A- and B-exciton photoluminescence intensity ratio as a measure of sample quality for transition metal dichalcogenide monolayers

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 direct-gap 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 [Figs. 1(a) and 1(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 studies 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.^6–8 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 B-emissions.^4,9,10

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,¹¹ whereas others claim the opposite.¹² It has been suggested that B-peak emission can only occur in W-based TMDs¹³ or when a sample is optically excited below the electronic bandgap.¹⁴ 

Similar issues exist for the degree of polarization observed in the A- and B-exciton emission from these materials.^15–17 The 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′) are populated by spin up (spin down) holes, leading to valley dependent optical selection rules^15,16 [Fig. 1(c)]. A high degree of valley polarized emission is expected in the isolated monolayers.¹⁵ However, experimental values are scattered and typically much lower than predicted.^18–20 

Here we address the discrepancies in interpretation of these PL emission features by analyzing a large number of different monolayer TMDs (MoS₂, MoSe₂, WS₂, and WSe₂) to better understand the conditions responsible for various emission characteristics and valley polarizations. We find that 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 a high defect density and poor-quality material. By comparing the degree of valley polarization from A- and B-excitons for a given sample, we find a notably higher valley polarization in the B-exciton. The high polarization is a consequence of the shorter B-exciton lifetime resulting from rapid relaxation of excitons from the higher energy spin-orbit split state (B-exciton) to the ground state (A-exciton) of the valence band. This additional relaxation pathway shortens the effective lifetime for B-excitons, subsequently reducing the opportunity for intervalley scattering and enhancing the degree of valley polarization.

Monolayer transition metal dichalcogenides are synthesized via chemical vapor deposition (CVD) on SiO₂/Si substrates (275 nm oxide) as detailed at the end of the manuscript. Figure 1(d) displays an optical image of MoS₂ following a growth. The nucleation density and lateral size of randomly oriented MoS₂ flakes vary across the substrate, providing regions of isolated monolayer islands as well as continuous film regions. Triangular growth is typical, although we have also observed hexagonal, star-like, and rounded flakes.

The as-grown TMDs are characterized at room temperature under ambient conditions. Raman, PL, and reflectance measurements are acquired using a commercial system equipped with a 50× objective so that the area analyzed is approximately a 2 µm diameter circle. The Raman spectra [Fig. 2(a)] of a representative MoS₂ sample display the in-plane E¹_2g mode at 384 cm⁻¹ and out-of-plane A_1g mode at 404 cm⁻¹, consistent with monolayer MoS₂.^21,22 The normalized differential reflection spectrum (1 − R/R₀, where R₀ is the background signal from the bare substrate) is measured at the same location and displays clear peaks in Fig. 2(b) at 1.86 eV and 2.01 eV, corresponding to the A- and B-excitonic transitions, respectively. By contrast, only the A-peak is easily discernible in the photoluminescence spectra for this particular MoS₂ monolayer [Fig. 2(c)], corresponding to radiative recombination via the lowest energy channel. Upon closer inspection and re-plotting the PL intensity on a log-scale [Fig. 2(d)], the B-peak is also evident in PL emission, albeit approximately two orders of magnitude lower than the dominant A-peak.

Significant qualitative differences in the PL emission are reported in the literature for single monolayers, particularly regarding the presence or absence of the B-peak. To gain further insight into these reported differences and to understand the sources and implications of these variations, we examined the PL emission from additional as-grown MoS₂ monolayer samples. Figure 3(a) displays spectra obtained under identical conditions from five different monolayer samples synthesized in three growth runs. The PL intensity of the A-exciton varies over an order of magnitude, from 0.113 ct/ms [Fig. 3(a), red] to 2.315 ct/ms [Fig. 3(a), light green]. Small variations in peak emission energy are also observed, typically within ∼10 meV of 1.84 eV, which are likely due to inhomogeneous distributions of strain, doping, and sample-to-substrate distances.^8,23 Figure 3(b) displays the same spectra as Fig. 3(a) after normalizing to the A-peak intensity and emission energy (E_A). 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., Figs. 3(a) and 3(b) red curve].

To quantify individual contributions from A- and B- emissions, each PL spectrum is fit with the sum of two independent Lorentzian curves [the inset of Fig. 3(a)]. In addition to the five samples presented in Figs. 3(a) and 3(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) [Fig. 3(c)] 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). A straightforward extrapolation of the observed linear relationship suggests that there may be a non-zero B-peak intensity even as the A-emission becomes vanishingly small.

In the majority of samples measured, the B-emission appears to be only a small fraction of the A-intensity and one might overlook the emission from this higher energy feature. However, 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 Figs. 3(a) and 3(b) corresponding to samples with the lowest values of I(A). To quantify the contribution of the B-emission feature to the photoluminescence spectra, we calculate the B/A ratio, I(B)/I(A), for each of the 24 MoS₂ samples [Fig. 3(d)]. Notably, the B/A ratio exhibits considerable variation across the samples investigated and monotonically increases with decreasing I(A). We observe a ratio of 29% for the sample exhibiting the lowest A-emission intensity [Fig. 3(a), red curve]. Samples with I(A) greater than 8 ct/ms exhibit B/A <1% (horizontal line) and are not shown for clarity. The observed behavior suggests that the A- and B-emission intensities may become comparable (B/A = 1) in samples that exhibit even lower intensity A-exciton emission, and that the B-exciton emission will dominate (B/A > 1) when the A-emission 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 [Fig. 3(e)]. Careful inspection reveals a small PL emission peak identified as the B-exciton ∼190 meV above the A-exciton [Fig. 3(f)], consistent with the expected valence band splitting and previous observations.²⁴ 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, a linear relationship between the A- and B-peak intensities with a non-zero intercept [Fig. 3(g)], and a variety of B/A ratios [Fig. 3(h)]. 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 MoSe₂.²⁵ 

For completeness, we also investigate the tungsten-based TMDs and present the results in Fig. 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, the B/A ratio varies across the measured samples and is found to monotonically decrease as the A-intensity increases [Figs. 4(c) and 4(f)]. We therefore conclude that these are general characteristics for TMD monolayers.

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 (τ_E) is sensitive to both radiative recombination time (τ_R) and non-radiative recombination time (τ_NR) through the relationship²⁶ 

This is applicable for the A-exciton lifetime, τ_E,A, as well as the B-exciton lifetime, τ_E,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 (I_PL) observed for a given monolayer material can be related to variations in the exciton lifetime as $IPL∝τEτR$⁠.²⁶ The radiative recombination time is an intrinsic property, and unlikely to vary from sample to sample in a particular TMD material at a given temperature.²⁷ Non-radiative recombination, however, depends on a variety of factors and can vary widely. In particular, progressively shorter non-radiative recombination times are expected as the defect density increases, providing more non-radiative channels.^28–30 Thus the PL intensity of both A- and B-peaks will be sensitive to changes in the density of defects mediating non-radiative recombination, with the emission intensity decreasing as τ_NR 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 τ_B−A, is known to occur on the sub-picosecond timescale³¹ for MoS₂. The additional relaxation pathway will modify Eq. (1) to

for the B-exciton. While relevant experiments in other TMD monolayers are unavailable, we surmise that the associated τ_B−A is comparable to or faster than in MoS₂, due to the larger valence band splitting in the other TMDs. This relaxation will reduce the available exciton population in the B-channel while simultaneously increasing the A-band population, resulting in significantly different exciton lifetimes, τ_E,A and τ_E,B, and corresponding emission intensities $IPL∝τEτR$⁠. Following Eq. (2), we see that τ_B−A provides an upper bound of ∼1 ps for the B-exciton lifetime, which is significantly shorter than the expected lifetime of ∼800 ps for the A-exciton in MoS₂ at room temperature.²⁷ We note that the radiative lifetime is strongly temperature dependent in monolayer TMDs, with lifetime decreasing as temperature decreases.^32,33 In this manuscript, all measurements and discussion focus on room temperature conditions.

In the ideal case, where only radiative recombination and the τ_B−A recombination occur, a significantly higher PL intensity is expected for A-excitons than B-excitons. However, in reality, non-radiative pathways are common, arising from factors such as defects, charge trapping, and exciton-exciton anihiliation,^34–36 and will modify both τ_E,A and τ_E,B. The subsequent impact of these additional non-radiative pathways is very different for A- and B-excitons, in that the effect on B-excitons will be minimized due to the very rapid intraband relaxation provided by the τ_B−A pathway. According to Eq. (1), an A-exciton having radiative recombination time of 800 ps and non-radiative recombination of 10 ps would result in an effective A-exciton lifetime, τ_E,A of ∼10 ps. By contrast, a B-exciton radiative lifetime of 800 ps combined with the τ_B−A = 1 ps would first result in an effective B-exciton lifetime of ∼1 ps, which is then only moderately impacted to τ_B ∼ 900 fs by the addition of the 10 ps non-radiative recombination.

Importantly, this indicates that the relative intensities of the A- and B-exciton emission features of monolayers can be used to qualitatively assess the non-radiative recombination, and thus the quality of the sample. A clearly dominant A-emission indicates a long A-exciton lifetime, relative to the B-exciton lifetime, and a low density of non-radiative defects. By contrast, comparable intensities of A-and B-peaks indicate that non-radiative recombination due to a high density of defects has significantly reduced the effective A-exciton lifetime such that it is nearly as rapid as that of the B-to-A relaxation pathway, τ_B−A. Thus, the B/A peak ratio directly reflects the quality of the sample, with low B/A indicating a low density of non-radiative defects and long A-exciton lifetime. Note that this information can be obtained using cw lasers and steady state conditions, avoiding the more complex apparatus of time-resolved measurement as well as the use of pulsed lasers, which are known to alter the emission spectra and potentially damage the sample due to transient high power densities.³⁷ Additional Raman spectra of representative MoS₂ and WS₂ samples are presented in the supplementary material and provide an independent assessment of sample quality. The in-plane E¹_2g Raman mode is associated with crystalline quality, with sharper FWHM indicative of lower defect density.^7,9,38 Raman spectra exhibit a considerably narrower E¹_2g mode in samples exhibiting lower B/A ratio, providing further support for our assertions that the smaller B/A ratio indicates a lower defect density.

The short lifetime of the B-exciton is ideal for valley polarization. The degree of circularly polarized emission, P_circ, is related to both exciton lifetime and valley lifetime through the relationship^17,20,39

where P₀ is the initial polarization and τ_s is the valley relaxation time. As evident in Eq. (3), for a fixed P₀, higher P_circ 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, τ_E,B is shorter than τ_E,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 [Fig. 5(a), dashed lines]. The degree of valley polarization is measured using 588 nm (2.11 eV) excitation for the A-peak and 488 nm (2.54 eV) excitation for the B-peak measurement to be near resonance for each feature, with the excitation energies indicated by the orange and green lines [Fig. 5(a)], 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.^18,20,28

The sample is excited with σ₊ helicity light, and the emission is analyzed for σ₊ and σ₋ helicity. The subsequent degree of circular polarization is computed as¹⁷ 

where I(σ_+/−) are the polarization resolved PL intensities. As evident in Fig. 5(b), a P_circ of 7% is measured at the A-emission peak for 588 nm excitation, comparable to previously reported values under similar conditions.^18,39 However, the circularly polarized emission at the B-peak on the same sample [Fig. 5(c), inset 2.36 eV, dashed line] is significantly enhanced to a value of 25% for 488 nm excitation. The narrow peaks present above 2.4 eV arise from Raman features and do not affect the measured valley polarization at the B- emission energy. The considerably higher P_circ for B-emission than A-emission can be attributed to the shorter τ_E,B compared to τ_E,A as discussed previously in our model.

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 components have been reported in the literature and enhances our fundamental understanding of excitonic dynamics and valley polarization for both A- and B-emissions in monolayer transition metal dichalcogenides. We identify non-zero PL emission from the B-exciton in all TMD monolayers investigated (MoS₂, MoSe₂, WS₂, and WSe₂). Sample-to-sample differences in non-radiative recombination, stemming from differences in defect densities, lead to variations in the A- and B-emission intensities and emission profiles. The variations in the photoluminescence (in the form of B/A intensity ratio) can be utilized to assess sample quality, with a large B/A ratio indicative of high defect density and low sample quality. While all samples exhibit B-exciton emission, the intensity can be orders of magnitude lower than the ground-state A-emission, making identification challenging in high-quality samples. Emission from the B-exciton exhibits an increased degree of valley polarization, relative to the A-exciton. The enhanced polarization results from the presence of an additional relaxation pathway, τ_B−A, which is available only to the B-exciton population and shortens the lifetime τ_Ε,B, subsequently reducing the opportunity for intervalley scattering.

The final paragraphs detail the growth techniques and characterization conditions used in this study. Synthesis of monolayer TMDs is performed at ambient pressure on SiO₂/Si (275 nm oxide) substrates. A dedicated 2″ quartz tube furnace is used for each material to prevent cross contamination. Prior to use, all SiO₂/Si substrates undergo a standard cleaning procedure consisting of: (i) ultrasonic in acetone; (ii) ultrasonic in isopropyl alcohol; (iii) submersion in Piranha etch (3:1 mixture of H₂SO₄:H₂O₂); and (iv) thorough rinsing in de-ionized water. Although exact precursor amounts, gas flow, and growth temperatures are optimized for each material, a similar methodology is utilized to grow the MoS₂, MoSe₂, WS₂, and WSe₂ monolayers. A quartz boat containing metal oxide powder (Alfa Aesar 10812 MoO₃ or Alfa Aesar 13398 WO₃) is positioned at the center of the tube furnace. Two SiO₂/Si wafers are positioned face-down, directly above the oxide precursor. The upstream wafer contains perylene-3,4,9,10-tetracarboxylic acid tetrapotassium salt (PTAS) seeding molecules, while the downstream substrate is untreated. The hexagonal PTAS molecules are carried downstream to the untreated substrate and promote lateral growth of the TMD materials.⁴⁰ Growth occurs on both upstream (PTAS coated) and downstream (untreated) substrates. A separate quartz boat containing the chalcogen powder (Alfa Aesar 36208 Se or Alfa Aesar 10755 S) is placed upstream, outside the furnace-heating zone. High purity argon (99.999%, Airgas) flows through the furnace as the temperature is ramped from room temerature to the target temperature. Upon reaching the target temperature, H₂ (99.999%, AirGas) is added to the Ar flow for WS₂, WSe₂, and MoSe₂ growth and maintained throughout the 10 min soak and subsequent cooling. During MoS₂ growth, Ar is the only carrier gas used and continues to flow during the 10 min soak and cooling. Growth temperatures are 825 °C, 825 °C, 625 °C, and 700 °C for WS₂, WSe₂, MoS₂, and MoSe₂, respectively. Additional growth details can be found in our previous studies.^41,42

Optical spectroscopy measurements are performed at room temperature in an atmosphere using a Horiba LabRam confocal Raman/PL microscope system. A 50× objective is used for all Raman and PL measurements, which focuses the laser to a diameter of ∼2 µm at the sample surface. The laser power is measured at the sample position and is optimized for each material system to achieve high signal-to-noise ratio. Raman and PL spectra presented in Fig. 2 are acquired using 532 nm excitation of 20 µW. Photoluminescence spectra presented in Figs. 3 and 4 are acquired using 488 nm excitation with 3 µW power for WS₂, 488 nm excitation with 6 µW power for WSe₂, 532 nm excitation with 20 µW power for MoS₂, and 532 nm excitation with 37 µW power for MoSe₂. Photoluminescence spectra presented in Figs. 5(b) and 5(c) are acquired using 588 nm excitation with 10 µW and 488 nm excitation with 10 µW, respectively.

See supplementary material for additional Raman and PL characterization.

This research was performed while S.V.S. held a National Research Council fellowship at NRL. This work was supported by core programs at NRL and the NRL Nanoscience Institute.