Exciton Kinetics, Quantum Efficiency, and Efficiency Droop of

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Exciton Kinetics, Quantum Efficiency, and Efficiency Droop of Monolayer MoS2 Light-Emitting Devices O. Salehzadeh, N. H. Tran, X. Liu, I. Shih, and Z. Mi* Department of Electrical and Computer Engineering, McGill University, 3480 University Street, Montreal, Quebec H3A 0E9, Canada S Supporting Information *

ABSTRACT: We have investigated the quantum efficiency of monolayer MoS2 light-emitting devices through detailed temperature and power-dependent photoluminescence studies and rate equation analysis. The internal quantum efficiency can reach 45 and 8.3% at 83 and 300 K, respectively. However, efficiency droop is clearly measured with increasing carrier injection due to the unusually large Auger recombination coefficient, which is found to be ∼10−24 cm6/s at room temperature, nearly 6 orders of magnitude higher than that of conventional bulk semiconductors. The significantly elevated Auger recombination in the emerging two-dimensional (2D) semiconductors is primarily an indirect process and is attributed to the abrupt bounding surfaces and the enhanced correlation, mediated by magnified Coulomb interactions, between electrons and holes confined in a 2D structure. KEYWORDS: MoS2, photoluminescence, quantum efficiency, efficiency droop, Auger recombination, carrier lifetime

T

performance, including the maximum achievable internal quantum efficiency and its dependence on carrier injection has not been possible. Moreover, it has remained unclear if efficiency droop, one of the primary performance-limiting factors of GaN quantum well LEDs, can be mitigated in the emerging monolayer light-emitting devices. In this Letter, we aim to elucidate the maximum achievable quantum efficiency of such unique monolayer light-emitting devices and to further compare with GaN quantum well LEDs, the presently dominant technology for solid-state lighting. We have investigated the radiative and various nonradiative recombination processes in 1L MoS2 through temperatureand power-dependent photoluminescence measurements and detailed rate equation analysis. The radiative recombination and nonradiative Auger recombination coefficients are found to be in the range of ∼10−7 cm3/s and ∼10−24 cm6/s at room temperature, which are nearly 3 and 6 orders of magnitude higher than those of bulk semiconductors with equivalent bandgap, respectively. These extremely large values are directly related to the magnified Coulomb interactions and, consequently, significantly enhanced correlation between electrons and holes confined in a 2D structure. The presence of such a strong correlation was confirmed by the observed quadratic dependence of the radiative recombination lifetime on temperature. We have further measured that the internal quantum efficiency can reach ∼45 and 8.3% at 83 and 300 K in 1L MoS2, respectively. We have also identified that the maximum achievable quantum efficiency is limited by Shockley−Read−Hall recombination and indirect Auger

he transition-metal dichalcogenide (TMD) semiconductors, such as molybdenum disulfide (MoS2), are indirect bandgap in their bulk case with a crossover to direct bandgap semiconductors in a monolayer limit due to quantum confinement effects.1,2 In the past few years, there have been a great deal of theoretical and experimental works to understand the evolution of optical properties and to analyze the electronic band structure of TMDs.1−4 Recent studies have further suggested that these two-dimensional (2D) materials are promising candidates for ultimate miniaturized, efficient, and flexible nanophotonic devices including light-emitting diodes (LEDs),5 solar cells,6 and photodetectors7 due to their high optical absorption3 and strong band-to-band photoluminescence (PL) emission.1 The carrier dynamics, exciton kinetics, and consequently performance of such monolayer devices, however, could be drastically different from conventional quantum well devices. For example, the carrier recombination in 2D geometry is strongly affected by the enhanced Coulomb interactions between electrons and holes due to the confinement,8 the lower electrostatic screening caused by the reduced dielectric constants9,10 and the large effective masses of electrons and holes of TMDs.11 In addition, the large trap density on the surface of these atomically thin materials and their interfaces with the host substrate could dramatically affect the device efficiency. Previous optical spectroscopy studies12,13 have shown that the carrier lifetime in single and few-layer MoS2 samples is below 100 ps, which is nearly an order of magnitude smaller than that in the state-ofthe-art quantum well devices operating in the same wavelength range. The relative contribution of Shockley−Read−Hall recombination, radiative recombination, and Auger recombination to the carrier lifetime, however, has remained unknown. Consequently, a fundamental understanding of the device © 2014 American Chemical Society

Received: May 8, 2014 Revised: June 3, 2014 Published: June 6, 2014 4125

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The PL spectra of a 1L MoS2 measured at various temperatures are shown in Figure 1b. Two transitions at 1.83 and 1.99 eV are clearly observed, which are denoted as mode A and mode B, respectively. These two modes are attributed to two excitonic transitions at ±K-points at the corners of the hexagonal Brillouin zone.1 The degeneracy of the valence band of TMDs is lifted by the spin−orbit interactions, originated mainly from the d-orbital of the heavy metal atom with a predicted separation of 150 meV for 1L MoS2. This spin splitting is allowed in 1L TMDs due to the breakdown of the inversion symmetry along the Γ-K lines, while it is expected to be suppressed for a sample with even number of layers.4,14 The shape of both modes remained symmetric with expected red shifts and broadenings with increasing temperature from 83 to 423 K. The PL spectra can be accurately fitted using Lorentzian curves at all temperatures with an example shown in Figure 1b. The peak shifts of both modes can be well described using the Varshni’s semiempirical equation15 (see Figure S1a in Supporting Information). A reduction of the valence band slitting from 182 to 137 meV with increasing temperature from 83 to 423 K is also observed (see Figure S1b in Supporting Information), which, as will be explained later, is the result of phonon-mediated optical transitions. The increase of full width at half-maximum (fwhm, Γ(T)) with temperature, shown in Figure 1c, is mainly due to the exciton−optical phonon scattering, specially longitudinal optical phonon (LO).16 This broadening process is described by Bose−Einstein type expression

recombination at low and high carrier injection conditions, respectively. Because of the unprecedentedly large Auger recombination coefficient, efficiency droop is clearly measured in monolayer MoS2. The monolayer MoS2 flakes were fabricated via mechanical exfoliation on Si/SiO x substrates. Measurements were performed using a confocal PL setup equipped with an atomic force microscopy (AFM) system that enabled us to locate and excite the flakes and perform AFM imaging at the same spot. Figure 1a shows an AFM image of a fairly large MoS2 flake (∼4

Γ(T ) = Γinh +

e

ΓLO ωLO / kβT

−1

(1)

where ΓLO denotes the exciton-LO coupling strength and Γinh accounts for nonphonon scatterings such as exciton−exciton, exciton−carrier and exciton−defect scattering.17 The best fits were obtained by Γinh = 65 ± 6 meV, ΓLO = 400 ± 10 meV, ℏωLO = 42 ± 8 for mode B, and Γinh = 67 ± 3 meV, ΓLO = 150 ± 10 meV, ℏωLO = 44 ± 10 for mode A. The obtained value of the LO phonon energy is in agreement with the theoretically predicted18 and experimentally reported value of ∼50 meV.19 The value of ΓLO in bulk semiconductors typically varies in the range of 20 meV (GaAs with ℏωLO = 36 meV) to 180 meV (GaN with ℏωLO = 93 meV).20,21 Therefore, our derived values of ΓLO, especially the value for mode B, are unusually large, which could be a result of reduced dimensionality and exciton localization at the distorted crystal points.16,22 The very large exciton−LO coupling strength can significantly enhance the efficiency of phonon-assisted nonradiative Auger recombination, as will be discussed later. It is also seen that the inhomogeneous broadening for both modes is large (∼66 meV). Detailed analysis suggests that the large inhomogeneous broadening is largely due to exciton-defect scattering (see Figure S2 in Supporting Information). Recent studies suggested that the inhomogeneous broadening of monolayer MoS2 could be reduced by the proper choice of a host substrate, pointing out the importance of the defects localized at the MoS2/ substrate interface.23 Variations of the integrated PL intensity with temperature are plotted in Figure 1d for both modes A and B, which show drastically different behavior. For mode A, the PL intensity decreases with increasing temperature, which has been commonly observed for bulk semiconductors. The observed quenching of the PL intensity can be well fitted using an Arrhenius-type formula, I(T) = I0/(1 + B exp(−E0/kBT)) with

Figure 1. (a) AFM image of a 1L MoS2 flake with an embedded thickness profile. (b) Typical PL spectra (normalized to the respective A mode intensity) measured from 83 to 373 K. An example of a Lorentzian fit is shown for the spectrum at 373 K. (c) Variations of the fwhm as a function of temperature for mode A and mode B. (d) Plot of the integrated PL intensity as a function of 1/(kBT). Solid lines in (c) and (d) are the fits to data as described in text. Error bars are based on at least five measurements for a given excitation power.

μm × 9 μm) with an average thickness of 0.65 nm, indicated by the line profile in Figure 1a, which is consistent with the expected thickness of a monolayer MoS2. The PL measurements were performed using a 50× objective lens (beam size ∼2 μm) with excitation wavelength of 514 nm and power in the range of 1 μW to 10 mW. The temperature was varied between 83 and 500 K. Prior to the measurements, the samples were first annealed at 200 °C under N2 gas inside the cryostat for 10 min and then cooled down to the measurement temperature. The measurements were carried out under N2 ambient. 4126

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a single activation energy of E0 = 80 ± 10 meV. Moreover, the activation energy stays constant for excitation power in the range of 10 μW to 10 mW (see Figure S3 in Supporting Information). This indicates that the quenching is not the result of any nonradiative recombination processes but rather due to thermal dissociation of excitons. It is therefore suggested that the obtained value of 80 meV is directly related to the exciton binding energy in a monolayer MoS2. This value is nearly an order of magnitude larger than those reported for other bulk and quantum well semiconductors with a similar bandgap24,25 but is somewhat smaller than the theoretically calculated value for monolayer MoS2.8,26,27 In contrast to mode A, the PL intensity of mode B shows an unusual increase with temperature, which can be fitted using IBPL ∼ exp(9 ± 2 meV/kBT), shown in Figure 1d. To explain this unusual trend and also to derive the internal quantum efficiency of monolayer MoS2, we have employed the following rate equation to analyze the experimental data and the radiative and nonradiative recombination processes G = An + Bn2 + Cn3 ηi =

Bn2 G

IPL = θBn2

(2)

(3) (4)

where G is the steady state carrier generation/recombination rate, ηi is the internal quantum efficiency, and IPL is the integrated PL intensity. A, B, and C represents the nonradiative Shockley−Read−Hall, radiative bimolecular, and Auger recombination coefficients, respectively. n is the photoexcited carrier (electron) concentration, and θ is a constant determined by the sample and the measurement setup details. In addition, G can be separately determined from the experimental parameters by G=

Plaser(1 − R )α A spot hν

Figure 2. Plot of the relative external quantum efficiency (EQE) (left axis) and internal quantum efficiency (IQE) (right axis) as a function of carrier generation rate (G) for (a) mode A and (b) mode B. (c) Plot of the B2/AC (left axis, solid symbols) and peak IQE (right axis, open symbols) as a function of temperature. Solid lines are the fitting to the model described in the text.

efficiency first shows an increase with carrier injection due to the saturation of nonradiative Shockley−Read−Hall recombination. Efficiency droop, however, is clearly measured with further increasing carrier density for both modes A and B, which suggests the dominance of Auger recombination at high carrier injection conditions. Variations of the peak internal quantum efficiency versus temperature are further plotted in Figure 2c (right axis). It is seen that the internal quantum efficiency of mode A decreases from 45 to 5.2% with increasing temperature from 83 to 373 K, while the internal quantum efficiency of mode B shows an unusual increase from 2.1 to 5.6% in this temperature range. The room-temperature internal quantum efficiency of the A and B modes in 1L MoS2 are 8.3 and 4.5%, respectively. To our knowledge, this is the first reveal of the temperature-dependent internal quantum efficiency of any monolayer light-emitting devices. The inverse of the product of the two fitting parameters A/√B and C/B1.5, that is, B2/(AC), is also plotted in Figure 2c (left axis) versus temperature for modes A and B, which is consistent with our observed trend of the internal quantum efficiency (right axis). To further elucidate the limiting factors for the maximum achievable quantum efficiency, we have subsequently derived the temperature-dependent radiative and nonradiative recombination coefficients. In monolayer MoS2, Shockley−Read−Hall recombination, which is the dominating carrier recombination process under relatively low carrier injection, is primarily related to defects localized on the free surface and the interface with the host substrate. Therefore, the Shockley−Read−Hall recombination is not expected to be diffusion limited in

(5)

where Plaser, Aspot, and hν are the laser power, excitation area, and excitation photon energy, respectively. R and α are the Fresnel reflection coefficient and absorption coefficient of MoS2. In this study, we used R = 0.6 calculated using the refractive index of ∼8 and α ∼ 0.05 per layer.28,3 From eq 2, one could solve for √Bn as a function of (A/√B, C/B1.5, G) and therefore define the relative external quantum efficiency (EQE ∝ IPL/G = θ × IQE) as a function of (A/√B, C/B1.5, θ, G). In this analysis, A/√B, C/B1.5 and θ were determined as fitting parameters, while G was calculated from eq 5. A constant value for θ was used throughout all the analysis, and A/√B and C/B1.5 vary only with temperature. The afore-described rate equation has been a well-established method for analyzing the quantum efficiency of light-emitting devices.29,30 In this model, the derived internal quantum efficiency does not depend on any preassumption on the values of A, B, or C and, therefore, is directly related to the intrinsic properties of monolayer MoS2. The measured relative external quantum efficiency (IPL/G), the calculated results, and the derived internal quantum efficiency are shown in Figure 2a,b for modes A,B, respectively. The simulation shows near-perfect agreement with the experimental results in the entire temperature range of 83 to 373 K and for carrier generation rates of ∼1026 to 1029 cm−3 s−1. It is seen that at a given temperature the external quantum 4127

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Figure 3. (a) Plot of the calculated Auger recombination coefficients as a function of 1/(kBT). (b) Plot of the calculated radiative recombination coefficients as a function of temperature. (c) Schematic of the proposed phonon-assisted Auger recombination pathway in a 1L MoS2. (d) Plot of the derived radiative lifetime as a function of temperature for A exciton. Solid lines are the fit to the data as described in text.

monolayer MoS213 and, as a consequence, should have extremely weak temperature dependence. This has been further confirmed by recent studies showing that the carrier lifetime of monolayer MoS2 is ∼0.1 ns under low to moderate excitation conditions in a wide temperature range.12,13 Therefore, we have utilized a temperature-independent Shockley−Read−Hall recombination rate (A) of 1010 s−1 in this study. Variations of Auger coefficient (C) and radiative recombination coefficient (B) can then be derived as a function of (kBT)−1 or T. Shown in Figure 3a, the Auger coefficient varies as e(−Ea)/(kBT), indicated by solid fitting lines, as expected for a band-to-band Auger recombination.31 The activation energy Ea is derived to be ∼22 ± 3 meV for mode A and 16 ± 5 meV for mode B, respectively, which are much smaller than that expected for direct band-toband Auger recombination (on the order of the bandgap), suggesting the dominance of indirect Auger recombination. This observation is consistent with the fact that indirect Auger recombination is the primary dissipative process in nanostructures with abrupt bounding surfaces.32 Moreover, it is expected that the efficiency of indirect Auger processes can be drastically enhanced due to the partial breakdown of the translational symmetry and relaxation of the momentum conservation rule in the direction normal to the MoS2 layer. An important scattering channel for the indirect Auger is the electron−phonon interaction, due to the extremely large exciton−phonon coupling coefficient in monolayer MoS2, as discussed earlier. Further studies of the temperature-dependent radiative recombination coefficient provide direct insight on the involved Auger recombination processes. Variations of the radiative recombination coefficient B with temperature are shown in Figure 3b. It decreases with increasing temperature according to T(−1.6±0.2) for mode A, which is consistent with the behavior expected for a typical bulk semiconductor (B ∝ T−1.5).33 For mode B, however, the radiative recombination coefficient shows an anomalous behavior: it increases with temperature as

T(0.9±0.2). We explain the observed increase of B with temperature by considering the involvement of the two valence sub-bands in the Auger recombination pathway (CSASBSA), shown in Figure 3c. This phonon-assisted process leads to the annihilation of an electron and two holes in the conduction band and valence sub-band A, respectively, while creating a hole in sub-band B. The radiative transition between the conduction band and valence band is proportional to the joint density of states weighted by the corresponding hole occupation number that increases with temperature in sub-band B, due to the aforedescribed Auger process, thereby leading to an effective enhancement of the quantum efficiency for mode B with increasing temperature. The increase of hole concentration in valence sub-band B with temperature, however, is not captured by the carrier concentration (n) in the commonly used rateequation. As a consequence, the afore-described analysis shows an apparent increase of the radiative recombination coefficient with temperature for mode B. It is interesting to note that the magnitude of the obtained B and C coefficients are nearly 3 and 6 orders of magnitude larger than the values reported for conventional bulk and quantum well semiconductors.34−36 The thickness of a monolayer MoS2 is comparable to its exciton Bohr radius.26 Therefore, Coulomb interactions between electrons and holes are enhanced due to the strong spatial confinement. Moreover, the large carrier effective mass and low dielectric screening of MoS2 also contribute to the extremely large Coulomb interaction strength. Such strong electrostatic interactions and the resulting significant correlation between carriers will drastically enhance the efficiency of radiative bimolecular and nonradiative Auger recombination processes.8 The presence of such a strong correlation between electrons and holes manifests itself in the temperature-dependent characteristics of the radiative recombination lifetime (τr). For a typical 2D semiconductor,8,37 τr ∝ T. However, our analysis indicate τr ∝ T2 for monolayer MoS2, 4128

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shown by the solid fitting curve in Figure 3d, which is a signature of correlated electrons and holes mediated by Coulomb interactions.8 Additionally, in nanostructures with sizes less than the corresponding Bohr radius, the large Auger rate is partly related to the abrupt and infinite confinement potential created by the rigid bounding surfaces. Recent studies have shown that in a strong confinement regime an abrupt confinement potential can enhance the Auger rate by more than 3 orders of magnitude, compared to a confinement potential with relatively smooth shape.32 It is worth noting the relative Auger recombination strength of mode A and mode B. Despite the stronger exciton−LO coupling coefficient of mode B compared to that of mode A, Auger coefficient of mode A is slightly larger than that of mode B (see Figure 3a). According to the model shown in Figure 3c, Auger recombination annihilates one electron in the conduction band affecting both A and B modes equally. However, this process further annihilates two holes in valence sub-band A. Therefore, the Auger recombination process has a stronger impact on mode A than mode B, resulting in a slightly larger apparent Auger recombination coefficient for mode A. We have further examined the overall carrier recombination lifetime of monolayer MoS2 and its dependence on excitation power (carrier generation rate). The carrier lifetime (τ) at ∼80 K and its constituting components, including Shockley−Read− Hall lifetime (τSRH = 1/A), radiative lifetime (τr = 1/(Bn)), and Auger lifetime (τA = 1/(Cn2)) of mode A, are shown in Figure 4. Under low excitation conditions, the carrier lifetime stays

lifetime is not sensitive to temperature (see Figure S4 in Supporting Information) due to the very low activation energy of the indirect Auger processes and the nearly temperatureinvariant Shockley−Read−Hall recombination. This trend and the derived lifetime are also in excellent agreement with the previous reports based on time-resolved PL experiments.12 In summary, we have investigated the temperature-dependent excitonic transitions of monolayer MoS2 and further determined the radiative bimolecular and nonradiative Auger recombination coefficients. The internal quantum efficiency of monolayer MoS2 light-emitting devices can reach as high as 45% at 83 K, which is attributed to the very large radiative recombination rate (∼10−7 cm3 s−1) due to the significant carrier correlation in 2D structures, evidenced by the observed τr ∝ T2 dependence. The strong carrier correlation, together with the abrupt bounding surfaces of 2D structures, however, also leads to very efficient indirect Auger recombination processes. Consequently, efficiency droop is clearly measured in MoS2 light-emitting devices under large carrier injection conditions. Our studies suggest that further improved quantum efficiency can be achieved in the relatively low carrier generation regime by reducing the nonradiative Shockley− Read−Hall recombination. Compared to the relatively mature GaN-based LEDs, it is expected that the emerging monolayer transition-metal dichalcogenides may be well suited for ultrahigh efficiency and flexible devices for low power lighting, display, sensing, and communication applications.

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ASSOCIATED CONTENT

S Supporting Information *

Detailed analysis on the variation of the PL peak energy and valence band splitting with temperature, origin of the inhomogeneous broadening, exciton binding energy, and temperature dependence of recombination lifetime. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 1-514-398-7114. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Natural Sciences and Engineering Research Council of Canada. Part of the work was performed in the McGill Nanotools-Microfab facility and the LCM facility in École Polytechnique de Montréal.

Figure 4. Plot of the derived overall recombination lifetime for monolayer MoS2 as a function of excitation power (carrier generation rate) at 83 K. Also shown in the figure are its components, including nonradiative Shockley−Read−Hall (SRH) recombination lifetime, radiative recombination lifetime, and nonradiative Auger recombination lifetime.

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REFERENCES

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