Excitons and Trions in MoS2 Quantum Dots: The Influence of the Dispersing Medium.

Single-layer MoS2 has been reported to exhibit strong excitonic and trionic signatures in its photoluminescence (PL) spectra. Here, we report that the emission spectra of MoS2 QDs strongly depend on the dielectric constant of the solvent and the relative difference in the electronegativity between the solvent and QDs. Due to the difference in electronegativity, electrons are either added to the QD or withdrawn from it. Consequently, depending upon the dielectric permittivity and the electronegativity of the surrounding medium, the signature peaks of excitons and trions exhibit a significant change in the PL spectra of MoS2 QDs. Our findings are helpful to understand the effect of the surrounding environment on the optical properties of QDs and the importance of the selection of solvent since MoS2 QDs are potential candidates for valleytronics applications.

Introduction

Two-dimensional materials such as graphene and transition-metal dichalcogenides (TMDCs) are attracting a great deal of attention due to their unique optical and electronic properties resulting from the confinement of charge carriers in two dimensions.[1] However, since graphene is semimetallic in nature with zero band gap, semiconducting TMDCs are of more importance for optoelectronic applications. Among such two-dimensional materials, molybdenum disulfide (MoS2) has an indirect band gap of 1.2 eV in its bulk form. It turns into a direct band gap material with a band gap of 1.9 eV in the monolayer form.[2] The band gap is further tunable when MoS2 is in the nanoparticle or quantum dot (QD) form due to the strong quantum confinement of charge carriers. In addition, MoS2 QDs have interesting features such as large surface area, controllability in scaling in both lateral and vertical directions, good optical properties, biocompatibility, and strong hydrogen adsorption properties. Due to these peculiar features, MoS2 QDs are useful in biological applications and hydrogen evolution reactions.[3−5] Such quantum dots were often prepared by the liquid-phase exfoliation method,[4] exfoliation based on Li-intercalation,[6] electrochemical exfoliation, hydrothermal methods, and liquid-phase laser ablation.[7]

Several mechanisms that can modulate the optical and electronic properties of MoS2 have been reported, which include covalent functionalization by phase engineering,[8] modulation via photoinduced charge transfer,[9] tunable photoluminescence properties via chemical doping,[10] etc. If the synthesis method for the QDs is liquid-assisted exfoliation, the proper selection of the solvent can control the production yield and the respective properties.[11] It should be noted that unlike other QDs, MoS2 QDs have no dangling bonds on their basal planes except at edges and defect sites.[12,13] Therefore, most of the atoms of the QDs are exposed to the solvent in which they are suspended.[12,14] As a result, these surrounding environments can play an important role in the optical properties of MoS2 QDs. It is known that the many-body effects resulting from the Coulomb interactions influence the optical transitions in TMDCs,[15,16] and such interactions are related to the dielectric constant of the surroundings.[17] Therefore, the dielectric screening of the surrounding media will influence the behavior of quasiparticles (excitons and charge excitons, also called trions) in the optical transition. Choi et al.[18] and Lin et al.[17] have performed an elaborate study on the effect of dielectric screening effects of the surrounding media on the properties emanating from the quasiparticle confinements in monolayer MoS2, charge transfer dynamics due to solvent effects in TMDC, etc. However, QDs are a versatile tool for band gap engineering, and such a detailed study on TMDC QDs has not been reported extensively in the literature.

In this work, we show the influence of the dielectric medium on the blue shift in the emission properties of MoS2 QDs prepared by a simple liquid-phase exfoliation method. To study the effect of the surrounding media, MoS2 QDs have been dispersed in various solvents with relative dielectric constants ranging from 1.85 to 37.5. We find that distinct peaks for charged and neutral excitons are visible in QDs prepared in lower dielectric media, which result from the charge transfer of the solvent to the QDs due to the relative difference in electronegativity. The observed blue shift in band gap calculated from absorption spectra in the low dielectric constant range is also attributed to the dielectric screening effect.

Results and Discussion

The MoS2 QDs were prepared in the following solvents: toluene, benzene, N-methyl-2-pyrrolidone (NMP), dimethylformamide (DMF), water, isopropyl alcohol (IPA), and acetone by the liquid-phase exfoliation method. To investigate the optical properties of MoS2 QDs in different solvents, UV–vis spectra have been obtained.

Generally, the UV–vis spectrum of bulk MoS2 exhibits two exciton absorption bands at around 672 nm (1.85 eV) and 615 nm (2.02 eV).[19] These bands originate from the direct band gap transition at the K-point, and the energy splitting arises due to the valence band spin-orbital coupling.[19] The peaks or the small shoulders observed near the UV region in Figure are attributed to the strong quantum confinement effect in MoS2 QDs.[6,7]Figure S1 shows the image of Figure in the 200–800 nm range, in which no absorption peaks are observed in the 600–800 nm region, and the spectra of our samples depict a substantial blue shift in the absorption peaks of the QDs. The respective band gaps of the QDs were calculated using the Tauc plot[20] (see Figure S2) by assuming it as a direct band gap material and are tabulated in Table S1. The variation in the estimated band gap of QDs prepared in different solvents is attributed to the variations in the quantum dot size.

Figure 1

UV–vis absorption spectrum of MoS2 QDs prepared in solvents such as toluene DMF, NMP, benzene, water, IPA, and acetone. Peaks or shoulders near the UV region represent the absorption peak’s strong blue shift due to quantum confinement.

The representative transmission electron microscopy (TEM) images of QDs prepared in DMF and toluene are shown in Figure a,b. The particle size distribution shows that the average particle sizes are 3 and 7 nm in DMF and toluene, respectively. Figure c,d illustrates the active Raman modes of MoS2. The in-plane (E2g1) mode corresponds to the two S atoms vibrating in the same direction and Mo atoms vibrating in the direction opposite to S atoms. However, in the out-of-plane (A1g) mode, the two S atoms vibrate in the opposite way out of the plane and the Mo atom is stationary.[21] Raman spectra of the samples are shown in Figure e, which were obtained in the ambient environment. For the bulk MoS2 powder, it can be observed that the characteristic peaks E2g1 and A1g at 374 and 400 cm–1, respectively, correspond to the optical phonon modes. At the same time, for the exfoliated QDs, these distinct peaks blue-shifted to around 380 and 406 cm–1, respectively. Usually, it has been found that the E2g1 vibration red shifts, while the A1g vibration blue shifts with increasing sample thickness from monolayer to bulk.[22,23] Our Raman results for the exfoliated sample reveal that both the characteristic Raman modes have become stiffened. This means that our samples are scaled down not only in the vertical direction but also in all three directions. As a result, both in-plane and out-of-plane vibrations are found to stiffen.[24] As the bulk MoS2 was exfoliated to QDs, the E2g1 and A1g peaks are observed to be blue-shifted due to the quantum confinement effects, which is consistent with the previous reports.[24,25] The shift of A1g mode is likely due to the decrease in the interlayer van der Waals interaction that causes weaker restoring forces in the vibration as MoS2 becomes quantum dots.[20,26] The shift of the E2g1 mode could be due to the reduced long-range Coulomb interaction between the effective charges caused by an increase in the dielectric screening on stacking-induced changes in the interlayer bonding.[26] The characteristic difference of Raman shifts between the E2g1 and A1g peaks are found to be ∼26 cm–1 for QDs and the bulk MoS2. The observation of a similar difference of 26 cm–1 between the E2g1 and A1g modes originates from the local symmetry of the MoS2 because the local symmetry mostly remains unaltered even after the formation of QDs.[27]

Figure 2

(a, b) Transmission electron microscopy (TEM) images of MoS2 quantum dots prepared in DMF and toluene, respectively. Inset shows respective particle size distribution TEM analysis. (c, d) Illustration of Raman active modes of MoS2 E2g1 and A1g, respectively, gives the schematic representations of in-plane and out-of-plane vibrations of Mo and S atoms. (e) Raman spectra MoS2 bulk and QDs, showing the in-plane (E2g1) and out-of-plane (A1g) vibrational modes of the S atoms.

The signatures of excitonic transitions of MoS2 are evident in its emission characteristics. Therefore, the PL spectra of MoS2 QDs in different organic solvents were obtained, as shown in Figure (see Figures S3–S8). We can observe the strong dependence of the excitation wavelength from these emission spectra, which can be attributed to the size heterogeneity commonly seen in transition-metal dichalcogenides.[13] The PL spectra show two different types of emissions from the quantum dots. One type is from the MoS2 QDs prepared in solutions with low dielectric constants, such as benzene and toluene, which depict multiple distinct peaks in the PL spectra. The other type of spectra is from MoS2 QDs prepared in solutions with high dielectric constants, such as NMP and DMF, which had a single broad peak centered around 500 nm. The additional peaks present in the former one are assigned to the vibronic coupling to the high-frequency local vibrational modes, which may come from the edge bonds in the QDs.[13]

Figure 3

Photoluminescent spectrum of liquid-phase exfoliated QDs in (a) DMF, (b) NMP, (c) benzene, and (d) toluene.

To interpret the multiple PL peaks in MoS2 QDs, the PL spectrum has been deconvoluted by fitting with four Gaussian peaks. The multiple peaks appearing in the PL spectra correspond to the optical transitions of A exciton, B exciton, and A– trions (“charged” excitons, i.e., the bound state of two electrons and a hole or two holes and one electron) and the defect-bound exciton (X) respectively.[17] The detailed extraction of the peaks is shown in Figure , in which a typical PL spectrum of QDs dispersed in toluene is studied. The spectrum was fitted with three peaks that originated from the radiative recombinations of B exciton, A exciton, and A– trions, respectively. The presence of strong radiative recombinations of trions in MoS2 is consistent with our result.[17,28,29]

Figure 4

(a) Typical PL spectrum of MoS2 QDs prepared in toluene. The black circles represent the experimental data, and the green lines represent the fitting of peaks. The red dotted line is the cumulative fitting. The peaks are fitted with a Gaussian peak fitting with an R2 value of 0.999. (b) Diagram of the generation and recombination of the exciton and the trion. Here, Eg is the band gap, Δ is the valence band splitting, and εA, εB, and εA denote the binding energy of A exciton, B exciton, and A– trions, respectively.

Figure b illustrates the radiative recombination of A exciton, B exciton, and A– trions at the K-point of the Brillouin zone. While the A exciton is formed by the Coulomb interaction between a hole from the top of the valence band (VB) and an electron from the bottom of the conduction band (CB), the B exciton is formed by the Coulomb interaction of a hole from the lower level of the split VB and an electron from the bottom of the CB. Similarly, A– trions are formed by the Coulomb interaction of an A exciton and an electron. And the X exciton peak is assigned to the radiative recombination of bound excitons from the trap states.[30]

The PL peak energy of direct band gap semiconductors, i.e., the optical band gap, is equal to the difference between the electronic band gap calculated from the electronic dispersion relation and the binding energy of the quasiparticles originating from the Coulomb interaction between electrons and holes. Lin et al.[17] have reported the detailed expression for PL peak energies of A exciton, B exciton, and A– trions for monolayer MoS2. As seen in the previous reports, the emission peak energy corresponding to the trion, A exciton, and B exciton for a monolayer MoS2 was found to be 1.77 eV (633 nm), 1.81 eV (683 nm), and 1.96 eV (700 nm), respectively.[31] But, in this present work, QD emissions were centered around the 400–500 nm region, which is due to the size reduction and quantum confinement. As a result, trion and excitonic emission peaks blue shift with a decrease in the layer number or size of the QDs.[32] Therefore, in the case of QDs, additional confinement energy terms also have to be added to the PL peak energies and are given as followsFrom the above equations, one can understand the direct correlation between quasiparticle binding energy and PL peak energies. The addition of confinement energy causes the blue shift of emission spectra compared to the few-layer or bulk MoS2, which is clearly visible in Figure . While plotting the emission peak energy as a function of excitation energy (see Figures a,b and S9), QDs prepared in toluene and benzene follow a distinct trend as compared to QDs prepared in other solvents. The PL peaks of B exciton, A exciton, and A– trions follow a steplike behavior with a step size of ∼200 meV. There could be two possible reasons for this: first, the density of states (DOS) of a monolayer or bilayer MoS2 follows that of a two-dimensional electron gas because of the confinement in the Z direction.[33] Since QDs are zero-dimensional relative to the bulk, the DOS depends upon how QDs are arranged or, in other words, whether or not they are aggregated. Therefore, as reported earlier, for a series of QDs, the electronic charges in the QDs cause repulsion to another charge and it leads to a steplike DOS in aggregates.[34] It implies that in the case of QDs arranged in series, it acts similar to a 2D electron gas system. Therefore, the energy will be proportional to the quantum number n.

Figure 5

(a) Emission energy is plotted as a function of excitation energy for QDs prepared in toluene. Black, red, and blue dots correspond to A– trions, A exciton, and B exciton. (b) Emission energy is plotted as a function of excitation energy for QDs prepared in acetone, ethanol, IPA, water, NMP, and DMF.

It is rather surprising that the three excitonic peaks appear in QDs prepared in toluene-like solvents but not in QDs prepared in DMF-like solvents. At this point, it is crucial to consider the effect of the surrounding environment of QDs or the proper selection of solvent for the preparation of the QDs for tuning the optical properties. Taking the case of graphene, Srivastava et al.[11] suggest that the dielectric environment acted as a key factor in enhancing the production yield in the exfoliation process. Similarly, the exfoliation of MoS2 will be different in both solutions. According to Hernandez et al.,[35] for the liquid-phase exfoliation to occur, the net energy cost or, in other words, the enthalpy of mixing should be very small. In our case, the enthalpy of mixing ΔH ∝ (SMoS – Ssolvent)2, where SMoS2 and Ssolvent are the surface energies of MoS2 and solvent. SMoS is defined as the energy per unit area required to overcome the van der Waals force when separating two MoS2 sheets apart.[11] It is clear from the equation that the minimal energy will be spent for exfoliation if the surface energy of the solvents matches that of MoS2. The surface energy of MoS2 was 46.5 mJ/m2,[36] and those for DMF and toluene were 68 and 59 mJ/m2.[11] Since both solutions have their surface energy almost in the range of MoS2, the net energy cost will be almost the same.

If the surface energy solely governs the visible presence of exciton nodes in the toluene, the same should be observed in DMF as well but are absent in DMF. This indicates that there are other parameters also involved in the appearance of the excitonic peaks in the emission spectra of the QDs.

To elucidate the influence of the solvent in the PL spectra of the MoS2 QDs, some of the parameters such as electronegativity and dielectric constant were examined. Electronegativity, being a measure of the tendency of a medium to attract electrons, will determine which of the two interacting molecular systems will become electron donors or acceptors.[37] According to the difference in electronegativity, electron transfer will occur from the solvent to the QDs or vice versa. The electronegativity is expressed as , where IP is the ionization potential and EA is the electron affinity.[37] Using the above expression, the electronegativity of DMF has been calculated to be 4.57 eV, and for toluene, it has been calculated to be 3.86 eV.[18] The electronegativity values of MoS2 have been obtained from the literature (χMoS = 5.06–5.2 eV).[18]

To study the effect of the solvent’s electronegativity on PL spectra, the MoS2 QD sample prepared in toluene was vacuum dried and dispersed again in DMF. To confirm that drying does not affect the properties, the absorption spectrum of dried MoS2 QDs was obtained, as shown in Figure S10. The absorption spectrum does not exhibit much change, as compared to Figure , indicating that drying does not change the QD properties. The corresponding PL spectra of the redispersed QD at different excitation wavelengths are shown in Figure S11. One such PL spectrum is shown in Figure . It can be observed that the intensity ratio of trion to exciton varies from QDs in toluene to the QDs redispersed in DMF. The intensity ratio of A– trion to A exciton reduced from 93.9 to 71.2%. To confirm that the drying process does not have any influence, the PL spectrum of QDs prepared in toluene that had been dried and redispersed in toluene obtained at 370 nm excitation is shown in Figure S12. Significant peaks corresponding to excitons and trions indicate that there is no formation of aggregates. If two systems with different electronegativity interact with each other, the medium with higher electronegativity withdraws electrons from the other until the associated chemical potential reaches equilibrium.[37] In our case, if we are considering the electronegativity values of toluene, MoS2, and DMF, the MoS2 QDs will attract more electrons from toluene than from DMF because of the higher electronegativity values of MoS2 QDs. This electron transfer will result in changes in the intensity of the PL spectrum. As a result, there will be an increase in the electron density in MoS2 QDs, which leads to PL quenching, which causes destabilized exciton recombination by an increased formation of charged excitons, i.e., A– trions. A similar mechanism has been observed, such as tunable PL properties of single-layer MoS2, using a molecular chemical doping technique where the PL intensity of single-layer MoS2 was drastically enhanced by the adsorption of p-type dopants[10] and electron doping via surface functionalization, where the adsorbed molecule ultimately modulates the emission characteristics.[38]

Figure 6

Typical photoluminescent spectrum of MoS2 QDs prepared in toluene at 370 nm excitation is shown in black lines. The peaks correspond to A– trions, A exciton, and B exciton. The red line in the graph represents the PL spectrum of MoS2 QDs prepared in toluene, which was vacuum dried and redispersed in a DMF solution. Interestingly, the excitonic and trionic peaks have quenched in the latter.

It is important to note that the PL peak energy described in equations earlier, i.e., the optical band gap, is equal to the difference between the electronic band gap and the binding energy of the quasiparticles originating from the Coulomb interaction between electrons and holes. The binding energy of the quasiparticle (trions and excitons) corresponds to the Coulomb interaction between negatively charged electrons and holes. This Coulomb potential distribution is strongly screened by the dielectric environments. The dielectric-screened Coulomb potential for the electron and hole separated by a distance L can be expressed as[17], where ε0 is the vacuum permittivity, e the electronic charge, κeff is the effective dielectric constant, L0 is the screening length, and f(L/L0) is a dimensionless function. Also, the exciton binding energy has a scaling relationship with the surrounding effective dielectric constant, i.e., εX = εX0 (κeff)−αX, where εX0 is the binding energy in vacuum and αX is the empirical scaling factor, X represents A exciton, B exciton, and A– trions.[17] From these expressions, we can find the relation between the dielectric constant of the surroundings and the binding energy of the quasiparticles. At the same time, PL peak energies of the quasiparticles are also directly related to the binding energy.

To study the effect of dielectric constants of the surrounding media on the quasiparticle emission energy, QDs prepared in toluene have been dried and dispersed in solvents of different dielectric constants, and the corresponding set of emissions is shown in Figure S13. The respective PL energy corresponding to A– trions, A exciton, and B exciton at an excitation wavelength of 370 nm with a varying dielectric constant is shown in Figure . It can be observed that from εr 1.89 (hexane) to 7.58 (THF), the PL peak energies shift faster, and from εr 20.7 (acetone) onward, the peak energies become almost constant, i.e., there is no significant shift after that. Also, it should be noted that the emission energy of A– trions shifts faster than that of A exciton. That means the trion binding energy increases with an increase in the dielectric constant since PLA – PLA = εA. Similar to the PL peak energy, the intensity ratio of trions to excitons can be tuned by the surrounding dielectric. From the mass action model reported previously,[17] the intensity ratio can be derived as , where K and δ are the fitting parameters and , where ΓA and ΓA are the radiative recombination rates. As seen in Figure b, it can be observed that the A–/A intensity ratio decreases with an increase in the dielectric permittivity of the surrounding medium. The A–/A intensity ratio drops from 1.89 to 0.4 as the dielectric constant varies from 1.89 to 37.5. Theoretically, it means that the radiative recombination rate of A exciton changes faster with environmental dielectric than that of the radiative recombination rate of A– trion.

Figure 7

(a) Emission energy plotted for MoS2 QDs in various solvents as a function of the dielectric constant. Here, blue, red, and black squares correspond to the PL emission energy of A– trions, A exciton, and B exciton, respectively. (b) Dependence of the A–/A intensity ratio on the dielectric constant of the surrounding media. Here, blue dots represent the experimental data, and the red line represents the exponential fit. The fitting has been done with double exponential decay function with an adjusted R2 value of 0.85.

To confirm whether the radiative recombination rate of A exciton changes faster with environmental dielectric than that of A– trion, we have done the lifetime decay measurements of MoS2 QDs in the different dielectric environments. The measurement is done in such a way that the lifetime decay has been measured at three emission wavelengths, which correspond to the A exciton, B exciton, and A– trion for each sample. Even though there will be overlapping emission peaks corresponding to trions and excitons, the maximum probable emission arises from the respective quasiparticle while choosing the particular wavelength. However, the wavelength chosen accounts for the trion binding energy of the order 100 meV (). In the case of monolayer MoS2, the trion binding energy is reported to be 20 meV.[29] However, when QDs are formed, due to the addition of quantum confinement, it will likely increase the trion binding energy.[39−41]

Figure shows the lifetime measurements of the QDs redispersed in (Figure a) toluene, DMF (Figure b), and ethanol (Figure S14). The average lifetime has been extracted using IRF-included exponential fitting.[42] Details regarding the fitting and the three components are given in Table S2. The extracted lifetime with respect to the dielectric constant is plotted in Figure c,d. As evident from the figure, the extracted lifetime corresponding to the A– trion tends to saturate after the dielectric constant of 24.6. At the same time, the extracted lifetime corresponding to A exciton tends to reduce with the increase in the dielectric constant of the solvents. It implies that the average lifetime of A exciton changes faster than that of A– trion. Since the lifetime and radiative recombination are directly related, one can say that the radiative recombination rate of A exciton will be faster than that of the trion, which validates our arguments regarding the dielectric dependence of the intensity ratio of trions to excitons.

Figure 8

Lifetime decay of MoS2 QDs prepared in toluene and redispersed in (a) toluene and (b) DMF. Here black, red, and blue dots correspond to the lifetime decay of to A– trions, A exciton, and B exciton, respectively, at an excitation of 375 nm. (c, d) Average lifetime of excitons in MoS2 QDs in different dielectric media. (c) Average lifetime of A exciton and A– trion, and (d) B exciton.

Conclusions

The dielectric permittivity of the medium that surrounds the MoS2 QDs has a significant influence on the emission properties of the QDs. We find that the surrounding medium donates electrons to the QDs, which in effect causes destabilized exciton recombination by an increased formation of A– trions. Also, we find that the PL peak energies of A– trions shift faster than those of A exciton with respect to the increase in the dielectric constant. And the radiative recombination rate of A exciton changes more quickly with dielectric permittivity than that of the A– trions. Moreover, we can control the generation of A– trion and A exciton by properly tuning and selecting the surrounding environment. This will be a valuable information for tuning the emission properties of TMDC QDs for various optoelectronics and valleytronics applications.

Experimental Methods

We employed the liquid-phase exfoliation method for the preparation of MoS2 QDs. MoS2 powder (Sigma-Aldrich) was mixed with the intended solvent in a ratio of 1 g/100 mL and probe-sonicated for 3 h. The solvents used were DMF, NMP, IPA, acetone, water, toluene, and benzene. The sonicated dispersion was again stirred using a magnetic stirrer at a temperature below the boiling point of the respective solvent for 6 h. Afterward, this dispersion was centrifuged to filter out the sediments. The resultant supernatants containing QD suspensions were used for further characterizations.

To study the dielectric dependence, MoS2 QDs prepared in toluene was vacuum dried at 240 mbar pressure at 60 °C and redispersed in solvents such as hexane (k = 1.89), benzene (k = 2.28), toluene (k = 2.38), ethyl acetate (k = 3.099), diethyl ether (k = 4.33), chloroform (k = 4.81), THF (k = 7.58), acetone (k = 20.7), ethanol (k = 24.6), methanol (k = 32.6), NMP (k = 33), DMF (k = 37.2), and acetonitrile (k = 37.5).

The UV–vis absorption spectrum of the MoS2 quantum dots was measured using a Cary 100 Bio UV spectrometer. Raman spectra of the molecular vibrational levels were studied using a HORIBA Scientific-Jobin Yvon Technology Raman spectrometer with 532 nm laser with a laser power of 50 mW, and the photoluminescence measurements were taken using a HORIBA Scientific FluoroMax-4 spectrometer. The transmission electron micrographs were taken using a JEOL JEM 2100 high-resolution electron microscope, with a maximum acceleration voltage of 200 kV. The lifetime measurement was carried out using an IBH FluoroCube time-correlated picosecond single-photon counting (TCSPC) system. The samples were excited using a diode laser of 375 nm (<100 ps pulse duration) with a repetition rate of 250 kHz.