A- and B-Exciton Photoluminescence Intensity Ratio as a Measure of Sample Quality for Transition Metal Dichalcogenide Monolayers

The photoluminescence (PL) in monolayer transition metal dichalcogenides (TMDs) is dominated by recombination of electrons in the conduction band with holes in the spin-orbit split valence bands, and there are two distinct emission features referred to as the A-peak (ground state exciton) and B-peak (higher spin-orbit split state). The intensity ratio of these two features varies widely and several contradictory interpretations have been reported. We analyze the room temperature PL from MoS2, MoSe2, WS2, and WSe2 monolayers and show that these variations arise from differences in the non-radiative recombination associated with defect densities. Hence, the relative intensities of the A- and B-emission features can be used to qualitatively asses the non-radiative recombination, and thus the quality of the sample. A low B/A ratio is indicative of low defect density and high sample quality. Emission from TMD monolayers is governed by unique optical selection rules which make them promising materials for valleytronic operations. We observe a notably higher valley polarization in the B-exciton relative to the A-exciton. The high polarization is a consequence of the shorter B-exciton lifetime resulting from rapid relaxation of excitons from the B-exciton to the A-exciton of the valence band.

The photoluminescence (PL) in monolayer transition metal dichalcogenides (TMDs) is dominated by recombination of electrons in the conduction band with holes in the spin-orbit split valence bands, and there are two distinct emission features referred to as the A-peak (ground state exciton) and B-peak (higher spinorbit split state). The intensity ratio of these two features varies widely and several contradictory interpretations have been reported. We analyze the room temperature PL from MoS2, MoSe2, WS2, and WSe2 monolayers and show that these variations arise from differences in the non-radiative recombination associated with defect densities. Hence, the relative intensities of the A-and B-emission features can be used to qualitatively asses the non-radiative recombination, and thus the quality of the sample. A low B/A ratio is indicative of low defect density and high sample quality. Emission from TMD monolayers is governed by unique optical selection rules which make them promising materials for valleytronic operations. We observe a notably higher valley polarization in the B-exciton relative to the Aexciton. The high polarization is a consequence of the shorter B-exciton lifetime resulting from rapid relaxation of excitons from the B-exciton to the A-exciton of the valence band.
Monolayer transition metal dichalcogenides (TMDs) are a new class of materials that hold promise for electronic and optoelectronic applications. 1,2 In the past several years, extensive experimental and theoretical research has provided a growing foundation of knowledge for these materials, led by the discovery that many TMDs (e.g., MoS2, MoSe2, WS2, and WSe2) transition from indirect-to directgap semiconductors at the monolayer limit. 3,4 Structurally, they are composed of a plane of metal atoms positioned between a top and bottom chalcogen layer, arranged in a hexagonal lattice as viewed normal to the surface (Figure 1 a,b).
Despite rapid progress, there are many fundamental optoelectronic aspects of monolayer TMDs that are not fully understood. The photoluminescence (PL) emission character and interpretation thereof have varied widely. As a case in point: in monolayer MoS2, some works report only a single emission feature associated with optical transitions between the highest valence band and the conduction band at the K-points, often referred to as the ground state A-exciton emission. 3,5 However, others observe a strong A-emission feature accompanied by a weaker second emission peak at 100-200 meV higher energy. 6 This second peak, referred to as the B-exciton peak, is associated with transitions between the spin-orbit split valence band and the conduction band. Finally, a number of groups identify two distinct emission peaks of comparable intensities, associated with both A-and Bemissions. 4,7,8 In addition to disparities in the number of spectral components observed, published interpretations of the relative intensities of these two features are varied and contradictory. The presence of B-peak emission has been associated with high quality samples by some, 9 whereas others claim the opposite. 10 It has been suggested that B-peak emission can only occur in W-based TMDs 11 or when a sample is optically excited below the electronic band gap. 12 Similar issues exist for the degree of polarization observed in the A-and Bexciton emission from these materials. [13][14][15] Isolated monolayers have two inequivalent K-valleys at the edges of the Brillouin zone, labeled K and K'. The valence band maxima at K (K') is populated by spin up (spin down) holes, leading to valley dependent optical selection rules 13,14 (Figure 1c). A high degree of valley polarized emission is expected in isolated monolayers. 13 However, experimental values are scattered and typically much lower than predicted. [16][17][18] Here we address the discrepancies in interpretation of these PL emission features by analyzing a large number of different monolayer TMDs (MoS2, MoSe2, WS2, WSe2) to better understand the conditions responsible for various emission characteristics and valley polarizations. We find both A-and B-emission intensities can vary widely from sample-to-sample, consistent with other reports, leading to a variety of emission profiles as well as B/A intensity ratios. We show that these observed variations arise from differences in the non-radiative recombination associated with the defect density in a given sample. This relationship between PL profile and exciton dynamics provides a facile method to assess sample quality: a low B/A ratio indicates low defect density and high sample quality, whereas a large B/A ratio signals high defect density and poor-quality material. In comparing the degree of valley polarization from A-and B-excitons for a given sample, we find a  Figure 3a after normalizing to the A-peak intensity and emission energy (EA). It is apparent that the relative contribution of the B-peak changes significantly from sample-to-sample. Furthermore, there appears to be a trend between the intensity of the prominent A-peak and the appearance of a B-peak; samples having lower intensity A-peak emission exhibit a more noticeable B-peak (e.g., Figure 3a,b red curve).
To quantify individual contributions from A-and B-emissions, each PL spectrum is fit with two Lorentzian curves (inset of Figure 3a). In addition to the five samples presented in Figure 3a,b, 19 other MoS2 monolayers, synthesized in 4 separate growth runs, were measured. Interestingly, we observe a non-zero B-peak intensity in all 24 samples. Furthermore, there is a monotonic relationship between the maximum peak intensity for the A-and B-emissions I(A) and I(B) (Figure 3c) which is well-fit with a simple linear relationship: I(B)=0.008+0.009*I(A). We note that, surprisingly, the fit does not pass through the origin (0,0), indicating there will be a non-zero B-peak intensity even as the A-emission becomes vanishingly small.
In the majority of samples measured, the B-emission is only a fraction of the A-intensity (<1%) and one could easily overlook the emission from this higher energy feature, particularly when plotting on a linear scale. However, when plotted on a log scale, the B-peak contribution is apparent. For samples exhibiting low-intensity emission from the A-peak, the B-peak becomes especially evident, as shown by the red and dark-blue curves in Figure 3a,b corresponding to samples with the lowest values of I(A). This analysis indicates that the A and B emission intensities will become comparable in samples that exhibit extremely low intensity A-exciton emission, and that the B-exciton emission will dominate when the Aemission is below 0.008 ct/ms for our measurement conditions. Photoluminescence measurements were also performed on monolayers of the closely related TMD MoSe2. Emission from the dominant A-exciton occurs at lower energy (relative to MoS2 monolayers) and is observed near 1.52 eV ( Figure   3d). Careful inspection reveals a small PL emission peak identified as the B-exciton ~190 meV above the A-exciton (Figure 3e), consistent with the expected valence band splitting and previous observations. 23 Behavior in the selenium-based material is nearly identical to that observed in MoS2 monolayers, with all samples exhibiting a non-zero B-peak emission and a linear relationship between the A-and B-peak intensities with a non-zero intercept, indicating that B-exciton emission persists even as A-emission vanishes (Figure 3f). We note that a similar behavior is observed when using a different laser excitation of 488 nm (2.54 eV). Such excitation is expected to be well above the measured electronic bandgap of ~2.2 eV for MoSe2. 24 For completeness, we also investigate the tungsten-based TMDs and present the results in Figure 4. In both WS2 and WSe2, the general behaviors observed in MoX2 are repeated; all samples exhibit a measurable B-exciton emission with a linear correlation between A and B emission intensities. Additionally, extrapolation to low emission intensities indicates that the emission from the higher energy Bexciton persists even in the absence of measurable emission from the ground state A-exciton. We therefore conclude that these are general characteristics for TMD monolayers.

Discussion:
In order to explain the general behavior we observe in our PL data of monolayers, various radiative and non-radiative recombination pathways must be considered. The exciton lifetime (tE) is sensitive to both the radiative recombination time (tR) and non-radiative recombination time (tNR) through the relationship (1) This is applicable for the A-exciton lifetime, tE,A, as well as the B-exciton lifetime, tE,B.
Each material system is investigated using steady-state (cw) excitation conditions which should generate similar initial exciton populations in each sample. Therefore, the sample-to-sample differences in PL intensity (IPL) observed for a given monolayer material can be related to variations in the exciton lifetime as )* ∝ " # " % . The radiative recombination time is an intrinsic property, and unlikely to vary at a particular temperature. 25 Non-radiative recombination, however, depends on a variety of factors and can vary widely. In particular, progressively shorter nonradiative recombination times are expected as the defect density increases, providing more non-radiative channels. [26][27][28] Thus the PL intensity of both A-and Bpeaks will be sensitive to changes in the density of defects mediating non-radiative recombination, with the emission intensity decreasing as tNR becomes shorter.
Excitons in the B-band have an additional available pathway, in which they scatter to the lower energy A-band. This energetically favored rapid relaxation process, having recombination time tB-A, is known to occur on the sub-picosecond timescale 29 for MoS2. The additional relaxation pathway will modify equation (1) where P0 is the initial polarization and ts is the valley relaxation time. As evident in equation (3), for a fixed P0, higher Pcirc can be obtained either by increasing valley lifetime, or by decreasing exciton lifetime. In a TMD monolayer such as WS2 where the A-emission is dominant, tE,B is shorter than tE,A, as discussed previously.
Consequently, emission from the B-exciton should exhibit a higher degree of polarization and provides an internal check of our arguments above.
We test our assertions in monolayer WS2 measured at room temperature.
The normalized differential reflection spectrum identifies the A-and B-excitonic features at 1.96 eV and 2.35 eV, respectively (Figure 5a, dashed lines). The degree of valley polarization is measured using 588nm (2.11eV) excitation for the A-peak and 488nm (2.54eV) excitation for the B-peak measurement to be near resonance for each feature, with the excitation energies indicated by the orange and green lines (Figure 5a), respectively. These excitation conditions ensure that the energy separation between laser excitation and PL emission energy is nearly equal for the A-and B-peak measurements, suppressing any dependence on excitation energy. 16,18,26 The sample is excited with s+ helicity light, and the emission is analyzed for s+ and shelicity. The subsequent degree of circular polarization is computed as where I(s+/-) are the polarization resolved PL intensities. As evident in Figure 5b, a Pcirc of 7% is measured at the A-emission peak for 588nm excitation, comparable to previously reported values under similar conditions. 16,34 However, the circularly polarized emission at the B-peak on the same sample (Figure 5c,  We conclude that the ratio of the B-and A-exciton intensities reflects the density of non-radiative defects, thereby providing a qualitative measure of sample quality. This information helps clarify why significant variations in these PL

Methods:
Separate crucibles of metal trioxide (WO3 or MoO3) and chalcogen (S or Se) serve as the precursors for the monolayer materials MoS2, WS2, MoSe2, and WSe2. A dedicated 2" quartz tube is used for each material to prevent cross contamination, and additional growth details can be found in our previous works. 35,36 Optical spectroscopy measurements are performed at room temperature in atmosphere using a Horiba LabRam confocal Raman / PL microscope system.