLQY ratio reveals a dramatical increasement (fitted by exponential Chapman function) as lowering the G. R. pump WSe2 within low carrier density region.Furthermore, in Fig. 2(d), it's not difficult to find that for both contacted and suspended WSe2, the PLQY value does not have absolute positive or negative correlation to the G. R. pump , that is, the PLQY will slightly decrease as the pumping power is either too low or too high.That is probably due to the differences of carrier's distribution to distinct recombination pathway at different G. R. pump .To understand more details, we applied the ABC model which had been widely applied for semiconductor 55 and 2-D materials, 56,57  =  +  2 +  3 (2 where G is the carrier generation/recombination rate at steady state.A, B, C represents the nonradiative SRH, radiative and Auger recombination coefficient, respectively.n is the carrier density. In the low carrier density region (small G. R. pump ), most of the carrier may be trapped to localized state forming SRH recombination, which is nearly a non-radiative pathway at room temperature.
As the carrier density increases, the more partial of carriers can form exciton and generate PL at the bang gap.While the number of carriers keeps increase (large G. R. pump ), some non-radiative multi-carrier recombination, like Auger-like or exciton-exciton annihilation (EEA) recombination, may start to be dominant. 52,54,58,59Looking back to Fig. 2(d), suspended WSe2 is found to reach its maximal PLQY (red arrow) at G. R. pump = 9 × 10 18 (cm -2 s -1 ), however, contacted WSe2 needs larger G. R. pump = 5 × 10 19 (cm -2 s -1 ) of pumping to get to its PLQY maximum (blue arrow).This is coincided with the theory that suspended WSe2 exhibits stronger exciton effect. 42When carrier concentration is not high, strong exciton effect in suspended WSe2 can keep carriers from trapping to the localized state which makes it reveal larger radiative recombination coefficient B and smaller non-radiative SRH recombination coefficient A than the contacted WSe2 (will be proved later).
And that's also the reason why we can observe the largest PLQY enhancement at the small G. R. pumping region.To have quantitative understanding to the carrier concentration and its recombination rate, time-resolved photoluminescence (TRPL) measurements were taken with our time-correlated single photon counting (TCSPC) system in room temperature (detail please see Method).And the measurements were centered to 745 nm, which is the exciton wavelength of WSe2 in room temperature.Fig. 3(a), 3(b) shows the TRPL decay curve of contacted and suspended WSe2, respectively, pumped by 450 nm 25 MHz-pulsed laser with average pumping power range from 0.2 to 5 μW.No matter in contacted or suspended case, the intensity exhibits a bi-exponential decay with time and the lifetime can be observed decreased with enlarging the pumping power, which is corresponded to the early theory and literature. 60,68To obtain the recombination rate of radiative and non-radiative part, the TRPL intensity were then fitted by bi-exponential decay function, 60,61  () =    ( And averaged PL lifetime   has further been calculated by where t is the delay time.A r , A nr represents the radiative and non-radiative decay coefficient, respectively.τ r , τ nr represents the radiative and non-radiative lifetime, respectively.All the fitting results including τ r , τ nr and   are organized in Fig. S3(a).Averaged lifetime   for contacted and suspended WSe2 under different pumping power is plotted in Fig. 3(c).Here, we can clearly observe that the carrier lifetime of contacted WSe2 is shorter in the low pumping power range.As the average pumping power increases, a crossover point occurs at near 1 μW of averaged pumping power.In the following discussion, we explore the physical significance of this phenomenon and Thus, by plotting the relation between total photon generated rate Φ photon (s −1 ) and carrier density square n 2 (cm −4 ), we can determine the slope as recombination coefficient B (cm 4 s −1 ).
For radiative recombination coefficient in contacted WSe2 (B con ) equals to 9.24 × 10 −13 (cm 4 s −1 ) , in contrast, suspended WSe2 shows a 2.94 × 10 −11 (cm 4 s −1 ) value of coefficient (B sus ), which is over 30 times-larger than B con [Fig.4 where the   and   can be substituted with the value revealed in Fig. 4(a) to make the fitting easier and more accurate.The fitting results (dashed line in Fig. 4 WSe2 as the carrier density getting lower, which again prove the theory that strong exciton effect in suspended WSe2 can effectively diminish the probability of carriers going through SRH recombination pathway.3][54] Based on the comprehensive discussion of TRPL and recombination rates, it can be concluded that for carrier injection densities below 1 × 10 10 (cm −2 ), both suspended and contacted WSe2 exhibit recombination rates predominantly governed by the SRH mechanism.The strong exciton effect in suspended WSe2 effectively suppresses defectassisted SRH recombination.Additionally, Fig. 2(d) illustrates a pronounced decrease in the PLQY of contacted WSe2 when the pumping generation rates fall below 3 × 10 19 (cm −2 s −1 ), with a significant drop of 70% relative to the maximum PLQY even at pumping generation rates below 1× 10 18 (cm −2 s −1 ).Conversely, the PLQY of suspended WSe2 only decreases by 30% compared to the maximum PLQY at lower pumping powers.These results highlight the favorable characteristics of suspended WSe2 for developing low-power devices, enabling high efficiency and ultra-low threshold laser applications in the field of optoelectronics.For further realization to the defect-assisted localized-state radiation, the system was cooled down to liquid-nitrogen temperature (78 K) to diminish the interference from phonon scattering.Thus, WSe2 PL spectrum become more distinct to identify the radiation from different quasi-particle/energy state in low temperature [Fig.5(a), 5(b)].Compared to PL spectrum in room temperature [Fig.S2], the spectrum in 78 K exhibit an apparent 50 meV blue-shift (from 1.67 to 1.72 eV) for both contacted and suspended WSe2, which can be described using the Varshni's semiempirical equation. 52,56And also, several distinguishable peaks from neutral exciton (X 0 ), negative-doped trion (X − ) and defect-mediated localized state (D) have shown at 1.744 eV, 1.716 eV and 1.631 eV under low temperature condition, respectively.The binding energy of trion and the energy difference between exciton and localized state emissions are estimated to be 28 meV and 113 meV, accordingly, which is corresponded to literature. 63,63,67However, when we make a comparison between these two spectra, contacted WSe2 brings out a quite more obvious shoulder at low energy, confirming the stronger tendency of localized state radiation in contacted WSe2.To quantitatively analyze the localized state radiation discrepancy between contacted and suspended WSe2, we further extracted distinct peaks from each pumping power's spectrum with typical gaussian fitting.Fig. S5 shows one of the spectra (contacted; 20 μW-pumping) fitted with three gaussian peaks, substantially representing defect-mediated localized state (green area), negative trion (orange area) and neutral exciton (blue area) from low to high energy.A little mismatch around 1.68 eV may come from the existences of some more complicated quasi-particle (e.g., biexciton, dark exciton), [65][66][67] which is not really clear enough to be identify here.Like With increasing power (P), intensity (I) of localized state, trion and exciton increase exponentially, obeying the power law ( ∝   ).Fitting by the power law, contacted WSe2 exhibits smaller constant  from exciton (  0 = 0.87) than suspended WSe2 does (  0 = 1.07), again confirming the stronger exciton effect revealing in suspended WSe2.To have an even clearer comparison, defect-mediated localized-state intensity percentage (LIP) has been calculated, where   0 ,   − and   represents the integrated PL intensity from exciton, trion and localized state, respectively.LIPs of contacted and suspended WSe2 under different pumping power are plotted in Fig. 5(c).Since carriers in WSe2 will be trapped in defect site more seriously in low carrier density region, LIP for contacted and suspended cases both increase when lowering the pumping power.The proportion of localized state intensity reveals over 50% higher in contacted than suspended WSe2.Even a 60% of disparity is reached toward the lowest power pumping (0.1 μW) condition in our experiment, that is, LIP = 83% and 23% for contacted and suspended WSe2, respectively, proving the concept that suspending can effectively diminish the affection of carrier trapping from localized state especially when the carrier density is low.Finally, in Fig. 5

S1. Raman spectrum of the monolayer contacted and suspended WSe2
Raman spectrum of (a) contacted and (b) suspended WSe2 measured in this paper were presented in Figure S1.2][3] And the absence of interlayer  2 1 signal at near 310 cm -1 confirms the monolayer structure.On the other hand, from the comparison of Figure S1a and Figure S1b, no clear Raman peak shift was found, showing neglectable strain affection to the suspended WSe2.Additionally, the relative intensity Raman spectrum of the contacted and suspended monolayer WSe2 is also presented in FIG.S1 (c).Comparing the peak intensities of the  2 1 in these two structures reveals a difference of only about 5%.

S3. Radiative and non-radiative lifetime extracted from TRPL
Values of radiative lifetime (  ) , non-radiative lifetime (  ) and averaged lifetime (  ) extracted from different pumping power have been organized in Figure S3a, and further plotted in Figure S3b, Figure S3c and Figure 3c in a function of pumping power, respectively.Suspended WSe2 reveals apparently shorter   in the pumping range where radiative recombination dominant (Figure S3b).In contrast, suspended WSe2 exhibits relatively longer   under any pumping power than contacted WSe2 (Figure S3c).

S5. Integrated PL intensity of Exciton, Trion and Defect state in 78 K
Under liquid-nitrogen temperature (78 K), the interference from the phonon scattering can be diminished, which makes the radiation of each state can be easier identified from the PL spectrum.
Like example in Figure S5, with gaussian-peak fitting to the PL spectrum, the radiation from exciton X 0 (blue area), trion X − (orange area) and defect-mediated localized state D (green area) can be distinguished, and the intensity from each state can also be integrated individually.

FIG. 1 .
FIG. 1.(a) Optical image of monolayer WSe2 suspended on a square hole with approximately 3 μm side length.The blue and red mark represent the pumping/collecting site of contacted and suspended WSe2 in this paper, respectively.The white dash line is the edge of CVD-grown WSe2 flake.(b) PL spectrum of contacted and suspended WSe2 pumped by 450-nm CW laser in room temperature.(c) Schematic illustration of a comparison on how strong exciton effect in suspended WSe2 can diminish the trapping from localized state and further reveals stronger PL intensity.

[Fig. 2 (
e)].A 15-times PLQY enhancement exhibits at the lowest G. R. pump in our experiment after suspending the material, giving the evidence of severe carrier trapping from defects in contacted

FIG. 2 .
FIG. 2. PL spectrum with different pumping power (from 10 nW to 2 μW) of (a) contacted and (b) suspended WSe2 in room temperature.(c) Photon generated rate on contacted (blue) and suspended (red) WSe2 as a function of pumping power (ranging from 200 nW to 100 μW).(d) Plot of the PLQY with different pumping generation rate.(e) PLQY ratio between suspended and contacted WSe2 in function of pumping generation rate.Dots represent the raw data from contacted (blue) and suspended (red) WSe2.Dashed lines are polynomial fitting and exponential fitting for clearer tendency in (c), (d) and (e), respectively.

Shown in Fig. 3 (
FIG. 3. Normalized TRPL decay curve of (a) contacted and (b) suspended WSe2 with 450-nm pulsed laser of pumping in room temperature.(c) Plot of the average lifetime   and (d) exciton recombination rate as a function of averaged pumping power.Dots represent the raw data and solid lines are biexponential fits to the data for clearer tendency.
(a)].Next, coefficient A and C can also be determined by fitting to the G-n plot [Fig.4(b)].From eq. 2 (ABC model), we know the relation between carrier density n and the carrier generation/recombination rate G, thus the data from contacted (suspended) WSe2 can further be fitted by the equation,55,56 ( −1 ) =  +  ()  2 + 3

FIG. 4 .
FIG. 4. (a) Plot of the photon generated rate Φ photon as a function of carrier density square n 2 .Dashed lines are linear fitting to the raw data to extract the slope as value of radiative recombination coefficient B. (b) Plot of the relation between carrier generation rate G and carrier density n.Dashed lines are fitting results from the ABC model (eq.8).(c)(d) SRH (violet), exciton radiation (orange), Auger (green) recombination rate as a function of carrier density n in (c) contacted and (d) suspended WSe2.Solid lines are polynomial fitting for clearer tendency.
Fig. S5 has been done, all the power-dependent spectrum from Fig. 5(a), 5(b) have been well-fitted in same way and the integrated PL intensity extracted from each state has been plotted in Fig. S6(a), 6(b).

FIG. 5 .
FIG. 5. PL spectrum with different pumping power (from 0.1 μW to 100 μW) of (a) contacted and (b) suspended WSe2 in 78 K. X 0 , X − and D stand for neutral exciton, negative trion and defect state radiation, respectively.(c) Plot of localized-state intensity percentage (LIP) in function of pumping power.(d) The bar chart of the radiation percentage comparison between contacted and suspended WSe2 under the smallest pumping power (0.1 μW).Inset: Schematic of excitonic and localized state radiation mechanism.

FIG. S1 .
FIG. S1.Normalized intensity of the Raman spectrum for (a) the contacted and (b) suspended FIG. S3.(a) List of all fitted   ,   and   results (pumping power range from 200 nW to 100 μW).Plot of (b) radiative lifetime   and (c) non-radiative lifetime   in a function of pumping FIG. S5.PL spectrum of contacted WSe2 under 20 μW pumping fitted with three gaussian peaks, further investigate the recombination mechanisms in suspended and contacted WSe2 under different pumping power conditions by incorporating the recombination rate equation.Contacted WSe2 have its   shorter (faster recombination rate) than suspended WSe2's at low power region where the SRH recombination dominant, in contrast, suspended WSe2 reveals its   apparent shorter than contacted WSe2's above the intersection near 2 μW-averaged pumping power, where the radiative recombination starts to be dominant in the process.After reasonable bi-exponential fitting to TRPL decay curve, radiative (non-radiative) lifetime has been revealed, therefore the radiative (non-radiative) recombination rate can also be well-known [Fig.S3(b)-(e)].Radiative and non-radiative recombination rate (  ,   ) is the reciprocal of τ r and τ nr , respectively.

Table 1 .
The fitting parameter of recombination rate equation for contacted and suspended WSe2  •  2 for excitonic radiation recombination rate (  ) and  • 3for Auger recombination rate (  ), respectively.Making a comparison to Fig.4(c) and Fig.4(d),   is faster than   at any carrier density (maybe will cross at higher carrier density) According to the fitting results, it can be observed that the SRH coefficient A for contacted WSe2 is approximately twice as large as that for suspended WSe2.This finding provides evidence that the trend of defect-assisted non-radiative recombination is much stronger in contacted WSe2 compared to suspended WSe2.Moreover, to look into clearly on the distribution and tendency of carrier generation rate G, each process' recombination rate has been estimated based on their corresponded coefficient individually.The magnitude of recombination rate equals to  •  for SRH recombination rate (  ), 10 (cm −2 ) of carrier density, where the   starts to exceed   .Also, the percentage of   among all recombination pathway have been estimated in Fig.S4.It's clear to realize that there exhibits about two times of   percentage difference between contacted and suspended