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Kota Nakama, Mitsuhiro Okada, [Ryo Kitaura](https://orcid.org/0000-0001-8108-109X), Hideo Kishida, Takeshi Koyama

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Template for Electronic Submission to ACS JournalsTrion formation in monolayer MoS2 observed via femtosecond time-resolved photoluminescence measurementsKota Nakama,1 Mitsuhiro Okada,2,* Ryo Kitaura,2,3 Hideo Kishida,1 and Takeshi Koyama1,†1Department of Applied Physics, Nagoya University, Chikusa, Nagoya 464-8603, Japan2Department of Chemistry, Nagoya University, Chikusa, Nagoya 464-8602, Japan3Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan*Present address: Nano Carbon Device Research Center, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8565, Japan†Correspondence should be addressed to koyama@nuap.nagoya-u.ac.jpABSTRACT. An ultrathin two-dimensional (2D) semiconductor, monolayer MoS2, holds stable excitons and charged excitons (trions) even at ambient temperature. Trion formation time is of interest to the physics of 2D electron systems, because it relates to strengths of interactions between excitons and charges, exciton size, and exciton diffusion, which depend on dimensionality. In this paper, we investigate the trion formation via exciton-to-trion relaxation using femtosecond time-resolved photoluminescence (PL) measurements for monolayer MoS2 on a sapphire substrate. The number of layers and defect concentration were evaluated by measuring Raman scattering spectra. The electron concentration was estimated from the PL peak-energy difference between A excitons and trions. The time evolutions of exciton and trion PL in the femtosecond and picosecond regions were obtained. The rate-equation analysis provided the time constant of the relaxation from exciton to trion, i.e., the time constant of trion formation. This time constant was compared with that of other 2D electron systems and discussed in terms of the 2D confinement determined by the thickness. In this paper, we advance our understanding of exciton physics in low-dimensional systems.PhySH: Excitons, Trions, Transition metal dichalcogenides, Femtosecond laser spectroscopy, Time-resolved photoluminescenceI. INTRODUCTIONMoS2, a transition-metal dichalcogenide (TMD), is a layered material. Multilayer MoS2 is an indirect semiconductor, while monolayer MoS2 is a direct semiconductor [1,2]. The two-dimensionality of monolayer MoS2 with three-atom thickness results in the formation of stable excitons at room temperature [3]. The use of exciton luminescence allows the application of monolayer MoS2 in large-area light-emitting devices [4]. MoS2 monolayers on various substrates are in the electron-doped state. Owing to their two-dimensionality, charged excitons consisting of two electrons and one hole (negative trions) are stable even at ambient temperature [5]. Depending on the doping concentration, the luminescence of trions can be stronger than that of excitons [6]. Theoretical calculations have shown that trion luminescence is stronger than exciton luminescence at room temperature, even at realistic doping concentrations [7]. Because the trion spectral region is transparent in monolayer MoS2 compared with the exciton bands, reabsorption of luminescence is weak, bringing an advantage for emission devices especially lasers, where the emitted light travels through a laser medium many times in an oscillator. Trion luminescence provides another opportunity to apply monolayer MoS2 in emission devices. Therefore, it is important to understand the behavior of trion luminescence. Although the decay of trion luminescence in monolayer MoS2 has been investigated in previous studies [8], the rising behavior of trion luminescence is still not clear because of low time resolution for many measurements.When trions are formed via the exciton state, the rise time of trion luminescence is governed by the exciton-to-trion relaxation time constant (τex-tr). According to the fundamental physics of two-dimensional (2D) electron systems, the determining factor of the value of τex-tr is of interest because it relates to, for example, strengths of interactions between excitons and charges, exciton size, and exciton diffusion, which depend on dimensionality. Previous time-resolved photoluminescence (PL) measurements had shown that τex-tr ~ 100 ps in a GaAs/AlGaAs quantum well with a well width of 20 nm and electron concentration of 2 × 10-3 cm-2 [9] and τex-tr ~ 100 ps in an InGaAs/GaAs quantum well with a well width of 8 nm and electron concentration of 1 × 10-4 cm-2 [10]. In the case of monolayer TMDs, pump-probe measurements of monolayer MoS2 with 40 fs pulses [11] presented a rapid increase in the photoinduced signal of trions and a subsequent buildup until ~5 ps. The authors explained that the rapid increase and delayed buildup could be related to many-body effects and trion formation, respectively. Other pump-probe measurements with ~1.5 ps pulses [12] and time-resolved PL measurements with a temporal resolution of 4 ps [13] showed a slow increase of trion signals in monolayer MoSe2 and indicated τex-tr ~ 2 ps. Singh et al. [12] pointed out that, although τex-tr depended on several factors, the strength of Coulomb interactions dependent on dimensionality and screening was the key factor that determined the order of magnitude of τex-tr. However, the electron concentrations of monolayer TMDs were not mentioned in the above reports. Moreover, the value of τex-tr also depended on the charge concentration, as shown in other materials [10,14]. The origin of the short exciton-to-trion relaxation time in monolayer TMDs remained an open question. In this paper, we investigated the trion formation via exciton-to-trion relaxation using femtosecond time-resolved PL measurements of excitons and trions in monolayer MoS2, where the electron concentration was evaluated. Time-resolved PL measurements revealed time-dependent population changes in the exciton and trion levels, because the PL intensity was proportional to the population of each level. In contrast, pump-probe measurements provided not only a bleaching signal proportional to the population but also stimulated emission, induced absorption, and optical Stark effect, which sometimes changed the shape of the bleaching signal.II. METHODSMonolayer MoS2 was prepared on a sapphire substrate by chemical vapor deposition (CVD). Raman scattering and steady-state PL measurements were conducted using a microRaman spectrometer (Renishaw inVia, excitation wavelength 488 nm, excitation power 3.2 mW). A 50× objective lens (numerical aperture 0.75) was used, and a spot size diameter on the sample was 2 μm. Light transmittance was measured using a microscopic spectrophotometer (Jasco MSV-5200). Here, 16× cassegrain reflectors (numerical aperture 0.57) were used, and an aperture size diameter on the sample was 50 m. The frequency up-conversion method was used in the femtosecond time-resolved PL measurements. The light source was a Ti:sapphire laser (repetition rate 82 MHz, pulse width 100 fs, and central wavelength 800 nm). The excitation light was the second-harmonic pulse of the laser output, and the gate light was the residual fundamental pulse. The details have been provided in previous works [15-17]. The spot size of the excitation light on the sample was 50 μm, and the excitation density was 4 J cm-2/pulse (the corresponding photon flux was 8 × 1012 photons cm-2/pulse). Nonlinear processes such as absorption saturation and exciton–exciton annihilation were not observed for this excitation density; however, a linear response was observed [16,18,19]. The instrument response function was evaluated as the cross-correlation between the gate light and excitation light scattered on the sample. The full width at half maximum (FWHM) was 230 fs, which was the temporal resolution of the measurement. For the fitting analysis, a convolution method was used with a gate pulse in the shape of a Gaussian function with a FWHM of 100 fs, and the precision of the fitting was 20 fs [20]. All measurements were performed in air at 298 K.III. RESULTS AND DISCUSSIONFigure 1(a) shows a 200× optical microscope image of monolayer MoS2 on a sapphire substrate. Monolayer MoS2 crystals grow in a triangular form on the substrate [21]. The microscopic image shows that the triangles are connected to each other, covering a large area enclosed by a rectangle with a black outline (size 65.0 × 87.5 µm). As shown in the Raman scattering spectra map later, the region where the triangles appear to overlap is also covered by monolayer MoS2. The Raman scattering spectrum (laser spot size 2 μm) at the lower left point of this enclosed area is shown in Fig. 1(b). The peaks at ~384 and 404 cm-1 are attributed to the  and A1g vibrational modes, respectively, of MoS2 [22] and the peak at 417 cm-1 corresponds to the vibrational mode of sapphire. The Raman scattering spectrum is fitted using the sum of three Lorentzian functions (orange, blue, and green solid lines) and a constant value (black dashed line). The fitted result is indicated by a solid black line and the experimental spectrum is well reproduced. The obtained peak wavenumbers of the  and A1g modes are 384 and 404 cm-1 and their FWHMs are 3.48 and 4.75 cm-1, respectively. The difference in the peak wavenumbers of the  and A1g modes is 20 cm-1, indicating that this measurement point is covered by monolayer MoS2 [23]. The defect concentration can also be estimated from the FWHM of the  mode [24] and is <2 × 1012 cm-2. This value is the upper limit of defect concentration, because a strain-induced line broadening might be involved in monolayer MoS2 synthesized by CVD method on the sapphire substrate.Figure 1. (a) Optical microscope image of the sample (magnification 200×). (b) Raman scattering spectrum at the lower left point of the area enclosed by a rectangle with black outline in (a). Circles indicate experimental results; lines are the fitted results. Maps of (c) the full width at half maximum of the  mode and (d) the difference in peak wavenumbers of  and A1g modes over the area enclosed by the rectangle with black outline in (a). The interval between the measured points is 1.25 μm. (e) Steady-state 1T spectrum (red line) and photoluminescence (PL) spectrum (blue line) of the sample.To make these evaluations over the area enclosed by the rectangle with black outline in Fig. 1(a), the Raman scattering measurements (laser spot size 2 μm) were performed at 4001 points at intervals of 1.25 μm. Figure 1(c) shows a map of the FWHM of the  mode. As the average FWHM is 3.51 cm-1 with a standard deviation of 0.17 cm-1 over all the points covered by MoS2, the defect concentration is almost uniform and <2 × 1012 cm-2. Figure 1(d) shows a map of the difference in the peak wavenumbers of the  and A1g modes. The difference is in the range of 19.6–20.6 cm-1 at 92% of all the points covered by MoS2, indicating that 92% of MoS2 is a monolayer in this area.The optical transmittance (T) measurement (aperture size diameter 50 μm) was performed for the area enclosed by a circle indicated in Fig. 1(a). Figure 1(e) shows the 1T spectrum (red line). Here, 1T reflects the optical absorption and reflectance. In the region <1.8 eV, the value of 1T is ~0.4, owing to the high dielectric constant (~20 [25]) of the monolayer MoS2. Peaks at 1.87 and 2.03 eV are attributed to the A- and B-exciton absorptions, respectively [1, 2]. The broad absorption band peaks at 2.90 eV, which is attributed to the C-exciton absorption [26]. The absorption bands in the higher-energy region are considered higher interband transitions. As the absorption is ~0.3 at 3.10 eV, the absorbed photon flux in the femtosecond time-resolved PL measurements is 2 × 1012 photons cm-2/pulse.The steady-state PL spectrum at a point (laser spot size 2 μm) in the circle in Fig. 1(a) is shown by a blue line in Fig. 1(e). The peak at 1.87 eV corresponds to that in the 1T spectrum and is attributed to the A-exciton peak. The PL spectrum shows a tail in the lower-energy side, indicating superposition of the trion PL [6]. No B-exciton PL is observed in this PL spectrum. The absence of an indirect transition peak at ~1.50 eV in the PL and 1T spectra supports the monolayer nature of the sample. To separate the A-exciton and trion PL components, the PL spectrum is fitted with the sum of two Lorentzian functions. The fitted results are presented in Fig. 2(a). The obtained peak energies of the PL components of the trion (green line) and A exciton (blue line) are 1.832 and 1.873 eV, respectively, and the energy difference between the two peaks is 0.041 eV. The electron concentration can be estimated from this difference [5, 27] to be 6 × 1012 cm-2 for this sample. The PL intensity ratio of the A exciton to the trion is 1:6 at 1.79 eV and 7:1 at 1.89 eV. Thus, the PL at 1.89 and 1.79 eV consist mainly of the A-exciton and trion PL, respectively.Figure 2. (a) Enlarged plots of steady-state 1T and photoluminescence (PL) spectra in Fig. 1(e). The spectra are plotted by black lines, and the labels are placed close to respective spectra. Green and blue solid lines are the fitted curves for the trion and A-exciton PL components, respectively. The gray dashed line indicates the overall fit of the PL spectrum. Vertical lines indicate the detection energies of the time-dependent PL in (b), (c), and (d): red 2.03 eV (B exciton), blue 1.89 eV (A exciton), and green 1.79 eV (trion). Time-dependent PL intensities of monolayer MoS2 at (b) 2.03 eV (B exciton), (c) 1.89 eV (A exciton), and (d) 1.79 eV (trion). (e) Enlarged semilog plots of time-dependent PL of B exciton (red), A exciton (blue), and trion (green). Figures 2(b)-2(d) show the time-dependent PL intensities at photon energies of 2.03, 1.89, and 1.79 eV, respectively. The 1T spectrum in Fig. 2(a) shows that the energy of 2.03 eV corresponds to the B-exciton transition. The B-exciton PL in Fig. 2(b) decays to zero at ~1.5 ps within the error. This fast decay is consistent with the absence of B-exciton PL in the steady-state PL spectrum shown in Fig. 2(a) because the steady-state PL is considered a time integration of time-dependent PL. (As the PL decay of B excitons is faster than that of A excitons and trions, the time integration of B-exciton PL is relatively small.) The time-dependent PL at 1.89 eV (A exciton) in Fig. 2(c) decreases to one-third of the maximum intensity until 0.5 ps, followed by a slow decay over 10 ps. These PL decay behaviors at 2.03 eV (B exciton) and 1.89 eV (A exciton) are consistent with the previous work [16]. The time-dependent PL at 1.79 eV (trion) in Fig. 2(d) shows a decay like that at 1.89 eV (A exciton). To observe the increase behaviors of the exciton and trion PLs around the time origin in detail, semilog plots of the A- and B-exciton and trion PLs around the time origin are presented in Fig. 2(e). The rise times of the A- and B-exciton PLs are almost the same, whereas the rise of the trion PL is slower. This slow rise indicates trion formation via exciton-to-trion relaxation. Figure 3: Schematic energy diagram of relevant levels and transitions in the rate-equation analysis.To estimate τex-tr, we performed rate-equation analysis considering the transitions depicted in Fig. 3. Exciton-trapping deep and shallow energy levels such as sulfur vacancies and surface states were observed [11-13,28-30], which could also act as trap levels for trions. The trapping of excitons and trions by these levels competed with their radiative decay and nonradiative transitions between them. Trapping to a deep level led to nonradiative decay, at least in the detected spectral region, whereas detrapping from the shallow level was thermally possible. In the rate-equation analysis, we considered the energy levels of not only the free B excitons (number density NB), A excitons (NA), and trions (NT), but also B excitons (NB*), A excitons (NA*), and trions (NT*) bound in shallow traps. The biexciton formation [31] is not involved in our model because the excitation-density dependence of PL decay was not observed in our excitation density range [16]. The rate equations for these species are as follows:where GB and GA are the generation terms of the B and A excitons, respectively. The excitation photon energy of 3.10 eV is situated in the continuum band. The pump-probe measurement under the continuum band excitation [32] showed that the formation times of the B and A excitons are ~30 fs. As this value is much shorter than the excitation pulse duration (FWHM) of 210 fs in our experiments, the generation term is a Gaussian function with the same shape as the excitation pulse. This pump-probe measurement also showed bleaching signals of A and B excitons have spectral weights with a ratio of ~1:2 [32]. Hence, areas of GA and GB are set to 1/3 and 2/3 of the absorbed excitation photon flux, respectively. Here, γmn is a transition rate from level m to n, where m and n can denote B (free B exciton), A (free A exciton), T (free trion), B* (trapped B exciton), A* (trapped A exciton), T* (trapped trion), and D (deep trap). Also, γm (m = B, A, T, B*, A*, and T*) is a sum of the other relaxation rates such as the radiative rate and multiphonon emission rate, and they are small enough to be neglected here [33, 34]; for example, the multiphonon emission rate of the A exciton is (50 ps)-1 = 2 × 1010 s-1 [33].In the equation of , the terms of  and  were included because the free B(A) excitons could diffuse and relax to both the deep and shallow traps. Because the energy difference between the shallow-trapped exciton level and free exciton level was small [12], a thermal transition from the trapped-to-free exciton level was possible. Hence, the term  was considered. Similarly, the term  was included in the equation of . The free B(A) exciton had a chance to encounter and create a bound state with a free electron to form a free trion, and the term  was involved. The B exciton could relax to the A exciton, and the value of γBA was fixed at 1.0 ps-1 [35, 36]. (The fitting is insensitive to this value. If the value varies from 0.07 to 2.0 ps-1, the sum of squares of the residuals in least-squares fitting changes only a few percent.)In the equation of , the term  was included, because the trion formed by a trapped B(A) exciton and electron could be bound in a shallow trap. Similarly, when the trapped B exciton relaxed to A exciton, the A exciton would also be bound at the trap, and the term  would be included. In the equation of , the term  was considered, because a thermal transition from the trion to A exciton level was possible: The energy difference  between the trion and A exciton levels was 41 meV [Fig. 2(a)] and close to the energy of room temperature  ( is the Boltzmann constant and  is the room temperature of 298 K) of 26 meV. In contrast, a thermal transition from trion (A exciton) to B exciton level was almost impossible, because the energy difference between the trion (A exciton) and B exciton levels was 0.19 (0.15) eV [Fig. 2(a)] and much larger than . Indeed, the steady-state PL of the B excitons was not observed in Fig. 2(a).In an ideal case, where the deep and shallow traps are not present, the law of mass action among A excitons, trions, and free electrons in the steady state is given by  [6,37]. Here,  is the reduced Planck constant; , , and  are the effective masses of the electrons, A excitons, and trions, respectively. The effective masses of the electrons and holes in monolayer MoS2 are 0.35 m0 and 0.45 m0, respectively, where m0 is the electron rest mass [38]. The A exciton and negative trion masses are 0.80 m0 and 1.15 m0, respectively. In the steady state for this ideal case, the equation  holds. As described above,  is small enough to be neglected here. Thus, . In our sample, ne is 6 × 1012 cm-2. Hence, . Because the diffusion coefficient is inversely proportional to the mass of translational motion, the ratio of the diffusion coefficient of excitons to that of negative trions is 0.80/1.15. Hence,  and  are 0.80/1.15, when the trapping probability at the trap is taken as unity. The rate equations were numerically solved with the freely adjustable parameters γAD (= γBD), γAA* (= γBB*), γA*A (= γB*B), γT*T, γAT (= γBT), and γA*T* (= γB*T*). Here, transition rates from A and B excitons to trap levels and inverse rates are taken to be the same value; γAD = γBD, γAA* = γBB*, and γA*A = γB*B. In the n-type monolayer MoS2, formation energies of negatively-monovalent, neutral, and positively-monovalent sulfur vacancies are higher in this order [39]. Hence, the sulfur vacancies trap electrons rather than holes. The electrons of A and B excitons possess almost the same energy in the band picture, because the spin degeneracy at the conduction-band edges of the K and K′ valleys is only slightly lifted (3 meV [40,41]). For the A and B excitons, excess energies released during trapping by the vacancies (gaining during detrapping) are almost same, resulting in the same trapping (detrapping) rate. As the energy difference of electrons with respective spin directions at the conduction-band edges is negligible compared with the room temperature (298 K = 26 meV), the trion formation from A and B excitons is almost unrestricted by the spin difference, and we take γAT = γBT and γA*T* = γB*T*. To obtain the time-dependent PL of the B and A excitons and trions, NB(NB*), NA(NA*), and NT(NT*) were multiplied by their respective oscillator strengths fB, fA, and fT [42]. The values of the oscillator strengths were taken from the literature [43]. As shown in Fig. 2(a), the PL spectra of A excitons and trions overlap. The intensity ratio of the A exciton to the trion is 1:6 at 1.79 eV and 7:1 at 1.89 eV. Hence, the time-dependent PL curves at 1.79 and 1.89 eV were fitted by fA(NA+NA*)+6fT(NT+NT*) and 7fA(NA+NA*)+fT(NT+NT*), respectively. To fit the PL curve at 2.03 eV, fB(NB+NB*) was used. The numerically obtained solutions of the rate equations were convoluted with a gate pulse in the shape of a Gaussian function with a FWHM of 100 fs, and least-squares fitting was performed.The values of the adjustable parameters are listed in Table 1, and the fitted results are presented as solid lines in Figs. 2(b)-2(d). The overall behavior was reproduced, including an increase in the trion PL [Fig. 2(e)]. The value of () of 5.5 ps-1 was consistent with the value of 4.2 ps-1 estimated by the expression D/l2. Here, D is the exciton diffusion coefficient, the value of which was reported to be 2.1 cm2 s-1 [44]. Also, l is the separation between defects, i.e., inverse of the square root of defect concentration, which was estimated to be 2 × 1012 cm-2 by using the Raman spectrum [Figs. 1(b) and 1(c)]. This relaxation rate to the deep traps causes the fast PL decay of excitons and trions. When the excitons were trapped in a shallow level, the encounter probability between the trapped excitons and electrons would be low. Indeed, the fitted value of  was zero. Here, τex-tr was the inverse of AT, BT, and its value was 0.3 ps. Recent femtosecond pump-probe measurements of monolayer MoS2 demonstrated that the photoinduced signal of trions after excitation exhibited a large and rapid increase, followed by a small delayed buildup until ~5 ps [11]. The authors explained that the rapid increase and delayed buildup could be related to many-body effects and trion formation, respectively. However, our results of 0.3 ps revealed that the rapid-increase component could involve trion formation.TABLE I. Freely adjustable parameters. γmn is the transition rate from level m to n, where m and n can denote B (free B exciton), A (free A exciton), T (free trion), B* (trapped B exciton), A* (trapped A exciton), T* (trapped trion), and D (deep trap). AD, BD(ps-1) AA*, BB*(ps-1) A*A, B*B(ps-1) T*T(ps-1) A*T*, B*T*(ps-1) AT, BT(ps-1) 5.5 ± 0.3 (2.8 ± 0.1) × 10-1 (1.1 ± 0.1) × 10-1 (2.0 ± 0.1) × 10-1 0 3.7 ± 0.9The obtained value of τex-tr was compared with the previously reported values for 2D electron systems in Table 2. The value of τex-tr in monolayer MoS2 was 0.3 ps, which was approximately two orders of magnitude smaller than that of the quantum-well structures InGaAs/GaAs and GaAs/AlGaAs. The exciton-to-trion relaxation depended on the encounter probability of an exciton and electron, as well as the strengths of interactions between them. The exciton–electron encounter probability can be evaluated as the exciton diffusion constant D and ratio of the exciton volume to the occupation volume per doped electron, V = (rex2 2zex) (ne/L), where rex is the exciton radius in the 2D plane, zex exciton extension along the thickness direction, ne is the 2D electron concentration, and L is the thickness of 2D electron system (ne/L is the three-dimensional electron concentration). In InGaAs/GaAs [10] and GaAs/AlGaAs [9] quantum wells, 2zex is two or three times smaller than L, and the 2D confinement is not strong. The reduced effective masses and dielectric constants of wells and barriers have similar values in the two wells [58,59], resulting in the similar strengths of screened Coulomb interactions. Indeed, the trion binding energies in the two wells are almost the same. The value of D in GaAs/AlGaAs is ~14 times larger than that in InGaAs/GaAs, while the value of V in GaAs/AlGaAs is ~20 times larger than that in InGaAs/GaAs. Hence, the encounter probabilities in the two wells are comparable. Therefore, τex-tr has the same value in the two quantum wells. In the monolayer MoS2, the top of valence bands consists of Mo d and S p orbitals, and the bottom of conduction bands involves mainly Mo d orbitals [26]. Hence, 2zex ~ L, indicating the strong 2D confinement. This strong 2D confinement and surrounding low dielectric constant (air above MoS2/sapphire) cause strong screened Coulomb interactions, which is evidenced by the large trion binding energy. Consequently, the value of τex-tr is orders of magnitude smaller than that in the two quantum wells, although the values of V and D are comparable with or smaller than those of the two quantum wells. It is noted that a typical example of monolayer TMD (WS2) has exhibited temperature dependence of the diffusion coefficient, which has a smaller value at 10 K than that at 275 K [60]. If the similar temperature dependence is present in monolayer MoS2, the encounter probability is dependent on temperature, leading to the variation of τex-tr.TABLE II. Exciton-to-trion relaxation time constants for various 2D electron systems. L is the thickness of 2D electron system. rex is the exciton radius in the 2D plane. zex is the exciton extension along the thickness direction. Eex is the energy difference between the band edge and lowest bright exciton level, which is positively correlated with exciton binding energy. Etr is the energy difference between the lowest bright exciton and trion levels, which is positively correlated with trion binding energy. D is the diffusion coefficient. ne is the electron concentration. V [= (rex2 2zex)(ne/L)] is the ratio of the exciton volume to the occupation volume per doped electron, which is a measure of the exciton–electron encounter probability. τex-tr is the time constant of exciton-to-trion relaxation.  L(nm) rex(nm) zex(nm) Eex(eV) Etr(meV) D(cm2 s-1) ne(nm-2) V τex-tr(ps) MoS2 (this paper) 0.65a 1b,c  1.03d0.63befg 41 2.1h 6×10-2 2×10-1 0.3 (298 K) MoSe2 0.7i 1j,k  0.91c0.55k0.5l 30j,m    2 (13 K)j2 (12 K)m InGaAs/GaAsn 8 14o 1.8o 6.5×10-3 1.6 24p 10-4 3×10-2 100 (16 K) GaAs/AlGaAsq 20 17o 3.4o  1.1 6.2r 2×10-3 6×10-1 100 (2 K)a Reference [45]b Reference [26].c Reference [46].d Reference [47].e Reference [48].f Reference [49].g Reference [50].h Reference [44] (room temperature).i Reference [37].j Reference [12].k Reference [51].l Reference [52].m Reference [13].n In0.05Ga0.95As/GaAs quantum well [10].o Calculated using the relationship of exciton radius between bulk (14 nm in GaAs [53] and 31 nm in InAs [54]) and quantum well in Ref. [55].p Carrier diffusion coefficient in In0.1Ga0.9As/GaAs quantum well (thickness 7.5 nm, room temperature) [56].q GaAs/AlxGa1-xAs quantum well [9].r GaAs/Al0.5Ga0.5As quantum well (thickness 15 nm, temperature 20 K) [57].IV. CONCLUSIONSIn this paper, we investigated the trion formation via exciton-to-trion relaxation in monolayer MoS2. The Raman scattering and steady-state PL spectra were analyzed to evaluate the defect concentration, layer number, and electron concentration. The defect concentration was <2 × 1012 cm-2, the number of layers was almost uniformly 1, and the electron concentration was 6 × 1012 cm-2. Femtosecond time-resolved PL measurements, where the absorbed photon flux was ~2 × 1012 photons cm-2/pulse, were conducted to obtain the luminescence kinetics of the A and B excitons and trions. A rate equation analysis was performed to estimate the exciton-to-trion relaxation time constant, that is, the trion formation time constant, and the obtained value was 0.3 ps. A comparison with semiconductor quantum wells showed that the exciton-to-trion relaxation time constant was governed by strong exciton–electron interactions owing to the small thickness and low surrounding dielectric constant. 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